THE DEVELOPMENT OF UNDERSTANDING OF SOCIAL SYSTEMS by ROBERT GORDON BOUTILIER M.A., The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREEOOF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department o f P s y c h o l o g y We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA August 1981 R o b e r t Gordon B o u t i l i e r , 1981 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of /^"yC- /lQ /O The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date -7Q ^ i i ABSTRACT The c h i l d ' s u n d e r s t a n d i n g o f open s y s t e m s , as e x e m p l i f i e d by an eco-s y s t e m and a s o c i o - e c o n o m i c s y s t e m , was a s s e s s e d i n a P i a g e t i a n t y p e i n t e r v i e w w i t h 8 males and 8 f e m a l e s i n each o f grades 3, 5, 7, 9, 11 and f i r s t y e a r p o s t - s e c o n d a r y (n=96). S i n c e P i a g e t i a n t h e o r y has been b a s e d on t a s k s u s i n g m a i n l y i n a n i m a t e , p h y s i c a l c o n t e n t , the g e n e r a l i z a b i l i t y o f P i a g e t i a n s t a g e s and sequences t o the two open systems c o n t e n t domains was t e s t e d . Tasks a s s e s s i n g t h e f o u r c o n c r e t e o p e r a t i o n s examined were r e p e a t e d i n each o f t h e p h y s i c a l , t he b i o - e c o l o g i c a l and t h e s o c i e t a l domains. T y p i -c a l s t a g e and sequence p a t t e r n s were o b s e r v e d i n a l l t h r e e domains. P o s t -c o n c r e t e o p e r a t i o n s were r e p r e s e n t e d by t h r e e f o r m a l o p e r a t i o n s i n t h e p h y s i c a l domain and f o u r s y s t e m i c o p e r a t i o n s i n each o f the open systems domains. L o g i c a l and p h i l o s o p h i c a l arguments f o r t h e q u a l i t a t i v e d i f f e r e n c e between f o r m a l and s y s t e m i c l o g i c were p r e s e n t e d . Three b l i n d j u d g e s r e a c h -ed spontaneous agreement on 84.6% o f t h e s c o r e s a s s i g n e d f o r the s y s t e m i c t a s k p r o t o c o l s . A s c a l o g r a m a n a l y s i s and comparisons o f the d i f f e r e n c e s between p a s s / f a i l p r o p o r t i o n s i n d i c a t e d t h a t the s y s t e m i c o p e r a t i o n s o f systems s y n t h e s i s and t r a n s i t i v e r e c y c l i n g were more d i f f i c u l t t h a n the f o r m a l o p e r a t i o n a l t a s k s by a Guttman s t e p o f t h e same s i z e a s t h a t between th e f o r m a l and c o n c r e t e s t a g e s . A c l u s t e r a n a l y s i s showed t h o s e most d i f -f i c u l t s y s t e m i c t a s k s t o be grouped as i f th e y were a p a r t o f a s e p a r a t e s t r u c t u r e d'ensemble. F u r t h e r a n a l y s e s i n d i c a t e d t h a t t h e g r e a t e r d i f f i c u l t y o f t h e s e two s y s t e m i c o p e r a t i o n s c o u l d n o t be a t t r i b u t e d t o t h e g r e a t e r un-f a m i l i a r i t y o f t h e t a s k c o n t e n t s . S y s t e m i c t a s k s u c c e s s r a t e s were z e r o f o r r e s p o n d e n t s below grade 9 (14 y e a r s ) and c o n s i s t e n t l y f e l l f a r b e l o w i i i f o r m a l t a s k s u c c e s s r a t e s f o r same aged peers'. The most d i f f i c u l t s y s t e m i c o p e r a t i o n s s a t i s f i e d the c r i t e r i a f o r membership i n a f i f t h s t a g e as w e l l as any o t h e r P i a g e t i a n o p e r a t i o n s do f o r t h e i r i mputed s t a g e membership. N e v e r t h e l e s s , an a l t e r n a t i v e i n t e r p r e t a t i o n c o n s t r u i n g s y s t e m i c o p e r a t i o n s as p o s t - c o n c r e t e developments p a r a l l e l and complementary t o f o r m a l o p e r a -t i o n s c o u l d n o t be r u l e d o u t . The i m p l i c a t i o n s of t h e f i n d i n g s f o r the a r e a s o f c o g n i t i v e development, s o c i a l development and s o c i a l p s y c h o l o g y were d i s c u s s e d . i v TABLE OF CONTENTS A b s t r a c t T a b l e o f C o n t e n t s i v L i s t o f T a b l e s v i i i L i s t o f F i g u r e s 1 X Acknowledgement x I . I n t r o d u c t i o n -1 A. Two S y s t e m i c C o g n i t i v e S t r u c t u r e s 5 B. P a r a l l e l Development A c r o s s Domains 7 ( i ) The B i o - e c o l o g i c a l Domain 9 £ii) F a m i l i a r i t y 10 I I . S t r u c t u r e s and C o n t e n t s 12 A. S o c i e t a l S t r u c t u r e s 12 ( i ) S t r u c t u r e s and O p e r a t i o n s 12 ( i i ) S t r u c t u r e s I m p l i c i t i n H i e r a r c h i e s 16 ( i i i ) S y s t e m i c S t r u c t u r e s 19-B. C o g n i t i v e S t r u c t u r e s 23 ( i ) C o n c r e t e Stage 24 ( i i ) S y s t e m i c S t r u c t u r e s 26 ( i i i ) Compared t o F o r m a l O p e r a t i o n s 31 C. Domains o f C o n t e n t 34 ( i ) C o m p a r a b i l i t y o f C o n t e n t s 35 ( i i ) F a m i l i a r i t y I s s u e s 37 ( i i i ) F a m i l i a r i t y and Task D i f f i c u l t y 40 ( i v ) Age and D i f f i c u l t y L e v e l 41 V D. Hypotheses 42 ( i ) L i s t o f Hypot h e s e s 43 ( i i ) A C o n t i n g e n t S u c c e s s i o n 44 ( i i i ) N u l l H ypotheses 45 I I I . Method 47 A. Measures 47 ( i ) The C o n c r e t e Tasks ; 48 ( i i ) The F o r m a l T a s k s 50 ( i i i ) The S y s t e m i c Tasks 51 ( i v ) F a m i l i a r i t y A s s e s s m e n t s f o r S y s t e m i c T a s k s 51 B. Respondents • 52 C. P r o c e d u r e s 54 ( i ) Data C o l l e c t i o n 54 ( i i ) D a t a S c o r i n g 58 IV. R e s u l t s 60 A. F i r s t H y p o t h e s i s w i t h Composite S y s t e m i c S c o r e s 61 ( i ) S c a l o g r a m D i f f i c u l t y O r d e r i n g s 62 ( i i ) Guttman S t e p s 65 ( i i i ) C o n v e r g i n g T e c h n i q u e s 66 ( i v ) R e p r o d u c i b i l i t y C o e f f i c i e n t 67 (v) F r e q u e n c i e s and P r o p o r t i o n s 69 ( v i ) Z S c o r e s f o r P r o p o r t i o n s 75 B. F i r s t H y p o t h e s i s w i t h Component S y s t e m i c S c o r e s 82 ( i ) C y c l i c T r a n s i t i v i t y Components 82 ( i i ) C y c l i c I n t e g r a t i o n Components 83 ( i i i ) S c a l o g r a m and Z S c o r e s f o r Components 84 C. Second H y p o t h e s i s 91 ( i ) C l u s t e r A n a l y s i s o f Components 91 v i D. T h i r d H y p o t h e s i s . 97 ( i ) U n f a m i l i a r i t y v s . C o m p l e x i t y as Reasons f o r D i f f i c u l t y 99 ( i i ) V a r y i n g F a m i l i a r i t y w i t h C o n s t a n t C o m p l e x i t y 100 ( i i i ) V a r y i n g O p e r a t i o n s w i t h C o n s t a n t C o n t e n t 107 E. Age o f M a s t e r y D a t a 108 F. Summary o f R e s u l t s 110 V. D i s c u s s i o n 112 A. The Three Hypotheses 112 ( i ) F i r s t H y p o t h e s i s : E x t e n d i n g P i a g e t i a n Theory ... 112 ( i i ) Second H y p o t h e s i s : Upper S y s t e m i c Tasks 117 ( i i i ) T h i r d H y p o t h e s i s : G r e a t e r C o n t e n t D i f f i c u l t y 118 ( i v ) Age R e l a t e d C r i t e r i a 120 (v) Summary 122 B. I n t e r p r e t a t i o n s o f S y s t e m i c D i f f i c u l t y L e v e l s 122 ( i ) I n t e r p r e t i v e C a v e a t s 122 ( i i ) P i a g e t ' s P a r a l l e l P o s i t i o n 126 ( i i i ) L a b o u v i e - V i e f ' s P a r a l l e l P o s i t i o n 128 ( i v ) S t a g e s and Pa r a d i g m s 129. V I . I m p l i c a t i o n s f o r Three A r e a s o f Study 131 A. C o g n i t i v e Development 131 ( i ) C o r r o b o r a t i v e Work on A d u l t C o g n i t i o n 132 ( i i ) P o s t - C o n c r e t e D i v e r s i f i c a t i o n 134 ( i i i ) P r o b l e m F i n d i n g and S o l v i n g i n e i t h e r L o g i c 135 ( i v ) C y c l i c T r a n s i t i v i t y and t h e Feedback Concept 136 (v) C y c l i c I n t e g r a t i o n and i t s Components 139-B. S o c i a l Development 140 ( i ) O r d i n a t i o n 142 v i i ( i i ) Hierarchy 143 ( i i i ) Systems Analysis 143 (iv) Systems Synthesis 143 C. S o c i a l Psychology 145 (i) Towards an Interactive Framework . 146 ( i i ) Towards Specifying the Structure of the S o c i a l S i t u a t i o n . 149 D. Conclusions 152 References 154 Appendix A: Physical Domain Tasks 161 Appendix B: B i o - e c o l o g i c a l Domain Tasks 170 Appendix C: S o c i e t a l Domain Tasks 182 Appendix D. Scoring Manual for Systemic Interviews 197 Appendix E: Difference Between Formal and Systemic Logics 213 v i i i L IST OF TABLES T a b l e I . F r e q u e n c i e s and p r o p o r t i o n s o f r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t h e o t h e r ;,70 T a b l e I I . Z s c o r e s f o r d i f f e r e n c e s between p r o p o r t i o n s o f r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t h e o t h e r 79 T a b l e I I I . Z s c o r e s f o r d i f f e r e n c e s between p r o p o r t i o n s o f r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t h e o t h e r , r e p o r t e d w i t h s y s t e m i c s c o r e s i n components .86 T a b l e I V . Z s c o r e s between f o r m a l t a s k s and s y s t e m i c components 90 T a b l e V. Z s c o r e s and f r e q u e n c i e s o f p a s s e s between t a s k s and f a m i l i a r i t y a s s e s s m e n t s 101 T a b l e V I . Age p r o f i l e s f o r p a s s e s on f o r m a l and s y s t e m i c s c o r e s and on t h e most d i f f i c u l t s y s t e m i c f a m i l i a r i t i e s ...109 i x LIST OF FIGURES-F i g u r e 1. S c a l o g r a m d i f f i c u l t y o r d e r i n g s w i t h , c o m p o s i t e s y s t e m i c s c o r e s By domain .. , ...................... .63 F i g u r e 2. S c a l o g r a m d i f f i c u l t y o r d e r i n g s w i t h , component s y s t e m i c s c o r e s (a) by domain, and (b) a c r o s s domains ......... .85 F i g u r e 3 . C l u s t e r a n a l y s i s dendrogram with- s c o r e s by domain and s y s t e m i c s c o r e s by components .92 F i g u r e 4. C l u s t e r a n a l y s i s dendrogram w i t h a c r o s s domain s c o r e s and s y s t e m i c s c o r e s by components .95 F i g u r e 5. C l u s t e r a n a l y s i s dendrogram on a c r o s s domain s c o r e s w i t h ambiguous s y s t e m i c s c o r e s d e l e t e d .96 F i g u r e 6. C l u s t e r a n a l y s i s dendrogram f o r s t a g e s c o r e s and l e a s t d i f f i c u l t upper s y s t e m i c s c o r e a c r o s s domains 98 F i g u r e 7. Some p o s s i b l e forms o f b o t t o m t o t o p p r o c e s s e s i n c y c l i c i n t e g r a t i o n 141 F i g u r e B l . D i s p l a y c a r d f o r b i o - e c o l o g i c a l domain c l a s s i n c l u s i o n t a s k .174' F i g u r e C I . D i s p l a y c a r d f o r s o c i e t a l domain c l a s s i n c l u s i o n t a s k .188 X ACKNOWLEDGEMENTS I * I w i s h t o thank Dr. P a t r i c i a A r l i n , Dr. Mer r y B u l l o c k , Dr. D a l e M i l l e r , and Dr. James S t e i g e r f o r t h e v a l u a b l e a d v i c e and i n s i g h t f u l c r i t i c a l commen-t a r y t h a t t h e y o f f e r e d as members o f the t h e s i s committee. I a l s o t h a n d Dr. ' I r v i n g S i g e l f o r s e r v i n g as the E x t e r n a l Examiner and D r s . G a a l e n E r i c k s o n and Ta n n i s W i l l i a m s f o r s e r v i n g as U n i v e r s i t y E x a m i n e r s . My mentor t h r o u g h o u t t h e e n t i r e r e s e a r c h endeavor was Dr. M i c h a e l C h a n d l e r . H i s c o l l a b o r a t i o n c o n t r i b u t e d t o my own c o g n i t i v e development as w e l l as t o e v e r y a s p e c t o f the t h e s i s . Thanks i s a l s o owing t o the s t u d e n t s , p a r e n t s , t e a c h e r s , p r i n c i p a l s , and s c h o o l b o a r d o f f i c i a l s who v o l u n t e e r e d t h e i r time and/or r e s o u r c e s . I am g r a t e f u l t o Anne B o y l e , Wendy G r o i s s , and N e i l K y l e f o r t h e i r a s s i s t a n c e i n s c o r i n g and c o l l e c t i n g the d a t a . I am i n d e b t e d t o my w i f e , Ann Svendsen, f o r h e r e m o t i o n a l and f i n a n c i a l s u p p o r t . T h i s s t u d y was completed w i t h the f i n a n c i a l a s s i s t a n c e o f a r e s e a r c h g r a n t from the E d u c a t i o n a l R e s e a r c h I n s t i t u t e o f B r i t i s h C o l u m b i a . 1 The purpose o f t h i s r e s e a r c h was t o c h a r t t h e development o f t h e c h i l d ' s u n d e r s t a n d i n g o f c e r t a i n d i s t i n g u i s h i n g f e a t u r e s o f s o c i a l o r g a n i z a t i o n and t o r e l a t e t h i s sequence t o o t h e r s t r u c t u r a l l y a n a l o g o u s changes i n c o g n i t i v e development. T h i s r e s e a r c h was somewhat e x p l o r a t o r y because t h e u n d e r s t a n d -i n g o f s o c i a l o r g a n i z a t i o n s a p p ears t o r e q u i r e c o g n i t i v e s t r u c t u r e s t h a t have r e c e i v e d l i t t l e a t t e n t i o n t o d a t e . These a r e t h e s t r u c t u r e s , i n t r o d u c e d h e r e i n , w h i c h d e a l w i t h t h e u n d e r s t a n d i n g o f open systems"'". Thus t h i s r e -s e a r c h came t o examine t h e development o f s y s t e m i c c o g n i t i v e s t r u c t u r e s i n the c o u r s e o f e x a m i n i n g the development o f u n d e r s t a n d i n g o f s o c i a l o r g a n i z a -t i o n . I n v e r y b r i e f d e t a i l , an a t t e m p t was made t o compare t h e c o g n i t i v e s t r u c t u r e e v i d e n t i n c h i l d r e n ' s t h i n k i n g as t h e y a t t e m p t e d t o r e a s o n about p h y s i c a l , b i o - e c o l o g i c a l and s o c i a l s ystems. P a r a l l e l s i n t h e c o u r s e o f development a c r o s s t h e s e t h r e e domains were sought and s p e c i a l a t t e n t i o n was f o c u s e d upon t h o s e c o g n i t i v e s t r u c t u r e s n e c e s s a r y t o a d e q u a t e l y under-s t a n d the open systems f e a t u r e s c h a r a c t e r i s t i c o f b i o - e c o l o g i c a l and s o c i a l s ystems. T h i s p r o c e s s l e d t o the p o s t u l a t i o n and l a t e r assessment of two n o v e l c o g n i t i v e s t r u c t u r e s dubbed " c y c l i c t r a n s i t i v i t y " and " c y c l i c i n t e g r a -1. I n t h i s r e s e a r c h a s y s t e m i s d e f i n e d a s : A s e t o f elements i n some o r d e r e d r e l a t i o n s h i p s u c h t h a t i n f o r m a -t i o n and/or m a t e r i a l f l o w s , e i t h e r d i r e c t l y o r i n d i r e c t l y , f rom e v e r y element ( o r c l a s s o f e l e m e n t s ) t o e v e r y o t h e r element i n ways w h i c h a f f e c t t h e f u n c t i o n i n g of a l l e l e m e n t s . A c l o s e d s y s t e m i s s u b j e c t t o e n t r o p y . An open s y s t e m , by c o n t r a s t , i s c h a r a c t e r i z e d by p e r i o d s o f i n c r e a s i n g l y o r g a n i z e d c o m p l e x i t y . The tendency t o become more o r g a n i z e d and complex, r a t h e r t h a n l e s s , has been c a l l e d " n e g e n t r o p y " ( B r i l l o u i n , 1961). Open systems a r e negen-t o p i c , p a r t i a l l y b ecause t h e y c a n , a t l e a s t t e m p o r a r i l y , e x p o r t e n t r o p y . O v e r t o n (19.75) d i s t i n g u i s h e s open f r o m c l o s e d systems as f o l l o w s : "A c l o s e d s y s t e m i s one w h i c h i s f u n c t i o n a l l y i s o l a t e d from i t s e n v i r o n -ment o r , a t most, exchanges o n l y energy w i t h i t s e n v i r o n m e n t . Open systems a r e t h o s e w h i c h a r e c h a r a c t e r i z e d by i m p o r t and e x p o r t o f mat-e r i a l as w e l l as e nergy". (See A p p e n d i x E f o r a f u r t h e r d i s c u s s i o n . ) 2. t i o n " . These c o n c e p t s and t h e i r r e l a t i o n s h i p t o one a n o t h e r and t o o t h e r b e t t e r u n d e r s t o o d a s p e c t s o f c o g n i t i v e development s t r u c t u r e s became t h e p i n i o n p o i n t around w h i c h t h i s s t u d y r e v o l v e d . Because of t h e i r n o v e l t y and c o m p l e x i t y a good d e a l o f groundwork needed t o be l a i d i n o r d e r t o make t h e s e c o n c e p t s m e a n i n g f u l and i n o r d e r t o j u s t i f y what was seen t o be t h e i r i m p o r t a n c e r e l a t i v e t o o t h e r b e t t e r u n d e r s t o o d a s p e c t s o f c o g n i -t i v e development. An att e m p t i s made t o l a y out t h a t groundwork i n C h a p t e r I I . The a p p roach t a k e n from the o u t s e t i n t h i s work was one w h e r e i n t h e s t r u c t u r e o f " t h e t h i n g s b e i n g t h o u g h t a b o u t " i s d e s c r i b e d a l o n g w i t h t h e s t r u c t u r e o f t h e t h i n k i n g i t s e l f . I n o t h e r w ords, " t h e known" has a s t r u c -t u r e j u s t as " t h e knower" does. A more e x p l i c i t and f o r m a l s t a t e m e n t o f t h i s g e n e r a l a p p r o a c h i s c o n t a i n e d i n t h e f o l l o w i n g t h r e e a s s u m p t i o n s w h i c h o r i e n t e d t h i s r e s e a r c h : 1) t h a t p e r s o n s , i n t h e c o u r s e o f t h e i r o n t o g e n e t i c development, p r o g r e s s t h r o u g h a r e g u l a r sequence o f d i f f e r e n t modes o f c o g n i t i v e o r g a n i z a t i o n s ; 2) t h a t i m p o r t a n t o r g a n i z a t i o n a l a s p e c t s o f t h e s o c i a l e n v ironment a r e t h e m s e l v e s a r r a n g e d as systems a c c o r d i n g t o d e f i n a b l e r u l e s and r e g u l a r i t i e s , a n d , s o m e w h a t l e s s r o u t i n e l y , 3) t h a t t h e same l o g i c o - m a t h e m a t i c a l p r i n c i p l e s w h i c h have been used t o d e s c r i b e t h e v a r i o u s s t r u c t u r e s o f c o g n i t i v e o r g a n i z a t i o n can a l s o be u s e f u l l y a p p l i e d 2 t o c h a r a c t e r i z e the s t r u c t u r e o f c e r t a i n s o c i a l o r g a n i z a t i o n s . These a s s u m p t i o n s , t a k e n as a group, l e a d t o t h e s u g g e s t i o n , t o be t e s t e d i n t h i s 2°. F o l l o w i n g P i a g e t ( 1 9 7 0 ) , t h e r u l e s and methods by means o f w h i c h i n t r a -p s y c h i c elements a r e c o o r d i n a t e d and o t h e r w i s e p r o c e s s e d a r e h e r e i n r e -f e r r e d t o as " c o g n i t i v e s t r u c t u r e s " . I n p a r a l l e l f a s h i o n , t h e r u l e s and methods by means o f w h i c h t h e elements o f a s o c i o - e c o n o m i c o r g a n i z a t i o n a r e c o o r d i n a t e d and i n t e g r a t e d a r e c a l l e d , " s o c i e t a l s t r u c t u r e s " . F o r the sake o f s i m p l i c i t y , t h e v a r i o u s c o g n i t i v e and s o c i a l s t r u c t u r e s , and t h e l o g i c o - m a t h e m a t i c a l p r i n c i p l e s used t o d e s c r i b e them w i l l a l l be a s s i g n e d p a r a l l e l l a b e l s . 3. r e s e a r c h , t h a t a c h i l d ' s a b i l i t y t o comprehend v a r i o u s s o r t s o f s o c i a l o r g a n -i z a t i o n s w i l l p r o v e t o be a p r e d i c t a b l e f u n c t i o n o f h i s o r h e r c u r r e n t l e v e l o f c o g n i t i v e m a t u r i t y . Because o f t h e c e n t r a l r o l e w h i c h t h e y have p l a y e d i n t h e f r a m i n g o f t h i s s t u d y , each o f t h e s e o r i e n t i n g a s s u m p t i o n s needs f u r t h e r e l a b o r a t i o n . The f i r s t , w h i c h a s s e r t s t h a t c o g n i t i v e development u n f o l d s a c c o r d i n g t o an o r g a n i z e d and o r d e r e d sequence, i s a commonplace f o l l o w i n g from t h e work o f P i a g e t and many o t h e r s . T h a t work, however, has emphasized t h e development of u n d e r s t a n d i n g o f the i m p e r s o n a l , n o n - s o c i a l w o r l d . The s y s t e m a t i c s t u d y o f t h e development o f u n d e r s t a n d i n g i n t h e i n t e r p e r s o n a l and s o c i e t a l domains i s much more r e c e n t and i n much s h o r t e r s u p p l y ( e . g . , Selman & Ja.quette, 1977; F u r t h , 1977; J a h o d a , 1979). The second a s s u m p t i o n s t a t e s t h a t t h e s o c i a l e n v ironment can be seen as o r g a n i z e d a c c o r d i n g t o l o g i c o - m a t h e m a t i c a l p r i n c i p l e s and, p a r e n t h e t i c a l l y , t h a t c e r t a i n o f t h o s e p r i n c i p l e s may be d i f f e r e n t f r o m t h e ones h i t h e r t o emphasized i n the s t u d y o f c o g n i t i v e de-velopment. I n p a r t i c u l a r , t h e s t r u c t u r e o f s o c i a l o r g a n i z a t i o n s may be b e s t r e p r e s e n t e d i n l o g i c o - m a t h e m a t i c a l p r i n c i p l e s t h a t d e a l w i t h t h e o r g a n i z a -t i o n o f syst e m s . The t h i r d a s s u m p t i o n , w h i c h b r i n g s t o g e t h e r the f i r s t and se c o n d , presumes t h a t s o c i e t y and t h e mind a r e o r g a n i z e d a c c o r d i n g t o some o f the same a b s t r a c t p r i n c i p l e s . T h i s p r e m i s e , w h i c h can be j u s t i f i e d p a r t -i a l l y on l o g i c a l g r o u n d s , i s p r e s e n t e d i n g r e a t e r d e t a i l i n s e c t i o n s A and B o f c h a p t e r I I . S e c t i o n A o f c h a p t e r I I i s d e v o t e d t o showing how t h e s o c i e -t a l s t r u c t u r e s examined i n t h i s s t u d y a r e a d e q u a t e l y d e s c r i b e d by c o r r e s p o n d -i n g l o g i c o - m a t h e m a t i c a l p r i n c i p l e s . I n s e c t i o n B o f c h a p t e r I I i t i s a r g u e d t h a t t h e d e v e l o p m e n t a l l y s u c c e s s i v e t h o u g h t s t r u c t u r e s c o n s i d e r e d h e r e i n a r e d e s c r i b e d by t h e s e same l o g i c o - m a t h e m a t i c a l p r i n c i p l e s . T o g e t h e r , s e c t i o n s 4 A and B argue t h a t t h e s e p r i n c i p l e s f o r m a b r i d g e between t h e s o c i e t a l s t r u c -t u r e s and the c o g n i t i v e s t r u c t u r e s t h a t a r e presumably n e c e s s a r y f o r compre-h e n d i n g t h e s o c i e t a l o r g a n i z a t i o n s . Some s o c i e t a l s t r u c t u r e s embody, and can be u n d e r s t o o d by t h e use o f , c o g n i t i v e s t r u c t u r e s o f t h e s o r t made f a m i l i a r by P i a g e t ' s t h e o r y . More commonly, however, s o c i a l o r g a n i z a t i o n s , and s o c i e t y i n g e n e r a l , a r e b e s t c h a r a c t e r i z e d as open s y s t e m s . C h i l d r e n ' s u n d e r s t a n d i n g o f such open systems c o n s e q u e n t l y was t a k e n as t h e c e n t r a l f o c u s o f t h i s s t u d y . H i s t o r i c a l l y t h e work o f P i a g e t and h i s c o l l a b o r a t o r s has emphasized c h i l d r e n ' s u n d e r s t a n d i n g 3 o f i n a n i m a t e , p h y s i c a l phenomena ( e . g . , c h e m i c a l r e a c t i o n s . , pendulums) . S o c i e t y , s o c i a l o r g a n i z a t i o n s and even e c o s y s t e m s , because t h e y a t t a i n a h i g h s t a t e o f o r g a n i z e d c o m p l e x i t y , a r e s t r i k i n g l y open systems ( O v e r t o n , 1975). I n o r d e r t o s t u d y c h i l d r e n ' s u n d e r s t a n d i n g o f s o c i a l s t r u c t u r e s one must s h i f t t h e r e f o r e f r o m a t r a d i t i o n a l emphasis on p h y s i c a l systems t o a more n o v e l emphasis on an i m a t e , open sys t e m s . T h i s r e f o c u s i n g upon t h e comprehension o f s o c i a l o r g a n i z a t i o n , w i t h i t s consequent s h i f t i n emphasis t o more open s y s t e m s , l e a v e s open t h e q u e s t i o n o f t h e e x t e n t t o w h i c h the work o f P i a g e t and h i s c o l l e g u e s a l s o a p p l i e s t o t h e s e new c o n t e n t a r e a s . I t was n e c e s s a r y , t h e r e f o r e , t o v e r i f y t he g e n e r a l i z a b i l i t y o f P i a g e t i a n t h e o r y t o the new c o n t e n t domains i n w h i c h open systems a r e t y p i c a l l y f o und. T h i s p r e p a r a t o r y s t e p became t h e f i r s t c o n c e p t u a l o r d e r o f b u s i n e s s i n t h i s s t u d y . 3. " S t a n d a r d " P i a g e t i a n c o n t e n t u s u a l l y means t h a t t h e t a s k s d e a l w i t h non-s o c i a l problems i n t h e p h y s i c a l s c i e n c e s l i k e p h y s i c s and c h e m i s t r y . F o r example, I n h e l d e r and P i a g e t (1958) combined t h e i r s t u d y o f f o r m a l o p e r -a t i o n a l t h o u g h t w i t h t h e s t u d y o f c h i l d r e n ' s u n d e r s t a n d i n g o f p h y s i c a l phenomena . l i k e o s c i l l a t i n g pendulums, f l o a t i n g b o d i e s , ' f a l l i n g b o d i e s on an i n c l i n e d p l a n e and e q u i l i b r i u m i n t h e h y d r a u l i c p r e s s . 5 H a v i n g e s t a b l i s h e d t h e g e n e r a l i z a b i l i t y o f P i a g e t i a n t h e o r y and method to t h e c l o s e d a s p e c t s o f s o c i a l s y s t e m s , i t was p o s s i b l e t o t u r n a t t e n t i o n t o t h e main f o c u s o f t h i s s t u d y , t h e c h i l d ' s u n d e r s t a n d i n g o f t h e open s y s t e m a s p e c t s o f s o c i a l systems and eco s y s t e m s . T h i s f o c u s l e d t o t h e i d e n t i f i c a -t i o n o f two h i t h e r t o u n s t u d i e d c o g n i t i v e s t r u c t u r e s u n i q u e t o the u n d e r s t a n d -i n g o f open systems. These a r e d i s c u s s e d f u r t h e r i n s e c t i o n A o f t h i s i n t r o -d u c t i o n . I n s e c t i o n s B o f c h a p t e r I and C o f c h a p t e r I I t h e r e i s a d i s c u s -s i o n o f t h e i s s u e s s u r r o u n d i n g t h e p r e l i m i n a r y p r o b l e m o f e s t a b l i s h i n g t h e a p p l i c a b i l i t y o f P i a g e t i a n t h e o r y t o t h e c o n t e n t domains where t h e under-s t a n d i n g o f open systems can more r e a d i l y be s t u d i e d . A. Two S y s t e m i c C o g n i t i v e S t r u c t u r e s T h i s s e c t i o n p r o v i d e s a v e r y b r i e f i n t r o d u c t i o n t o t h e open systems s t r u c t u r e s t h a t were t h e c e n t r a l f o c u s o f t h i s s t u d y . T h e i r m a n i f e s t a t i o n s as s o c i e t a l s t r u c t u r e s a r e d e s c r i b e d more f u l l y i n s e c t i o n A ( i i i ) o f chap-t e r I I . S e c t i o n B ( i i ) o f c h a p t e r I I c o n t a i n s more d e t a i l s about t h e i r m a n i f e s t a t i o n s as c o g n i t i v e s t r u c t u r e s and about t h e g e n e r a l f e a t u r e s o f the t a s k s used t o a s s e s s m a s t e r y o f t h e s e c o g n i t i v e s t r u c t u r e s . The d i s t i n c -t i o n between open v e r s u s c l o s e d s t r u c t u r e s i n v a r i o u s a s p e c t s o f t h e w o r l d was r e f l e c t e d i n t h i s r e s e a r c h by a c o r r e s p o n d i n g d i s t i n c t i o n r e g a r d i n g t h e s t r u c t u r e o f t h e i n d i v i d u a l ' s c o g n i t i o n about t h o s e v a r i o u s a s p e c t s o f t h e w o r l d . S p e c i f i c a l l y , an a n a l y s i s o f t h e s t r u c t u r a l r e g u l a r i t i e s e v i d e n t i n c e r t a i n f a m i l i a r and w e l l u n d e r s t o o d s o c i a l o r g a n i z a t i o n s l e d t o t h e p o s t u -l a t i o n o f two p r e v i o u s l y u n d e s c r i b e d c o g n i t i v e s t r u c t u r e s . I t was thought t h a t s i n c e p e o p l e do, a t l e a s t o c c a s i o n a l l y , u n d e r s t a n d t h e s t r u c t u r e o f 6. t h e i r s o c i a l o r g a n i z a t i o n s , t h e r e must be c o g n i t i v e s t r u c t u r e s o f c o r r e s p o n d -4 i n g c o m p l e x i t y by w h i c h s u c h u n d e r s t a n d i n g i s m e d i a t e d . The a t t e m p t t o i d e n t i f y and document t h e d e v e l o p m e n t a l p r e s e n c e o f t h e s e c o u n t e r p a r t c o g n i -t i v e s t r u c t u r e s was one o f t h e o r i g i n a l c o n t r i b u t i o n s o f t h i s r e s e a r c h . These two c o g n i t i v e s t r u c t u r e s c o n c e r n e d w i t h the u n d e r s t a n d i n g o f open systems a r e l a b e l e d " c y c l i c t r a n s i t i v i t y " and " c y c l i c i n t e g r a t i o n " . F o r the sake o f b r e v i t y , t h e p h r a s e " s y s t e m i c c o g n i t i v e s t r u c t u r e s " ( o r some v a r i a n t t h e r e o f ) i s h e r e a f t e r used t o r e f e r t o b o t h c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n t o g e t h e r . A t h o r o u g h d e s c r i p t i o n o f t h e s e s y s t e m i c c o g n i t i v e s t r u c t u r e s i s p r e -s e n t e d l a t e r . F o r now i t i s s u f f i c i e n t t o n o t e t h a t c y c l i c t r a n s i t i v i t y r e l a t e s t o s t r u c t u r e s known as n e g a t i v e f e e d b a c k l o o p s and c y c l i c i n t e g r a -t i o n i s r e l a t e d t o h i e r a r c h i c a l s t r u c t u r e s where t h e s u p r a o r d i n a t e and t h e s u b o r d i n a t e l e v e l s m u t u a l l y i n f l u e n c e e ach o t h e r . The l o g i c o - m a t h e m a t i c a l p r i n c i p l e s e x h i b i t e d by t h e s e s y s t e m i c s t r u c t u r e s can be d i s c e r n e d i n open systems t h r o u g h o u t n a t u r e ( i n c l u d i n g human s o c i e t i e s ) . S i n c e t r a d i t i o n a l 4 . From t h i s p e r s p e c t i v e , t h e s o c i a l e n v ironment may be seen as a r e l a t i o n -s h i p between s o c i a l systems ( e . g . , o r g a n i z a t i o n s ) and p s y c h o l o g i c a l systems ( i . e . , i n d i v i d u a l s ) . P s y c h o l o g i c a l systems a r e component p a r t s o f s o c i a l systems and as such must adapt t o an environment t h a t i s s i g -n i f i c a n t l y i n f l u e n c e d by t h e s o c i a l system. By t h e same t o k e n , p s y c h -o l o g i c a l systems a r e an i n f l u e n t i a l f o r c e i n t h e . m a i n t e n a n c e , r e s t r u c -t u r i n g , and d i s s o l u t i o n o f s o c i a l systems (Payne, 1968). P s y c h o l o g i c a l systems a r e , i n a manner of s p e a k i n g , the i n t e r n a l e n v ironment o f s o c i a l s y s t e m s . D i f f e r e n t i n d i v i d u a l s w i l l o f t e n r e s p o n d i n d i f f e r e n t ways t o t h e same s o c i a l s y s t e m depending upon t h e i r d i v e r s e c o n c e p t u a l i z a t i o n s o f t h a t s o c i a l s y s t e m and t h e i r i n d i v i d u a l r o l e s w i t h i n i t . B e f o r e t h e s e m u t u a l i n f l u e n c e s can be s t u d i e d we must have some u n d e r s t a n d i n g o f how t h e i n d i v i d u a l c o n c e p t u a l i z e s s u c h s o c i a l s y s t e m s . I n t h e p r e s e n t r e -s e a r c h , s o c i a l o r g a n i z a t i o n and t h e i n d i v i d u a l ' s u n d e r s t a n d i n g o f i t a r e d e p i c t e d i n common s t r u c t u r a l terms. S e v e r a l s o c i a l p s y c h o l o g i s t s ( e . g . , S m e l s e r and S m e l s e r , 1970; D i R e n z o , 1977; M a i n e s , 1977) have f o r some tim e been c a l l i n g f o r j u s t s u c h a model, a model t h a t w o u l d p r o v i d e a s i n g l e framework f o r a n a l y z i n g b o t h p e r s o n systems and s o c i a l s y s t e m s . 7 P i a g e t i a n t h e o r y has n o t f o c u s e d a t t e n t i o n upon th e c h i l d ' s a b i l i t y t o a p p r e -hend systems of any s o r t ^ , i t f o l l o w s t h a t c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n have y e t t o appear i n t h e s t a n d a r d pantheon o f P i a g e t i a n c o g n i -t i v e s t r u c t u r e s . Beyond th e a t t e m p t t o d e f i n e and document t h e s e s y s t e m i c c o g n i t i v e s t r u c t u r e s , an e f f o r t was a l s o made t o compare them i n v a r i o u s ways t o o t h e r more w e l l documented and t h o r o u g h l y s t u d i e d s t r u c t u r e s . C o n s e q u e n t l y , f o u r o f t h e s i x c o g n i t i v e s t r u c t u r e s a s s e s s e d i n t h i s r e s e a r c h have a l r e a d y been s t u d i e d by numerous i n v e s t i g a t o r s w o r k i n g w i t h i n a P i a g e t i a n t r a d i t i o n ( i . e . , s e r i a t i o n , l i n e a r t r a n s i t i v i t y , l o g i c a l m u l t i p l i c a t i o n , c l a s s i n c l u s i o n ) . These f o u r a r e commonly c l a s s i f i e d as a c h i e v e m e n t s o f t h e c o n c r e t e o p e r a t i o n -a l s t a g e . That c l a s s i f i c a t i o n , however, i s b a s e d upon t h e c h i l d ' s use o f t h e s e c o g n i t i v e s t r u c t u r e s t o u n d e r s t a n d i n a n i m a t e , p h y s i c a l r e a l i t y o n l y . The ages a t w h i c h t h e s e f o u r c o g n i t i v e s t r u c t u r e s can be a p p l i e d i n e f f o r t s t o u n d e r s t a n d a n i m a t e and/or s o c i e t a l r e a l i t y r emains unknown. N e i t h e r i s i t known i n what o r d e r t h e s e s t r u c t u r e s w o u l d be m a s t e r e d i n t h e open systems domains. B. P a r a l l e l Development A c r o s s Domains L e a r n i n g s o m e t h i n g about ages and o r d e r s o f m a s t e r y i n t h e b i o - e c o l o g i -c a l and t h e s o c i e t a l domains e n t a i l e d d e t e r m i n i n g t h e e x t e n t t o w h i c h c o g n i -t i v e development u n f o l d s i n a p a r a l l e l o r yoked f a s h i o n a c r o s s t h e v a r i o u s c o n t e n t domains. I f c o g n i t i v e s t r u c t u r e s a r e m a s t e r e d a t d i f f e r e n t ages i n 5. T h i s i s s u e , t o o , i s d e a l t w i t h more e x t e n s i v e l y l a t e r . See A p p e n d i x E f o r a d i s c u s s i o n o f the d i f f e r e n c e between f o r m a l l o g i c and s y s t e m i c l o g i c . d i f f e r e n t c o n t e n t domains t h e n i t i s a l s o p o s s i b l e t h a t t h e y may be m a s t e r e d i n a d i f f e r e n t o r d e r . T h i s w o u l d a t t e n u a t e t h e g e n e r a l i z a b i l i t y o f P i a g e t i a n t h e o r y t o the b i o - e c o l o g i c a l and the s o c i e t a l domains. Q u e s t i o n s o f g e n e r a l -i z a b i l i t y , o f c o u r s e , a r e q u e s t i o n s o f degree. There a r e a t l e a s t two de-grees o f d e t a i l a t w h i c h e v i d e n c e o f g e n e r a l i z a b i l i t y c o u l d be so u g h t . A t what s h a l l be c a l l e d t he " m a c r o s c o p i c " l e v e l , e v i d e n c e c o u l d be sought f o r a c r o s s domain r e p l i c a t i o n o f t h e major s t a g e s . I f , i n the open systems domains, t h e r e i s no d i s c o n t i n u i t y between t h e most advanced c o n c r e t e s t a g e c o g n i t i v e s t r u c t u r e and t h e s i m p l e s t f o r m a l s t a g e c o g n i t i v e s t r u c t u r e , t h e n t h e l e g i t i m a c y o f a p p l y i n g a P i a g e t i a n a n a l y s i s t o c h i l d r e n ' s u n d e r s t a n d i n g o f s u c h ecosystems o r s o c i a l systems w o u l d be c a s t i n t o s e r i o u s doubt. I f , by c o n t r a s t , c h i l d r e n who were found t o be a t P i a g e t ' s c o n c r e t e o r f o r m a l o p e r a t i o n a l l e v e l s i n t h e t r a d i t i o n a l i m p e r s o n a l o r p h y s i c a l domain were shown t o e v i d e n c e e q u i v a l e n t s t r u c t u r e s when r e a s o n i n g about the b i o - e c o l o -g i c a l o r s o c i e t a l domains, th e n p a r a l l e l i s m w o u l d be d e m o n s t r a t e d a t t h i s "macro'' l e v e l . A t what s h a l l be c a l l e d t h e " m i c r o s c o p i c " l e v e l , however, t h e r e i s more room f o r e r r o r . The m i c r o s c o p i c l e v e l o f a n a l y s i s i s a more f i n e g r a i n e d , d e t a i l e d v e r s i o n o f the m a c r o s c o p i c l e v e l . Here the c r i t e r i a f o r a c r o s s domain p a r a l l e l i s m i n c o g n i t i v e development a r e s e t a t t h e i r h i g h e s t . What i s sought a t t h i s l e v e l o f a n a l y s i s i s e v i d e n c e t h a t t h e r e i s a u n i f o r m p r o -g r e s s i o n o f m a s t e r y o f l o g i c o - m a t h e m a t i c a l p r i n c i p l e s r e g a r d l e s s o f t h e con-t e n t used t o i l l u s t r a t e t h o s e p r i n c i p l e s . I f t h i s s t r i n g e n t c r i t e r i o n were n o t met owning t o some m i s o r d e r i n g o f c o g n i t i v e s t r u c t u r e s w i t h i n s t a g e s , t h e r e would be no need t o q u e s t i o n the whole o f P i a g e t i a n t h e o r y as i n a p p l i -c a b l e . M i s o r d e r i n g o f c o g n i t i v e s t r u c t u r e s a c r o s s s t a g e s , however, w o u l d r a i s e s i g n i f i c a n t d o u b t s . The whole i s s u e o f d e t e r m i n i n g t h e l e g i t i m a c y o f a p p l y i n g a P i a g e t i a n a p p roach t o c h i l d r e n ' s u n d e r s t a n d i n g i n t h e b i o - e c o l o g i c a l and s o c i e t a l domain r e c e i v e s more a t t e n t i o n i n s e c t i o n E. There t h e i s s u e s s u r r o u n d i n g t h e s e a r c h f o r p a r a l l e l p a t t e r n s o f development a c r o s s domains a r e d i s c u s s e d more f u l l y . Two o f t h o s e i s s u e s , however, must be b r i e f l y i n t r o d u c e d a t t h i s p o i n t i n o r d e r t o f a c i l i t a t e t h e d e t a i l e d d i s c u s s i o n o f s o c i e t a l and c o g n i t i v e s t r u c t u r e s i n s e c t i o n A and B o f c h a p t e r I I . The f i r s t o f t h e s e c o n c e r n s t h e r e a s o n s u n d e r l y i n g t h e d e c i s i o n t o i n c l u d e t h e b i o - e c o l o g i c a l domain ( s u b s e c t i o n B ( i ) , c h a p t e r I ) . The second i s s u e ( s u b s e c t i o n B ( i i ) , c h a p t e r I ) , c o n c e r n s the p r o b l e m o f u n e q u a l l e v e l s o f f a m i l i a r i t y w i t h t h e m a t e r i a l s used i n the v a r i o u s c o n t e n t domains, ( i ) The B i o - e c o l o g i c a l Domain Because the f o c u s o f t h i s r e s e a r c h i s upon an e x t e n s i o n o f P i a g e t ' s r e s e a r c h i n t h e domain o f p h y s i c a l phenomena t o t h e s o c i e t a l domain, i t m i ght appear t h a t t h i s s t u d y c o u l d have been p e r f o r m e d u s i n g o n l y c o n t e n t sampled from t h e s e two domains. The c h i l d ' s u n d e r s t a n d i n g o f t h e p h y s i c a l domain i s r e l a t i v e l y w e l l documented w h i l e r e l a t i v e l y l i t t l e i s known about c o g n i t i v e s t r u c t u r e s r e l a t i n g t o t h e u n d e r s t a n d i n g o f s o c i e t y . G i v e n an i n t e n t i o n t o p r o c e e d from t h e known to the unknown, i t w o u l d seem r e a s o n -a b l e t o a t t e m p t a d i r e c t c o m p a r i s o n o f p e r f o r m a n c e i n t h e p h y s i c a l domain w i t h p e r f o r m a n c e i n the s o c i e t a l domain. There were, however, two r e a s o n s f o r d e c i d i n g t o i n c l u d e m a t e r i a l s drawn from a t h i r d domain r e p r e s e n t i n g b i o - e c o l o g i c a l s y s t e m s . F i r s t , t h e p h y s i c a l domain of s t a n d a r d P i a g e t i a n t a s k s d i f f e r s f rom t h e s o c i e t a l domain on a t l e a s t two d i m e n s i o n s . They i n c l u d e a) the p h y s i c a l v e r s u s n o n - p h y s i c a l , and b) t h e i n a n i m a t e v e r s u s 10 animate. I t was thought t h a t c o mparisons o f t h e p h y s i c a l domain w i t h t h e s o c i e t a l domain would be f a c i l i t a t e d by t h e i n c l u s i o n o f a t h i r d domain, the b i o - e c o l o g i c a l , h a v i n g one c h a r a c t e r i s t i c i n common w i t h each o f t h e o t h e r two. E c o s y s t e m s , l i k e s o c i a l systems , a r e a n i m a t e , b u t a l s o c o n t a i n p h y s i c a l elements ( e . g . , b i r d s , i n s e c t s ) w h i c h a r e j u s t as p a l p a b l e as the p h y s i c a l o b j e c t s used i n s t a n d a r d P i a g e t i a n t a s k s . Second, as men t i o n e d e a r l i e r , t he l o g i c o - m a t h e m a t i c a l p r i n c i p l e s o f c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n have few unambiguous m a n i f e s t a t i o n s i n p u r e l y p h y s i c a l , i n a n i m a t e phenomena. There a r e , c o n s e q u e n t l y , no s t a n d a r d t a s k s among t h e r e p e r t o i r e o f u s u a l P i a g e t i a n assessment p r o c e d u r e s w i t h w h i c h t o a s s e s s t h e s e c o g n i -t i v e s t r u c t u r e s i n t h e p h y s i c a l domain. U s i n g b i o - e c o l o g i c a l c o n t e n t , how-e v e r , i t was p o s s i b l e t o c o n s t r u c t assessment p r o c e d u r e s f o r c y c l i c t r a n s i -t i v i t y and c y c l i c i n t e g r a t i o n . I t was the n p o s s i b l e t o compare p e r f o r m a n c e s i n t h e s o c i e t a l domain t o o t h e r measures w h i c h s h a r e d t h e i r open systems c h a r a c t e r i s t i c s b u t w h i c h were n o t n e c e s s a r i l y s o c i a l i n c o n t e n t , ( i i ) F a m i l i a r i t y The c u r r e n t f o c u s on sequences o f c o g n i t i v e development a c r o s s c o n t e n t domains r a i s e d an i m p o r t a n t m e t h o d o l o g i c p r o b l e m c o n c e r n i n g the r e s p o n d e n t s ' r e l a t i v e f a m i l i a r i t y w i t h the m a t e r i a l s used i n d i f f e r e n t c o n t e n t domains. F o r example, c r o s s - c u l t u r a l P i a g e t i a n r e s e a r c h shows t h a t l o g i c a l problems e a s i l y s o l v e d u s i n g f a m i l i a r m a t e r i a l s a r e o f t e n f a i l e d w i t h u n f a m i l i a r t e s t i n g m a t e r i a l s ( G r e e n f i e l d , 1976). S i n c e c h i l d r e n p a r t i c i p a t e o n l y m i n i -m a l l y i n the p o l i t i c a l and economic l i f e o f a s o c i e t y , i t i s p o s s i b l e t h a t t h e c o n t e n t s o f t h i s a d u l t w o r l d might be l i k e m a t e r i a l s f r o m a f o r e i g n 6. The term " s o c i a l " i s ambiguous. Sometimes i t i s used t o mean " i n t e r -p e r s o n a l " ; o t h e r t i m e s i t i s i n t e n d e d t o mean " s o c i e t a l " . I n t h e p r e s e n t work the term " s o c i a l " i s n e v e r used t o mean " i n t e r p e r s o n a l " . Where i t i s w a r r a n t e d by t h e c o n t e x t , the term " s o c i a l " may be used i n the sense o f " s o c i e t a l " . 11 c u l t u r e t o them. Throughout t h i s r e s e a r c h t h e c h i l d r e n were c o n s e q u e n t l y q u e r i e d about t h e i r f a m i l i a r i t y w i t h t h e m a t e r i a l s b e i n g used. I t was t h e r e -f o r e p o s s i b l e t o compare t h e f a m i l i a r i t y o f the s o c i e t a l domain m a t e r i a l s w i t h (a) p e r f o r m a n c e on t h e s o c i e t a l domain t a s k s , and (b) t h e f a m i l i a r i t y o f m a t e r i a l s i n t h e o t h e r two domains. These c o m p a r i s o n s p r o v i d e d c e r t a i n c hecks and c o n t r o l s o v e r t h e i s s u e o f f a m i l i a r i t y and promoted the a t t e m p t t o e x t e n d P i a g e t i a n t h e o r y t o the u n d e r s t a n d i n g o f s o c i e t y . They d i d so by b e g i n n i n g t o d e s c r i b e t h e ways i n w h i c h s o c i e t a l c o n t e n t i s s i m i l a r t o , and d i f f e r e n t from, the c o n t e n t upon w h i c h P i a g e t b a s e d most o f h i s t h e o r i z -i n g , e s p e c i a l l y i n h i s l a t e r w o r k s. I n summary, t h i s s t u d y a t t e m p t e d t h e i d e n t i f i c a t i o n and d o c u m e n t a t i o n o f two new c o g n i t i v e s t r u c t u r e s n e c e s s a r y f o r t h e u n d e r s t a n d i n g o f open systems f e a t u r e s o f s o c i e t a l o r g a n i z a t i o n s . That u n d e r t a k i n g r e q u i r e d p r e -l i m i n a r y groundwork on t h e g e n e r a l i z a b i l i t y o f the P i a g e t i a n model to new c o n t e n t domains. That a t t e m p t t o examine t h e e x t e n t o f p a r a l l e l s e q u e n c i n g o f c o g n i t i v e s t r u c t u r e s a c r o s s domains n e c e s s i t a t e d the i n c l u s i o n o f (a) a p h y s i c a l y e t animate domain, the b i o - e c o l o g i c a l domain, and (b) f a m i l i a r i t y a s sessments f o r the c o n t e n t s o f each domain. 12 I I . STRUCTURES AND CONTENTS S e c t i o n A o f t h i s c h a p t e r b e g i n s w i t h some c l a r i f i c a t i o n o f t e r m i n o l o g y and c o n t i n u e s w i t h a d e s c r i p t i o n o f some s o c i e t a l s t r u c t u r e s . I n s e c t i o n B the c o g n i t i v e s t r u c t u r e s examined i n t h i s r e s e a r c h a r e d e s c r i b e d and v a r i o u s i n t e r p r e t a t i o n s o f what c o n s t i t u t e s a s t a g e o f c o g n i t i v e development a r e d i s c u s s e d . I n s e c t i o n C t h e i s s u e s s u r r o u n d i n g the r o l e o f c o n t e n t d e t e r -m i n i n g t a s k d i f f i c u l t y a r e r a i s e d a l o n g w i t h a c o n s i d e r a t i o n o f age and s t a g e i s s u e s r e l a t e d t o t a s k d i f f i c u l t y . F i n a l l y , t he h y p o t h e s e s o f the s t u d y a r e f o r m a l l y s t a t e d and t h e n e x p l a i n e d i n s e c t i o n D o f t h i s c h a p t e r . A. S o c i e t a l S t r u c t u r e s S i n c e the purpose o f t h i s r e s e a r c h was t o c h a r t t h e development of the c h i l d ' s u n d e r s t a n d i n g o f s o c i a l o r g a n i z a t i o n s , i t i s i m p o r t a n t t o b e g i n by a r t i c u l a t i n g more e x p l i c i t l y what i s i n t e n d e d by t h e concept o f s o c i a l s t r u c t u r e . B e f o r e t h e s u b s t a n t i v e n a t u r e o f t h e s o c i e t a l s t r u c t u r e s u s e d i n t h i s s t u d y can be d i s c u s s e d i n d e t a i l , t he more g e n e r i c c o n c e p t s o f s t r u c t u r e s and o p e r a t i o n s must be examined more g e n e r a l l y . (1) S t r u c t u r e s and O p e r a t i o n s There a r e s e v e r a l i n t e r r e l a t e d terms t h a t a r e used t h r o u g h o u t t h i s work ( i . e . , s t r u c t u r e , o p e r a t i o n , p r i n c i p l e ) . I n o r d e r t o a v o i d l a t e r c o n f u s i o n , t h i s s e c t i o n i s i n c l u d e d as an a t t e m p t t o examine t h e r e l a t i v e l y f i n e d i s -t i n c t i o n s among t h e s e terms and the s t r o n g l i n k a g e s among t h e s e c o r r e s p o n d -i n g c o n c e p t s . The two most c l o s e l y r e l a t e d c o n c e p t s a r e s t r u c t u r e s and 13 operations"'". S t r u c t u r e s and o p e r a t i o n s a r e , a c c o r d i n g t o P i a g e t , b o t h based on l o g i c o - m a t h e m a t i c a l p r i n c i p l e s . The p r i n c i p l e might be a t o p o l o g i c a l p a t -t e r n , a s e t o f t r a n s f o r m a t i o n r u l e s , a r e l a t i o n s h i p between s y m b o l s , e t c . L o g i c o - m a t h e m a t i c a l p r i n c i p l e s a r e always embedded i n some k i n d o f c o n t e n t . The c o n t e n t may be s y m b o l i c , b e h a v i o u r a l , s o c i a l , p h y s i c a l , o r w h a t e v e r . The p r i n c i p l e s , once u n d e r s t o o d , can be d i s c e r n e d i n o r g a n i z e d p a r t s o f t h e e n v i r o n m e n t , ( e . g . , r e g u l a r phenomena, v a r i o u s s y s t e m s ) . When a l o g i c o -m a t h e m a t i c a l p r i n c i p l e i s m a n i f e s t e d i n some o r g a n i z e d a s p e c t of the w o r l d t h e n t h a t p a r t o f the w o r l d i s s t r u c t u r e d a c c o r d i n g t o t h a t p r i n c i p l e . The p r i n c i p l e d e s c r i b e s t h e s t r u c t u r e o f t h e o r g a n i z a t i o n . One o f t h e i m p l i c a t i o n s o f t a k i n g a s t r u c t u r a l i s t a p p roach towards t h e environment as w e l l as towards c o g n i t i o n i s t h a t l o g i c o - m a t h e m a t i c a l p r i n c i -p l e s a r e assumed t o r e s i d e i n b o t h thought and o b j e c t s o f t h o u g h t . I n o t h e r words, i t i s b e i n g assumed t h a t i f a t r e e f e l l i n t h e f o r e s t and t h e r e were no one t h e r e t o " h e a r " i t ( i n t h i s c a s e , " t h i n k o f i t " ) t h e r e w o u l d n e v e r t h e -l e s s be a sound made by t h e t r e e h i t t i n g t h e ground. That i s , t h e w o r l d i s s t r u c t u r e d whether we a p p r e c i a t e i t o r n o t . S i n c e t h e human mind i s p a r t o f n a t u r e , i t too i s s t r u c t u r e d a c c o r d i n g t o t h e same l o g i c o - m a t h e m a t i c a l p r i n -c i p l e s by w h i c h t h e r e s t of n a t u r e i s o r g a n i z e d . A s w i n g i n g pendulum i s an o r g a n i z e d p a r t o f t h e w o r l d . I t s s t r u c t u r e i s d e s c r i b e d by l o g i c o - m a t h e m a t i c a l p r i n c i p l e s d e r i v a b l e f r o m t h e INRC group 1. I n P i a g e t ' s t h e o r y b o t h o f t h e s e terms a r e r e l a t e d t o l o g i c o - m a t h e m a t i c a l p r i n c i p l e s . An a t t e m p t i s b e i n g made i n t h e p r e s e n t work t o use t h e s e terms t o mean th e same t h i n g t h a t P i a g e t meant by them. However, h i s usage sometimes v a r i e s . T h e r e f o r e , t h e r e a d e r may o c c a s i o n a l l y sense d i s c r e p a n c i e s between P i a g e t ' s use o f terms and t h e i r use t h r o u g h o u t t h i s work. 14 ( P i a g e t and I n h e l d e r , 1956). An e c o s y s t e m i s an o r g a n i z e d p a r t o f t h e w o r l d . I t s s t r u c t u r e i s d e s c r i b e d by l o g i c o - m a t h e m a t i c a l p r i n c i p l e s l i k e c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n . The same can be s a i d o f a s o c i o - e c o n o m i c system. To r e f e r t o t h e m a n i f e s t a t i o n o f a l o g i c o - m a t h e m a t i c a l p r i n c i p l e i n the o r g a n i z a t i o n o f s o c i e t y I s h a l l use t h e term ' ' s o c i e t a l s t r u c t u r e " . To r e f e r t o i t s m a n i f e s t a t i o n i n t h e o r g a n i z a t i o n o f human c o g n i t i v e a b i l i t i e s I s h a l l use the term " c o g n i t i v e s t r u c t u r e " . W h i l e s t r u c t u r e s a r e p a t t e r n s o f o r g a n i z a t i o n w h i c h e x h i b i t t h e e s s e n -t i a l c h a r a c t e r i s t i c s o f l o g i c o - m a t h e m a t i c a l p r i n c i p l e s , o p e r a t i o n s a r e t h e i m p l e m e n t a t i o n o f t h e s t r u c t u r e s . The s t r u c t u r e s make c e r t a i n k i n d s o f pe r f o r m a n c e s p o s s i b l e . The o p e r a t i o n s a r e t h e p e r f o r m a n c e s made p o s s i b l e by the s t r u c t u r e s . The o p e r a t i o n s a r e t h e p r o c e s s i n g , t r a n s f o r m a t i o n , c o -o r d i n a t i o n , r e o r g a n i z a t i o n , e t c . o f i n f o r m a t i o n and/or m a t e r i a l s a c c o r d i n g t o t h e v a r i o u s l o g i c o - m a t h e m a t i c a l p r i n c i p l e s . C o g n i t i v e o p e r a t i o n s a r e p e r f o r m e d i n t e r n a l l y , w i t h i n i n d i v i d u a l s . I n assessment s i t u a t i o n s where t h e i n d i v i d u a l i s p r e s e n t e d w i t h a p r o b l e m t a s k , t h e p e r s o n ' s p r o b l e m s o l v i n g c o g n i t i v e a c t i v i t y i s a c o g n i t i v e o p e r a t i o n , o r more l i k e l y , a s e t o f c o g n i t i v e o p e r a t i o n s . The t a s k i s an o r g a n i z e d p a r t o f the e n v i r o n m e n t . I t has a s t r u c t u r e w h i c h f o r p u r p o s e s o f i n f e r e n t i a l c l a r i t y i d e a l l y m a n i f e s t s o n l y one l o g i c o - m a t h e m a t i c a l p r i n c i p l e . The p e r s o n i s a l s o o r g a n i z e d and has v a r i o u s c o g n i t i v e s t r u c t u r e s a t h i s o r h e r d i s p o s a l . When the p e r s o n b r i n g s a p a r t i c u l a r c o g n i t i v e s t r u c t u r e t o b e a r upon t h e s t r u c t u r e o f the t a s k , he o r she i s p e r f o r m i n g a c o g n i t i v e o p e r a t i o n . When t h e s t r u c -t u r e o f t h e t a s k o u t s t r i p s t h e s o p h i s t i c a t i o n o f any o f t h e c o g n i t i v e s t r u c -t u r e s a v a i l a b l e t o the p e r s o n , t h e n we say t h a t the p e r s o n has n o t y e t m a s t e r -ed the c o g n i t i v e o p e r a t i o n t h a t w o u l d l e a d t o t a s k s o l u t i o n . The p e r s o n has 15 n o t y e t a c q u i r e d t h e c o g n i t i v e s t r u c t u r e t h a t matches t h e s t r u c t u r e o f t h e t a s k . J u s t as c o g n i t i v e s t r u c t u r e s a r e t h e p a t t e r n o f o r g a n i z a t i o n t h a t make c o g n i t i v e o p e r a t i o n s p o s s i b l e , s o c i e t a l s t r u c t u r e s a r e the p a t t e r n s o f o r g a n i z a t i o n t h a t make s o c i a l o r g a n i z a t i o n a l o p e r a t i o n s p o s s i b l e . S o c i a l o r g a n i z a t i o n s and whole s o c i e t i e s f a c e problems p r e s e n t e d by n a t u r e and/or o t h e r s o c i a l g r o u p s . The s t r u c t u r e o f t h o s e problems may be more o r l e s s s o p h i s t i c a t e d t h a n the s t r u c t u r e o f t h e s o c i a l o r g a n i z a t i o n . L i k e w i s e , t h e s o c i a l s t r u c t u r e may be more o r l e s s s o p h i s t i c a t e d t h a n the c o g n i t i v e s t r u c -t u r e s o f v a r i o u s i n d i v i d u a l members o f t h e s o c i e t y o r o r g a n i z a t i o n . I n d e e d , s o c i a l s t r u c t u r e s can e x i s t w i t h o u t any members o f t h e s o c i e t y f u l l y u n der-s t a n d i n g them. The M a r x i s t n o t i o n o f f a l s e c o n s c i o u s n e s s i s p a r t i a l l y b a s e d on t h i s p r e m i s e . By f o l l o w i n g p r e s c r i b e d , r o u t i n e p r o c e d u r e s , by e n a c t i n g a s s i g n e d r o l e s , e t c . , members can a c t c o o p e r a t i v e l y i n such a way as t o p e r -form an ( s o c i e t a l ) o p e r a t i o n on some i n f o r m a t i o n w i t h o u t anyone o f them e v e r n e c e s s a r i l y p e r f o r m i n g t h e c o r r e s p o n d i n g c o g n i t i v e o p e r a t i o n on a l l the same i n f o r m a t i o n . The s i x c o g n i t i v e s t r u c t u r e s examined i n t h i s s t u d y have a n a l o g o u s s o c i a l s t r u c t u r e s t h a t a r e commonly f o u n d i n the s o c i o - e c o n o m i c systems o f w e s t e r n i n d u s t r i a l i z e d s o c i e t i e s . Two o f the most common f e a t u r e s o f w e s t e r n s o c i a l o r g a n i z a t i o n s a r e t h e i r h i e r a r c h i c a l and s y s t e m i c a s p e c t s . The h i e r -a r c h i c a l model o f s o c i e t y has been p a r t o f t h e w e s t e r n h e r i t a g e s i n c e a t l e a s t as f a r back as t h e m i d d l e ages. I n c o m p l e t e o r f r a g m e n t a r y v e r s i o n s o f t h e sy s t e m model were i m p l i c i t i n t h e s o c i a l commentary o f t h e r o m a n t i c movement and o f Marx (Peckham, 1965; W i l k i n s o n , 1971). P a r s o n s (1950) p r e -s e n t e d a n o t h e r fragment w h i c h complemented t h e M a r x i s t v i e w . The f u l l scope 16 o f the s y s t e m i c model has been made e x p l i c i t o n l y r e c e n t l y ( B o u l d i n g , 1962; E a s t o n , 1965; Sztomka, 1974; M y s i o r , 1977). S o c i e t a l h i e r a r c h i e s and systems a r e c o n s t i t u t e d f r o m t h e c o m b i n a t i o n s of s o c i e t a l s t r u c t u r e s . H i e r a r c h i e s and systems a l m o s t a l w a y s appear t o -g e t h e r i n s o c i a l o r g a n i z a t i o n s . F o r t h e purpose o f a n a l y z i n g t h e i r c o n s t i t u e n t s o c i a l s t r u c t u r e s , however, t h e y a r e d i s c u s s e d s e p a r a t e l y . The ones t h a t a r e t h o u g h t t o be e a s i e r t o u n d e r s t a n d a r e d i s c u s s e d f i r s t . The s o c i a l s t r u c -t u r e s i m p l i c i t i n h i e r a r c h i e s a r e d i s c u s s e d b e f o r e t u r n i n g t o t h e two s t r u c t u r e s e x h i b i t i n g s y s t e m i c r e l a t i o n s . The o v e r a l l g o a l o f t h e f o l l o w i n g r e v i e w o f s o c i e t a l s t r u c t u r e s i s t o c l e a r l y s p e c i f y e x a c t l y what a s p e c t s o f s o c i e t y a r e b e i n g s i n g l e d out f o r s t u d y v i s a v i s t h e c h i l d ' s d e v e l o p i n g u n d e r s t a n d i n g o f s o c i e t y , ( i i ) S t r u c t u r e s I m p l i c i t i n H i e r a r c h i e s E lements o f h i e r a r c h i e s can always be c o n c e p t u a l i z e d as (a) p o i n t s a l o n g a c o n t i n u u m , and a s , (b) members o f d i s c r e t e c l a s s e s o r s e t s . E v e r y h i e r a r c h y has a t l e a s t one continuum, namely, i t s v e r t i c a l r a n k i n g from t h e apex t o the b ase. I f t h e h i e r a r c h y i s a c l a s s i f i c a t i o n s y s t e m , t h e continuum might be one o f a b s t r a c t n e s s o r o f l o g i c a l p r i o r i t y . I n some h i e r a r c h i e s t h e co n t i n u u m may denote t e m p o r a l p r i o r i t y . I n some s o c i a l o r g a n i z a t i o n s t h e continuum r e f l e c t s d e c i s i o n making power and s u p e r v i s o r y a u t h o r i t y . E l e m e n t s o f h i e r a r c h i e s can a l s o be c o n c e p t u a l i z e d as members o f d i s c r e t e c l a s s e s o r s e t s i n s o f a r as t h e apex r e p r e s e n t s t h e s e t o f a l l e l e m e n t s i n t h e h i e r a r c h y and each s u b o r d i n a t e element r e p r e s e n t s a s u b s e t o f e l e m e n t s . I n s o c i e t i e s t h a t a r e a l s o n a t i o n s t a t e s , f o r example, t h e s u b s e t s c o r r e s p o n d t o e n t i t i e s l i k e p r o v i n c e s , s t a t e s , m u n i c i p a l i t i e s , e t c . A s o c i e t y ' s economy may be sub-c l a s s i f i e d a c c o r d i n g t o p u b l i c v e r s u s p r i v a t e s e c t o r s o r v a r i o u s i n d u s t r i a l s e c t o r s . 17 A h i e r a r c h y can be decomposed i n t o a t l e a s t f o u r c o n s i t i u e n t s t r u c -2 t u r e s . I n t h i s r e s e a r c h , the f o l l o w i n g a r e c o n s i d e r e d t o be t h e most im-p o r t a n t s o c i a l s t r u c t u r e s i n a h i e r a r c h y : (a) s e r i a t i o n o r o r d i n a t i o n , (b) l i n e a r t r a n s i t i v i t y , (c) l o g i c a l m u l t i p l i c a t i o n , (d) c l a s s i n c l u s i o n . These c o r r e s p o n d t o the c o g n i t i v e o p e r a t i o n s , o f t h e same names. When t h e y a p p e a r , the s o c i a l s t r u c t u r e s o f o r d i n a t i o n and t r a n s i t i v i t y t e n d t o i n v o k e t h e arrangement of e l e m e n t s as p o i n t s a l o n g a continuum. L o g i c a l m u l t i p l i c a t i o n and c l a s s i n c l u s i o n , on the o t h e r hand, r e l y on the d i s c r e t e c a t e g o r i c a l p r o p e r t i e s o f e l e m e n t s . S e r i a t i o n . S e r i a t i o n r e f e r s t o t h e arrangement o f elements ( i . e . , c o m p a n i e s , committees, r o l e s , e t c . ) s u c h t h a t a l o n g some d i m e n s i o n each s u c c e s s i v e element has an a s c e n d i n g v a l u e . F o r example, s o c i a l o r g a n i z a -t i o n s w i t h d i f f e r e n t l e v e l s o f s u p e r v i s o r y s t a f f a l l o c a t e a t l e a s t some o f t h e i r r e s o u r c e s ( e . g . , s a l a r i e s , o f f i c e space) a c c o r d i n g t o s u p e r v i s o r y r a n k . More a b s t r a c t d i m e n s i o n s c o u l d be used t o d e s c r i b e t h e v e r t i c a l c o n -tinuum. S u p e r v i s o r y r a n k might be i n d e x e d by t h e l o g i c a l p r i o r i t y o f t a s k s b e i n g p e r f o r m e d by each e l e m e n t . F o r example, t h e top r a n k s m i g h t d e c i d e what g o a l s t h e o r g a n i z a t i o n w i l l a t t e m p t t o a c h i e v e . The n e x t l o w e r l e v e l m ight d e c i d e what means w i l l be used t o a c h i e v e t h o s e g o a l s . The bottom r a n k might t h e n p e r f o r m t h e t a s k s d e s i g n e d t o a c h i e v e t h e g o a l s . E l e m e nts 2. I t i s i m p o s s i b l e t o p r o v e t h a t t h e s e a r e the o n l y c o n s t i t u e n t s t r u c t u r e s t h a t anyone e v e r h a s , o r e v e r w i l l , a t t r i b u t e t o h i e r a r c h i e s . M o r e o ver, the c o n c ept of h i e r a r c h y i s n o t as l o g i c a l l y p r e c i s e as i t may seem. There a r e d i f f e r e n t m a t h e m a t i c a l t h e o r i e s w h i c h u t i l i z e the concept b u t w h i c h a l l use d i f f e r e n t language t o d e s c r i b e i t s f e a t u r e s and make d i f -f e r e n t a s s u m p t i o n s about what r e l a t i o n s may o b t a i n among elements ( e . g . , s e t t h e o r y , l a t t i c e t h e o r y ) . The concept o f h i e r a r c h y i n i t s e l f , however, does n o t i m p l y a s i n g l e l i s t o f f e a t u r e s . R a t h e r , t h e term " h i e r a r c h y " i s l o o s e l y used t o r e f e r t o any arrangement w h i c h can be r e p r e s e n t e d as a b r a n c h i n g , t r e e - l i k e s t r u c t u r e . The l i s t o f c o n s t i t u e n t s t r u c t u r e s p r e s e n t e d h e r e seems t o a c c o u n t f o r a l l o f t h e i m p o r t a n t l o g i c a l a s p e c t s of a h i e r a r c h y i n t h e sense o f a b r a n c h i n g t r e e - l i k e s t r u c t u r e h a v i n g a t l e a s t two b i f u r c a t i o n s i n s e r i e s . 18 c o u l d a l s o be o r d i n a t e d a l o n g a d i m e n s i o n o f t e m p o r a l p r i o r i t y e i t h e r w i t h i n o r among l e v e l s o f ra n k . Imagine a m u n i c i p a l revenue o f f i c e where the f i r s t c l e r k t o r e c e i v e t h e t a x r e t u r n s checks the f o r m f o r m i s s i n g i n f o r m a t i o n . The second c l e r k checks the a c c u r a c y o f c a l c u l a t i o n s . The t h i r d c l e r k f i l e s t he form f o r f u t u r e r e f e r e n c e . I n t h i s h y p o t h e t i c a l example, t h e el e m e n t s a r e o r d i n a t e d i n a t e m p o r a l s e r i e s c o r r e s p o n d i n g t o the c a r d i n a l numbers, 1 s t t o n t h , where n i s t h e number of elements i n t he s e r i e s . L i n e a r T r a n s i t i v i t y . L i n e a r t r a n s i t i v i t y i s a ty p e o f s o c i a l s t r u c -t u r e based on t h e l o g i c o - m a t h e m a t i c a l r e l a t i o n o f t h e same name. I n l o g i -c a l f o r m i t i s e x e m p l i f i e d by t h e s t a t e m e n t "A i s g r e a t e r t h a n B_, and C_ i s l e s s e r t h a n .B, t h e r e f o r e A i s g r e a t e r t h a n C\!. When m a n i f e s t e d i n s o c i a l c o n t e n t i t i s e x e m p l i f i e d by p a t t e r n s o f s o c i a l o r g a n i z a t i o n as the f o l l o w i n g : "CPR c o r p o r a t i o n owns Marathon R e a l t y , and F a l s e Creek Development C o r p o r a t i o n i s owned by Marath o n R e a l t y , t h e r e f o r e CPR owns F a l s e Creek Development C o r p o r a t i o n " . L o g i c a l M u l t i p l i c a t i o n . L o g i c a l m u l t i p l i c a t i o n as a l o g i c o - m a t h e -m a t i c a l r e l a t i o n i n v o l v e s c o n s i d e r i n g a t l e a s t two s e t s o f e l e m e n t s , t h o s e w i t h a t t r i b u t e p_ and t h o s e w i t h a t t r i b u t e c[. E v e r y element can be c l a s s i -f i e d as b e i n g e i t h e r i n s i d e o r o u t s i d e o f e i t h e r s e t ( i . e . , _p o r n o t p; iL o r n o t - q ) • A l l e l e m e n t s can the n be l o c a t e d i n a t w o - f o l d c l a s s i f i c a t i o n m a t r i x ( i . e . , p_ and _q_; p_ and n o t q; q_ and n o t p; n o t _q_ and n o t p) . I n t h i s s i m p l e s t o f examples, l o g i c a l m u l t i p l i c a t i o n i s t h e i d e n t i f i c a t i o n o f t h o s e elements r e p r e s e n t i n g s e t i n t e r s e c t i o n ( i . e . , p_ and q j . I n s o c i o -economic terms l o g i c a l m u l t i p l i c a t i o n c o u l d be i l l u s t r a t e d by c o n s i d e r i n g 19 v a r i o u s i n d u s t r i e s as elements i n a n a t i o n a l economy. I n t h e f i r s t s e t we may f i n d i n d u s t r i e s t h a t have t h e a t t r i b u t e o f b e i n g p u b l i c (p_) . The com-plement w o u l d be p r i v a t e i n d u s t r i e s ( n o t p ) . The second s e t may be b a s e d on a t t r i b u t e s l i k e p r i m a r y (q_) v e r s u s s e c o n d a r y ( n o t q) p r o c e s s i n g . By l o g i c a l m u l t i p l i c a t i o n we c o u l d t h e n i d e n t i f y a s u b s e t o f i n d u s t r i e s t h a t were b o t h p u b l i c and p r i m a r y ( e . g . , P e t r o c a n ) . C l a s s I n c l u s i o n . - ' C l a s s i n c l u s i o n i s a l o g i c o - m a t h e m a t i c a l r e l a t i o n i n v o l v i n g s u b o r d i n a t e and s u p r a o r d i n a t e c l a s s e s . L i k e l o g i c a l m u l t i p l i c a -t i o n , t h e elements ( e . g . , a^ and a2) have two a t t r i b u t e s e a c h . U n l i k e l o g i -c a l m u l t i p l i c a t i o n t he a t t r i b u t e s a r e n e s t e d . That i s , s u b o r d i n a t e c l a s s i f y -i n g a t t r i b u t e s a r e s p e c i a l c ases o f , o r i n s t a n c e s o f , the s u p r a o r d i n a t e c l a s s i f y i n g a t t r i b u t e . The elements a^ and a2 a r e b o t h examples o f A e l e -ments. As a s o c i o - e c o n o m i c example, c o n s i d e r p o s t a l w o r k e r s (a-^) and f e d e r a l government c l e r k s (a£). B o t h groups o f p e o p l e a r e members o f a s u p r a o r d i n a t e c l a s s , f e d e r a l government employees ( i . e . , c l a s s A ) . T h i s s o c i a l s t r u c t u r e e x i s t s i n d e p e n d e n t l y o f whether o r n o t any p o s t a l w o r k e r s o r c l e r k s o r o t h e r f e d e r a l employees a r e c o g n i z a n t o f i t . ( i i i ) S y s t e m i c S t r u c t u r e s The o r g a n i z a t i o n a l s t r u c t u r e s d e s c r i b e d thus f a r r e f l e c t t h e i m p o r t a n t l o g i c a l f e a t u r e s o f a h i e r a r c h y . The l o g i c o - m a t h e m a t i c a l p r i n c i p l e s i m p l i c i t i n h i e r a r c h i e s have r e c e i v e d c o n s i d e r a b l e a t t e n t i o n f r o m P i a g e t and o t h e r s . As we b e g i n t o duscuss s y s t e m i c s t r u c t u r e s , however, we a r e moving onto more u n f a m i l i a r ground. A h i e r a r c h y i s n o t n e c e s s a r i l y a system a l t h o u g h i t can be i f c e r t a i n c r i t e r i a a r e met. The c l a s s i f i c a t i o n o f b i r d s , f o r example, i n t o w a t e r f o w l and n o n - w a t e r f o w l w i t h w a t e r f o w l f u r t h e r s u b c l a s s i f i e d i n t o ducks and non-ducks i s a h i e r a r c h y . I t i s n o t a sy s t e m , however, because we 20 have n o t y e t d e a l t w i t h t h e f l o w o f i n f o r m a t i o n and/or m a t e r i a l s w i t h i n and/ o r between l e v e l s of the h i e r a r c h y . I f we go on t o examine how changes i n t h e f e e d i n g h a b i t s o f the duck p o p u l a t i o n e f f e c t t h e r e p r o d u c t i v e p a t t e r n s of the w a t e r f o w l p o p u l a t i o n , t h e n we a r e t r e a t i n g t h e h i e r a r c h y as a s y s tem. I n t h i s r e s e a r c h a s y s t e m i s d e f i n e d a s : A s e t o f e l e m e n t s i n some o r d e r e d r e l a t i o n s h i p s u c h t h a t i n -f o r m a t i o n and/or m a t e r i a l s f l o w s , e i t h e r d i r e c t l y o r i n d i r e c t -l y , f rom e v e r y element ( o r c l a s s o f e l e m e n t s ) t o e v e r y o t h e r element i n ways w h i c h a f f e c t the f u n c t i o n i n g o f a l l e l e m e n t s . The c h a n n e l s o f s u c h i n f o r m a t i o n f l o w a r e t y p i c a l l y r e f e r r e d t o as f e e d b a c k l o o p s ( L a z l o , 1972). A c y c l e w i t h a t l e a s t two e l e m e n t s , each o f w h i c h r e c e i v e s and t r a n s m i t s i n f o r m a t i o n and/or m a t e r i a l , i s a s i m p l e s y s t e m w h i c h , i n i t s l i m i t i n g c a s e , c o n t a i n s o n l y one f e e d b a c k l o o p . C y c l i c T r a n s i t i v i t y . C y c l i c t r a n s i t i v i t y , as the name s u g g e s t s , i s a s o c i a l s t r u c t u r e t y p i f i e d by a c y c l i c a l f l o w o f m a t e r i a l s and/or i n f o r m a t i o n . The movement o f m a t e r i a l s and/or r e s o u r c e s f r o m one element to a n o t h e r i s c a l l e d " t r a n s m i s s i o n " . I n l o g i c o - m a t h e m a t i c a l terms a s e t o f t h r e e e l e m e n t s (A, B, and C) w o u l d e x e m p l i f y c y c l i c t r a n s i t i v i t y i f A t r a n s m i t s t o B, B t r a n s m i t s t o C, and C t r a n s m i t s t o A. Each element may o r may n o t t r a n s f o r m what i t r e c e i v e s . I n e i t h e r c a s e , t h e s t a r t i n g element e v e n t u a l l y r e c e i v e s p a r t o f i t s own o u t p u t back as i n p u t , perhaps i n a l t e r e d form. As an example o f such a c y c l i c t r a n s i t i v e s t r u c t u r e drawn f r o m t h e s o c i o - e c o n o m i c r e a l m , c o n s i d e r a company h a v i n g s e v e r a l d e p a r t m e n t s , a l l of w h i c h send monthly i n -v e n t o r y r e p o r t s t o t h e company's a c c o u n t i n g o f f i c e . Suppose t h a t w i t h i n the a c c o u n t i n g o f f i c e , the f i r s t c l e r k r e c e i v e s the i n v e n t o r y r e p o r t f r o m the department head and p u t s i t t o g e t h e r w i t h the r e p o r t s f o r t h a t department f o r the p r e v i o u s y e a r . The f i r s t c l e r k t h e n sends a l l t h a t i n f o r m a t i o n t o a 21 second c l e r k who c a l c u l a t e s an i n d e x o f i n v e n t o r y t u r n o v e r f o r the i m m e d i a t e l y p r e v i o u s month. The t h i r d c l e r k r e c e i v e s a l l t h a t i n f o r m a t i o n and t r a n s f o r m s i t i n t o a c o m p a r i s o n o f l a s t month's r a t e w i t h the a v e r a g e r a t e f o r the p r e -v i o u s y e a r . A f o u r t h c l e r k might e x p r e s s t h i s i n f o r m a t i o n i n t h e f o r m of a s t a n d a r d i z e d m o n t h l y r e p o r t and send a copy o f i t back t o the department head. The i n f o r m a t i o n has gone i n a c i r c l e such t h a t the department head r e c e i v e d h i s own o u t p u t back i n an a l t e r e d f o r m as i n p u t . F o r a p e r s o n t o be a b l e t o a p p r e c i a t e t h e c y c l i c t r a n s i t i v i t y i n the arrangement d e s c r i b e d above, he o r she w o u l d r e q u i r e a c o g n i t i v e s t r u c t u r e e q u a l i n c o m p l e x i t y w i t h the s o c i e t a l s t r u c t u r e b e i n g u n d e r s t o o d . S o c i a l systems commonly i n c o r p o r a t e t h e s o c i e t a l s t r u c t u r e o f c y c l i c t r a n s i t i v i t y . I n s o f a r as p e o p l e u n d e r s t a n d t h a t s o c i e t a l s t r u c t u r e , t h e y must p e r f o r m t h e a p p r o p r i a t e c o g n i t i v e o p e r a t i o n s needed t o m e n t a l l y model t h e c y c l i c t r a n s i -t i v e o p e r a t i o n s t r a n s p i r i n g i n the ^ s o c i a l e n v i r o n m e n t . C y c l i c I n t e g r a t i o n . . C y c l i c i n t e g r a t i o n i s t o c y c l i c t r a n s i t i v i t y as c l a s s i n c l u s i o n i s t o l i n e a r t r a n s i t i v i t y . B o t h l i n e a r t r a n s i t i v i t y and c y c l i c t r a n s i t i v i t y d e a l w i t h one d i m e n s i o n w h i l e c l a s s i n c l u s i o n and c y c l i c i n t e g r a t i o n e n t a i l s u b o r d i n a t e / s u p r o r d i n a t e r e l a t i o n s . I n c y c l i c t r a n s i t i v i t y t h e r e i s o n l y one c y c l e . , The e l e m e n t s o f the c y c l e a r e t r a n s m i t t e d i n one c i r c u l a r l i n e , and t h e y a r e n o t n e s t e d w i t h i n each o t h e r . I n c y c l i c i n t e g r a -t i o n a s u b o r d i n a t e s e t o f elements r e c e i v e s f e e d b a c k from, and i s s u e s f e e d -back t o , a s u p r a o r d i n a t e element o r s e t o f e l e m e n t s . The s t r u c t u r e of a computer program p r o v i d e s a f a m i l i a r example. C o n s i d e r a main program w h i c h s i m p l y reads d a t a , c a l l s a s u b r o u t i n e , and w r i t e s t h e r e s u l t s . W i t h o u t t h e s u b r o u t i n e t h e main program w o u l d l e a v e t h e d a t a u n a l t e r e d as i f t h e main program had n e v e r been r u n . The s u b r o u t i n e p e r f o r m s c a l c u l a t i o n s on t h e 22 d a t a b u t w i t h o u t t h e main program i t too w o u l d l e a v e t h e d a t a u n a l t e r e d . I n o r d e r t o work, t h e two programs must be " i n t e g r a t e d " . I f t h e main program reads and w r i t e s d a t a c a s e s s u c c e s s i v e l y , as i t w o u l d i f t h e READ and WRITE s t a t e m e n t s were i n s i d e a FORTRAN DO-loop f o r example, t h e n t h e e x e c u t i v e c o n t r o l f l o w s i n a " c y c l e " back and f o r t h between the main program and t h e s u b r o u t i n e . The " t r a n s m i s s i o n l i n e s " f o r the c y c l e w o u l d be the CALL s t a t e -ment and t h e RETURN s t a t e m e n t . The t r a n s f e r o f c o n t r o l from t h e main p r o -gram, t o the s u b r o u t i n e , and back a g a i n i n a c y c l i c a l f a s h i o n a c c o m p l i s h e s t h e i r i n t e g r a t i o n . Thus t h e r e l a t i o n s h i p between a main program and a sub-r o u t i n e i l l u s t r a t e s c y c l i c i n t e g r a t i o n . W i t h t h e a d d i t i o n o f c o n d i t i o n a l c o n t r o l t r a n s f e r s t a t e m e n t s ( e . g . , FORTRAN I F ' s and GO TO's) t h e main program and the s u b r o u t i n e a c q u i r e t h e c a p a c i t y t o a l t e r each o t h e r ' s f u n c t i o n i n g a c c o r d i n g t o c o n t i n g e n c i e s . F o r a s o c i o - e c o n o m i c example, l e t us t a k e t h e n a t i o n a l government as the s u p r a o r d i n a t e s y s t e m and t h e t e l e p h o n e company as a s u b o r d i n a t e s y s tem. The government g i v e s t h e company a l i c e n s e t o o p e r a t e and t h e company g i v e s the government t a x r e v e n u e s . The company must obey government r e g u l a t i o n s on i t s o p e r a t i o n b u t l i k e w i s e the government must c r e a t e and/or update l e g i s -l a t i o n t o d e a l w i t h many changes and i n n o v a t i o n s i n t h e company's o p e r a t i o n s ( e . g . , r a t e i n c r e a s e s , t e c h n o l o g i c a l a d v a n c e s ) . Sometimes governments must r e s p o n d t o changes i n t h e p o l i c i e s o f companies t h a t the companies have made i n r e s p o n s e t o e a r l i e r government r e g u l a t i o n s . C o n v e r s e l y , sometimes companies change t h e i r p r o c e d u r e s i n r e s p o n s e t o government r e g u l a t i o n s d e s i g n e d t o d e a l w i t h e a r l i e r company p o l i c i e s . The c y c l e o f m u t u a l i n f l u e n c e e x e m p l i -f i e s t h e s o c i a l s t r u c t u r e c a l l e d c y c l i c i n t e g r a t i o n . Readers may g e n e r a t e t h e i r own examples o f c y c l i c i n t e g r a t i o n u s i n g s u p r a o r d i n a t e / s u b o r d i n a t e 23 p a i r s o f systems s u c h as t h e c u l t u r e and i n d i v i d u a l p e r s o n a l i t i e s , t h e economy and i n d i v i d u a l c a r e e r s , the f e d e r a l government and p a r t i c u l a r p r o v i n c e s , t h e f o o t b a l l team and i n d i v i d u a l p l a y e r p e r f o r m a n c e s , and so on. B. C o g n i t i v e S t r u c t u r e s The aim of t h i s s e c t i o n i s t o s p e c i f y e x a c t l y what p a t t e r n s o f c o g n i t i v e o r g a n i z a t i o n a r e b e i n g s t u d i e d i n t h i s r e s e a r c h . The c o g n i t i v e s t r u c t u r e s under s t u d y a r e d e s c r i b e d i n t h e m s e l v e s and a r e r e l a t e d t o each o t h e r i n terms o f a n t i c i p a t e d d i f f i c u l t y l e v e l s . A g a i n , the r e a d e r i s reminded t h a t the p u r p o s e o f e s t a b l i s h i n g a case f o r t h e o r d e r e d a c q u i s i t i o n o f v a r i o u s c o g n i t i v e o p e r a t i o n s i s t h a t i f s u c h an o r d e r h o l d s , t h e n the d e v e l o p i n g c h i l d ' s a b i l i t y t o comprehend v a r i o u s s t r u c t u r e s i n t h e n a t u r a l and the s o c i a l e n v i r o n m e n t s can be u n d e r s t o o d to be l i m i t e d by, and yoked w i t h , h i s o r h e r own d e v e l o p m e n t a l p r o g r e s s as d e s c r i b e d i n P i a g e t i a n t h e o r y . T h e o r i s t s from F r e u d t o P i a g e t have a r g u e d t h e n e c e s s i t y o f p o s t u l a t i n g s t a g e - l i k e p r o g r e s s i o n s i n t h e c o u r s e o f human development. A l t h o u g h c o n -t i n u i t i e s i n development can be f o u n d ( B r a i n e r d , 1 9 74), t h e i r manner o f mani-f e s t a t i o n and p a t t e r n o f i n t e r r e l a t i o n s h i p s have more commonly been seen t o undergo d i s c r e t e changes a t p r e d i c t a b l e p o i n t s i n m a t u r a t i o n . To d a t e , no c o n t i n u o u s , l i n e a r v a r i a b l e s have been found c a p a b l e o f q u a n t i f y i n g t h e q u a l i t a t i v e p a t t e r n o f s t r u c t u r e o f b e h a v i o r and i t s development ( L a r s e n , 1977). N e v e r t h e l e s s , i t i s c l e a r from a m a c r o s c o p i c p e r s p e c t i v e t h a t the a c h i e v e m e n t s o f e a r l i e r s t a g e s of development p r o v i d e a n e c e s s a r y groundwork f o r s u s p e c t -i n g t h a t m a s t e r y o v e r the c o g n i t i v e o p e r a t i o n s o f s e r i a t i o n ( o r d i n a t i o n ) , . l i n e a r t r a n s i t i v i t y , l o g i c a l m u l t i p l i c a t i o n , and c l a s s i n c l u s i o n r e g u l a r l y 24 appear i n t h a t r e s p e c t i v e o r d e r w i t h i n t he s t a g e o f c o n c r e t e o p e r a t i o n s ( e . g . , G i n s b e r g and Opper, 1969). L i k e w i s e , w i t h i n t h e l a t e r s t a g e o f f o r m a l o p e r a t i o n s , i t can be argu e d t h a t m a s t e r y o f c y c l i c t r a n s i t i v i t y p r e c e d e s c y c l i c i n t e g r a t i o n . Of c o u r s e t h e r e a r e l i k e l y t o be o c c a s i o n a l v a r i a t i o n s i n t h e t i m i n g o f t h e i r appearance f r o m c h i l d t o c h i l d , b u t l e t us examine t h e arguments f o r t h e i r i n v a r i a n t s e q u e n t i a l o r d e r i n g w i t h i n t h e major s t a g e s . Some o f t h e s e arguments a r e e m p i r i c a l w h i l e o t h e r s d e a l w i t h t he l o g i c a l and c o g n i t i v e p r e r e q u i s i t e s f o r m a s t e r y o f p a r t i c u l a r o p e r a t i o n s . W h i l e the arguments f o r t h e i r i n v a r i a n t s e q u e n t i a l o r d e r i n g a r e b e i n g examined, an a n c i l l a r y aim of t h i s s e c t i o n i s t o a l s o p r e s e n t more d e t a i l s about the n a t u r e o f each c o g n i t i v e s t r u c t u r e . The o r d e r i n w h i c h we d i s c u s s each c o g n i t i v e s t r u c t u r e i s from t h e h y p o t h e s i z e d l e a s t d i f f i c u l t t o the most d i f f i c u l t , ( i ) C o n c r e t e Stage S e r i a t i o n . When asked t o o r d e r a s e t o f s t i c k s a c c o r d i n g t o l e n g t h , c h i l d r e n who cannot s e r i a t e o f t e n g e n e r a t e a p p a r e n t l y random o r d e r i n g s . D u r i n g what i s a p p a r e n t l y a t r a n s i t i o n a l p e r i o d , t he c h i l d can, by a t r i a l and e r r o r method, c o r r e c t l y o r d e r a g i v e n s e t o f s t i c k s b u t makes e r r o r s when asked t o i n s e r t a new s t i c k i n t o t h e s e r i e s . F i n a l l y , by a p p r o x i m a t e l y the age o f s e v e n , t h e c h i l d can t y p i c a l l y s e r i a t e w i t h o u t e r r o r s o r h e s i t a -t i o n s . L i n e a r T r a n s i t i v i t y . Any s e t o f s t i m u l i t h a t can be s e r i a t e d can a l s o be s u b j e c t e d t o l i n e a r t r a n s i t i v i t y . On the s i m p l e s t m a t e r i a l s and w i t h t he s i m p l e s t mode o f p r e s e n t a t i o n , most seven y e a r o l d s show e v i d e n c e o f h a v i n g m a s t e r e d t h i s c o g n i t i v e o p e r a t i o n . I n d e e d , s e r i a t i o n i s a p r e r e q u i s i t e f o r b e g i n n i n g l i n e a r t r a n s i t i v e o p e r a t i o n s i f l i n e a r t r a n s i t i v i t y p r oblems a r e 25 p r e s e n t e d u s i n g h e t e r o t r o p i c comparisons ( e . g . , A i s g r e a t e r t h a n B, C i s l e s s t h a n B ) . I n o r d e r t o s e r i a t e , t h e c h i l d need o n l y compare A t o B. For s u c c e s s f u l t r a n s i t i v e i n f e r e n c e t h e c h i l d must a l s o compare A d i r e c t l y t o C w h i l e a b r o g a t i n g B's f o r m e r s t a t u s as t h e one t h a t was t a l l e r t h a n C. T h i s a d d i t i o n a l l o g i c a l r e q u i r e m e n t l e a d s t o the p r e d i c t i o n made h e r e , and by o t h e r s ( e . g . , Formanek and G u r i a n , 1 976), t h a t most c h i l d r e n w o u l d f i n d l i n e a r t r a n s i t i v i t y more d i f f i c u l t t h a n s e r i a t i o n . L o g i c a l M u l t i p l i c a t i o n and C l a s s I n c l u s i o n . The s i m p l e s t p r o c e d u r e f o r a s s e s s i n g m a s t e r y o f l o g i c a l m u l t i p l i c a t i o n i s the two-way c l a s s i f i c a -t i o n t a s k ( I n h e l d e r and P i a g e t , 1964). The c h i l d i s p r e s e n t e d w i t h a 2 x 2 m a t r i x h a v i n g one empty c e l l w h i c h must be f i l l e d u s i n g one of f i v e a l t e r n a -t i v e s from an a r r a y o f p o s s i b l e answers. The c l a s s i n c l u s i o n t a s k s used were a d a p t e d from I n h e l d e r and P i a g e t ( 1 9 6 4 ) . F o r example, i n the p h y s i c a l domain the s u p r a o r d i n a t e c l a s s was "wooden beads" and the two s u b o r d i n a t e c l a s s e s were g r e e n beads (5) and r e d beads ( 2 ) . When a s k e d i f t h e r e were more green beads o r more wooden beads, c h i l d r e n who had n o t m a s t e r e d c l a s s i n c l u s i o n o f t e n answered t h a t t h e r e were more g r e e n beads. They c o n f u s e d the c o m p a r i s o n between two s u b o r d i n a t e c l a s s e s w i t h the comparison between a s u b o r d i n a t e c l a s s and the s u p r a o r d i n a t e c l a s s . L o g i c a l m u l t i p l i c a t i o n s and c l a s s i n c l u s i o n a r e , a c c o r d i n g t o P i a g e t (1953, p. 1 3 ) , p a r t o f the same g r o u p i n g o r " o p e r a t i o n a l system". E m p i r i -c a l l y , i t i s n o t u n t i l t he age o f 8 o r 9 t h a t t h e m a j o r i t y o f c h i l d r e n be-come competent wi-th t h i s g r o u p i n g ( P i a g e t , 1953). Kohnstamm ( 1 9 6 8 ) , however, argues t h a t t h i s g r o u p i n g does n o t e x i s t and t h a t competence w i t h c l a s s i n -c l u s i o n o p e r a t i o n s d e v e l o p s i n d e p e n d e n t l y o f competence w i t h l o g i c a l m u l t i p l i -c a t i o n . I n h e l d e r and P i a g e t (1964) found l o g i c a l m u l t i p l i c a t i o n t o be mas-26 t e r e d l a t e r t h a n c l a s s i n c l u s i o n w h i l e o t h e r s have found the r e v e r s e ( A r l i n , 1978) . On l o g i c a l grounds c l a s s i n c l u s i o n was p r e d i c t e d t o be t h e more d i f f i c u l t o f t h e two. W h i l e b o t h o p e r a t i o n s e n t a i l a t t e n d i n g t o two a t t r i -b u t e s p e r e l e m e n t , i n l o g i c a l m u l t i p l i c a t i o n t h e a t t r i b u t e s need o n l y be l i s t e d . F o r c l a s s i n c l u s i o n , however, the a t t r i b u t e s s t a n d i n a n e s t e d o r embedded r e l a t i o n s h i p t o one a n o t h e r . One subsumes th e o t h e r i n much th e same way t h a t M i l l e r , K e s s e l and F l a v e l l ' s (.1970) r e c u r s i v e t h o u g h t s about t h o u g h t s about t h o u g h t s .... i 4 subsume each o t h e r . Barenboim (1978) found t h a t t y p e o f r e c u r s i v e embedding t o be c h a l l e n g i n g even t o 16 y e a r o l d s . T h e r e f o r e , on t h e a s s u m p t i o n t h a t a l i s t i s e a s i e r t o h a n d l e t h a n an em-bedded r e l a t i o n , i t was p r e d i c t e d t h a t l o g i c a l m u l t i p l i c a t i o n w o u l d be m a s t e r e d by most c h i l d r e n e a r l i e r t h a n c l a s s i n c l u s i o n , ( i i ) S y s t e m i c S t r u c t u r e s W h i l e t h e c o g n i t i v e s t r u c t u r e s o f s e r i a t i o n , l i n e a r t r a n s i t i v i t y , l o g i -c a l m u l t i p l i c a t i o n and c l a s s i n c l u s i o n have been much r e s e a r c h e d and d e b a t e d , the s y s t e m i c c o g n i t i v e s t r u c t u r e s o f c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a -t i o n have n o t . I n s e c t i o n A, p a r t ( i i i ) o f t h i s c h a p t e r t h e s y s t e m i c s o c i e -t a l s t r u c t u r e s o f c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n were d i s c u s s e d as common f e a t u r e s o f t h e s o c i a l o r g a n i z a t i o n o f , a t l e a s t most, w e s t e r n s o c i e t i e s . What f o l l o w s n e x t i s a d i s c u s s i o n o f t h e s y s t e m i c c o g n i t i v e s t r u c t u r e s p r e sumably n e c e s s a r y f o r u n d e r s t a n d i n g t h e c o r r e s p o n d i n g s o c i e t a l s t r u c t u r e s . P a r t i c u l a r a t t e n t i o n i n t h i s s e c t i o n i s g i v e n t o h y p o t h e s i z i n g t h e o r d e r i n w h i c h t h e s e s y s t e m i c o p e r a t i o n s a r e m a s t e r e d r e l a t i v e t o each o t h e r and t o more w e l l s t u d i e d c o g n i t i v e o p e r a t i o n s . The s y s t e m i c t a s k s i n v o l v e d u n d e r s t a n d i n g v a r i o u s a s p e c t s o f p a r t i c u l a r c y c l e s . An i n t e r v i e w f o r m a t was used to p r e s e n t s u b s t a n t i v e i n f o r m a t i o n about t h e c y c l e s and t o 27 q u e r i e the r e s p o n d e n t s l e v e l o f u n d e r s t a n d i n g . The c o n t e n t o f t h e c y c l e s i n the two domains i s t h e f i r s t t h i n g d e s c r i b e d i n t h i s s e c t i o n . N e x t , the two components o f c y c l i c t r a n s i t i v i t y a r e i l l u s t r a t e d . Then, t h e two com-ponents o f c y c l i c i n t e g r a t i o n a r e a l s o examined b e f o r e t h e d i s c u s s i o n t u r n s t o a c o m p a r i s o n o f s y s t e m i c c o g n i t i v e o p e r a t i o n s w i t h f o r m a l o p e r a t i o n s i n terms o f d i f f i c u l t y l e v e l and s t a g e . The C y c l e s . The c y c l e used i n t h e b i o - e c o l o g i c a l domain s y s t e m i c i n -t e r v i e w was the n i t r o g e n n u t r i e n t c y c l e . The elements were a n i t r o g e n mole-c u l e , a p r o d u c e r (one p l a n t o f a f a r m e r ' s c r o p ) , a h e r b i v o r e (a c a t e r p i l l a r ) , a c a r n i v o r e (a b i r d ) , and a decomposer (a n i t r i f y i n g b a c t e r i a ) . The p l a n t used the n i t r o g e n as a m i n e r a l n u t r i e n t . The c a t e r p i l l a r a t e the p l a n t . The b i r d a t e t h e c a t e r p i l l a r . When i t d i e d the b i r d was e a t e n by n i t r i f y i n g b a c t e r i a . The b a c t e r i a l e f t more n i t r o g e n i n t h e s o i l f o r the p l a n t . The c y c l e used i n t h e s o c i e t a l ^domain .was -the wheat c y c l e : ; -The-elements were t h e wheat f a r m e r , the wheat m a r k e t i n g b o a r d (WMB), the f l o u r m i l l , t he b a k e r y and the supermarket ( g r o c e r ) . Assuming t h a t t h e f a r m e r g e t s h i s b r e a d a t t h e s u p e r m a r k e t , t h e s e form a commodity c y c l e . F o r b o t h c y c l e s each o f t h e f i v e e l e m e n t s was r e p r e s e n t e d g r a p h i c a l l y on an i n d i v i d u a l i n d e x c a r d . C y c l i c T r a n s i t i v i t y . There were two components t o t h e c y c l i c t r a n s i t i v -i t y measure. I t was n o t known b e f o r e h a n d whether o r n o t t h e y w o u l d t u r n out to be a l t e r n a t e forms o f each o t h e r ( i . e . , h i g h l y c o r r e l a t e d ) as t h e y were i n t e n d e d t o be. The "layout"'component r e q u i r e d t h e r e s p o n d e n t t o p l a c e i n d e x c a r d s i n d i c a t i n g each element b e s i d e each o t h e r i n s u c h a way as t o show w h i c h ones needed o r depended upon w h i c h o t h e r ones. I n b o t h domains th e c o r r e c t " l a y o u t " i n r e s p o n s e t o t h i s r e q u e s t w o u l d be a c i r c u l a r arrange-^ 28 merit r e p r e s e n t i n g t h e n i t r o g e n n u t r i e n t c y c l e f o r t h e b i o - e c o l o g i c a l domain, o r the f l o w o f w h e a t / f l o u r / b r e a d t h r o u g h t h e s e r i e s o f exchanges f o r t h e s o c i e t a l domain. W i t h t h e p r o p e r arrangement of i n d e x c a r d s l a y e d out i n f r o n t o f t h e r e s p o n d e n t , t h e i n t e r v i e w e r i n t r o d u c e d t h e se c o n d measure o f competence w i t h the o p e r a t i o n o f c y c l i c t r a n s i t i v i t y . T h i s measure was c a l l e d t h e " t r a n s i t i v e r e c y c l i n g " component. I n t h e b i o - e c o l o g i c a l domain the r e s p o n -dent was t o l d how a s p r a y i n g o f t h e p l a n t s w i t h DDT c o u l d k i l l b i r d s as w e l l •as c a t e r p i l l a r s . The concept o f a s i n g l e m o l e c u l e o f DDT was a l s o e x p l a i n e d a l o n g w i t h a r e p r e s e n t a t i v e d r a w i n g on an i n d e x c a r d . Then the r e s p o n d e n t was asked i f t h e same s i n g l e m o l e c u l e o f DDT c o u l d e v e r k i l l two b i r d s . O p t i m a l answers had the m o l e c u l e t r a v e l i n g a r o u n d t h e c y c l e i n much the same way as a n i t r o g e n m o l e c u l e m i g h t . The m o l e c u l e n o t o n l y r e t u r n s t o the i n i t i a l element b u t a l s o p a s s e s t h r o u g h t h a t element a g a i n . I n the s o c i e t a l domain the t r a n s i t i v e r e c y c l i n g component i n v o l v e d t h e movement o f a d o l l a r b i l l t h r o u g h t h e c y c l e . The r e s p o n d e n t was a s k e d i f the f a r m e r c o u l d e v e r spend the same d o l l a r b i l l t w i c e . O p t i m a l answers showed an awareness o f the f l o w o f money i n t h e d i r e c t i o n o p p o s i t e t o the f l o w o f wheat. The f a r m e r pays the g r o c e r who p a s s e s t h e d o l l a r on u n t i l t h e WMB g i v e s i t back t o the f a r m e r t o spend a g a i n . C y c l i c I n t e g r a t i o n . F o r r e a s o n s o u t l i n e d i n ' t h e p r e v i o u s s e c t i o n , c y c l i c t r a n s i t i v i t y was p r e d i c t e d t o be m a s t e r e d e a r l i e r t h a n c y c l i c i n t e g r a t i o n . The f o r m e r i n v o l v e s l i n k i n g t h e elements w i t h o u t a t t e n d i n g t o the s u b o r d i n a t e / s u p r a o r d i n a t e a s p e c t s o f t h e i r r e l a t i o n s t o one a n o t h e r . I n c y c l i c i n t e g r a -t i o n , however, one element o r s e t o f elements i n some sense subsumes o t h e r e l e m e n t s . The l i n k s between t h e s u b o r d i n a t e and t h e s u p r a o r d i n a t e e lements 29 can be u n d e r s t o o d i n terms o f c y c l i c t r a n s i t i v i t y . But w i t h c y c l i c i n t e g r a -t i o n t h e r e i s a f u r t h e r r e q u i r e m e n t t o keep the s u b o r d i n a t e / s u p r a o r d i n a t e d i s t i n c t i o n i n mind. By way o f i l l u s t r a t i n g the i m p o r t a n c e of the s u b o r d i n a t e / s u p r a o r d i n a t e d i m e n s i o n , t h e s p e c i f i c c o n t e n t s o f the b i o - e c o l o g i c a l and t h e s o c i e t a l c y c l i c i n t e g r a t i o n t a s k s a r e s u r v e y e d below. Upon r e v i e w i n g t h e i r p a r t i c u l a r r e q u i r e m e n t s i t s h o u l d become c l e a r e r w h y - c y c l i c t r a n s i t i v i t y was p r e d i c t e d t o be t h e e a s i e r o f t h e two. I n the b i o - e c o l o g i c a l domain, the s u b o r d i n a t e e l e m e n t s o f t h e n i t r o g e n c y c l e were t h e p o p u l a t i o n s ( e . g . , t h e b i r d p o p u l a t i o n , t h e amount o f n i t r o g e n i n t h e s o i l ) . The s u p r a o r d i n a t e l e v e l was t h e e c o s y s t e m o f t h e farm. The s u b o r d i n a t e e l e m e n t s i n t h e s o c i e t a l domain were t h e b u s i n e s s e s i n t h e wheat c y c l e ( e . g . , t h e wheat f a r m e r , t h e f l o u r m i l l , t h e b a k e r y ) . The s u p r a o r d i n a t e l e v e l was t h e government. The government i n f l u e n c e d t h e v i -a b i l i t y o f each element r e l a t i v e l y by i m p o s i n g t a x e s . I t s p o s i t i v e i n f l u e n c e on t h e i r v i a b i l i t y was m e d i a t e d t h r o u g h t h e WMB's s u b s i d i e s t o f a r m e r s when e i t h e r s u p p l y (wheat c r o p s ) o r demand was i n a d e q u a t e f o r the f i n a n c i a l s u r -v i v a l o f i n d i v i d u a l f a r m e r s . The whole c y c l e would be harmed i f t o o many o f t h e f a r m e r s went b a n k r u p t . Hence, by s u b s i d i z i n g f a r m e r s and by i m p o s i n g p r o d u c t i o n q uotas t o p r e v e n t c o s t l y o v e r p r o d u c t i o n , the government was i n -f l u e n c i n g t h e v i a b i l i t y o f a l l t h e e l e m e n t s . The c y c l i c i n t e g r a t i o n s c o r e s were ba s e d on e v i d e n c e o f awareness of two t y p e s of i n t e r d e p e n d e n c y between t h e whole s y s t e m and i t s p a r t s . These c o r -r esponded t o t h e two components o f c y c l i c i n t e g r a t i o n and, as w i t h t h e c y c l i c t r a n s i t i v i t y , i t was n o t known b e f o r e h a n d how h i g h l y c o r r e l a t e d t h e s e a l t e r n a t e measures w o u l d be w i t h one a n o t h e r . 30 What i s b e i n g c a l l e d t h e "systems s y n t h e s i s " component c h a l l e n g e d t h e r e s p o n d e n t t o f o r e s e e how changes i n one element c o u l d i n f l u e n c e t h e whole c y c l e . F o r example, i n t h e b i o - e c o l o g i c a l domain t h e i n t r o d u c t i o n o f DDT i n t o the n i t r o g e n c y c l e had t h e p o t e n t i a l t o a l t e r the e q u i l i b r i u m s i z e s o f t h e p o p u l a t i o n s . The a l t e r a t i o n s might be so d r a s t i c as t o e n t i r e l y e l i m i n -a t e a whole t r o p h i c l e v e l ( i . e . , c a r n i v o r e s ; b i r d s ) . I n a n o t h e r example, the amount o f n i t r o g e n i n the s o i l was d r a s t i c a l l y and p e r m a n e n t l y r e d u c e d . The whole e c o s y s t e m w o u l d t h e r e b y be t r a n s f o r m e d i n t o a t r a c e d e s e r t . I n t h e s o c i e t a l domain, systems s y n t h e s i s was e x e m p l i f i e d by the u nder-s t a n d i n g o f t h e e f f e c t s o f t h e s t o c k p i l i n g o f wheat by t h e f l o u r m i l l . The s t o c k p i l i n g w o u l d have meant a l o w e r volume o f s a l e s f o r wheat f a r m e r s . T h a t , . i n t u r n , w o u l d have i m p l i e d h i g h e r WMB s u b s i d i e s and t h a t w o u l d have n e c e s s i t a t e d h i g h e r t a x e s f o r e v e r y element i n t h e c y c l e . I n t h e s e c a s e s the whole c y c l e was i n f l u e n c e d by s u b o r d i n a t e e l e m e n t s . The e f f e c t on t h e whole had t o be " s y n t h e s i z e d " out o f a knowledge o f how t h e p a r t s w o u l d t h e n be i n t e r r e l a t e d . F o r what i s b e i n g c a l l e d the "systems a n a l y s i s " component t h e r e s p o n d e n t was p r e s e n t e d w i t h t h e p r o b l e m o f r e d u c i n g t h e c y c l e t o i t s e s s e n t i a l c o r e . The c o r e was t h a t s e t o f e l ements i n a p a r t i c u l a r r e l a t i o n s h i p s u c h t h a t no one o f them c o u l d be e l i m i n a t e d w i t h o u t t h e e l i m i n a t i o n o f t h e whole c y c l e . I n the b i o - e c o l o g i c a l domain t h e two top t r o p h i c l e v e l s ( i . e . , t h e b i r d s and t h e c a t e r p i l l a r ) c o u l d have been removed w i t h o u t e l i m i n a t i n g the r e m a i n i n g e l e m e n t s . The p l a n t , b a c t e r i a and n i t r o g e n were i n t e r r e l a t e d such t h a t each one would e v e n t u a l l y be d e p l e t e d i f one were removed. I n t h e wheat c y c l e t h e most e s s e n t i a l element was the wheat f a r m e r . He c o u l d have made h i s own b r e a d b u t t h o s e t a s k s w o u l d s t i l l have t o be p e r f o r m e d . The e l e m e n t s 31 t h a t n o r m a l l y p e r f o r m e d them were t h e f l o u r m i l l and t h e b a k e r y . Respondents c o u l d have e l i m i n a t e d any element b e s i d e s the wheat f a r m e r so l o n g as t h e f l o u r making f u n c t i o n and the b r e a d b a k i n g f u n c t i o n were a c c o u n t e d f o r i n the r e m a i n i n g s e t o f e lements ( e . g . , "The g r o c e r c o u l d bake t h e b r e a d and s e l l i t i n h i s s t o r e " . ) . I n e f f e c t , t h e n , i t was thought t h a t m a s t e r i n g t h e c o g n i t i v e o p e r a t i o n o f c y c l i c t r a n s i t i v i t y r e q u i r e s s e e i n g how t h e p a r t s o f t h e c y c l e a r e r e -l a t e d t o each o t h e r w h i l e c y c l i c i n t e g r a t i o n r e q u i r e s s e e i n g how t h e i n t e r -r e l a t e d p a r t s a r e r e l a t e d t o t h e w h o l e , and v i c e v e r s a . S i n c e t a k i n g a c c o u n t of the whole c y c l e o v e r and above t h e i n t e r r e l a t e d e l ements seemed t o be an a d d i t i o n a l c o g n i t i v e demand, i t was p r e d i c t e d t h a t c y c l i c i n t e g r a t i o n w o u l d be more d i f f i c u l t t h a n c y c l i c t r a n s i t i v i t y r e g a r d l e s s o f domain, ( i i i ) Compared to F o r m a l O p e r a t i o n s H a v i n g o r d e r e d the two s y s t e m i c s t r u c t u r e s w i t h r e s p e c t t o each o t h e r , we now have o c c a s i o n t o ask how b o t h o f them m i g h t be o r d e r e d w i t h r e s p e c t t o the more f a m i l i a r c o n c r e t e s t a g e and f o r m a l s t a g e c o g n i t i v e s t r u c t u r e s o f P i a g e t ' s model. C y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n were p r e d i c t e d t o be p o s t -c o n c r e t e s t a g e c o g n i t i v e a c h i e v e m e n t s . We c a n n o t , however, b e g i n by assuming t h a t they a r e t h e r e f o r e f o r m a l o p e r a t i o n s . F o r m a l o p e r a t i o n s a r e b a s e d on a b s t r a c t f o r m a l l o g i c . S y s t e m i c o p e r a t i o n s a r e b a s e d on s y s t e m i c l o g i c . Assuming t h a t t h e s e a r e i n d e e d two d i s t i n c t t y p e s o f l o g i c ( s ee A p p e n d i x E f o r a d e f e n s e o f t h i s a s s u m p t i o n ) , i t i s p o s s i b l e t h a t s y s t e m i c o p e r a t i o n s may be a p a r a l l e l development d u r i n g P i a g e t ' s f o u r t h s t a g e o r t h a t t h e y may be a f i f t h s t a g e unto t h e m s e l v e s . The c r i t e r i a f o r i d e n t i f y i n g a s t a g e de-s e r v e some a t t e n t i o n i n t h i s r e g a r d . 32 F i r s t o f a l l , t he n o t i o n o f a f i f t h s t a g e i s r e a l l y j u s t a v e h i c l e f o r d i s c u s s i n g t h e n a t u r e o f a d u l t c o g n i t i o n . No one s t u d y c o u l d e v e r e s t a b l i s h the e x i s t e n c e o f a s t a g e as a n a t u r a l phenomenon. B e s i d e s , t h e u s e f u l n e s s o f the whole concept o f s t a g e s i n P i a g e t i a n t h e o r y has been s e r i o u s l y c h a l -l e n g e d ( e . g . , B r a i n e r d , 1978; F l a v e l l , 1977). W o h l w i l l (1973) has s u g g e s t e d f o u r d i f f e r e n t v e r s i o n s o f t h e concept o f a s t a g e and c o n c l u d e d t h a t t h e one w h i c h a c c o u n t e d f o r r e s e a r c h f i n d i n g s t h e b e s t was the one w h i c h was t h e l e a s t " s t a g e - l i k e " . W i t h t h e s e c a v e a t s i n mind, l e t us r e v i e w t h e c r i t e r i a f o r i d e n t i f y i n g s t a g e s . P i a g e t (1960) l i s t e d f o u r c r i t e r i a f o r a s t a g e . F i r s t , t h e r e s h o u l d be a q u a l i t a t i v e change i n c o g n i t i v e f u n c t i o n i n g . Second, the s t a g e s s h o u l d f i t w i t h i n a c u l t u r a l l y u n i v e r s a l i n v a r i a n t sequence w i t h r e s p e c t t o one a n o t h e r . T h i r d , t h e r e s h o u l d be e v i d e n c e o f h i e r a r c h i z a t i o n . That i s , t h e c o g n i t i v e s t r u c t u r e s o f each p r e c e d i n g s t a g e s h o u l d be i n c l u d e d i n each subsequent s t a g e . F o u r t h , t h e r e s h o u l d be an o v e r a l l i n t e g r a t i o n o f t h e s t r u c t u r e s o f each s t a g e . P i a g e t r e f e r s t o t h i s as t h e p r i n c i p l e o f " s t r u c t u r e s d'ensemble". F l a v e l l (1977) a l s o l i s t s f o u r s t a g e c r i t e r i a . Two of them, s t r u c t u r e d'en- semble and q u a l i t a t i v e change, were a l s o l i s t e d by P i a g e t . F l a v e l l l e a v e s out h i e r a r c h i z a t i o n and a u n i v e r s a l i n v a r i a n t sequence„but he i n c l u d e s con-c u r r e n c e and a b r u p t n e s s . By a b r u p t n e s s F l a v e l l (1971a) means t h a t , "each i n -d i v i d u a l i t e m f u n c t i o n e d a t a s y m p t o t i c , a d u l t - l e v e l p r o f i c i e n c y as soon as i t f u n c t i o n e d a t a l l , i . e . , as soon as i t c o u l d be s a i d t o have been ' a c q u i r e d ' i n any se n s e " . By c o n c u r r e n c e F l a v e l l means t h a t a l l the c h i l d ' s o p e r a t i o n s s h o u l d be o b s e r v e d t o go t h r o u g h an a b r u p t , q u a l i t a t i v e change s i m u l t a n e o u s l y . A f u l l e x p l o r a t i o n o f t h e q u a l i t a t i v e d i f f e r e n c e s between f o r m a l l o g i c and s y s t e m i c l o g i c w o u l d r e q u i r e a n o t h e r d i s s e r t a t i o n . I n l i e u o f t h a t , an e x t r a c h a p t e r has been w r i t t e n on t h e t o p i c and i s i n c l u d e d as an a p p e n d i x 33 (see A p p e n d i x E ) . S i n c e t h i s c r i t e r i o n r e q u i r e s a judgement o f q u a l i t a t i v e r a t h e r t h a n q u a n t i t a t i v e d i f f e r e n c e , t h e r e l e v a n t arguments a r e p h i l o s o p h i c a l and l o g i c o - m a t h e m a t i c a l . I n A p p e n d i x E i t was c o n c l u d e d t h a t t h e two l o g i c s a r e q u a l i t a t i v e l y d i s t i n c t . I n a s e n t e n c e , s y s t e m i c l o g i c f o c u s s e s on t h e i d e n t i f i c a t i o n o f w holes w h i l e f o r m a l l o g i c f o c u s s e s on t h e c o m p a r i s o n and/or 3 c l a s s i f i c a t i o n o f w h o l e s . Taken t o g e t h e r , P i a g e t ' s c r i t e r i a o f h i e r a r c h i z a t i o n and a u n i v e r s a l 4 i n v a r i a n t sequence i m p l y t h a t , e m p i r i c a l l y , s t a g e s s h o u l d form a Guttman s c a l e w i t h r e s p e c t t o one a n o t h e r . Three f o r m a l o p e r a t i o n a l t a s k s were i n -c l u d e d i n t h e d e s i g n o f t h i s s t u d y as r e p r e s e n t a t i v e s o f t h e f o r m a l o p e r a t i o n a l s t a g e . I f t h e s y s t e m i c t a s k s were t o become c a n d i d a t e s f o r a f i f t h s t a g e , t h e y w o u l d have t o be a Guttman s t e p above t h e f o r m a l o p e r a t i o n a l t a s k s on t h e whole. The c r i t e r i o n o f s t r u c t u r e s d'ensemble ( l i t e r a l l y " s t r u c t u r e s o f t h e w h ole"; l o o s e l y " s t r u c t u r e d w h o l e s " ) i m p l i e s r o u g h l y e q u i v a l e n t d i f f i c u l t y l e v e l s w i t h i n s t a g e s on t h e a v e r a g e . E v i d e n c e t h a t w o u l d s a t i s f y t h i s c r i t e r i o n i n c l u d e s (a) the e x i s t e n c e o f t h e same s i z e o f a gap between t h e s c a l o g r a m d i f f i c u l t y l e v e l s o f c o n c r e t e and f o r m a l t a s k s as between t h e s y s t e m i c 3. F o r m a l l o g i c o p e r a t e s on r e l a t i o n s o f s i m i l a r ! t y / d i s s i m i l a r i t y and o f i n c l u s i o n . S y s t e m i c l o g i c o p e r a t e s on t o p o l o g i c a l r e l a t i o n s and p a r t -whole r e l a t i o n s . The t r u t h v a l u e of f o r m a l l o g i c a l arguments can be d e c i d e d i n t h e a b s t r a c t . The t r u t h v a l u e o f s y s t e m i c l o g i c a l p r o p o s i -t i o n s depends upon t h e p r i o r s p e c i f i c a t i o n o f s p a t i o - t e m p o r a l p a r t i c u -l a r s . S y s t e m i c l o g i c a p p l i e s t o t h e m e n t a l c o n s t r u c t i o n s o f w h o l e s . F o r m a l l o g i c p r e s u p p o s e s t h e known i d e n t i t y o f t h e wholes and goes on t o compare and c l a s s i f y them. S t a t i c w holes a r e c l o s e d systems and a r e ap-prehended t h r o u g h what P i a g e t c a l l e d " s u b l o g i c " . S y s t e m i c l o g i c subsumes s u b l o g i c b u t a l s o a l l o w s f o r t h e a p p r e c i a t i o n o f dynamic w h o l e s o r open systems. Open systems a r e c h a r a c t e r i z e d by n e g e n t r o p i c s t r u c t u r e s . 4. The h i e r a r c h i z a t i o n c r i t e r i o n i m p l i e s l o g i c a l s u b s u m p t i o n as w e l l as a Guttman s c a l e arrangement o f s t a g e s . I n a Guttman s c a l e of a b i l i t y , t h e i t e m s a r e o r d e r e d f r o m t h e l e a s t t o t h e most d i f f i c u l t s u c h t h a t p a s s i n g a p a r t i c u l a r i t e m i m p l i e s h a v i n g p a s s e d a l l i t e m s o f l e s s e r d i f f i c u l t y . The i n t e r v a l s between a d j a c e n t i t e m s of a Guttman s c a l e a r e Guttman s t e p s . 34. and f o r m a l t a s k s , (b) s m a l l e r ( t h a n ( a ) ) gaps among t h e d i f f i c u l t y l e v e l s o f t a s k s w i t h i n s t a g e s , and (c) c l u s t e r a n a l y s i s r e s u l t s w h i c h group t a s k s o f the same s t a g e t o g e t h e r . F i n a l l y , F l a v e l l f s c r i t e r i o n o f a b r u p t n e s s w o u l d r e q u i r e a s h o r t t i m e span between c o g n i t i v e f u n c t i o n i n g a t one s t a g e and f u n c t i o n i n g a t t h e n e x t h i g h e r s t a g e . The ages a t w h i c h f o r m a l v e r s u s s y s t e m i c t a s k s a r e m a s t e r e d becomes r e l e v a n t h e r e . F o r e v i d e n c e o f a f i f t h s t a g e F l a v e l l w o u l d r e q u i r e a sudden o n s e t o f m a s t e r y o f t h e s y s t e m i c t a s k s . W o h l w i l l (1973) on t h e o t h e r hand w o u l d a l l o w f o r a g r a d u a l m a s t e r y o f the s y s t e m i c "ensemble". The i n t e r p r e t a t i o n o f f o r m a l and s y s t e m i c l o g i c as " p a r a l l e l " p o s t -c o n c r e t e developments w o u l d be f a v o r e d i f s e v e r a l o f t h e above c r i t e r i a were n o t met. The p a r a l l e l i n t e r p r e t a t i o n w o u l d appear e s p e c i a l l y s t r o n g i f t h e s y s t e m i c t a s k s t u r n e d o u t t o be o f t h e same d i f f i c u l t y as f o r m a l t a s k s and m a s t e r e d a t t h e same ages. The f i f t h s t a g e i n t e r p r e t a t i o n w o u l d be weakened i f the s y s t e m i c t a s k s were more d i f f i c u l t b u t t h e i r g r e a t e r d i f f i c u l t y c o u l d be w h o l l y a t t r i b u t e d t o a g r e a t e r u n f a m i l i a r i t y w i t h the s u b s t a n t i v e c o n t e n t m a t e r i a l s used i n t h e s y s t e m i c t a s k s . F o r t h a t v e r y r e a s o n , the n e x t s e c t i o n d e a l s w i t h i s s u e s r e l a t e d t o f a m i l i a r i t y and domains of c o n t e n t . C. Domains o f C o n t e n t The e m p i r i c a l work t o be d e s c r i b e d i n c l u d e d s e v e r a l c o n t e n t domains. T h i s s e c t i o n d e s c r i b e s ' s i m i l a r i t i e s and d i f f e r e n c e s among domains ( s u b -s e c t i o n i ) and the n a d d r e s s e s t h e i m p l i c a t i o n s o f d i f f e r e n t i a l f a m i l i a r i t y 35 w i t h domain c o n t e n t i n c l u d i n g t a s k d i f f i c u l t y ( i i ) c o m p a r i s o n w i t h f o r m a l o p e r a t i o n a l t a s k s ( i i i ) and age r e l a t e d a b r u p t n e s s o f m a s t e r y , ( i ) C o m p a r a b i l i t y o f C o n t e n t s The c o n t e n t o f s t a n d a r d P i a g e t i a n t e s t i n g p r o c e d u r e s i s n o t d i r e c t l y comparable t o the s o c i e t a l domain c o n t e n t , n o t o n l y because t h e i r m a n i f e s t c o n t e n t s d i f f e r , b u t because t h e two c l a s s e s o f phenomena encompassed by t h e p h y s i c a l and s o c i e t a l domains e x h i b i t d i f f e r e n t t y p e s o f l o g i c o - m a t h e m a t i c a l p r i n c i p l e s as w e l l . I n terms o f m a n i f e s t c o n t e n t s , the c o n t e n t s o f t h e p h y s i c a l domain a r e p h y s i c a l l y p a l p a b l e whereas t h o s e o f t h e s o c i e t a l domain a r e n o t . I n terms o f l o g i c o - m a t h e m a t i c a l p r i n c i p l e s , t he p h y s i c a l domain tends t o o v e r - r e p r e s e n t c l o s e d systems whereas t h e s o c i e t a l domain emphasizes open*systems. I n o r d e r t o e x t e n d t h e P i a g e t i a n approach t o t h e s t u d y o f c h i l d r e n ' s u n d e r s t a n d i n g o f s o c i e t a l s y s t e m s , t h e b i o - e c o l o g i c a l domain was chosen as an i n t e r m e d i a t e s t e p . The b i o - e c o l o g i c a l c o n t e n t i s p h y s i c a l l y p a l p a b l e l i k e t h e p h y s i c a l domain c o n t e n t and u n l i k e the s o c i e t a l c o n t e n t . On t h e - o t h e r -hand the b i o - e c o l o g i c a l c o n t e n t d e a l s w i t h a n i m a t e , open systems l i k e t h e s o c i e t a l domain does, " w h i l e t h e " p h y s i c a l domain c o n t e n t i s ' i n a n i m a t e ' and d e a l s - w i t h more' c l o s e d s y s t e m s . . The i n c l u s i o n o f - t h r e s e - c o n t e n t domains^' 5. F o r the s p e c i f i c d e t a i l s o f t h e c o n t e n t s and m a t e r i a l s employed i n each domain, see A p p e n d i c i e s A, B and C. B r i e f l y , t he c o n t e n t o f t h e p h y s i c a l domain c o n s i s t e d s p e c i f i c a l l y o f o b j e c t s l i k e wooden beads o f d i f f e r e n t c o l o r s , p l a s t i c f l o w e r s o f d i f f e r e n t h e i g h t s , c a r d b o a r d c y l i n d e r s o f d i f -f e r e n t h e i g h t s , and so on. The b i o - e c o l o g i c a l domain d e a l t w i t h b i r d s , p l a n t s , f i s h , m o l e c u l e s , b a c t e r i a , and t r e e s . The s y s t e m i c t a s k s c e n t e r e d around t h e c o n c e p t s o f t r o p h i c l e v e l s , n u t r i e n t c y c l e s , and p o p u l a t i o n dyna-m i c s . The e l e m e n t s i n v o l v e d were a l l d e p i c t e d g r a p h i c a l l y f o r t h e s u b j e c t s e x c e p t f o r p r i n t e d v e r b a l r e p r e s e n t a t i o n i n t h e l o g i c a l m u l t i p l i c a t i o n t a s k . I n t h e s o c i e t a l domain the c o n t e n t s were more c o n c e p t u a l b u t were s t i l l a c -companied by g r a p h i c r e p r e s e n t a t i o n s . The s e r i a t i o n t a s k i n v o l v e d r a n k i n g p e o p l e i n terms o f t h e i r r i g h t s o f a c c e s s t o a j o i n t l y owned p i e c e o f mach-^ i n e r y . The l i n e a r t r a n s i t i v i t y i n v o l v e d t h r e e o c c u p a t i o n a l r o l e s compared i n terms o f l e g i s l a t i v e a u t h o r i t y ( i . e . , p r i m e m i n i s t e r , j u d g e , p o l i c e m a n ) . The l o g i c a l m u l t i p l i c a t i o n and c l a s s i n c l u s i o n t a s k s d e a l t w i t h t h e economic s i t u s e s o f p r o d u c e r s and consumers. The s y s t e m i c i n t e r v i e w s i n t r o d u c e d con-c e p t s l i k e p r o f i t s , t a x a t i o n , and the law o f s u p p l y and demand i n t o a con-s i d e r a t i o n o f t h e C a n a d i a n wheat i n d u s t r y . 36 a l l o w s f o r i n f e r e n c e s about t h e d i r e c t e f f e c t s o f c o n t e n t on p e r f o r m a n c e . The b i o - e c o l o g i c a l domain p r o v i d e s a l i n k between the i m p e r s o n a l con-t e n t s o f s t a n d a r d P i a g e t i a n r e s e a r c h and the s o c i o - e c o n o m i c c o n t e n t w h i c h c o n s t i t u t e s the p r i m a r y f o c u s o f t h i s r e s e a r c h . C h i l d r e n ' s u n d e r s t a n d i n g o f t h e b i o - e c o l o g i c a l domain was j u d g e d t o be l i k e t h e more t r a d i t i o n a l p h y s i -c a l domain i n t h a t e lements of the t a s k a r e p a l p a b l e e n t i t i e s ( e . g . , b i r d s , p l a n t s , f i s h ) . I t i s l i k e t h e s o c i o - e c o n o m i c domain i n t h a t , l i k e s o c i a l s y s t e m s , i t s elements f o r m open syst e m s . These p h y s i c a l e n t i t i t e s a r e a l i v e and t h e n e t w o r k s w h i c h t h e y form a r e open syst e m s . S y s t e m i c s t r u c t u r e s , e s p e c i a l l y t h o s e t h a t show t h e p r o p e r t y o f c y c l i c i n t e g r a t i o n , a r e most o f t e n f ound i n open syst e m s . Ecosystems and s o c i o - e c o n o m i c systems a r e , c o n s e q u e n t -l y e q u a l l y w e l l s u i t e d f o r i l l u s t r a t i n g t h e l o g i c o - m a t h e m a t i c a l p r i n c i p l e o f c y c l i c i n t e g r a t i o n . I t i s d i f f i c u l t , i n n o t i m p o s s i b l e , t o d e v i s e an i n -animate exemplar of the same p r i n c i p l e s 0 . P erhaps i t i s f o r t h i s r e a s o n t h a t P i a g e t ' s c h a r a c t e r i s t i c f o c u s on i n a n i m a t e p h y s i c a l phenomenon might have c o n t r i b u t e d t o h i s n e g l e c t o f s y s t e m i c s t r u c t u r e s and s y s t e m i c o p e r a -t i o n s i n p o s t - c o n c r e t e c o g n i t i o n . F a c e d w i t h t h i s s h o r t f a l l , a d e c i s i o n was made t o i n c l u d e o n l y s t a n d a r d measures o f f o r m a l o p e r a t i o n s ( i . e . , i s o l a t i o n o f v a r i a b l e s , c o m b i n a t i o n o f v a r i a b l e s , and p r o b a b i l i t y ) as an i d e x o f p o s t - c o n c r e t e l e v e l t h i n k -6. A l t h o u g h computer s o f t w a r e w o u l d q u a l i f y , i t i s n o t r e a l l y a p h y s i c a l o b j e c t i n any m e a n i n g f u l s e n s e . I have been f o r c e d t o c o n c l u d e t h a t t h e c a t e g o r y o f e v e n t s w h i c h have t h e f e a t u r e of b e i n g s i m u l t a n e o u s l y (a) e a s i l y e x p l a i n e d t o c h i l d r e n i n l e s s t h a n an h o u r , (b) i n a n i m a t e , and (c) c h a r a c t e r i z e d by c y c l i c i n t e g r a t i o n , f o r m an empty s e t . There a r e complex models i n p a r t i c l e p h y s i c s and i n a s t r o p h y s i c s w h i c h use t h e p r i n c i p l e o f c y c l i c i n t e g r a t i o n (see J a n t s c h and Waddington, 1976). These a r e i n a n i m a t e phenomena b u t (a) t h e y do n o t r e f e r t o p a l p a b l e en-t i t i e s , and (b) i t w o u l d t a k e weeks o r months t o i n t r o d u c e them to c h i l d -r e n as p a r t of a c o g n i t i v e assessment t a s k . 37 i n g ^ . As m entioned e a r l i e r , ' t h i s d e c i s i o n a l l o w e d a c o m p a r i s o n o f d i f f i c u l t y l e v e l s between p o s t - c o n c r e t e t a s k s b a s e d on f o r m a l l o g i c and s y s t e m i c l o g i c , as e v i d e n c e d i n t h e b i o - e c o l o g i c a l and s o c i e t a l domains. N e c e s s a r i l y m i s s -i n g , however, was any o p p o r t u n i t y t o d i r e c t l y compare s y s t e m i c l o g i c i n t h e p h y s i c a l and s o c i e t a l domains. The s y s t e m i c t a s k s o f t h e b i o - e c o l o g i c a l domain p a r t i a l l y f i l l e d t h e gap. ( i i ) F a m i l i a r i t y I s s u e s The f a m i l i a r i t y o f t a s k c o n t e n t s has r e l e v a n c e f o r t h e a t t e m p t t o v a l i d a t e t h e e x t e n s i o n o f P i a g e t i a n t h e o r y t o t h e b i o - e c o l o g i c a l and s o c i e t a l domains o f c o n t e n t . I f r e s p o n d e n t s a r e l e s s f a m i l i a r w i t h one o r b o t h o f t h e s e t y p e s of c o n t e n t t h e n t a s k p e r f o r m a n c e c o u l d s u f f e r . Such an outcome i n i t s e l f w o uld n o t v i t i a t e t h e a p p l i c a b i l i t y o f P i a g e t i a n t h e o r y t o t h o s e c o n t e n t do-mains. I t i s i m p o r t a n t , however, t o be a b l e t o d i s t i n g u i s h c o n t e n t r e l a t e d p e r f o r m a n c e d i f f e r e n c e s from d i f f e r e n c e s t h a t might a r i s e from more s e r i o u s d e p a r t u r e s f r o m t h e g e n e r a l p i c t u r e o f c o g n i t i v e development c o n t a i n e d i n P i a g e t i a n t h e o r y . I n t h e i n t e r e s t o f b e i n g a b l e t o make t h a t d i s t i n c t i o n c l e a r l y , i t i s n e c e s s a r y (a) t o s p e c i f y the v a r i a n t o f t h e f a m i l i a r i t y con-7.. I t w o u l d have been p o s s i b l e t o d e v i s e t a s k s b a s e d on known f o r m a l o p e r a -t i o n s f o r t h e b i o - e c o l o g i c a l and the s o c i e t a l domains. T h a t , however, w o u l d have changed the t o p i c o f t h i s r e s e a r c h somewhat. T h i s s t u d y was n o t i n t e n d e d t o be a w h o l e s a l e r e p l i c a t i o n o f P i a g e t i a n t a s k s i n n o v e l domains. To be s u r e , a t the s t a g e o f c o n c r e t e o p e r a t i o n s t h e same c o g n i -t i v e s t r u c t u r e s were examined a c r o s s a l l t h e c o n t e n t domains i n t h i s s t u d y . P a r t o f t h e r e a s o n f o r t h a t was a d e s i r e t o have o b s e r v a t i o n s a v a i l a b l e on t h e c o g n i t i v e s t r u c t u r e s t h a t can be seen as t h e l o w e r rungs o f t h e v e r t i c a l l a d d e r o f c o g n i t i v e s t r u c t u r e s w i t h i n each domain. The c o n c r e t e s t r u c t u r e s , a c c o r d i n g t o P i a g e t , a r e t h e p r e r e q u i s i t e u n d e r p i n n i n g s o f l a t e r , p o s t - c o n c r e t e a c h i e v e m e n t s . A t t h e p o s t - c o n c r e t e s t a g e , however, th e c o g n i t i v e a c h i e v e m e n t s o f p r i m a r y i n t e r e s t were n o t t h e f o r m a l o p e r a -t i o n s b u t r a t h e r the s y s t e m i c o p e r a t i o n s . An e x a m i n a t i o n o f how w e l l f o r -mal o p e r a t i o n s a c c o u n t f o r t h e c h i l d ' s u n d e r s t a n d i n g o f v a r i o u s open s y s -tems i s a n o t h e r t o p i c . V e r y i n t e r e s t i n g work i n t h a t t o p i c a r e a has been s t a r t e d by D e n i s Kargbo a t t h e U.B.C. Department of S c i e n c e E d u c a t i o n . H i s EdU. d i s s e r t a t i o n c o n c e r n s t h e r o l e o f INRC c o g n i t i v e o p e r a t i o n s i n t h e u n d e r s t a n d i n g of e c o s y s t e m s . 3 8 cept that i s most relevant i n t h i s research and (b) to examine the r e l a t i o n -ship between content f a m i l i a r i t y and h o r i z o n t a l de*calage across whole domains. Un f a m i l i a r i t y as Foreignness. The subject's f a m i l i a r i t y or lack of i t with t e s t i n g materials can powerfully influence task performance, as several c r o s s - c u l t u r a l studies have shown (for a review see G l i c k , 1975). There are, however, many ways i n which materials can be unfamiliar. G l i c k notes c u l t u r a l differences may a r i s e due to two-dimensional representations of three dimensional objects, or due to differences i n which features of objects i t i s usual to note and analyze. Used i n t h i s sense, the word " f a m i l i a r i t y " means "not foreign". "Familiar" materials or perceptual/conceptual approaches are those indigenous to the subject's own culture. Awareness of the importance of c u l t u r a l f a m i l i a r i t y leads to a greater s e n s i t i v i t y to the possible e f f e c t s of f i n e r degrees of foreignness. Of p a r t i c u l a r importance i n the present research i s the p o s s i b i l i t y that the adult world of p o l i t i c s and economics might be somewhat l i k e a foreign culture to c h i l d r e n and that consequently developmental claims about children's a b i l i t i e s to comprehend such content might e a s i l y be confounded with the l e s s t h e o r e t i c a l l y i n t e r e s t i n g matter of f a m i l i a r i t y . U n f a m i l i a r i t y as Meaninglessness. Thus far we have dealt with f a m i l i a r i t y i n the sense of c u l t u r a l foreignness. The meaning of familia'rity, however, looses some of i t s crispness when we move from c u l t u r a l differences to develop-mental di f f e r e n c e s . I t then becomes necessary to speak i n terms of continuous degrees of f a m i l i a r i t y or l e v e l s of f a m i l i a r i t y . For example, one sense of the term comes from t r a d i t i o n a l verbal learning studies where the more f a m i l i a r a stimulus i s , the quicker i t can be recognized or the quicker i t s a s s o c i a t i o n with another stimulus can be relearned. This i s f a m i l i a r i t y i n the sense of p r i o r "exposure" or "acquaintanceship". 39 A t t h e o p p o s i t e end o f t h e c o n t i n u u m , we may speak of f a m i l i a r i t y as knowing t h i n g s about a s t i m u l u s , l i k e what i t does, what o t h e r o b j e c t s i t i s i m p o r t a n t l y r e l a t e d t o , what i t s s i g n i f i c a n c e i s i n a l a r g e r c o n t e x t , and, p erhaps what i t s m e t a p h o r i c a l and/or a l l e g o r i c a l p o t e n t i a l m i g h t be. T h i s i s f a m i l i a r i t y i n t h e s e n s e o f " m e a n i n g f u l n e s s " , A s t i m u l u s t h a t c a n be p l a c e d i n t o t h e c o n t e x t o f o t h e r knowledge i s one w i t h w h i c h t h e p e r c e i v e r i s more f a m i l i a r . When i t c o n n o t e s " m e a n i n g f u l n e s s " , t h e c o n c e p t o f f a m i l i a r i t y i s l i n k e d t o t h e c o n c e p t s o f knowledge and u n d e r s t a n d i n g . I n t h i s s ense c o g n i t i v e development can be l o o s e l y d e s c r i b e d as t h e p r o c e s s of f a m i l i a r i z a t i o n w i t h t h e w o r l d . I n t h i s b r o a d meaning, f a m i l i a r i t y c e a s e s t o be i m p o r t a n t l y d i f -f e r e n t from t h e i s s u e of s o c i a l u n d e r s t a n d i n g w h i c h t h i s r e s e a r c h s e t out t o e x p l o r e . Any a t t e m p t t o c o n t r o l f o r o r a s s e s s f a m i l i a r i t y i n t h i s sense w o u l d e i t h e r b l o c k , o r p r o v e e q u i v a l e n t t o , t h e s t u d y as a w hole. As a r e s u l t , i t i s f a m i l i a r i t y i n t h e e a r l i e r s ense o f f o r e i g n n e s s o r a c q u a i n t a n c e s h i p w h i c h must now be c o n s i d e r e d . H o r i z o n t a l D e c a l a g e . The p r o p o s i t i o n t h a t t h e c o n t e n t of t h e s o c i e t a l domain t a s k s m ight be more f o r e i g n t o c h i l d r e n i n any s o c i e t y l e a d s t o an e x p e c t a t i o n t h a t a l l of t h e s o c i e t a l domain t a s k s might be more d i f f i c u l t t h a n t a s k s f r o m o t h e r more f a m i l i a r c o n t e n t domains. T h i s has i m p l i c a t i o n s f o r t h e a t t e m p t t o v e r i f y t h e g e n e r a l i z a b i l i t y o f P i a g e t i a n t h e o r y t o t h e s o c i e t a l domain. I f t h e s o c i e t a l domain t a s k s a r e f o u n d t o be b o t h (a) l e s s f a m i l i a r i n terms o f c o n t e n t and (b) more d i f f i c u l t i n terms o f o v e r a l l s u c -c e s s r a t e s , t h e n i t i s p o s s i b l e t h a t r e s p o n d e n t s who p a ss f o r m a l o p e r a t i o n a l t a s k s on more f a m i l i a r t u r f :• might f a i l s t r u c t u r a l l y l e s s complex " c o n c r e t e " t a s k s i n t h e l e s s f a m i l i a r s o c i e t a l domain. A t f i r s t g l a n c e t h i s t y p e o f o u t -come might appear t o f a l s i f y t h e P i a g e t i a n p r e m i s e o f a d i s c o n t i n u o u s s h i f t i n c o g n i t i v e o r g a n i z a t i o n between s t a g e s . A l t e r n a t i v e l y , s u c h " b e t w e e n - s t a g e " 40 d i s c o n t i n u i t y f o r s o c i e t a l c o n t e n t m ight s t i l l be p r e s e n t , but s i m p l y o c c u r a t an o l d e r age. The s t a g e t r a n s i t i o n m i g h t s i m p l y be d e l a y e d i n t h e s o c i e t a l domain owing t o e i t h e r (a) t h e f o r e i g n n e s s o f i t s c o n t e n t o r (b) t h e p u r e l y v e r b a l , n o n - p h y s i c a l n a t u r e o f i t s c o n t e n t . I f s u c h e v i d e n c e o f d e c a l a g e were o b s e r v e d o n l y i n t h e s o c i e t a l domain i t c o u l d be a t t r i b u t e d t o t h e n o n p a l p a b i l i t y o f t h e c o n t e n t s . I f i t were fo u n d i n b o t h t h e b i o - e c o l o g i c a l and s o c i e t a l domains e q u a l l y , t h e n t h e a n i m a t e , open systems n a t u r e o f b o t h o f t h e s e c o n t e n t s w o u l d be i m p l i c a t e d and t h i s g r e a t e r d i f f i c u l t y w o u l d appear more f o r m a l o r s t r u c t u r a l r a t h e r t h a n s i m p l y a m a t t e r of u n f a m i l i a r c o n t e n t , ( i i i ) F a m i l i a r i t y and Task D i f f i c u l t y A p a r t from a s s i s t i n g i n t h e e v a l u a t i o n of t h e a p p l i c a b i l i t y o f P i a g e t i a n t h e o r y t o o t h e r c o n t e n t domains, d a t a about f a m i l i a r i t y c o u l d a l s o a l l o w a c o m p a r i s o n between s y s t e m i c c o g n i t i v e o p e r a t i o n s and f o r m a l o p e r a t i o n s . ' I n p a r t i c u l a r , one c o u l d a s s e s s t h e r e l a t i v e i m p o r t a n c e o f l o g i c a l c o m p l e x i t y v e r s u s c o n t e n t f a m i l i a r i t y f o r b o t h k i n d s o f t a s k s . F i r s t , c o m p a r i s o n s c o u l d be made between t a s k s t h a t had t h e same l o g i c a l r e q u i r e m e n t s ( i . e . , i n v o l v e d t h e same c o g n i t i v e s t r u c t u r e s ) b u t d i f f e r e d i n terms of t h e f a m i l i a r i t y o f t h e i r c o n t e n t s . Second, t h e r e may be c a s e s where t h e c o n t e n t s i n v o l v e d i n two c o g n i t i v e o p e r a t i o n s were i d e n t i c a l d e s p i t e d i f f e r e n t l o g i c a l r e q u i r e -ments. An i m p o r t a n t i s s u e t h a t c o u l d be r e s o l v e d i n t h i s manner i s t h e m a t t e r o f whether t h e s y s t e m i c o p e r a t i o n s a r e more advanced t h a n t h e f o r m a l o p e r a t i o n s . I t was e x p e c t e d t h a t b o t h s e t s of o p e r a t i o n s w o u l d be p o s t - c o n c r e t e a c h i e v e -ments. What remained t o be d e t e r m i n e d was whether o r n o t t h e s y s t e m i c o p e r a -t i o n s w o u l d p r o v e t o be a d e v e l o p m e n t a l l y l a t e r achievement than f o r m a l 41 o p e r a t i o n s even.when t h e e f f e c t s o f . p o s s i b l y l e s s f a m i l i a r c o n t e n t have been a c c o u n t e d f o r . I n sum, t h e d a t a on t h e f a m i l i a r i t y o f t a s k c o n t e n t s i n terms of f o r e i g n -n e s s f a c i l i t a t e s t h e i n t e r p r e t a t i o n o f t h e d a t a i n two ways. F i r s t , i t c o u l d i n d e x a c o n s t a n t f a c t o r o f t a s k d i f f i c u l t y a c r o s s domains. T h i s a l l o w s f o r an i n f e r e n c e o f t h e p r e s e n c e o r absence o f h o r i z o n t a l d e c a l a g e and t h e r e b y c l a r i f i e s t h e m a t t e r o f how g e n e r a l i z a b l e P i a g e t i a n t h e o r y i s t o b i o - e c o l o g i c a l and s o c i e t a l c o n t e n t i n g e n e r a l . Second, t h e f a m i l i a r i t y d a t a m i g h t h e l p e s t a b -l i s h t h e d e v e l o p m e n t a l p r i o r i t y o f f o r m a l o p e r a t i o n s V i s a. V i s s y s t e m i c o p e r a t i o n s i n d e p e n d e n t l y o f t h e c o n t e n t r e l a t e d f a c t o r s t h a t i n f l u e n c e p e r f o r m a n c e on t h e t a s k s d e s i g n e d t o a s s e s s m a s t e r y o f t h o s e o p e r a t i o n s , ( i v ) Age and D i f f i c u l t y L e v e l The d i f f i c u l t y l e v e l o f a t a s k i s a l w a y s r e l a t i v e t o o t h e r t a s k s a d m i n i s -t e r e d t o t h e same r e s p o n d e n t s . I t i s n o t an a b s o l u t e l e v e l . W i t h a sample o f 7 t o 9 y e a r o l d s a l l f o r m a l o p e r a t i o n a l t a s k s would appear t o be o f e q u a l d i f -f i c u l t y ( i . e . , no one would p a s s ) . W i t h a sample o f 11 t o 15 y e a r o l d s t h e same f o r m a l o p e r a t i o n a l t a s k s would be o r d e r e d w h i l e t h e c o n c r e t e s t a g e d t a s k s would show l i t t l e v a r i a n c e . I n t h e p r e s e n t s t u d y t h e sample o f r e s p o n d e n t s c o v e r e d a wide range o f ages (8 t o 1 8 ) , t o o p t i m i z e t h e u t i l i t y o f d a t a on t h e d i f f i c u l t y l e v e l o f t a s k s w i t h h e t e r o g e n e o u s a b i l i t y l e v e l s . The i n t e n t i o n was t o maximize t h e v a r i a n c e i n t h e d i f f i c u l t y l e v e l * d a t a . A l t h o u g h t h e d i f f i c u l t y l e v e l d a t a were t h e c e n t r a l a n a l y t i c a l f o c u s i n t h i s s t u d y t h e age o f m a s t e r y d a t a were a l s o u s e f u l f o r i n t e r p r e t i n g d i f f e r -ences i n d i f f i c u l t y l e v e l s . Where two t a s k s were found t o be v e r y d i f f e r e n t i n terms o f d i f f i c u l t y l e v e l , t h e r e c o u l d be no a s s u r a n c e f r o m t h a t d a t a p e r se t h a t one t a s k i s m a s t e r e d a t a l a t e r age t h a n t h e o t h e r by most c h i l d r e n . 42 Here t h e age o f m a s t e r y d a t a had t o be b r o u g h t i n t o c l a r i f y t h e i n t e r p r e t a t i o n o f t h e d i f f i c u l t y l e v e l d a t a . D. Hypotheses I n t h e a t t e m p t t o e x t e n d t h e P i a g e t i a n a p p r o a c h t o r e l a t i v e l y u n e x p l o r e d domains o f c o n t e n t , t h i s s t u d y a t t e m p t s t o show (a) on t h e m i c r o s c o p i c l e v e l o f a n a l y s i s , t h a t t h e o r d e r i n w h i c h v a r i o u s o p e r a t i o n s a r e m a s t e r e d r e m a i n s t h e same a c c r o s s domains, and (B) on t h e m a c r o s c o p i c l e v e l o f a n a l y s i s , t h a t t h e r e l a t i v e c o n t i n u i t i e s and d i s c o n t i n u i t i e s i n modes o f c o g n i t i v e o r g a n -i z a t i o n ( e . g . , s t a g e s ) a l s o r e m a i n t h e same a c r o s s domains. These p o i n t s , once e s t a b l i s h e d , p r e p a r e t h e way f o r a c o n s i d e r a t i o n o f t h e main f o c u s o f t h i s s t u d y . The c e n t r a l f o c u s i s on t h e c o g n i t i v e s t r u c t u r e s r e q u i r e d t o u n d e r s t a n d open systems. I n u n d e r s t a n d i n g s u c h systems r e s p o n d e n t s w o u l d presumably be p e r f o r m i n g c o g n i t i v e o p e r a t i o n s a t l e a s t as d i f f i c u l t as f o r m a l o p e r a t i o n s . The e x a c t d i f f i c u l t y o f t h e s e s y s t e m i c c o g n i t i v e o p e r a t i o n s v i s a v i s p r e v i o u s l y s t u d i e d f o r m a l o p e r a t i o n s r e m a i n s t o be d e t e r m i n e d . A t t h e same ti m e some a t t e n t i o n must be g i v e n t o t h e r e l a t i v e c o n t r i b u t i o n o f c o n t e n t r e l a t e d ( i . e . f i g u r a t i v e ) f a c t o r s v e r s u s l o g i c a l c o m p l e x i t y ( i . e . o p e r a t i v e ) f a c t o r s i n a c c o u n t i n g f o r t h e o b s e r v e d d i f f i c u l t y l e v e l s o f t h e s y s t e m i c o p e r -a t i o n s . The a t t e m p t t o e x t e n d t h e P i a g e t i a n a p p r o a c h t o f u r t h e r c o n t e n t domains • t r a n s l a t e s i n t o t h e m a c r o s c o p i c and m i c r o s c o p i c a s p e c t s o f t h e f i r s t h y p o t h e s i s . The second-and t h i r d h y p o t h e s e s i n t h i s s t u d y d e a l w i t h t h e i s s u e s r e l a t e d t o t h e d i f f i c u l t y l e v e l s o f t h e s y s t e m i c c o g n i t i v e o p e r a t i o n s . A l t h o u g h a l l t h e h y p o t h e s e s a r e i n d e p e n d e n t , t h e y a l s o s t a n d i n a c o n t i n g e n t r e l a t i o n s h i p w i t h one a n o t h e r . B e f o r e t h e n a t u r e o f t h a t r e l a t i o n s h i p i s ex-amined ( i n s u b s e c t i o n ( i i ) ) , t h e h y p o t h e s e s t h e m s e l v e s w i l l be l i s t e d ( i n sub-s e c t i o n ( i ) ) . Each h y p o t h e s i s i s examined i n more d e t a i l a l o n g w i t h i t s 43 c o r r e s p o n d i n g " n u l l h y p o t h e s i s " i n s u b s e c t i o n ( i i i ) . ( i ) L i s t o f Hypotheses The h y p o t h e s e s o f t h i s s t u d y a r e as f o l l o w s : F i r s t . M i c r o s c o p i c : The o r d e r o f t a s k d i f f i c u l t y as d e t e r m i n e d by a s c a l o g r a m a n a l y s i s w i l l be t h e same a c r o s s a l l domains. The d i f f i c u l t y o r d e r i n g , f r o m e a s i e s t t o most d i f f i c u l t , f o r t h e c o n c r e t e s t a g e t a s k s w i l l be as f o l l o w s : s e r i a t i o n , l i n e a r t r a n s i t i v i t y , l o g i c a l m u l t i p l i c a t i o n , c l a s s i n c l u s i o n . I n t h e p h y s i c a l domain a l l o f t h e f o r m a l o p e r a t i o n a l t a s k s w i l l be more d i f f i c u l t t h a n a l l o f t h e c o n c r e t e o p e r a t i o n a l t a s k s . I n t h e b i o - e c o l o g i c a l and s o c i e t a l domains t h e c y c l i c t r a n s i t i v i t y t a s k s w i l l b o t h be more d i f f i -c u l t t h a n a l l o f t h e c o n c r e t e o p e r a t i o n a l t a s k s and t h e c y c l i c i n t e g r a t i o n t a s k s w i l l b o t h be more d i f f i c u l t t h a n b o t h o f t h e c y c l i c t r a n s i t i v i t y t a s k s . M a c r o s c o p i c : Whatever o r d e r i n g s a r e o b s e r v e d w i t h i n s t a g e s , t h e most d i f f i -c u l t c o n c r e t e o p e r a t i o n a l t a s k w i l l be a Guttman s t e p l e s s d i f f i c u l t t h a n t h e l e a s t d i f f i c u l t p o s t - c o n c r e t e s t a g e d t a s k i n t h e same domain and t h e r e w i l l be no Guttman s t e p s between t a s k s o f t h e same s t a g e . T h i s p a t t e r n w i l l be f o u n d i n a l l t h r e e c o n t e n t domains w i t h o u t e x c e p t i o n . Second. At l e a s t one o f t h e components o f t h e s y s t e m i c o p e r a t i o n s w i l l , i n b o t h t h e b i o - e c o l o g i c a l and t h e s o c i e t a l domains, be more d i f f i c u l t t h a n t h e The term " n u l l h y p o t h e s i s " i s used h e r e i n a f i g u r a t i v e s e n s e . U s u a l l y t h e term i s used i n t h e c o n t e x t o f q u a n t i t a t i v e a n a l y s e s . I t r e f e r s t o t h e a s -su m p t i o n o f no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e . I n t h i s work t h e te r m i s u s e d l e s s f o r m a l l y t o r e f e r t o " t h e t h e o r e t i c a l p o s i t i o n w h i c h w o u l d p r e v a i l were no e v i d e n c e found t o s u p p o r t t h e t h e o r e t i c a l p o s i t i o n c o n ^ t a i n e d i n a p r o p o s e d h y p o t h e s i s . " 44 most d i f f i c u l t f o r m a l o p e r a t i o n a l t a s k by a m a r g i n t h a t i s comparable t o t h e d i f f e r e n c e i n d i f f i c u l t y between t h e l e a s t d i f f i c u l t f o r m a l o p e r a -t i o n a l t a s k and t h e most d i f f i c u l t c o n c r e t e o p e r a t i o n a l t a s k . M o r e o v e r , t h e s t e p between t h e most d i f f i c u l t f o r m a l t a s k and t h e more d i f f i c u l t s y s t e m i c t a s k ( s ) w i l l be a Guttman s t e p . T h i r d . The d i f f i c u l t y l e v e l o f t h e most d i f f i c u l t s y s t e m i c t a s k ( s ) w i l l n o t be w h o l l y a t t r i b u t a b l e t o f a m i l i a r i t y o f t a s k c o n t e n t v a r i a b l e s , ( i i ) A C o n t i n g e n t S u c c e s s i o n S t r i c t l y s p e a k i n g , t h e t h r e e h y p o t h e s e s o f t h i s s t u d y a r e i n d e p e n d e n t o f one a n o t h e r . I t i s p o s s i b l e t o l o c a t e t h e d i f f i c u l t y l e v e l s (second h y p o t h e s i s ) o f t h e s y s t e m i c o p e r a t i o n s v i s a v i s f o r m a l o p e r a t i o n s even i f t h e s t a g e and sequence p a t t e r n s found i n t r a d i t i o n a l P i a g e t i a n r e s e a r c h do n o t g e n e r a l i z e t o t h e b i o - e c o l o g i c a l o r t h e s o c i e t a l domains ( f i r s t h y p o t h e s i s ) . L i k e w i s e , one c o u l d f e r r e t out t h e i n f l u e n c e o f c o n t e n t on s y s t e m i c t a s k d i f f i c u l t y l e v e l s ( t h i r d h y p o t h e s i s ) even i f t h e s y s t e m i c t a s k s a r e o b s e r v e d t o be o f t h e same d i f f i c u l t y l e v e l s as t h e f o r m a l o p e r a t i o n a l t a s k s . D e s p i t e t h i s s t r i c t i n d e p e n d e n c e , however, t h e r e i s t h e p o s s i b i l i t y o f a l l t h r e e h y p o t h e s e s becoming s u c c e s s i v e s t e p s i n t h e t e s t i n g o f an o v e r a r c h i n g h y p o t h e s i s . The o v e r a r c h i n g h y p o t h e s i s i s t h a t t h e s y s t e m i c o p e r a t i o n s a r e r e p r e s e n t a t i v e s o f a f i f t h s t a g e o f c o g n i t i v e development. The e x i s t e n c e o f a f i f t h s t a g e c o u l d n o t be c a t e g o r i c a l l y d e m o n s t r a t e d i n o n l y one s t u d y no m a t t e r how ex-t e n s i v e . N e v e r t h e l e s s , f u t u r e r e s e a r c h e x p l i c i t l y d i r e c t e d a t t h e f i f t h s t a g e h y p o t h e s i s c o u l d be pre-empted by t h e f i n d i n g s o f t h e p r e s e n t s t u d y . The t h r e e h y p o t h e s e s o f t h i s s t u d y c o u l d be v i e w e d as t e s t s o f t h e p r e c o n d i t i o n s r e q u i r e d f o r p o s i t i n g a f i f t h s t a g e . From t h i s p e r s p e c t i v e t h e f i r s t h y p o t h e s i s p r o v i d e s a t e s t o f t h e l e a s t s t r i n g e n t r e q u i r e m e n t s f o r a f i f t h s t a g e h y p o t h e s i s t o s u r v i v e . I f t h o s e c o n d i t i o n s were met t h e second h y p o t h e s i s c o u l d be seen 45 as a s e a r c h f o r e v i d e n c e o f t h e n e x t most b a s i c c o n d i t i o n s t h a t w o u l d have t o be met i n o r d e r f o r a f i f t h s t a g e h y p o t h e s i s t o r e m a i n v i a b l e . I f t h i s second s e t o f p r e r e q u i s i t e s were found t o o b t a i n t h e n t h e t h i r d h y p o t h e s i s c o u l d l i k e w i s e be c o n s t r u e d as a s u c c e s s i v e l y more r e f i n e d s e t s o f c o n d i -t i o n s t h a t would have t o be d e m o n s t r a t e d . A l t h o u g h e a c h o f t h e t h r e e h y p o t h e s e s c o u l d s t a n d o r f a l l i n d e p e n d e n t l y when c o n s i d e r e d i n d i v i d u a l l y , t h e r e l e v a n c e o f each s u c c e s s i v e h y p o t h e s i s t o t h e f i f t h s t a g e n o t i o n i s c o n t i n g e n t upon a r e j e c t i o n o f t h e n u l l h y p o t h e s i s f o r each' p r e c e d i n g h y p o t h e s i s , ( i i i ) The N u l l Hypotheses The f i r s t n u l l h y p o t h e s i s i s t h a t t h e P i a g e t i a n a p p r o a c h does n o t g e n e r a l -i z e t o t h e b i o - e c o l o g i c a l o r t h e s o c i e t a l domains. The v a s t b u l k o f P i a g e t i a n t h e o r y i s based on r e s e a r c h i n t o c h i l d r e n s ' u n d e r s t a n d i n g o f t h e i n a n i m a t e p h y s i c a l w o r l d . There i s no a s s u r a n c e t h a t t h e same t h e o r y can be e x t e n d e d t o u n d e r s t a n d i n g t h e a n i m a t e w o r l d , e s p e c i a l l y when i t i s a n o n - p a l p a b l e w o r l d as i s t h e c a s e w i t h s o c i e t a l r e a l i t y . S p e c i f i c a l l y , t h e c o g n i t i v e o p e r a t i o n s might be r a n k e d i n an u n p r e d i c t a b l e o r d e r based on d i f f i c u l t y l e v e l and t h e more m a c r o s c o p i c d i s c o n t i n u i t i e s i n d i f f i c u l t y l e v e l s f r o m one s t a g e t o a n o t h e r m i ght n o t appear o r might be l e s s G u t t m a n - l i k e . I n o p p o s i t i o n t o t h e f i r s t n u l l h y p o t h e s i s t h e f i r s t p r e d i c t i v e h y p o t h e s i s s t a t e s t h a t t h e r e w i l l be ample e v i d e n c e o f P i a g e t i a n t h e o r y a p p l y i n g w e l l i n t h e B i o - e c o l o g i c a l and s o c i e t a l domains. I f t h e f i r s t n u l l h y p o t h e s i s cannot Be r e j e c t e d t h e n we have no e v i d e n c e o f any s t a g e s , as we know them, i n t h e B i o - e c o l o g i c a l and/or s o c i e t a l domains. That a u t o m a t i c a l l y r u l e s o u t t h e p o s s i B i l i t y o f a f i f t h P i a g e t i a n t y p e s t a g e . C o g n i t i v e o p e r a t i o n s o f a f i f t h s t a g e w o u l d have t o meet th e p r e r e q u i s i t e o f B e i n g more d i f f i c u l t t h a n f o r m a l o p e r a t i o n s . G i v e n t h a t t h e r e a r e P i a g e t i a n 46 s t a g e s , t h e second n u l l h y p o t h e s i s a s s e r t s t h a t t h e r e a r e o n l y t h o s e P i a g e t i a n s t a g e s a l r e a d y d i s c o v e r e d . There i s no f i f t h s t a g e . The s y s t e m i c o p e r a t i o n s a r e a t t h e same l e v e l o f d i f f i c u l t y as t h e f o r m a l o p e r a t i o n s and a r e t h e r e f o r e a n o t h e r a s p e c t o f t h e f o u r t h s t a g e o f c o g n i t i v e development. The second p r e d i c t i v e hypo-t h e s i s a n t i c i p a t e s t h a t on t h e B a s i s o f d i f f i c u l t y l e v e l s and Guttman s c a l e o r d e r -i n g s , a t l e a s t one o f t h e s y s t e m i c o p e r a t i o n s w i l l Be l o c a t e d aBout as f a r a p a r t f r o m f o r m a l o p e r a t i o n s as f o r m a l o p e r a t i o n s c l u s t e r a p a r t f r o m c o n c r e t e o p e r a -t i o n s . I f t h a t p r e d i c t i o n p r o v e s c o r r e c t , t h e n , on t h e B a s i s o f t h e i r g r e a t e r d i f f i c u l t y , c a n d i d a t e s f o r a f i f t h s t a g e w o u l d have Been i d e n t i f i e d . G i v e n t h a t t h e r e a r e some c o g n i t i v e o p e r a t i o n s more d i f f i c u l t t h a n f o r m a l o p e r a t i o n s , a f i f t h s t a g e i n t e r p r e t a t i o n o f t h a t g r e a t e r d i f f i c u l t y w o u l d r e q u i r e t h a t i t Be a r e s u l t o f t h e g r e a t e r o p e r a t i v e d i f f i c u l t y o f t h e a s s e s s -ment t a s k s . The t h i r d n u l l h y p o t h e s i s , on t h e o t h e r hand, a t t r i B u t e s s u c h g r e a t e r d i f f i c u l t y t o c o n t e n t r e l a t e d f a c t o r s . I f i t c o u l d Be shown t h a t t h e g r e a t e r d i f f i c u l t y o f t h e t a s k s a s s e s s i n g t h e s y s t e m i c c o g n i t i v e o p e r a t i o n s c o u l d Be w h o l l y a c c o u n t e d f o r By t h e g r e a t e r d i f f i c u l t y o f t h e t a s k c o n t e n t , t h e n i t w o u l d Be u n p a r s i m o n i o u s t o p o s t u l a t e t h e e x i s t e n c e o f a f i f t h s t a g e . I f t h e p r e d i c t e d g r e a t e r d i f f i c u l t y o f some s y s t e m i c o p e r a t i o n s cannot Be w r i t t e n o f f as a r t i f a c t u a l s i d e e f f e c t s of t h e t a s k s used t o a s s e s s them, t h e n f u r t h e r a n a l y s e s can Be p e r f o r m e d and a d d i t i o n a l d a t a can Be i n t r o d u c e d t o a s s e s s t h e e x t e n t t o w h i c h t h e c r i t e r i a f o r a s t a g e have Been s a t i s f i e d . F o r example, i f t h e r e were more t h a n one o p e r a t i o n B e i n g p r o p o s e d as a c a n d i d a t e f o r a f i f t h s t a g e t h e n i t would make sense t o put t h e s t r u c t u r e d'ensemBle c r i t e r i o n t o a f u r t h e r t e s t by p e r f o r m i n g a c l u s t e r a n a l y s i s . The f i f t h s t a g e c a n d i d a t e s s h o u l d f o r m a s e p a r a t e c l u s t e r , as s h o u l d t h e t a s k s f o r t h e t h i r d and f o u r t h s t a g e s r e s p e c t i v e l y . W i t h more t h a n one c a n d i d a t e f o r a f i f t h s t a g e i t would a l s o Be p o s s i b l e t o check f o r non-Guttman s t e p s among them. 47 • I I I . METHOD A. Measures B r i e f l y s t a t e d , there were three domains of content i n which the c o g n i t i v e operations were presented. These were (a) standard P i a g e t i a n m a t e r i a l s i n v o l v i n g common p h y s i c a l objects (see Appendix A ) , (b) b i o -e c o l o g i c a l content represented v e r b a l l y and i n mnemonic p i c t u r e s (see Appendix B), (c) s o c i a l o r g a n i z a t i o n a l content a l s o represented i n drawings and words (see Appendix C) . W i t h i n a l l three domains there were tasks"*" a s s e s s i n g the concrete o p e r a t i o n a l c o g n i t i v e operations of ( i ) s e r i a t i o n ( i i ) l i n e a r t r a n s -i t i v i t y ( i i i ) l o g i c a l m u l t i p l i c a t i o n and ( i v ) c l a s s i n c l u s i o n . In the b i o - e c o l o g i c a l and the s o c i e t a l domains the proposed c o g n i t i v e operations of (v) c y c l i c t r a n s i t i v i t y and ( v i ) c y c l i c i n t e g r a t i o n were a l s o assessed (see Aprendix D f o r s c o r i n g d e t a i l s ) . For reasons already discussed, there was no p h y s i c a l domain equivalent to these measures so i n s t e a d measures were taken of the formal stage c o g n i t i v e operations of combination of v a r i a b l e s , p r o b a b i l i t y and i s o l a t i o n of v a r i a b l e s . What f o l l o w s i s a b r i e f d e s c r i p t i o n of a l l the measures w i t h s e l e c t e d reference m a t e r i a l s concerning t h e i r use i n other research. 1 . Some of these simpler c o g n i t i v e operations measured (e.g., s e r i a t i o n ) were so elementary that there might appear to be very l i t t l e across domain v a r i a t i o n i n the design of the tasks meant to assess them. That i s , the v a r i a t i o n s i n task content may appear t r i v i a l compared to the c o n s i s t e n c i e s i n task s t r u c t u r e . This was an unavoidable s i d e e f f e c t of i n s u r i n g across domain consistency i n the c o g n i t i v e demands made by tasks assessing very simple c o g n i t i v e operations. 48 :(i) The C o n c r e t e T a s k s I n a l l t h r e e domains t h e s e r i a t i o n t a s k was base d on t h e s t a n d a r d p r o -c e d u r e d e s c r i b e d i n many p l a c e s ( e . g . , Formanek and G u r i a n , 1976). The i n t e r p o l a t i o n v a r i a t i o n was i n c l u d e d i n o r d e r t o h e l p d i s t i n g u i s h p r e - o p e r a t i o n a l r e s p o n s e s f r o m c o n c r e t e o p e r a t i o n a l r e s p o n s e s ( G i n s b e r g and Opper, 1969; 137-138). I f and when t h e o b j e c t s have been c o r r e c t l y s e r i a t e d , t h e i n t e r -p o l a t i o n v a r i a t i o n i n v o l v e s a s k i n g t h e c h i l d t o p l a c e an a d d i t i o n a l o b j e c t i n t o t h e s e r i e s . I n t h e p h y s i c a l domain v e r s i o n r e s p o n d e n t s were asked t o s e r i a t e seven r e d c a r d b o a r d c y c l i n d e r s . The b i o - e c o l o g i c a l v e r s i o n e n t a i l e d a r r a n g i n g t r e e s a c c o r d i n g t o how deep t h e i r r o o t s were. Only t h e crown o f the t r e e s were shown b u t r e s p o n d e n t s were t o l d t h a t t h e d e p t h o f t h e r o o t s was p r o p o r t i o n a l t o t h e h e i g h t o f t h e t r e e . The t r e e s were a l l hand drawn on i n d i v i d u a l i n d e x c a r d s . Thus, t h e s e r i a t i o n was t o be p e r f o r m e d a c c o r d i n g t o an i n v i s i b l e d i m e n s i o n ( r o o t s ) t h a t was r e p r e s e n t e d by a v i s i b l e one ( c r o w n s ) . S i n c e t h e s o c i e t a l domain d i m e n s i o n o f s e r i a t i o n was t o be i n v i s i b l e , i t was i m p o r t a n t t o r e p l i c a t e t h e same d i s t i n c t i o n i n t h e b i o - e c o l o g i c a l domain f o r p u r p o s e s o f c o m p a r i s o n . The " o b j e c t s " t o be s e r i a t e d i n t h e s o c i e t a l domain v e r s i o n were p e o p l e ' s r i g h t s . Respondents were t o l d t h a t seven f a r m e r s had a l l c o n t r i b u t e d d i f f e r e n t amounts o f money t o j o i n t l y buy a t r a c t o r . Where two f a r m e r s b o t h wanted t o use i t a t once, t h e one who had p u t i n t h e most money had t h e r i g h t t o use i t f i r s t . F o r each f a r m e r t h e r e was an i n d e x c a r d showing how many $100 b i l l s he had c o n t r i b u t e d . The r e s p o n d e n t s were asked t o use t h e i n d e x c a r d s t o queue t h e f a r m e r s on a day when t h e y a l l wanted t o use t h e t r a c t o r a t t h e same t i m e . The t h r e e l i n e a r t r a n s i t i v i t y t a s k s f o l l o w e d t h e s t a n d a r d p r o c e d u r e s 49 i n v e s t i g a t e d by G l i c k and Wapner (1 9 6 8 ) . Three c a r d b o a r d c y l i n d e r s o f d i f -f e r e n t h e i g h t s and c o l o r s were employed i n t h e p h y s i c a l domain t a s k . I n t h e b i o - e c o l o g i c a l domain i t was t h r e e d i f f e r e n t s p e c i e s o f b i r d s w h i c h l a y e d d i f f e r e n t numbers o f eggs. They were d e p i c t e d g r a p h i c a l l y on i n d e x c a r d s . I n t h e s o c i a l c o n t e n t domain t h r e e o c c u p a t i o n a l r o l e s ( p r i m e minister:," j u d g e , p o l i c e m a n ) were r e p r e s e n t e d by t h r e e p a p e r mache d o l l s , a l l t h e same s i z e , w e a r i n g d r e s s a p p r o p r i a t e t o t h e i r r o l e s . The d i m e n s i o n o f c o m p a r i s o n was how much each one, "had t o say about what t h e l a w s would be." M a s t e r y o f l o g i c a l m u l t i p l i c a t i o n i n t h e t h r e e domains was a s s e s s e d by t h e two-way c l a s s i f i c a t i o n t a s k ( I n h e l d e r and P i a g e t , 1 9 6 4 ) . The i n t e r s e c t i n g d i m e n s i o n s i n t h e p h y s i c a l domain l o g i c a l m u l t i p l i c a t i o n t a s k were shape ( s t a r s , s q u a r e s ) and c o l o r ( r e d , y e l l o w ) . A t w o f o l d m a t r i x was p r e s e n t e d on an i n d e x c a r d . One o f t h e f o u r c e l l s was empty. The c h i l d was a s k e d w h i c h o f t h e f i v e a l t e r n a t i v e answers d i s p l a y e d a t t h e b o t t o m o f t h e c a r d w o u l d " f i t b e s t " i n t h e empty c e l l . I n b o t h " t h e b i o - e c o l o g i c a l and t h e s o c i a l domain t h e s t i m u l i f o r t h e m a t r i c e s were t y p e w r i t t e n words. The i n t e r s e c t i n g b i o -e c o l o g i c a l d i m e n s i o n s were genus C f i s h , b i r d ) and d i e t ( m e a t - e a t i n g , p l a n t -e a t i n g ) . I n t h e s o c i a l domain t h e c h o i c e s were between p r o d u c e r s v e r s u s consumers o f wheat v e r s u s f l o u r . I n h e l d e r and P i a g e t ' s (1964) s t a n d a r d c l a s s i n c l u s i o n t a s k was a d a p t e d f o r use w i t h c o n t e n t f r o m t h e t h r e e domains. F o r t h e p h y s i c a l domain t h e s u p e r o r d i n a t e c l a s s was wooden beads w i t h c o l o r as t h e s u b c l a s s e s . The s u p r a -o r d i n a t e c l a s s i n t h e b i o - e c o l o g i c a l domain was " b i r d s " and t h e s u b c l a s s e s o r c a t e g o r i e s i n c l u d e d i n t h a t c l a s s were ducks and crows. These were t y p e -w r i t t e n i n a h a p h a z a r d s p a t i a l a r r a y on an i n d e x c a r d . So were t h e p a r t i c u l a r e l e ments of t h e s u p r a o r d i n a t e c l a s s i n t h e s o c i a l domain. The i n d e x c a r d 50 d i s p l a y e d noun p h r a s e s f o r each o f t h e members o f t h e wheat m a r k e t i n g b o a r d . Some were p r o d u c e r r e p r e s e n t a t i v e s ; some were consumer r e p r e s e n t a t i v e s . A l l were government a p p o i n t e e s , ( i i ) The For m a l T a s k s The c o m b i n a t i o n o f v a r i a b l e s p r o c e d u r e was adapt e d By A r l i n (1978) f r o m a v e r s i o n by S i l l s and H e r r o n (1976) w h i c h r e c o n s t r u c t e d t h e e s s e n t i a l l o g i c a l f e a t u r e s o f I n h e l d e r and P i a g e t ' s (1958) " c o m b i n a t i o n o f C o l o r e d and C o l o r l e s s C h e m i c a l B o d i e s " t a s k . The c h e m i c a l s a r e r e p l a c e d by f i v e p ush b u t t o n e l e c t r i c a l s w i t c h e s a t o p a s m a l l b l a c k box. O n l y one c o m b i n a t i o n o f t h r e e b u t t o n s pushed s i m u l t a n e o u s l y w o u l d i l l u m i n a t e t h e r e d l i g h t a l s o a t o p t h e box. One b u t t o n was n o t w i r e d ( t h e a n a l o g u e o f w a t e r ) and one b r o k e , r a t h e r t h a n c l o s e d , t h e c i r c u i t ( t h e a n a l o g u e o f t h e n e u t r a l i z i n g c h e m i c a l ) . The measure o f comprehension o f p r o b a b i l i t y was A r l i n ' s (1.978) s t a n d a r d -i z a t i o n o f a l e s s s t r u c t u r e d p r o c e d u r e d e s c r i b e d By P i a g e t and I n h e l d e r (1975; 116-130). S i x r e d , s i x y e l l o w , and s i x g r e e n wooden Beads were mixed i n a Bowl. Respondents e s t i m a t e d t h e p r o B a B i l i t y o f d r a w i n g a p a r t i c u l a r c o l o r t w i c e w i t h o u t r e p l a c e m e n t . The i s o l a t i o n o f v a r i a B l e s t a s k was d e v i s e d By Kuhn and Ho 0-977) w i t h m inor a d a p t a t i o n s by C h a n d l e r , S i e g a l and Boyes (1980) and t h e a u t h o r . Respondents were f a c e d w i t h two a r r a y s o f p l a s t i c p l a n t s , seven r o s e s and seven l e a f y p l a n t s . They were t o l d t o i m a g i n e t h a t t h r e e t y p e s o f p l a n t f o o d s were b e i n g f e d t o t h e p l a n t s . P l a s t i c v i a l s w i t h l e t t e r e d l a b e l s s t o o d B e s i d e each p l a n t t o r e p r e s e n t t h e p l a n t f o o d B e i n g f e d t o t h a t p l a n t . Some p l a n t s were t a l l e r t h a n o t h e r s . Respondents were a s k e d t o i d e n t i f y t h e most e f f e c t i v e and e f f i c i e n t c o m B i n a t i o n o f p l a n t f o o d s t o pro d u c e t a l l p l a n t s . 51 ( i i i ) The S y s t e m i c Tasks C y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n were a s s e s s e d i n an i n t e r v i e w f o r m a t d e v i s e d f o r t h i s s t u d y . A s i t u a t i o n was d e s c r i b e d and t h e n t h e r e s p o n d -ant was asked what would happen n e x t . T h i s was f o l l o w e d by more s p e c i f i c s t a n d a r d i z e d p r o b e s and w h a t e v e r a d d i t i o n a l p r o b e s were needed t o r e d u c e a m b i g u i t y o r c o n f u s i o n i n r e s p o n s e s . I n t h e b i o - e c o l o g i c a l domain i n t e r v i e w s , t h e r e s p o n d e n t s were asked about t h e s y s t e m i c r e l a t i o n s i m p l i c i t i n n u t r i e n t c y c l e s (Kargbo, 1979). The s o c i a l domain i n t e r v i e w d e a l t w i t h t h e s y s t e m i c r e l a t i o n s i n t h e s o c i o - p o l i t i c o - e c o n o m i c o r g a n i z a t i o n o f t h e C a n a d i a n wheat i n d u s t r y . S p e c i f i c a l l y , i t i n v o l v e d ' t h e wheat commodity c y c l e f r o m t h e f a r m e r , t o t h e wheat m a r k e t i n g b o a r d , t o t h e f l o u r m i l l , t o t h e b a k e r y , t o t h e r e t a i l e r , back t o t h e f a r m e r . ( i v ) F a m i l i a r i t y A ssessments f o r S y s t e m i c Tasks F o r e v e r y t a s k t h e r e was a t l e a s t one i t e m a s s e s s i n g how f a m i l i a r t h e r e s p o n d e n t was w i t h t h e m a t e r i a l s and/or c o n c e p t s b e i n g used i n t h e t a s k . F o r the c o n c r e t e t a s k s t h e f a m i l i a r i t y i t e m s were l e s s c o n c e p t u a l ( e . g . , "Do you know what t h e s e beads a r e made o f ? " ; "How do you t e l l how deep a t r e e ' s r o o t s go?"' "Have you e v e r h e a r d o f a j u d g e b e f o r e ? Do you know what he d o e s ? " ) . The p o s t - c o n c r e t e f a m i l i a r i t y a s s e s s m e n t s were more c o n c e p t u a l and more e x t e n s i v e . F o r t h e s y s t e m i c i n t e r v i e w s some as s e s s m e n t s t o o k t h e f o r m o f p r e l i m i n a r y p r o b l e m s . F o r example, f a m i l i a r i t y w i t h t h e c o n c e p t o f p r o f i t was a s s e s s e d by a s k i n g , " I f t h e g r o c e r bought b r e a d a t 80<;/loaf, w o u l d he s e l l i t f o r more t h a n 80<:, l e s s t h a n 80<;, o r 80C?" F o r r e a s o n s d i s c u s s e d i n t h e i n t r o d u c t i o n , i t was i m p o r t a n t t o d i s -t i n g u i s h f a m i l i a r i t y f r o m o p e r a t i v e u n d e r s t a n d i n g even though t h e y may be i n t e r d e p e n d e n t . I t o b v i o u s l y would n o t do t o f a m i l i a r i z e s u b j e c t s w i t h t h e m a t e r i a l s t o such an e x t e n t t h a t competence w i t h t h e c o g n i t i v e o p e r a t i o n b e i n g 52 a s s e s s e d becomes a p r e r e q u i s i t e f o r p r e s e n t i n g t h e t a s k . C o n v e r s e l y , t h e a t t r i b u t i o n o f f a i l u r e t o a l a c k o f competence w i t h a p a r t i c u l a r c o g n i t i v e o p e r a t i o n would be u n j u s t i f i e d when t h e r e i s a r e a s o n a b l e doubt t h a t r e s p o n -d e n t s knew enough about t h e c o n s t i t u e n t e lements o f t h e t a s k t o be a b l e t o a p p l y t h a t p a r t i c u l a r c o g n i t i v e o p e r a t i o n m e a n i n g f u l l y i n ' some c o n t e x t . These c o n s i d e r a t i o n s s u g g e s t e d t h e s t r a t e g y o f i d e n t i f y i n g a minimum l e v e l o f u n d e r s t a n d i n g o f ( o r " f a m i l i a r i t y w i t h " ) t h e m a t e r i a l s , c o n c e p t s , p r e m i s e s , e t c . f o r each t a s k and t h e n i n t r o d u c i n g t h e t a s k w i t h , i n s t r u c t i o n s d e s i g n e d 2 t o p r o v i d e t h a t l e v e l o f u n d e r s t a n d i n g . The i n f o r m a t i o n g a i n e d by t h e use o f t h i s s t r a t e g y a l l o w s one t o gauge t h e i n f l u e n c e o f t h e " f a m i l i a r i t y / u n f a m i l i a r i t y o f t h e t a s k c o n t e n t s on t h e o v e r a l l d i f f i c u l t y l e v e l of t h e t a s k f o r t h e whole sample o f r e s p o n d e n t s . B. Respondents A t o t a l o f 96 s u b j e c t s were t e s t e d . There were 8 m a les and 8 f e m a l e s i n each o f grades 3, 5, 7, 9, and 11. An a d d i t i o n a l 8 m a les and 8 f e m a l e s had c o m p l e t e d grade 12 t h e p r e v i o u s academic y e a r . The mean ages o f r e s p o n d -e n t s a t each grade l e v e l , e x p r e s s e d i n y e a r s and months, were: grade 3, 8-7; grade 5, 10-8; grade 7, 12-5; grade 9, 14-7; grade 11, 16-10; f i r s t y e a r p o r t - s e c o n d a r y , 18-11. The grade 3, 5, and 7 r e s p o n d e n t s were f r o m an e l e m e n t a r y s c h o o l t h e grade 9 and 11 r e s p o n d e n t s a t t e n d e d a s e c o n d a r y s c h o o l , and t h e p o s t - s e c o n d a r y r e s p o n d e n t s were e i t h e r f u l l - t i m e members o f t h e work f o r c e o r p o s t - s e c o n d a r y s t u d e n t s . A l l s c h o o l s were i n t h e g r e a t e r V a n c o u v e r m e t r o p o l i t a n a r e a . 2. T h i s p r a c t i c e has a l w a y s been f o l l o w e d i n P i a g e t i a n research.. The i n t r o -d u c t i o n p r o c e d u r e s f o r t h e c l a s s i n c l u s i o n t a s k (p. 1155) a r e a good example. 53 The elementary and secondary school students were randomly s e l e c t e d from a pool of p o t e n t i a l respondents that remained a f t e r the f o l l o w i n g con-s t r a i n t s has been met. F i r s t , the student had to be E n g l i s h speaking, but E n g l i s h d i d not have to be the student's n a t i v e language.' Second, the student had to v e r b a l l y agree to v o l u n t a r y p a r t i c i p a t i o n . T h i r d , the number of males and females had to be equal at each grade l e v e l . Fourth, the student's ' p a r t i c i p a t i o n had to have been approved through the standard channels f o r o b t a i n i n g permission to conduct research i n schools. An attempt was made to match the sample of f i r s t year post-secondary respondents to the p o p u l a t i o n of graduates from the secondary school the previous academic year. The c h a r a c t e r i s t i c on which the matching attempt was made was f u l l time e d u c a t i o n a l or occupational s t a t u s i n the f i r s t p ost-secondary year. School records were a v a i l a b l e f o r graduates of the previous year. The records included the students' p r e d i c t i o n s about t h e i r a n t i c i p a t e d e d ucational and/or occupational a c t i v i t i e s f o r t h e i r f i r s t post-secondary year. Excluding those who gave no c l e a r i n d i c a t i o n of what they would be doing, 47% of the students a n t i c i p a t e d becoming f u l l - t i m e members of the work fo r c e . Fourty-two percent a n t i c i p a t e d a t t e n d i n g a community c o l l e g e or t e c h -n i c a l school. Eleven percent a n t i c i p a t e d a t t e n d i n g a u n i v e r s i t y . The pro-p o r t i o n of f i r s t year post-secondary respondents i n t h i s study who were f u l l -time members of the work f o r c e i s e s p e c i a l l y low by comparison to the estimates obtained from the secondary school graduates. A good deal of time and e f f o r t was expended to ameliorate t h i s c o n d i t i o n but to l i t t l e a v a i l . The p r o p o r t i o n s obtained i n t h i s study were 25% f u l l - t i m e members of the work f o r c e , 37.5% atten d i n g a community c o l l e g e . o r a t e c h n i c a l s c h o o l , and 37.5% atte n d i n g a u n i v e r s i t y . The respondents a t t e n d i n g a u n i v e r s i t y were a l l e n r o l l e d i n 54 I n t r o d u c t o r y P s y c h o l o g y a t U.B.C. The r e s p o n d e n t s a t t e n d i n g a community c o l l e g e were a l l e n r o l l e d i n I n t r o d u c t o r y P s y c h o l o g y a t t h e New W e s t m i n s t e r campus o f Douglas C o l l e g e . The r e s p o n d e n t s who were f u l l - t i m e members o f t h e work f o r c e were r e c r u i t e d e i t h e r t h r o u g h t h e p a r t i c i p a t i n g u n i v e r s i t y s t u d e n t s who had e l i g i b l e f r i e n d s C two r e s p o n d e n t s were o b t a i n e d by t h i s means) o r t h r o u g h t h e a u t h o r ' s ' p e r s o n a l f r i e n d s , r e l a t i v e s , and a c q u a i n t a n c e s Ctwo more r e s p o n d e n t s ) . C. P r o c e d u r e T h i s s e c t i o n i s d i v i d e d i n t o two p a r t s : p r o c e d u r e s f o r c o l l e c t i n g t h e d a t a and p r o c e d u r e s f o r s c o r i n g t h e d a t a . A f t e r d e s c r i b i n g t h e d a t a c o l l e c t i o n p r o c e d u r e t h e t r a i n i n g o f s c o r e r s and t h e s c o r i n g p r o c e d u r e i t s e l f w i l l be d i s c u s s e d . ( i ) D a t a C o l l e c t i o n F o r a l l r e s p o n d e n t s t h e t o t a l p a r t i c i p a t i o n t i m e was a p p r o x i m a t e l y 50 t o 55 m i n u t e s . These s e s s i o n s were r e f e r r e d t o as " i n t e r v i e w s " even though, s t r i c t l y s p e a k i n g , p a r t o f t h e s e s s i o n was d e v o t e d t o t e s t i n g r a t h e r t h a n i n t e r v i e w i n g . W i t h t h e e l e m e n t a r y and s e c o n d a r y s c h o o l s t u d e n t s t h e i n t e r -v i e w s were c o n d u c t e d i n o f f i c e s i n t h e s c h o o l . I n t h e e l e m e n t a r y s c h o o l t h e i n t e r v i e w e r o r h i s a s s i s t a n t went t o t h e c l a s s r o o m and l e d t h e c h i l d t o t h e i n t e r v i e w room. I n t h e s e c o n d a r y s c h o o l groups of 4 t o 6 s t u d e n t s were c a l l e d t o t h e main o f f i c e when d a i l y announcements were made. A t t h a t t i m e t h e s t u d y was b r i e f l y e x p l a i n e d t o them and t h e y were asked t o v o l u n t e e r . I f t h e y a g r e e d a t i m e was a r r a n g e d f o r them t o come t o t h e i n t e r v i e w room p e n d i n g th e a p p r o v a l o f t h e i r t e a c h e r ' f o r t h a t c l a s s t i m e p e r i o d . S t u d e n t s whose p a r e n t s had n o t d i s a l l o w e d t h e i r p a r t i c i p a t i o n were randomly s e l e c t e d f r o m 55 c l a s s l i s t s u n t i l 8 males and 8 females had been i n t e r v i e w e d , With the f i r s t year post-secondary students the u n i v e r s i t y students and the community c o l l e g e students were interviewed i n Psychology Department research rooms. Two of the working'respondents were a l s o interviewed i n a U.B.C. Psychology Department research room. One was interviewed i n her own home and one was interviewed at the home of a mutual acquaintance. The i n t e r v i e w s themselves c o n s i s t e d of 19 tasks. These were 12 concrete o p e r a t i o n a l tasks (3 domains x 4 c o g n i t i v e o p e r a t i o n s ) , 3 formal o p e r a t i o n a l t a s k s , and 4 systemic t a s k s / i n t e r v i e w s (2 domains x 2 c o g n i t i v e o p e r a t i o n s ) . 1. S e r i a t i o n 2. L i n e a r T r a n s i t i v i t y 3. L o g i c a l M u l t i p l i c a t i o n 4. Glass I n c l u s i o n 5. S e r a t i o n 6. L i n e a r T r a n s i t i v i t y 7. L o g i c a l M u l t i p l i c a t i o n 8. Glass I n c l u s i o n 9. S e r i a t i o n 10. L i n e a r T r a n s i t i v i t y 11. L o g i c a l M u l t i p l i c a t i o n 12. Glass I n c l u s i o n 13. Combination of V a r i a b l e s 14. P r o b a b i l i t y 15. I s o l a t i o n of V a r i a b l e s 16. C y c l i c T r a n s i t i v i t y 17. C y c l i c I n t e g r a t i o n The order of task p r e s e n t a t i o n was Concrete Standard Domain (Appendix A., Sections ( i ) to ( i v ) ) B i o l o g i c a l Domain (Appendix B, Sections ( i ) to ( i v ) ) S o c i a l Domain (Appendix C, Sections ( i ) tio ( i v ) ) Formal Appendix A, Sec t i o n (v) Systemic B i o l o g i c a l Domain (Appendix B, Se c t i o n (v) and Appendix D) S o c i a l Domain 18. C y c l i c T r a n s i t i v i t y (Appendix C. S e c t i o n (v) and Appendix D) 19. C y c l i c I n t e g r a t i o n Owing to scheduling d i f f i c u l t i e s four of the elementary school students received the systemic t a s k s , as a bl o c k , before the concrete and formal b l o c k s . 3 The order of task p r e s e n t a t i o n w i t h i n blocks was always the same . The d e t a i l s of how each of these tasks were administered and scored are presented i n the appendicies i n d i c a t e d above. W r i t t e n records were made of responses on the concrete and formal t a s k s . Responses on the systemic tasks were tape recorded and some were a l s o w r i t t e n . The tasks covered a vast range of a b i l i t i e s w i t h some being c h a l l e n g i n g to 8 year olds and others being c h a l l e n g i n g to 18 year o l d s . Since the s e r i e s of tasks were presented i n an order roughly thought, f o r t h e o r e t i c a l reasons, to be c o r r e l a t e d w i t h t h e i r d i f f i c u l t y l e v e l , i t was expected that the most d i a g n o s t i c phases of the i n t e r v i e w f o r p a r t i c u l a r responses would g r a d u a l l y s h i f t from the e a r l i e r to the l a t e r tasks as the t e s t i n g proceeded from the youngest to the o l d e s t respondents. There are advantages and disadvantages to o r d e r i n g p r e s e n t a t i o n on an a p r i o r i b a s i s . The danger i n making the p r e s u p p o s i t i o n I s that "experimenter" expectancy, i n i t s v a r i o u s m a n i f e s t a t i o n s , might have c o n t r i -buted to i n s u r i n g the expected d i f f i c u l t y o r d e r i n g of tasks. The advantage i s that steps can be taken to avoid l o o s i n g rapport w i t h the respondent. Before d e a l i n g w i t h the nexus between order of task p r e s e n t a t i o n and respond-ent rapport we w i l l review the measures adopted to guard against experimenter expectancies i n f l u e n c i n g the r e s u l t s . 3. F u l l counterbalancing of order of task p r e s e n t a t i o n would have re q u i r e d over a m i l l i o n respondents i n order to have one respondent per order. F u l l randomization of order of p r e s e n t a t i o n would have extended the dur a t i o n of each s e s s i o n Beyond that permitted by both the school author-i t i e s and the a t t e n t i o n spans of the c h i l d r e n . 57 F i r s t , i n t h e e l e m e n t a r y s c h o o l , a Ph.D. c a n d i d a t e i n p s y c h o l o g y was a v a i l a b l e as an a s s i s t a n t . The a s s i s t a n t a d m i n i s t e r e d t h e c o n c r e t e o p e r a t i o n a l and f o r m a l o p e r a t i o n a l t a s k s and t h e a u t h o r a d m i n i s t e r e d t h e s y s t e m i c i n t e r -v i e w s . The communication between them was k e p t t o a minimum a t t h a t p o i n t i n o r d e r t o m i n i m i z e t h e communication o f any e x p e c t a n c i e s . The second s t e p t a k e n t o guard a g a i n s t e x p e r i m e n t e r e x p e c t a n c y was t h e a d o p t i o n o f t h e g e n e r a l r u l e t h a t a l l r e s p o n d e n t s would be p r e s e n t e d w i t h a l l t a s k s beyond t h e supposed d i f f i c u l t y l e v e l o f t h e i r f i r s t u n s u c c e s s f u l t a s k . I t was n o t assumed t h e f i r s t f a i l u r e a f t e r a s t r i n g o f s u c c e s s e s n e c e s -s a r i l y s i g n a l e d a s t r i n g o f f a i l u r e s t o f o l l o w . S i n c e one o f t h e p r i m e c o n -c e r n s i n a b i l i t y t e s t i n g i s t o e s t a b l i s h and m a i n t a i n r a p p o r t w i t h r e s p o n d e n t s , i t was i m p o r t a n t t o a v o i d (a) o verwhelming t h e younger r e s p o n d e n t s w i t h p r o b -lems f a r beyond t h e i r a b i l i t i e s and (b) i n s u l t i n g t h e i n t e l l i g e n c e o f young a d u l t s w i t h problems f a r below t h e i r a b i l i t i e s . When p r e s e n t e d w i t h - t h e more complex c y c l i c i n t e g r a t i o n i t e m s t h e f i r s t t h r e e t o f i v e s t u d e n t s i n t e r v i e w e d i n grades 3 and 5 became e i t h e r " f i d g e t y " or u n r e s p o n s i v e . P a t t e r s o n , C o s g r o v e , and 0 ' B r i a n (1980) have documented r e l i a b l e n o n v e r b a l i n d i c a n t s o f non-compre-h e n s i o n i n c h i l d r e n . The most r o b u s t i n d i c a n t s a r e more hand movements and l o n g e r r e a c t i o n t i m e s . S i n c e t h e i r n o n - r e s p o n d i n g o r m o n o s y l l a b i c r e s p o n d i n g " had t o be coded as " f a i l i n g " r e s p o n s e s anyway, i t was d e c i d e d t h a t t h e y w o u l d n o t be p r e s e n t e d w i t h t h e more d i f f i c u l t c y c l i c i n t e g r a t i o n i t e m s u n l e s s t h e y had succeeded a t t h e s i m p l e r , q u a s i - p r e r e q u i s i t e i t e m s . The i m p l e m e n t a t i o n o f t h i s p o l i c y ( a f t e r t h e f i r s t 3 t o 5 r e s p o n d e n t s i n each grade had been i n t e r v i e w e d ) made a marked d i f f e r e n c e i n t h e moods o f t h e c h i l d r e n l e a v i n g t h e i n t e r v i e w room. E s p e c i a l l y w i t h t h e grade 3 c h i l d r e n , t h e d i f f i c u l t c y c l i c i n t e g r a t i o n i t e m s l e d t o q u i t e despondent demeanours. None o f t h e c h i l d r e n a c t u a l l y began c r y i n g d u r i n g t h a t p a r t o f the i n t e r v i e w , b u t t h e r e seemed t o be l i t t l e j u s t i f i c a t i o n f o r b r i n g i n g them so c l o s e t o s u c h e m o t i o n s . 58 A r e c i p r o c a l p r o b l e m a r i s e s when a 14, 16, o r 18 y e a r o l d i s p r e s e n t e d w i t h a s e r i a t i o n t a s k . The tendency i s t o c o n c l u d e t h a t t h e i n t e r v i e w e r i s " p l a y i n g games" g i v e n t h e " c h i l d i s h " l e v e l o f t h e t a s k . I n p i l o t i n t e r v i e w s a d o l e s c e n t s tended t o e i t h e r become s u l l e n o r f l i p p a n t when p r e s e n t e d w i t h c o n c r e t e o p e r a t i o n a l t a s k s . E i t h e r r e s p o n s e i s u n d e s i r a b l e when r e s p o n d e n t s are f i n a l l y p r e s e n t e d w i t h problems t h a t do c h a l l e n g e t h e i r i n t e l l e c t s . I n v i e w o f t h i s , t h e o n l y c o n c r e t e s t a g e d t a s k p r e s e n t e d t o s t u d e n t s i n grade 9 o r h i g h e r was c l a s s i n c l u s i o n . E m p i r i c a l j u s t i f i c a t i o n f o r t h i s r e s i d e s i n t h e f i n d i n g t h a t i n grade 7, where a l l t a s k s were p r e s e n t e d , o n l y one o f t h e seven s t u d e n t s c l a s s i f i e d as f o r m a l o p e r a t i o n a l f a i l e d any c o n c r e t e t a s k . L i k e w i s e , among t h e f i f t e e n f o r m a l o p e r a t i o n a l grade 9 s t u d e n t s o n l y two f a i l e d two o f t h e t h r e e c l a s s i n c l u s i o n t a s k s . Thus, even though t h e remote p o s s i b i l i t y r e -mains t h a t a v e r y few grade 9 s t u d e n t s m i ght have f a i l e d even more c o n c r e t e s t a g e d t a s k s had such t a s k s been p r e s e n t e d , t h e b e n e f i t s i n terms o f r e s p o n d e n t i n t e r e s t and r a p p o r t seemed t o o u t w e i g h t h e c o s t s o f f o r e g o i n g t h a t i n f o r m a t i o n , ( i i ) Data S c o r i n g The c o n c r e t e and f o r m a l t a s k s were s c o r e d upon a d m i n i s t r a t i o n . The s c o r i n g c r i t e r i a f o r a l l t a s k s a r e d e s c r i b e d i n t h e a p p e n d i c i e s under the h e a d i n g f o r each t a s k . The s y s t e m i c t a s k s were s c o r e d l a t e r a c c o r d i n g t o t h e p r o c e d u r e s d e s c r i b e d i n Ap p e n d i x D. The j u d g e s o r " s c o r e r s " , as th e y w i l l be r e f e r r e d t o h e r e , s c o r e d o n l y t h e c y c l i c i n t e g r a t i o n i n t e r v i e w s . What f o l l o w s i s a b r i e f summary o f t h e t r a i n i n g and s c o r i n g p r o c e d u r e s . When a l l t h e d a t a had been c o l l e c t e d , t h e tape r e c o r d e d s e c t i o n s o f t h e i n t e r v i e w were t r a n s c r i b e d v e r b a t i m . The a u t h o r s c o r e d the c y c l i c t r a n s i t i v i t y t a s k s (see Ap p e n d i x D). The c y c l i c i n t e g r a t i o n s e c t i o n s o f t h e 59 t r a n s c r i p t s were t y p e w r i t t e n i n t o p r o t o c o l s and independently r a t e d by two female s c o r e r s ^ . I t was impossible to t e l l how long i t would take the t r a i n e e s to reach the 90% c r i t e r i o n of agreement that had been p r e v i o u s l y chosen as a goal of the t r a i n i n g . As i t turned out, the scorers agreed w i t h each other on 81.2% of the items by the time they had scored 1/5 of the data. They stayed between 83.2% and 86.4% f o r the remaining four f i f t h s and f o r a r e s c o r i n g of the f i r s t f i f t h . The o v e r a l l agreement r a t e f o r the l a t t e r s c o r i n g was 84.8%. A f t e r an i n i t i a l t r a i n i n g s e s s i o n on one spare grade 11 p r o t o c o l and two f i c t i c i o u s pro-t o c o l s , the scorers and author then met a f t e r each successive 20 p r o t o c o l s had been scored"*. W i t h i n each "batch" of 20 p r o t o c o l s the respondents were arranged i n a second random order. The order i n which the respondents had been i n t e r -viewed was only random w i t h i n grade l e v e l s . The order i n which the sc o r e r s received the p r o t o c o l s was random across the whole sample. There were s i x of these " r e l i a b i l i t y check" meetings at a r a t e of approximately two per week. At each of the r e l i a b i l i t y check meetings s p e c i f i c items of disagreement were discussed. The c r i t e r i o n f o r s e t t i n g f i n a l scores was a m a j o r i t y agreement. In 80% of the cases, however, spontaneous unanimity was achieved. 4.. One was a 25 year o l d teacher and the other was a 20 year o l d psychology major. They were p a i d from a d i s c r e t i o n a r y grant awarded by the Ed u c a t i o n a l Research I n s t i t u t e of B r i t i s h Columbia. The scorers made t h e i r r a t i n g s from the p r o t o c o l s . This added c l e r i c a l step had two advantages over having the scorers make t h e i r r a t i n g s d i r e c t l y from audio tapes themselves. F i r s t , i t reduced the p o s s i b i l i t y of a r t i f a c t u a l contamination of the scores on the b a s i s of v o i c e and speech cued i n f o r m a t i o n about the age of the respondents. The scorers might have been prone to a s s i g n lower scores to younger respondents and higher scores to o l d e r respondents on at l e a s t a p a r t i a l l y a p r i o r i b a s i s . The t r a n s c r i p t i o n of responses i n t o p r o t o c o l s was an attempt to minimize the opportunity f o r such a r t i f a c t s . Second, many of the audio tapes were flawed by high l e v e l s of background n o i s e . I f scorers had had to decode s i g n a l s against such high noise l e v e l s , t h e i r task would have been immensely more cumbersome and time consuming. 5 . One batch of p r o t o c o l s contained only 16 p r o t o c o l s s i n c e the t o t a l number of respondents was 4 short of 100. 60 I V . RESULTS As mentioned i n s e c t i o n F o f t h e i n t r o d u c t i o n , t h e h y p o t h e s e s o f t h i s s t u d y a r e a r r a n g e d ' s u c h t h a t a f a i l u r e t o r e j e c t e a r l i e r n u l l h y p o t h e s e s a u t o m a t i c a l l y i m p l i e s a f a i l u r e t o r e j e c t l a t e r n u l l h y p o t h e s e s . A t l e a s t one o f t h e two l e v e l s ( i . e . , m a c r o s c o p i c v s . m i c r o s c o p i c ) o f t h e f i r s t n u l l h y p o t h e s i s - m u s t be r e j e c t e d b e f o r e t h e c o n d i t i o n s needed t o t e s t t h e second h y p o t h e s i s a r e met. L i k e w i s e , i f t h e second n u l l h y p o t h e s i s were n o t r e j e c t e d t h e phenomenon d e a l t w i t h by t h e t h i r d h y p o t h e s i s w o u l d n o t have been o b s e r v e d . The t h i r d n u l l h y p o t h e s i s w o u l d t h e r e f o r e a u t o m a t i c a l l y r e m a i n u n r e j e c t e d . As i t t u r n s o u t , t h e phenomena p r e d i c t e d by t h e f i r s t and second h y p o t h e s e s were o b s e r v e d . I t was t h e r e f o r e p o s s i b l e t o p r o c e e d t h r o u g h t o t e s t i n g t h e t h i r d h y p o t h e s i s . The o r g a n i z a t i o n o f t h i s c h a p t e r r e f l e c t s t h e c o n t i n g e n t r e l a t i o n s h i p s among t h e t h r e e h y p o t h e s e s . The f i r s t h y p o t h e s i s i s r e v i e w e d and i t s q u a n t i t a t i v e i m p l i c a t i o n s a r e made e x p l i c i t . That i s f o l -lowed by t h e c o r r e s p o n d i n g q u a n t i t a t i v e a n a l y s e s . Then t h e second h y p o t h e s i s i s r e s t a t e d and t h e s t a t i s t i c a l a p p r o a c h e s most a p p r o p r i a t e f o r i t s q u a n t i t a -t i v e e v a l u a t i o n a r e d i s c u s s e d . A f t e r t h o s e s t a t i s t i c a l a n a l y s e s have been p r e s e n t e d t h e t h i r d h y p o t h e s i s i s r e v i e w e d . A g a i n , t h e s t a t i s t i c a l a p p r o a c h e s most s u i t a b l e f o r i t s e v a l u a t i o n a r e d i s c u s s e d and t h e r e s u l t s a r e p r e s e n t e d . The b a s i c d a t a i n t h i s s t u d y were dichotomous s c o r e s . Many a u t h o r s have commented upon t h e r e l a t i v e l y u n d e v e l o p e d s t a t e o f t h e s t a t i s t i c i a n s a r t w i t h r e s p e c t t o dichotomous d a t a and n o n - p a r a m e t r i c a n a l y s e s , e s p e c i a l l y f o r hypo-t h e s e s s u c h as t h o s e common i n d e v e l o p m e n t a l p s y c h o l o g y where o r d e r p r e d i c t i o n s a r e common ( e . g . , W o h l w i l l , 1973; Froman & H u b e r t , 1980). F o r t u n a t e l y , t h e r e l a t i v e c l a r i t y o f t h e r e s u l t s i n t h i s s t u d y c o u p l e d w i t h t h e o r d i n a l n a t u r e 6 1 o f t h e p r e d i c t i o n s make i t easy t o c i r c u m v e n t t h e d i f f i c u l t i e s posed by t h a t l a c u n a . T h i s i s a s i t u a t i o n i n w h i c h t h e dichotomous d a t a , t h e o r d i n a l p r e d i c -t i o n s , and t h e c l e a n c u t r e s u l t s make s o p h i s t i c a t e d s t a t i s t i c s and p a r a m e t r i c a n a l y s e s ( w h i c h a r e l a r g e l y u n a v a i l a b l e i n any c a s e ) i n a p p r o p r i a t e . The f i n d i n g s w i t h r e s p e c t t o t h e f i r s t h y p o t h e s i s i n c l u d e d p e c u l i a r i t i e s t h a t w a r r a n t e d more d e t a i l e d a t t e n t i o n . The c o m p o s i t e s c o r e s f o r t h e s y s t e m i c c o g n i t i v e o p e r a t i o n s were o f e x t r e m e l y d i v e r s e d i f f i c u l t y l e v e l s . T h e r e f o r e t h e y were decomposed i n t o t h e component s y s t e m i c s c o r e s and r e a n a l y s e d i n s e c t i o n B. S e c t i o n C c o n t a i n s t h e r e s u l t s f o r t h e second h y p o t h e s i s . S e c t i o n s D and E show t h e a n a l y s e s f o r h y p o t h e s e s t h r e e and f o u r r e s p e c t i v e l y . I n s e c t i o n F a l l o f t h e r e s u l t s a r e summarized. A. F i r s t H y p o t h e s i s w i t h Composite S y s t e m i c S c o r e s The b a s i c t h r u s t o f t h e f i r s t h y p o t h e s i s i s t h a t t h e c o g n i t i v e o p e r a t i o n s w i l l have t h e same r e l a t i o n s h i p s t o one a n o t h e r r e g a r d l e s s o f c o n t e n t domain. That i s , one need n o t d r a s t i c a l l y r e f o r m u l a t e P i a g e t i a n t h e o r y i n o r d e r t o examine c o g n i t i v e development i n t h e b i o - e c o l o g i c a l o r s o c i e t a l domains o f c o n t e n t . There w i l l s t i l l be a c o n c r e t e s t a g e and a p o s t - c o n c r e t e s t a g e . The c o g n i t i v e o p e r a t i o n s w i l l s t i l l be m a s t e r e d i n p r e t t y much t h e same s e q u e n t i a l o r d e r . More s p e c i f i c a l l y , t h e f i r s t h y p o t h e s i s makes two r e l a t e d p r e d i c t i o n s . One o f t h e s e p r e d i c t i o n s i s a more m a c r o s c o p i c v e r s i o n o f t h e o t h e r . The more m i c r o s c o p i c , o r f i n e g r a i n e d , p a r t p r e d i c t s t h a t t h e d i f f i c u l t y o r d e r i n g s o f c o g n i t i v e o p e r a t i o n s w i l l be t h e same a c r o s s domains ( i . e . , s e r i a t i o n , l i n e a r t r a n s i t i v i t y , l o g i c a l m u l t i p l i c a t i o n , c l a s s i n c l u s i o n , 62 c y c l i c t r a n s i t i v i t y * c y c l i c i n t e g r a t i o n ' ' ' ) . The more m a c r o s c o p i c v e r s i o n o f h y p o t h e s i s one complements t h e m i c r o s c o p i c v e r s i o n , i n a l l o w i n g f o r some m i s o r d e r i n g among t a s k s w i t h i n t h e same s t a g e a c r o s s domains w h i l e p r e d i c t i n g t h a t i n no domain w i l l t a s k s o f d i f f e r e n t s t a g e s be m i s o r d e r e d . S t a t e d i n a d i f f e r e n t way, t h e second o r more m i c r o s c o p i c v a r i a t i o n o f h y p o t h e s i s one p r e d i c t s t h a t , w h a t e v e r d i f f i c u l t y o r d e r i n g o f t a s k s may be e m p i r i c a l l y o b s e r v e d , a l l o f t h e r e s p o n d e n t s who s u c c e e d a t t h e l e a s t d i f f i c u l t p o s t c o n c r e t e t a s k w i l l a l s o have succeeded a t t h e most d i f f i c u l t c o n c r e t e s t a g e t a s k , b u t n o t v i c e v e r s a . The n u l l h y p o t h e s i s , a l s o . i n two p a r t s , s t a t e s (a) t h a t t h e d i f -f i c u l t y o r d e r i n g s o f the t a s k w i l l v a r y h a p h a z a r d l y a c r o s s domains, and (b) t h a t a l l t a s k s w i l l be o f t h e same s t a g e i n s o f a r as t h e r e w i l l be no s i g n i f i -c a n t d i s c o n t i n u i t i e s i n d i f f i c u l t y r a n k i n g s Between c o n c r e t e s t a g e t a s k s and p o s t - c o n c r e t e s t a g e t a s k s i n any domain, ( i ) S c a l o g r a m D i f f i c u l t y O r d e r i n g s The B a s i c d a t a needed t o o b t a i n d i f f i c u l t y o r d e r i n g a r e t h e f r e q u e n c i e s o f p a s s e s on each t a s k a c r o s s t h e whole sample. S c a l o g r a m a n a l y s i s (Guttman, 1950) y i e l d s d i f f i c u l t y o r d e r i n g s as a p r e l i m i n a r y s t e p i n g a u g i n g t h e Guttman s c a l e p r o p e r t i e s o f a s e t o f i t e m s ( i n t h i s c a s e t h e " i t e m s " a r e " t a s k s " ) . F i g u r e 1 shows t h e p e r c e n t a g e o f r e s p o n d e n t s f a i l i n g each t a s k . The t h r e e v e r t i c a l v e c t o r s c o r r e s p o n d t o t h e t h r e e c o n t e n t domains. The t a s k s f a l l i n g i n t h e upper r e g i o n o f t h e graph can Be s a i d t o Be more d i f f i c u l t t h a n t h o s e 1. S i n c e no p h y s i c a l domain v e r s i o n o f c y c l i c t r a n s i t i v i t y and c y c l i c i n -t e g r a t i o n e x i s t , t h e c o m p l e t e range o f t a s k s o n l y appeared i n t h e B i o l o g i c a l and s o c i e t a l c o n t e n t domains. However, s i n c e t h e s y s t e m i c c o g n i t i v e op-e r a t i o n s were p r e d i c t e d t o Be more d i f f i c u l t t h a n any o f t h e c o n c r e t e o p e r a t i o n a l t a s k s i t was supposed t h a t t h e y w o u l d Be a t l e a s t t h e same d i f f i c u l t y l e v e l as f o r m a l o p e r a t i o n a l t a s k s . T h e r e f o r e t h r e e f o r m a l o p e r a t i o n a l t a s k s appear i n t h e p h y s i c a l domain as r e f e r e n c e p o i n t s a g a i n s t w h i c h t h e d i f f i c u l t y o f t h e s y s t e m i c t a s k s c a n be gauged. 63 F i g u r e 1 KEY S c a l o g r a m d i f f i c u l t y o r d e r i n g s w i t h S = S e r i a t i o n c o m p o s i t e s y s t e m i c s c o r e s by domain. LT = L i n e a r T r a n s i t i v i t y LM = L o g i c a l M u l t i p l i c a t i o n C = C l a s s I n c l u s i o n Prob = P r o b a b i l i t y I s o = I s l o a t i o n o f V a r i a b l e s CV = C o m b i n a t i o n o f V a r i a b l e s CyTr = C y c l i c T r a n s i t i v i t y C y l h = C y c l i c I n t e g r a t i o n 100 9.0 • 80 r P e r c e n t a g e F a i l i n g ( D i f f i c u l t y ) s i c a l n 1 0 . n S o c i e t a l e c o l o g i c a l Domains 64 i n the lower r e g i o n . In f i g u r e 1 i t can be seen that the p r e d i c t e d d i f f i c u l t y o r d e r i n g of tasks was obtained i n the b i o - e c o l o g i c a l and s o c i e t a l domains. In the p h y s i c a l domain, however, c e r t a i n of the concrete o p e r a t i o n a l tasks were misordered. This was mainly a r e s u l t of the l i n e a r t r a n s i t i v i t y task being more d i f f i c u l t than the l o g i c a l m u l t i p l i c a t i o n and the c l a s s i n c l u s i o n t a s k s . The l a t t e r two were t i e d w i t h each other. The s e r i a t i o n tasks i n a l l domains were the e a s i e s t , so much so that there were no cases of f a i l u r e s at that c o g n i t i v e operation i n e i t h e r the p h y s i c a l or the b i o - e c o l o g i c a l domain. O v e r a l l , the tasks conformed to the p r e d i c t e d d i f f i c u l t y orderings across domains. The scalogram r e s u l t s a l s o provide p r e l i m i n a r y i n f o r m a t i o n r e l e v a n t to the macroscopic v e r s i o n of the f i r s t hypothesis. The macroscopic v e r s i o n amounted to a p r e d i c t i o n of s t a g e - l i k e d i s c o n t i n u i t i e s i n d i f f i c u l t y rankings w i t h i n each domain. The v i s u a l impression given by f i g u r e 1 i s that there are s t a g e - l i k e gaps and they appear i n every domain at approximately the same pl a c e s . The concrete o p e r a t i o n a l tasks a l l f a l l between the 0% to 18.8% f a i l u r e l e v e l . The formal o p e r a t i o n a l tasks span a range comparable to that covered by the concrete tasks (approx. 15 to 19 percentage p o i n t s ) . The two c y c l i c t r a n s i t i v i t y scores encompass the formal o p e r a t i o n a l scores and appear to be about the same di s t a n c e from the concrete scores as the formal scores are. The distance from the highest concrete task ( i . e . , c l a s s i n c l u s i o n , b i o -e c o l o g i c a l domain) to the lowest formal o p e r a t i o n a l task i s 21.8 percentage p o i n t s . The distance to the lowest systemic ( i . e . , c y c l i c t r a n s i t i v i t y , s o c i e t a l domain) task i s 17.7 percentage p o i n t s . Therefore the di s t a n c e that separates the most d i f f i c u l t concrete stage task from the l e a s t d i f f i c u l t post-concrete stage tasks i s approximately 17.7 to. 21.-8 -percentage p o i n t s ; That i s roughly the-same range covered 1' by a l l the: tasks i n a -single stage 65 ( i . e . , 15 t o 19 p e r c e n t a g e p o i n t s ) . On t h e f a c e o f i t , t h e n , i t a p p e a r s t h a t t h e r e a r e a t l e a s t two s e p a r a t e s t a g e s i n a l l domains, t h e c o n c r e t e and t h e p o s t - c o n c r e t e . These d a t a p r e d i s p o s e one t o r e j e c t t h e n u l l h y p o t h e s i s t h a t a l l t h e t a s k s a r e f r o m t h e same s t a g e . M o r e o ver, g i v e n t h e a s s u m p t i o n t h a t t h e d a t a do r e f l e c t two d i f f e r e n t s t a g e s , a " s t a g e s i z e d gap" between t a s k s can be e s t i m a t e d t o be a p p r o x i m a t e l y 17.7 t o 21.8 p e r c e n t a g e p o i n t s . W h i l e t h e c y c l i c t r a n s i t i v i t y t a s k s f a l l i n r o u g h l y the same d i f f i c u l t y r ange as t h e f o r m a l o p e r a t i o n a l t a s k s , t h e l e a s t d i f f i c u l t c y c l i c i n t e g r a t i o n t a s k was 21.8 p e r c e n t a g e p o i n t s more d i f f i c u l t t h a n t h e most d i f f i c u l t f o r m a l o p e r a t i o n a l t a s k . T h i s i s e x a c t l y t h e same d i s t a n c e as t h a t between t h e h i g h e s t c o n c r e t e t a s k and t h e l o w e s t f o r m a l t a s k . S i n c e a s t a g e s i z e d gap s e p a r a t e s t h e c y c l i c i n t e g r a t i o n t a s k s f r o m t h e b u l k o f t h e o t h e r p o s t -c o n c r e t e t a s k s , i t make sense t o i n q u i r e i n t o t h e p o s s i b i l i t y o f c y c l i c i n t e -g r a t i o n c o n s t i t u t i n g a p o s s i b l e f i f t h s t a g e o f c o g n i t i v e development, ( i i ) Guttman S t e p s The i n f o r m a t i o n p r e s e n t e d on f i g u r e 1 does n o t i n d i c a t e how much v a r i a n c e t h e r e was i n t h e d i f f i c u l t y l e v e l d a t a . I f t h e r e were no r e s p o n d e n t s v i o l a t i n g t h e mean o r d e r i n g , t h e n t h e i n c r e a s e i n d i f f i c u l t y f r o m one t a s k t o t h e n e x t most d i f f i c u l t t a s k i n t h e sequence w o u l d be c a l l e d a "Guttman s t e p . " Where the comparison.between two t a s k s forms a Guttman s t e p p r a c t i c a l l y a l l of-„ the r e s p o n d e n t s who p a s s e d t h e more d i f f i c u l t t a s k a l s o p a s s e d t h e l e s s d i f -f i c u l t t a s k b u t n o t n e a r l y as many o f t h o s e who p a s s e d t h e e a s i e r t a s k a l s o p a s s e d t h e h a r d e r t a s k . Non-Guttman s t e p s a r e c h a r a c t e r i z e d by v a r y i n g d e g r e e s o f e q u i v a l e n c e between t h e a d j a c e n t t a s k s i n terms of t h e p r o b a b i l i t y o f p a s s -i n g o r f a i l i n g e i t h e r . W i t h non-Guttman s t e p s t h e r e . w i l l t e n d t o be as many 66 respondents who passed the harder task but f a i l e d the e a s i e r one as v i c e versa. The macroscopic part of the f i r s t hypothesis p r e d i c t s that there should be non-Guttman steps between adjacent concrete stage t a s k s , a Guttman step between the most d i f f i c u l t concrete task and the l e a s t d i f f i c u l t post-concrete task, and non-Guttman steps between adjacent post-concrete t a s k s , ( i i i ) Converging Techniques There i s no one s t a t i s t i c which adequately informs us about the Guttman-l i k e nature of each step i n the d i f f i c u l t y o r d e r i n g . There are, however, s e v e r a l approaches which give p a r t i a l i n f o r m a t i o n . By usi n g a l l of these s t a t i s t i c s c o n j o i n t l y as d e s c r i p t i v e a i d s :'.enough r e l e v a n t i n f o r m a t i o n can be e x t r a c t e d to evaluate the second hypothesis. I t must be emphasized, however, that the nature of t h i s probing does not al l o w any s i g n i f i c a n c e t e s t i n g . The r e s u l t s are reported i n terms of degree of a s s o c i a t i o n or d i f f e r e n c e be-tween and among ta s k s . The hypothesis does not and cannot stand or f a l l on the r e s u l t s of any one of these s t a t i s t i c a l analyses. The f i n a l d e c i s i o n on the second hypothesis i s e n t i r e l y dependent upon the composite p i c t u r e pro-vided by these v a r i o u s d e s c r i p t i v e a i d s . The Guttman-like nature of the d i f f i c u l t y orderings i n each domain were examined by drawing together the r e s u l t s of s e v e r a l s t a t i s t i c s . Figure 1 , based as i t i s on percentages of respondents passing each task, has already provided some in f o r m a t i o n . Guttman's c o e f f i c i e n t of r e p r o d u c i b i l i t y f o r scalogram analyses c o n t r i b u t e s i n f o r m a t i o n about the Guttman s c a l e q u a l i t i e s of the whole sequence of tasks i n each domain. Looking at s p e c i f i c steps w i t h i n sequences, the frequencies and proport i o n s of respondents f o l l o w i n g or v i o l a t i n g the p r e d i c t e d p a s s / f a i l p a t t e r n are reported. Using t e s t s f o r the s i g n i f i c a n c e of d i f f e r e n c e s between p r o p o r t i o n s , z^ scores are obtained 67 which, used for d e s c r i p t i o n only, provide a more refined index of the Guttman nature of the r e l a t i o n s h i p between adjacent tasks. With each of the above mentioned s t a t i s t i c s there are strengths, weak-nesses and"general operating c h a r a c t e r i s t i c s which must be made e x p l i c i t . This i s undertaken as each of these s t a t i s t i c s i s introduced and brought to bear upon a p a r t i c u l a r hypothesis. Hopefully, t h i s s e r i a l presentation w i l l contribute to c l a r i t y by staying close to the data and avoiding a contextless debate about the pros and cons of various s t a t i s t i c a l a l t e r n a t i v e s , (iv) R e p r o d u c i b i l i t y C o e f f i c i e n t Guttman's c o e f f i c i e n t of r e p r o d u c i b i l i t y i s a s t a t i s t i c that gives information about the o v e r a l l Guttman-like q u a l i t i e s of an ordered set of items. I t gives no information about which steps i n the ordering are Guttman steps. Coombs, Dawes, and Tversky (1970) state that a r e p r o d u c i b i l i t y coef-f i c i e n t of 0.90 i s "good". T h e . r e p r o d u c i b i l i t y c o e f f i c i e n t f o r a l l of the tasks i n figure 1, ordered together i r r e s p e c t i v e of domain, i s 0.918. The c o e f f i c i e n t s by domain are (a) p h y s i c a l 0.958, (b) b i o l o g i c a l 0.942, and (c) s o c i a l 0.950. Therefore t h i s c r i t e r i o n t e l l s us that the observed task order-ings do, i n f a c t , c o nstitute Guttman scales. The problem i s that t h i s i s not p r e c i s e l y what we want to know. The huge Guttman step between the easiest s e r i a t i o n task and the most d i f f i c u l t c y c l i c i n t e g r a t i o n task contributes to the magnitude of the r e p r o d u c i b i l i t y c o e f f i c i e n t . The hypothesis under consider-ation does not deal with that huge Guttman step. I t deals only with steps between adjacent tasks. Therefore Guttman's c o e f f i c i e n t of r e p r o d u c i b i l i t y i s i n i t s e l f e s s e n t i a l l y i r r e l e v a n t f o r the present purposes. The c o e f f i c i e n t of r e p r o d u c i b i l i t y , however, can be combined with the c o e f f i c i e n t of minimum marginal r e p r o d u c i b i l i t y to produce a more us e f u l index c a l l e d "the c o e f f i c i e n t of s c a l a b i l i t y " . The c o e f f i c i e n t of minimum marginal r e p r o d u c i b i l i t y (MMR) i s the minimum c o e f f i c i e n t of r e p r o d u c i b i l i t y that could 68 have been o b t a i n e d g i v e n t h e p r o p o r t i o n o f r e s p o n d e n t s p a s s i n g and f a i l i n g e ach o f t h e i t e m s . I t i s a f f e c t e d by c e i l i n g e f f e c t s - and extreme skews on i n d i v i d u a l i t e m s . When t h e MMR i s s u b t r a c t e d from'one ' ( i . e . 1-MMR = the " r e c i p r o c a l " o f t h e MMR) t h e r e s u l t i s a measure o f t h e range i n w h i c h t h e c o e f f i c i e n t o f r e p r o d u c i b i l i t y was f r e e t o v a r y . When t h e MMR i s s u b t r a c t e d f r o m t h e c o e f f i c i e n t o f r e p r o d u c i b i l i t y t h e r e s u l t i s a measure o f t h e " p e r c e n t improvement" i n p r e d i c t i o n t h a t t h e o b t a i n e d p a t t e r n y i e l d s o v e r t h e MMR base l e v e l o f p r o d i c t i o n . The c o e f f i c i e n t o f s c a l a b i l i t y u ses b o t h o f t h e s e mea-s u r e s . D i v i d i n g t h e p e r c e n t improvement by t h e r e c i p r o c a l o f t h e MMR y i e l d s t h e c o e f f i c i e n t o f s c a l a b i l i t y . The c o e f f i c i e n t o f s c a l a b i l i t y " s h o u l d be w e l l above .6 i f t h e s c a l e i s t r u l y u n d i m e n s i o n a l and' c u m u l a t i v e ( N i e , H u l l , J e n k i n s , S t e i n b r e n n e r , and B e n t , 1975, p. 5 3 3 ) " . The s c a l a b i l i t y c o e f f i c i e n t , f o r a l l o f t h e t a s k s i n f i g u r e 1, o r d e r e d t o g e t h e r i r r e s p e c t i v e o f domain i s 0.585. T h i s i s as one would e x p e c t c o n s i d e r -i n g t h a t t h e s e a r e t h r e e domains c o r r e s p o n d i n g t o t h r e e c o r r e l a t e d b u t d i s t i n c t d i m e n s i o n s i n t h e . d a t a . The s c a l a b i l i t y c o e f f i c i e n t s by domain a r e (a) p h y s i c a l 0.838, (b) b i o - e c o l o g i c a l 0.696, and (c) s o c i e t a l 0.714. T h i s c r i t e r i o n t e l l s us t h a t , W i t h i n domains, t h e t a s k s may fo r m u n d i m e n s i o n a l , c u m u l a t i v e s c a l e s . We do n o t know t h a t t h e y do form u n d i m e n s i o n a l , c u m u l a t i v e s c a l e s b u t one f a l s i f i c a t i o n t e s t has been p a s s e d . Two o t h e r d e s c r i p t i v e s t a t i s t i c s a r e used t o p r o v i d e i n f o r m a t i o n t h a t i s r e l e v a n t t o t h e second p a r t o f t h e f i r s t h y p o t h e s i s . F i r s t , i n s u b s e c t i o n ( v ) , we examine t h e f r e q u e n c i e s and p r o p o r t i o n s o f r e s p o n d e n t s f a i l i n g t h e e a s i e r t a s k o f a p a i r w h i l e p a s s i n g t h e supposed h a r d e r t a s k . Second, i n s u b s e c t i o n ( v i ) , we l o o k a t t h e d i f f e r e n c e s between t h e p r o p o r t i o n s o f 69 r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t h e o t h e r . P a r t i c u l a r s c o n c e r n i n g t h e use o f each s t a t i s t i c a r e d i s c u s s e d when t h e s t a t i s t i c i s f i r s t i n t r o d u c e d . (v) F r e q u e n c i e s and P r o p o r t i o n s The i n f o r m a t i o n p r e s e n t e d i n f i g u r e 1 s t r o n g l y s u g g e s t s t h a t t h e w e l l documented d i s c o n t i n u i t y between c o n c r e t e o p e r a t i o n a l t a s k s and f o r m a l o p e r a t i o n a l t a s k s i n t h e p h y s i c a l domain i s p a r a l l e l e d by a s i m i l a r gap be-tween c o n c r e t e t a s k s and s y s t e m i c t a s k s i n t h e b i o - e c o l o g i c a l and s o c i e t a l domains. What rema i n s t o be shown i s t h a t t h e s e l a t t e r two s t a g e - l i k e gaps a r e as c l e a n c u t as t h e gap between t h e c o n c r e t e and t h e f o r m a l t a s k s . I f t h e b i o - e c o l o g i c a l and s o c i e t a l s t e p s f r o m c o n c r e t e t o p o s t - c o n c r e t e s t a g e s a r e l e s s Guttman i n c h a r a c t e r t h a n t h e c o r r e s p o n d i n g p h y s i c a l domain s t e p t h e n t h e p r e d i c t i o n s o f p a r a l l e l s e q u e n c i n g a c r o s s domains a r e l e s s t h a n f u l l y s u p p o r t e d . T a b l e I i s p r e s e n t e d i n t h r e e p a r t s , , one f o r each c o n t e n t domain. The t a b l e shows t h e f r e q u e n c i e s o f r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t h e o t h e r . T h i s i n c l u d e s p a i r s t h a t a r e a d j a c e n t i n t h e d i f f i c u l t y o r d e r i n g s . The h i g h e s t r a n k e d (most d i f f i c u l t ) c o n c r e t e o p e r a t i o n a l t a s k t o t h e p h y s i c a l domain ( t a b l e I , p a r t A) was l i n e a r t r a n s i t i v i t y . I t i s a d j a c e n t t o t h e l e a s t d i f f i c u l t f o r m a l o p e r a t i o n a l t a s k ( i . e . p r o b a b i l i t y ) . Note t h a t as one r e a d s f r o m l e f t t o r i g h t i t i s a t t h e j u n c t u r e between t h e s e two t a s k s where t h e f a i l u r e r a t e i n c r e a s e s d r a m a t i c a l l y f o r t h e group o f r e s p o n d e n t s who p a s s e d each o f t h e s u c c e s s i v e c o n c r e t e o p e r a t i o n a l t a s k s ( i . e . t h e top f o u r r o w s ) . By c o n t r a s t , t h e b o t t o m t h r e e rows show d a t a f o r r e s p o n d e n t s who had p a s s e d f o r m a l o p e r a t i o n a l t a s k s . When one r e a d s t h e f r e -quency d a t a f r o m l e f t t o r i g h t f o r t h e s e r e s p o n d e n t s , t h e r e i s no d r a m a t i c Table I Frequencies and proportions of respondents passing one task of a p a i r while f a i l i n g the other. Part A: Physical Domain Fa i l e d Task Passed Total Logical Class Linear , M 1 . I s o l a t i o n Combination Task Passes M u l t i p l i c a t i o n Inclusion T r a n s i t i v i t y ^ r o t , a b : L - L : L t y o f v a r i a b l e s of Variables S e r i a t i o n 96 5 .052 5 .052 12 .125 39 .406 44 .458 53 .552 L o g i c a l M u l t i p l i c a t i o n 91 4 .044 11 .121 34 .374 39 .429 48 .527 Class Inclusion 91 4 .044 10 .110 34 .374 39 .429 49 .538 Linear T r a n s i t i v i t y 84 4 .048 3 .036 28 .333 32 .381 44 .524 P r o b a b i l i t y 57 0 .000 0 .000 1 .018 7 .123 18 .316 I s o l a t i o n of Variables 52 0 .000 0 .000 0 .000 2 .038 15 .288 Combination of Variables 43 0 .000 1 .023 3 .070 4 .093 6 .140 T a b l e I ( c o n t ' d ) P a r t B: B i o - e c o l o g i c a l Domain F a i l e d Task P a s s e d Task T o t a l P a s s e s L i n e a r T r a n s i t i v i t y L o g i c a l M u l t i p l i c a t i o n C l a s s I n c l u s i o n C y c l i c T r a n s i t i v i t y C y c l i c I n t e g r a t : S e r i a t i o n 96 8 .083 9 '.092 18 .188 61 .635 74 .771 L i n e a r T r a n s i t i v i t y 88 7 .080 13 .148 53 .602 66 .750 L o g i c a l M u l t i p l i c a t i o n 87 6 .069 15 .172 52 .598 65 .747 C l a s s I n c l u s i o n : 7 8 3 .038 6 .077 43 .551 57 .731 C y c l i c T r a n s i t i v i t y 35 0 .000 0 .000 0 .000 20 .571 C y c l i c I n t e g r a t i o n 22 0 .000 0 .000 1 .045 7 .318 I—1 Table I (cont'd) Part C: S o c i e t a l Domain Fai l e d Task Passed Task Total Passes Linear T r a n s i t i v i t y L o g i c a l M u l t i p l i c a t i o n Class Inclusion C y c l i c T r a n s i t i v i t y C y c l i c Integrat: S e r i a t i o n 92 8 .087 ... • 9 .098 14 .152 32 .348 82 .891 Linear M u l t i p l i c a t i o n 85 7 .082 10 .118 27 .318 75 .882 Lo g i c a l M u l t i p l i c a t i o n 84 6 .071 11 .131 26 .310 74 .881 Class Inclusion 80 5 .063 7 .087 26 .325 70 .875 C y c l i c T r a n s i t i v i t y 61 3 .049 3 .049 7 .115 51 .836 C y c l i c Integration 10 0 .000 0 .000 0 .000 0 .000 73 i n c r e a s e i n f a i l u r e f r e q u e n c i e s as t h e c o n c r e t e t o p o s t - c o n c r e t e j u n c t u r e i s c r o s s e d . T h i s p a t t e r n r e f l e c t s t h e w e l l documented d i s c o n t i n u i t y between modes o f c o g n i t i v e o r g a n i z a t i o n i n t h e c o n c r e t e o p e r a t i o n a l s t a g e v e r s u s t h e f o r m a l o p e r a t i o n a l s t a g e . P a r t s B and C o f t a b l e 1 i n d i c a t e t h a t t h i s p a t t e r n i s r e p l i c a t e d w i t h t h e n o n - t r a d i t i o n a l c o n t e n t and t h e s y s t e m i c p o s t - c o n c r e t e o p e r a t i o n s . The b i o - e c o l o g i c a l domain f r e q u e n c i e s a r e shown on p a r t B o f t a b l e 1. The c o n c r e t e t o p o s t - c o n c r e t e d i s c o n t i n u i t y i n f a i l u r e r a t e s i s r e p l i c a t e d h e r e . I n f a c t , i t i s even more pronounced. I n t h e p h y s i c a l domain ( t a b l e I , p a r t A) t h e f a i l u r e f r e q u e n c y f o r t h e e a s i e s t f o r m a l t a s k was 27 r e s p o n d e n t s h i g h e r t h a n f o r t h e h a r d e s t c o n c r e t e t a s k . I n t h e b i o - e c o l o g i c a l domain ( t a b l e I , p a r t B) however, t h e e a s i e s t p o s t - c o n c r e t e t a s k i s 43 r e s p o n d e n t s more d i f f i c u l t t h a n t h e h a r d e s t c o n c r e t e t a s k . T h i s r a t e d r o p s c o n s i d e r a b l y i n t h e s o c i e t a l domain ( t a b l e I , p a r t 0) t o a d i f f e r e n c e o f 19 r e s p o n d e n t s . The r e a s o n f o r t h i s a t t e n u a t i o n o f t h e between s t a g e gap seems t o have so m e t h i n g t o do w i t h one t a s k , t h e s o c i e t a l c y c l i c t r a n s i t i v i t y task.. The s o c i e t a l c y c l i c t r a n s i t i v i t y f a i l u r e r a t e s a r e c l o s e r t o t h o s e f o r c o n c r e t e t a s k s t h a n t o t h o s e f o r t h e s o c i e t a l c y c l i c i n t e g r a t i o n t a s k . The s o c i e t a l c y c l i c t r a n s i t i v i t y t a s k was a l w a y s p r e s e n t e d a f t e r t h e b i o - e c o l o g i c a l v e r s i o n o f t h e same t a s k . P e r h a p s t h e c y c l i c t r a n s i t i v i t y o p e r a t i o n s a r e p a r t i c u l a r l y s u s c e p t i b l e t o p r a c t i c e e f f e c t s . P e r h a p s one o f t h e components o f c y c l i c t r a n s i t i v i t y i s a c t u a l l y a c o n c r e t e s t a g e o p e r a t i o n . I n s e c t i o n B o f t h i s c h a p t e r , t h a t p o s s i b i l i t y w i l l be e x p l o r e d w i t h an e x a m i n a t i o n o f t h e p e r f o r m a n c e s o f t h e components o f t h e s y s t e m i c o p e r a t i o n s . The o v e r a l l i m p r e s s i o n g i v e n by a l e f t t o r i g h t r e a d i n g o f t h e f r e q u e n c y t a b l e s i s t h a t t h e s t a g e - l i k e d i s c o n t i n u i t i e s i n d i f f i c u l t y l e v e l s o f t a s k s 74 a r e found a c r o s s a l l domains. The s o c i e t a l c y c l i c t r a n s i t i v i t y t a s k seems t o be a somewhat i n t e r m e d i a t e c a s e b u t o v e r a l l i t a p p e a r s t h a t t h e P i a g e t i a n n o t i o n s o f s t a g e s c a n s a f e l y be e x t e n d e d t o t h e b i o - e c o l o g i c a l and t h e s o c i e t a l c o n t e n t domains. On a l l t h r e e p a r t s o f t a b l e I t h e r e i s a; d i a g o n a l o f b l a n k c e l l s r u n n i n g f r o m t h e t o p l e f t t o t h e b o t t o m r i g h t . The e n t r i e s below t h i s d i a g o n a l r e p r e s e n t f r e q u e n c i e s \ o f c a s e s where r e s p o n d e n t s p a s s e d t h e h a r d e r t a s k o f t h e p a i r b u t f a i l e d t h e e a s i e r one. These a r e c a s e s o f non-Guttman p a t t e r n s . I n t h e p h y s i c a l domain t h e c e l l s a t t h e i n t e r s e c t i o n o f p a s s e d f o r m a l t a s k s and f a i l e d c o n c r e t e t a s k s have t h e l o w e s t f r e q u e n c i e s . T h i s i n d i c a t e s a Guttman s t e p between c o n c r e t e o p e r a t i o n s and f o r m a l o p e r a t i o n s . The f r e q u e n -c i e s o f non-Guttman c a s e s i s h i g h e r f o r t a s k s o f t h e same s t a g e . I n o t h e r words, i t i s more p r o b a b l e t h a t a r e s p o n d e n t w o u l d p a s s a h a r d e r c o n c r e t e t a s k , f o r example, w h i l e f a i l i n g an e a s i e r one t h a n i t i s t h a t he o r she w o u l d p a s s a f o r m a l t a s k and f a i l a c o n c r e t e t a s k . L i k e w i s e , t h e r e were more c a s e s o f non-Guttman p e r f o r m a n c e among th e f o r m a l t a s k s when p a i r e d w i t h each o t h e r . L o o k i n g a c r o s s domains, a g a i n , we see t h a t t h e p a t t e r n f o u n d w i t h t r a d i t i o n a l P i a g e t i a n t a s k c o n t e n t s i s r e p e a t e d w i t h . b i o - e c o l o g i c a l c o n t e n t s ( p a r t B) and, t o a l e s s e r e x t e n t , w i t h s o c i e t a l c o n t e n t s ( p a r t C ) . I n t h e s o c i e t a l domain t h e c y c l i c i n t e g r a t i o n t a s k shows t h e s t a g e - l i k e d i s c o n t i n u i t y more c l e a r l y t h a n does t h e c y c l i c t r a n s i t i v i t y t a s k . A g a i n , t h e a n a l y s i s o f t h e d a t a w i t h t h e s y s t e m i c s c o r e s grouped by components i s i n t e n d e d t o h e l p c l a r i f y t h e i n t e r p r e t a t i o n o f t h i s f i n d i n g . The p r o p o r t i o n s p r e s e n t e d i n t a b l e I show th e same p a t t e r n o f r e s u l t s as t h e f r e q u e n c i e s . There a r e d i s c o n t i n u i t i e s i n d i f f i c u l t y l e v e l s a c r o s s s t a g e s i n a l l domains and i n a l l domains t h e e v i d e n c e f o r Guttman s t e p s i s 75 s t r o n g e r a c r o s s s t a g e s t h a n w i t h i n s t a g e s . The advantage o f c o n s i d e r i n g p r o p o r t i o n s o v e r f r e q u e n c i e s i s t h a t t h e p r o p o r t i o n s t a k e i n t o a c c o u n t how many r e s p o n d e n t s p a s s e d t h e f i r s t t a s k o f t h e p a i r b e i n g c o n s i d e r e d . T h i s f a c i l i t a t e s t h e c o m p a r i s o n o f p a i r s . The p r o p o r t i o n s a r e i n c l u d e d i n t a b l e I m a i n l y f o r t h e i r r e l e v a n c e t o t h e a n a l y s e s p r e s e n t e d i n t h e n e x t s u b s e c t i o n where t h e d i f f e r e n c e s between p r o p o r t i o n s a r e examined ( t a b l e I I ) . ( v i ) Z S c o r e s f o r P r o p o r t i o n s Thus f a r Guttman s t e p s have been d i s c u s s e d i n g e n e r a l terms. I n t h i s s e c t i o n an a t t e m p t i s made t o g i v e some q u a n t i t a t i v e d e f i n i t i o n o f t h e con-c e p t so f a r as i s p o s s i b l e . A t t h e same t i m e one more s t a t i s t i c a l a p p r o a c h i s b r o u g h t t o b e a r upon t h e p a r t o f t h e f i r s t h y p o t h e s i s d e a l i n g w i t h a c r o s s domain p a t t e r n s i n d i f f i c u l t y g r o u p i n g s . By u s i n g p r o p o r t i o n s i t i s p o s s i b l e t o t a k e i n t o a c c o u n t t h e v a r i a b i l i t y i n t h e number o f r e s p o n d e n t s p a s s i n g t h e " p a s s e d " member o f each "pass; A / f a i l B " p a i r o f . t a s k s . T h i s a l l o w s f o r t h e i n f o r m a t i v e c o m p a r i s o n o f t h e "pass.••"A/fail B" p a i r w i t h t h e "pas s B / f a i l A" p a i r . I t must be r e i t e r a t e d , however, t h a t no s i g n i f i c a n c e t e s t i n g i s p o s s i b l e . These s t a t i s t i c s a r e p r e s e n t e d f o r p u r e l y d e s c r i p t i v e p u r p o s e s . The c l o s e s t we can come t o s i g n i f i c a n c e t e s t i n g i s t o s e t out c r i t e r i a f o r u n e q u i v o c a l c a s e s o f a Guttman s t e p and a non-Guttman s t e p . I n ambiguous c a s e s the s t a t i s t i c s a r e r e p o r t e d f o r t h e sake o f c o m p l e t e n e s s b u t no a t t e m p t w i l l be made t o use t h o s e c a s e s i n d e t e r m i n i n g t h e f a t e o f t h e h y p o t h e s e s . The degree t o w h i c h a s t e p i s a Guttman s t e p can be i n d e x e d by z s c o r e s p r o d u c e d by t e s t s o f s i g n i f i c a n c e between p r o p o r t i o n s o f r e s p o n d e n t s p a s s i n g o r f a i l i n g o r d i n a l l y a d j a c e n t t a s k s w i t h i n domains. The f o r m u l a f o r t h e z: s c o r e s ( B r u n i n g & K i r i t z , 1 9 6 8 ) has t h e d i f f e r e n c e between t h e two p r o p o r t i o n s b e i n g d i v i d e d by t h e s t a n d a r d e r r o r o f t h e d i f f e r e n c e . The z s c o r e s compare r a t e s o f n o n - d i s c o n f i r m a t i o n a g a i n s t r a t e s o f ' d i s c o n f i r m a t i o n f o r b o t h t a s k s . They t a k e i n t o a c c o u n t t h e number o f r e s p o n d e n t s p a s s i n g each t a s k o f a, p a i r r e g a r d l e s s o f p e r f o r m a n c e on t h e o t h e r t a s k . I f A and B a r e two a d j a c e n t t a s k s , t h e n t h e s t e p from A ( t h e e a s i e r t a s k ) t o B. ( t h e more d i f f i c u l t t a s k ) would n o t be a Guttman s t e p i f t h e p r o p o r t i o n o f r e s p o n d e n t s s i m u l t a n e o u s l y p a s s i n g A w h i l e f a i l i n g B were much t h e same as t h e p r o p o r t i o n p a s s i n g B w h i l e f a i l i n g A. The s t e p would be a Guttman s t e p i f t h e p r o p o r t i o n p a s s i n g A w h i l e f a i l i n g B were much g r e a t e r t h a n t h e c o n v e r s e p r o p o r t i o n . Those who p a s s e d B w o u l d have a l s o p a s s e d A, n o t f a i l e d i t , because A w o u l d be e a s i e r t h a n B f o r e v e r y o n e . A c e r t a i n amount o f e r r o r must, o f c o u r s e , be a l l o w e d . The q u e s t i o n i s , how much? There a r e no c o n v e n t i o n a l c r i t e r i a f o r d e c i d i n g when a z s c o r e does o r does n o t r e f l e c t a Guttman s t e p . A l s o , h a v i n g d e c i d e d t h a t s i g n i f i c a n c e t e s t i n g w o u l d be i n a p p r o p r i a t e h e r e , i t w o u l d be i n a p p r o p r i a t e t o r e t r e a t t o t h e t r a d i t i o n a l c r i t e r i o n o f a 95% c o n f i d e n c e i n t e r v a l . I n s t e a d , a v a i l a b l e t h e o r e t i c a l c r i t e r i a w i l l be a p p l i e d . On t h e b a s i s o f w e l l a c c e p t e d t h e o r e t i c a l s t a t e m e n t s backed up by y e a r s o f r e s e a r c h , i t can be s a f e l y assumed t h a t t h e s t e p f r o m t h e most d i f f i c u l t c o n c r e t e o p e r a t i o n a l t a s k t o t h e l e a s t d i f f i c u l t f o r m a l o p e r a t i o n a l t a s k i s a Guttman s t e p . I f i t i s n o t a s t a t i s t i c a l l y p e r f e c t Guttman s t e p , i t i s a t l e a s t as G u t t m a n - l i k e as i t needs t o be f o r t h e p u r p o s e o f i n d e x i n g a s t a g e - l i k e d i s c o n t i n u i t y i n d i f f i c u l t y l e v e l s f o r t h e t a s k s a d m i n i s t e r e d t o t h e p r e s e n t sample o f r e s p o n d e n t s . The l e a s t d i f f i c u l t f o r m a l o p e r a t i o n a l t a s k was t h e p r o b a b i l i t y t a s k . The most d i f f i c u l t c o n c r e t e o p e r a t i o n a l t a s k was t h e c l a s s i n c l u s i o n t a s k i n t h e b i o - e c o l o g i c a l domain. The p r o p o r t i o n o f r e s p o n d e n t s p a s s i n g p r o b a b i l i t y w h i l e f a i l i n g b i o - e c o l o g i c a l c l a s s i n c l u s i o n was 0.053. The p r o p o r t i o n ' p a s s i n g b i o - e c o l o g i c a l c l a s s i n c l u s i o n w h i l e f a i l i n g p r o b a b i l i t y was 0.308. The d i f f e r e n c e between t h e s e -two p r o p o r t i o n s ( B r u n i n g and K i n t z , 1968, p.199) was z = 5.822. I t m i g h t be a r g u e d , however, t h a t t h i s z u n d e r e s t i m a t e s t h e s i z e o f t h e d i f f e r e n c e . The b i o - e c o l o g i c a l c o n t e n t m ight have added t o t h e d i f f i c u l t y o f t h e c l a s s i n c l u -s i o n t a s k . I n t h a t c a s e f i g u r a t i v e f a c t o r s a l o n e w o u l d be l e a d i n g us t o deem some gaps as s t a g e - l i k e o r G u t t m a n - l i k e , T h e r e f o r e a more s t r i n g e n t c r i t e r i o n was a d o p t e d . I n s t e a d o f t a k i n g t h e d i f f e r e n c e between t h e p r o p o r t i o n p a s s i n g and f a i l i n g t h e p r o b a b i l i t y t a s k and t h e h i g h e s t c o n c r e t e t a s k f r o m any o f t h e t h r e e domains, i t was d e c i d e d t o r e p l a c e t h e l a t t e r t a s k w i t h t h e h i g h e s t c o n -c r e t e t a s k i n t h e p h y s i c a l domain o n l y . That was t h e p h y s i c a l domain l i n e a r t r a n s i t i v i t y t a s k . T h i s r e s t r i c t i o n t o p h y s i c a l domain t a s k s i s a l s o more i n a c c o r d w i t h t h e s u p p o r t i n g t h e o r y and r e s e a r c h t h a t j u s t i f y c h o o s i n g the con ^ c r e t e t o f o r m a l d i f f e r e n c e as an example o f an u n e q u i v o c a l Guttman s t e p . The r e s e a r c h was l a r g e l y b a s e d on t a s k s c o n t a i n i n g p h y s i c a l c o n t e n t . The p r o p o r t i o n o f r e s p o n d e n t s p a s s i n g p r o b a b i l i t y w h i l e f a i l i n g p h y s i c a l l i n e a r t r a n s i t i v i t y was 0.018 (see t a b l e I , p a r t A ) . The p r o p o r t i o n p a s s i n g l i n e a r t r a n s i t i v i t y w h i l e f a i l i n g p r o b a b i l i t y was 0.333. The d i f f e r e n c e between t h e s e p r o p o r t i o n s was z = 7.663. A l l z s c o r e s t h a t a r e e q u a l t o o r g r e a t e r 2 t h a n + 7.663 w i l l c o n s e q u e n t l y be t a k e n t o be u n e q u i v o c a l Guttman s t e p s . A t t h e o t h e r end, t h e r e i s a need f o r an u n e q u i v o c a l example of a non-Guttman s t e p . One p o s s i b l e c r i t e r i o n m i g ht be b a s e d on t h e a s s u m p t i o n t h a t t h e s t e p between t a s k s o f t h e same s t a g e a r e non-Guttman s t e p s . G i v e n t h a t a s s u m p t i o n , one m ight use t h e a v e r a g e z f o r d i f f e r e n c e s between a d j a c e n t : t a s k s w i t h i n s t a g e s as t h e c r i t e r i o n f o r a non-Guttman s t e p . That w o u l d p r o -b a b l y be a f a i r e s t i m a t e b u t s i n c e t h e a i m i s t o have an u n e q u i v o c a l c r i t e r i o n , 2. S i n c e t h e o l d e r r e s p o n d e n t s d i d n o t r e c e i v e a l l c o n c r e t e t a s k s and t h e younger ones d i d n o t r e c e i v e a l l s y s t e m i c t a s k s , t h i s c r i t e r i o n i s c o n -s e r v a t i v e l y b i a s e d . The grade 7 s t u d e n t s were g i v e n a l l t a s k s . The c r i t e r i o n z f o r a Guttman s t e p c a l c u l a t e d on t h e i r d a t a a l o n e i s z = 1.214. The c r i -t e r i o n o f z = 7.663, t h e r e f o r e , i s v e r y s t r i n g e n t . -7 8 a more stringent c r i t e r i o n would be desi r a b l e . A second p o s s i b i l i t y would be to take the z f o r the smallest step within a stage. In.the p h y s i c a l domain the smallest step i s between l o g i c a l m u l t i p l i c a t i o n and c l a s s i n c l u s i o n . In f a c t , these two tasks were t i e d i n terms of d i f f i c u l t y l e v e l . That means that the smallest step i n the p h y s i c a l domain was no step at a l l . This seems to be the most unequivocal example of a non-Guttman step that one could expect to f i n d . I t i s not only a non-Guttman step-,' i t i s a non-step. The proportion of respondents passing l o g i c a l m u l t i p l i c a t i o n while f a i l i n g c l a s s i n c l u s i o n was 0 . 0 4 4 . The same proportion of respondents passed class i n c l u s i o n while f a i l i n g l o g i c a l m u l t i p l i c a t i o n . • The z score f o r the difference between these proportions was z = 2 . 3 8 0 . Therefore, z scores equal to or l e s s than 2 . 3 8 0 are taken to be-unequivocal cases'of non-Guttman steps. Again, the intermed-i a t e scores (between 2 . 3 8 0 and 7 . 6 6 3 ) are categorized as ambiguous cases ("?") and l e f t at that. Table II shows the z scores f o r a l l the steps by domain of content.-» These are on the diagonals. For the standard domain the only unequivocally Guttman step i s between the concrete tasks and the formal tasks. Within each of those stages there i s one clear non-Guttman step and one ambiguous case. In the b i o l o g i c a l domain c l e a r Guttman steps separate the concrete tasks from a l l the systemic tasks. There i s a non-Guttman step between l i n e a r trans-i t i v i t y and l o g i c a l m u l t i p l i c a t i o n . The other steps are ambiguous. In the s o c i e t a l domain the diagonal contains two non-Guttman steps between concrete stage tasks and one ambiguous case. The c y c l i c t r a n s i t i v i t y task i s only an ambiguous step apart from any of the concrete tasks except the easiest one ( i . e . s e r i a t i o n ) . The c y c l i c i n t e g r a t i o n task was a Guttman step more d i f f i c u l t than a l l the other tasks i n the s o c i e t a l domain including the c y c l i c trans-i t i v i t y task. T a b l e I I Z s c o r e s f o r d i f f e r e n c e s between p r o p o r t i o n o f r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t h e o t h e r . P a r t A: P h y s i c a l Domain L e s s D i f f i c u l t Task o f P a i r More D i f f i c u l t T a s k o f P a i r C l a s s I n c l u s i o n S e r i a t i o n * L o g i c a l M u l t i p l i c a t i o n 2.380 (NC) C l a s s L i n e a r I n c l u s i o n T r a n s i t i v i t y P r o b a b i l i t y I n s o l a t i o n o f V a r i a b l e s L i n e a r T r a n s i t i v i t y - 2.489 (?) 2.698 (?) P r o b a b i l i t y - 9.396 (G) 9.396 (G) 7.663 (G) I s o l a t i o n o f V a r i a b l e s -10.356 (G) 10.356 (G) 9.148 (G) 2.315 (NG) C o m b i n a t i o n o f V a r i a b l e s -12.230 (G) 11.451 (G) 9.126 (G) 4.064 (?) 2.545 (?) * No v a r i a n c e on t h i s v a r i a b l e NG = Non-Guttman s t e p (*2.380) G = Guttman s t e p (^7.663) ? = ambiguous s t e p (between 2.380 and 7.663) VO T a b l e I I ( c o n t ' d ) P a r t B: B i o - e c o l o g i c a l Domain L e s s D i f f i c u l t Task o f P a i r More D i f f i c u l t S e r i a t i o n * L i n e a r L o g i c a l C l a s s C y c l i c Task o f P a i r e o n T r a n s i t i v i t y M u l t i p l i c a t i o n I n c l u s i o n T r a n s i t i v i t y L o g i c a l 0.378 M u l t i p l i c a t i o n (NG) C l a s s 3.488 2.653 I n c l u s i o n (?) (?) C y c l i c . 13.648 13.463 11.783 T r a n s i t i v i t y CG) CG) (G) C y c l i c I n t e g r a t i o n 18.166 (G) 17.946 13.985 2.813 CG) CG) (?) T a b l e I I ( c o n t ' d ) P a r t C: S o c i e t a l Domain L e s s D i f f i c u l t Task o f P a i r More D i f f i c u l t L i n e a r L o g i c a l Task o f P a i r o e r i a c x o n T r a n s i t i v i t y M u l t i p l i c a L i n e a r 3.316 T r a n s i t i v i t y (?) L o g i c a l 3.604 0.377 M u l t i p l i c a t i o n (?) (NG) C l a s s 4 . 2 5 9 1 .758 1 .265 I n c l u s i o n (?) (NG) (NG) C y c l i c 8.317 6.319 6.142 T r a n s i t i v i t y (G) (?) (?) C y c l i c 28.921 2 6 . 6 9 3 26.374 I n t e g r a t i o n (G) (G) CG) C l a s s C y c l i c i c l u s i o n T r a n s i t i v i t y 4 . 4 0 7 C?) 2 5 . 1 0 0 1 9 . 0 2 9 CG) CG) 82 To summarize, t h e f i r s t h y p o t h e s i s was g e n e r a l l y s u p p o r t e d by t h e d a t a . The s t a g e s and d i s c o n t i n u o u s gaps between them were f o u n d i n t h e two new domains. The f i n d i n g t h a t t h e s o c i e t a l c y c l i c t r a n s i t i v i t y t a s k was i n t e r m e d -i a t e between t h e c o n c r e t e s t a g e t a s k s and t h e c y c l i c i n t e g r a t i o n t a s k d e s e r v e s f u r t h e r a t t e n t i o n . I n t h e n e x t s e c t i o n t h e s y s t e m i c s c o r e s a r e grouped by t h e i r c o n s t i t u e n t components i n an a t t e m p t t o p r o v i d e a f i n e r g r a i n e d a n a l y s i s . B. F i r s t H y p o t h e s i s w i t h Component S y s t e m i c S c o r e s The s y s t e m i c t a s k s were d e v i s e d t o a s s e s s t h e upper r e a c h e s o f t h e c h i l d ' s d e v e l o p i n g u n d e r s t a n d i n g o f s o c i a l o r g a n i z a t i o n s . W h i l e t h e f o r m a l l y s t a t e d h y p o t h e s e s b e a r upon i n t e r p r e t a t i o n s o f t h e ontogeny o f t h a t u nder-s t a n d i n g , t h e s y s t e m i c c o g n i t i v e o p e r a t i o n s i n t h e m s e l v e s a r e an a t t e m p t t o f a t h o m t h e n a t u r e o f t h a t u n d e r s t a n d i n g when i t i s d e v e l o p e d . T h e r e f o r e l e t us t a k e a c l o s e r l o o k a t t h o s e t a s k s . S i n c e t h e s y s t e m i c t a s k s were newly d e v i s e d f o r t h i s s t u d y , t h e r e r e m a i n s scope f o r t h e i r r e f i n e m e n t . The r e p o r t i n g o f d e t a i l e d i t e m a n a l y s e s l e a d i n g t o improved v e r s i o n s o f t h e t a s k i s an u n d e r t a k i n g f o r a n o t h e r s t u d y . F o r now, however, t h e r e a r e some immediate r e f i n e m e n t s t h a t can be a t t e m p t e d i n o r d e r t o s h a r p e n o u r u n d e r s t a n d i n g o f what t h e s e s y s t e m i c c o g n i t i v e o p e r a t i o n s e n t a i l . S p e c i f i c a l l y , b o t h t h e c y c l i c t r a n s i t i v i t y and t h e c y c l i c i n t e g r a t i o n s c o r e s can be e a s i l y decomposed i n t o p a i r s o f s u b s c o r e s w h i c h seem t o r e f l e c t t h e m a s t e r y o f q u i t e d i f f e r e n t c o g n i t i v e o p e r a t i o n s , ( i ) C y c l i c T r a n s i t i v i t y Components The s c o r e s f o r t h e s y s t e m i c t a s k s were based on w o r k i n g d e f i n i t i o n s o f t h e i r c o g n i t i v e o p e r a t i o n s . F o r c y c l i c t r a n s i t i v i t y t h e d e f i n i t i o n was o p e r a -t i o n a l i z e d i n two ways. F i r s t , i n t h e " l a y o u t " p r o c e d u r e r e s p o n d e n t s were . 83 presented with "five cards, each showing a pi c t u r e of an element i n the cyc l e . The respondent was asked to arrange the pict u r e s beside one another i n a way that would show how they were r e l a t e d . The wording'of the request va r i e d depending on the content of the cycle but successful performance always i n -volved arranging the cards i n a c i r c l e . Second, the " r e c y c l i n g " procedure involved the respondent i n explaining how a commodity could pass through the same element twice. In the b i o l o g i c a l domain the commodity was a DDT molecule and i n the s o c i a l domain i t was a $1 b i l l . Correct explanations had the com-modity moving around the c i r c l e from one adjacent element to the next. This procedure presupposed that respondents had the correct c i r c u l a r ' arrangement of cards displayed i n front of them. Thus an understanding of the r e l a t i o n s underlying the "layout" was a pr e r e q u i s i t e f o r the " t r a n s i t i v e r e c y c l i n g " component. Since i t was not known a p r i o r i whether these two procedures would be of equal d i f f i c u l t y , i t was decided that t h e i r scores would be combined i n order to have an o v e r a l l p i c t u r e of the respondents a b i l i t y with the c y c l i c t r a n s i t i v i t y operation (see Appendix D f o r scoring rules and rules f o r combining scores). Below, these two components are treated separately i n a reanalysis of the data. ( i i ) C y c l i c Integration Components In the c y c l i c i n t e g r a t i o n task the cycle used i n the c y c l i c t r a n s i t i v i t y task remained displayed on cards i n front of the respondent but the cycle i t s e l f was construed as one of three l e v e l s of organization. The elements of the cycle were the subordinate l e v e l and the forces which integrated the cycle across time and changing circumstances were the supraordinate l e v e l . The component that i s being c a l l e d "systems a n a l y s i s " involved the a b i l i t y to explain the impact of c y c l i c processes on i n d i v i d u a l elements of the cycle. 84 The other component o£ the o v e r a l l c y c l i c i n t e g r a t i o n score i s being r e f e r r e d to as "systems s y n t h e s i s " . Systems synt h e s i s i n v o l v e d e x p l a i n i n g how the nature of the c y c l e i t s e l f would change under the impact of supraordinate f o r c e s . There were no graphic r e p r e s e n t a t i o n s of the supraordinate l e v e l . Rather, i t had to be i n f e r r e d , discovered or "sy n t h e s i z e d " out of the a v a i l a b l e knowledge about the c y c l e and i t s p a r t s . The c y c l i c i n t e g r a t i o n scores were combinations of the scores f o r systems a n a l y s i s and systems syn t h e s i s (see Appendix D f o r s c o r i n g r u l e s and combining r u l e s ) . The combination of component scores i n t o c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n scores was based on the assumption that the components measured aspects of the same c o g n i t i v e o p e r a t i o n . This assumption can be v e r i f i e d by r e a n a l y s i n g the data w h i l e s u b s t i t u t i n g two component scores f o r each of the four composite systemic scores. F i r s t , a scalogram a n a l y s i s i s examined to see how d i f f i c u l t the com-ponents were r e l a t i v e to other tasks and to each other. Then a t a b l e of z scores i s reviewed to see how w e l l the f i r s t hypothesis fared w i t h the com-ponent scores. ( i i i ) Scalogram and Z Scores f o r Components Scores by Domain. The d i f f i c u l t y l e v e l s are shown i n f i g u r e 2 . The most notable r e v e l a t i o n i s the r e l a t i v e easiness of the c y c l i c t r a n s i t i v i t y l ayout procedure, e s p e c i a l l y i n the s o c i e t a l domain. Table I I I shows the z scores f o r p a i r w i s e comparisons of the component scores w i t h each other and w i t h the other t a s k s . The z scores f o r the s o c i e t a l domain c y c l i c t r a n s i t i v i t y l a y o ut procedure w i t h each of the four concrete tasks shows that i n no case i s i t an unambiguous Guttman step apart. This was not true f o r the layout procedure i n the b i o - e c o l o g i c a l domain nor f o r any other component score. 85 F i g u r e 2 S c a l o g r a m d i f f i c u l t y o r d e r i n g s w i t h component s y s t e m i c s c o r e s (a) by domain, and (b) a c r o s s domains. KEY s = S e r i a t i o n Lay = L a y o u t Component o f LT = L i n e a r T r a n s i t i v i t y C y c l i c T r a n s i t i v i t y LM = L o g i c a l M u l t i p l i c a t i o n SyAn = Systems A n a l y s i s Component o f C = C l a s s I n c l u s i o n C y c l i c I n t e g r a t i o n Prob = P r o b a b i l i t y SySy = Systems S y n t h e s i s Component o f I s o = I s o l a t i o n o f V a r i a b l e s C y c l i c I n t e g r a t i o n CV = C o m b i n a t i o n o f V a r i a b l e s TRec = T r a n s i t i v e R e c y c l i n g Component o f C y c l i c T r a n s i t i v i t y T a b l e I I I , P a r t A B i o - e c o l o g i c a l domain "L_ s c o r e s f o r d i f f e r e n c e s between p r o p o r t i o n s o f r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t he o t h e r , r e p o r t e d w i t h s y s t e m i c s c o r e s i n components More D i f f i c u l t Task o f P a i r L o g i c a l M u l t i p l i c a t i o n C l a s s I n c l u s i o n L a y o u t P r o c e d u r e Systems .'. A n a l y s i s Systems S y n t h e s i s T r a n s i t i v e R e c y c l i n g L e s s D i f f i c u l t Task o f P a i r S e r i a t i o n L i n e a r " L o g i c a l C l a s s L a y o u t Systems T r a n s i t i v i t y M u l t i p l i c a t i o n I n c l u s i o n P r o c e d u r e A n a l y s i s — 0.378 (NG) — 3.488 2.653 (?) (?) 12.161 11.984 9.041 (G) (G) (G) _ 13.383 13.200 10.671 0.889 (G) (G) (G) (NG) — 14.491 14.301 10.671 1.894 0.936 (G) (G) (G) (NG) (NG) _ 17.711 17.495 15.541 4.632 3.084 (G) (G) (G) (?) (?) Systems 2.319 (NG) 00 ON T a b l e I I I , P a r t B S o c i a l domain Z s c o r e s f o r d i f f e r e n c e s between p r o p o r t i o n s o f r e s p o n d e n t s p a s s i n g one t a s k o f a p a i r w h i l e f a i l i n g t h e o t h e r , r e p o r t e d w i t h s y s t e m i c s c o r e s i n components L e s s D i f f i c u l t Task o f P a i r More D i f f i c u l t Task o f P a i r S e r i a t i o n L i n e a r T r a n s i t i v i t y L o g i c a l M u l t i p l i c a t i o n C l a s s I n c l u s i o n L a y o u t P r o c e d u r e Systems A n a l y s i s Systems S y n t h e s i s L i n e a r T r a n s i t i v i t y 3.316 (?) L o g i c a l M u l t i p l i c a t i o n i 3.604 (?) 0.377 (NG) C l a s s I n c l u s i o n 4.259 (?) 1.758 (NG) 1.265 (NG) L a y o u t P r o c e d u r e 7.238 (?) 4.930 (?) 4.738 (?) 3.174 (?) Systems ',:. .'. -: ?. A n a l y s i s 15.248 (G) 11.803 (G) 12.592 (G) 10.998 (G) 8.811 (G) T r a n s i t i v e R e c y c l i n g 16.926 (G) 15.511 (G) 15.308 (G) 13.067 (G) 10.665 (G) 1.015 (NG) Systems S y n t h e s i s 19.045 (G) 17.505. (G) 17.284 (G) 14.357 • (G) 11* 89.4 • (G) 1.534 (NG) 1.005 (NG) 00 88 These r e s u l t s p a r a l l e l t h o s e o b t a i n e d w i t h t h e c o m p o s i t e c y c l i c t r a n s i t i v i t y s c o r e . A p p a r e n t l y i t was t h e l a y o u t component o f t h e c y c l i c t r a n s i t i v i t y s c o r e t h a t was p u l l i n g t h a t o p e r a t i o n towards t h e c o n c r e t e t a s k s and away fr o m t h e c y c l i c i n t e g r a t i o n t a s k . The s c a l a b i l i t y c o e f f i c i e n t s ' B y domain a r e (a) p h y s i c a l ; 0 . 8 3 8 , (b) b i o -e c o l o g i c a l 0.5868, and (c) s o c i e t a l 0.5436. These c o e f f i c i e n t s a r e c o n s i d e r -a b l y l o w e r t h a n t h e s e o b t a i n e d u s i n g t h e c o m p o s i t e s c o r e s f o r t h e s y s t e m i c t a s k s ( i . e . p h y s i c a l 0.838, b i o - e c o l o g i c a l 0.696, s o c i e t a l 0.714). The p h y s i c a l domain had no s y s t e m i c t a s k s so i t i s t h e same. W i t h component s c o r e s t h e b i o - e c o l o g i c a l and t h e s o c i e t a l domains f a l l b e l o w t h e 0.6 c r i t e r i o n f o r b e i n g u n d i m e n s i o n a l and c u m u l a t i v e s c a l e s . The drop i n t h e s c a l a b i l i t y c o e f f i c i e n t s may p a r t i a l l y r e f l e c t t h e r e l a t i v e l y g r e a t e r w e i g h t t h a t t h e p o s t - s y s t e m i c t a s k s have when t h e t a s k s f o r t h e domain i n c l u d e component s c o r e s r a t h e r t h a n c o m p o s i t e s c o r e s . There a r e 2 c o m p o s i t e s c o r e s p e r domain. S i n c e t h e r e a r e 4 c o n c r e t e t a s k s , t h e c o m p o s i t e s a r e one t h i r d o f t h e s i x i t e m t o t a l . T h e r e f o r e t h e s y s t e m i c t a s k s a f f e c t t h e s c a l a b i l i t y c o e f f i c i e n t s more when th e y a r e r e p o r t e d as components t h a n when t h e y a r e r e p o r t e d as c o m p o s i t e s . Even though t h e " p e r c e n t improvement" v a l u e s s t a y e d about t h e same, th e minimum m a r g i n a l r e p r o d u c i b i l i t y c o e f f i c i e n t s were l o w e r when th e domains c o n t a i n e d component s c o r e s t h a n when t h e y c o n t a i n e d c o m p o s i t e s c o r e s . T h i s means t h e r e was more p o s s i b l e v a r i a t i o n t o be a c c o u n t e d f o r by t h e o r d e r i n g p a t t e r n s . However, t h e r e were a l s o more v i o l a t i o n s o f t h e o r d e r i n g p a t t e r n s when t h e s y s t e m i c t a s k s were r e p o r t e d as components. T h i s i s c o n s i s t e n t w i t h t h e z s c o r e s i n the b o t t o m r i g h t c o r n e r s o f p a r t s A and B o f T a b l e I I I . The 89 i m p l i c a t i o n i s t h a t t h e r e i s c o n s i d e r a b l e m i s o r d e r i n g o f t h e s y s t e m i c components amongst t h e m s e l v e s i n b o t h domains. A c r o s s Domain S c o r e s . The r i g h t m o s t column i n f i g u r e 2 shows t h e d i f -f i c u l t y o r d e r i n g o f t h e components when we c o l l a p s e a c r o s s domains. T h i s " a c r o s s domain" o r d e r i n g i s based on a c r o s s domain s c o r e s . The a c r o s s domain component s c o r e s were p r o d u c e d by c o u n t i n g s i m u l t a n e o u s p a s s e s o f b o t h domains as p a s s e s on t h e a c r o s s domain s c o r e . I f t h e component s c o r e f o r one domain had been a f a i l , t h e n t h e a c r o s s domain s c o r e w o u l d a l s o be a f a i l . The a c r o s s domain column i n f i g u r e 2 shows t h e f o r m a l s c o r e s clumped t o g e t h e r b e l o w t h e s y s t e m i c s c o r e s . T a b l e I V shows t h e z s c o r e s f o r t h e s t e p s between t h e f o r m a l t a s k s and t h e s y s t e m i c component t a s k s . Those s y s t e m i c t a s k s w h i c h a r e a c l e a r Guttman s t e p more d i f f i c u l t t h a n two out o f t h e t h r e e f o r m a l t a s k s a r e marked w i t h a "G" ( f o r Guttman s t e p ) i n t h e s t e p column. Those t h a t a r e c l e a r non-Guttman s t e p s a p a r t f r o m two o f t h e t h r e e f o r m a l t a s k s a r e marked w i t h a n , "NG" ( f o r non-Guttman s t e p ) . Q u e s t i o n marks i n d i c a t e t h e ambiguous c a s e s . The o v e r a l l i m p r e s s i o n f r o m f i g u r e 2 'and t a b l e TV i s t h a t a s t a g e - s i z e d gap s e p a r a t e s b o t h t r a n s i t i v e r e c y c l i n g and systems s y n t h e s i s f r o m t h e f o r m a l o p e r a t i o n a l t a s k s . I f t h e s t a g e - s i z e d gap r e s u l t s f r o m t h e g r e a t e r d e v e l o p -m e n t a l m a t u r i t y r e q u i r e d t o m a s t e r t h e s y s t e m i c c o g n i t i v e o p e r a t i o n s i n v o l v e d t h e n i t c o u l d be argued t h a t t h o s e s y s t e m i c o p e r a t i o n s c o n s t i t u t e a f i f t h s t a g e o f c o g n i t i v e development. The d a t a a v a i l a b l e a r e i n a d e q u a t e t o s e t t l e t h e f i f t h s t a g e q u e s t i o n c o n c l u s i v e l y b u t f u r t h e r a n a l y s e s c o u l d e s t a b l i s h how w e l l t h e d a t a meet some o f t h e c r i t e r i a f o r a s t a g e i n t e r p r e t a t i o n . The z s c o r e s have a l r e a d y c o n t r i b u t e d t o p r o v i n g t h e s i z e o f t h e gap. A f u r t h e r c o n t r i b u t i o n i s p r o v i d e d by c l u s t e r a n a l y s e s (see s e c t i o n C ( i ) ) . 90 T a b l e I V Z s c o r e s between f o r m a l t a s k s and s y s t e m i c components NG ^ 2.380 G = 7,663 2.380< ?< 7.663 For m a l T a s k s P r o b a b i l i t y P r o b a b i l i t y -I s o l a t i o n o f V a r i a b l e s 2.315 C o m b i n a t i o n o f V a r i a b l e s 4.064 B i o - e c o l o g i c a l Components L a y o u t T r a n s i t i v e R e c y c l i n g Systems A n a l y s i s Systems S y n t h e s i s S o c i a l Components L a y o u t T r a n s i t i v e R e c y c l i n g Systems A n a l y s i s Systems S y n t h e s i s A c r o s s Domain S c o r e s L a y o u t T r a n s i t i v e R e c y c l i n g Systems A n a l y s i s Systems S y n t h e s i s 3.943 9.669 5.046 6.991 -3.010 8.720 6.040 9.915 4.115 11.730 5.716 10.875 I s o l a t i o n o f V a r i a b l e s -2.315 2.545 2.493 7.794 4.141 5.547 -4.936 7.69.9 4.004 7.984 2.812 10.682 4.802 8.643 C o m b i n a t i o n o f V a r i a b l e s -4.064 -2.545 0.415 6.013 1.672 2.234 -5.953 3.042 2.371 4.357 0.605 7.522 2.314 4.997 O v e r a l l S t e p Type* NG NG NG NG G *The o v e r a l l s t e p t y p e f o r each component a g a i n s t a l l t h r e e f o r m a l o p e r a t i o n s d e t e r m i n e d by wh a t e v e r s t e p t y p e two out o f t h r e e o f t h e Z s c o r e s happen t o be Where a l l t h r e e Z s c o r e s a r e o f a d i f f e r e n t t y p e , t h e o v e r a l l t y p e i s a " ? " . 91 C. Second Hypothesis The second hypothesis states that the systemic operations, or at l e a s t some of t h e i r components represent a f i f t h stage of cognitive development above formal operations. The corresponding n u l l hypothesis i s that the systemic operations and a l l of t h e i r components are alternate forms of adult cognition, equal i n d i f f i c u l t y to formal operations. The quantitative t e s t i n g of t h i s hypothesis amounts to an attempt to locate the d i f f i c u l t y l e v e l s of the systemic tasks i n r e l a t i o n to those f o r the formal operations. Do they c l u s t e r together or i s the diff e r e n c e i n .their d i f f i c u l t y l e v e l s enough to set at le a s t some systemic components apart from the formal operational cluster? As the terminology used i n phrasing the problem suggests, the most appropriate s t a t i s t i c to assess the second hypothesis i s c l u s t e r a n a l y s i s , ( i ) Cluster Analysis of Components Cluster analysis i s often referred to as an analogue of factor analysis for dichotomous data. The c l u s t e r i n g algorithm used was an aglomerative one by Ward (1963). I t produces a dendrogram which, at one end, indicates which of the n items entered are most s i m i l a r and, at the other end, shows which of the c l u s t e r s of items b u i l t up i n the middle are l e a s t s i m i l a r . Figure 3 shows the dendrogram produced by t h i s a nalysis on a l l the concrete, formal, and component systemic scores. The l a s t two c l u s t e r s to be forced together by the algorithm are the concrete tasks and the remaining formal and systemic tasks. The error produced by f o r c i n g these two c l u s t e r s i n t o one c l u s t e r i s by f a r the greatest error produced by any j o i n i n g operation i n the en t i r e a n a l y s i s . This dramatic r i s e i n the error term, however, must be interpreted with some caution. According to E v e r i t t (1974; p.78), Ward's method t y p i c a l l y , "...produces 92 F i g u r e 3 o o * o C l u s t e r A n l y s i s Dendrogram w i t h S c o r e s by Domain and S y s t e m i c S c o r e s by Component o o • CN O O » O CM Domain Code The l a s t c a p i t a l l e t t e r i n each a b b r e v i a t e d t a s k l a b e l ( s e e KEY f o r F i g u r e s 1 and 2) i n d i c a t e s t h e do-main. A = P h y s i c a l B = B i o - e c o l o g i c a l C = S o c i e t a l CM* v o . oo« ON» u a CO u P-u 3 w O H o o •H e m o 4J •H °. , M U i—i cu CO 60 0 O 3 —* < •—I ON . o , CM C J CO C J pq H t-1 C J H i-l < H n4 C J s i-l u PQ > >, o > e o !>. o q cO CO o CJ N CO >N CO 93 a dendrogram with large changes i n l e v e l , e s p e c i a l l y going from two groups to one group. This would probably lead the i n v e s t i g a t o r to i n f e r the presence of two groups." E v e r i t t made these comments i n comparing ward's method with the sin g l e linkage method and the centroid method. Each method has i t s advantages and disadvantages. The i n v e s t i g a t o r can avoid being misled i f the d i s t o r t i n g operating c h a r a c t e r i s t i c s of each algorithm are kept i n mind and taken into account i n i n t e r p r e t i n g the r e s u l t s . With Ward's method i t i s important to remember that the error term f o r the l a s t j o i n i n g w i l l be unusually high and may obscure equally important differences between the groups joined i n going 3 from 3 to 2 groups. Scores by Domain. The logrithmic graph of error terms shown along the ordinate of f i g u r e 3 i s designed to give an approximate v i s u a l c o r r e c t i o n for the d i s t o r t i o n . The higher the error rate and the steeper the slope the more d i s s i m i l a r are the groups being joined i n that step. In the present analysis the concrete versus non-concrete groupings are the most d i f f e r e n t , The diff e r e n c e that separates them i s not proportionately as large as the error term would i n d i c a t e . The diff e r e n c e i s probably more comparable to that separating the c l u s t e r s joined i n the second l a s t grouping. That i s , the concrete tasks are not much further from the other tasks than the predominantly formal operational c l u s t e r i s from the systemic tasks. While the z scores indicated that the top c l u s t e r was smaller than the formal c l u s t e r , t h i s c l u s t e r analysis showed the reverse. The ambiguous cases 3. I t i s a c t u a l l y the l a s t 5% + 3% of the joinings which are subject to the d i s t o r t i o n i n error terms. In the present case, with 17 items, the d i s -t o r t i o n only takes noticeable e f f e c t i n the l a s t 2 j o i n i n g s ( i . e . , from 3 to 2 groups and from 2 to 1 groups). 94 were grouped upwards. The fact that they s p l i t away from the formal tasks and joined the top systemic tasks only emphasizes how ambiguous these cases are. Across Domain Scores. Some of the ambiguity can be reduced by entering the across domain scores into a c l u s t e r a n a l y s i s . Figure 4 shows the dendrogram produced by the c l u s t e r analysis on the across domain scores. From t h i s per-spective, the impression gained from the z scores i s corroborated. The c y c l i c t r a n s i t i v i t y r e c y c l i n g score and the systems synthesis score form a separate c l u s t e r above formal operations i n d i f f i c u l t y . To s i m p l i f y the discussion of these two scores we w i l l r e f e r to them as the "upper systemic" scores or tasks, as the case may be. Even with the logarithmic s c a l i n g , the error term f o r the l a s t j o i n i n g s t i l l appears disproportionately large r e l a t i v e to the e a r l i e r error terms. Also the systemic c l u s t e r would appear more d i s t i n c t from the formal c l u s t e r i f the lower systemic scores (systems analysis and the layout component) were not included i n the a n a l y s i s . Deleting those scores makes sense i f we are mainly interested i n seeing how f a r and upper systemic operations are from the standard formal operations alone. I t i s , a f t e r a l l , the three standard formal operations by themselves which give us the best estimate of where formal operations f a l l r e l a t i v e to systemic operations. Therefore, two a d d i t i o n a l c l u s t e r analyses are presented i n order to gauge the s i z e of the gap between formal operations and the d i s t i n c t i v e upper systemic operations. Figure 5 shows the dendrogram f o r a c l u s t e r analysis of across domain scores. The concrete operational scores were coded as "passes" i f two out of the three examples of that cognitive operation had been passed. The l o g r i t h m i c a l l y scaled error term increases on the ordinate show that the increase F i g u r e 4 95 C l u s t e r A n a l y s i s Dendrogram w i t h A c r o s s Domain S c o r e s and S y s t e m i c S c o r e s by Components ST pass = LT pass = MT pass = CT pass = Lay C o d i n g o f A c r o s s Domain S c o r e s pass 2/3 o f l i n e a r t r a n s i t i v i t y t a s k s pass 2/3 o f l o g i c a l m u l t i -p l i c a t i o n t a s k s pass 2/3 o f c l a s s i n c l u s i o r t a s k s pass i n one domain and n o t l e s s t h a n a 2 - l e v e l f a i l i n t he o t h e r . SyAn pass = same as Lay pass SySy pass = same as Lay pass TRec pass = same as Lay pass H H CO H J H >~, o CO CO O U P-l > C J fi < CO CO CO CJ Pi F i g u r e 5 o o m C l u s t e r A n a l y s i s Dendrogram on A c r o s s Domain S c o r e s w i t h Lower S y s t e m i c S c o r e s D e l e t e d (see F i g u r e 2 f o r KEY and F i g u r e 4 f o r Coding o f A c r o s s Domain S c o r e s ) o o CM O O O m o CM oo« y •H •£ <4-l | f o co •u 0) P-o 60 u s o o u 3 tJ w 53 H co H H C_> o u o CO H > CO CO 97 caused by j o i n i n g the systemic operations with the formal operations i s f a i r l y comparable to that caused by j o i n i n g the concrete operations with the r e s t . Summary Scores. F i n a l l y , i n order to get the broadest overview, the concrete and formal stage scores were reduced to one number each and were submitted to a c l u s t e r a n alysis along with the scores for the lowest of the upper systemic components ( i . e . , across domain systems synthesis). We should expect a f a i r l y even sized error term increase across the two j o i n i n g s only i f the systemic score were as f a r from the formal stage score as the formal stage score i s from the concrete stage score. This i s p r e c i s e l y what i s shown i n f i g u r e 6. Numerically, the increase i n error for the j o i n i n g of the formal score with the systemic score (67.5) was only 1.5 error units more than the increase i n error f o r the j o i n i n g of the l a t t e r two with the concrete score (66.5). The two increases were v i r t u a l l y i d e n t i c a l . These r e s u l t s corroborate the impression given by Table I I I parts B and C where non-Guttman steps were found among the upper systemic tasks, while Guttman steps separated them from the formal tasks (see Table IV). The patterns displayed on three tables and i n t h i s c l u s t e r a n alysis are consistent with the structures d'ensemble c r i t e r i o n for a stage. These analyses i n d i c a t e that i t i s unquestionably plaus-i b l e to consider systems synthesis and t r a n s i t i v e r e c y c l i n g as cognitive opera-tions belonging to a f i f t h stage of cognitive development. The next section reports the a v a i l a b l e data which contribute to an evaluation of the " f i f t h stage" i n t e r p r e t a t i o n . D. Third Hypothesis T r a n s i t i v e r e c y c l i n g and systems synthesis are the two cognitive opera-98 F i g u r e 6 C l u s t e r A n a l y s i s Dendrogram f o r Stage S c o r e s and L e a s t D i f f i c u l t Upper S y s t e m i c S c o r e A c r o s s Domains o o CM cn cn o o O o CM U cd 60| o 1 - 1 r—1 0) CU ain m i-l S-i g o O o CO o te Sc Sc Q CO • H CO S-i CO cu i H CO e CU U cu CU cfl CU CO cu o £ 3 a 60 6 60 o 4-1 4J S-I 0 o 3 cd CO S-i CO 3 !-i 3 u O o 4J a >, >N W Z o c_> CO PM CO < CO CO 99 tions which are being considered as candidates for a f i f t h s tage. 4 The four component task scores indexing mastery of these cognitive operations have been shown to be the most d i f f i c u l t tasks used i n t h i s study. The t h i r d hypothesis i s that the greater d i f f i c u l t y of the upper systemic tasks i s due to t h e i r greater s t r u c t u r a l complexity. That i s , the operations needed to solve them belong to a f i f t h stage. The corresponding n u l l hypothesis :". i s that the greater d i f f i c u l t y of these tasks i s wholly a t t r i b u t a b l e to non-s t r u c t u r a l content re l a t e d f a c t o r s . The f i f t h stage i n t e r p r e t a t i o n would be weakened i f i t could be shown that at l e a s t part of the greater d i f f i c u l t y of the upper systemic tasks i s a t t r i b u t a b l e to factors other than the greater d i f f i c u l t y of the cognitive operations they require. This section examines the data a v a i l a b l e on the f a m i l i a r i t y of the task content and i t s d i f f i c u l t y r e l a t i v e to the tasks. (i) U n f a m i l i a r i t y vs. Complexity as Reasons f o r D i f f i c u l t y I f Piaget's approach extends to the study of systemic operations as well as the study of s o c i a l understanding then the u n i v e r s a l i s t f l a v o r of h i s theory should be vindicated with the upper systemic tasks. That would require evidence that competence with the upper systemic operations would be manifested evenly across v a r i a t i o n s i n content. Large differences i n how f a m i l i a r respondents were with various contents should make a n e g l i g i b l e d i f f e r e n c e i n the d i f f i c u l t y l e v e l s of the tasks. I f , on the other hand, there were evidence that task per" formance varied along with the f a m i l i a r i t y of the content then (a) a l i m i t would have been discovered to Piaget's u n i v e r s a l i s t approach, and (b) the d i f f i c u l t y 4. A stage, of course, i s a whole group of cognitive operations that form a "structured whole" (e.g., Inhelder and Piaget, 1958). Two cognitive opera-tions would not l i k e l y constitute a stage i n themselves but they may be representatives of a stage. 100 of the upper systemic tasks could be a t t r i b u t e d to factors other than the subsumptive power of the cognitive operations involved. That would amount to suggestive evidence against a f i f t h stage i n t e r p r e t a t i o n . In t h i s section the f a m i l i a r i t y data are compared with the task perform-ance data i n an attempt to discern whether or not there are grounds for b e l i e v i n g that successful task performance on the most d i f f i c u l t systemic tasks required anything over and above f a m i l i a r i t y with contents of those tasks. Two main arguments are marshalled i n support of the n u l l hypothesis. F i r s t , data are presented to show how differences i n f a m i l i a r i t y with whole domains of content produced no correlated differences i n performance on tasks. Second, the complementary case i s made that when f a m i l i a r i t y with content i s held constant and i t i s the s t r u c t u r a l complexity of the task that i s va r i e d , corresponding changes i n task performance are observed, ( i i ) Varying F a m i l i a r i t y With Constant Complexity In. the concrete stage performance on a l l tasks f e l l ' w i t h i n a f a i r l y consistent range regardless of the f a m i l i a r i t y of the task content. More p a r t i c u l a r l y , the b i o - e c o l o g i c a l and s o c i e t a l tasks showed a s t r i k i n g degree of p a r a l e l l i s m i n t h e i r d i f f i c u l t y l e v e l s despite the fa c t that the content of the s o c i e t a l tasks was considerably le s s f a m i l i a r to the sample as a whole. Table V, part A shows the frequencies of respondents f a m i l i a r with the contents of each of the concrete stage tasks i n each of the three domains. The un-f a m i l i a r i t y rate f o r the b i o - e c o l o g i c a l domain va r i e s between 0 and 10 respond-ents. By contrast the u n f a m i l i a r i t y rate f o r the s o c i e t a l domain ranges from 24 to 56 respondents. While the s o c i e t a l content i s c l e a r l y l e s s f a m i l i a r there i s never more than a n e g l i g i b l e d i f f e r e n c e ( i . e . , four respondents) between the T a b l e V, P a r t A F r e q u e n c i e s o f p a s s e s and Z s c o r e s between c o n c r e t e o p e r a t i o n a l t a s k s and f a m i l i a r i t y a s s e s s m e n t s P h y s i c a l B i o - e c o l o g i c a l S o c i e t a l S e r i a t i o n Frequency o f P a s s F a m i l i -Task a r i t y Z 96 96 0.0 (NG) 96 96 0.0 (NG) 92 70 -7.135 ( ? ) L i n e a r T r a n s i t i v i t y F requency of. Pass F a m i l i -Task a r i t y Z 84 96 5.071 (?) 88 93 2.714 (?) 85 72 -3.706 (?) L o g i c a l M u l t i p l i c a t i o n F r e q u e n c y o f P a s s F a m i l i -Task a r i t y Z 91 95 3.226 (?) 87 86 -0.247 (NG) 84 55 -7.578 (?) C l a s s I n c l u s i o n F r e q u e n c y of _Pass . F a m i l i -Task a r i t y Z 91 96 3.203 (?) 78 91 5.310 (?) 80 40 -10.198 CG) 102 T a b l e V, P a r t B F r e q u e n c i e s and Z s c o r e s between b i o - e c o l o g l c a l domain t a s k s and f a m i l i a r i t y a s s e s s m e n t s F a m i 1 i a r i t i e s Fre q u e n c y T a s k s c L a y o u t P r o c e d u r e T r a n s i t i v e R e c y c l i n g C y c l i c T r a n s i t i v i t y Systems A n a l y s i s Systems .Sy n t h e s i s C y c l i c I n t e g r a t i o n N i t r o g e n Repro- S t a r v a -P a s s e s M o l e c u l e B a c t e r i a d u c t i o n t i o n 44 67 59 65 41 0.715 6.285 (NG) C?) 23 6.920 13.122 (?) (G) 35 2.675 8.251 (?) CG) 36 2.121 6.297 4.548 6.749. (NG) (?) (?) (?) 32 2.879 8.19-4 6,378 7.864 (?) CG). C?) C G i 22 5.822 9.660 8.408 11.505 (?) (G) CG) CG) KEY N i t r o g e n = f a m i l i a r i t y w i t h c o n c e p t o f n i t r o g e n M o l e c u l e m o l e c u l e B a c t e r i a = f a m i l i a r i t y w i t h b a c t e r i a R e p r o d u c t i o n = f a m i l i a r i t y w i t h c o n c e p t o f p o p u l a t i o n r e p r o d u c t i o n S t a r v a t i o n = f a m i l i a r i t y w i t h c o n c e p t o f s t a r v a t i o n i n a p o p u l a t i o n T a b l e V 3 P a r t C Z s c o r e s and f r e q u e n c i e s o f p a s s e s f o r s o c i e t a l domain t a s k s and f a m i l i a r i t y a s s e s s m e n t s F a m i l i a r i t y Assessment Task Frequency of P a s s e s WMB FM Bakery P r o f i t s Taxes S/D Own Wheat L a y o u t P r o c e d u r e 67 29 -8.670 (G) 81 4.398 (?> 92 7.238 (?) 73 78 46 77 3.237 (?) T r a n s i t i v e R e c y c l i n g 27 0.282 (NG) 14.697 (G) 16.926 •(G) 13.878 (G) C y c l i c T r a n s i t i v i t y 61 -8.310 (G) 5.940 (?) 8.818 (G) 5.535 (?) Systems A n a l y s i s 32 -0.612 (NG) 13.154 (G) 15.248 (G) 9.840 (G) 10.671 (G) 3.049 (?) 12.381 (G) Systems S y n t h e s i s 22 1.045 (NG) 16.620 (G) 19.045 (G) 14.840 (G) 15.954 (G) 4.439 (?) 15.732 (G) C y c l i c I n t e g r a t i o n 10 2.732 ' (?) 25.418 (G) 28.921 (G) 22.867 (G) 24.462 (G) 7.041 (?) 24.143 (G) G = NG = ? = Guttman s t e p (-7'.663.0 non-Guttman s t e p (=2.380) ambiguous s t e p (between 2.380 and : 7.6.63.) KEY WMB = f a m i l i a r i t y w i t h t h e wheat m a r k e t i n g b o a r d FM = f a m i l i a r i t y w i t h t h e f l o u r m i l l B a k e ry = f a m i l i a r i t y w i t h t h e b a k e r y P r o f i t s = f a m i l i a r i t y w i t h c o n c e p t o f p r o f i t s Taxes = f a m i l i a r i t y w i t h c o n c e p t o f t a x e s S/D = f a m i l i a r i t y w i t h l a w o f s u p p l y and demand Own Wheat = I n t r o d u c t o r y i t e m f o r t r a n s i t i v e r e c y c l i n g component, " C o u l d t h e f a r m e r e v e r e a t b r e a d made f r o m h i s own wheat i f he s e l l s a l l t h e wheat t h a t he grows?" o , 104 success r a t e s f o r s o c i e t a l tasks and the success r a t e s f o r b i o - e c o l o g i c a l t a s k s . The z scores on pa r t A of t a b l e V t e l l the same s t o r y i n a more synop t i c form. The z scores are f o r d i f f e r e n c e s between p r o p o r t i o n s . The f i r s t pro-p o r t i o n represents those respondents who were f a m i l i a r w i t h the contents but who f a i l e d the task. The second p r o p o r t i o n represents respondents who passed the task but were u n f a m i l i a r w i t h the content. When the d i f f e r e n c e between these two proport i o n s y i e l d s a negative z score then the task was passed by more people than were f a m i l i a r w i t h i t s contents. P o s i t i v e z scores a r i s e when more people are f a m i l i a r w i t h the contents than are capable of succeeding on the task. Z scores i n the non-Guttman range i n d i c a t e a n e g l i g i b l e d i f f e r e n c e between r a t e s of task success and r a t e s of f a m i l i a r i t y w i t h task content. Negative z scores of the Guttman step magnitude i n d i c a t e that respondents as a whole were q u i t e unacquainted w i t h the contents of the task but nevertheless performed q u i t e w e l l on i t . Such i s the case f o r the s o c i e t a l domain. The z scores are a l l negative and w i t h i n or c l o s e to the Guttman step range. The s i t u a t i o n i s reversed f o r the b i o - e c o l o g i c a l domain. Two of the z scores are non-Guttman and the other two are ambiguous range p o s i t i v e . The c o n t r a s t be-tween the l a r g e negative z scores f o r the s o c i e t a l domain and the near zero to moderately p o s i t i v e z scores i n the b i o - e c o l o g i c a l domain i n d i c a t e s once again that the content of the s o c i e t a l domain was much l e s s f a m i l i a r to respondents as a whole. Yet t h i s u n f a m i l i a r i t y was not accompanied by any decrement i n success r a t e s on the task. I t d i d not i n f l a t e the d i f f i c u l t y l e v e l of the s o c i e t a l domain t a s k s . Thus one p o t e n t i a l source of c o r r o b o r a t i v e evidence f o r a content r e l a t e d i n t e r p r e t a t i o n of the greater d i f f i c u l t y of the upper systemic components has been abrogated. Of more d i r e c t relevance are,the' data f o r the upper systemic components 105. themselves. Here again, differences i n the f a m i l i a r i t y of task content are not accompanied by s i m i l a r differences i n task performance. Part B of table V shows the data f o r the b i o - e c o l o g i c a l domain. The columns are headed by the four most important content items i n the b i o - e c o l o g i c a l interview."' The rows show both the systemic components and the composite systemic operations. Part C of table V shows the comparable data for the s o c i e t a l systemic scores. For both domains the most important f a m i l i a r i t y items to note are the ones that were most unfamiliar. These items set the l i m i t s on the sample's f a m i l i a r i t y with the respective systems under consideration. The most unfamiliar item i n the b i o - e c o l o g i c a l domain was the nitrogen molecule. Only 44 respondents were f a m i l i a r with that concept. In the s o c i e t a l domain the most unfamiliar item was the wheat marketing board (WMB). Only 29 respondents were f a m i l i a r with t h i s item. An inspection of the f a m i l i a r i t y rates with s p e c i a l emphasis on -these two items indicates that, as with the concrete tasks, the s o c i e t a l con-tent was l e s s f a m i l i a r than the b i o - e c o l o g i c a l content. Also, the rate of successful task performance on the upper systemic components was again roughly within the same range (22 to 32 passes). Unlike the concrete stage pattern, however, successful task performance i n both domains was l e s s frequent than f a m i l i a r i t y with the most unfamiliar content items. Hence, there are no 5 . The d e t a i l s of the f a m i l i a r i t y assessments are given i n Appendicies A, B, and C along with procedures for task administration. 6. For the b i o - e c o l o g i c a l and s o c i e t a l domain c y c l i c t r a n s i t i v i t y tasks, the same two f a m i l i a r i t y items s u f f i c e d f o r the materials used i n both the layout and the r e c y c l i n g procedures. Likewise with c y c l i c i n t e g r a t i o n , the a n a l y t i c and synthetic components used the same materials and concepts. Hence, the same set of f a m i l i a r i t y assessments apply to both components. Since the systemic tasks were arranged such that information gained i n p r i o r tasks continued to be of relevance for l a t e r tasks comparisons are reported between a l l systemic f a m i l i a r i t i e s and a l l systemic tasks. 106 n e g a t i v e z s c o r e s f o r c o m p a r i s o n s o f t h e upper s y s t e m i c components w i t h t h e most u n f a m i l i a r c o n t e n t i t e m s . N e v e r t h e l e s s , t h e p a t t e r n o f d i f f e r e n c e s among t h e z s c o r e s i s t h e same as i n t h e c o n c r e t e s t a g e . S p e c i f i c a l l y , t h e s o c i e t a l domain z s c o r e s a r e a g a i n l o w e r t h a n t h o s e i n t h e b i o - e c o l o g i c a l domain. T h i s means t h a t once a g a i n t h e g r e a t e r u n f a m i l i a r i t y o f t h e s o c i e t a l c o n t e n t i s n o t accompanied by a t a s k p e r f o r m a n c e d e f i c i t o f s i m i l a r magnitude.' Hence t h e g r e a t e r u n f a m i l i a r i t y o f t h e s y s t e m i c t a s k c o n t e n t does n o t appear t o a c c o u n t f o r t h e b u l k o f t h e g r e a t e r s y s t e m i c t a s k d i f f i c u l t y . S u c c e s s on t h e upper s y s t e m i c t a s k s i n b o t h domains a p p a r e n t l y depends on f a c t o r s o v e r Q .. and above f a m i l i a r i t y Cor u n f a m i l i a r i t y ) w i t h t h e i r c o n t e n t s . I n t h e s o c i e t a l domain t h e l a y o u t p r o c e d u r e does f a l l a Guttman s t e p away f r o m t h e f a m i l i a r i t y s c o r e f o r t h e l e a s t f a m i l i a r element i n t h e c y c l e ( i . e . , t h e wheat m a r k e t i n g b o a r d ; see t a b l e V, p a r t C ) . A l t h o u g h , t h e element was l e s s f a m i l i a r , t a s k p e r f o r m a n c e was more s u c c e s s f u l t h a n i n t h e b i o -e c o l o g i c a l domain. T h i s would seem t o be e v i d e n c e f o r a p r a c t i c e e f f e c t w i t h t h e l a y o u t p r o c e d u r e . Even though o r d e r o f p r e s e n t a t i o n i s confounded w i t h domain o f c o n t e n t i t was known t h a t t h e c o n t e n t i n t h e second domain (I.e., s o c i e t a l ) was more n o v e l . D e s p i t e t h a t c o u n t e r v a l i n g f a c t o r , p e r f o r m a n c e a c r o s s t h e w h ole sample s t i l l i m proved on t h e l a y o u t component o f c y c l i c t r a n s i t i v i t y . 7 . O r d i n a r i l y , i t w o u l d be a p p r o p r i a t e a t t h i s p o i n t t o p r e s e n t c o r r e l a t i o n ( e . g . , P h i ) c o e f i c i e n t s f o r t h e above c o m p a r i s o n s . W i t h t h e p r e s e n t d a t a , however, most r e s p o n d e n t s e i t h e r p a s s e d b o t h v a r i a b l e s o r f a i l e d b o t h v a r i a -b l e s . C o r r e l a t i o n c o e f f i c i e n t s g i v e d i s t o r t e d i n f o r m a t i o n on t h i s p r e s e n t d a t a because none o f t h e v a r i a b l e s a r e s e n s i t i v e a c r o s s t h e whole range o f a b i l i t y l e v e l s i n t h e sample. . • 8. A t t h e i n d i v i d u a l l e v e l . . o f / - a n a l y s i s t h i s c o n c l u s i o n i s a l s o u p h e l d . F o r ex-ample, o f t h e 22 r e s p o n d e n t s who p a s s e d s o c i e t a l systems s y n t h e s i s , 13 (59%) were u n f a m i l i a r w i t h t h e WMB. Nor was f a m i l i a r i t y w i t h t h e most d i f f i c u l t c o n t e n t s u f f i c i e n t f o r t a s k s u c c e s s . Of the 29 r e s p o n d e n t s who were f a m i l i a r w i t h t h e WMB, o n l y 9 (34%) p a s s e d s o c i e t a l systems s y n t h e s i s . : 107 9 In summary, when the b i o - e c o l o g i c a l and the s o c i e t a l domain are con-sidered together, however, the f i f t h stage idea appears stronger. Referring back to the scalogram that produced fi g u r e 2 and the z scores on table IV, i t can be seen that the upper systemic scores are of more or l e s s the same d i f f i c u l t y l e v e l regardless of content domain. This implies that v a r i a t i o n s i n content f a m i l i a r i t y such as e x i s t between the b i o - e c o l o g i c a l and s o c i e t a l domains do not a f f e c t the d i f f i c u l t y l e v e l s of the upper systemic tasks very s u b s t a n t i a l l y . In the next subsection we consider cases where the content i s held constant but performance nevertheless v a r i e s , ( i i i ) Varying Operations with Constant Content The above conclusion i s corroborated by the data for the lower systemic components. I f l e s s f a m i l i a r content of the systemic interviews r e a l l y caused detriments i n task performance then the detriment should have been j u s t as evident i n the lower systemic tasks as the upper. Both sets of tasks used the same cycles with the same elements. Yet despite the same f a m i l i a r i t y / u n f a m i l i a r i t y of the task contents within domains the upper components were more d i f f i c u l t . This suggests again that the greater d i f f i c u l t y of the upper systemic components cannot be written o f f as an a r t i f a c t of t h e i r more d i f f i c u l t f i g u r a t i v e contents. 9. One f i n a l item of i n t e r e s t from Table V, C i s the rightmost column labeled "Own Wheat". This was an item used to introduce the t r a n s i t i v e r e c y l c i n g problem i n the s o c i e t a l domain. The respondents were asked, "Could the farmer ever eat bread made from h i s own wheat i f he s e l l s a l l the wheat he grows?" Approximately 75% of the respondents were able to trace the t r a i l of the wheat around the cycle, back to the farmer i n the form of bread. The actual t r a n s i t i v e r e c y c l i n g item required t r a c i n g the t r a i l of a one d o l l a r b i l l along exactly the same path but i n the opposite d i r e c t i o n . Only about 25% of the respondents could do t h i s . The two items were a large Guttman step apart (z = 13.878). On the face of i t , the two items seem l o g i c a l l y equivalent. The obvious existence of psychological differences between them impels us to r e f i n e the t r a n s i t i v e r e c y c l i n g concept. 108 O v e r a l l , i t a p p e a r s t h a t t h e t h i r d h y p o t h e s i s .cannot be r e j e c t e d . The g r e a t e r d i f f i c u l t y o f t h e upper s y s t e m i c t a s k s i s n o t , f o r t h e most p a r t , a t t r i b u t a b l e t o t h e u n f a m i l i a r i t y o f t h e i r c o n t e n t s . Thus a f i f t h s t a g e i n t e r p r e t a t i o n o f t h e i r g r e a t e r d i f f i c u l t y r e m a i n s v i a b l e . E. Age o f M a s t e r y D a t a I n t h i s s e c t i o n a n c i l l a r y d a t a a r e r e p o r t e d t h a t , are, r e l e v a n t ' t o ; t h e - s t a g e i s s u e . F l a v e l l (1971a) posed a b r u p t n e s s o f t r a n s i t i o n c r i t e r i o n f o r t h e i d e n t i f i c a t i o n o f a s t a g e b u t Wohlw.ill': ,(1973) s u g g e s t e d a model w h e r e i n most o f t h e t i m e spent " i n " a s t a g e was a c t u a l l y a l o n g g r a d u a l t r a n s i t i o n p e r i o d p r e c e d i n g f i n a l c o n s o l i d a t i o n . T a b l e V I shows age d a t a t h a t i s r e l e v a n t .-.v:- -t o t h e s e d i f f e r i n g v i e w s o f how l o n g a t r a n s i t i o n p e r i o d m ight l a s t . T a b l e V I shows t h e f r e q u e n c i e s o f s u c c e s s f u l p e r f o r m a n c e s on v a r i o u s s c o r e s r e l a t e d t o age o f m a s t e r y f o r f o r m a l v e r s u s s y s t e m i c l o g i c . The s c o r e s f o r a l l t h r e e f o r m a l o p e r a t i o n a l t a s k s a r e shown a l o n g w i t h a c a l c u l a t e d s c o r e i n t e n d e d t o c l a s s i f y r e s p o n d e n t s as e i t h e r f o r m a l o p e r a t i o n a l o r p r e - f o r m a l . T h i s measure o f f o r m a l o p e r a t i o n a l s t a g e a t t a i n m e n t s i m p l y i n d i c a t e s whether o r n o t t h e r e s p o n d e n t p a s s e d a t l e a s t two o u t o f t h e t h r e e f o r m a l o p e r a t i o n a l t a s k s . F o r t h e p u r p o s e s o f c o m p a r i s o n , a s i m i l a r summary s c o r e was c a l c u l a t e d f o r o v e r a l l m a s t e r y o f s y s t e m i c l o g i c . T h i s "summary systems t h i n k i n g s c o r e " a s s i g n s a " p a s s " t o t h o s e who have p a s s e d a t l e a s t t h r e e o f t h e f o l l o w i n g f o u r t a s k s : 1) b i o l o g i c a l domain t r a n s i t i v e r e c y c l i n g , 2) s o c i a l domain t r a n s i t i v e r e c y c l i n g , 3) b i o l o g i c a l domain systems s y n t h e s i s , 4) s o c i a l domain systems s y n t h e s i s . I n a d d i t i o n t a b l e V I p r e s e n t s a l l t h e a c r o s s domain s y s t e m i c component s c o r e s and a l l o f t h e component s c o r e s by domain. 109 Table VI Age p r o f i l e f o r pass es on formal and systemic scores and on the most d i f f i c u l t systemic f a m i l i a r i t i e s X Age. 8 10- . 12 14 16 18 Grade II I V VII IX XI XII] Systemic F a m i l i a r i t i e s Number out of sixteen/grade pas Sing Nitrogen Molecule 0 0 3 11 14 16 Wheat Marketing Board 0 0 6 4 7 12 Summary Scores Formal Stage 0 0 6 15 16 16 Summary Systems A n A Thinking Score U U u 6 3 9 Formal Tasks P r o b a b i l i t y 1 0 9 14 16 16 I s o l a t i o n of Variables 0 0 6 15 16 15 Combination of Variables 0 1 5 7 14 15 C y c l i c T r a n s i t i v i t y B i o - e c o l o g i c a l : layout 0 1 7 10 11 12 B i o - e c o l o g i c a l : r e c y c l i n g 0 0 1 5 7 10 B i o - e c o l o g i c a l : combined 0 1 5 8 9. 12 S o c i a l : layout 4 5 12 16 16 14 S o c i a l : r e c y c l i n g 0 0 2 8 8 a S o c i a l : combined 1 3 11 16 15 15 Across Domain: layout 0 1 6 10 11 12 *Across Domain: r e c y c l i n g 0 0 0 5 3 7 C y c l i c Integration B i o - e c o l o g i c a l : sy.analysis 1 2 4 5 10 14 B i o - e c o l o g i c a l : sy.synthesis 0 1 2 8 10 11 B i o - e c o l o g i c a l : combined 0 1 1 4 7 9 S o c i a l : sy.analysis 1 1 6 5 9 10 S o c i a l : sy.synthesis 0 1 0 8 7 6 S o c i a l : combined 0 0 0 2 5 3 Across Domain: analysis 1 1 3 5 11 13 *Across Domain: synthesis 0 0 0 7 8 8 *Best i n d i c a t o r s of age p r o f i l e s f o r top systemic scores 110 As expected, the 8 and 10 year olds r a r e l y succeeded on any of the tasks. Successes on the formal operational tasks s t a r t appearing at age 12 but i t i s not u n t i l age 14 that the majority of the respondents pass the majority of the formal operational tasks. The o v e r a l l impression given by the frequencies for the systemic scores i n table VI i s that systemic thinking lags about two years behind formal abstract thinking. Successes s t a r t appearing i n some numbers around age 14. At age 16 several = of-: the scores show successful performance f o r the majority of the respondents. At no age l e v e l , however, does any systemic score show frequencies of success that match those f o r the formal stage score. Most s t r i k i n g i n that regard i s the across domain t r a n s i t i v e r e c y c l i n g score. We do not know at what age, i f ever, the majority becomes competent with t h i s opera-t i o n . There are high f a i l u r e rates on systemic scores throughout the older age groups. The t r a n s i t i o n into the formal stage appears to s a t i s f y F l a v e l l ' s abruptness c r i t e r i o n . The mastery of the upper systemic tasks i s more i n l i n e with the pattern of gradual t r a n s i t i o n that Wohlwill suggests * as a char-a c t e r i s t i c of Piagetian stages. The contrast may be a function of the inherent d i f f i c u l t y of the operations chosen to represent each "stage". The formal tasks used i n t h i s study might be r e l a t i v e l y easy compared to other formal tasks which might show a more gradual t r a n s i t i o n pattern. F. Summary of Results ... In accord with the p r e d i c t i o n made ,in the f i r s t .hypothesis,., the Piagetian approach -appearechtq "generallzeT^ell^to^tli&c-b^xecelogical - and I l l s o c i e t a l content domains. The p r e d i c t i o n made by the second hypothesis was supported for two subcomponents of the systemic operations. The systems syn-thesis and t r a n s i t i v e r e c y c l i n g components were more d i f f i c u l t than the formal operational tasks. The diff e r e n c e was of a stage sized magnitude and i t was Guttman-like. Meanwhile, the s o c i e t a l c y c l i c t r a n s i t i v i t y layout component tended to f a l l towards the concrete stage c l u s t e r i n terms of d i f f i c u l t y l e v e l and the systems analysis component f e l l w ithin the same range of d i f -f i c u l t y as the formal operational tasks. Under the t h i r d hypothesis the res-pondents' r e l a t i v e f a m i l i a r i t y with the content of tasks was examined. The greater d i f f i c u l t y of the upper systemic components i s not a t t r i b u t a b l e i n any s u b s t a n t i a l way. to the r e l a t i v e l y novel content of the tasks assessing them. The systemic tasks and t h e i r subcomponents were found to be mastered approximately two years l a t e r than the formal operational tasks but within each age l e v e l the frequencies of success on the systemic tasks were generally lower than those f o r the formal operational tasks. I t appears that the upper systemic tasks represent a f i f t h stage of cognitive development although the p a r a l l e l development i n t e r p r e t a t i o n has not been ruled out. "V. DISCUSSION This chapter begins with a review of the r e s u l t s corresponding to each of the three hypotheses and then proceeds to an examination of the issues rel a t e d to the i n t e r p r e t a t i o n of the r e s u l t s . A. The Three Hypotheses The rec u r r i n g theme of t h i s section concerns the r e l a t i v e d i f f i c u l t y of the "upper systemic" tasks and the merits of evoking a f i f t h stage of cognitive development i n an e f f o r t to account for. t h i s f a c t . The f i r s t hypothesis deals with groundwork that i s p r e r e q u i s i t e to an examination of t h i s issue. In the second subsection ( i i ) the findings with regard to the second hypothesis are evaluated against the structures d'ensemble and the Guttman scale c r i t e r i a for i d e n t i f y i n g a stage of cognitive development. In the t h i r d subsection the content re l a t e d a l t e r n a t i v e i n t e r p r e t a t i o n s are examined. Then age r e l a t e d stage c r i t e r i a are discussed with reference to the age data. In the f i n a l subsection the evidence for and against the stage versus p a r a l l e l development i n t e r p r e t a t i o n s i s summarized, (i) F i r s t Hypothesis: Extending Piagetian Theory Before an examination of children's understanding of s o c i a l organization could be undertaken i t was necessary to f i r s t i d e n t i f y and document some of the cognitive operations involved i n understanding such open systems. This requirement led to the use of hitherto seldom studied types of contents i n the assessment tasks ( i . e . , contents more often containing open systems). Before these content domains could be used to introduce novel cognitive operations, i t was necessary to demonstrate that the more thoroughly studied cognitive operations were not d r a s t i c a l l y a l t e r e d by a s h i f t to open systems contents. 113 The f i r s t hypothesis,>which states that Piaget's account of cognitive development i n the impersonal sphere can Be extended to B i o - e c o l o g i c a l and s o c i e t a l content, was generally supported. Data Bearing upon t h i s hypothesis were examined from two viewing distances. These macroscopic and microscopic analyses are B r i e f l y summarized Below. Microscopic Level of A n a l y s i s . At t h i s l e v e l i t was predicted that the d i f f i c u l t y orderings of equivalent tasks would Be the same across a l l domains. S p e c i f i c a l l y , i t was predicted that the order of these tasks, from l e a s t d i f -f i c u l t to most d i f f i c u l t , would Be as follows: s e r i a t i o n , l i n e a r t r a n s i t i v i t y , l o g i c a l m u l t i p l i c a t i o n ^ c l a s s i n c l u s i o n , -cyclic t r a n s i t i v i t y , and c y c l i c i n t e -gration. This i s exactly the order that was observed i n Both the B i o - e c o l o g i c a l and s o c i e t a l domains. For reasons outlined e a r l i e r , measures of only the f i r s t four of these cognitive operations were.potentially a v a i l a B l e within the p h y s i c a l domain. Contrary to expectations, the p h y s i c a l domain cla s s i n c l u s i o n task was t i e d f o r d i f f i c u l t y with, the l o g i c a l m u l t i p l i c a t i o n task and they were Both l e s s d i f f i c u l t than the l i n e a r t r a n s i t i v i t y task. Somewhat paradoxically, then, the order of d i f f i c u l t y p r e d i c t i o n s Based upon Piagetian theory were more accurate i n the novel B i o - e c o l o g i c a l and s o c i e t a l domains than i n the more f a m i l i a r standard p h y s i c a l domain. The oBserved equivalency of the c l a s s i n c l u s i o n and l o g i c a l m u l t i p l i c a t i o n tasks could be a simple function of sampling p e c u l i a r i t i e s ' and i t might Be assumed that with a larger numBer of suBjects, i n d i v i d u a l s might have emerged who demonstrated the expected pattern of understanding l o g i c a l m u l t i p l i c a t i o n , But not class i n c l u s i o n . The misordering of l i n e a r t r a n s i t i v i t y i s more d i f f i c u l t to explain away, however. The current research was designed to determine what the d i f f i c u l t y orderings of these tasks were and why they did or did not conform to t h e i r hypothesized i n -o r d e r i n g i s n o t r e a d i l y a p p a r e n t f r o m t h e s e d a t a . T h i s s i n g l e d i f f i c u l t y a s i d e , however, s u p p o r t i n g d a t a were o b t a i n e d f o r t h i r t e e n o f the- o r d e r i n g . r e l a t i o n s h i p s p r e d i c t e d by h y p o t h e s i s one. I n o n l y one- c a s e was t h e r e a d i r e c t v i o l a t i o n o f e x p e c t a t i o n s . From t h i s e v i d e n c e i t seems r e a s o n a b l y s a f e t o c o n c l u d e t h a t t h e same r e a s o n i n g d e v e l o p e d by P i a g e t t o a c c o u n t f o r t h e o r d e r o f d i f f i c u l t y o f t a s k s i n t h e p h y s i c a l domain may be--extended t o t h e b i o - e c o l o g i c a l and s o c i e t a l domains as w e l l . B e f o r e t u r n i n g t o t h e m a c r o s c o p i c l e v e l i n o r d e r t o see how w e l l t h e d i s c o n t i n u i t i e s p r e d i c t e d by P i a g e t i a n t h e o r y a p p l y t o t h e n o v e l c o n t e n t domains, t h e m a t t e r o f s t a g e s as s t r u c t u r e d w h o l e s must be d i s c u s s e d . w i t h r e g a r d t o t h e s t a g e o f c o n c r e t e o p e r a t i o n s . The f i r s t t o be d e a l t w i t h i s t h e m a t t e r o f s t a g e s as s t r u c t u r e d w h o l e s . A f t e r t h a t t h e p o s s i b i l i t y o f a c o n c r e t e s t a g e d s y s t e m i c o p e r a t i o n a l t a s k i s d i s c u s s e d . S t r u c t u r e d Wholes. The d i f f i c u l t y o r d e r i n g s o f c o g n i t i v e o p e r a t i o n s change q u i t e r e a d i l y f r o m p e r s o n t o p e r s o n , f r o m mode o f p r e s e n t a t i o n t o mode o f p r e s e n t a t i o n and f r o m domain t o domain. M o r e o v e r , i t a p p e a r s t h a t each c o g n i t i v e o p e r a t i o n i s d i f f e r e n t i a l l y s e n s i t i v e t o t h e s e , and o t h e r , f o r c e s . The d i f f i c u l t y o f one c o g n i t i v e o p e r a t i o n may be r e d u c e d on second p r e s e n -t a t i o n , r e g a r d l e s s o f changed c o n t e n t , w h i l e a n o t h e r o p e r a t i o n ' s d i f f i c u l t y may be i n d e p e n d e n t o f number o f t r i a l s b u t c l o s e l y l i n k e d t o t h e n o v e l t y o f the m a t e r i a l s and/or c o n t e n t . The i n c o n s i s t e n c i e s o b s e r v e d a c r o s s domains i m p l y t h a t a t t h e most f i n e g r a i n e d l e v e l o f a n a l y s i s t h e s t a g e s r e a l l y a r e s t r u c t u r e s d'ensemble o r " s t r u c t u r e d w h o l e s " as P i a g e t has c l a i m e d t h e y a r e ( e . g . , I n h e l d e r and P i a g e t , 1 9 5 8 ) . The i n c o n s i s t e n c i e s e v i d e n t i n t h e p r e s e n t , d a t a . w o u l d n o t have a r i s e n i f a l l t h e c o n c r e t e o p e r a t i o n s were n o t i n t e r r e l a t e d i n some s t r u c t u r a l way 115; ( i . e . , by v i r t u e o f t h e i r common s t a g e ) . The i d i o s y n c r a s i e s o f each c o g n i t i v e o p e r a t i o n may a r i s e f r o m o u r v i e w i n g them as p a r t s s e p a r a t e d f r o m t h e s t r u c t u r e d w h ole. T h e i r i n d i v i d u a l o p e r a t i n g c h a r a c t e r i s t i c s become u n p r e d i c t a b l e when t h e y a r e t a k e n o u t o f t h a t c o n t e x t and t h e n compared w i t h each o t h e r . As a whole s t a g e o f o p e r a t i o n s , however, t h e c o n c r e t e o p e r a t i o n s a r e p r e d i c t a b l e . S p e c i f i c a l l y , t h e y a r e a l l m a s t e r e d i n m i d d l e c h i l d h o o d . The impetus t o compare i n d i v i d u a l c o n c r e t e o p e r a t i o n s w i t h one a n o t h e r comes f r o m e a r l i e r e m p i r i c a l e v i d e n c e t h a t t h e y a r e o r d e r e d w i t h i n t h e s t a g e o f c o n c r e t e o p e r a t i o n s . The p r e s e n t d a t a , by a l s o c omparing them a c r o s s d i v e r s e c o n t e n t domains, shows t h a t t h e e a r l i e r e v i d e n c e o f s y s t e m a t i c o r d e r i n g s was s o m e t h i n g o f an a r t i f a c t o f t a s k c o n t e n t . That i s , a l l t h e assessment t a s k s tended t o employ i n a n i m a t e p h y s i c a l o b j e c t s as t e s t i n g m a t e r i a l s ( e . g . , G l i c k and Wapner, 1968; Kohnstamm, 1968; Formanek and G u r i a n , 1 9 7 6 ) . C o n t e n t a r e a s t h a t d e a l w i t h n o n - p h y s i c a l e n t i t i e s ( e . g . , economic s i t u s e s ) can o n l y be r e p r e s e n t e d v e r b a l l y and t h e y may y i e l d d i f f e r e n t sequences. .The work on o r d e r i n g o p e r a t i o n s w i t h i n s t a g e s must be tempered by t h e p r e s e n t e v i d e n c e t h a t changes i n c o n t e n t can change t h e o r d e r i n g s . P e r h a p s because i t was l e s s f o c u s e d on t h e r e l a t i v e d i f f i c u l t y o f o n l y a few t a s k s o f s i m i l a r c o n t e n t , t h e p r e s e n t d a t a s u p p o r t t h e i d e a o f " s t r u c t u r e d w h o l e s . " That i s n o t t o say t h a t t h e r e a r e no p r e d i c t a b l e o r d e r -i n g s w i t h i n s t a g e s . I f e x t e n s i v e enough c o m p a r i s o n s a r e made among c o n c r e t e o p e r a t i o n a l t a s k s on v e r y l a r g e samples o f r e s p o n d e n t s , s u c h o r d e r i n g s do emerge. The s e a r c h f o r s u c h o v e r a l l w i t h i n - s t a g e o r d e r i n g s , h o w e v e r , i s now seen as a much more e l a b o r a t e u n d e r t a k i n g . A g r e a t e r s e n s i t i v i t y t o t y p e o f c o n t e n t i s r e q u i r e d . M a c r o s c o p i c L e v e l o f A n a l y s i s . A t t h i s l e v e l o f a n a l y s i s t h e f i r s t h y p o t h e s i s p r e d i c t e d Guttman s t e p s between s t a g e s i n a l l t h r e e domains. T h i s 1 1 6 i s p r e c i s e l y what was.observed w i t h the exception of the s o c i e t a l c y c l i c t r a n s i t i v i t y task. That exception i s discussed i n more d e t a i l below. Generally, the c e n t r a l Piagetian notion of a d i s c o n t i n u i t y between concrete and post-concrete thought was supported by the appropriate corresponding pattern i n the d i f f i c u l t y l e v e l data. Given the support provided by these macroscopic and microscopic analyses, the general Piagetian approach would appear to apply quite well to the b i o - e c o l o g i c a l and s o c i e t a l domains. Hence, we can be more confident that there were no major hidden confounds v i t i a t i n g the comparisons that were to be made between the systemic operational tasks and the formal operational tasks. Before the discussion goes on to the comparisons between the systemic tasks and the formal tasks there i s one more issue that must be mentioned. That i s the i n t e r p r e t a t i o n of the unusually low d i f f i c u l t y l e v e l s f o r the layout components of c y c l i c t r a n s i t i v i t y . ; Concrete Stage Systerns Logic? I t was suggested e a r l i e r that the s o c i e t a l domain layout procedure may have been e x t r a o r d i n a r i l y easy owing to a p r a c t i c e e f f e c t . I t i s also possible that the layout procedure may be a concrete stage example of a systemic operation. Future research could compare the d i f f i c u l t y l e v e l s obtained across f a c t o r i a l v a r i a t i o n s of element f a m i l i a r -i t y and order of presentation (practice) with a smaller range of respondents. For example, Kates and K'atz (1977) studied uninstructed understanding of the hydrologic (water) cycle i n 3, 4, and 5 year olds. With the pretest f a m i l i a r -i z a t i o n entailed i n the layout procedure, a l l the elements of the water cycle would be f a m i l i a r enough to concrete operational and early formal operational c h i l d r e n to inform us better about the e a r l i e s t appearance of mastery over t h i s type of operation. . 117 ( i i ) Second Hypothesis: Upper Systemic Tasks The second hypothesis was supported by the d i f f i c u l t y l e v e l data. Hypo-thesis two predicted that there would be a gap i n d i f f i c u l t y l e v e l s of the same s i z e between at l e a s t some systemic components and the most d i f f i c u l t formal operational task as there was Between the l e a s t d i f f i c u l t formal task and the most d i f f i c u l t concrete task. T h i s amounted to a p r e d i c t i o n that the gap i n terms of d i f f i c u l t y l e v e l s Between the formal tasks and the upper systemic components would B e a stage sized gap. In other words, i t was predicted that the d i f f i c u l t y l e v e l s data would suggest the p o s s i b i l i t y of a f i f t h stage. Since the corroboration of the o v e r a l l f i r s t hypothesis pre-cludes an i n t e r p r e t a t i o n of the predicted greater d i f f i c u l t y of the upper systemic tasks i n terms of confounding content re l a t e d differences i n the discreteness of stages, any observed greater d i f f i c u l t y i s a l l the more reason-ably interpreted as a function of the greater s t r u c t u r a l complexity ( i . e . , form r e l a t e d d i f f i c u l t y ) of the upper systemic components. The r e s u l t s of the Guttman step analyses ( i . e . , z scores for the differences between pro-portions) and the c l u s t e r analyses show that the systems synthesis and t r a n s i -t i v e r e c y c l i n g components were indeed a stage sized gap more d i f f i c u l t than the formal operational tasks. The t h i r d hypothesis dealt', w i t h a content rel a t e d a l t e r n a t i v e to a f i f t h stage i n t e r p r e t a t i o n . Before the v i a b i l i t y of the f i f t h stage i n t e r p r e t a t i o n i s examined i n that context, the argument for i t s reasonableness i s discussed i n d e t a i l with respect to the second hypothesis. The second hypothesis e n t a i l e d analyses' which were relevant to the structures d'ensembleo cr±tex;ton:-(P,iaget.;.;i$60| F l a v e l l , 1971a) f o r -identifying a stage and ;.to. -the- criterion:- that stages form q Guttman scale, (i.. e; Piaget's (I960) sequence 118 and hierarchy c r i t e r i a ) . The upper systemic tasks did indeed appear to be structures d'ensemble. They clustered e x c l u s i v e l y together i n the c l u s t e r analyses. They were separated from each other i n d i f f i c u l t y by non-Guttman step ( i . e . passing t r a n s i t i v e r e c y c l i n g and f a i l i n g systems synthesis was about as common as the reverse). Also, the s c a l a b i l i t y c o e f f i c i e n t s indicated that the systemic components were not unidimerisional and cumulative amongst themselves. The c r i t e r i o n that stages form a Guttman scale was also s a t i s f i e d with respect to the upper systemic tasks. The z : scores f o r differences between proportions — gave unequivocal evidence of t h i s . Evidence relevant to the abruptness and concurrence c r i t e r i a ( F l a v e l l , 1971a) for i d e n t i f y i n g stages i s examined i n subsection A, (IV) of t h i s chapter ("Age Related C r i t e r i a " ) . The systems analysis and layout'component were^not : acSuttmanr-stepmore d i f f i c u l t than the most d i f f i c u l t formal operation. S t r i c t l y speaking t h i s neither corroborates nor detracts from neither the f i f t h stage i n t e r p r e t a t i o n nor the p a r a l l e l i n t e r p r e t a t i o n . Nevertheless the fa c t that the s o c i e t a l domain layout component was so close to the most d i f f i c u l t concrete operation does suggest that concrete staged systemic operations might e x i s t . I f such operations were found, systemic operations would be p a r a l l e l to more than j u s t formal operations. They would be a whole cla s s of l o g i c a l operations develop-ing along with those exemplars of, and precursors of, formal l o g i c a l operations studied by Piaget and h i s collegues. ( i i i ) Third Hypothesis; Greater Content D i f f i c u l t y The t h i r d hypothesis predicted that the d i f f i c u l t y of the most d i f f i c u l t systemic tasks would not be wholly a t t r i b u t a b l e to any greater u n f a m i l i a r i t y of task content p e c u l i a r to those tasks. The z scores for the differences .11-9 between t h e p r o p o r t i o n s o f r e s p o n d e n t s p a s s i n g t h e f a m i l i a r i t y a s s e s s m e n t s and t h e a s s o c i a t e d t a s k s , and t h e f r e q u e n c i e s o f p a s s e s on b o t h p r e c l u d e any s t r a i g h t f o r w a r d a t t r i b u t i o n o f t h e g r e a t e r d i f f i c u l t y o f t h e upper s y s t e m i c t a s k s t o c o n t e n t d i f f i c u l t y ( s e e t a b l e s V and V I ) . W i t h t h e s e r e s u l t s t h e f i f t h s t a g e i n t e r p r e t a t i o n has s u r v i v e d a s i g n i f i c a n t f a l s i f i c a t i o n a t t e m p t . To d e c i d e what e f f e c t c o n t e n t f a m i l i a r i t y has on t a s k d i f f i c u l t y i t i s n e c e s s a r y t o d i s t i n g u i s h t h e c o n t e n t f r o m t h e r e q u i r e d o p e r a t i v e knowledge. A p r i o r i i t seemed that' t h e e l e m e n t s o f t h e n i t r o g e n c y c l e and t h e wheat c y c l e w o u l d be t h e o n l y c o n c e p t s t h a t a r e s p o n d e n t needed t o be f a m i l i a r w i t h i n o r d e r t o a p p l y t h e o p e r a t i o n s o f c y c l i c t r a n s i t i v i t y and systems a n a l y s i s t o t h o s e c o n t e n t s . E m p i r i c a l l y , however, i t t u r n e d o u t t h a t some r e s p o n d e n t s m a s t e r e d t h e t a s k s even w i t h o u t c o m p l e t e i n i t i a l f a m i l i a r i t y w i t h t h o s e e l e m e n t s . The systems s y n t h e s i s components seemed a p r i o r i t o r e q u i r e f u r t h e r f a m i l i a r i t y w i t h t h e c o n c e p t s o f s t a r v a t i o n and r e p r o d u c t i o n on t h e p o p u l a t i o n l e v e l i n t h e b i o - e c o l o g i c a l domain and w i t h p r o f i t s , t a x e s , and supply/demand r e l a t i o n s h i p s i n t h e s o c i a l domain. A g a i n , t h e e m p i r i c a l e v i d e n c e i s t h a t some r e s p o n d e n t s who ma s t e r e d t h e systems s y n t h e s i s t a s k s were u n f a m i l i a r w i t h t h e e n t a i l e d c o n t e n t . Added t o t h i s i s t h e e v i d e n c e t h a t w i t h i n domains t h e l o w e r s y s t e m i c components were n o t as d i f f i c u l t as t h e upper components d e s p i t e t h e f a c t t h a t t h e most u n f a m i l i a r e l e m e n t s were i n t e g r a l c o n t e n t s i n b o t h . F i n a l l y , t h e v a r i a t i o n s i n c o n t e n t f a m i l i a r i t y a c r o s s domains was n o t accompanied by as l a r g e v a r i a t i o n s i n t h e d i f f i c u l t y o f t h e t a s k s . A l l o f t h e s e f i n d i n g s make i t v e r y d i f f i c u l t t o argue t h a t t h e g r e a t e r d i f f i c u l t y o f t h e upper s y s t e m i c t a s k s i s a t t r i b u t a b l e i n l a r g e p a r t t o t h e g r e a t e r d i f f i c u l t y o f t h e i r c o n t e n t s . T h i s does n o t p r o v e t h a t c o n t e n t d i f f i c u l t y n e v e r i n f l u e n c e s t a s k d i f f i c u l t y for the upper systemic tasks. Nor does i t prove that the upper systemic tasks required more sophisticated cognitive operations. There may be a l t e r n a t i v e expla-nations that cannot be assessed with ..the data at hand but none spring to .mind. The i n t e r p r e t a t i o n that the tasks were more d i f f i c u l t because the cognitive operations they required were more d i f f i c u l t remains v i a b l e , (iv) Age Related. C r i t e r i a The data presented on Table VI were not connected with any hypothesis but they are relevant to the abruptness and concurrence c r i t e r i a ( F l a v e l l , 1971a) fo r i d e n t i f y i n g stages. These data ind i c a t e d that the mastery of various systemic operations i s concurrent (with the noted exception of the layout component of c y c l i c t r a n s i t i v i t y ) but not abrupt. The concurrence c r i t e r i o n i s a c t u a l l y subsumed by Piaget's i n t e r p r e t a t i o n of the structures d'ensemble. F l a v e l l made a more s t r i c t l y l o g i c a l i n t e r p r e t a t i o n of the structures d'ensemble c r i t e r i o n but supplemented i t with the concurrence c r i t e r i o n . Therefore the data already discussed i n connection with structures d'ensemble (see subsection A ( i i ) ; "Second Hypothesis") are more relevant to the concurrence c r i t e r i a than are these age data. The age data do not i n d i c a t e whether or not the mastery occurred as concurrently within i n d i v i d u a l s as i t did among i n d i v i d u a l s with-i n age groups. The z scores between the upper systemic tasks, however, do i n d i c a t e concurrence within i n d i v i d u a l s . The abruptness c r i t e r i o n , requires that the t r a n s i t i o n into the next higher stage be short i n duration. The age data have bearing on t h i s requirement at the l e v e l of groups of same aged peers but not at the l e v e l of the i n d i v i d u a l . I f the t r a n s i t i o n appear abrupt across independently sampled age groups then i t was l i k e l y to have been abrupt for the i n d i v i d u a l s a l s o . I f , however, the 121 cro s s - s e c t i o n a l data shows a gradual r i s e across age groups i n the frequency: of mastery then i t remains impossible to determine whether or not the i n d i v i d -uals undergo the t r a n s i t i o n abruptly. The c r o s s - s e c t i o n a l data reported i n Table VI showed an abrupt t r a n s i t i o n into the formal operational stage but a gradually increasing frequency of mastery over the upper systemic tasks. In f a c t , the frequency f o r successes on the upper systemic components never goes as high at any of the ages sampled as the frequencies f o r the formal tasks. Perhaps the upper systemic operations do not blossom i n the majority u n t i l an age beyond the oldest sampled here. Perhaps systemic thinking i s simply not a l l that common i n adults. The c r i t e r i a f o r i d e n t i f y i n g stages do not require that a f i f t h stage would have to be acquired by a l l adults. The v i a b i l i t y of the f i f t h stage i n t e r p r e t a t i o n remains unaffected by the abruptness c r i t e r i o n mainly because there are. no relevant data a v a i l a b l e . Even i f appropriate data were obtained that showed a gradual mastery of the upper systemic tasks, the f i f t h stage i n t e r p r e t a t i o n might s t i l l survive. Wohlwill (1973) argued that abruptness of t r a n s i t i o n i s not a necessary con-d i t i o n f o r a stage. F l a v e l l (1977) commented that Wohlwill's more dynamic notion of a stage seemed unconvincing. F l a v e l l ' s view i s that the whole idea of stages may have to be abandoned since attempts to save i t lead to such a d i l u t i o n of the concept that i t ceases to be u s e f u l . F l a v e l l may w e l l be correct but what i s at issue here i s the extent to which the upper systemic tasks meet stage c r i t e r i a at l e a s t as well as do other tasks i n other Piagetian stages. None of Piaget's stages may be very stage-like but we want to know i f the upper systemic c l u s t e r i s any le s s stage-like than the others. 122 (v) Summary A l l t h r e e h y p o t h e s e s were c o r r o b o r a t e d . The upper s y s t e m i c o p e r a t i o n s ( t r a n s i t i v e r e c y c l i n g and systems s y n t h e s i s ) seem t o meet t h e c r i t e r i a f o r b e i n g r e p r e s e n t a t i v e s o f a f i f t h s t a g e a t l e a s t as w e l l as o t h e r o p e r a t i o n s do f o r o t h e r s t a g e s . The a b r u p t n e s s o f t r a n s i t i o n c r i t e r i o n ' c o u l d n o t be e v a l u a t e d w i t h t h e p r e s e n t d a t a . The p a r a l l e l development i n t e r p r e t a t i o n a l s o r e m a i n s v i a b l e even though i t r e q u i r e s one t o s p e c u l a t e t h a t t h e upper s y s t e m i c o p e r a t i o n s were m e r e l y u n u s u a l l y d i f f i c u l t r e p r e s e n t a t i v e s o f a t y p i c a l e a s i e r s e t o f o p e r a t i o n s . The i s s u e i s f a r f r o m s e t t l e d . B. I n t e r p r e t a t i o n s o f S y s t e m i c D i f f i c u l t y L e v e l s I n t h i s s e c t i o n , t h e p a r a l l e l development i n t e r p r e t a t i o n i s g i v e n more a t t e n t i o n . Then i n t e r p r e t a t i o n s w h i c h i n v o l v e c u l t u r a l e v o l u t i o n as w e l l as , c o g n i t i v e development a r e c o n s i d e r e d . F i r s t , however, t h e n e x t s u b s e c t i o n examines some o f t h e l i m i t a t i o n s t h a t must be b o r n e i n mind when i n t e r p r e t i n g t h e r e s u l t s . ( i ) I n t e r p r e t i v e . C a v e a t s T h i s i s n o t i n t e n d e d t o be an e x h a u s t i v e l i s t o f t h e f a c t o r s c o n s t r a i n i n g i n t e r p r e t a t i o n o f t h e f i n d i n g s . The method and r e s u l t s c h a p t e r s c o n t a i n s e v e r a l comments on p o s s i b l e a r t i f a c t s and s o u r c e s o f u n r e l i a b i l i t y . What f o l l o w s h e r e a r e t h e most i m p o r t a n t c a v e a t s t o b e a r i n mind as one c o n s i d e r s . v a r i o u s i n t e r p r e t a t i o n s o f t h e g r e a t e r d i f f i c u l t y o f t h e upper s y s t e m i c t a s k s . Sample. The age p r o f i l e d a t a show t h a t n o t even among t h e 18 y e a r o l d s was t h e r e a s u b s t a n t i a l m a j o r i t y o f r e s p o n d e n t s who had m a s t e r e d t h e upper 123 s y s t e m i c t a s k s . We do n o t know how even o l d e r r e s p o n d e n t s might have p e r -formed. I t woul d be i n t e r e s t i n g t o s e a r c h f o r t h e e a r l i e s t age group a t w h i c h m a s t e r y o f t h o s e t a s k s was more o r l e s s u n i v e r s a l . T h e r e m i g h t be no such age group b u t f r o m t h e p r e s e n t sample o f ages i t i s i m p o s s i b l e t o know one way o r t h e o t h e r . A l s o , a l t h o u g h an a t t e m p t was made t o match t h e 18 y e a r o l d group t o t h e o t h e r age groups^'dlii terms o f p r o j e c t e d e d u c a t i o n a l / o c c u p a t i o n a l s t a t u s upon l e a v i n g s e c o n d a r y s c h o o l , t h e match was f a r f r o m p e r f e c t . I d e a l l y t h e 18 y e a r o l d group w o u l d have c o n t a i n e d a m a j o r i t y o f r e s p o n d e n t s who were o r who w i s h e d t o be f u l l t i m e members o f t h e l a b o u r f o r c e . Task D e f i n i t i o n s . To some e x t e n t t h i s i s a s e m a n t i c p r o b l e m . The q u e s t i o n i s w h e t h e r o r n o t t h e s y s t e m i c o p e r a t i o n s o f c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n s h o u l d be d i s p e n s e d w i t h i n f a v o r o f t h e more e l e m e n t a r y component s c o r e s . On l o g i c a l grounds i t seems j u s t i f i a b l e t o group t h e l a y o u t component t o g e t h e r w i t h t h e t r a n s i t i v e r e c y c l i n g component and t o group t h e systems a n a l y s i s component w i t h t h e systems s y n t h e s i s component. Now t h a t t h e d i f f i -c u l t y l e v e l r e s u l t s a r e a v a i l a b l e , however, t h o s e g r o u p i n g s c a n be q u e s t i o n e d on e m p i r i c a l grounds. The d i f f i c u l t y l e v e l s between t h e components o f t h e same s y s t e m i c o p e r a t i o n s were q u i t e d i f f e r e n t . P e r h a p s t h e s a f e s t p r o c e d u r e i s t h e one t h a t has been f o l l o w e d h e r e . That i s t o r e p o r t t h e r e s u l t s by com-po n e n t s as w e l l as by c o m p o s i t e o p e r a t i o n . F u t u r e r e s e a r c h w i l l have t o be based on f u r t h e r r e f i n e m e n t o f t h e s e c o n c e p t s . The i d e n t i f i c a t i o n o f t h i s p r o b l e m f o r f u t u r e t h e o r y and r e s e a r c h can be seen as one o f t h e h e u r i s t i c c o n t r i b u t i o n s o f t h i s s t u d y . M e anwhile, a measure o f c i r c u m s p e c t i o n i s i n o r d e r when i n t e r p r e t i n g any o f t h e c o m p o s i t e s c o r e s r e p o r t e d h e r e . T h i s i s s u e i s t a k e n up f u r t h e r i n C h a p t e r V s e c t i o n A, where t h e p o s s i b l e v a r i a t i o n i n ": 124 t h e . l o g i G o - m a t h e m a t i c a l forms o f c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n a r e c o n s i d e r e d , A p a r t i a l l y r e l a t e d p r o b l e m c o n c e r n s t h e c o m p o s i t i o n o f t h e component s c o r e s t h e m s e l v e s . A p p e n d i x D d e t a i l s t h e i t e m s f r o m w h i c h t h e s e s c o r e s were o b t a i n e d . F u t u r e r e s e a r c h ought t o i n c l u d e some a n a l y s e s o f t h e i n t e r n a l c o n s i s t e n c y o f t h e i t e m s used h e r e a l o n g w i t h w h a t e v e r n o v e l i t e m s can be d e v i s e d . I n t h i s r e g a r d i t w o u l d a l s o be d e s i r a b l e . t o d e v i s e assessment p r o c e d u r e s based on o t h e r open systems c y c l e s . The n i t r o g e n c y c l e and t h e wheat c y c l e c e r t a i n l y seem a p p r o p r i a t e f o r t h e p u r p o s e s a t hand b u t t h e ex-a m i n a t i o n o f a d d i t i o n a l c y c l e s w o u l d p r o v i d e an o p p o r t u n i t y t o i n c r e a s e t h e r e l i a b i l i t y and v a l i d i t y o f t h e assessment p r o c e d u r e s . A g a i n , no one s t u d y can s e t t l e a q u e s t i o n as b r o a d as e i t h e r t h e e x i s t e n c e o f a d e v e l o p m e n t a l s t a g e o r t h e e x i s t e n c e o f a p a r a l l e l t y p e o f l o g i c . Task A d m i n i s t r a t i o n . Most o f t h e i s s u e s s u r r o u n d i n g t h e f i x e d o r d e r i n w h i c h t h e t a s k s were p r e s e n t e d have a l r e a d y been d i s c u s s e d i n t h e method c h a p t e r . Now t h a t t h e r e s u l t s a r e a v a i l a b l e h i n d s i g h t r a i s e s one f u r t h e r i s s u e . I t t u r n s o u t t h a t t h e t a s k s w h i c h were a d m i n i s t e r e d l a s t were a l s o t h e ones t h a t appeared most d i f f i c u l t . A f t e r c l o s e t o an hour o f t e s t i n g some r e s p o n d e n t s might have e x p e r i e n c e d m e n t a l f a t i g u e and t h e r e f o r e p e r f o r m e d l e s s t h a n o p t i m a l l y on t h o s e v e r y t a s k s . There a r e some grounds f o r d i s c o u n t -i n g t h i s p o s s i b i l i t y . F i r s t o f a l l , a f a t i g u e h y p o t h e s i s w o u l d p r e d i c t a more o r l e s s s t e a d y p e r f o r m a n c e decrement. T h i s was n o t t h e c a s e . The b i o - e c o l o g i c a l systems s y n t h e s i s and t r a n s i t i v e r e c y c l i n g t a s k s were p r e s e n t e d b e f o r e any o f t h e s o c i e t a l s y s t e m i c t a s k s b u t p e r f o r m a n c e on some o f t h e l a t t e r was a c t u a l l y s u p e r i o r . The s o c i e t a l systems a n a l y s i s component and, e s p e c i a l l y , t h e l a y o u t component were much e a s i e r t h a n t h e upper s y s t e m i c t a s k s i n t h e 125 b i o - e c o l o g i c a l domain. To the extent that fatigue might have shortened at t e n t i o n spans, the e f f e c t would probably have been most pronounced among younger respondents. Although the r e l a t i v e easiness of the lower systemic tasks i n the s o c i e t a l domain argues against any such i n t e r p r e t a t i o n i t i s not known how much better performance, e s p e c i a l l y that of the younger respon-dents, might have been on those lower.systemic tasks had they been presented e a r l i e r . Therefore one ought to remain.undecided on t h i s issue. Were future research to circumvent the p o s s i b i l i t y of a fatigue e f f e c t , the r e l a t i v e l a t e -ness and infrequency of mastery of the systemic tasks might disappear. Note that t h i s caveat i s more damaging to the f i f t h stage i n t e r p r e t a t i o n than to the p a r a l l e l development i n t e r p r e t a t i o n . I f the d i f f i c u l t y l e v e l s f o r the upper systemic tasks are a r t i f i c i a l l y i n f l a t e d then the case for a p a r a l l e l development i n t e r p r e t a t i o n i s stronger. S t a t i s t i c s . The most obvious problem wi t h the s t a t i s t i c a l analyses i s the novelty of using z scores f o r differences between proportions. This s t a t i s t i c was not designed for t h i s use. It was meant to be re l a t e d to the normal d i s t r i b u t i o n . In adapting the z score for use i n indexing the Guttman l i k e nature of steps between adjacent tasks great pains were taken to avoid any reference to the normal d i s t r i b u t i o n and associated confidence i n t e r v a l s . The r a t i o n a l e f o r the use of t h i s s t a t i s t i c i s given i n the r e s u l t s chapter. Perhaps i t s greatest shortcoming as i t has been used here i s i t s cumbersome character. A more elegant technique has been recently published by Froman and Hubert (1980). Aside from i t s novelty, however, that technique appears to be suited f or more f i n e grained analyses of order hypotheses than was appropriate for the o v e r a l l f i r s t hypothesis. Froman and Hubert's technique would require p r i o r s p e c i f i c a t i o n of the precise s i z e of gaps between tasks within stages i2.6 v and w i t h i n c o n t e n t domains as w e l l as s p e c i f i c a t i o n o f c o r r e s p o n d i n g o r d e r s o f d i f f i c u l t y . F o r t h e p u r p o s e o f j u s t i f y i n g t h e e x t e n s i o n o f P i a g e t i a n t h e o r y t o t h e two n o v e l c o n t e n t domains t h e i r t e c h n i q u e seems i n a p p r o p r i a t e l y s p e c i f i c . I t w o u l d be more a p p r o p r i a t e f o r s t u d i e s w i t h l a r g e r samples o f r e s p o n d e n t s w i t h i n a much more r e s t r i c t e d age r a n g e . B a r t and A i r a s i a n ' s (1974) o r d e r i n g method might have been used w i t h t h e p r e s e n t d a t a w i t h r e g a r d t o t h e s t r u e t u r e s d'enseiiib 1 e c r i t e r i o n . T h at method, however, uses p a i r w i s e c o m p a r i s o n s o f " p a s s / f a i l " c a s e s w i t h " f a i l / p a s s " c a s e t o a p p r o x i m a t e t h e o r d e r i n w h i c h t a s k s may have been m a s t e r e d by r e -s p o ndents even though t h e r e s p o n d e n t s , whose d a t a a r e used t o c o n s t r u c t t h e o r d e r i n g may a c t u a l l y have f o l l o w e d a d i f f e r e n t o r d e r t h e m s e l v e s . O n l y l o n g i t u d i n a l o b s e r v a t i o n c o u l d p r o p e r l y , e s t a b l i s h an o r d e r i n g a t t h e i n d i v i d -u a l l e v e l o f a n a l y s i s . A l s o , B a r t and A i r a s i a n ' s r e l a t i o n o f " i n d e p e n d e n c e " may a c t u a l l y o b s c u r e r e a l l o n g i t u d i n a l o r d e r s by c o n s t r u i n g j o i n t - n e c e s s i t y as i n d e p endence. I n t h e i r s y s t e m i t i s i m p o s s i b l e t o d i s t i n g u i s h between a s i t u a t i o n w h e r e i n •the c h i l d must m a s t e r one o r a n o t h e r t a s k b e f o r e p r o c e e d i n g t o more advanced t a s k s and a s i t u a t i o n w h e r e i n t h e c h i l d must m a s t e r b o t h t a s k s b e f o r e p r o c e e d i n g . T h i s s h o r t c o m i n g c o u l d become c r i t i c a l where B a r t and A i r a s i a n ' s method was b e i n g used t o a s s e s s t h e e x t e n t t o w h i c h a group o f t a s k s were s t r u c t u r e s d'ensemble. One m ight be m i s l e d i n t o p o s t u l a t i n g two " i n d e p e n d e n t " s e t s o f t a s k s where a c t u a l l y r e l a t i o n s o f j o i n t n e c e s s i t y were i n e f f e c t . T h at s h o r t c o m i n g was n o t shared by t h e s t a t i s t i c s t h a t were used i n t h e p r e s e n t s t u d y . They were l e s s s o p h i s t i c a t e d b u t t h e y s e r v e d t h e i r f u n c t i o n a d e q u a t e l y , ( i i ) P i a g e t ' s P a r a l l e l P o s i t i o n So f a r t h e f i f t h s t a g e i n t e r p r e t a t i o n r e m a i n s v i a b l e . However, t h e 127 same c a n be s a i d o f t h e p a r a l l e l development i n t e r p r e t a t i o n . I n f a c t a v e r s i o n o f t h e p a r a l l e l p o s i t i o n was f a v o r e d by P i a g e t , a l b e i t b e f o r e t h e e v i d e n c e f r o m t h e p r e s e n t s t u d y had been o b t a i n e d . P i a g e t h o l d s t h a t no f u r t h e r q u a l i t a t i v e developments o c c u r a f t e r f o r m a l o p e r a t i o n s . There a r e no more s u b s u m p t i v e o p e r a t i o n s . A c c o r d i n g t o P i a g e t , development beyond f o r -mal o p e r a t i o n s p r o g r e s s e s i n terms o f h i g h e r and h i g h e r o r d e r s o f c o n c a t e n a -t i o n o f o p e r a t i o n s , n o t new s t a g e s . P i a g e t (1972) a d m i t s , however, t h a t t h e r e may be more c o g n i t i v e o p e r a t i o n s t h a n t h o s e t h a t he has i d e n t i f i e d . He con-cedes t h a t h i s work has f o c u s e d on f o r m a l l o g i c and t h a t l e s s f o r m a l l y l o g i -c a l o p e r a t i o n s o r whole c l a s s e s o f o p e r a t i o n s may y e t be d i s c o v e r e d . From t h i s p e r s p e c t i v e one c o u l d v i e w s y s t e m i c o p e r a t i o n s as q u a l i t a t i v e l y d i f f e r e n t f rom f o r m a l o p e r a t i o n s y e t n o t s u b s u m p t i v e o f them. They w o u l d r e p r e s e n t an a s p e c t o f p o s t - c o n c r e t e d i v e r s i f i c a t i o n i n c o g n i t i v e development. Some i n d i v i d u a l s may s p e c i a l i z e i n one t y p e o f p o s t - c o n c r e t e l o g i c o r t h e o t h e r . F o r t h e whole s p e c i e s , however, t h e two t y p e s c o n s t i t u t e " p a r a l l e l " d e v e l o p -m e n t a l p a t h s . The p a r a l l e l development i n t e r p r e t a t i o n i s n o t r u l e d out by t h e f a c t o f the g r e a t e r d i f f i c u l t y o f t h e upper s y s t e m i c t a s k s . W i t h i n t h e s t r u c t u r a l ensemble o f f o r m a l o p e r a t i o n s one f i n d s v a r i a t i o n s i n d i f f i c u l t y l e v e l f rom one c o g n i t i v e o p e r a t i o n t o a n o t h e r . The " p a r a l l e l " i n t e r p r e t a t i o n w o u l d a l l o w f o r t h e same amount o f v a r i a t i o n among s y s t e m i c o p e r a t i o n s . I t must be remem-b e r e d t h a t t h e r e a r e p r o b a b l y many o t h e r s y s t e m i c o p e r a t i o n s b e s i d e s t h e ones used i n t h i s s t u d y . T h e r e f o r e t h e p a r a l l e l i n t e r p r e t a t i o n i s n o t d i m i n i s h e d by e v i d e n c e t h a t some s y s t e m i c o p e r a t i o n s a r e a Guttman s t e p more d i f f i c u l t t h a n some f o r m a l o p e r a t i o n s because p o s s i b l y j u s t as many r e v e r s e c a s e s e x i s t . A l s o , w i t h a j u d i c i o u s s e l e c t i o n o f t h e more d i f f i c u l t c o n c r e t e o p e r a t i o n a l t a s k s ( e . g . , t r a n s i t i v i t y and c o n s e r v a t i o n o f w e i g h t ; M i l l e r , S c h w a r t z and 128 S t e w a r t , 1973) and t h e l e s s d i f f i c u l t f o r m a l o p e r a t i o n a l t a s k s , t h e gap be- 1 tween s t a g e s c o u l d be made t o appear non-Guttman. I f t h i s can be done f o r t h e gap i n d i f f i c u l t y l e v e l s between t h e t h i r d and f o u r t h s t a g e s , p r e s u m a b l y i t c o u l d a l s o be a r r a n g e d f o r t h e gap between t h e f o u r t h and p r o p o s e d f i f t h s t a g e s . I n o t h e r words t h e p a r a l l e l i n t e r p r e t a t i o n g a i n s by d e f a u l t t o t h e e x t e n t t h a t t h e whole c o n c e p t o f s t a g e s i s found t o be i n c o n s i s t e n t w i t h t h e a c t u a l c o u r s e o f development, ( i i i ) L a b o u v i e - V i e f ' s P a r a l l e l P o s i t i o n . L a b o u v i e - V i e f (1980) o f f e r s an i n t e r p r e t a t i o n o f l i f e span d i f f e r e n c e s i n p r e f e r r e d t y p e s o f l o g i c w h i c h w o u l d a c c o u n t f o r t h e l e s s t h a n a b r u p t age p r o f i l e o b s e r v e d on t h e s y s t e m i c components. She arg u e s t h a t p u r e f o r m a l l o g i c i s good f o r e x p l o r i n g p o s s i b i l i t i e s i n a c u l t u r e ' s a d a p t a t i o n t o i t s en-v i r o n m e n t and t h a t t h e more p r a g m a t i c a p p r o a c h o f o l d e r a d u l t s i s good f o r c o n -s e r v i n g a c c u m u l a t e d c u l t u r a l a r t i f a c t s t h a t have p r o v e n a d a p t i v e v a l u e . F o r a b i o l o g i c a l p o p u l a t i o n s h a r i n g a common c u l t u r e i t w o u l d be advantageous t o have a d u l t s c a p a b l e o f b o t h t y p e s o f l o g i c a l t h i n k i n g . A l s o , t h e g e n e r a t i o n r e l a t e d s p e c i a l i z a t i o n i n each t y p e o f l o g i c w o u l d enhance t h e p o p u l a t i o n ' s a d a p t i v e n e s s by s e t t i n g up a h o m e o s t a t i c mechanism f o r r e g u l a t i n g t h e a d a p t i v e v a l u e , v i s a v i s a s t a b l e o r c h a n g i n g e n v i r o n m e n t , o f t h e c u l t u r a l knowledge a v a i l a b l e t o t h e p o p u l a t i o n ' s members. Hence, a l t h o u g h i t was fo u n d t h a t t h e a b i l i t y t o p e r f o r m s y s t e m i c o p e r a t i o n s was a v a i l a b l e a t age 14, v e r y few o f t h e teen^aged r e s p o n d e n t s i n t h i s s t u d y showed s i g h s o f b e i n g s p e c i a l i s t s i n t h i s t y p e o f l o g i c . On t h e o t h e r hand, a l m o s t a l l o f them e x c e l l e d a t t h e t y p e o f l o g i c t h a t s u i t e d t h e s o c i o - b i o l o g i c a l c u l t u r a l f u n c t i o n o f t h e i r 129 1 age group. (iv) Stages and Paradigms One way to discount the non-abrupt age p r o f i l e data and thereby strengthen a f i f t h stage i n t e r p r e t a t i o n , would be to argue that the f i f t h stage l o g i c i s i n the process of being created i n our cu l t u r e . I f adult cognitive structures are assumed to be a product of the structures a v a i l a b l e i n the p a r t i c u l a r culture then the very f a c t of c u l t u r a l evolution guarantees the emergence of new sets of cognitive operations among the adult members of that cu l t u r e . Systemic operations may be part and p a r c e l of a " c u l t u r a l paradigm s h i f t " . Hence one would expect t h e i r prevalence to be low but increasing. The pre-valance of successful use of systemic l o g i c was low f o r the teen-aged respon-dents i n t h i s study. Long term follow up studies would be required to deter-mine whether or not a c u l t u r a l paradigm s h i f t i s underway. I f i t i s , there i s s t i l l a chance that perhaps at around ages 18 to 21 ( common ages of majority) or perhaps 27 to 30 (see G i l l i g a n and Murphy, 1979) systemic l o g i c would come to supercede formal l o g i c i n a culture where systemic l o g i c was well accepted among adults. 1. By way of adding texture to Labouvie-Vief 1s thesis I would l i k e to r e l a t e two pieces of anecdotal information obtained from secondary school teachers. An ecology teacher t o l d me that the grade 11 students who he found to be more adept i n understanding e c o l o g i c a l systems also tended to be those who were more conservation minded. Conserving, of course, i s the c u l t u r a l r o l e that Labouvie-Vief notes i s the s p e c i a l t y of older persons, those who use more pragmatic l o g i c . A h i s t o r y teacher made a s i m i l a r observation with regard to understanding s o c i a l systems. He noted that h i s grade 12 students who were more adept at t h i s were those who had more p r a c t i c a l experience i n p o l i t i c a l a c t i v i t y . Further, he f e l t that the students who were more "bookish", i n h i s words, were l e s s quick to see the systemic nature of s o c i e t a l organization. Again, t h i s corroborates the equation of systemic thinking with long term>activities aimed at maintaining a heritage and serv-ing a structure to which one has made a personal commitment. As Labouvie-V i e f (1980, p.153) states, "This conscious commitment to one pathway and the del i b e r a t e disregard of other l o g i c a l a l t e r n a t i v e s may indeed mark the onset of adult cognitive maturity." 13.0 One could, however, a l s o imbue the p a r a l l e l p o s i t i o n w i t h a modified v e r s i o n of the "paradigm s h i f t " argument. The modified paradigm s h i f t approach would again assume that c u l t u r e i n f l u e n c e s the form of a d u l t c o g n i t i o n (Buck-Morss, 1975; Buss, 1977; R i e g e l , 1976; L u r i a , 1979) but would not assume that one form was u n i v e r s a l l y s u p e r i o r t o , or subsumptive o f , another. Rather, the form of l o g i c p r e f e r r e d by a c u l t u r e would be a matter of adaptation to a p a r t i c u l a r environment and/or niche. Labouvie-Vief's t h e s i s could be asserted s i m u l -taneously. In t h i s case i t would produce an i n t e r p r e t a t i o n to the e f f e c t that our c u l t u r e must adapt i t s e l f to a very q u i c k l y changing environment. Another v a r i a n t i s that our c u l t u r e has chosen the adaptation s t r a t e g y (niche) of being very q u i c k l y changeable, very f l e x i b l e . I n e i t h e r case, that would n e c e s s i t a t e emphasizing formal l o g i c and suppressing systemic l o g i c as the p r e f e r r e d a d u l t form of c o g n i t i o n . Hence, the appearance of systemic c o g n i t i v e s t r u c t u r e s might be a l i t t l e delayed as deserved i n the age p r o f i l e data. A l s o , the m a j o r i t y of persons would never develop a f u l l f a c i l i t y w i t h , or c o n s o l i d a t i o n o f , the systemic s t r u c t u r e s e x a c t l y because they would be c u l -t u r a l l y , non-preferred. Again, t h i s i s . c o n s i s t e n t w i t h the age p r o f i l e data. In summary then, i t i s i m p o s s i b l e , given only the present data to decide whether the upper systemic operations develop i n p a r a l l e l w i t h formal operations or are a c t u a l l y r e p r e s e n t a t i v e s of a f i f t h stage. To a c e r t a i n extent the u n c e r t a i n t y may be a r e f l e c t i o n of the ambiguity that e x i s t s i n the l i t e r a -t ure on P i a g e t ' s f i r s t f our stages. In any case, w i t h regard to the more fundamental i s s u e of e l u c i d a t i n g the nature of a d u l t c o g n i t i o n , the present study serves to emphasize the importance of systemic operations. V. I m p l i c a t i o n s f o r Three A r e a s o f S t u d y The s p e c i f i c c o n t e n t s o f t h e s y s t e m i c i n t e r v i e w s a r e most r e l e v a n t f o r some a r e a s o f s t u d y w h i l e t h e f o r m o f t h e c o g n i t i o n s t u d i e d i s o f more i n t e r e s t f o r o t h e r a r e a s . T h i s c h a p t e r o u t l i n e s some o f t h e i m p l i c a t i o n s o f t h e r e -s u l t s f o r p a s t and f u t u r e r e s e a r c h and t h e o r y i n t h e a r e a s o f c o g n i t i v e d evelopment, s o c i a l development, and s o c i a l p s y c h o l o g y . A. C o g n i t i v e Development The r e s u l t s r e p o r t e d h e r e r a i s e a h o s t o f q u e s t i o n s f o r f u t u r e t h e o r y and r e s e a r c h i n c o g n i t i v e development. The p o s t u l a t i o n o f a d i f f e r e n t t y p e of l o g i c i s p e r h a p s t h e most f a r r e a c h i n g n o t i o n . The r e l a t i o n s h i p between f o r m a l and s y s t e m i c l o g i c cannot be f u l l y e l u c i d a t e d w i t h o u t more work. L o g i c o - m a t h e m a t i c a l a n a l y s e s w i l l be r e q u i r e d s i m p l y t o i d e n t i f y t h e p r e s e n c e o r absence o f each i n any p a r t i c u l a r c a s e . E m p i r i c a l s t u d i e s w i l l be needed t o s e t t l e q u e s t i o n s o f d e v e l o p m e n t a l p r i o r i t y v e r s u s s i m u l t a n e i t y a t a l l s t a g e s o f development. S y s t e m i c l o g i c b e a r s s i m i l a r i t i e s t o t h e t y p e o f t h i n k i n g t h a t s e v e r a l a u t h o r s have s u g g e s t e d t y p i f i e s mature a d u l t c o g n i t i o n . I t a l s o , however, seems t o be an e x t e n s i o n o f t h e c o n c r e t e s t a g e t o p o l o g i c a l l y based s u b l o g i c a l o p e r a t i o n s t h a t P i a g e t c l a i m s p r e c e d e an e u c l i d i a n c o n c e p t i o n o f space ( P i a g e t and I n h e l d e r , 1956; P i a g e t , I n h e l d e r and S z e m i n s k a , 1 9 6 0 ) . I f s y s t e m i c l o g i c does i n d e e d d e v e l o p i n p a r a l l e l w i t h f o r m a l l o g i c t h e n i t would have p r e c u r s o r s i n m i d d l e c h i l d h o o d and e a r l y a d o l e s c e n c e , F u t u r e r e s e a r c h i n c o n c r e t e s t a g e c o g n i t i v e development might l o o k f o r t h o s e p r e c u r s o r s . By way o f c l a r i f y i n g what i t i s we a r e t o l o o k f o r , t h i s s e c t i o n b e g i n s w i t h an e x a m i n a t i o n o f t h e c h a r a c t e r i s t i c s o f mature a d u l t c o g n i t i o n . 132. (i ) Corroborative Work bri Adult Cognition While the present research was i n progress, several a r t i c l e s have ap-peared on various aspects of adult cognition. In the realm of moral develop-ment, Gibbs (1979) reconceptualized Kohlberg's theory as a two-phase model. For the present, discussion the relevant aspect of Gibbs' reconceptualization i s h i s fourth and l a s t stage during the p r e - e x i s t e n t i a l , pre-adult phase. His fourth stage i s c a l l e d the "systems" stage. Gibbs, a f t e r an apology for the sketchiness of his d e s c r i p t i o n s of the stages describes the systems stage as follows: Evidence for a fourth stage i s apparent p r i m a r i l y i n the sociomoral realm, although such a d i s t i n c t i o n may also be helpful:'.in the l o g i c o -cognitive realm (e.g., Wyatt and Geis, 1978). Over the course of the adolescent years, there i s a progressive a b i l i t y to discern the system-a t i c arrangements which are necessary to form a v i a b l e society, r e a l or hypothetical (see Adelson and O'Neil, 1966; Adelson et a l . , 1969). In t h e i r seminal studies, Adelson et a l . found that the adolescent comes to appreciate law and the r e l a t i o n between the i n d i v i d u a l and society not simply i n terms of p r o s o c i a l i n t e n t i o n and benevolent authority (stage 3), but more.broadly i n terms of s o c i a l functions and p r a c t i c e s . Thus, there i s an 'expansion' (Selman, 1976, p. 307) i n second-order thinking such that an o v e r a l l perspective i s applied not only to face-to-face r e l a t i o n s h i p s , but also to complex s o c i a l systems as represented by modern society (cf. Edwards, 1975, i n press). (Gibbs, 1979, p. 102)" Although the present study was not concerned with the moral aspects of understanding s o c i a l systems, i t i s i n t e r e s t i n g that Gibbs should independently characterize thinking about society as systemic. There seems to be a consensus emerging that (a) society i s best described as a system, and Cb) and understand-ing of society requires systemic thought. To be f a i r , the l a t t e r comment a c t u a l l y requires q u a l i f i c a t i o n . Piaget 133 (1972) d i d come t o s t r e s s t h a t t h e r e were some problems c r e a t e d by t h e i d e n t -i f i c a t i o n o f o p t i m a l c o g n i t i v e development w i t h s c i e n t i f i c a n a l y s i s . I n h i s own c o n s i d e r a t i o n o f some f o r m o f p a r a l l e l development i n t e r p r e t a t i o n , P i a g e t s t a t e s : We c o u l d , t h e r e f o r e , f o r m u l a t e t h e f o l l o w i n g h y p o t h e s i s : i f t h e f o r m a l s t r u c t u r e s d e s c r i b e d i n p a r t 1 do n o t appear i n a l l c h i l d r e n o f 14-15 y e a r s and d e m o n s t r a t e a l e s s g e n e r a l d i s t r i b u t i o n t h a n t h e c o n c r e t e s t r u c t u r e s o f c h i l d r e n f r o m 7-10 y e a r s o l d , t h i s c o u l d be due t o t h e d i v e r s i f i c a t i o n o f a p t i t u d e s w i t h age. A c c o r d i n g t o t h i s i n t e r p r e t a t i o n , however, we would have t o admit t h a t o n l y i n d i v i d u a l s t a l e n t e d f r o m t h e p o i n t o f v i e w o f l o g i c , m athematics and p h y s i c s would manage t o con -s t r u c t s u c h f o r m a l s t r u c t u r e s , whereas l i t e r a r y , a r t i s t i c and p r a c t i c a l i n d i v i d u a l s would be i n c a p a b l e o f d o i n g s o . I n t h i s c a s e i t w o u l d n o t be a p r o b l e m o f under-development compared t o n o r m a l development b u t more s i m p l y a g r o w i n g d i v e r s i f i c a t i o n i n i n d i v i d u a l s , t h e span o f a p t i t u d e s b e i n g g r e a t e r a t t h e l e v e l o f 12-15 y e a r s , and above a l l between 15 and 20 y e a r s , t h a n a t 7-10 y e a r s . I n o t h e r words, our f o u r t h p e r i o d can no l o n g e r be c h a r a c t e r i z e d as a p r o p e r s t a g e , b u t would a l r e a d y seem t o be a s t r u c t u r a l advancement i n t h e d i r e c t i o n o f s p e c i a l i z a t i o n . ( P i a g e t , 1972, p. 9 ) " B o s w e l l ' s (1979) f i n d i n g t h a t 'mature!, t h o u g h t ••i-simpre-'-l^ytithfesl^lng' and j -as I w o u l d c a l l - i t , , s y s t e m i c , i s c o r r o b o r a t e d by l i f e - s p a n r e s e a r c h "showing d i f f e r e n c e s a c r o s s p r o f e s s i o n a l s p e c i a l i z a t i o n s i n t h e ages a t w h i c h c r e a t i v e c o n t r i b u t i o n s a r e most f r e q u e n t ( e . g . , D e n n i s , 1 9 6 6 ) . M a t h e m a t i c i a n s t e n d t o make t h e i r b e s t c o n t r i b u t i o n s e a r l i e s t . N a t u r a l s c i e n t i s t s , a r t i s t s , p h i l o s o p h e r s , and h i s t o r i a n s f o l l o w i n t h a t a p p r o x i m a t e o r d e r . M a t h e m a t i c s , o f c o u r s e , i s t h e epitome o f f o r m a l a b s t r a c t i o n . H i s t o r y , on t h e o t h e r hand, i s i n c o m p r e h e n s i b l e w i t h o u t a r i c h b ase o f c o n t e x t u a l d e t a i l s o u t o f w h i c h t h e s t o r y o f t h e e v o l u t i o n o f s o c i e t y can be s y n t h e s i z e d . 134 The f i f t h s t a g e i n t e r p r e t a t i o n r e c e i v e d some c o r r o b o r a t i o n i n a. .study by M i c h a e l B a s s e c h e s (1980) on t h e development o f d i a l e c t i c a l t h i n k i n g . As mentioned i n A p p e n d i x E, t h e o v e r l a p between systems l o g i c and what i s u s u a l l y meant by d i a l e c t i c a l l o g i c i s c o n s i d e r a b l e . B a s s e c h e s c l a i m e d t o have found s u p p o r t f o r , " t h e i d e a o f a p o s t - f o r m a l - o p e r a t i o n a l s t a g e o f c o g n i t i v e o r g a n i z a t i o n b a s e d on t h e e l a b o r a t i o n o f d i a l e c t i c a l t h i n k i n g . " ( i i ) P o s t - C o n c r e t e D i v e r s i f i c a t i o n t The r e s u l t s o f t h e p r e s e n t s t u d y c o n t r i b u t e t o t h e g r o w i n g consensus t h a t t h e r e ' s more t o p o s t - c o n c r e t e t h o u g h t t h a n j u s t f o r m a l o p e r a t i o n s . I n o r d e r t o a v o i d c o n f u s i n g a d o l e s c e n t and a d u l t t h o u g h t i n g e n e r a l f r o m f o r m a l o p e r a t i o n a l t h o u g h t i n p a r t i c u l a r , I p r e f e r t o r e f e r t o t h e f o u r t h s t a g e o f c o g n i t i v e development as t h e " p o s t - c o n c r e t e " s t a g e . P o s t - c o n c r e t e t h o u g h t encompasses f o r m a l o p e r a t i o n s , s y s t e m i c o p e r a t i o n s , and y e t - t o - b e - d i s c o v e r e d o p e r a t i o n s . P o s t - c o n c r e t e t h o u g h t i s c h a r a c t e r i z e d by a g r o w i n g d i v e r s i f i c a -t i o n o f a b i l i t i e s . The p r e s e n t s t u d y has fo u n d e v i d e n c e s u g g e s t i n g o n l y one g r o s s b i f u r c a t i o n , t h a t between f o r m a l l o g i c and s y s t e m i c l o g i c . The p a r e l l e l i n t e r p r e t a t i o n o f t h e r e s u l t s o f t h e p r e s e n t s t u d y a l o n g w i t h B o s w e l l ' s f i n d i n g s and L a b o u v i e - V i e f ' s arguments s u g g e s t an o v e r a l l v i e w o f c o g n i t i v e development t h a t i s s i m i l a r t o P i a g e t ' s b u t b r o a d e r . T h i s expanded v i e w o f c o g n i t i v e development s e e s a d d i t i o n a l l i n e s o f d e v e l o p -ment moving a l o n g i n p a r a l l e l w i t h t h e development o f a b s t r a c t l o g i c . I n l a t e r w r i t i n g s P i a g e t (1972) a l s o c o n s i d e r e d t h i s expanded v i e w . The o v e r -a r c h i n g n o t i o n i s t h a t w i t h i n c r e a s i n g age i n d i v i d u a l s become more d i f f e r e n t f r o m one a n o t h e r i n s o f a r as some l o g i c a l a b i l i t i e s g e t more e l a b o r a t e d and s o p h i s t i c a t e d i n some i n d i v i d u a l s b u t n o t i n o t h e r s . The " o t h e r s " , however, 135' might be s p e c i a l i z i n g i n d i f f e r e n t l o g i c a l a b i l i t i e s . ^ ( i i i ) Problem F i n d i n g and S o l v i n g i n E i t h e r l o g i c One i n t e r e s t i n g f e a t u r e of the upper systemic tasks i s that t h e i r empha-s i s on feedback loops and dynamic i n t e r r e l a t e d n e s s allows the person us i n g these operations to d i s c o v e r hidden, non-obvious i m p l i c a t i o n s and r a m i f i c a -t i o n s of p a r t i c u l a r events. With formal l o g i c the v a r i a b l e s or elements main-t a i n t h e i r i d e n t i t i e s , or t h e i r i d e n t i t i e s are recoverable, through r e v e r s i b i l -i t i e s of thought, r e g a r d l e s s of whatever transforming operations may be per-formed upon them. With systems l o g i c the elements are c o n s t a n t l y changing each others' o r g a n i z a t i o n and/or c a p a c i t y . Perhaps " c o - e v o l u t i o n " i s the best term to describe the c y c l e of continuous mutual i n f l u e n c e c h a r a c t e r i s t i c of systems operating according to the p r i n c i p l e of c y c l i c i n t e g r a t i o n . The i d e n t i t i e s of the elements i n v o l v e d are not f i x e d . They evolve. Hence, the use. o f systemicT l o g i c may make, i t e a s i e r , i n " some s i tuatiohs.-,to. d i scover unexpected i n t e r a c t i o n s or phenomena. In t h i s sense systemic l o g i c overlaps w i t h A r l i n ' s (1975) candidate f o r a f i f t h stage, "problem f i n d i n g " . A r l i n d i s t i n g u i s h e d problem f i n d i n g from "problem s o l v i n g " , which i s seen as a hallmark of formal l o g i c . But Labouvie-Vief (1980) notes that formal l o g i c a l s o generates novel and u n t r i e d s o l u t i o n s . I f the terminology i s adjusted, i t can be seen how both forms of l o g i c can both promote and i n h i b i t c r e a t i v i t y . 1. The more advanced systemic operations are s t i l l being a r t i c u l a t e d by math-ematicians and philosophers. The p r i n c i p l e s of General Systems Theory seem the most l i k e l y candidates here. P r i n c i p l e s such as emergence, e q u i f i n a l i t y , and c o - e v o l u t i o n are a few examples. For researchers i n t e r e s t e d i n t a k i n g up t h i s quest, von B e r t a l a n f f y (1968), K l i r (1972), and Weinberg 0-975) pro-v i d e good i n t r o d u c t i o n s . A l s o , Jantsch and Waddington (1976) have compiled a panoramic sampling of the a p p l i c a t i o n s of these p r i n c i p l e s i n v a r i o u s sciences 136 Problem solving could also be c a l l e d " s o l u t i o n f i n d i n g " . That l a b e l brings out Labouvie-Vief's point about the c r e a t i v i t y of formal l o g i c j u s t as A r l i n 1 s phrase brings out i t s f o r e c l o s i n g properties. "Problem f i n d i n g " suggests the creative side of systemic l o g i c . New d e f i n i t i o n s of problems are the key to new invention. On the other hand, i f problem f i n d i n g i s taken to mean f i n d i n g reasons f o r not attempting new solutions we can see the i n h i b i t o r y r o l e i t plays i n creative exploration. C r e a t i v i t y i s a multifaceted phenomenon and thankfully neither form of l o g i c seems to have i t cornered, (iv) C y c l i c T r a n s i t i v i t y and the Feedback Concept. C y c l i c t r a n s i t i v i t y i s based on the fundamental systemic concept of feedback. The r e c y c l i n g component c l e a r l y requires an understanding of the feedback concept. The layout procedure, however, could be solved without i t . Adjacent elements could be considered successively without ever entertaining any notion about how an element receives i t s own output back as input. In Selman and Jaquette's (1977) stage, theory of s o c i a l perspective taking, the stage 3 c h i l d can see a l l the perspectives but cannot see them a l l at once. Likewise, the c y c l i c t r a n s i t i v i t y layout procedure could be solved by consider-ing the l i n k s between elements successively only. At the next phase i n Selman and Jaquette's framework the c h i l d can deal with mutualities and see two per-spectives simultaneously. The basic features of feedback could be read into the layout procedure through the simultaneous appreciation of an element's input as i t s output and of i t s output as i t s input. This l e v e l of s o p h i s t i c a -t i o n , however, would not be necessary to produce a correct answer for the layout procedure. In a two element cy c l e , the equation of one elements out-puts with i t s l a t e r inputs amounts to solving the layout problem:through the 137' use o£ a t r a n s i t i v e r e c y c l i n g operation. Perhaps the layout component, with a more f a m i l i a r content, would prove to be a task simulating the operations underlying Selman and Jaquette's second stage ( s e l f - r e f l e c t i o n ) . Likewise, what underlies t h e i r t h i r d stage (mutual perspectives) might be the opera-t i o n of t r a n s i t i v e r e c y c l i n g . Future research i n the area of s o c i a l perspective 2 taking might examine the relevance of t h i s systemic cognitive operation. Conversely, future research on c y c l i c t r a n s i t i v i t y might examine the e f f e c t s of reducing (or increasing) the number of elements i n the c y c l e . A two element cycle would be a closer analogue of the perspective taking problem. One of the most curious findings with respect to c y c l i c t r a n s i t i v i t y was i n the s o c i a l domain t r a n s i t i v e r e c y c l i n g section. The introductory "Own Wheat" item (see table V), which assessed the a b i l i t y of respondents to trace the commodity flow i n the d i r e c t i o n opposite to that of the d o l l a r flow, was not intended to measure a b i l i t y with c y c l i c t r a n s i t i v e operations. None-theless, as the data came i n , the item began to appear more and more i n t e r e s t i n g . The "own wheat" item was serendipitously constructed to be am exact mirror image of the "same d o l l a r twice" item from which the s o c i a l t r a n s i t i v e r e c y c l i n g scores were obtained. The only l o g i c a l d ifference was that the wheat went from the farmer to the WMB f i r s t ( l e t us c a l l t h i s the clock-wise d i r e c t i o n ) while the d o l l a r went from the farmer to the grocery store 2 . I f i t proved f r u i t f u l , t h i s l i n e of reasoning might lead future i n v e s t i -gators to the next l o g i c a l question: what more sophisticated version of c y c l i c t r a n s i t i v i t y might under l i e Selman and Jaquette's fourth stage ( s o c i a l and conventional system)? At f i r s t glance i t appears that the fourth stage ( s o c i a l and conventional system)? At f i r s t glance i t appears that the fourth stage moves away from any sort of t r a n s i t i v e operation to-wards a c l a s s i f i c a t i o n of a l l the elements under one heading. The elements cease to be viewed as d i s t i n c t e n t i t i e s and come to be seen as parts of an integrated whole. This sounds l i k e systems synthesis. 1:38 f i r s t (counterclockwise d i r e c t i o n ) . S u r p r i s i n g l y , the clockwise item was much easier than the counterclockwise item. I f we look closer at the nature of what i s being cycled we see that t r a c i n g bread around the wheat cycle i s easier than t r a c i n g money around i t . Maybe t h i s i s because the younger c h i l d r e n can imagine wheat, f l o u r , and bread moving without the r e c i p r o c a l movement of money. They might have more trouble thinking of money moving without the r e c i p r o c a l movement of goods. I f so then the movement of goods i s an " u n i d i r e c t i o n a l " t r a n s i t i v e r e c y c l i n g because only one thing moves i n only one d i r e c t i o n . The movement of money would be l i k e a " b i d i r e c t i o n a l " t r a n s i t i v e r e c y c l i n g because every time the money moves i n one d i r e c t i o n there must be goods moving i n the opposite d i r e c t i o n . This i n t e r p r e t a t i o n i s consonant with the findings of Furth, et a l . (1979) that c h i l d r e n understand that you get food from the grocer before they understand that you have to give the grocer money i n return. In any case future research ought to examine the differences between more c l e a r l y constructed cases of u n i d i r e c t i o n a l and b i d i r e c t i o n a l t r a n s i t i v e r e c y c l i n g . Another p o s s i b l e i n t e r p r e t a t i o n of the di f f e r e n c e has to do with what happens to the recycled commodity when the farmer receives i t . The bread stops going around the cycle because the farmer e a t s , i t . The "same d o l l a r twice" item, on the other hand, makes s p e c i f i c reference to the release of the r e -cycled commodity f or a second time. The bread goes around once but the d o l l a r can go around an i n d e f i n i t e number of times. The wheat/flour/bread t r a v e l s i n a s i n g l e c i r c l e ; the d o l l a r t r a v e l s around the c i r c l e an i n d e f i n i t e number of times, giving the impression of a s p i r a l motion. Future research might also examine the importance of t h i s a d d i t i o n a l v a r i a b l e i n c y c l i c t r a n s i t i v i t y . 139 (v) C y c l i c Integration and I t s Components. The systems analysis sections of the interviews assessed the respondent's a b i l i t y to decompose the whole cy c l e , into i t s minimally e s s e n t i a l subcycles while s t i l l preserving i t s i n t e g r i t y . In the b i o - e c o l o g i c a l domain, f o r example, t h i s meant di s p l a y i n g a r e a l i z a t i o n that the carnivores and herbivores could be eliminated without eliminating the remaining elements but that none of the three remaining elements (producers, decomposers, nutrients) could be eliminated without destroying the whole cy c l e . The systems analysis operation seems to be a systemic analogue of the i s o l a t i o n of v a r i a b l e s operation i n formal l o g i c . Some systems t h e o r i s t s con-sider the phrase "systems a n a l y s i s " to be a contradiction i n terms since analysis per se e n t a i l s untangling the complex web of interconnectedness. Perhaps i t i s f o r that very reason that the term "systems analysis has come to r e f e r to the study of more closed systems, notably computers. During the l a t e 1950's and early 1960's, systems theory was synonymous with systems a n a l y s i s . Later systems t h e o r i s t s , concerned with more open systems (e.g., b i o l o g i s t s l i k e Ludwig von B e r t a l a n f f y and Conrad Waddington), t r i e d to expand systems theory into areas concerned with synthesis, co-evolution and emergence. This l a t t e r thrust seems to require the type of thinking that the systems synthesis component has tapped. As o r i g i n a l l y conceived, c y c l i c i n t e g r a t i o n was to subsume c y c l i c t r a n s i -t i v i t y i n s o f a r as the subordinate (bottom) and supraordinate (top) l e v e l s mutually influence one another through b i d i r e c t i o n a l feedback loops. Part of the influence flows from the bottom to the top and part of i t flows from the top to the bottom. The systems synthesis qomponent captured more of the i4:o f l a v o r of what c y c l i c i n t e g r a t i o n was intended to be than did the systems analysis component. The systems synthesis section dealt d i r e c t l y with the flow of influence from the subordinate l e v e l to the supraordinate l e v e l (see figure 7, part A). There i s need f o r further logico-mathematical refinement of the c y c l i c i n t e g r a t i o n construct before what was intended by i t can be more e f f e c t i v e l y assessed. Is systems synthesis to be considered the bottom to top component of a larger grouping of operations to be c a l l e d c y c l i c integration? I f so, shouldn't there also be some operation included i n the grouping that treats the subordinate l e v e l by each single element and traces t h e i r e f f e c t s on the multiple facets of the supraordinate l e v e l (see f i g u r e 7, part B)? Or should we consider i n t e g r a t i o n to be a type of multiple concatenation i n v o l v i n g t r a n s i t i v e recycling? I f so, then both the supraordinate and the subordinate l e v e l s would be treated by sing l e elements (see fi g u r e 7, part C). The same questions could be posed i n reverse when dealing with the top to bottom part of c y c l i c i n t e g r a t i o n . Obviously, there i s much room for future work at the most advanced l e v e l s of systemic thinking. B. S o c i a l Development The implications of t h i s reasearch f o r s o c i a l development i n the sense of understanding interpersonal i n t e r a c t i o n were mentioned i n section A (iv) of t h i s chapter i n connection with Selman and Jaquette's (1977) stage theory of s o c i a l perspective taking. The present section deals e x c l u s i v e l y with s o c i a l development i n the sense of i n t e r a c t i o n between the i n d i v i d u a l and society. F i g u r e 7 Some p o s s i b l e forms o f b ottom t o top p r o c e s s e s i n c y c l i c i n t e g r a t i o n . Many to one: systems s y n t h e s i s s i n g l e e n t i t y S u p r a o r d i n a t e L e v e l •Subordinate L e v e l m u l t i p l e e n t i t i e s ( e . g . , a p o p u l a t i o n ) B. One t o m a n y : l i k e Marx's " i n t e r n a l r e l a t i o n s " m u l t i p l e e n t i t i e s s i n g l e e n t i t y ( e . g . , an i n d i v i d u a l ) T r a n s i t i v e form: t a k e s r e p r e s e n t a t i v e e n t i t i e s from b o t h p o p u l a t i o n s m u l t i p l e e n t i t i e s t r e a t e d s i n g l y if .-0* m u l t i p l e e n t i t i e s t r e a t e d s i n g l y I n terms o f t h e development o f u n d e r s t a n d i n g o f s o c i a l s y s t e m s , we have begun t o f o r m a l i z e , o r p e r h a p s a b e t t e r word wo u l d be "mathematize", t h e c h i l d ' s p r o g r e s s . The: p i o n e e r work o f F u r t h ( 1 9 7 7 ) , Jahoda (1979) and o t h e r s was l a r g e l y d e s c r i p t i v e , as i t s h o u l d be a t t h a t i n i t i a l s t a g e o f i n v e s t i -g a t i o n . Now t h a t s e v e r a l s t u d i e s have a c c u m u l a t e d , t h e p r e s e n t s t u d y a t t e m p t e d t o u n e a r t h t h e u n d e r l y i n g c o g n i t i v e o p e r a t i o n s . S i n c e some o f t h e i n d i v i d u a l c o g n i t i v e o p e r a t i o n s show a s e n s i t i v i t y ( i n terms o f d i f f i c u l t y l e v e l ) t o s l i g h t changes i n c o n t e n t , p e r h a p s t h a t i s n o t t h e most u s e f u l l e v e l on w h i c h to r e p o r t t h e r e s u l t s . I n s t e a d , t h e f i n d i n g s a r e d e s c r i b e d a t a g r o s s e r b u t more s t a b l e l e v e l , t h e l e v e l o f g r o u p i n g s o f o p e r a t i o n s . As f a r as can be d e t e r m i n e d f r o m t h e r e s e a r c h done up t o how, c h i l d r e n seem t o go t h r o u g h f o u r phases i n t h e i r p r o g r e s s towards an a d u l t u n d e r s t a n d i n g o f s o c i a l s y s t e m s . T h i s p r o p o s i t i o n s h o u l d be t r e a t e d as a h y p o t h e s i s r a t h e r t h a n a c o n c l u s i o n . T h i s i s an a r e a where t h e f i n d i n g s o f t h e p r e s e n t s t u d y a r e o f h e u r i s t i c v a l u e . W i t h t h a t i n mind, l e t us p r o c e e d t o a more d e t a i l e d e x a m i n a t i o n o f t h i s " f o u r p h a s e s " h y p o t h e s i s . I t i s b e i n g s u g g e s t e d t h a t t h e f i r s t two phases appear d u r i n g t h e s t a g e o f c o n c r e t e o p e r a t i o n s . The l a s t two seem t o appear d u r i n g t h e p o s t - c o n c r e t e s t a g e . A l l c h i l d r e n w o u l d p r e s u m a b l y go t h r o u g h t h e s t a g e s i n t h e same sequence b u t t h e appearance o f phases W i t h i n s t a g e s i s s u b j e c t t o a g r e a t d e a l more i n d i v i d u a l v a r i a t i o n i n o r d e r i n g t h a n t h e i r appearance between s t a g e s , ( i ) O r d i n a t i o n The f i r s t t h i n g t h a t c h i l d r e n seem t o a p p r e c i a t e about s o c i a l o r g a n i z a t i o n i s t h a t some p e o p l e a r e more i m p o r t a n t t h a n , o r "come b e f o r e " o t h e r s . There a r e t h e p e o p l e a t t h e t o p , t h e p e o p l e i n t h e m i d d l e , and t h e p e o p l e a t t h e bottom. T h i s r e a l i z a t i o n i s r e f l e c t e d i n e v e r y t h i n g f r o m t h e i r u n d e r s t a n d i n g o f t h e " f i r s t come f i r s t s e r v e " r u l e t o t h e i r t h r e a t s t o t a t t l e t a l e on each o t h e r . 143 ( i i ) Hierarchy The understanding of nested c l a s s i f i c a t i o n s and whole-part r e l a t i o n s h i p s usually develops a l i t t l e l a t e r . This i s when government s t a r t s to be seen as a permanent apparatus of power, a state structure. P r i o r to that c h i l d r e n often speak of the government as "he", and "he" has personal power (Connell, 1971; Easton and Dennis, 1969). The understanding of h i e r a r c h i c a l s o c i a l ordering also extends to g e o - p o l i t i c a l areas (Jahoda, 1964). Children begin to r e a l i z e that being a Vancouverite does not preclude one from being a B r i t i s h Columbian and a Canadian at the same time. ( i i i ) Systems Analysis The a b i l i t y to mentally remove elements from a s o c i a l feedback loop without destroying the cycle i t s e l f would appear to emerge early i n the post-concrete stage. Adelson and h i s colleagues (Adelson, Green and O'Neil, 1969; Adelson and O'Neil, 1966; Adelson, 1970) has commented on the extremely draconian and a u t h o r i t a r i a n approach that adolescents often take to s o c i a l order. Perhaps t h i s i s a natural r e s u l t of being able to c o g n i t i v e l y remove (e.g., execute, outlaw, ban) the elements that a cursory causal analysis i d e n t i f i e s as the pre-c i p i t a t i n g causes of the disorder (e.g., lawbreakers, unions, opposition p a r t i e s ) . The adolescent r e l y i n g s o l e l y on systems analysis s t a r t s by'taking the s o c i a l system as a given. The changes that are seen as possible involve changes i n the parts of the system, not the whole system. There i s l i t t l e appreciation for how the whole evolves into something else when one of i t s interdependent parts i s changed. (iv) Systems Synthesis With the mastery of systems synthesis the adolescent can now also envisage changes i n the whole s o c i a l system a r i s i n g from the actions and i n t e r a c t i o n s of the parts across time. Systems synthesis allows the adolescent to relate;.effects across personal and s o c i e t a l l e v e l s . For example, seeing the interrelatedness -144 between personal finances and the national economy was counted as evidence of systems synthesis. The amount of taxes paid are rela t e d both to how much one earns and how much the government-spends. Likewise, government expenditures are r e l a t e d to how much the government charges i n taxes and how much the national currency w i l l fetch i n t e r n a t i o n a l l y . Note here that there are two l e v e l s of finance, the personal and the n a t i o n a l . Each l e v e l i s affected by factors on the same h o r i z o n t a l l e v e l . Discretionary personal income f o r an i n d i v i d -ual or p r o f i t s f o r a business are affected by both gross income and cost. The balance of a na t i o n a l budget i s affected by the value of the currency and that i n turn r e l a t e s to the governments " p r o d u c t i v i t y " i n terms of fore i g n p o l i c y , i n t e r n a l s t a b i l i t y , i n t e r n a t i o n a l trade agreements, etc. Those are the feeback loops that operate on each respective l e v e l alone. But the f i n a n c i a l p i c t u r e for each l e v e l i s also influenced by feedback loops that operate across l e v e l s . The i n d i v i d u a l ' s d i s c r e t i o n a r y income and the business's p r o f i t s are influenced by taxes and government expenditures. The balance of the national budget i s conversely influenced by the amount of goods and services produced .by the in d i v i d u a l s (GNP pri v a t e s e c t o r ) . There are, of course, innumerable other influences across l e v e l s too but the ones c i t e d here are s u f f i c i e n t to make the point. The point i s that systems synthesis applied to s o c i e t a l a f f a i r s involves t r a c i n g the l i n e s of mutual influence across l e v e l s of organization. These v e r t i c a l feedback loops provide control information f o r both l e v e l s of organization simultaneously. The wheat cycle could be treated as a h o r i z o n t a l feedback loop i f the WMB i s conceived as a type of wholesaler. Such a con-ception would i n d i c a t e a f a i l u r e to perceive the h i e r a r c h i c a l arrangement between taxpayer and government. The concrete operational achievement of mastering h i e r a r c h i e s i s a p r e r e q u i s i t e f o r systemic thinking. When the . 145 respondent gave responses di s p l a y i n g an appreciation of the WMB's ro l e i n the v e r t i c a l feedback loop, as w e l l as the h o r i z o n t a l loop, then a pass was scored on systems synthesis. In general then the chart of development i n the c h i l d ' s understanding of society s t a r t s with understanding s o c i a l ordering, then s o c i a l h i e r a r c h i e s . With the advent of the post-concrete stage systems analysis becomes possible. Systems synthesis might become possible at the same time but i t s employment may depend much more on a p r e - r e q u i s i t e base of s o c i e t a l knowledge. Perhaps systemic l o g i c i s simply neglected by the culture (Buck-Morss, 1975; Buss, 1977b) and so the use of i t s more d i f f i c u l t forms (e.g., systems synthesis) has not become prevalent among adolescents. Perhaps by t h e i r i n t e r a c t i v e nature, feedback loops cannot be apprehended thoroughly without i n t e r a c t i o n of some sor t . Partaking of the in t e r a c t i o n s that these loops describe would at l e a s t help one to acquire a broader base of f a c t s about the system. Insofar as understanding feedback loops requires i n t e r a c t i n g with them systemic thinking i s more pragmatic i n nature. I f a systemic understanding of society c a r r i e d with i t a heavy p r e r e q u i s i t e of i n t e r a c t i o n on the s o c i e t a l l e v e l , i t would be no wonder that only a minority of the oldest adolescents i n t h i s study evinced a mastery of systems synthesis. C. ''Social Psychology The present study takes a step towards cor r e c t i n g some of s o c i a l psychology's shortcomings i d e n t i f i e d by c r i t i c s i n what has come to be c a l l e d "the c r i s i s l i t e r a t u r e " . In the c r i s i s l i t e r a t u r e several authors have c r i t i -146 c i z e d the tendency f o r p s y c h o l o g i c a l s o c i a l psychology (PSP) to i s o l a t e i t s e l f from developments (a) outside North America (Smith, 1978; Silverman, 1977), and, (b) i n other d i s c i p l i n e s C S h e r i f , 1977). In the s o c i o l o g i c a l wing of s o c i a l psychology (SSP) there has been concern over an opposite trend. What i s e s s e n t i a l l y s o c i a l p s y c h o l o g i c a l research tends to be presented and l a -beled as belonging to a s u b s t a n t i v e s u b f i e l d of s o c i o l o g y thus promoting the d i s s i p a t i o n of SSP ( L i s k a , 1977; Hewitt, 1977). S t a r k l y s t a t e d , the s i t u a t i o n i s t h i s : those who pursue v a r i o u s i n t e r d i s c i p l i n a r y l i n e s emanating from s o c i a l psychology seldom r e l a t e t h e i r work back to the d i s c i p l i n e i t s e l f w h i l e those who are committed to the d i s c i p l i n e tend-towards i s o l a t i o n i s m . Both responses are unhealthy f o r the; d i s c i p l i n e . • ( i ) Towards an I n t e r a c t i v e Framework I t needn't be one or the other. There i s another a l t e r n a t i v e . S o c i a l psychology stands at the i n t e r s t i c e between the complexity of the person and the complexity of s o c i e t y . The task of understanding how the two relate..to one another i s an uniquely s o c i a l p s y c h o l o g i c a l problem. Yet i t i s a problem that recurs i n a l l branches of s o c i a l s cience. The nature of person-society i n t e r -a c t i o n i s of v i t a l importance i n anthropology, economics, geography, h i s t o r y , p o l i t i c a l science and s o c i o l o g y as w e l l as psychology. For t h i s reason, s o c i a l p s y c h o l o g i s t s are i n an e x c e l l e n t p o s i t i o n to f i l l the r o l e of s o c i a l science g e n e r a l i s t s . In order to make t h i s type of c o n t r i b u t i o n , however, there must be a general framework f o r studying person-society i n t e r a c t i o n . G.H. Mead (1944) made a f r u i t f u l c o n t r i b u t i o n along those l i n e s . I t l e d to a good deal of e m p i r i c a l research on v a r i o u s aspects of the t o p i c but that research has become d i f f u s e . There i s a need f o r an i n t e r d i s c i p l i n a r y s o c i a l p s y c h o l o g i c a l 147 framework t h a t w i l l i n t e g r a t e , a l l t h e d i v e r s i t y o f i n s i g h t s t h a t have a c c u -m u l a t e d w i t h r e g a r d t o p e r s o n - s o c i e t y i n t e r a c t i o n ( B o u t i l i e r , Roed, and Svendsen, 1980). T h e r e a r e s a t i s f a c t o r y " t h e o r i e s about t h e s o c i a l s y s t e m and s a t i s f a c t o r y t h e o r i e s about t h e p e r s o n - s y s t e m b u t i n t h e a u t h o r ' s o p i n i o n t h e r e a r e no adequate t h e o r i e s about t h e p r o c e s s e s t h a t c h a r a c t e r i z e t h e i n t e r a c t i o n o f t h o s e s y s t e m s . DiRenzo (1977) has s u g g e s t e d t h a t a d e s i d e r a t u m i n such, a framework w o u l d be t h e d e s c r i p t i o n o f b o t h systems i n i s o m o r p h i c t e r m s . That i s , the p e r s o n and t h e s o c i a l o r g a n i z a t i o n s h o u l d be d e s c r i b e d i n a common m e t a t h e o r e t i c a l l a n g u a g e . The p r e s e n t r e s e a r c h i s an attempt t o move towards t h e k i n d o f i n t e g r a t i v e framework t h a n B o u t i l i e r , e_t a l . and DiRenzo c a l l e d f o r . C u r r e n t t h e o r i e s i n PSP t e n d t o c o n s t r u e t h e i n d i v i d u a l as a p a s s i v e o b s e r v e r o f an a c t i v e e n v i r o n m e n t ( N e i s s e r , 1980). The s o v i e t p s y c h o l o g i s t , S.L. R u b e n s t i e n ( c i t e d by Payne, 1968), a t t e m p t e d an a l t e r n a t i v e a p p r o a c h . He sought a t h e o r y w h i c h w o u l d v i e w the i n d i v i d u a l as an a c t i v e p a r t i c i p a t o r i n an a c t i v e e n v i r o n m e n t . S i n c e open systems must, by d e f i n i t i o n , r e m a i n a c t i v e i n o r d e r t o ward o f f e n t r o p y , an i n t e r a c t i o n i s t v i e w o f b o t h t h e p e r s o n and t h e s o c i a l e n v ironment p r o m i s e s t o p r o v i d e a framework f o r t h e o r i e s t h a t p o s t u l a t e an a c t i v e p e r s o n i n ah a c t i v e e n v i r o n m e n t . P i a g e t ' s t h e o r y o f t h e p e r s o n ' s c o g n i t i v e m o d e l i n g o f t h e environment i s a good example o f how an i n t e r a c t i o n i s t p o s i t i o n c o u l d be a p p l i e d t o d e s c r i b i n g t h e p e r s o n system. P i a g e t c o n s t r u e s the i n d i v i d u a l as an a c t i v e and i n t e r a c t i v e c o n s t r u c t o r o f r e a l i t y . I n s e v e r a l p l a c e s one can a l r e a d y f i n d c o r r e s p o n d i n g t h e o r i e s o f the a c t i v e s o c i a l s y s t e m ( e . g . , B a l l , 1978; B o u l d i n g , 1962; E a s t o n , 1965; M y s i o r , 1977; Sztompka, 197'4). The t a s k , t h e n , was t o e x t e n d P i a g e t t o b e a r upon t h e p e r s o n ' s i n t e r a c t i o n w i t h t h e s o c i a l s y s tem. I t was hoped t h a t t h i s w o u l d h e l p p r o v i d e t h e framework needed t o (a) i n t e g r a t e t h e s o c i a l p s y c h o l o g y b e i n g done i'48 i n d i v e r s e d i s c i p l i n e s , and, (b) f a c i l i t a t e b r i n g i n g the s o c i o - c u l t u r a l context to bear upon the study of the i n d i v i d u a l . Numerous s o c i a l p s y c h o l o g i c a l t o p i c s can be b e t t e r understood once we have a framework f o r d e s c r i b i n g how w e l l i n d i v i d u a l s understand those aspects of s o c i e t y that they are i n f l u e n c i n g ( i . e . , a c t i v e person) or that are i n f l u e n c -i n g them ( i . e . , a c t i v e s o c i a l system). For example, locus of c o n t r o l w i t h respect to s o c i e t y , e s p e c i a l l y p o l i t i c s , i s a subfactor of the I-E s c a l e (Lao, 1970; C o l l i n s , 1974). The analogous construct i n s o c i o l o g i c a l s o c i a l psychology i s a l i e n a t i o n (Seeman, 1959). Scale scores on the p o l i t i c a l c o n t r o l f a c t o r do not t e l l us i f a persons f e e l i n g s of powerlessness, f o r example, are a r e s u l t of a l a c k of understanding of the p o l i t i c a l system or r e a l disenfranchisement or both. The present study provides a means of d e s c r i b i n g the person's l e v e l of understanding of the p o l i t i c a l system i n more d e t a i l . According to Piaget (e.g., 1970) understanding advances through i n t e r -a c t i o n w i t h a p a r t i c u l a r environment. Extending t h i s p r i n c i p l e to the under-standing of s o c i a l systems, we should expect a microgenetic r e c a p i t u l a t i o n (Werner, 1948) of the ontogenetic sequence found i n t h i s study. Each time a person enters a new o r g a n i z a t i o n , f o r example, t h e i r understanding of the o r g a n i z a t i o n should progress through the phases described e a r l i e r (i..e.» o r d i n a t i o n , h i e r a r c h y , systems a n a l y s i s , systems s y n t h e s i s ) . The p r i n c i p l e of understanding through i n t e r a c t i o n a l s o p r e d i c t s t h a t , f o r any i n d i v i d u a l , lower l e v e l s of understanding w i l l be found w i t h respect to those aspects of s o c i e t y that they i n t e r a c t w i t h l e s s . For example, medical doctors might have a very poor understanding of the r e l a t i o n s h i p between we l f a r e agencies and t h e i r c l i e n t s . Extending t h i s i d e a , we might even be able to c h a r a c t e r i z e peoples general views of s o c i e t y as being b u i l t around those aspects of i t w i t h which they have the more frequent and/or important i n t e r a c t i o n s . Thus we would p r e d i c t that the core c y c l e s i n a lawyer's view 149 of society would involve government and l e g i s l a t i o n . The c e n t r a l cycles i n a housewife's view of society may involve the various phases of family l i f e from marriage, through c h i l d r e a r i n g , to grandparenthood. Members of i n d u s t r i a l labor unions might be prone to see the i n f l a t i o n a r y s p i r a l as the most s i g n i -f i c a n t cycle that makes society meaningful to them. Rokeach (1973) has found that d i f f e r e n t occupational groups have d i f f e r e n t sets of values. P o l i t i c a l , s o c i a l , and economic value orientations may w e l l a r i s e from i n d i v i d u a l s ' and group's understandings of what moves do and do not produce desired outcomes i n i n t e r a c t i o n with society through some p a r t i c u l a r feedback loop. For example, Kohn (1969) finds that working c l a s s people value obedience much more than do middle cl a s s people. In terms of f i n a n c i a l s e c u r i t y , obedience gets workers more of what they want than autonomy or disobedience. Workers and management are i n a r e l a t i o n s h i p of c y c l i c i n t e g r a t i o n where autonomy produces negative feedback for the workers. In general then, values and at t i t u d e s may be s i g n i -f i c a n t l y r e l a t e d to, and perhaps, generated by, the types of feedback loops that i n d i v i d u a l s p a r t i c i p a t e i n i n t h e i r i n t e r a c t i o n s with various aspects of society. ( i i ) Towards S p e c i f l y i n g the Structure of the S o c i a l S i t u a t i o n For some time now s o c i a l psychologists have emphasized the power of "the s o c i a l s i t u a t i o n " to control behavior. The Milgram (1963) obedience study and Zimbardo's prison study (Zimbardo, Haney, Banks, and J a f f e , 1972) are c l a s s i c examples. The work on bystander in t e r v e n t i o n emphasizes the r o l e of the i n d i v i d u a l ' s i n t e r p r e t a t i o n of the s i t u a t i o n i n c o n t r o l l i n g behavior. As yet, however, no system has been devised f o r analysing or c l a s s i f y i n g s o c i a l s i t u a t i o n s . Perhaps the l e v e l s of understanding society presented i n t h i s study 150 would h e l p do t h a t by p r o v i d i n g a framework f o r d e s c r i b i n g t h e i n d i v i d u a l ' s c o n s t r u c t i o n o f t h e s i t u a t i o n . The phases r e p o r t e d , and p e r s p e c t i v e s d i s c u s s e d i n t h e p r e s e n t s t u d y c o u l d h e l p s o c i a l p s y c h o l o g i s t s s p e c i f y j u s t what f e a t u r e s o f " t h e s i t u a t i o n " a r e s a l i e n t t o d i f f e r e n t p e r s o n s . The v e r s i o n o f i n t e r -a c t i o n i s m a d v o c a t e d by Bowers (1973) sees b e h a v i o r (B) as a j o i n t f u n c t i o n o f t h e p e r s o n (P) and t h e s i t u a t i o n (S) s u c h t h a t B = f ( P , S ) . That f o r m o f i n t e r -a c t i o n i s m l e a v e s t h e p r o b l e m o f d e f i n i n g t h e s i t u a t i o n u n s o l v e d . Buss (1977a), E n d l e r and Magnusson (1976), O v e r t o n and Reese C1973) a d v o c a t e a f o r m o f i n t e r a c t i o n i s m where t h e s i t u a t i o n and t h e p e r s o n a r e f u n c t i o n s o f e a c h o t h e r s u c h t h a t ( P < —*S). T h i s t y p e o f i n t e r a c t i o n i s m would be f a c i l i t a t e d by t h e framework p r e s e n t e d h e r e because t h e s i t u a t i o n a l s i d e o f t h e i n t e r a c t i o n c o u l d be s p e c i f i e d i n terms t h a t r e l a t e t o t h e s u b j e c t ' s own c o n s t r u a l o f t h e s i t -u a t i o n . Note t h a t t h i s i s v e r y d i f f e r e n t f r o m d e f i n i n g t h e s i t u a t i o n (a) e x a c t l y as t h e s u b j e c t d o e s , a c c e p t i n g h i s v e r b a l r e p o r t s p u r e l y a t f a c e v a l u e , and (b) a u t i s t i c a l l y , w i t h o u t any r e f e r e n c e t o what s u b j e c t s o r anyone e l s e say t h e y f i n d s a l i e n t i n t h e s i t u a t i o n . E x t e nded t o t h e u n d e r s t a n d i n g o f s o c i a l r e a l i t y t h e P i a g e t i a n a p p r o a c h p r o m i s e s t o i d e n t i f y o n l y t h e f o r m o f t h e s u b j e c t s phenomenal s i t u a t i o n . The c o n t e n t w i l l v a r y f r o m p e r s o n t o p e r s o n . T h i s i s where t h e t r a i t s i d e o f i n t e r a c t i o n i s m becomes i m p o r t a n t . Few, i f any, s o c i a l s i t u a t i o n s c a n have o n l y one p o s s i b l e f o r m . U n l e s s s o c i a l p s y c h o l o g i s t s can d e s c r i b e t h e p o s s i b l e forms t h a t a s i t u a t i o n may t a k e f o r d i f f e r e n t p e o p l e , t h e o n l y p e r s o n by s i t u a t i o n i n t e r a c t i o n s t h a t w i l l p r o d u c e c o n s i s t e n t r e s u l t s w i l l be t h o s e where t h e s i t u a t i o n i s c o n s t r u e d more o r l e s s t h e same way by e v e r y o n e . P e r s o n a l i t y v a r i a b l e s a r e p o o r p r e d i c t o r s o f b e h a v i o r i n t h e M i l g r a m o b e d i e n c e s i t u a t i o n . P e r h a p s t h i s i s because i t s a c t u a l l y s e v e r a l s i t u a t i o n s o v e r l a i d , one upon t h e o t h e r . P e r s o n a l i t y v a r i a b l e s m i ght be more p r e d i c t i v e i f t h e i r 151 i n t e r a c t i o n w i t h the form of the s i t u a t i o n ( i . e . , o r d i n a l , h i e r a r c h i c a l , sys-tems a n a l y t i c , systems s y n t h e t i c ) Being perceived By the subject were examined. '1-52 D. CONCLUSIONS P i a g e t 1 s o r g i n a l notion of stages as structured wholes fares quite well when the tasks used to test the notion are not r e s t r i c t e d to a p a r t i c u l a r type of content and when a wide range of a b i l i t y l e v e l s are sampled. The general Piagetian approach seems to generalize quite w e l l to b i o - e c o l o g i c a l and s o c i e t a l content. The observed d i f f i c u l t y orderings and stage r e l a t e d d i s c o n t i n u i t i e s were generally as predicted. The systemic tasks, which appeared only i n the two open systems domains, were therefore not l i k e l y to have been confounded with any abnormal content r e l a t e d a r t i f a c t s . The c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n structures i d e n t i f i e d and examined i n t h i s study turned out to be composed of four quite d i s t i n c t components which are cognitive structures i n t h e i r own r i g h t . The most d i f f i c u l t operations f or the sample were the t r a n s i t i v e r e c y c l i n g component and the systems synthesis component. These upper systemic tasks were as much more d i f f i c u l t than the formal operations as the formal operations were more d i f f i c u l t than the concrete operations. Moreover, the gap i n d i f f i c u l t y l e v e l s was a Guttman step but there were no Guttman steps among the upper systemic tasks. The greater d i f f i c u l t y of the upper systemic tasks could not be c l e a r l y a t t r i b u t e d to the more unfamiliar nature of t h e i r contents. These r e s u l t s raised the p o s s i b i l i t y that these tasks might assess operations r e -presentative of a f i f t h stage of cognitive development. The upper systemic tasks s a t i s f i e d a l l the c r i t e r i a f o r a f i f t h stage except concurrence (for which there were no relevant data available) and abruptness of t r a n s i t i o n . The upper systemic components were f i r s t mastered ' '1*5-3' by respondents who were about two years older than those beginning to master the formal operations. The majority of respondents at a l l age l e v e l s never mastered the systemic components;, whereas from age 14 onward the vast majority had mastered the formal operations. I t was noted that gradual stage t r a n s i t i o n s are not incompatible with stage i n t e r p r e t a t i o n s . I t was suggested that success on the upper systemic tasks might be observed to Be more frequent were future research to sample older age groups. Although the f i f t h stage p o s s i b i l i t y remains v i a b l e , so does the a l t e r n a -t i v e p o s i t i o n that systemic operations develop i n p a r a l l e l w i t h formal operations as a complementary aspect of cognitive d i v e r s i f i c a t i o n i n the post-concrete stage. A re l a t e d suggestion was put forward to the e f f e c t that formal l o g i c and systemic l o g i c are complementary and develop i n p a r a l l e l throughout the concrete stage as well as the post-concrete stage Cand perhaps even through-out a l l stages). The c h i l d ' s understanding of society was described as going through two stages with two overlapping phases within each stage. According to t h i s d e s c r i p t i o n , i n the concrete stage, f i r s t o r d i n a l , then h i e r a r c h i c a l s t r u c -tures would become comprehensible to the c h i l d . E a r l y i n the post-concrete stage the adolescent would be able to use systems analysis to make s o c i e t a l r e a l i t y meaningful. Later, systems synthesis would emerge as a conceptual t o o l . This research was designed to allow ample scope for exploration and discovery. Quite a few discoveries were made and even more questions were ra i s e d . Perhaps the most important outcome was the empirical v i n d i c a t i o n of the existence of a second type of l o g i c . In t h i s research the p h i l o s p h i c a l p o s s i b i l i t y of systemic l o g i c was succ e s s f u l l y translated into procedures for assessing the presence of systemic l o g i c a l structures. 154 REFERENCE NOTE 1. K a r g b o , D e n n i s . 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W o h l w i l l , J.F. The Study of B e h a v i o r a l Development. New York: Academic P r e s s , 1973. Zimbardo, P.C., Haney, C , Banks, W.C., and J a f f e , D. Stanford P r i s o n Experiment. Stanford, C a l i f o r n i a : P h i l i p G. Zimbardo, Inc.1972 (Tape r e c o r d i n g ) . •161 APPENDIX A; Physical Domain Tasks The methods f o r assessing mastery over each of the eight cognitive operations i n the standard domain i s described herein. For each cognitive operation the source of the task and miscellaneous background information i s given i n the introduction. Then the materials are described before the questions assessing the respondent's f a m i l i a r t i t y with them are presented. The in s t r u c t i o n s and probes to be directed towards the respondent appear next and are followed by a de s c r i p t i o n of the scoring procedures and c r i t e r i a . Since Piaget was not e s p e c i a l l y concerned with studying the understanding of open systems, there are no standard Piagetian tasks f o r c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n . Instead, the phys i c a l domain contained three formal operational tasks that acted as markers i n the scalogram analyses. They made i t possible to locate the d i f f i c u l t y l e v e l s of the systemic tasks with respect to formal operations. A. S e r i a t i o n (i) Int roduction The standard s e r i a t i o n task, described i n many places (e.g., Formanek and Gurian, 1976) was used. The respondents were also required to in t e r p o l a t e an element into the s e r i e s . The i n t e r p o l a t i o n requirement helped to d i s t i n -guish stage II responses from stage I I I responses (Ginsberg and Opper, 1969, pp. 137-138). ( i i ) Procedure Materials. -Seven cardboard cyclinders that stand on end, a l l one color (red), ranging i n height from 2" to 8". -One i n t e r p o l a t i o n c y l i n d e r 5 V i n height. F a m i l i a r i t y A s s e s s m e n t . The seven cyclinders were placed standing on end i n a random array i n front of the respondent. The respondent was asked, "Can you t e l l me what these things are?" and, i f not already answered by the respondent, "Do you know what they are made of?" Pass: Tubes, Cardboard. F a i l : Other, Don't know, No response. Instructions. Part A: The respondent was asked to arrange the cylinders i n order. Size was not mentioned i n order to test whether the respondent ser i a t e d spont-neously. •162 Part B: The respondent was t o l d to arrange the cylinders going from the "smallest to the l a r g e s t " , or from the " l i t t l e s t to the biggest" i f t h i s had not already been done. Part C: If the cylinders were seri a t e d c o r r e c t l y , the repondent was shown the i n t e r p o l a t i o n c y l i n d e r and was asked to, "Put i t i n the r i g h t place with the r e s t . " ( i i i ) Scoring The responses were c l a s s i f i e d i n t o three stages. Only stage I I I responses were counted as evidence f o r the mastery of o r d i n a l r e l a t i o n s for the purpose of dichotomous scoring. I ( F a i l ) : The c h i l d often divides the objects i n t o two groups such as large and small. II ( F a i l ) : The c h i l d sometimes divides- the objects into three groups: small, medium, and large. Correct s e r i a t i o n sometimes occurs a f t e r considerable unsystematic t r i a l and e r r o r . In stage IT the Interpolated object i s misplaced. II I (Pass): The c h i l d i s able to s e r i a t e a l l eight objects c o r r e c t l y . (i) Introduction Following the standard procedure ( C l i c k and Wapner, 1968). f o r determining the a b i l i t y to perform t r a n s i t i v e operations we used three objects d i f f e r i n g i n magnitude along one dimension. The objects were cardboard cylinders varying i n height, each one a d i f f e r e n t c o l or. The cylinders were presented i n p a i r s with the cylinder of intermediate length being a member of both p a i r s . The respondent memorized the r e l a t i o n s between the members of both p a i r s (e.g., shorter than) and the designations of each member (e.g., names, c o l o r s ) . The r e l a t i o n s between the member of each p a i r were presented hetero-t r o p i c a l l y . In heterotropic presentation the r e l a t i o n a l terms used i n each p a i r are antonyms (e.g., "A i s longer than B" and "C i s shorter than B"). G l i c k and Wapner found heterotropic r e l a t i o n s to be more d i f f i c u l t than i s o -t r o p i c r e l a t i o n s with t h i s procedure. Heterotropic r e l a t i o n s were used because they focus a t t e n t i o n on the b i v o c a l nature of the intermediate element. ( i i ) Procedure Materia l s. -Three cardboard cylinders (A,B,C) varying i n length, and color. B. Linear T r a n s i t i v i t y Color Length A. Red 9' ii B. White 6 II C. Blue 3 ii 163 F a m i l i a r i t y Assessment. The c y l i n d e r s were presented i n p a i r s (B w i t h A, and, B w i t h C). The c h i l d was t o l d that he/she would be shown two p a i r s of c y l i n d e r s (or "tubes") and would than Be asked, "Which was the t a l l e s t ? " and "Which one was the s h o r t e s t ? " The c h i l d was asked to name the c o l o r of each c y l i n d e r as i t was presented. The white c y l i n d e r (B) was d i s p l a y e d f i r s t and then the red c y l i n d e r (A). The red one was to the c h i l d ' s r i g h t v i s a v i s the white one. The cylinders;.were then removed from s i g h t and the c h i l d was asked, "Which c y l i n d e r d i d I show you f i r s t ? " Pass: White "Which c y l i n d e r d i d I show you second?" Pass: Red The same procedure was repeated f o r the second p a i r w i t h the white c y l i n d e r Being d i s p l a y e d to the subject's l e f t v i s a V i s the Blue one and the Blue one Being presented f i r s t . I n s t r u c t i o n s . . When the i n v e s t i g a t o r was c e r t a i n that the c h i l d rememBered the c o l o r s of a l l three c y l i n d e r s , he asked, "Which one was the t a l l e s t ? " and "How can you t e l l t h a t ? " followed By, "Which one was the sho;rtest?"and "How can you t e l l t h a t ? " ( i i i ) S coring I ( f a i l ) : I n c o r r e c t choice f o r one or Both endpoints. I I ( F a i l ) : Correct choice of endpoints But i n c o r r e c t e x p l a n t i o n f o r choice (e.g.,, t a u t o l o g y ; temporal order as height p r e d i c t o r ) I I I (Pass): Correct choice of endpoints w i t h c o r r e c t r a t i o n a l e f o r choice. C. L o g i c a l M u l t i p l i c a t i o n (1) I n t r o d u c t i o n The l o g i c a l m u l t i p l i c a t i o n of c l a s s e s i s the ope r a t i o n u n d e r l y i n g m u l t i p l e c l a s s i f i c a t i o n . I t a l s o u n d e r l i e s the concept of the "gre a t e s t lower Bound" i n l a t t i c e s t r u c t u r e s . L o g i c a l m u l t i p l i c a t i o n i s sometimes r e f e r r e d to i n l o g i c as the " i n t e r s e c t i o n " of sets of "c o n j u n c t i o n " (Gorovitz and W i l l i a m s , 1969) i n t r u t h t a B l e s , symBolized By the operator " f l " . The simplest procedure f o r a s s e s s i n g mastery of l o g i c a l m u l t i p l i c a t i o n i s the two-way c l a s s i f i c a t i o n task (Inhelder and P i a g e t , 1964). 164 ( i i ) Procedure Materials. -A two-fold matrix with (a) yellow shapes i n the l e f t column and red shapes i n the r i g h t column, and (b) star shapes on the top row and square shapes on the bottom row, thereby y i e l d i n g : - L e f t top c e l l : yellow star -Right top c e l l : red star - L e f t bottom c e l l : yellow square -Right bottom c e l l : BLANK (.to be f i l l e d by respondent with correct entry of a red square) -Below the matrix was a row of f i v e a l t e r n a t i v e s that may be selected f o r the r i g h t bottom c e l l . These were: 1. red star 2. red square 3. yellow star 4. yellow square 5. red c i r c l e F a m i l a r i t y Assessment. The i n v e s t i g a t o r pointed to each object i n the matrix and asked the repondent what i t was. I f shape or color were not men-tioned, the i n v e s t i g a t o r asked what shape or color each object was. Pass: Correct shape and color. Instructions . The i n v e s t i g a t o r then pointed to each object i n the matrix from column to column, saying "OK, so here i s a yellow s t a r . Here i s a red sta r . Here i s a yellow square. Which of these (points to row of f i v e a l t e r -natives at bottom) goes best here (points to blank c e l l ) with t h i s yellow star , t h i s red star and t h i s yellow square?" Respondents' explanations were recorded. "Can anything else fo i n t h i s empty place j u s t as well as your choice of _ _ ? " ( i i i ) Scoring I ( F a i l ) : Incorrect choice II ( F a i l ) : Correct shoice; i n c o r r e c t explanation II I (Pass): Correct choice; correct explanation '-16'5 D. Class Inclusion (i ) Introduction The operation of c l a s s i n c l u s i o n requires a combined understanding of l o g i c a l a d d i t i o n and i n c l u s i o n r e l a t i o n s . L o g i c a l a d d i t i o n i s sometimes referred to i n l o g i c as the "union" of sets of " i n c l u s i v e d i s j u n c t i o n " i n truth tables (Gorovitz and Williams, 1 9 6 9 ) , symbolized by the operator " U " . Inclusion r e l a t i o n s are i m p l i c i t i n the concept of " l e a s t upper bound" i n l a t t i c e structures. The c l a s s i n c l u s i o n task used was adapted from Inhelder and Piaget ( 1 9 6 4 ) . The "whole" cl a s s was the construction material (wood) and the "part" class was the color (red vs_. green). ( i i ) Procedure Materials. -Seven wooden beads, f i v e green and two red, i n a bowl. F a m i l i a r i t y Assessment. -The respondent was asked "Can you t e l l me what I have here?" I f the subject f a i l e d to mention color the invest i g a t o r asked what color the objects were. Likewise, i f construction material (wood) was not mentioned, a prompt was given f o r that. Instructions . When the respondent had affirmed these premises,,.. the inves-t i g a t o r asked "Are there more wooden beads i n t h i s bowl of more geen beads?" While recording the responses the in v e s t i g a t o r continued with, " I f I took away a l l of the green beads would there be any beads l e f t i n the bowl? I f I took away a l l the wooden beads would there be any beads l e f t i n the bowl? Which are there more of i n t h i s bowl, green beads or wooden beads?" ( I i i ) Scoring I ( F a i l ) : More of the part c l a s s than the whole c l a s s . II (Pass): More of the whole cla s s than the part c l a s s . E. Combination of Variables ( i ) Introduction This version of the problem was adapted by A r l i n (1978) from a version by S i l l s and Herron (1976) which reconstructed the e s s e n t i a l l o g i c a l features of Inhelder and Piaget's (1958) "Combination of Colored and Colorless Chemical Bodies" task. The basic idea was for the respondent to engage i n a systematic search f o r the r i g h t combination of v a r i a b l e s that would produce the desired outcome. 16-6 ( i i ) Procedure Materials. A black box (10 cm. x 5h cm. x 4 cm.) with a row of 5 numbered momentary push buttons and a red i n d i c a t o r l i g h t on the top. The depression of three buttons simultaneously turned on the l i g h t . A fourth button turned i t o f f again. The f i f t h button was not wired to the battery. Instructions . The i n v e s t i g a t o r placed an index card between the f i v e buttons and the l i g h t such that the respondent could not see which buttons were being depressed but could see the l i g h t . The i n v e s t i g a t o r s a i d , "Now watch what ...happens (DEPRESS BUTTONS TO ILLUMINATE LIGHT) . I made t h i s l i g h t go on by pressing down on some of these buttons. Would you l i k e to try to make the l i g h t go on by f i n d i n g the buttons to push?" The i n v e s t i g a t o r recorded the attempts of the respondent to ill u m i n a t e the l i g h t , noting which buttons were pressed i n which sequence. The respondent was then asked why he/she pushed the bottons which had been attempted. The repondent was encouraged to con-tinue t r y i n g and was permitted to look at the numbers which the i n v e s t i g a t o r had written down representing each of the respondent's t r i e s . I f the respon-dent was successful i n turning on the red l i g h t he/she was asked "What would you do to f i n d any other possible combinations of buttons which might also turn on the l i g h t ? " ( i i i ) Scoring The scoring was the same as that used for the Piagetian "Combination of Colored and Colorless Chemicals" task (Inhelder and Piaget, 1958; 110-122). F a i l Concrete II A (1-2 p o i n t s ) : Empirical associations, precausal explanations and 2 x 2 t r i a l s of p a i r s of buttons. Concrete II B (3-5 p o i n t s ) : M u l t i p l i c a t i v e operations with the t r i a l and error introduction of n x n. combinations. Pass Formal I I I A (6-8 p o i n t s ) : Formation of systematic n x n combinations. Formal I I I B (9-10 p o i n t s ) : The combination and, more p a r t i c u l a r l y , the proofs appear i n a more systematic fashion. F. P r o b a b i l i t y i n Random Drawing (i) Introduction This task was A r l i n ' s (1978) standardization of the l e s s structured procedure described by Piaget and Inhelder (1975; 116-130). With each c h i l d 167 Piaget and Inhelder changed the number and color of items to be drawn. This more standard version made the r e s u l t s more q u a n t i t a t i v e l y comparable across c h i l d r e n and' s i m p l i f i e d the procedures for the i n v e s t i g a t o r . ( i i ) Procedure Materials, -box --beads: 6 yellow, 6 green, 6 red Instructions . The beads were counted*into the box i n front of the c h i l d . The i n v e s t i g a t o r said, "What do you think are your chances of drawing a red bead on your f i r s t reach into t h i s box? Why do you think so? I f the c h i l d did not understand the question, the question was rephrased to: "How many turns do you think you w i l l need to take before you w i l l get a red bead from t h i s box?". The i n v e s t i g a t o r l e t the c h i l d draw one bead. Then the c h i l d was asked, "What do you think are your chances of -getting another ... (the color the c h i l d had drawn was.named) bead on your second turn? Why do you think that?" ( i i i ) Scoring I ( F a i l ) Absence of systematic p r o b a b i l i t y . II (Pass) Beginnings of quantified p r o b a b i l i t y (e.g. 1/3 for f i r s t draw). III (Pass) Successful q u a n t i f i c a t i o n again a f t e r each drawing (e.g. 5/17 for second draw). G. I s o l a t i o n of Variables ( i ) Introduction This task was devised by Kuhn and Ho (19.77) with minor adaptations by Chandler, Siegel and Boyes (1980). The basic idea was to show the respondent two arrays of outcomes with the inputs that produced each. In the f i r s t array the respondent had to discern which two input v a r i a b l e s were equally e f f i -cacious i n independently producing an outcome. In the second array, the de-s i r e d ;outcome could only have been obtained through the use of two p a r t i c u l a r inputs c o n j o i n t l y . The repondent had to discern how the outcome was achieved. ( i i ) Procedure Materia l s. -Empty v i a l s with plant food l a b e l s - P l a s t i c plants 168 F i r s t array: Plant Food Label Height of Plant LEAFY PLANTS no food 3" a 3" b 6" c 6" ab 6" ac 6" be 6" abc 6" Second array: FLOWERY PLANTS no food 3" 1 3" 2 6" 3 6" 1.2 6" 1.3 6" 2,3 9" 1,2,3 9" Instructions.» One array at a time was placed i n front of the respondent. The i n v e s t i g a t o r s a i d , "We're t r y i n g out d i f f e r e n t types of plant food. The types we used on each plant are shown by the b o t t l e s i n front of each plant. A l l these plants were started at the same time. We're s t a r t i n g a new plant and we have to decide which would make the t a l l e s t plant. (INDICATE PLANTS AND FOOD INDIVIDUALLY AND STRESS THE HEIGHT). Now we don't want to use any more food than we have to, because i t s very expensive. Now, think about i t for a minute and t e l l me what you think we should feed the new plant we're s t a r t i n g i n order to make i t grow t a l l . " When the subject had responded the inv e s t i g a t o r asked, "Why do you think that would be the best thing to make the new plant grow t a l l e s t ? " Then the in v e s t i g a t o r asked "Does a,b,c,/l,2,3) (ONE AT A TIME) have anything to do with how the (leafy/flowery) plants turn out?" The procedure was repeated for the second array and then the subject was asked to compare both arrays as follows: "Now, the plant foods we're using on these plants are the same foods we're using on the flowery plants. A i s a. B i s b, (3 i s c_. Do the plant foods work d i f f e r e n t l y on the two types of plants? Does the type of plant make any difference to how the plant food work?" I f the subject did not explain his/her answer the following probes were given: "How can you t e l l that?" "What i s the di f f e r e n c e ? " 169 ( i i i ) Scoring The scoring was the same as that used by Kuhn and Ho (1977); F a i l I Concrete: Reasons s o l e l y on the basis of i s o l a t e d instances, ignores instances contradictory to own conclusions, makes l o g i c a l error of f a l s e i n c l u s i o n . II Emergent Formal. Begins to l o g i c a l l y exclude the inoperative v a r i a b l e s i f s p e c i f i c a l l y questioned. III T r a n s i t i o n a l . Spontaneously escludes the inoperative v a r i a b l e and includes operative ones but f a i l s to d i f f e r e n t i a t e between the two problems (al t e r n a t i v e i n f i r s t array ;additive i n second). Pass IV Early formal. Comprehends ei t h e r a l t e r n a t i v e or addi t i v e causes. V Consolidated formal. Comprehends and d i f f e r e n t i a t e s between a l t e r n a t i v e and additive causes. 170 APPENDIX B: B i o - e c o l o g i c a l Domain Tasks Except f o r the systemic r e l a t i o n s , Appendix B p a r a l l e l s Appendix A i n the tasks used. The tasks are from the same sources as those i n Appendix A. For the s e r i a t i o n , l i n e a r t r a n s i t i v i t y , l o g i c a l m u l t i p l i c a t i o n and c l a s s i n c l u s i o n tasks the s c o r i n g i s i d e n t i c a l to that used i n Appendix A. The reader i s r e f e r r e d t o Appendix A f o r s c o r i n g procedures. I n a l l Appendix B tasks where p r i n t e d words were the f o c a l s t i m u l i the words were read to a l l respondents as o f t e n as seemed necessary. The same general r u l e was a p p l i e d to the h i g h l y v e r b a l tasks of Appendix C ( S o c i e t a l Domain). A l s o , as i n Appendix C, concrete memory a i d s were used to reduce the memory load on the respondent. A. S e r i a t i o n ( i ) I n t r o d u c t i o n In the p h y s i c a l domain s e r i a t i o n task, as i n t h i s one, the dimension of comparison was the v e r t i c a l l e n g t h . I n the s o c i e t a l domain s e r i a t i o n task, as i n t h i s one, the c o r r e c t s o l u t i o n r e q u i r e d t r a n s l a t i n g each item's o r d i n a l p o s i t i o n on one dimension of comparison i n t o i t s o r d i n a l p o s i t i o n on another. Herein, the height of eight t r e e s had to be v e r b a l l y recoded as an index of each t r e e ' s r o o t s . The stimulus card bearingthe f o u r t h s h o r t e s t t r e e was used as the i n t e r p o l a t i o n card. Although v e r b a l s e r i a t i o n problems could have been constructed to n e c e s s i t a t e s t r a t e g i e s such as numbering and counting, these operations are not i d e n t i c a l to s e r i a t i o n . I t was th e r e f o r e decided that numberical s t r a t -egies would not be encouraged over any others. For t h i s reason, the items were not numbered on any of the stimulus cards. Instead, i n d i v i d u a l items were i d e n t i f i e d by q u a l i t a t i v e r a t h e r than q u a n t i t a t i v e features ( i . e . , h e i g h t ) . The v a r y i n g heights of the trees on each card presented sheer pe r c e p t u a l gradations that presumably were apparent to even p r e - l i t e r a t e respondents. To t h i s extent there i s no such t h i n g as a p u r e l y v e r b a l , non-perceptual s e r i a t i o n task that does not invoke metric concepts and a b i l i t i e s . ( i i ) Procedure M a t e r i a l s . -Eight index cards w i t h t r e e s of d i f f e r e n t heights depicted. A person was p i c t u r e d beside each t r e e to i n d i c a t e r e l a t i v e s i z e . The f i f t h t a l l e s t ( f o u r t h s h o r t e s t ) t r e e was used as the i n t e r p o l a t i o n s t i m u l u s . F a m i l i a r i t y Assessment. Seven of the cards d e p i c t i n g t r e e s (minus the i n t e r p o l a t i o n card) were d i s p l a y e d i n f r o n t of the respondent and the i n v e s -t i g a t o r s a i d , "Here are some p i c t u r e s of some t r e e s . The boy standing beside t h e t r e e s i s t h e same Boy i n e v e r y p i c t u r e . A l l t r e e s have r o o t s t h a t go i n t o t h e ground. You can t e l l how deep a t r e e ' s r o o t s go By l o o k i n g t o see how t a l l t h e t r e e i s . The t a l l e r t h e t r e e i s , t h e deeper i t s r o o t s go i n t o t h e ground. Which o f t h e s e two t r e e s has t h e d e e p e r - r o o t s ? ( P o i n t t o two t r e e s o f c l e a r l y d i f f e r e n t h e i g h t s ) . Here a n o t e was made o f t h e r e s p o n d e n t ' s u n d e r s t a n d i n g o f t h e c o r r e l a t i o n Between h e i g h t and d e p t h o f r o o t s . I f t h e r e s p o n d e n t d i d n o t u n d e r s t a n d t h e r e l a t i o n s h i p , i t was e x p l a i n e d a g a i n . P a s s : The t a l l e r t r e e had t h e deeper r o o t s . I n s t r u c t i o n s . P a r t A: The r e s p o n d e n t was a s k e d t o a r r a n g e t h e c a r d s g o i n g f r o m t h e one w i t h t h e d e e p e s t r o o t s t o t h e one w i t h t h e s h a l l o w e s t r o o t s . P a r t B: I f t h e c a r d s were s e r i a t e d c o r r e c t l y , t h e r e s p o n d e n t was shown t h e i n t e r p o l a t i o n c a r d and was a s k e d t o , "Put I t i n t h e r i g h t p l a c e w i t h t h e r e s t . " ( i i i ) S c o r i n g See A p p e n d i x A, S e c t i o n A ( i i i ) • B. L i n e a r T r a n s i t i v i t y ( i ) I n t r o d u c t i o n F o l l o w i n g t h e s t a n d a r d p r o c e d u r e ( G l i c k and Wapner, 1968). f o r d e t e r m i n -i n g t h e a B i l i t y t o p e r f o r m t r a n s i t i v e o p e r a t i o n s , t h r e e o B j e c t s d i f f e r i n g i n magnitude a l o n g one d i m e n s i o n were us e d . The d i m e n s i o n was t h e number o f eggs l a i d by t h r e e d i f f e r e n t s p e c i e s o f b i r d s . G l i c k and Wapner f o u n d h e t e r o t r o p i c r e l a t i o n s t o be more d i f f i c u l t t h a n i s o t r o p i c i n t h e v e r b a l mode. H e t e r o t r o p i c r e l a t i o n s were used b e c a u s e t h e y f o c u s e d a t t e n t i o n on t h e b i v o c a l n a t u r e o f t h e i n t e r m e d i a t e e l e m e n t . ( i i ) P r o c e d u r e M a t e r i a l s . -Drawings o f : an e a g l e , a r o b i n , a duck. The d r a w i n g s d i d n o t i n d i c a t e how many eggs e a c h l a i d . These were s i m p l y memory a i d s . F a m i l i a r i t y A ssessment. The i n v e s t i g a t o r s a i d t h a t he was g o i n g t o t e l l t h e r e s p o n d e n t how many eggs were l a i d by t h e t h r e e d i f f e r e n t k i n d s o f b i r d s and t h e n ask h i m o r h e r w h i c h k i n d l a y s t h e most eggs and w h i c h l a y s t h e 172 fewest. The i n v e s t i g a t o r then presented the c h i l d with two separate verbal statements as follows: -"Robins lay more eggs than eagles." -"Robins lay fewer eggs than ducks." The respondent was required to memorize and to repeat both premises aloud. The drawings were presented i n the appropriate p a i r s ( i . e . , robin and eagle; robin and duck) as the premises were rehearsed. Pass: Memorization of the two premises. Instructions . A f t e r the i n v e s t i g a t o r was sure that the respondent had memorized the premises, the respondent was then asked, "Which b i r d lays the most eggs?" and "How can you t e l l that?" Immediately afterward, the respondent was asked, "Which b i r d lays the fewest eggs?" and "How can you t e l l that?" ( i i i ) Scoring See Appendix A, Section B ( i i i ) ; C. L o g i c a l M u l t i p l i c a t i o n (i ) Introduction The task was e s s e n t i a l l y the same as that described i n Appendix A, section C except for the use of printed words i n the place of colored forms. ( i i ) Procedure Materials. -A two-fold matrix w i t h the (a) "Plant-eating" i n the top row and "Meat-eating" i n the bottom row, and, (b) " F i s h " i n the l e f t column and " B i r d " i n the r i g h t column, thereby y i e l d i n g : - L e f t top c e l l : "Plant-easting F i s h " -Right top c e l l : "Plant-eating B i r d " - L e f t bottom c e l l : "Meat-eating F i s h " -Right bottom c e l l : BLANK (To be f i l l e d by respondent with correct entry being the words "Meat-eating Bird".) -Below the matrix was a row of f i v e a l t e r n a t i v e s , one of which was to be selected for the r i g h t bottom c e l l . These were the words: 173 1. "Plant-easting Fish 1 2. "Meat-eating F i s h " 3. "Meat-eating Animal 1 4. "Meat-eating B i r d " 5, "Plant-eating B i r d " F a m i l i a r i t y Assessment. The i n v e s t i g a t o r read the c e l l e n t r i e s to the respondent and then pointed to each one asking what i t was. I f eating habits or phylum were not mentioned, the i n v e s t i g a t o r queried about them. Pass: Mention of the correct d i e t and phylum. Inst r u c t i o n s . I f necessary the features of each item were stressed again. Hereafter the i n s t r u c t i o n s were the same as those i n the p h y s i c a l domain task (Appendix A, Section C ( i i ) except that color and shape were replaced by eating habits and phylum. ( i i i ) Scoring See Appendix A. Section C ( I i i ) • D. Class Inclusion ( i ) Introduction Again the standard procedure was followed except that the array presented to the respondent was an array of words printed on a page and the classes were from b i o l o g i c a l science. ( i i ) Procedure Materia l s . -A sheet of paper wi t h the word "Crow" typed on i t i n two places and the word "Duck" typed on i t i n f i v e places, according to the s p a t i a l arrangement shown i n f i g u r e B - l . F a m i l i a r i t y Assessment. The words were read to a l l respondents and were re-read as often as was necessary to p r e — l i t e r a t e or p a r t i a l l y l i t e r a t e respondents. Pass: Knowledge of what a crow, duck and b i r d are. Instructions. The premises were reviewed with the respondent as follows: "Aifethe ducks b i r d s ? " "Are the crows birds?''''. . "Are they a l l b i r d s ? " F i g u r e B l D i s p l a y c a r d f o r b i o - e c o l o g i c a l domain c l a s s i n c l u s i o n t a s k . CROW DUCK DUCK DUCK CROW DUCK DUCK 175 When t h e r e s p o n d e n t had a f f i r m e d t h e s e p r e m i s e s t h e i n v e s t i g a t o r a s k e d , "Are t h e r e more B i r d s h e r e o r more d u c k s ? " W h i l e r e c o r d i n g t h e r e s p o n s e s t h e i n v e s t i g a t o r c o n t i n u e d w i t h , " I f I t o o k away a l l t h e ducks w o u l d t h e r e be any b i r d s l e f t h e r e ? I f I t o o k away a l l t h e b i r d s w o u l d t h e r e be any t h i n g s l e f t h e r e ? Which a r e t h e r e more o f h e r e , ducks o r b i r d s ? " ( i i i ) S c o r i n g I ( F a i l ) : More o f t h e p a r t c l a s s t h a n t h e w h o l e . I I ( P a s s ) : More o f t h e w h ole c l a s s t h a n t h e p a r t c l a s s . E. S y s t e m i c S t r u c t u r e s o f C y c l i c T r a n s i t i v i t y and C y c l i c I n t e g r a t i o n ( i ) I n t r o d u c t i o n The t a s k s used f o r a s s e s s i n g c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n do n o t e a s i l y decompose i n t o one s e c t i o n f o r e a c h c o g n i t i v e o p e r a t i o n . T h e r e -f o r e , t h e y a r e d i s c u s s e d t o g e t h e r . The s c o r i n g o f a l l s y s t e m i c r e l a t i o n s t a s k s i s c o v e r e d i n A p p e n d i x D. T h e r e f o r e , o n l y b r i e f m e n t i o n o f s c o r i n g i s made h e r e i n . The f a m i l i a r i t y a s s e s s m e n t s and c o r r e s p o n d i n g e x p l a n a t i o n s a r e p r e -s e n t e d a t t h e a p p r o p r i a t e p o i n t s t h r o u g h o u t t h e i n t e r v i e w . The i n t e r v i e w s c h e d u l e t h a t f o l l o w s can d o u b l e as a d a t a r e c o r d s h e e t . The s c o r i n g manual i s c r o s s r e f e r e n c e d w i t h t h e i t e m s i n t h e i n t e r v i e w s c h e d u l e . The b i o - e c o l o g i c a l s y s t e m t o be used was a n u t r i e n t c y c l e c o m p r i s e d o f p l a n t s , h e r b i v o r e s , c a r n i v o r e s , decomposing b a c t e r i a , and i n o r g a n i c p l a n t n u t r i e n t s . When a t t e m p t i n g t o draw s i m p l i f y i n g g e n e r a l i z a t i o n s , e c o l o g i s t s o f t e n r e p r e s e n t b o t h a q u a t i c and t e r r e s t i a l e cosystems i n terms o f t h e s e f i v e s t a g e s ( e . g . , Odum, 1971, p . 2 0 7 ) . C l o s e r a n a l y s i s r e v e a l s t h i s s c h e m a t i c t o be a compound o f many i n t e r a c t i n g c y c l e s ( S u t t o n and Harmon, 1973, p . 1 3 6 ) . T h i s n u t r i e n t c y c l e , however, was w e l l s u i t e d f o r t h e p r o p o s e d t a s k . I t was com-p r e h e n s i v e enough t o p e r m i t t h e e l a b o r a t i o n o f one o r two l e v e l s o f s u b c y c l e s w h i l e r e m a i n i n g s i m p l e enough t o e x p l a i n q u i c k l y t o t h o s e r e s p o n d e n t s who were n o t f a m i l i a r w i t h t h e e n t i r e c y c l e . The r e s p o n d e n t s d i d n o t need t o be fam-i l i a r w i t h t h e r e l a t i o n s among t h e e l e m e n t s o f t h e c y c l e because each element was d e s c r i b e d t o them (see b e l o w ) . N o n e t h e l e s s , few younger r e s p o n d e n t s t h o r o u g h l y u n d e r s t o o d c o n c e p t s l i k e b a c t e r i a and n u t r i e n t c h e m i c a l i n t h e s o i l . S i n c e i t m i g h t have t a k e n days t o t h o r o u g h l y t e a c h younger c h i l d r e n t h e s e c o n c e p t s i t was p r a c t i c a l l y i m p o s s i b l e t o i n s u r e t h a t a l l r e s p o n d e n t s were e q u a l l y f a m i l i a r w i t h t h e m a t e r i a l s o f t h i s t a s k . I n s t e a d t h e r e s p o n d e n t ' s degree o f f a m i l i a r i t y w i t h t h e m a t e r i a l s was measured. The i n t e r v i e w p r o c e e d s i n two main p h a s e s . Phase one i s t h e c y c l i c t r a n s i t -i v i t y phase. I t c o n t a i n s ( i ) f a m i l i a r i z a t i o n i t e m s , ( i i ) t h e l a y o u t p r o c e d u r e i t e m s , and ( i i i ) t h e t r a n s i t i v e r e c y c l i n g i t e m s , i n t h a t o r d e r . Phase two, t h e c y c l i c i n t e g r a t i o n s e c t i o n , c o n t a i n s ( i ) f u r t h e r f a m i l i a r i z a t i o n i t e m s , ( i i ) t h e systems s y s t h e s i s i t e m s , and ( i i i ) t h e systems a n a l y s i s i t e m s , i n t h a t o r d e r . The i n t e r v i e w s c h e d u l e p r e s e n t e d b e l o w i s a s t e p by s t e p g u i d e w h i c h i n c l u d e s i n s t r u c -t i o n s t o t h e i n t e r v i e w e r f o r d i s p l a y i n g m a t e r i a l s , r e a d i n g e x p l a n a t i o n s , and r e -c o r d i n g answers. I t a p p e a r s i n a f o r m a t s u i t a b l e f o r use as a d a t a r e c o r d s h e e t . ( i i ) P r o c e d u r e 176 Materials. -Tape recorder. ELEMENT EXEMPLAR Drawings of Ca) a producer a plant (b) a herbivore a c a t e r p i l l a r (c) a carnivore. a b i r d (.d) a decomposer a microscopic magnification of Bacteria (e) a mineral nutrient a molecule of nitrogen and, -a molecule of DDT -multiples of (b) and C c ) Interview Schedule. Phase One: CYCLIC TRANSITIVITY PRESENT PLANT DRAWING "Do you know what t h i s i s ? Can you t e l l me something about i t ? " RECORD FAMILIARITY ; Pass = I t ' s a plant READ FAMILIARIZATION This i s a plant. I t takes i n nutrients from the s o i l and combines them with sunlight and a i r to make new leaves and to grow. The plant foods i n the s o i l are chemicals l i k e nitrogen. Sometimes plants loose t h e i r leaves Because insects or animals eat them. PRESENT REST OF DRAWINGS ONE BY ONE IN AN IMPROPER ORDER IN A VERTICAL PILE SECOND DRAWING PRESENTED WAS .' ' y yy' "" p'Do you know what t h i s i s ? C l F NOT, NAME IT) Can you t e l me something about i t ? " RECORD FAMILIARITY _ READ FAMILIARIZATION THIRD DRAWING WAS REPEAT 0 FOURTH DRAWING WAS REPEAT © FIFTH DRAWING WAS _ _ REPEAT 0 177 CATERPILLAR FAMILIARIZATION: This i s a c a t e r p i l l a r . I t eats the leaves o f f of c e r t a i n kinds of plants. Some Birds catch c a t e r p i l l a r s and eat them. Pass: I t ' s a c a t e r p i l l a r BIRD FAMILIARIZATION: This i s a B i r d that eats a l l sorts of i n -sects and c a t e r p i l l a r s . When t h i s B i r d dies i t s Body gets eaten By the B a c t e r i a that l i v e i n the ground. Pass: I t ' s a B i r d BACTERIA FAMILIARIZATION: These are various kinds of t i n y animals c a l l e d Bacteria. They are so small that you can only see them with a powerful microscope. Bacteria l i v e i n the s o i l , the ground. They eat the dead Bodies of plants, i n s e c t s , Birds and animals. Bacteria turn these dead bodies into chemicals l i k e nitrogen that plants can then use for food. Pass: I t ' s a very small animal; l i k e a germ; etc. NITROGEN FAMILARIZATION: This i s a l i t t l e piece of nitrogen. Nitrogen i s a chemical that plants need to l i v e and grow. I t s a kind of plant food. A l o t of nitrogen gets put i n the s o i l by the b a c t e r i a which l i v e i n the ground. Pass: I t ' s a chemical; a kind of plant food LAYOUT .PROCEDURE "Put the drawings i n t h e i r proper order?" ?MISORDERED? "OK, that's good. Now put the drawings i n an order which shows which ones depend on which other ones.for t h e i r being there." ?STILL MISORDERED? START WITH LAST ELEMENT PUT IN PLACE AND REPEAT THE FOLLOWING QUESTIONS FOR DRAWINGS IN REVERSE ORDER. RECORD ELEMENT UNDER DISCUSSION IF EITHER OF THESE'TWO QUESTIONS ARE ANSWERED INCORRECTLY, REPEAT THE RELEVANT PART OF THE FAMILIARITY EXPLANATION. REPEAT (?) AS OFTEN AS NEEDED II-'Which one does t h i s (element) depend on? 'How does i t depend on (the l a s t one)? it ti 178 ?NOT A CIRCLE? "OK, now i s there any way you can think of to show which ones depend on which other ones besides putting them i n a s t r a i g h t l i n e ? Could the same thing be shown by some other arrangement of the cards?' RECORD ?ANYTHING STILL SUBOPTIMAL? WHAT? "You've put the drawings i n t h i s order that's a good way to do i t . Now l e t me show you another way i t could be done." CREATE PROPER CYCLIC ORDER • READ SUMMARY OF NUTRIENT CYCLE SUMMARY OF NUTRIENT CYCLE: In t h i s order the plant depends on the nitrogen f o r i t s food so the nitrogen molecule i s beside the plant. The nitrogen depends on the b a c t e r i a for being there so the b a c t e r i a i s next to the nitrogen molecule because the b a c t e r i a are what make the nitrogen that's i n the s o i l . The b a c t e r i a depend on the dead bodies of a l l sorts of l i v i n g things for t h e i r food because they eat dead bodies. So we put the b i r d beside the b a c t e r i a because the b a c t e r i a w i l l need the bird's body for food when the b i r d dies. The b i r d depends on the c a t e r p i l l a r f o r i t s food because i t eats c a t e r p i l l a r s so l e t s put the c a t e r p i l l a r beside the b i r d . The c a t e r p i l l a r eats plants so i t depends on the plant for i t s food The plant goes next to the c a t e r p i l l a r . OK, now l e t s leave the drawings i n t h i s order and I ' l l ask you some r i d d l e s about the things i n the drawings." CYCLE DISPLAYED IN PROPER ORDER PRESENT DDT DRAWING "This i s a molecule of DDT. Can you t e l l me what DDT i s ? " RECORD FAMILIARITY Pass: I t ' s a p e s t i c i d e ; a chemical; poison f o r bugs; etc. READ DDT INTRODUCTION AND FAMILIARIZATION: Let's suppose that these plants are being grown by a farmer on h i s farm. He doesn't want the c a t e r p i l l a r s to eat h i s plants so he sprays the plants-with a chemical c a l l e d DDT that w i l l k i l l the c a t e r p i l l a r s but won't k i l l the p l a n t s . " POINT TO DDT DRAWING "This i s a l i t t l e piece of DDT. DDT i s a chemical that k i l l s i n s e c t s and animals i f they eat enough of i t . Farmers put DDT on t h e i r plants i n order to k i l l the c a t e r p i l l a r s and other insects that would otherwise eat the plants. The molecules 179 of DDT are so small that the insects and animals don't t e l l when they're eating i t . The DDT molecule then stays i n the insect's or animal's body u n t i l he has eaten enough of i t to k i l l him. Plants can absorb DDT i f i t s i n the s o i l But i t doesn't k i l l p l a n t s . " "When the c a t e r p i l l a r eats a l e a f that has been sprayed with DDT the DDT goes into the c a t e r p i l l a r ' s body and stays there u n t i l the c a t e r p i l l a r dies. When a c a t e r p i l l a r has eaten a l o t of molecules of DDT i t dies. What might happen to a b i r d that eats a l o t of c a t e r p i l l a r s that are ..all f u l l of DDT?" ? N 0 PREDICTION OF FATALITY? EXPLAIN IT. TRANSITIVE RECYCLING "Could the same molecule of DDT ever help k i l l two b i r d s ? " ? N 0 ? "Why Not?" ?YES? "How could that happen?" ?UNSURE? "What happens to the b i r d ' s body a f t e r i t dies from eating too many molecules of DDT?" "And so what happens to the molecules that were i n the bird's body?" ?STILL UNSURE? "So could the same molecule of DDT ever help k i l l two birds? Why not/How? • Phase Two: CYCLIC:INTEGRATION FAMILIARITY READ GENERATION SPAN FAMILIARIZATION This kind of plant (POINT TO DRAWING OF PLANT ELEMENT) grows very f a s t . I f you put a seed from one of these plants i n the ground, i t would only take 3 months for that seed to grow into an adult plant that has seeds of i t s own. We say that three months i s the "generation span" of t h i s kind of plant. These c a t e r p i l l a r s (POINT) go through t h e i r l i f e cycle even f a s t e r . I t only takes 1 month f o r a c a t e r p i l l a r to grow from an egg to an adult that can lay eggs of i t s own. The generation span of these c a t e r p i l l a r s , then, i s 1 month. J180 This kind of b i r d only lays one nest f u l l of eggs a year. I t takes 1 year or 12 months f o r one of these b i r d s to go from being an egg to being an adult b i r d that lays eggs. Therefore the generation span of these birds i s 12 months. Reproduction F a m i l i a r i t y Item POINT TO DRAWING OF MULTIPLE CATERPILLARS AND BIRDS " I f there were these s i x c a t e r p i l l a r s and i t takes 1 month f o r t h e i r o f f -spring to grow up into adult c a t e r p i l l a r s then how many c a t e r p i l l a r s would there be i n j u s t over a month? More, les s or the same number?" (CIRCLE ONE) Pass: More 2UNFAMILIAR2 READ GENERATION SPAN EXPLANATION (REPRODUCTION).: When there are more c a t e r p i l l a r s being born than dying then every month there w i l l be more c a t e r p i l l a r s than there was before. That's because they keep mul t i p l y i n g . There are more eggs becoming adults than there are adults dying so i f conditions are good, the t o t a l number of c a t e r p i l l a r s w i l l go up." Stavation F a m i l i a r i t y Item MULTIPLE CATERPILLAR AND BIRD DRAWING STILL DISPLAYED " I f there were these two bir d s and each one needed 142 c a t e r p i l l a r s to l i v e f o r 12 months but they only had these 6 to eat between them, how many bir d s would there be i n 12 months? More, same number or fewer?" (CIRCLE ONE) Pass: Starvation ?UNFAMILIAR? READ STARVATION EXPLANATION: "When there are so many bir d s that they don't a l l have enough food to l i v e f o r 12 months, then some of them w i l l starve to death. I f they starve f a s t e r than they can have babies then the number of b i r d s w i l l go down." C a t e r p i l l a r Population Item (Population Fluctuations) "Suppose that when the farmer sprayed h i s plants with DDT, 9 out of every 10 c a t e r p i l l a r s died but 1 out of every 10 survived. T e l l me everything you can about the e f f e c t s t h i s would have. What would happen 'Why? (a) (b) (c) 1 month a f t e r spraying? 3 months a f t e r spraying?" 12 months after, spraying? ti it 181 SYSTEMS SYNTHESIS ?BELOW EFFECTS NOT MENTIONED? PROBE FOR THEN AS FOLLOWS: Rate Item "Could the DDT spraying ever lead to a time when the number of c a t e r p i l l a r s s t a r t s to r i s e sharply/rapidly? How? (MORE FOOD)/Why not? (RECORD PREDICTION & REASON) Renewed I n f e s t a t i o n I t em "Could the DDT spraying ever lead to fewer new leaves sprouting on plants or to plants not being as healthy as before the spraying? How? (MORE CATERPILLARS)/Why not?" Birds Item "Could the DDT spraying ever lead to an increase i n the number of birds l i v i n g i n the area of the farm? How? (MORE CATERPILLARS)? Why not?" Nitrogen Desert Item ALL DRAWINGS STILL ARRAYED. DDT & MULTIPLES DRAWINGS REMOVED FROM VIEW READ NITROGEN DESERT INTRODUCTION: "At the end of the growing season when he had harvested a l l h i s crops, the farmer got busy preparing the s o i l f o r the next spring. While he was ploughing and c u l t i v a t i n g , he usually added some f e r t i l i z e r to the s o i l . " Younger respon-dents have the term " f e r t i l i z e r " explained to them i n terms of plant food. "This year the farmer was t r y i n g some new kinds of f e r t i l i z e r that he made at home from a receipe he got from a f r i e n d . Well, he didn't f o l l o w the receipe properly and instead of making f e r t i l i z e r he a c c i d e n t a l l y made a chemical which destroys almost a l l of the nitrogen i n the s o i l . The farmer didn't know that he'd made t h i s mistake u n t i l i t was too l a t e . He had already put the chemical i n his s o i l and i t had already destroyed most of the nitrogen. There was nothing he could do. Even i f he put more nitrogen i n the s o i l , i t would be destroyed by the chemical too." "What do you think happened to the land?" "What would the place look l i k e a f t e r a while?" SYSTEMS ANALYSIS. DRAWINGS STILL ARRAYED AS ABOVE 5 MINUS 1 Item "Which of these (POINT TO DRAWINGS OF ELEMENTS) f i v e steps could you remove without e n t i r e l y destroying any other step?" REMOVE IT "How would the TWO ADJACENT) survive without the (ONE REMOVED)?" Core Item "Which of the remaining three could survive without the other two?" "Why wouldn't (THE ONE/THE OTHER) be able to survive without the other two?" 182 APPENDIX C; S o c i e t a l Domain Tasks The respondent's understanding of the cognitive operations of s e r i a t i o n , l i n e a r t r a n s i t i v i t y , l o g i c a l m u l t i p l i c a t i o n , c l a s s i n c l u s i o n , c y c l i c trans-i v i t y and c y c l i c i n t e g r a t i o n , as manifested i n content dealing with s o c i a l organization was engaged by the problems presented during the s o c i a l systems interview. The substantive content of the problems f o r a l l cognitive opera-tions deal with a mixed agrarian economy with a representative democracy. F a m i l i a r i t y with the concepts used i n the problem are assessed and the con-cepts are explained, as they were i n the b i o - e c o l o g i c a l domain interview. The problem are i n t r i n s i c a l l y verbal i n t h e i r mode of presentation but figures and drawings were used to help maintain i n t e r e s t and reduce memory load, e s p e c i a l l y f o r younger respondents. A l l of the problems were evolved from questions posed during p i l o t interviews with groups of 10, 8, and 17 subjects ranging i n age from 5 to 25. The questions tested during the p i l o t Interviews came from a v a r i e t y of sources. Sometimes the form of the question was borrowed and i n other cases i t was the substantive, issue. I acknowledge a debt i n t h i s early phase to Jahoda (1964), Adelson, Green, and O'Neil (1969), Greenstein and Tarrow (1970), Connell (1971), and Furth, Baer, and Smith (1976). The version of the interview presented here i s i n no way a comprehensive treatment of the develop-ment of understanding of s o c i a l organization. The substantive problems con-tained i n t h i s interview, however, were designed to exhibit the structure of most p o l i t i c a l and economic hierarc h i e s and cycle s . A. S e r i a t i o n ( i ) Introduction This task was s i m i l a r to the p h y s i c a l domain task and the b i o - e c o l o g i c a l task i n s o f a r as i t required that a one-to-one correspondence be established j u s t as i n Piaget's walking s t i c k s e r i a t i o n task (Ginsberg and Opper, 1969, p. 140). The dimension of ordering here was the p r i o r i t y of access that each of the 8 farmers had to the use of a cooperatively owned t r a c t o r . P r i o r i t y of access r i g h t s were i n a one to one correspondence with the number of shares that the farmer had i n the coop. ( i i ) Procedure Materi a l s . -Toy Tractor .1 83 -8 c a r d s c o r r e s p o n d i n g t o t h e 8 f a r m e r s . Each c a r d showed: th e f a r m e r ' s name - c o l o r d e s i g n a t i o n r a t h e r t h a n n o m i n a l numbers th e number o f s h a r e s C$100 ea c h )T t h a t t h e f a r m e r had i . e . Farmer Brown $100 Farmer B l a c k $100 $100 Farmer W h i t e $100 $100 $100 Farmer Green $100 $100 $100 $100 Farmer B l u e $100 $100 $100 $100 $100 Farmer G o l d $100 $100 $100 $100 $100 $100 Farmer Rose $100 $100 $100 $100 $100 $100 $100 Farmer Gray $100 $100 $100 $100 $100 $100 $100 $100 F a m i l i a r i t y Assessment. The co n c e p t o f s h a r e d o w n e r s h i p was e x p l a i n e d i n t h e i n s t r u c t i o n s . Then t h e r e s p o n d e n t s were a s k e d , "Who owns t h e t r a c t o r ? " o r "Whose t r a c t o r i s i t ? " I n c o r r e c t r e s p o n s e s were c o r r e c t e d . The r e s p o n d e n t was c o u n t e d as u n f a m i l i a r w i t h t h e t a s k m a t e r i a l s i f e i t h e r o f t h e above two c o n c e p t s had t o be e x p l a i n e d t o him o r h e r . I n s t r u c t i o n s . The p r o b l e m was i n t r o d u c e d w i t h t h i s a n e c d o t e . "Once t h e r e were 8 f a r m e r s . None o f them had a t r a c t o r . They got t o g e t h e r and d e c i d e d t h a t i f t h e y a l l p u t i n some money t h e y w o u l d have enough money t o buy one t r a c t o r amongst t h e 8 o f them. (POINT TO TOY TRACTOR. ASK TRACTOR FAMILIARITY QUESTION. I F NECESSARY, EXPLAIN). They a l l . h ad d i f f e r e n t amounts o f money t o p u t i n . They k e p t t r a c k o f how much/each one o f them has p u t i n towards b u y i n g t h e t r a c t o r . Then t h e y bought t h e t r a c t o r when t h e y had enough money. (ASK WHO OWNS THE TRACTOR. I F NECESSARY EXPLAIN COOPERATIVE OWNERSHIP). Whenever no one was u s i n g i t , anyone o f them c o u l d go get i t and use i t . I f two o f t h e 8 f a r m e r s wanted t o use t h e t r a c t o r a t t h e same t i m e t h e y would l o o k and see w h i c h one had p u t t h e most money towards b u y i n g t h e t r a c t o r . T h a t ' s what t h e s e c a r d s h e r e show. (POINT TO SHARE CARDS, READ NAMES OF FARMERS TO YOUNGER SUBJECTS. PRESENT CARDS IN A RANDOM ARRAY). Farmer B l a c k , f o r example, has put I n t h i s many hundreds o f d o l l a r s . Farmer B l u e has p u t i n t h i s many hundreds o f d o l l a r s . I f f a r m e r B l a c k and Farmer B l u e b o t h wanted t o use t h e t r a c t o r a t t h e same t i m e , who would get t o use i t f i r s t ? " E r r o r s were c o r r e c t e d e x p l a i n i n g t h a t t h e amount o f money i n i t i a l l y c o n t r i b u t e d d e t e r m i n e d p r i o r i t y f o r a c c e s s . "Now one day 7 o f t h e f a r m e r s wanted t o use t h e t r a c t o r a t t h e same t i m e . P u t t h e f a r m e r s i n o r d e r f r o m t h e one who g e t s t o use i t f i r s t t o t h e one who g e t s t o use i t l a s t . " 184 The i n t e r p o l a t i o n element was the $400 farmer, Farmer Green. "Here comes Farmer Green. Now he wants to use the t r a c t o r too at the same time as the r e s t of them. Put Farmer Green i n the place that shows which i t w i l l be h i s turn to use the t r a c t o r . " ( i i i ) Scoring Respondents were counted as having mastered s e r i a t i o n i n t h i s domain only when a l l the cards were placed i n the proper order without t r i a l and error and with the i n t e r p o l a t i o n card i n i t s proper place. B. Linear T r a n s i t i v i t y (i) Introduction The dimension of comparison used here was the degree of "power to make and change laws." The three elements i n the l i n e a r s e r i e s are the prime minister, a judge, and a policeman. This task extended one used by Greenstein and Tarrow 0-970). Greenstein and Tarrow were interested i n whether or not the c h i l d r e n had assimilated the idea of the supremacy of the law over the lawmaker. The present task examined the a b i l i t y to i n f e r the o r d i n a l r e l a t i o n between a prime minister, a judge, and a policeman i n terms of power to make and change laws. ( i i ) Procedure Ma t e r i a l s . Three d o l l s with a t t i r e appropriate to occupation and with the names of the occupation written on a card on which the d o l l stood: -prime minister d o l l -judge d o l l -policeman d o l l F a m i l i a r i t y Assessment. Respondents were presented with: the d o l l s one at a time i n a random order. Respondents were asked what each occupational r o l e was, and i f the c h i l d could not say that any one occupation had to do w i t h the law, he or she was counted as unfamiliar with the materials. For respondents whose d e s c r i p t i o n of each r o l e seemed inadequate the following explanations were given: Prime M i n i s t e r . The prime minister i s the elected leader of parliament. Parliament decides what the laws w i l l be f o r .the country. The prime minister i s the main person i n charge of making up the l i s t of new laws every year. He also makes up the l i s t of changes to old laws that already e x i s t . 185 Judge. The judge knows the laws made by the prime minister and parliament. The judge runs the courtroom and the t r i a l s that are held i n the courtroom. When the p o l i c e a r r e s t someone the judge decides whether or not the person has r e a l l y broken the law. The judge i s the one who has to decide what the law r e a l l y means. Policeman. I t s the policeman's job to make sure that nobody breaks the law. I f someone does break the law, the policeman has to f i n d the lawbreaker and bring him to court where the judge decides i f the policeman has caught the r i g h t man. Af t e r the above f a m i l i a r i z a t i o n information was given the invest i g a t o r said that he was going to t e l l the respondent about the r o l e figures j u s t i n -troduced and then ask the respondent which has the l e a s t power to make and change laws and which has the greatest power to make and change laws. The inv e s t i g a t o r then presented the respondent with the judge d o l l (to the re s -pondent's r i g h t ) and the prime minister d o l l (to the respondent's l e f t ) with the accompanying statement: -"The judge has l e s s power to make and change laws than the prime minister". The respondent was required to memorize and to repeat t h i s premise aloud. Then the f i r s t p a i r of d o l l s were replaced by the judge d o l l (again to the respondent's r i g h t ) and the policeman d o l l (to the respondent's l e f t ) with the accompanying statement: -"The judge has more power to make and change laws than the policeman." Again the respondent was asked to memorize and to repeat the premise. Inst r u c t i o n s. When the in v e s t i g a t o r was s a t i s f i e d that the respondent had memorized both premises, the respondent*was then asked, "Which person has the most6power to make and change laws?", and "How can you t e l l that?" Im-mediately afterward the respondent was asked, "Which person has the l e a s t power to make and change laws?" , and, "How can you t e l l that?" ( i i i ) Scoring I ( F a i l ) : Incorrect choice f o r one or both endpoints. II ( F a i l ) : Correct choice of endpoints but inc o r r e c t explnation f o r choice (e.g., tautology, temporal order as power p r e d i c t o r ) . II I (Pass) Correct choice of endpoints with correct r a t i o n a l e f o r choice. 186 C. L o g i c a l M u l t i p l i c a t i o n (i ) Introduction Like the p h y s i c a l and B i o - e c o l o g i c a l l o g i c a l m u l t i p l i c a t i o n tasks, t h i s one was Based on the format of the two-way c l a s s i f i c a t i o n task of Inhelder and Piaget (1964). The two dimensions, to Be intersected were (a) the form of a commodity a person deals with ( i . e . , wheat vs. f l o u r ) , and, (B) the person's economic function i n the exchange of the commodity ( i . e . , the producer vs. consumer). ( i i ) Procedure Materials. -Spice B o t t l e of f l o u r . -Printed two-fold matrix with, words naming (a)., consumers i n the top row and producers i n the Bottom row, and, (6) wheat dealers i n the l e f t column and f l o u r dealers i n the r i g h t column, therehy y i e l d i n g : - L e f t top c e l l : "Wheat Consumer" -Right top c e l l : "Flour Consumer" - L e f t Bottom c e l l : "Wheat Producers" -Right Bottom c e l l : BLAND (to Be f i l l e d By respondent w i t h the correct entry Being the words "Flour Producer"). -Below the matrix was c e l l . These were the a row of f i v e words: 1. "Wheat Producer" 2. "Wheat Consumer" 3. "Flour Consumer" 4. "Flour Inspector" 5. "Flour Producer" F a m i l i a r i t y Assessment. Respondents were asked i f they knew where the f l o u r came from. I f not, i t s d e r i v a t i o n from wheat was explained. Respondents could not say what a producer or a consumer were, were t o l d that a producer was someone who makes something and a consumer i s someone who uses what the pro-ducer has. made. Respondents who needed any of t h i s explained to them were counted as unfamiliar with the conceptual materials. 187 I n s t r u c t i o n s , The i n v e s t i g a t o r pointed to each c e l l i n the m a t r i x from column to column, saying, "Here i s a wheat consumer. Her i s a f l o u r consumer. Here i s a wheat producer. Which of these (POINT TO ROW OF FIVE ALTERNATIVES AT BOTTOM) goes best here (POINT TO BLANK CELL) w i t h t h i s wheat consumer, t h i s f l o u r consumer and t h i s wheat producer. The respondents choice was recorded. "Why d i d you choose '.»..".."?" Respondent's e x p l a n a t i o n i s noted. "Can anything e l s e go i n t h i s empty place j u s t as w e l l as your choice of ?" ( i i i ) S c o ring I ( F a i l ) : I n c o r r e c t choice. I I ( F a i l ) : Correct c h o i c e ; i n c o r r e c t e x p l a n a t i o n . I I I (Pass): Correct choice; c o r r e c t e x p l a n a t i o n . D. Class I n c l u s i o n ( i ) I n t r o d u c t i o n As w i t h the p h y s i c a l and b i o - e c o l o g i c a l domain tasks the c l a s s i n c l u s i o n task used here was adapted from Inhelder and Piaget (1964). The " p a r t s " to be c l a s s i f i e d were members of a wheat marketing board. The wheat marketing board i t s e l f was l a t e r used as an element i n the c y c l i c i n t e g r a t i o n problem. The use of the same conceptual e n t i t i e s i n s e v e r a l tasks was intended to minimize memory load f o r the respondent and'to save time f o r the i n v e s t i g a t o r . The supraordinate c l a s s here was the c l a s s of government appointed members of the wheat marketing board. The subordinate c l a s s was. composed of the two economic s i t u s e s mentioned i n the l o g i c a l m u l t i p l i c a t i o n task ( i . e . producer vs. consumer). There were more r e p r e s e n t a t i v e s of producers than of con-sumers on the board. A l l were govenment appointees. ( i i ) Procedure M a t e r i a l s . -A 4" x 6" piece of paper w i t h the phrases "Government Appointed Consumer Representative" and "Government Appointed Producer Representative" typed on i t . "Government Appointed Consumer Representative" was typed i n two places and "Government Appointed Producer Representative" was typed i n f i v e places according to the s p a t i a l arrangement shown i n f i g u r e C - l F a m i l i a r i t y Assessment. The two concepts to be introduced here were that of government appointee and that of the marketing board. Respondents were asked, "Can you t e l l me what a government appointee I s ? " , and, "Can you t e l l me what a wheat marketing board i s ? " Respondents who could not a c c u r a t e l y describe both were c l a s s i f i e d as u n f a m i l i a r w i t h the m a t e r i a l s . The concepts were then explained to a l l respondents. F i g u r e CI D i s p l a y c a r d f o r s o c i e t a l domain c l a s s i n c l u s i o n t a s k . 188 GOVERNMENT APPOINTED PRODUCER REPRESENTATIVE GOVERNMENT APPOINTED PRODUCER REPRESENTATIVE GOVERNMENT APPOINTED PRODUCER REPRESENTATIVE, GOVERNMENT APPOINTED CONSUMER REPRESENTATIVE GOVERNMENT APPOINTED PRODUCER REPRESENTATIVE GOVERNMENT APPOINTED PRODUCER REPRESENTATIVE GOVERNMENT APPOINTED CONSUMER REPRESENTATIVE 189 Government appointees were described as, "People who the government picks to do a job. They get picked f or the job. They don't have to be elect e d . " The wheat marketing board was described as, "A group of people whose job i t i s to decide how much wheat the farmers should grow and how much the wheat should cost when i t i s sold. So everybody who grows wheat has to ask the people on the wheat marketing board how much t h e y ' l l be allowed to grow and how much t h e y ' l l be able to s e l l i t f o r . " The words typed on the display card were read to a l l respondents and wererre-read as often as was necessary to pre- and q u a s i - l i t e r a t e respondents. Instructions . The premises were introduced as follows: " A l l of the people on the wheat marketing board are government appointees. Some are representatives of wheat producers. Some are representatives of wheat consumers. Now I'm going to ask you some questions about the wheat marketing board." The premises were reviewed as follows and any errors were corrected. "Are there more producer representatives or more consumer representatives?" "Are the producer representatives government appointees?" "Are a l l the members of the wheat marketing board government appointees?" When the respondents had affirmed a l l these premises, the in v e s t i g a t o r asked, "Are there more government appointees on the wheat marketing board or more producer representatives?" While recording the response the in v e s t i g a t o r continued with, " I f I took away a l l the producer representatives, would there be any government appointees l e f t on the wheat marketing board?" " I f I took away a l l the government appointees would there be any board members l e f t ? " Which are there more of here, producer representatives or govern-ment appointees?" ( i i i ) Scoring I ( F a i l ) More of the part class than the whole c l a s s . II (Pass) More of the whole cla s s than the part c l a s s . E. Systemic Structures of C y c l i c T r a n s i t i v i t y and C y c l i c Integration (i) Introduction The tasks used f o r assessing c y c l i c t r a n s i t i v i t y and c y c l i c i n t e g r a t i o n 190 c o u l d n o t be b r o k e n down e a s i l y i n t o one s e c t i o n f o r e ach c o g n i t i v e o p e r a t i o n . T h e r e f o r e , t h e y a r e d i s c u s s e d t o g e t h e r . The s c o r i n g o f a l l s y s t e m i c r e l a t i o n s t a s k s i s c o v e r e d i n A p p e n d i x D. T h e r e f o r e , o n l y b r i e f m e n t i o n o f s c o r i n g i s made h e r e i n . The o r g a n i z a t i o n a l s y s t e m t o be used was one i l l u s t r a t i n g t h e c y c l i c f l o w o f money i n one d i r e c t i o n and c o m m o d i t i e s i n t h e o p p o s i t e d i r e c t i o n . The commodity chosen was a commonplace b a s i c n e c e s s i t y so t h a t a minimum o f t i m e was w a s t e d e x p l a i n i n g t h e n a t u r e o f t h e commodity. I t a l s o i n v o l v e d government as w e l l as p r i v a t e economic i n t e r e s t s . The commodity chosen f o r t h e t a s k was wheat. There were f i v e e l e m e n t s i n t h e "wheat c y c l e " : 1) t h e f a r m e r , 2) t h e wheat m a r k e t i n g b o a r d , 3) t h e f l o u r m i l l , 4) t h e b a k e r y , 5) t h e r e t a i l e r . I n Canada, wheat m a r k e t i n g i s c o n t r o l l e d , o r a t l e a s t m oderated, by t h e f e d e r a l government t h r o u g h t h e wheat m a r k e t i n g b o a r d ( L i p s e y , S p a r k s , and S t e i n e r , 1976, p. 1 2 0 ) . Thus, t h e wheat c y c l e i s a s u b c y c l e o f t h e p o l i t i c a l a u t h o r i t y s t r u c -t u r e . I n a d d i t i o n , : t h e wheat c y c l e i s embeded i n v a r i o u s economic c y c l e s w h i c h i n f l u e n c e t h e s u p p l y and demand f o r B o t h money and wheat ( e . g . , v a l u e o f s t o c k o f f l o u r m i l l i n g company). T h e r e f o r e , w h i l e b e i n g embedded i n a h i e r a r c h y o f c y c l e s complex enough t o d e f y a t h o r o u g h s c i e n t i f i c e x p l i c a t i o n , t h e wheat c y c l e i s s i m p l e enough t o be e a s i l y e x p l a i n e d t o even t h e y o u n g e s t s u b j e c t s . E v e r y a t t e m p t was made t o e x p l a i n t h e c o n c e p t s b e h i n d each element o f t h e c y c l e t o t h o s e s u b j e c t s who were u n f a m i l i a r w i t h t h e e l e m e n t s . Whatever d i f f e r e n c e s i n c omprehension remained a f t e r t h a t were t a k e n as p a r t o f t h e phenomena under s t u d y . The f a m i l i a r i z i n g e x p l a n a t i o n s a r e p r e s e n t e d t h r o u g h o u t t h e i n t e r v i e w s c h e d u l e a t t h e a p p r o p r i a t e p l a c e s . The i n t e r v i e w p r o c e e d s i n two m ain p h a s e s . Phase one i s t h e c y c l i c t r a n s i -t i v i t y phase. I t c o n t a i n s ( i ) f a m i l i a r i z a t i o n i t e m s , ( i i ) t h e l a y o u t p r o c e d u r e i t e m s , and ( i i i $ t h e t r a n s i t i v e r e c y c l i n g i t e m s , i n t h a t o r d e r . Phase two, t h e c y c l i c i n t e g r a t i o n s e c t i o n , c o n t a i n s ( i ) f u r t h e r f a m i l i a r i z a t i o n i t e m s , ( i i ) t h e systems s y n t h e s i s i t e m s , and ( i i i ) t h e systems a n a l y s i s i t e m s , i n t h a t o r d e r . The i n t e r v i e w s c h e d u l e p r e s e n t e d b e l o w i s a s t e p by s t e p g u i d e w h i c h i n c l u d e s i n s t r u c t i o n s t o t h e i n t e r v i e w e r f o r d i s p l a y i n g m a t e r i a l s , r e a d i n g e x p l a n a t i o n s , and r e c o r d i n g answers. I t a p p e a r s i n a f o r m a t s u i t a b l e f o r use as a d a t a r e c o r d s h e e t . ( i i ) P r o c e d u r e M a t e r i a l s . P i c t u r e s o f (a) ELEMENT a f a r m e r DEPICTION photo o f wheat f i e l d w i t h combine h a r v e s t e r (b) wheat m a r k e t i n g b o a r d d r a w i n g o f b u s i n e s s m e e t i n g i n a b o a r d room Cc) a f l o u r m i l l i n g company photo o f e x t e r i o r o f a m i l l w i t h g r a i n e l e v a t o r s (d) a b a k e r y i n t e r i o r p hoto o f a b a k e r y w i t h ovens, l o a v e s , and b a k e r 191 (e) a r e t a i l e r drawing of ex t e r i o r view of a supermarket and, -a Canadian $1.00 b i l l -tape recorder Interview Schedule Phase One: CYCLIC TRANSITIVITY FAMILIARITY PRESENT DRAWING OF WHEAT FARM "Can you t e l l me what t h i s i s a pi c t u r e o f ? " RECORD FAMILIARITY Pass: I t s a farm READ FARM FAMILIARIZATION: This i s the wheat farmer harvesting h i s wheat. He s e l l s h i s wheat to the wheat marketing board f o r whatever p r i c e they set. The farmer grows as much wheat as the wheat marketing board w i l l l e t him. He buys h i s own bread from the supermarket. PRESENT REST OF DRAWINGS ONE BY ONE IN AN IMPROPER ORDER IN A VERTICAL PILE SECOND DRAWING (BESIDES FARM) WAS ' "Do you know what t h i s i s ? " NAME IT "Can you t e l l me something about i t ? " READ FAMILIARIZATION THIRD DRAWING WAS ' REPEAT (T) FOURTH DRAWING WAS - ' ' ' • , ' ' REPEAT Q . FIFTH DRAWING W A S / / REPEAT @ 192 WMB FAMILIARIZATION: This i s a meeting of the wheat marketing board. The WMB i s a part of the fede r a l government. The board buys wheat from farmers at a p r i c e set by the board i t s e l f . The board then s e l l s most of i t s wheat to f l o u r m i l l s f o r whatever p r i c e they can get f o r i t . I f the f l o u r m i l l s pay l e s s f o r the wheat than the board paid f o r i t , then the board looses money but the government gives the board more money to make up f o r whatever i t looses. The wheat marketing board t r i e s to keep the p r i c e of wheat the same a l l year so that farmers won't loose so much money that they would have to s e l l t h e i r farms. In order to keep wheat pr i c e s even, the wheat marketing board decides how much wheat w i l l be grown each year. The board t e l l s each farmer how much he can grow so that there's never too much wheat or not enough wheat. Pass: WMB buys and s e l l s wheat, subsidizes farmer, controls p r i c e s paid to farmers, imposes quotas of quantity grown FLOUR MILL FAMILIARIZATION: This i s the f l o u r m i l l . I t s a kind of factory where they turn wheat into f l o u r . They buy t h e i r wheat from the wheat marketing board, grind i t up into f l o u r and then s e l l most of i t to bakeries. Pass: They turn wheat into f l o u r BAKERY FAMILIARIZATION: This i s the bakery. I t s a kind of factory where they turn f l o u r into bread. They buy t h e i r f l o u r from the f l o u r company and use i t to bake bread. Then they s e l l t h e i r bread to supermarkets. Pass: They bake bread SUPERMARKET FAMILIARIZATION: This i s a supermarket where they s e l l a l l sorts of food inc l u d i n g bread. They buy t h e i r bread from the bakery. They s e l l t h e i r bread to everyone, in c l u d i n g the wheat farmer. Pass: I t s a supermarket, grocery store. LAYOUT PROCEDURE. "Put the drawings i n t h e i r proper order." RECORD ORDER: 7MIS0RDERED? "OK, that's good. Now put the drawings i n an order which shows which ones buy wheat, f l o u r , or bread from which other ones." RECORD ORDER ?STILL MISORDERED? START WITH LAST ELEMENT PUT IN PLACE AND REPEAT THE FOLLOWING QUESTIONS FOR DRAWINGS IN REVERSE ORDER 193 RECORD ELEMENT UNDER DISCUSSION "What does t h i s one buy?" "Who does he (do they) buy i t from?" IF EITHER OF THESE TWO QUESTIONS ARE ANSWERED INCORRECTLY, REPEAT THE RELEVANT PART OF THE FAMILIARITY EXPLANATION REPEAT (?) AS NEEDED ?NOT A CIRCLE? "OK, now i s there any way you can think of to show which ones buy from which other ones besides putting them i n a s t r a i g h t l i n e ? Could the same thing be shown by some other arrangement of the cards?" RECORD ?ANYTHING STILL SUBOPTIMAL? WHAT? "you've put the drawings i n t h i s order. That's a good way to do i t . Now l e t me show you another way i t could be done." CREATE PROPER CYCLIC ORDER READ SUMMARY OF WHEAT CYCLE: In t h i s order the farmer buys bread from the supermarket. So we put the supermarket beside the farmer. Now the supermarket buys i t s bread from the bakery. We put the bakery beside the supermarket. The bakery makes the bread out of f l o u r . The bakery buys i t s f l o u r from the f l o u r m i l l so we put the bakery beside the f l o u r m i l l . The f l o u r m i l l makes the f l o u r out of wheat. The f l o u r m i l l buys i t s wheat from the wheat marketing board. Lets put the wheat marketing board beside the f l o u r m i l l then. The WMB buys the wheat from the farmers who grow i t sothe farmers go here on the other side of the wheat marketing board. OK,now l e t ' s leave the drawings i n t h i s order and I ' l l ask you some r i d d l e s / questions about the things i n the p i c t u r e s . TRANSITIVE RECYCLING CYCLE DISPLAYED IN PROPER ORDER PRESENT CANADIAN $1.00 BILL "Could someone, a farmer for example (POINT TO FARM DRAWING), ever spend the same d o l l a r b i l l twice?" (IF SO)' How?;.' (IF NOT) Why not?" ?UNSURE? PROBE UNDERSTANDING: "Who does the farmer f i v e money to?. Does he ever get money from that person?" Own Wheat Item " I f the farmer never keeps any of h i s wheat f o r himself, could he ever eat h i s own wheat? (IF SO) How? (IF NOT) Why not?" 19.4 Phase Two: CYCLIC INTEGRATION FAMILIARITY Supply/Demand Item PRESENT JAR OF FLOUR "This i s f l o u r . I f one kilogram of f l o u r costs $1.00 when there i s j u s t enough f l o u r to go around, how much w i l l . i t cost when there's only h as much to go around as i s wanted? W i l l i t cost more, the same, or l e s s than $1.00/kg.?" (CIRCLE ONE) "Why?" Pass: More, because more people w i l l want i t so they w i l l charge more. People w i l l pay more to be the ones who get i t . ?UNFAMILIAR? READ S/D EXPLANATION: The f l o u r would cost more because when there's not enough f l o u r to go around the people who want f l o u r w i l l pay more f o r i t because the person who's s e l l i n g i t w i l l s e l l i t to whoever pays the most money. I f there were more f l o u r than was needed the p r i c e would go down because the people who are buying f l o u r would buy from whoever would s e l l t h e i r s f o r the lowest p r i c e . P r o f i t F a m i l i a r i t y Item " I f the supermarket bought i t s bread from the bakery f o r 30<:/ l o a f , how much w i l l the supermarket s e l l the bread for? W i l l i t be les s than, the same as, or more than 80<;/ l o a f ? " (CIRCLE ONE) "Why?" Pass: More because they want to make a p r o f i t IUNFAMILIAR? READ PROFIT EXPLANATION: The supermarket w i l l s e l l the bread for more than i t paid f o r the bread and i t w i l l keep that extra money to pay the people who work i n the super-market. That's how the supermarket people make money f o r t h e i r own use. They buy food at a low p r i c e , s e l l i t to customers at a higher p r i c e and keep the diffe r e n c e for themselves. The diffe r e n c e i s c a l l e d t h e i r p r o f i t . Taxation F a m i l i a r i t y Item "Sometimes the WMB looses money instead of making a p r o f i t . The WMB sometimes gives the farmers $1.00/kg. for t h e i r wheat but only asks a p r i c e of 90£/kg. from the f l o u r m i l l s . The wheat marketing board gets the extra lOc/kg. from the government. Where does the government get i t s money from?" 195 Pass: From taxes ?UNFAMILIAR? READ TAXATION EXPLANATION: The government gets i t s money from taxes. At the end of every year the government asks every person and every business i n the country how much p r o f i t they've made that year. Those who've made a l o t of p r o f i t have to give more money to the government i n taxes than those who have made a small p r o f i t or no p r o f i t . SYSTEMS SYNTHESIS READ INTRODUCTION TO WHEAT STORAGE AND FLOUR SURPLUS: Suppose that the f l o u r m i l l i n g company b u i l t some huge grain elevators of i t s own i n which to store wheat. Then the f l o u r company buys a l l the wheat i t can when the p r i c e i s low. Then a f t e r a few years the f l o u r company has stored up a l l the wheat i t needs and doesn't need to buy hardly any from the farmers for one year. T e l l me about a l l the things you can think of that would happen as a r e s u l t of t h i s . " RECORD Flour M i l l P r o f i t Item "Would the f l o u r m i l l i n g company make a bigger p r o f i t or a smaller p r o f i t ? " "Why?/Why not?" Wheat Farmer P r o f i t Item "Would the wheat farmers make a Bigger p r o f i t or a smaller p r o f i t ? Why/Why not?" WMB Do Item "What would the wheat marketing board do? Why?" Taxes Items "What would happen to taxes?" "Why?" National Taxes "How does the wheat marketing board both lower and r a i s e the farmer's income i n some way?" Farmer's taxes WMB Role Item "What i s the intended o v e r a l l e f f e c t of the WMB's work?" 196 SYSTEMS ANALYSIS No WMB I t e m "What would happen i n t h i s s i t u a t i o n o f wheat s u r p l u s i f t h e r e were no WMB?" "Why?" "What woul d happen t o t h e wheat f a r m e r s ? " "Why?" FM R e a c t i o n I t e m "What w o u l d t h e f l o u r m i l l i n g company t r y t o do?" "Why/How? What would happen t h e n ? " L e a s t I m p o r t a n t I t e m "Which one o f t h e s e s t e p s i n t h e c y c l e do you t h i n k c o u l d be g o t t e n r i d o f w i t h t h e l e a s t amount o f t r o u b l e f o r t h e r e m a i n i n g f o u r ? " "Why?" Most I m p o r t a n t I t e m "Which o f t h e s e s t e p s - d o you t h i n k w o u l d cause t h e most t r o u b l e f o r t h e r e s t i f we got r i d o f i t ? Which i s h a r d e s t t o do w i t h o u t ? " "Why?" 197 APPENDIX D: S c o r i n g Manual f o r S y s t e m i c I n t e r v i e w s A. S y s t e m i c S c o r e s t o Be O b t a i n e d The B a s i c s c o r e s B e i n g sought a r e t h e s y s t e m i c component s c o r e s By domain. There a r e two domains, B i o - e c o l o g i c a l and s o c i e t a l . W i t h i n each domain t h e r e a r e f o u r component s c o r e s . They a r e : - t h e l a y o u t component o f c y c l i c t r a n s i t i v i t y ( C y T / l a y ) - t h e t r a n s i t i v e r e c y c l i n g component o f c y c l i c t r a n s i t i v i t y ( C yT/rec) - t h e systems s y n t h e s i s component o f c y c l i c i n t e g r a t i o n CSySy) - t h e systems a n a l y s i s component o f c y c l i c i n t e g r a t i o n (SyAn) T h i s y i e l d s e i g h t s c o r e s , f o u r f o r e a c h domain. Those s c o r e s can Be comBined and condensed i n v a r i o u s ways. One way i s t o i g n o r e t h e d i s t i n c t i o n a c r o s s domains. That y i e l d s f o u r s c o r e s , one f o r each a c r o s s domain component. A n o t h e r way t o r e d u c e t h e numBer o f s c o r e s i s t o comBine t h e two c y c l i c t r a n -s i t i v i t y s c o r e s t o g e t h e r w i t h i n each domain and combine t h e two c y c l i c i n t e -g r a t i o n s c o r e s t o g e t h e r w i t h i n each domain. That a l s o y i e l d s f o u r s c o r e s . F i n a l l y , i f t h e l a t t e r s c o r e s were combined a c r o s s domains t h e r e s u l t w o u l d be two summary s c o r e s , a c r o s s domain c y c l i c t r a n s i t i v i t y and a c r o s s domain c y c l i c i n t e g r a t i o n . The e i g h t b a s i c component s c o r e s a r e o b t a i n e d f r o m t h e more e l e m e n t a r y i t e m s p r e s e n t e d i n t h e i n t e r v i e w s c h e d u l e s f o r each domain (see A p p e n d i x B, S e c t i o n E ( i i ) and A p p e n d i x C. S e c t i o n E ( i i ) . The r e s p o n s e s t o t h o s e i t e m s a r e c a t e g o r i z e d and a s s i g n e d a dichotomous p a s s / f a i l s c o r e . I n t h e c a s e o f t h e c y c l i c t r a n s i t i v i t y components, t h a t s c o r e becomes t h e component s c o r e . F o r t h e c y c l i c i n t e g r a t i o n components i t i s n e c e s s a r y t o combine t h e dichotomous e l e m e n t a r y s c o r e s i n t o t h e component s c o r e s . B. S c o r i n g M a t e r i a l s and P r o c e d u r e P a r t o f t h e d a t a t o be s c o r e d w i l l have been w r i t t e n d i r e c t l y on t h e i n t e r v i e w s c h e d u l e s i n c e t h e s c h e d u l e was d e s i g n e d t o d o u b l e as a d a t a r e c o r d s h e e t . The c y c l i c i n t e g r a t i o n s e c t i o n s o f t h e i n t e r v i e w s h o u l d a l s o have been t a p e r e c o r d e d . The t a p e r e c o r d i n g s s h o u l d Be t r a n s c r i b e d onto i n d i -v i d u a l p r o t o c o l s f o r each r e s p o n d e n t . F o r t h e c y c l i c t r a n s i t i v i t y components t h e component s c o r e s c a n be t a k e n d i r e c t l y o f f o f t h e d a t a r e c o r d s h e e t s . I t i s t h e c y c l i c i n t e g r a t i o n component s c o r e s t h a t r e q u i r e b l i n d j u d g e s and, hence, p r o t o c o l s . The s c o r e s a s s i g n e d t o t h e r e s p o n s e s t o t h e c y c l i c i n t e g r a t i o n i t e m s can be r e c o r d e d on a s t r e a m l i n e d s c o r e s h e e t . T h i s f a c i l i t a t e s t h e l a t e r c o n s t r u c t i o n o f the component s c o r e s . .198, Once the scorer i s f a m i l i a r with the scoring c r i t e r i a he/she simply (a) reads the response on the protocol, ( B ) derives and records the component score, and (e) l a t e r uses those scores to derive the summary scores. The l a t t e r two steps could a c t u a l l y B e done automatically Be computer, i f so desired. C. Ecosystem Scoring C r i t e r i a The scorers should Be f u l l y acquainted with these c r i t e r i a . The items to Be scored are a l l laBeled. These laBels can Be matched with those i n the interview schedules (Apprendicies B & C, Sections E ( i i ) i n each) i n order to f i n d the actual wording and context of the question. (i) C y c l i c T r a n s i t i v i t y Question: Layout component Answers: 1/F = Wrong order 2/F = Correct order But i n a l i n e instead of a c i r c l e 3/S = -Prompted c i r c l e ; correct order 4/S = Spontaneous c i r c l e ; correct order Question: T r a n s i t i v e Recycling component Answers: 1/F = No s o l u t i o n 2/F = Linear s o l u t i o n 3/S = DDT returns to s o i l , i s aBsorBed By plant, eaten By c a t e r p i l l a r , then By B i r d ( i i ) F a m i l i a r i t y Question: Reproduction Answers: 1/F = To say that they didn't have "BaBies" 2/S = To say that there would Be more or that they's reproduce Question: Starvation Answers: 1/F = More Birds predicted But the reason i s simply that they have BaBies. No mention of what they're going to eat f o r the year. 2/s = Realizes that 6 c a t e r p i l l a r s aren't enough and therefore pre-d i c t s s t a r v a t i o n 3/S = Realizes that the food shortage needn't n e c e s s a r i l y lead to starvation i f Both prey and p r e d i t o r populations increase i n p a r a l l e l proportion. * ( i i i ) PerturBation E f f e c t s Introduction. This three part open ended question may e l i c i t d i r e c t spontaneous answers to l a t e r s p e c i f i c items. 199-Question: C a t e r p i l l a r Population QCat. Pop.) Answers: This question i s about rate of reproduction but many respondents answer as i f they had been asked the p o s s i b l e changes i n the absolute siz e of the c a t e r p i l l a r population through reproduction. Therefore t h i s item can be used to index the depth of understanding of the r e l a t i o n between i n d i v i d u a l members of a species population and the whole population i n terms of reproduction. 1/F = The c a t e r p i l l a r population w i l l d e f i n i t e l y increase again so any p r e d i c t i o n to the contrary i s wrong as i s a p r e d i c t i o n of more c a t e r p i l l a r s f o r inadequate reasons (e.g., the DDT makes them grow f a s t e r ) . 2/S = At the l e v e l of i n d i v i d u a l c a t e r p i l l a r s the respondent sees that the immune survivors w i l l reproduce- thus- y i e l d i n g a l a r g e r population. At t h i s le v e l , , however, rate of increase i s conceived of s o l e l y i n terms of length of time f o r one i n d i v i -dual to complete the l i f e cycle (e.g., "They won't multiply f a s t e r because i t s t i l l takes them one month to reproduce. Their numbers w i l l go up at the same speed as before".) 3/S = At t h i s l e v e l the whole population can be dealt with conceptu-a l l y . Rate of increase i n population terms can be predicted by t r e a t i n g i n d i v i d u a l s as s t a t i s t i c a l averages. Doubling the food supply does not decrease mortality for the population i f the number of i n d i v i d u a l s competing f o r the food has t r i p l e d . The 10% surviving c a t e r p i l l a r s have a better chance of having t h e i r o f f s p r i n g survive because there i s l e s s competition f o r food among;-.the o f f s p r i n g and because at l e a s t at f i r s t , t h e i r numbers are too small to a t t r a c t many predators. There-fore t h e i r rate of increase would increase (e.g., "The numbers would r i s e f a s t e r because there i s plenty of food to go around for so few c a t e r p i l l a r s and there i s also plenty of good hiding spots to keep away from b i r d s ) . Question: Renew Infest Answer: The burgeoning of the c a t e r p i l l a r population would have a d e l i t e r i o u s e f f e c t on the plant population. Normal reproduction would eventually put the c a t e r p i l l a r population up to the l e v e l i f was at before so that the plants would be i n j u s t as bad shape but not worse. However, there i s a l a g time i n which the predator population remains pro-p o r t i o n a l l y smaller than i t was before the spraying. This allows fo r even greater numbers of c a t e r p i l l a r s than before the spraying and t h i s permits the conclusion that the plants would a c t u a l l y be doing worse at some time a f t e r the spraying. l / F = Denies that the plants could do worse or j u s t as bad a f t e r the spraying. A t t r i b u t e s i l l e f f e c t s on plants to some fac t o r other than renewed i n f e s t a t i o n by c a t e r p i l l a r s . 200 2/S = A t t r i b u t e s i l l e f f e c t s on plants to increased numbers of c a t e r p i l l a r s without saying why the numbers could increase more than before. Says numbers would be the same as before and therefore the e f f e c t on the plants would be the same too. A t t r i b u t e s i l l e f f e c t s to more c a t e r p i l l a r s and explains the greater number of c a t e r p i l l a r s by reference to reproduction or immunity or both. 3/S = Sees that the dearth of birds contributes to the plants doing worse than before. Question: Birds At f i r s t there would be fewer birds because (a) there are 90% l e s s c a t e r p i l l a r s and (b) the remaining c a t e r p i l l a r s are f u l l of poison. Slowly the b i r d population would increase provided that the farmer only sprayed once. Even though the c a t e r p i l l a r s are immune to DDT they won't be poison to the birds unless they (the c a t e r p i l l a r s ) have eaten DDT. Predictions could be based solely,on the a v a i l a b i l i t y of for t h i s l e v e l of understanding i n the "Cat. Pop." and "Renew In f e s t " items. In t h i s item the c r i t e r i o n of success i s r a i s e d . The answer must take i n t o account the q u a l i t y of the food a v a i l a b l e to the b i r d s ( i t s t o x i c i t y ) as w e l l as the quantity. I t doesn't matter whether more or less b i r d s are predicted so long as the q u a l i t y r e l a t e d reasons are given. I f the b i r d too became immune more bi r d s are predicted so long as the population of c a t e r p i l l a r s increased. Other-wise the b i r d s would be poisoned and decrease i n numbers unless the DDT has vanished from the c a t e r p i l l a r s ' d i e t . Then even non-immune birds could increase i n numbers. Answers: 1/F = P r e d i c t i o n unrelated to quantitiy. or q u a l i t y of food ( c a t e r p i l l a r s ) 2/F = P r e d i c t i o n of more birds due to more c a t e r p i l l a r s or fewer b i r d s due to fewer c a t e r p i l l a r s . No reference to DDT poisoning or immunity. 3/S = P r e d i c t i o n of more b i r d s , i f they are immune, due to more c a t e r p i l l a r s or fewer non-immune c a t e r p i l l a r s due to food poisoning. P r e d i c t i o n of>bird numbers proportional to c a t e r p i l l a r numbers i f DDT disappears from the scene. The disappearance of DDT must be e x p l i c i t l y mentioned. Question: Immunity Implications The score i s i n f e r r e d from the answers to a l l of the above items including the open-ended questions. The purpose of t h i s score i s to give more weight to successes l i k e those required for 3/S scores on the Renewed Infest and Birds Items. These successes require more than p r e d i c t i n g the e f f e c t of DDT on the ecosystem. They further require p r e d i c t i n g the e f f e c t s of immunities which are countereffects to DDT. I f DDT i s the " a c t i o n " then the immunity i s the " r e a c t i o n " . We wish to use t h i s item to given extra c r e d i t f or the accomplishment of being able to predict the ecosystem's reactions to the c a t e r p i l l a r r eaction (immunity) to the farmer's a c t i o n (DDT). -201 Answers: 1/F = None o f t h e answers gave any i n d i c a t i o n o f u n d e r s t a n d i n g what e f f e c t t h e c a t e r p i l l a r s ' immunity would have on o t h e r p o p u l a t i o n s 2/S = The I m p l i c a t i o n s . o f t h e immunity f o r e i t h e r t h e p l a n t o r t h e B i r d p o p u l a t i o n s were m e n t i o n e d i n answers t o p r e v i o u s i t e m s . F o r t h e p l a n t p o p u l a t i o n t h i s i n v o l v e s some m e n t i o n o f how t h e immunity o f t h e s u r v i v i n g c a t e r p i l l a r s t o DDT has made renewed i n f e s t a t i o n o f t h e p l a n t s p o s s i b l e . F o r t h e b i r d s t h e r e must be some m e n t i o n o f how t h e immunity a f f e c t s t h e q u a l i t y o f t h e i r f o o d s u p p l y . T h i s c o u l d i n v o l v e t h e b i r d s e i t h e r b e i n g p o i s o n e d o r becoming immune t o DDT t h e m s e l v e s . 3/S = The i m p l i c a t i o n o f t h e immunity f o r b o t h t h e p l a n t and b i r d p o p u l a t i o n s were m e n t i o n e d . Q u e s t i o n : N i t r o D e s e r t T h i s i s a s i m p l e r v e r s i o n o f t h e same l o g i c a l move b e h i n d t h e DDT s t o r y . T h i s t i m e i n s t e a d o f a d d i n g a t o x i n t o t h e sys t e m we a r e rem o v i n g a v i t a l n u t r i e n t ( n i t r o g e n ) f r o m i t . T h i s v e r s i o n i s s i m p l e r because t h e r e i s no an a l o g u e o f t h e immunity r e a c t i o n . The rem o v a l o f n i t r o g e n , however, i s s t i l l a change i n one element o f t h e c y c l e w h i c h c a u s e s e v o l u t i o n o f the whole e c o s y s t e m . The f a r m e v o l v e s i n t o what e c o l o g i s t s c a l l a " t r a c e d e s e r t " . T h e r e w o u l d be l i t t l e l i f e l e f t because t h e r e a r e o n l y " t r a c e s " o f v i t a l n u t r i e n t s p r e s e n t . Answer: 1/F = Wrong o r i n a d e q u a t e p r e d i c t i o n s c o n f u s i o n o f t h e c h e m i c a l f e r t i l i z e r w i t h DDT. 2/S = C o r r e c t p r e d i c t i o n s about t h e numbers o f v a r i o u s p o p u l a t i o n s t h a t w o u l d be l e f t b u t no e x p l a n a t i o n o f t h e c h a i n r e a c t i o n t h a t l e d t o t h i s c i r c u m s t a n c e . 3/S = C o r r e c t p r e d i c t i o n s w i t h e x p l a n a t i o n o f how t h e f o o d s h o r t a g e c h a i n r e a c t i o n works f r o m p l a n t s t o b i r d s . No p r e d i c t i o n s . about what w o u l d happen t o t h e b a c t e r i a a r e r e q u i r e d . Comments about t h e f a t e o f t h e b a c t e r i a a r e e s s e n t i a l l y i r r e l e v a n t . ( i v ) Systems S y n t h e s i s T h i s i s a second o r d e r s c o r e . I t i s a summary o f t h e p r e v i o u s f o u r i t e m s and i s d e r i v e d f r o m them a c c o r d i n g t o f a i r l y m e c h a n i c a l r u l e s . The o n l y s c o r e s a l l o w e d a r e 1/F, 2/F and 3/S. M i s s i n g d a t a a s s i g n m e n t s a r e n o t p e r m i t t e d . The s c o r i n g r u l e s a r e as f o l l o w s : Maximum C o n s t i t u e n c y . Renew I n f e s t B i r d s Imm. Imp. . N i t r o . D e s e r t The o n l y i t e m s t h a t a r e co u n t e d a r e : M a j o r i t y R u l e . These f o u r i t e m s c o n s t i t u t e t h e maximum c o n s t i t u e n c y S u b j e c t t o t h e below c o n s t r a i n s t , t h e systems s y n t h e s i s s c o r e i s n o r m a l l y w h a t e v e r t h e m a j o r i t y o f t h e c o n s t i t u e n t s a r e i n terms o f s u c c e s s / f a i l u r e . 202 No S without 3. In order to score 3/S on systems synthesis there must be at l e a s t one 3/S among the voting constituents. Mutual Cancellation. P a i r s of constituents can cancel out each others votes and thereby remove each other from the voting. The following cancel each other: 1/F with 3/S = no vote f o r e i t h e r 2/F with 2/S - no vote f o r e i t h e r The following do NOT cancel each other: 1/F with 2/S = 1 " f a i l " vote and 1 "success" vote 2/F with 3/S = 1 " f a i l " vote and 1 "success" vote T i e s . Where the voting, a f t e r c a n c e l l a t i o n s , y i e l d s e i t h e r 1 F a i l vs. 1 Success or 2 F a i l s vs. 2 Successes, the systems synthesis score w i l l b 2/F" Other 2/F's. Since a score of SySy = 3/S i s not permitted unles one of the voting constituents i s a 3/S, i t i s possible to obtain a score of 2/F without having a draw. I f the majority vote i s "S" but there i s no 3/S among the voting constituents then the systems synthesis score i s 2/F. Missing Data. Missing data simply reduce the s i z e of the voting constituency. Sometimes the open-ended and Cat. Pop. items contain information that can be used i n judging the extent to which the respondent appreciated the implications of the immunity and so on. (v) Element Elimination Question: 5 minus 1 Answers: 1/F = Any other than the b i r d (or c a t e r p i l l a r under circumstances outlined below) 2/S = B i r d , the -top trophic l e v e l , or, c a t e r p i l l a r given that respon^ dent e x p l i c i t l y states what the b i r d would eat instead of c a t e r p i l l a r s without being prompted. Question: 4 minus 1 Answers: 1/F = Anything other than c a t e r p i l l a r . I f 5 minus 1 answer was c a t e r p i l l a r with new food for b i r d spontaneously s p e c i f i e d than " b i r d " i s a permissible answer here. 2/S = C a t e r p i l l a r , or, under conditions s p e c i f i e d above, b i r d . Question: Core Answers: 1/F = F a i l s to see the interdependence among b a c t e r i a , nitrogen, and plant 2/S = Claims that none can e x i s t by i t s e l f 3/S = Realizes the interdependencies but knows that nitrogen can e x i s t independently. 203 (vi) Systems Analysis The scoring i s programmable. There are three constituent items that combine to determine the systems- a n a l y s i s component score ( i . e . , 5 minus 1; 4 minus 1; core). The p o s s i b i l i t i e s f o r the component score are: 1/F = requires that at l e a s t two of the constituents items have scores of 1/F. 2/F = requires that none of the constituent items be a 3/S and that not more than one of them be a 1/F. 3/S = requires that one of the constituent scores be a 3/S ( i . e . , core) with not more than one 1/F OR, that a l l three constituent scores b 2's. These rules generate the following table: Core 5 minus 1 4 minus 1 Sy An 1 1 1 . 1/F 1 1 2 1/F 1 2 1 1/F 2 1 1 1/F 3 1 1 1/F 2 1 2 2/F 2 2 1 2/F 2 2 2 3/S 3 1 2 3/S 3 2 1 3/S 3 ,2 2 3/S D. S i m i l a r i t i e s Across the Two Systems Fluctuations i n p r o f i t per unit commodity are analogous to the F l u c t u -ations i n population s i z e dealt with i n the b i o - e c o l o g i c a l interview. I f food supply goes up, reproduction allows b i r t h s to exceed deaths and population s i z e goes up, a l l else equal. I f demand goes up, p r o f i t goes up, a l l e l s e equal. I f s t a r v a t i o n causes deaths to exceed b i r t h s , population s i z e decreases. I f supply catches up with and then exceeds demand, p r o f i t s decrease. 204 The exogenous factor of predation decreases population s i z e e s p e c i a l l y when population s i z e i s at the higher end of i t s range of f l u c t u a t i o n s . T h e o r e t i c a l l y , the exogenous factor of taxation decreases p r o f i t s e s p e c i a l l y when p r o f i t s are i n the upper Brackets. Predation r e l a t e s the population s i z e of the higher trophic l e v e l to the population s i z e of the lower trophic l e v e l . Taxation r e l a t e s the income of the higher order system to the income of the lower order system. E. S o c i e t a l Scoring C r i t e r i a ( i ) C y c l i c T r a n s i t i v i t y Question: Layout procedure Answers: 1/F = Wrong order 2/F = Correct order But i n a l i n e instead of a c i r c l e 3/S = Prompted c i r c l e ; correct order 4/S = Spontaneous c i r c l e , correct order Question: Recycling component Answer: 1/F = No so l u t i o n 2/F = Short cut around the cycle; gets d o l l a r back, as change f or a larger b i l l spent l a t e r 3/S = D o l l a r passes around the cycle. ( i i ) F a m i l i a r i t y Question: Supply/Demand CS/D) This item assesses f a m i l i a r i t y with- the law of supply and demand some-times r e f e r r e d to as "the law of p r i c e . " An understanding of t h i s concept i s a p r e r e q u i s i t e f o r understanding transactions within exchange cycles l i k e the wheat cy c l e . Answers: 1/F = The p r i c e i s predicted to stay the same or decrease. 2/F = The p r i c e i s predicted to r i s e but for an inadequate reason (e.g. "They're so greedy they want more money so they r a i s e the p r i c e . " "There'd be more bags of f l o u r so i t ' d cost more."). 205 Answers:' 1/F = I t would have no e f f e c t or taxes would go down. 2/F = The taxes of the elements making a bigger p r o f i t (FM") would go up. Taxes would go up fo r i r r e l e v a n t re'as'ons (e.g. i n f l a t i o n ) . 3/S = Taxes' go up to pay the WMB's d e f i c i t . Question: Famer's Taxes Treating t h i s as two independent -questions (1. lowers, 2. raises) w i l l be considered l e s s i n d i c a t i v e of systemic thinking than t r e a t i n g i t as a si n g l e question about a si n g l e money cycle ( i . e . WF—• Gov't—* WMB). - — / Answers: 1/F = WMB sometimes pays l e s s and sometimes pays more. 2/S = Treated as two separate questions answered thus: (a) WMB r a i s e s WF's income by subs i d i z i n g wheat p r i c e s or ideas to that e f f e c t . (b) WMB lowers the WF's income by causing him to apy higher rates of income tax ( s p e c i f i c a t i o n of other types of tax also acceptable). This higher rate need not be part of a nati o n a l tax hike. I t could merely be a r e s u l t of higher taxable personal income one year. 3/S = Statements to the e f f e c t that the WF i s i n part paying himself because higher national tax rates are caused by the WMB's subsidy of the WF himself. Question: WMB's Role Scores f o r t h i s item can also very often be in f e r r e d from answers to previous items. The scorer should check back to see i f there i s other relevant information i n previous answers. Respondents who understand the WMB's o v e r a l l r o l e give answers (a) to th i s and previous items, that do not contain any erroneous implications (e.g., saying that the WF wouldn't have any one to s e l l h i s wheat t o ) , (b) that attempt to describe i t s regulatory economic function, (c) that describe i t s r o l e i n terms of i t s i n t e r a c t i o n s with more than one other element, and (d) that im-p l i c i t l y aor e x p l i c i t y r e f e r to i t s e f f e c t s upon the whole wheat cy c l e . Answers: 1/F = Incorrect or inadequate descriptions 2/F = Correct but p a r t i a l answers. Answers that only r e f e r to the WMB's dealings with one other element>\Answers that only r e f e r to the WMB's ph y s i c a l handling of wheat. The WMB as only a private wholesaler or a middleman. Answers that would q u a l i f y as "3/S" but are preceded by erroneous statements i n previous answers. 3/S = Wholistic answers describing the WMB's r e s p o n s i b i l i t y f o r the whole cycle. The WMB as a market s t a b i l i z e r , an economic regulator. 206 3/S = P r i c e r i s e i s a t t r i b u t e d to things l i k e the s c a r c i t y of the f l o u r , the greater clamour Cdemand) f o r each bag, the main-tenance of p r o f i t margins given undersupply. Question: P r o f i t The concept of p r o f i t applys to one economic u n i t ' s transactions. Together these units form various exchange cycles, l i k e commodity cycles, l i k e the wheat cy c l e . The respondent has to understand what these elementary units are doing before he can understand t h e i r transactions with each other. Answers: 1/F = Thinks that the supermarket won't take a p r o f i t or that, i f the s e l l i n g p r i c e i s set higher than the cost, t h i s i s what you c a l l " i n f l a t i o n . " Any s i m i l a r l y inadequate explanation of the p r o f i t . 2/S = Sees p r o f i t as a normal means of obtaining income. Explains the p r i c e r i s e e x p l i c i t l y i n terms of p r o f i t . Question: Taxes This item comes: a f t e r an exercise i n explaining that the government uses tax money to make up WMB d e f i c i t s . T h i s item r e l a t e s government revenues back to p r o f i t s through probing f o r the c o r r e l a t i o n between income earned and taxes paid. Understanding t h i s concept i s a p r e - r e q u i s i t e f or being able to see how the WMB also lowers the farmer's income. Answers: 1/F = No idea that making more money means paying more taxes. 2/.S = Knows at l e a s t that making more money means paying more taxes. ( i i i ) Perturbation E f f e c t s This open-ended item may e l i c i t spontaneous.answers to l a t e r s p e c i f i c items. Question: FM P r o f i t s The FM pretty well has to make more money because they bought the wheat cheap and have at l e a s t a steady demand. I n f l a t i o n also works i n t h e i r favor. Answers: 1/F = Same p r o f i t as previous year or l e s s . More p r o f i t but f o r inadequate reasons (e.g. Just having more wheat doesn't j u s t i f y p r e d i c t i n g that t h e y ' l l make more money. The wheat has to be i n greater demand than normal supplies could s a t i s f y . ) 2/S = Adequate reasons f o r p r e d i c t i n g a bigger p r o f i t are: (a) lower than normal costs of the surplus wheat (b) i n f l a t i o n a r y r i s e i n s e l l i n g p r i c e without concomitant r i s e i n cost of the surplus wheat. Cc) greater volume of sales, provided respondent e x p l i c i t l y mentions a concomitant demand for the volume. 207 Q u e s t i o n : WF P r o f i t s I f t h e r e s p o n d e n t remembers what he's j u s t been t o l d a b o ut how t h e WMB wo r k s , he s h o u l d r e a l i z e t h a t t h e F's p r o f i t s a r e c o n t r o l l e d by t h e p r i c e s e t by t h e WMB. F a i l u r e t o m e n t i o n t h e WMB's i n t e r v e n t i o n i n t h i s m a t t e r i n d i c a t e s a f a i l u r e t o a p p r e c i a t e t h e WMB's r o l e a s a r e g u l a t o r y arm o f a l a r g e r , more encompassing s y s t e m C L e . t h e government). Answers: 1/F = WF's p r o f i t s u n r e l a t e d t o WMB d e c i s i o n s . D i r e c t l i n k t o FM (e.g . "The FM's n o t b u y i n g any wheat so t h e f a r m e r won't have anyone t o s e l l h i s wheat t o . " ) . 2/S = I m p o s s i b l e t h a t t h e WF would l o o s e a l o t o f money. H i s income might go down a l i t t l e i f t h e WMB p a i d h i m l e s s f o r h i s wheat but w h a t e v e r happens, t h e p r i c e p a i d by t h e WMB i s t h e c r u c i a l f a c t o r . Q u e s t i o n : WMB Do B e s i d e s j u s t p l a i n wrong answers, some o s t e n s i b l y c o r r e c t answers a r e a l s o c o u n t e d as f a i l u r e s h e r e because we a r e i n t e r e s t e d i n i d e n t i f y i n g t h o s e r e s p o n -d e n t s who de m o n s t r a t e an u n d e r s t a n d i n g o f how t h e WMB can a c t upon t h e wheat c y c l e f r o m a l o n g range p e r s p e c t i v e t h a t i s n o t c o n s t r a i n e d by t h e e x i g e n c i e s o f immediate p r o f i t s and l o s s e s . Wrong o r c o n f u s e d answers. C o r r e c t answers t h a t d i s p l a y no u n d e r s t a n d i n g o f t h e WMB's r o l e . e.g. G l u t "The WMB would end up w i t h a l o t o f wheat t h a t t h e y c o u l d n ' t s e l l " L o o s e $ "The WMB w o u l d l o o s e money." These a r e c o r r e c t answers t h a t g o t t h e WMB out o f i t s own immediate g l u t s i t u a t i o n b u t do n o t h i n g t o remedy t h e i m b a l a n c e i n t h e whole wheat c y c l e . e.g. S e l l e l s e w h e r e "They c o u l d s e l l i t t o a n o t h e r c o u n t r y / F M " S t o r e "They c o u l d keep i t u n t i l t h e FM r a n o u t . " Get g o v ' t $ "They c o u l d go t o t h e government f o r more money." These a r e answers t h a t d e s c r i b e a c t i o n s t h a t w o u l d r e s t o r e a b a l a n c e . e.g. Quotas "They c o u l d t e l l t h e WF t o grow l e s s n e x t y e a r . " "They c o u l d p u t a l i m i t on how much t h e ' 1 1 a l l o w t h e FM t o buy i n one y e a r . " D e s t r o y " T h e y might b u r n t h e wheat so t h a t t h e r e w o u l d be a demand f o r n e x t year's c r o p . " Q u e s t i o n : N a t i o n a l Taxes One way o f m i s u n d e r s t a n d i n g t h i s q u e s t i o n i s more advanced t h a n o t h e r s . C o r r e c t u n d e r s t a n d i n g i n d i c a t e s an awareness o f how t h e a c t i o n s o f one element (FM) i n one subsystem ( t h e wheat c y c l e ) can i n f l u e n c e t h e s u p r a o r d i n a t e s y s t e m ( t h e n a t i o n a l economy). Answers: 1/F = 2/S = 3/S = 208 (iv) Systems Synthesis The r u l e s are exactly the same as those f o r systems synthesis i n the EGOSYSTEM. The maximum constituency i s , again, four items. They, are: WMB Do Nat'l Taxes Farmer's Taxes WMB's Role (v) E1ement E1imiriation In t h i s section, instead of going from e f f e c t s on subsidiary elements up to the supraordinate system, we go i n the opposite d i r e c t i o n . We s t a r t with the whole system and see If the respondent can s i m p l i f y i t by p i c k i n g out v i a b l e independent subsystems latent within the supraordinate system. There are two parts to t h i s section. F i r s t we see i f the respondent can appreciate the readjustments that would be required to make a p a r t i c u l a r sub-system v i a b l e . Second we l e t the respondent choose h i s own subsystem and explain what readjustments would be required for i t to be v i a b l e . Question: No WMB I t takes a c e r t a i n amount of understanding to r e a l i z e that with the WMB gone the WF could s e l l d i r e c t l y to the FM. I t takes even more understanding to see that the WF would s u f f e r heavy f i n a n c i a l losses given a s i t u a t i o n of wheat surplus. It i s the l a t t e r r e a l i z a t i o n that we wish to count as success on t h i s item. Answer: 1/F = Misses t h e . f i n a n c i a l i m p l i c a t i o n f o r the WF (e.g. "The WF would have a l o t of wheat l a y i n g around."). 2/S = E x p l i c i t l y states that the WF would loose money or even go broke. Question: FM Reaction Success on t h i s item requires at l e a s t seeing that the FM would experience a supply shortage l a t e r on i f too many farmers l o s t too much money. Seeing t h i s i m p l i c a t i o n requires moving from the l e v e l of .the i n d i v i d u a l farmer's p r o f i t p i c t u r e to the l e v e l of the average p r o f i t p i c t u r e for the whole pop-u l a t i o n of farmers. Short-term remedies to t h i s s t o c k p i l i n g generated problem a l l involve the FM i n exercising more s e l f - r e s t r a i n t . These are possible but improbable solutions because the FM operates on the p r o f i t motive and that pre-cludes d e l i b e r a t e l y neglecting p r o f i t opportunities i n the future. More c r e d i t i s given to solutions which incorporate readjustments i n the f u n c t i o n a l r e -l a t i o n s h i p s between the elements. That i s , the system ei t h e r evolves into a new form or i t evolves r i g h t out of existence. The readjustments mean that at l e a s t one element must s u b s t a n t i a l l y a l t e r i t s r o l e i n the scheme of things or else an analogue of the WMB must be reintroduced. 209 The future supply problems of the FM are not a n t i c i p a t e d . Realizes- that a supply problem would develop for the FM but attempts to resolve the supply problem do not involve any change i n the.functional r e l a t i o n s h i p s between elements. Often the s o l u t i o n suggested involves a change i n the "motives" or " t r a i t s " of the economic elements involved. e.g., "The FM shouldn't t r y to s t o c k p i l e cheap wheat anymore." "The FM should be more c a r e f u l about how much, wheat he buys at one time." "The FM should s e l l more f l o u r to the bakery so he can buy more wheat from the farmer." Sees that the FM depends on the s u r v i v a l and f i n a n c i a l w e ll being of the farmer's. e.g., "The FM would go broke too because they can't get no wheat." Evolutionary solutions (including devolution) e.g., "The FM could buy out the farmers and j u s t pay them a salary to grow wheat." "The farmers could form a coop that does what the WMB used to do." "The farmers could set up t h e i r own f l o u r m i l l and s e l l to the bakery." "The federal government could make s p e c i a l loans to farmers to keep them going." Question: Least Important The better answers here demonstrate a concern f o r how: the remaining elements would take up the functions that were previously performed by the removed element. Answers: •- 1/F = No adaptation of remaining elements mentioned. Adaptations suggested are u n r e a l i s t i c (e.g. "The farmer could s e l l h i s wheat to the supermarket.") 2/S = Functions of the departed element are taken over by others (e.g. "The supermarket could bake the bread." "The .bakery could r e t a i l the bread." "The FM could bake the f l o u r into bread." etc., etc.. Question: Most Important The answer to t h i s one is. f a i r l y unanimous - the wheat farmer. The economic system i s predicated upon the e x p l o i t a t i o n of nature. F a i l u r e s to recognize t h i s i n d i c a t e a very shakey understanding of the i n t e r r e l a t i o n s h i p s among the elements i n the c y c l e . In t h i s sense t h i s item i s almost l i k e a FAMILIARITY item. Answers: 1/F = Any answer other than the WF. 2/S = The WF. Answers: 1/F 2/S 3/S = 210 (vi) Systems Analysis This score is- a summary of items No WMB, FM Reaction, Least Important, and Most Important. The scoring i s mechanical except where 2 of (1). No WMB, (2) FM Reaction, and (3) Least Important have -missing data C*). In that case the remaining item determines the score unless there are comments i n answers e l s e -where which would lead the scorer to judge otherwise. I f the remaining score i s a 2/S i t Becomes a 3/S. The r u l e s f o r combining items into systems analysis scores are: Constituency. The only voting constituents are FM Reaction, and Least Important. They combine according to the following taBle: FM Reaction Least Systems Important Analysis 1/F 1/F 1/F 1/F 2/S 2/F 2/S 1/F 2/F 2/S 2/S 3/S 3/S 1/F 3/S 3/S 2/S. 3/S Vetos. No WMB can "veto" KM Reaction and Most Important can veto Least Important. That i s , i f No WMB = 1/F, then FM Reaction = 1/F, no matter what was said under FM Reaction. Likewise, i f Most Important = 1/F then Least Important = 1/F no matter what was said under Least Important. Missing Data. I f l e a s t Important = * (has missing data) then count i t as a vote of 1/F i n the voting, constituency, If FM Reaction = * then the votxng:Constituency Becomes No WMB and Least Important. They y i e l d scores according to t h i s taBle: No WMB Least Systems Important Analysis 1/F 1/F 1/F 1/F 2/S 2/F 2/S 1/F 2/F 2/S 2/S 3/S F. Summary Scores (i ) Across Domain Components Layout. The two c y c l i c t r a n s i t i v i t y components that go into t h i s scores are (a) the B i o - e c o l o g i c a l domain layout procedure, and (B) the s o c i e t a l domain layout procedure. On each of these components the possiBle scores are 1/F, 2/F, and 3/S. They are dichotomous p a s s / f a i l scores (S,F) with two l e v e l s of f a i l u r e (1,2). The across domain summary score has two l e v e l s 1/F and 2/S. A passing score (2/S) requires at l e a s t a 3/S on one of the components and not l e s s than a 2/F score on the other. The followingtaBle l i s t s the possiBle combinations of component scores with t h e i r accompanying summary scores: 2-11 Bi o - e c o l o g i c a l S o c i e t a l Summary-Component Component Score 1/F 1/F 1/F 1/F 2/F 1/F 1/F 3/S 1/F 2/F 1/F 1/F 2/F 2/F 1/F 2/F 3/S 2/S 3/S 1/F 1/F 3/S. 2/F 2/S 3/S 3/S 2/S T r a n s i t i v e Recycling. The t r a n s i t i v e r e c y c l i n g components for the b i o - e c o l o g i c a l and s o c i e t a l domain go into t h i s summary score. The possible score on these components are again, 1/F, 2/F, and 3/S. The summary score i s again dichotomous (1/F, 2/S). The summary score i s constructed according to the same rules that y i e l d the table f o r the layout component score. Systems Ana l y s i s . Same rules as those encoded i n the table f o r the layout component score. Systems Synthesis. Same rules as those encoded i n the table f o r the layout component score. ( i i ) Within Domain Components C y c l i c T r a n s i t i v i t y . The two components comprising t h i s summary score were the layout and the r e c y c l i n g components (within domains). For a summary score of 2/S the layout component had to be an "S" (either a 3/S or a 4/S) and the r e c y c l i n g component could not be a 1/F. C y c l i c Integration. For a summary score of 2/S both component scores (SyAn and SySy) had to be 3/S. 212 APPENDIX E: Difference Between Formal and Systemic Logics "QUANTITY: DOES NOT DETERMINE PATTERN, It i s impossible, i n p r i n c i p l e , to explain any pattern By invoicing a s i n g l e quantity ...quantity and pattern are of d i f f e r e n t l o g i c a l type and do not r e a d i l y f i t together, i n the same thinking. What appears to be a genesis of pattern by quantity a r i s e s where the pattern was l a t e n t before the quantity had an impact on the system, (Bateson, G. Mirid and Nature: A Necessary Unity. New York: Bantam Books, 1979. p. 58)" The need to postulate another type of l o g i c f i r s t arose out of my attempts to understand society. At that point I was thinking i n terms of a new paradigm approach to s o c i a l theory. As my attention turned to the development of understanding of s o c i a l systems, the new paradgm was translated into some s p e c i f i c cognitive structures. A f t e r the data had been analyzed, these cognitive structures came to be seen l e s s as d i r e c t trans-l a t i o n s of the new paradgm and more as possible examples of a whole class . of structures that seem to follow a d i f f e r e n t sort of l o g i c . Only at t h i s point did I formulate the question addressed i n t h i s chapter: How do formal l o g i c and systemic l o g i c d i f f e r ? . In attempting to answer that question I began scanning the psychological l i t e r a t u r e on types or classes of l o g i c s . I t was then that I discovered some s t a r t l i n g (to me) passages i n Piaget and Inhelder's 0-956) The Child's Conception of Space. That i s where Piaget and Inhelder present t h e i r most extensive treatment of s u b - l o g i c a l operations and t o p o l o g i c a l relations,both of which are features of what I mean by systemic l o g i c . At one point Piaget and Inhelder even describe c y c l i c t r a n s i t i v i t y i n l o g i c a l notation (p. 463). Nevertheless they seem to have missed i t s s i g n i f i c a n c e . In other words, Piaget has dealt with systemic l o g i c but c a l l s i t by another name and treats i t i n an unnecessarily r e s t r i c t e d context. He and h i s colleagues did not r e a l i z e i t s generality. A f t e r summarizing Piaget's ideas on the r o l e s of sub-logic and t o p o l o g i c a l r e l a t i o n s i n cognitive development, the s i m i l a r i t i e s to systemic l o g i c w i l l be examined. Then what I see as the inadequacies i n Piaget's conceptions of sub-logic and t o p o l o g i c a l r e l a t i o n s w i l l be discussed. F i n a l l y , the d i s t i n c -t i o n between formal and systemic l o g i c w i l l be r e l a t e d back to various issues raised i n the text. A. Sublogic Piaget sees the c h i l d ' s developing understanding of space and geometry as the main arenas f o r the use of sub-logic and t o p o l o g i c a l r e l a t i o n s . The c h i l d ' s i n i t i a l ideas about space are t o p o l o g i c a l . These give way to p r o j e c t i v e notions which i n turn lead to E u c l i d i a n concepts of space. Topological r e l a t i o n s are non-metric; e u c l i d i a n space i s metric. A r i g i d l i n e i s a p r e r e q u i s i t e for measurement. Topological space i s e s s e n t i a l l y 213 e l a s t i c (Piaget, Inhelder and Szeminska, 19-60). The term "sub-logic" was i n s p i r e d by Ru'ssel's Theory of Types. The lowest type of l o g i c begins w i t h objects already being i d e n t i f i a b l e . When he speaks of sublogic Piaget r e f e r s to those operations needed, to construct the concept of the object i n the f i r s t place. The parts of objects according to Piaget, are r e l a t e d to the whole object by the following t o p o l o g i c a l r e l a t i o n s : proximity, separation, order, enclosure, continuity. In understanding those r e l a t i o n s h i p s the c h i l d i s performing the corresponding s u b l o g i c a l operations. L o g i c a l operations (as opposed to sublogical) Begin with the e u c l i d i a n assumption of shape constancy. Sublogical operations, Being appreciations of t o p o l o g i c a l r e l a t i o n s , do not. Sublogical operations en when the construction of the constant oBject has Been acheived. Sublogical operations are i d e n t i c a l i n form to systemic operations. The t r u t h value of propositions stated i n formal l o g i c can be decided i n the abstract. . Systemic l o g i c requires the s p e c i f i c a t i o n of spatio-temporal p a r t i c u l a r s before the t r u t h value of i t s propositions can be evaluated. Because of the t o p o l o g i c a l nature of the r e l a t i o n s under consideration, sublogic also requires .a s p e c i f i c a t i o n of spatio-temporal p a r t i c u l a r s before t r u t h value can be evaluated. Systemic l o g i c and sublogic also d i f f e r from formal l o g i c i n the treatment of sets.. In formal l o g i c supraordinate sets are related to subordinate sets by class:"inclusion. In both systemic l o g i c and sublogic the r e l a t i o n s h i p i s one of parts to wholes. Once again the d i f f e r e n c e i s traceable to a more to p o l o g i c a l s t r a i n i n systemic l o g i c and sublogic. The l a t t e r define sets i n terms of boundaries, enclosures and proximities. The proximities may be temporal as well as s p a t i a l . Formal l o g i c , on the other hand, defines sets i n terms of abstract a t t r i b u t e s l i k e c o lor, phylum, construction material, and so on. These sorts of a t t r i b u t e s express degrees of s i m i l a r i t y / d i s s i m i l a r i t y rather than proximity/distance. B. Sublogic vs. Systemic Logic Systemic l o g i c and sublogic are not i d e n t i c a l i n t h e i r range of r e f e r e n t s . Sublogic seems to me to be a s p e c i a l case of systemic l o g i c . In describing sublogic, Piaget described the form of systemic l o g i c w e l l . What he f a i l e d to mention i s that not a l l the spatio-temporal wholes contructed by the mind are p h y s i c a l objects. Sublogic, as described by Piaget, applies s t r i c t l y to the construction of palpable,.physical objects. Systemic l o g i c , as I would have i t , applies to a l l organized wholes. Kinship networks, economies and governments, are wholes i n the sens of being systems. Their cohesion as unitary e n t i t i e s does not n e c e s s a r i l y depend on spatio-temporal proximity so much as i t depends on i n t e r a c t i v e relatedness. S t a t i c wholes, such as p h y s i c a l objects, maintain t h e i r i n t e g r i t y through proximity, enclosure, etc. Dynamic wholes, such as s o c i a l systems, maintain t h e i r i n t e g r i t y through a s y n e r g i s t i c i n t e r a c t i o n amongst the parts. Piaget tended to ignore dynamic wholes. He chose to study the developing understanding of p h y s i c a l phenomena. 214 Once attention i s turned towards more s o c i a l content, however, i t becomes neces-sary to expand the r o l e played by sublogic i n cognitive development. Sublogic becomes systemic l o g i c , an equal counterpart to formal l o g i c . Ci) Dynamic Wholes and Open Systems The d i f f e r e n c e Between dynamic wholes and s t a t i c wholes i s l i k e the difference between open and closed systems. In t h i s research a system i s defined as: as set of elements i n some ordered r e l a t i o n s h i p such that information and/or material flows e i t h e r d i r e c t l y or i n d i r e c t l y , form every element (or cl a s s of elements) to every other element i n ways which e f f e c t the functioning of a l l elements. Open systems exchange materials, energies, or information with t h e i r environments. A flame, then, i s a simple, inanimate, open system. A c e l l i s an animate open system. In closed systems there i s no import or export of energies, materials, of information (Hall and Fagen, 1975) (e.g. a house, a chemical reaction i n a vacuum chamber). Closed systems are subject to entropy. By contrast, open systems can become incr e a s i n g l y organized. They can r e p a i r and maintain t h e i r s tructure over time. This tendency to v i o l a t e the second law of thermodynamics has been l a b e l l e d "negentropy" by B r i l l o u i n (19.61). An open system increases, or prevents a decline i n , i t s l e v e l of organization By exchanging things with i t s environ-ment. I f an open system i s considered together with i t s environment that coupled e n t i t y becomes a closed system subject to entropy. Eventually the open system would deplete the resources a v a i l a b l e to i t i n i t s environment. : By considered the r a t i o of negentropy to entropy one can determine the boundaries of van open, system..-. "The: boundaries would-be set at -whatever .places, yielded the most negentropic enclosure. The optimal l i n e s of demarkation between an open system and i t s environment would be those which construe the negentropic structures of the system-environment coupling as parts of the open system. Therefore, the problem of p e r c e i v i n g a o r c o g n i t i v e l y construct-ing dynamic wholes requires the a b i l i t y to appreciate.the presence of error reducing, uncertainty reducing, entropy reducing structures when one sees them. ( i i ) Negentropic Systemic Operations The system structures studied i n the present research are examples of entropy reducing structures. The components of c y c l i c t r a n s i t i v i t y both deal with structures e s s e n t i a l f or p o s i t i v e and negative feedback loops. Negative feedback loops reduce entropy by providing f o r the c o r r e c t i o n of e r r o r s . They reduce the discrepancy between the goal and the obtained outcome. P o s i t i v e feedback loops are associated with negentropic processes l i k e growth and development. Thy amplify the discrepancy between the i n i t i a l state and the attained state. For example, i t i s a p o s i t i v e feedback loop that makes i t possible f o r the r i c h to get r i c h e r . Negentropic feedback loops often appear i n an h i e r a r c h i c a l l y nested structure. Systems analysis e n t a i l s successively abrogating a l l those elements of a system which are not e s s e n t i a l f or the existence of at l e a s t one neg-entropic feedback loop. The nitrogen cycle and the wheat cycle can be -215 depicted with more of fewer elements. Increasing the number of elements amounts to s e t t i n g wider, more Incl u s i v e boundaies on the system. Decreasing the number of elements delimits- the system more narrowly. If the number of elements were to be decreased by eliminating an element e s s e n t i a l f o r the s u r v i v a l of a l l the other elements (e.g. the nitrogen i n the nitrogen cycl e ; the wheat farmer i n the wheat cycle)! then the elements would cease to constitute an open system. There would not be even one negentropic subcycle l e f t . Thus systems analysis i s a cognitive structure by which a person can apprehend the presence of a system, a dynamic whole. Systems synthesis i s s i m i l a r i n that respect. I t i s the operation by which one apprehends the supraordinate l e v e l of coordination among the elements of a system. That supraordinate coordination might be e f f e c t e d by the emergence of a c e n t r a l element s p e c i a l i z i n g i n a l l o c a t i n g resources to the others. Such i s the case with the wheat marketing board i n the wheat cy c l e . The supraordinate coordination, however, need not always be effected by a s i n g l e element. In the nitrogen c y c l e , f o r example,the mutually accomodating ope r a t i n g ' c h a r a c t e r i s t i c s of the arious populations i n t e r a c t i n such a way as to produce an o v e r a l l r e g u l a r i t y and order which could not be predicted from a knowledge of the s i n g l e parts. The o v e r a l l coordination i s an emergent pro-perty of the i n t e r a c t i o n s among the elements. The domain of influence of these negentropic coordinating structures are co-terminal with the boundaries of systems. Once again, the systemic operations have to do with the mental construction of dynamic wholes. Before considering what implications the d i s t i n c t i o n between formal and systemic l o g i c has for other issues l e t us review what has been discussed thus f a r . Formal l o g i c operates on r e l a t i o n s . o f s i m i l a r i t y / d i s s i m i l a r i t y and of i n c l u s i o n . Systemic l o g i c operations on t o p o l o g i c a l r e l a t i o n s and part-whole r e l a t i o n s . The t r u t h value of formal l o g i c a l arguments can be decided i n the abstract. The truth value of systems l o g i c a l propositions depends upon the p r i o r s p e c i f i c a t i o n of spatio-temporal p a r t i c u l a r s . Systemic l o g i c applies to the mental construction of wholes. Formal l o g i c presupposes the known i d e n t i t y of the wholes and goes on to compare and c l a s s i f y them. S t a t i c wholes are closed systems and are apprehended through what Piaget c a l l e d sublogic. System l o g i c subsumes sublogic but also allows f o r the appreciation of dynamic wholes or.open systems. Open systems are characterized by negentropic structures. The structures studied i n t h i s research are negentropic. They are indeed useful f o r the mental construction of dynamic whdes. They are examples of systemic l o g i c . C. A n c i l l a r y D i s t i n c t i o n s At t h i s point the i n i t i a l aim of t h i s chapter has been accomplished, Systemic l o g i c has been described and distinguished-from formal l o g i c . What follows i s a n c i l l a r y material intended to embue that d i s t i n c t i o n with greater 216 i n t u i t i v e cogency. The d i s t i n c t i o n between these two l o g i c s w i l l be r e l a t e d to other p h i l o s o p h i c a l and p s y c h o l o g i c a l i s s u e s , The d i s t i n c t i o n manifests i t s e l f i n many more areas- than can be mentioned here, H o p e f u l l y t h i s s m all sampling w i l l suggest other -manifestations., to : the. reader. The f i r s t i s s u e to Be d i s -cussed i s the treatment of c o n t r a d i c t i o n and i d e n t i t y i n e i t h e r l o g i c . Then the r o l e of purposiveness i n open systems: and t h i n k i n g about open systems i s explored. F i n a l l y , the complementarity Between systemic l o g i c and formal l o g i c i s examined. ( i ) C o n t r a d i c t i o n arid I d e n t i t y The f i r s t r e l a t e d i s s u e to be d e a l t w i t h i s the p h i l o s o p h i c a l problem of c o n t r a d i c t i o n and i d e n t i t y . Posing A a u t o m a t i c a l l y poses X (hot A),,an e x c l u s i v e d i s t i n c t c l a s s . Once there are two mutually e x c l u s i v e c l a s s e s there i s t h e ^ j p o s s i b i l i t y of c o n t r a d i c t i o n . I t i s a c o n t r a d i c t i o n to c a l l something A and A simultaneously. Thus, c o n t r a d i c t i o n becomes p o s s i b l e once there i s even one i d e n t i t y . A l s o , A cannot Be i t s e l f and A simultaneously. A must always be A. This g e n e r a l i z a t i o n r e c a l l s P i a g e t ' s statments that l o g i c ( i . e . , formal l o g i c as opposed to sublogic) assumes the existence of wholes from i t s s t a r t . In formal l o g i c c o n t r a d i c t i o n s i g n a l s f a u l t y reasoning and must Be avoided. The t e n s i o n Between c o n t r a d i c t i o n and i d e n t i t y can Be r e s o l v e d In the opposite manner. Contrary to formal l o g i c , what i s c a l l e d " d i a l e c t i c l o g i c " assumes the permanence of c o n t r a d i c t i o n and t r e a t s i d e n t i t y as the proBlematic ( R i e g e l , 1978). Hegel makes the p o i n t as f o l l o w s : "But i t i s one of the B a s i c p r e j u d i c e s of t r a d i t i o n a l l o g i c and of common-sense conception that c o n t r a d i c t i o n i s not such an e s s e n t i a l and immanent determination as i d e n t i t y ; indeed, i f we were to consider a rank order and i f Both determinations were to Be kept separated, c o n t r a d i c t i o n would have to Be accepted as deeper and more e s s e n t i a l . For i d e n t i t y , i n c o n t r a s t to i t , i s only the r e c o g n i t i o n of the s i n g l e immediate the dead Being; But c o n t r a d i c t i o n i s the source of a l l motion and v i t a l i t y ; only i n so f a r as something contains c o n t r a d i t i o n does i t move, has i t d r i v e and a c t i v i t y (Hegel, 1969 p. 545)". The focus on e s t a B l i s h i n g i d e n t i t y makes d i a l e c t i c l o g i c s i m i l a r to systemic l o g i c . The "motion and v i t a l i t y " that Hegel speaks of are a l s o c h a r a c t e r i s t i c of open systems. D i a l e c t i c l o g i c and systemic l o g i c may i n f a c t Be two aspects of the same greater ensemBle But a f u l l c o n s i d e r a t i o n of that p r o p o s i t i o n i s Beyond the scope of t h i s chapter, A focus on e s t a B l i s h i n g i d e n t i t y seems to r e q u i r e the use of systemic l o g i c no matter how a b s t r a c t or dynamic the system under c o n s i d e r a t i o n may be. For example, i n h i s quest f o r a method l e a d i n g to s e l f i d e n t i t y H u s s e r l (1969) proposed transcendental phenomenology. The method of transcendental phenomenology appears to t h i s w r i t e r to be an example of 1217 systems analysts applied to the s e l f . To take another example, Nietzsche (19.61) t r i e d to. p o s i t a supraordinate coordinating telos that might guide human evolution and e s t a b l i s h the dynamic i d e n t i t y of the species. His e f f o r t s seemed to have r e l i e d heavily on systems synthesis. These examples emphasize how a focus on e s t a b l i s h i n g i d e n t i t y i s often f r u s t r a t i n g f o r those who seek clear,-concise d e f i n i t i o n s of the e n t i t i e s under discussion. Systemic l o g i c i n i t s e l f does not begin by s e t t i n g f o r t h abstract d e f i n i t i o n s of systems. Rather, i t takes the d e f i n i t i o n of p a r t i c u l a r systems as the empirical proglem at hand. ( i i ) Purposiveness and Open Systems The study of purposive behavior i n psychology i s suffused with con-structed based on systemic l o g i c (e.g., M i l l e r , Gallanter and Pribram, 1960; Powers, 1973). Systemic concepts also permeate the study of relevance i n at t e n t i o n deployment (e.g., Hamilton, Hockey and Rejman, 1977). Open systems are purposive by v i r t u e of t h e i r negentropic structures;. The negentropic structures keep the system e i t h e r (a) developing towards a homeostatic state, and (b) i n a homeostatic state. The former i s the t e l e o l o g i c a l purposiveness t y p i c a l of organic growth and development. The l a t t e r i s homeostatic purposiveness more t y p i c a l of mature organisms and even mechanical systems. A feedback loop i s a negentropic structure. I t may serve either t e l e o -l o g i c a l or homeostatic purposes dependingxipon the nature of i t s reference point. The reference point of a negative feedback loop, for example, i s the c r i t i c a l value on the input v a r i a b l e that devides one output from another. In a thermo-stat set at 18 degrees Celsius the reference point i s 18 degrees Celsius.;. In-put temperatures above that point y i e l d output that consists of an " o f f " s i g -na l to the heater. Below that point the output i s an "on" s i g n a l . The a c t i v i t y c o n t r o l l e d by the feedback loop i s always goal d i r e c t e d . The goal i s to achieve a match between the input from the environment and the reference point. In using systemic l o g i c one i s always involved i n discerning the goal or purposes of systems. Information and/or a c t i v i t y w hichiis not relevant to the system's purpose i s ignored. The cross c u l t u r a l Piagetian research that finds adult cognition i n non-Western cultures to be l e s s abstract and more pragmatic (e.g., L u r i a , 1979) might be detecting the predominance of systemic l o g i c over formal l o g i c i n those cultures. An assemblage of unstructured p a r t i c u l a r contents i s dealt with pragmatically when i t i s dealt with according to some goal, i n t e n t i o n or purpose. Purposiveness imposes structure by turning contents into context. The p r i o r i t y given to contextual p a r t i c u l a r s i n non-Western thought might account for i t s seeming extremely pragmatic to v i s i t o r s from i n d u s t r i a l s o c i e t i e s . In formal l o g i c the rules of reasoning come f i r s t . They are the form and they play a greater r o l e i n determining the content. In systemic l o g i c the form i s unknown at the problem solving stage of i n t e r a c t i o n with a 218 n o v e l system. The f o r m emerges f r o m t h e p r o j e c t i o n o f an i n t e n t i o n o r p u r -pose o r g o a l i n t o a f i e l d o f c o n t e n t . W h i l e t h e f o r m i s eme r g i n g , t h e s y s t e m i c t h i n k e r m i g h t appear t o Be o p e r a t i n g i n t u i t i v e l y . He i s as y e t u n a b l e t o a r t i c u l a t e , t h e s t r u c t u r e s t h a t g u i d e .His; i n t e r a c t i o n s - w i t h t h e system. T h i s " i n t u i t i v e a p p r o a c h " might Be more t o l e r a t e d , o r even encouraged, i n non-i n d u s t r i a l c u l t u r e s . ( i i i ) C o m p l e m e n t a r i t y I t s h o u l d Be Borne i n mind t h a t s y s t e m i c l o g i c and f o r m a l l o g i c a r e complementary. A l t h o u g h t h e y a r e d e m o n s t r a B l y d i s t i n c t , t h e y seldom appear a p a r t . P e r s o n s may s p e c i a l i z e more o r l e s s i n one t y p e o f l o g i c o v e r a n o t h e r But I douBt t h a t anyone c o u l d use one t y p e o f l o g i c e x c l u s i v e l y . S y s t e m i c l o g i c y i e l d s t h e i d e n t i t i e s t h a t f o r m a l l o g i c compares, c l a s s i f i e s and i n n u m e r a t e s . F o r m a l l o g i c a l l o w s t h e p r o d u c t s o f s y s t e m i c t h o u g h t t o Be r a i s e d t o a l e v e l o f a b s t r a c t i o n t h a t makes knowledge g e n e r a l i z a B l e t o n o v e l But s i m i l a r s i t u a t i o n s . I t removes t h e n e c e s s i t y o f h a v i n g t o r e - i n v e n t t h e w h e e l e v e r y d a y . Because i t a B s t r a c t s knowledge f r o m p a r t i c u l a r c o n t e x t s f o r m a l l o g i c a l s o , l e n d s a measure o f o B j e c t i v i t y t o t h o u g h t . That i s , i t a l l o w s one t o p e r f o r m m e n t a l f e a t s l i k e i g n o r i n g i r r e l e v a n t v a r i a b l e s , and c o n s t r u c t i n g h y p o t h e t i c a l s i t u a t i o n s (models) i n w h i c h a l l e l s e i s e q u a l e x c e p t t h e v a r i a b l e - B e i n g t e s t e d . The e u c l i d i a n s i d e o f f o r m a l l o g i c i s i n t i m a t e l y r e l a t e d t o t h e development o f t h e c o n c e p t s o f numBer and measurement ( P i a g e t and I n h e l d e r , 1 9 5 6 ) . I n i t s q u a n t i t a t i v e a s p e c t s , f o r m a l l o g i c a l l o w s f o r more o B j e c t i v e c o m p a r i s o n s o f magnitude. S y s t e m i c l o g i c on t h e o t h e r hand may Be c h a r a c t e r i z e d as l e s s o B j e c t i v e . I t i s i n t i m a t e l y r e l a t e d t o c o n t e x t u a l p a r t i c u l a r s . T h i s i s no more a d e f e c t i n s y s t e m i c l o g i c t h a n a b s t r a c t o B j e c t i v i t y i s a d e f e c t i n f o r m a l l o g i c . O B j e c t i v i t y can r u n amuck By l o s i n g s i g h t o f p r i o r i t i e s and p u r p o s e s . Unchecked By s y s t e m i c t h i n k i n g , ; i t c a n g e n e r a t e i r r e l e v a n c i e s ad i n f i n i t u m . S y s t e m i c l o g i c , on t h e o t h e r hand, h a n d l e s p u r p o s e s and i n t e n t i o n s q u i t e c o m f o r t a B l y . I f one uses s y s t e m i c l o g i c e x c l u s i v e l y i t i s l i k e l y t h a t a g r e a t d e a l o f a c c u m u l a t e d e x p e r i e n c e would r e m a i n t i e d t o s p e c i f i c s i t u a t i o n s and g o a l s . F o r example, L u r i a make t h e f o l l o w i n g comments about the thought p r o c e s s e s o f t h e R u s s i a n p e a s a n t s he had i n t e r v i e w e d i n U z B e c k i s t a n i n C e n t r a l A s i a : " t h e y tended t o d e a l w i t h t h e t a s k as a p r a c t i c a l one o f g r o u p i n g o b j e c t s a c c o r d i n g t o t h e i r r o l e i n a p a r t i c u l a r s i t u a t i o n r a t h e r t h a n a s a t h e o r e t i c a l o p e r a t i o n o f c a t e g o r i z i n g them a c c o r d i n g t o a common a t t r i b u t e . As a r e s u l t , each s u b j e c t grouped t h e o B j e c t s i n an i d e o s y n c r a t i c 219 way depending on the p a r t i c u l a r graphic s i t u a t i o n he had i n mind. The concrete groups that our s u F j e c t s created on the b a s i s of t h i s s i t u a t i o n a l t h i n k i n g were extremely r e s i s t e n t to change. When we t r i e d to suggest another way to group the objects- based on a b s t r a c t p r i n c i p l e s , they g e n e r a l l y r e j e c t e d i t i n s i s t i n g that such an arrangement d i d not r e f l e c t the i n t r i n s i c r e l a t i o n s among the objects and that a person who had adopted such a grouping was " s t u p i d " . Only i n r a r e instances d i d they concede the p o s s i b i l i t y of employing such a means of c l a s s i f i c a t i o n , and even then they d i d so r e l u c t a n t l y , convinced that i t was not important. Only c l a s s i f i c a t i o n based on p r a c t i c a l experience s t r u c k them as proper or important" ( l u r i a , 1979; p. 69) Just as a b s t r a c t i o n can be c a r r i e d to extremes,so can c o n t e x t u a l s p e c i f i c i t y . Of course, what i s a maladaptive extreme i n one socio-economic environment might be o p t i m a l l y adaptive i n another. L i k e w i s e , at d i f f e r e n t stages of the l i f e c y c l e one type of l o g i c may be more adaptive than another. Younger people do not have a vast s t o r e of s i t u a t e d experiences to draw upon and they cannot t e l l what experiences they w i l l encounter l a t e r i n l i f e . Therefore t h e i r best s t r a t e g y would be to a b s t r a c t g e n e r a l i z e d knowledge from t h e i r experiences i n a n t i c i p a t i o n of f u t u r e changes. E l d e r l y persons have a sh o r t e r f u t u r e ahead of them and th e r e f o r e have l i t t l e need to prepare g e n e r a l i z e d schemes f o r meeting f u t u r e s i t u a t i o n s . The e l d e r l y do have enormous s t o r e s of contextualj-'.knowledge. They can th e r e f o r e q u i c k l y dispense w i t h i r r e l e v a n t i n f o r m a t i o n and i d e n t i f y the goal r e l e v a n t p a r t i c u l a r s . In summary, systemic l o g i c and formal l o g i c are d i f f e r e n t ; so are the environments and problems that people encounter. Chandler and Boyes ( i n press) suggest t h a t r e s e a r c h should look f o r matches and mismatches between the s o p h i s t i c a t i o n of people's c o g n i t i v e s t r u c t u r e s w i t h the complexity of t h e i r environmental challenges. The d i s t i n c t i o n between systemic l o g i c and formal l o g i c should help i n the design of such s t u d i e s by f a c i l i t a t i n g the d e s c r i p -t i o n s of both s t r u c t u r e s .