UBC Theses and Dissertations

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UBC Theses and Dissertations

The development of understanding of social systems Boutilier, Robert Gordon 1981

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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 <J <! <! pq pq pq CJ CJ a u >> >, o > e o !>. o q cO CO o CJ <l a) CO cu < l-J H Pr Sy TR Sy TR Sy C J >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)