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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 B O U T I L I E R 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 I N P A R T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREEOOF DOCTOR OF PHILOSOPHY  in 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 conforming  to the required  standard  THE U N I V E R S I T Y OF B R I T I S H COLUMBIA August 1981  Robert  Gordon B o u t i l i e r , 1981  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree at the  the  University  of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I  further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may  be  department o r by h i s or her  granted by  the head o f  representatives.  my  It i s  understood t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not  be  allowed without my  permission.  Department of  /^"yC- /lQ /O  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date  -7Q ^  Columbia  written  ii  ABSTRACT  The  child's understanding  s y s t e m and a s o c i o - e c o n o m i c  o f open s y s t e m s , as e x e m p l i f i e d by an  s y s t e m , was a s s e s s e d  i n t e r v i e w w i t h 8 males and 8 f e m a l e s first on  year post-secondary  tasks using mainly  P i a g e t i a n stages tested.  (n=96).  inanimate,  i n a P i a g e t i a n type  i n e a c h o f g r a d e s 3, 5, 7, 9, 1 1 a n d  S i n c e P i a g e t i a n theory has been based p h y s i c a l content,  the g e n e r a l i z a b i l i t y of  a n d s e q u e n c e s t o t h e two o p e n s y s t e m s c o n t e n t  d o m a i n s was  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  i n each o f t h e p h y s i c a l ,  eco-  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 a l stage and sequence p a t t e r n s were observed  repeated  domains.  i n a l l t h r e e domains.  TypiPost-  concrete o p e r a t i o n s were r e p r e s e n t e d by three 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 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 ed  o p e r a t i o n s i n each o f t h e open systems  l o g i c were p r e s e n t e d .  Three b l i n d judges  s p o n t a n e o u s agreement on 84.6% o f t h e s c o r e s a s s i g n e d  task protocols.  A scalogram  reach-  f o r the systemic  a n a l y s i s and comparisons o f t h e 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 systems s y n t h e s i s and t r a n s i t i v e  that the systemic  operations of  r e c y c l i n g were more d i f f i c u l t  than the  f o r m a l o p e r a t i o n a l t a s k s b y a G u t t m a n s t e p o f t h e same s i z e a s t h a t b e t w e e n the f o r m a l and c o n c r e t e ficult  systemic  two s y s t e m i c  familiarity  Further analyses  indicated  Systemic  b e l o w grade 9 (14 y e a r s )  task success  and c o n s i s t e n t l y  dif-  separate  that the greater  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  of the task contents.  f o r respondents  A c l u s t e r a n a l y s i s showed t h o s e m o s t  t a s k s t o be grouped as i f they were a p a r t o f a  s t r u c t u r e d'ensemble. of these  stages.  difficulty  t o t h e g r e a t e r unr a t e s were fell  zero  f a r below  i i i  formal  task success  operations  r a t e s f o r same a g e d peers'.  s a t i s f i e d the c r i t e r i a  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 Nevertheless,  f o r membership do f o r t h e i r  stage  imputed stage  developments p a r a l l e l and complementary  c o u l d n o t be r u l e d o u t .  The  discussed.  systemic as w e l l  membership. operations  to formal  opera-  i m p l i c a t i o n s of the f i n d i n g s f o r the  areas of c o g n i t i v e development, s o c i a l were  in a fifth  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  as p o s t - c o n c r e t e tions  The m o s t d i f f i c u l t  development and s o c i a l  psychology  iv TABLE OF CONTENTS  Abstract Table of Contents List  of Tables  List  of Figures  iv v  1  Acknowledgement I.  II.  Two  B.  P a r a l l e l Development A c r o s s Domains  Systemic Cognitive  5 7 9  £ii) F a m i l i a r i t y  10  and C o n t e n t s  12  Societal Structures  12  (ii) (iii)  C.  Structures  ( i ) The B i o - e c o l o g i c a l D o m a i n  (i) Structures  B.  X  -1  A.  Structures  and O p e r a t i o n s  Structures  Implicit  i n Hierarchies  Systemic Structures  Cognitive  Structures  12 16 1923  ( i ) Concrete Stage  24  ( i i ) Systemic Structures  26  (iii)  31  Compared t o F o r m a l O p e r a t i o n s  Domains o f C o n t e n t (i) Comparability (ii) (iii)  i  x  Introduction  A.  i  Familiarity Familiarity  34 of Contents Issues  37  and Task D i f f i c u l t y  ( i v ) Age a n d D i f f i c u l t y  35  Level  40 41  i  V D.  Hypotheses (i) List  III.  42 of Hypotheses  43  ( i i ) A Contingent Succession  44  (iii)  45  N u l l Hypotheses  Method  47  A.  47  Measures ( i ) The C o n c r e t e T a s k s (ii)  The F o r m a l T a s k s  (iii) (iv)  IV.  ;  50  The S y s t e m i c T a s k s  51  F a m i l i a r i t y Assessments  B.  Respondents  C.  Procedures  f o r Systemic Tasks  54  ( i ) Data C o l l e c t i o n  54  ( i i ) Data S c o r i n g  58 60  F i r s t H y p o t h e s i s w i t h Composite ( i ) Scalogram (ii)  (iv) (v)  Difficulty  Orderings  61 62 65  Converging Techniques  66  Reproducibility Coefficient  67  F r e q u e n c i e s and P r o p o r t i o n s  69  (vi)  Z Scores f o r P r o p o r t i o n s  F i r s t H y p o t h e s i s w i t h Component (i) Cyclic Transitivity (ii) (iii)  C.  Systemic Scores  Guttman Steps  (iii)  B.  51 • 52  Results A.  48  75 Systemic Scores  82  Components  82  C y c l i c I n t e g r a t i o n Components  83  Scalogram  and Z S c o r e s f o r Components  Second H y p o t h e s i s ( i ) C l u s t e r A n a l y s i s o f Components  84 91 91  vi  D.  Third Hypothesis  .  ( i ) U n f a m i l i a r i t y v s . Complexity  as Reasons  for D i f f i c u l t y ( i i ) Varying (iii)  V.  99  F a m i l i a r i t y w i t h Constant Complexity  Varying  97  Operations  w i t h Constant Content  100 107  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  Discussion A.  112  The T h r e e H y p o t h e s e s  112  (i) F i r s t Hypothesis: (ii) (iii)  Extending  Second H y p o t h e s i s : Third Hypothesis:  ( i v ) Age R e l a t e d  P i a g e t i a n Theory  Upper Systemic Tasks  117  Greater  118  Content D i f f i c u l t y  Criteria  120  ( v ) Summary B.  122  I n t e r p r e t a t i o n s of Systemic D i f f i c u l t y Levels  122  (ii) Piaget's P a r a l l e l Position  126  (iii)  128  Labouvie-Vief's  Parallel Position  129.  VI. I m p l i c a t i o n s f o rThree Areas of Study  131  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 o n A d u l t ( i i ) Post-Concrete (iii)  Cognition  Diversification  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  (iv) Cyclic T r a n s i t i v i t y  and t h e Feedback Concept  (v) C y c l i c I n t e g r a t i o n and i t s Components B.  122  (i) I n t e r p r e t i v e Caveats  ( i v ) Stages and Paradigms  A.  ... 112  S o c i a l Development (i) Ordination  132 134 135 136 139140 142  vii  C.  ( i i ) Hierarchy  143  ( i i i ) Systems A n a l y s i s  143  ( i v ) Systems S y n t h e s i s  143 145  S o c i a l Psychology ( i ) Towards an I n t e r a c t i v e Framework ( i i ) Towards S p e c i f y i n g t h e S t r u c t u r e  D.  .  146  o f the S o c i a l S i t u a t i o n . 149 152  Conclusions  154  References Appendix A:  P h y s i c a l 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.  S c o r i n g Manual f o r Systemic I n t e r v i e w s  197  Appendix E:  Difference  213  Between Formal and Systemic L o g i c s  viii  L I S T OF  Table  Table  Table  Table  Table  Table  I.  II.  III.  IV.  V.  VI.  TABLES  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 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  passing ;,70  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 of 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 the other 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 of 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 the other, reported w i t h systemic scores i n components Z s c o r e s between f o r m a l components  t a s k s and  79  .86  systemic  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 and f a m i l i a r i t y a s s e s s m e n t s  90 tasks  Age p r o f i l e s f o r p a s s e s o n f o r m a l a n d 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 familiarities  101  ...109  ix  L I S T OF FIGURES-  F i g u r e 1.  Scalogram d i f f i c u l t y systemic  F i g u r e 2.  F i g u r e 3.  s c o r e s B y d o m a i n ..  s c o r e s by components  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  F i g u r e 7.  ......... .85  .92 domain  s c o r e s by components  C l u s t e r a n a l y s i s dendrogram on a c r o s s s c o r e s w i t h ambiguous s y s t e m i c  F i g u r e 6.  ...................... .63  C l u s t e r a n a l y s i s dendrogram with- s c o r e s by  s c o r e s and s y s t e m i c F i g u r e 5.  ,  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  domain and s y s t e m i c F i g u r e 4.  orderings with, composite  .95  domain  scores deleted  .96  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 systemic score across domains  98  Some p o s s i b l e f o r m s o f b o t t o m t o t o p p r o c e s s e s in cyclic integration  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 inclusion task 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 inclusion task  class .174'  class .188  X  ACKNOWLEDGEMENTS I *  I wish and  t o thank Dr. P a t r i c i a A r l i n , Dr. Merry B u l l o c k , Dr. Dale  Miller,  D r . 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 a n d i n s i g h t f u l c r i t i c a l  t a r y t h a t they  commen-  o f f e r e d a s members o f t h e t h e s i s c o m m i t t e e . I a l s o t h a n d D r . '  I r v i n g S i g e l f o rs e r v i n g as t h e E x t e r n a l Examiner and D r s . Gaalen E r i c k s o n and Tannis  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 Examiners.  My m e n t o r t h r o u g h o u t t h e e n t i r e His  r e s e a r c h e n d e a v o r was D r . M i c h a e l  Chandler.  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 d e v e l o p m e n t a s w e l l a s t o  every  aspect  of the thesis.  Thanks i s a l s o owing t o t h e s t u d e n t s , p a r e n t s , 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  their  t o Anne B o y l e , Wendy G r o i s s , a n d N e i l K y l e collecting  time  t e a c h e r s , p r i n c i p a l s , and  and/or resources.  I am  grateful  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  the data.  I am i n d e b t e d  t o my w i f e , A n n S v e n d s e n , 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  support. T h i s s t u d y was c o m p l e t e d w i t h t h e 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 from the E d u c a t i o n a l Research I n s t i t u t e o f B r i t i s h  Columbia.  grant  1  The  purpose of t h i s  r e s e a r c h was  to c h a r t the development  understanding of c e r t a i n d i s t i n g u i s h i n g to r e l a t e t h i s development.  sequence  have r e c e i v e d l i t t l e  changes  the understand-  These a r e the s t r u c t u r e s ,  t h e u n d e r s t a n d i n g o f o p e n systems"'".  s e a r c h came t o e x a m i n e t h e d e v e l o p m e n t the course of examining the development  and  i n cognitive  to require c o g n i t i v e structures  a t t e n t i o n to date.  h e r e i n , which deal w i t h  analogous  somewhat e x p l o r a t o r y b e c a u s e  i n g of s o c i a l o r g a n i z a t i o n s appears  child's  features of s o c i a l organization  to other s t r u c t u r a l l y  T h i s r e s e a r c h was  of the  that introduced  Thus t h i s r e -  of systemic cognitive structures i n of understanding of s o c i a l  organiza-  tion. In very brief  detail,  a n a t t e m p t was  structure evident i n children's  was  systems.  Parallels  attention  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  systems.  features characteristic  under-  o f b i o - e c o l o g i c a l and  T h i s p r o c e s s l e d t o t h e p o s t u l a t i o n and l a t e r a s s e s s m e n t  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  about  i n the course of  a c r o s s t h e s e t h r e e domains w e r e s o u g h t and s p e c i a l  s t a n d the open systems  1.  cognitive  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  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 development  made t o c o m p a r e t h e  transitivity"  and " c y c l i c  social  of  two  integra-  In t h i s r e s e a r c h a system i s defined as: 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 f l o w s , e i t h e r d i r e c t l y or i n d i r e c t l y , from every element ( o r c l a s s o f elements) t o every 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 o f 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 o p e n s y s t e m , b y 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 t e n d e n c y t o become more o r g a n i z e d a n d c o m p l e x , r a t h e r t h a n l e s s , h a s been c a l l e d "negentropy" ( B r i l l o u i n , 1961). Open s y s t e m s a r e n e g e n t o p i c , p a r t i a l l y because they can, at l e a s t t e m p o r a r i l y , export entropy. O v e r t o n (19.75) d i s t i n g u i s h e s o p e n f r o m c l o s e d s y s t e m s a s 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 f r o m i t s e n v i r o n ment o r , a t m o s t , e x c h a n g e s o n l y e n e r g y w i t h i t s e n v i r o n m e n t . Open s y s t e m s 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 a n d e x p o r t o f m a t e r i a l as w e l l as e n e r g y " . (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.  tion".  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 d e v e l o p m e n t s t r u c t u r e s became t h e pinion point and  around which t h i s  complexity  study revolved.  a good d e a l o f groundwork needed t o b e l a i d  make t h e s e c o n c e p t s m e a n i n g f u l a n d i n o r d e r be  t h e i r importance r e l a t i v e  tive  Because of t h e i r  development.  to other  novelty  i n order  to  t o j u s t i f y w h a t was s e e n t o  better understood aspects of cogni-  A n a t t e m p t i s made t o l a y o u t t h a t  groundwork i n Chapter  II. The  approach taken from the outset  structure of "the things being  thought about" i s described  structure of the thinking i t s e l f . t u r e j u s t as " t h e knower" does. this  general  ontogenetic  this  research:  A more e x p l i c i t  and f o r m a l  i n the following three  statement of  assumptions  development, progress through a r e g u l a r  sequence o f d i f f e r e n t  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  aspects  t h e s o c i a l environment a r e themselves a r r a n g e d as systems a c c o r d i n g  definable the  with the  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  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 ; of  along  I n o t h e r w o r d s , " t h e known" h a s a s t r u c -  approach i s contained  which oriented  i n t h i s w o r k was o n e w h e r e i n t h e  to  r u l e s a n d 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  same l o g i c o - m a t h e m a t i c a l  the v a r i o u s  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  structures of cognitive organization  c a n a l s o be u s e f u l l y a p p l i e d 2  to c h a r a c t e r i z e  the s t r u c t u r e of c e r t a i n s o c i a l organizations  assumptions, taken as a group, l e a d  2°.  to the suggestion,  .  These  t o be t e s t e d i n t h i s  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 a n d m e t h o d s b y 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 m e t h o d s b y means o f w h i c h t h e e l e m e n t s 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 the logico-mathematical p r i n c i p l e s u s e d t o d e s c r i b e them w i l l a l l b e assigned p a r a l l e l l a b e l s .  3.  research, that a child's a b i l i t y izations w i l l  t o comprehend v a r i o u s s o r t s o f s o c i a 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  organlevel  of cognitive maturity. Because o f t h e c e n t r a l r o l e w h i c h they have p l a y e d  i n the framing of  t h i s s t u d y , each o f these o r i e n t i n g assumptions needs f u r t h e r e l a b o r a t i o n . The  first,  which 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  s e q u e n c e , i s a commonplace f o l l o w i n g  P i a g e t a n d many o t h e r s . of understanding  That work, however, has emphasized t h e development  of the impersonal,  non-social world.  of t h e development o f understanding  F u r t h , 1977; Jahoda, 1979).  The s y s t e m a t i c  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  i s much more r e c e n t a n d i n much s h o r t e r s u p p l y 1977;  from t h e work o f  study domains  ( e . g . , Selman & Ja.quette,  The s e c o n d 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 environment 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 b e  different  emphasized i n the study  from t h e ones h i t h e r t o  velopment.  In particular,  represented  i n logico-mathematical principles  t i o n of systems.  o f c o g n i t i v e de-  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 b e b e s t  The t h i r d a s s u m p t i o n ,  that deal with the organiza-  which brings together  t h e f i r s t and  s e c o n d , p r e s u m e s t h a t s o c i e t y a n d t h e m i n d 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 t h e same a b s t r a c t p r i n c i p l e s . ially  on l o g i c a l  of chapter tal  II.  This premise,  grounds, i s presented Section A of chapter  s t r u c t u r e s examined i n t h i s  study  ing logico-mathematical principles. that the developmentally d e s c r i b e d by these  w h i c h c a n be j u s t i f i e d  part-  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  I I i s devoted  t o s h o w i n g how t h e s o c i e -  are adequately  d e s c r i b e d by  I n s e c t i o n B of chapter  s u c c e s s i v e thought  correspond-  I I i ti s argued  structures considered herein are  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 .  Together,  sections  4  A and B argue t h a t these p r i n c i p l e s  form a b r i d g e between t h e s o c i e t a l  t u r e s and 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 a r e presumably necessary hending  struc-  f o r compre-  the societal organizations.  Some s o c i e t a l  s t r u c t u r e s embody, a n d c a n be u n d e r s t o o d  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 commonly, h o w e v e r , s o c i a l  was t a k e n  by P i a g e t ' s t h e o r y .  More  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 . consequently  by t h e use o f ,  Children's understanding  as t h e c e n t r a l f o c u s o f t h i s  o f such  study.  open systems  H i s t o r i c a l l y the  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  understanding 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 Society, social  o r g a n i z a t i o n s and even ecosystems, because they a t t a i n  high state of organized 1975).  reactions., pendulums) .  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  I n order t o study  children's understanding  of social  a  (Overton,  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 e m p h a s i s on p h y s i c a l s y s t e m s t o a more n o v e l e m p h a s i s o n a n i m a t e , o p e n s y s t e m s . comprehension o f s o c i a l  T h i s r e f o c u s i n g upon t h e  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 o p e n s y s t e m s , l e a v e s o p e n t h e q u e s t i o n o f t h e e x t e n t  to which the  w o r k o f P i a g e t a n d 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 I t was n e c e s s a r y , theory  therefore, to verify  t o t h e new c o n t e n t  the g e n e r a l i z a b i l i t y  areas.  of Piagetian  domains i n w h i c h open systems a r e t y p i c a l l y  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  conceptual  order of business  found.  i n this  study.  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 n o n 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 study of formal opera t i o n a l thought w i t h t h e study o f c h i l d r e n ' s understanding 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 p e n d u l u m s , 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 o n 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  Having e s t a b l i s h e d the g e n e r a l i z a b i l i t y of P i a g e t i a n theory 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 to the main focus o f t h i s aspects of s o c i a l  systems and ecosystems.  i n g o f open s y s t e m s .  applicability standing  Two S y s t e m i c C o g n i t i v e  a very  studied.  Structures  b r i e f i n t r o d u c t i o n t o t h e open  t h a t were t h e c e n t r a l focus o f t h i s s t u d y . more f u l l y  Section B ( i i ) of chapter I I contains  manifestations tasks  Their  manifestations  more d e t a i l s a b o u t  was r e f l e c t e d i n t h i s  research  i n various  their  The  distinc-  aspects of the world  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  s t r u c t u r e o f the i n d i v i d u a l ' s c o g n i t i o n about those v a r i o u s Specifically,  o f chap-  features of  used to assess mastery o f these c o g n i t i v e s t r u c t u r e s . structures  systems  i n section A ( i i i )  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  t i o n between open v e r s u s c l o s e d  world.  i s a discus-  t o t h e c o n t e n t domains where t h e u n d e r -  s o c i e t a l structures are described  ter I I .  intro-  the p r e l i m i n a r y problem of e s t a b l i s h i n g the  of P i a g e t i a n theory  section provides  structures  the  focus l e d to the i d e n t i f i c a -  further i n section A of this  o f o p e n s y s t e m s c a n more r e a d i l y b e  This  system  c o g n i t i v e s t r u c t u r e s unique to the understand-  These a r e d i s c u s s e d  surrounding  A.  as  This  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  sion of the issues  attention  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  t i o n o f two h i t h e r t o u n s t u d i e d  duction.  s y s t e m s , i t was p o s s i b l e t o t u r n  and method  aspects of the  an a n a l y s i s o f the s t r u c t u r a l r e g u l a r i t i e s  c e r t a i n f a m i l i a r and w e l l understood s o c i a l o r g a n i z a t i o n s 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 .  the  evident i n  l e d to the postuI 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. their social organizations,  t h e r e m u s t be  cognitive structures of correspond4  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 identify  T h e s e two  cyclic  one  of the o r i g i n a l c o n t r i b u t i o n s of t h i s  c o g n i t i v e s t r u c t u r e s concerned w i t h  are labeled " c y c l i c  the sake of b r e v i t y , variant  The  attempt  to  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  systems  .  transitivity"  and  research.  t h e u n d e r s t a n d i n g o f open "cyclic  integration".  the phrase "systemic c o g n i t i v e s t r u c t u r e s "  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  For  ( o r some  transitivity  and  integration together.  A thorough d e s c r i p t i o n of these systemic c o g n i t i v e s t r u c t u r e s i s p r e sented l a t e r . relates  F o r now  i t i s sufficient  to note that c y c l i c  t o s t r u c t u r e s known a s n e g a t i v e f e e d b a c k l o o p s a n d c y c l i c  tion i s related  p r i n c i p l e s e x h i b i t e d by  4.  integra-  to h i e r a r c h i c a l s t r u c t u r e s where the s u p r a o r d i n a t e and  subordinate l e v e l s m u t u a l l y i n f l u e n c e each other.  systems  transitivity  these systemic structures  the  The l o g i c o - m a t h e m a t i c a l can be d i s c e r n e d i n open  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 ) .  Since  traditional  F r o m 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 i r o n m e n t may b e s e e n a s a r e l a t i o n s h i p b e t w e e n s o c i a l s y s t e m s ( 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 s y s t e m s a n d a s s u c h m u s t a d a p t t o an e n v i r o n m e n t 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 s y s t e m s ( P a y n e , 1 9 6 8 ) . Psychological s y s t e m s a r e , i n a manner o f s p e a k i n g , t h e i n t e r n a l e n v i r o n m e n t o f s o c i a l systems. 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 d e p e n d i n g u p o n 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 of t h a t s o c i a l system 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 . Before these m u t u a l i n f l u e n c e s c a n b e s t u d i e d we m u s t h a v e some u n d e r s t a n d i n g o f how the i n d i v i d u a l c o n c e p t u a l i z e s such s o c i a l systems. In the present 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 t e r m s . Several s o c i a l psychologists (e.g., S m e l s e r and S m e l s e r , 1 9 7 0 ; D i R e n z o , 1 9 7 7 ; M a i n e s , 1977) h a v e f o r some time been c a l l i n g f o r j u s t such a model, a model t h a t would 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 systems.  7  Piagetian  t h e o r y has  h e n d s y s t e m s o f any i n t e g r a t i o n have yet tive  not  sort^, i t follows to appear i n the  that  cyclic  child's ability  transitivity  s t r u c t u r e s , an  attempt to define e f f o r t was  more w e l l d o c u m e n t e d a n d the  and  document t h e s e s y s t e m i c  appre-  cyclic cogni-  thoroughly studied  six cognitive structures  structures.  assessed i n t h i s  have a l r e a d y  been  research  These f o u r  are  al  That c l a s s i f i c a t i o n , however, i s based upon the  tradition  as  achievements of  the  concrete  operation-  c h i l d ' s use  to understand i n a n i m a t e , p h y s i c a l r e a l i t y  ages a t w h i c h t h e s e f o u r  (i.e.,  logical multiplication, class inclusion).  commonly c l a s s i f i e d  structures  other four  linear transitivity,  these cognitive  ways t o  Consequently,  seriation,  stage.  cognitive  a l s o made t o c o m p a r e them i n v a r i o u s  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  cognitive  structures  to understand animate and/or s o c i e t a l r e a l i t y it  and  standard pantheon of P i a g e t i a n  s t u d i e d by  The  to  structures. Beyond the  of  f o c u s e d a t t e n t i o n upon the  can  be  applied  r e m a i n s unknown.  known i n w h a t 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  mastered i n the  of only.  in efforts Neither  is  open systems  domains.  B.  P a r a l l e l Development A c r o s s  L e a r n i n g s o m e t h i n g a b o u t a g e s and c a l and  the  orders of mastery i n the  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 the  t i v e development u n f o l d s c o n t e n t domains.  5.  Domains  in a parallel  This i s s u e , too, for a discussion logic.  extent to which  or yoked f a s h i o n  If cognitive structures  bio-ecologi-  a c r o s s the  cogni-  various  are mastered a t d i f f e r e n t ages i n  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 o f t h e d i f f e r e n c e b e t w e e n f o r m a l l o g i c and  Appendix E systemic  different  content  d o m a i n s 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 b e m a s t e r e d  i n a different order. theory  the g e n e r a l i z a b i l i t y  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  izability, grees  This would attenuate  of course, a r e questions o f degree.  of d e t a i l a t which evidence  what s h a l l be c a l l e d across  domains.  level,  Questions  of general-  There a r e a t l e a s t  of g e n e r a l i z a b i l i t y  the "macroscopic"  of Piagetian  evidence  domain r e p l i c a t i o n o f t h e m a j o r s t a g e s .  two d e -  c o u l d be s o u g h t .  c o u l d be sought f o r  I f , i n t h e open  systems  d o m a i n s , t h e r e i s no d i s c o n t i n u i t y b e t w e e n t h e m o s t a d v a n c e d c o n c r e t e c o g n i t i v e s t r u c t u r e and the s i m p l e s t formal stage  cognitive structure,  the 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 of such by  At  stage then  understanding  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 ,  c o n t r a s t , c h i l d r e n who w e r e f o u n d  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  operational levels i n the t r a d i t i o n a l shown t o e v i d e n c e  impersonal  o r p h y s i c a l domain were  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 a b o u t 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 d o m a i n s , t h 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 room f o r e r r o r .  t h e " m i c r o s c o p i c " l e v e l , h o w e v e r , t h e r e i s more  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  d e t a i l e d v e r s i o n of the macroscopic  level.  Here the c r i t e r i a  grained,  f o r across  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 . is  sought a t t h i s  l e v e l of a n a l y s i s i s evidence  that there i s a uniform  gression of mastery of logico-mathematical p r i n c i p l e s t e n t used t o i l l u s t r a t e  those p r i n c i p l e s .  I f this  What pro-  r e g a r d l e s s o f t h e con-  stringent criterion  were  n o t met o w n i n g 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 w o u l d b e no n e e d t o q u e s t i o n t h e w h o l e o f P i a g e t i a n t h e o r y a s cable.  Misordering of cognitive structures across  inappli-  s t a g e s , however, would  raise significant The  doubts.  whole i s s u e of determining  the l e g i t i m a c y of a p p l y i n g a P i a g e t i a n  approach to c h i l d r e n ' s understanding  i n t h e b i o - e c o l o g i c a l and  d o m a i n 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. the  search  for p a r a l l e l patterns  more f u l l y .  Two  of  those  this point i n order  i s s u e s , h o w e v e r , must be the  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 concerns the  reasons underlying  domain ( s u b s e c t i o n B chapter  The  research  briefly  discussed  introduced  at  d e t a i l e d d i s c u s s i o n of s o c i e t a l B of chapter  I).  content  II.  The  first  of  and these  The  second i s s u e  (subsection B  (ii), the  domains,  B i o - e c o l o g i c a l Domain focus  of t h i s  research  i s u p o n an  extension  i n t h e d o m a i n o f p h y s i c a l phenomena t o t h e s o c i e t a l  might appear that t h i s  study  sampled from these  domains.  two  c o u l d have been performed u s i n g The  c h i l d ' s understanding  domain i s r e l a t i v e l y w e l l documented w h i l e cognitive structures relating intention  relatively  to the understanding  to attempt a d i r e c t  Piaget's  domain, i t only  b i o - e c o l o g i c a l systems. differs  content  of the p h y s i c a l  little  i s known a b o u t  of s o c i e t y .  Given  an  reason-  c o m p a r i s o n of p e r f o r m a n c e i n the p h y s i c a l domain domain.  T h e r e w e r e , h o w e v e r , two  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  i n c l u d e a)  of  t o p r o c e e d f r o m t h e known t o t h e u n k n o w n , i t w o u l d seem  w i t h performance i n the s o c i e t a l  tasks  domains a r e  I ) , concerns the problem of unequal l e v e l s o f f a m i l i a r i t y w i t h  Because the  able  surrounding  the d e c i s i o n to i n c l u d e the b i o - e c o l o g i c a l  ( i ) , chapter  m a t e r i a l s used i n the v a r i o u s (i)  There the i s s u e s  of development across  to f a c i l i t a t e  societal  First,  representing  the p h y s i c a l domain of s t a n d a r d  f r o m t h e s o c i e t a l d o m a i n on a t l e a s t  the p h y s i c a l versus  domain  non-physical,  and  b)  two the  reasons  Piagetian  dimensions. inanimate  They versus  10  animate. societal  I t was t h o u g h t t h a t c o m p a r i s o n s o f t h e p h y s i c a l  domain w i t h t h e  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,  t h e b i o - e c o l o g i c a l , h a v i n g o n e c h a r a c t e r i s t i c i n common w i t h e a c h o f t h e o t h e r two.  Ecosystems, l i k e  p h y s i c a l elements  s o c i a l systems  (e.g., b i r d s ,  , a r e animate, but also  insects) which are j u s t  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 . earlier,  as p a l p a b l e as t h e  Second,  the logico-mathematical p r i n c i p l e s of c y c l i c  contain  as m e n t i o n e d  transitivity  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.  T h e r e a r e , c o n s e q u e n t l y , n o 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  of u s u a l P i a g e t i a n assessment  procedures w i t h which to assess these  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. e v e r , i t was p o s s i b l e tivity in  and c y c l i c  Using bio-ecological  c o n t e n t , how-  t o c o n s t r u c t assessment procedures f o r c y c l i c  integration.  I t was t h e n p o s s i b l e  (ii)  transi-  t o compare p e r f o r m a n c e s  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  c h a r a c t e r i s t i c s b u t which were n o t n e c e s s a r i l y  cogni-  systems  s o c i a l i n content,  Familiarity 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  across content  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 t h e r e s p o n d e n t s ' relative  familiarity with  For example,  the m a t e r i a l s used i n d i f f e r e n t  content  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  easily solved using familiar materials are often f a i l e d with testing materials  ( G r e e n f i e l d , 1976).  mally i n the p o l i t i c a l  and economic  problems  unfamiliar  Since children participate only  life  of a society,  i t i s possible  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 m i g h t be l i k e m a t e r i a l s  6.  domains.  minithat  from a f o r e i g n  The t e r m " s o c i a l " i s a m b i g u o u s . S o m e t i m e s i t i s u s e d t o mean 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 " . In w o r k t h e t e r m " s o c i a l " i s n e v e r u s e d t o mean " i n t e r p e r s o n a l " . i s w a r r a n t e d b y t h e c o n t e x t , t h e t e r m " s o c i a l " may b e u s e d i n of " s o c i e t a l " .  "interthe present Where i t the sense  11 c u l t u r e t o them. q u e r i e d about  Throughout  their  t h i s r e s e a r c h the c h i l d r e n were c o n s e q u e n t l y  familiarity with  the m a t e r i a l s b e i n g used.  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 with  domains.  These  (b) t h e  and promoted  to extend P i a g e t i a n theory to the understanding of s o c i e t y . 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  the attempt  They d i d so  content i s s i m i l a r t o ,  i n his later  works.  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 a n d  documentation  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 of s o c i e t a l l i m i n a r y groundwork c o n t e n t domains.  organizations.  on t h e g e n e r a l i z a b i l i t y  That a t t e m p t t o examine  That u n d e r t a k i n g r e q u i r e d p r e of the P i a g e t i a n model to  the extent of p a r a l l e l  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 p h y s i c a l y e t animate domain, assessments  certain  f r o m , t h e 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 -  ing, especially  o f two new  familiarity  comparisons provided  c h e c k s 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 d i f f e r e n t  there-  o f the s o c i e t a l domain m a t e r i a l s  ( a ) p e r f o r m a n c e on t h e s o c i e t a l d o m a i n t a s k s , a n d  o f m a t e r i a l s i n t h e o t h e r two  I t was  domain.  sequencing  the i n c l u s i o n o f (a) a  the b i o - e c o l o g i c a l domain,  f o r the contents o f each  new  and  (b)  familiarity  12  II.  Section A of this  STRUCTURES AND CONTENTS  chapter  begins  w i t h some c l a r i f i c a t i o n o f  and  continues  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  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  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 stage discussed. mining  issues r e l a t e d to task d i f f i c u l t y .  study  a r e f o r m a l l y s t a t e d and then e x p l a i n e d  A.  in  this  Before  study  can be d i s c u s s e d  this  t o b e g i n by  of the s o c i e t a l  s t r u c t u r e s used concepts of  must b e examined more g e n e r a l l y .  Operations terms t h a t a r e used throughout t h i s  structure, operation, principle).  I n order  to avoid  later  among t h e s e  concepts.  terms and t h e s t r o n g  The two m o s t c l o s e l y  l i n k a g e s among t h e s e  work  confusion,  s e c t i o n i s i n c l u d e d as an attempt t o examine t h e r e l a t i v e l y f i n e  tinctions ing  chapter.  by t h e concept o f s o c i a l  i n d e t a i l , t h e more g e n e r i c  There a r e s e v e r a l i n t e r r e l a t e d (i.e.,  i n section D of this  r e s e a r c h was t o c h a r t t h e d e v e l o p m e n t o f t h e  the substantive nature  S t r u c t u r e s and  deter-  the hypotheses o f the  of s o c i a l o r g a n i z a t i o n s , i ti s important  s t r u c t u r e s and o p e r a t i o n s (1)  the r o l e of content  Finally,  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 structure.  and v a r i o u s  Societal Structures  the purpose of t h i s  c h i l d ' s understanding  are described  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  stage  Since  In section B  o f c o g n i t i v e development a r e  I n section C the issues surrounding  task d i f f i c u l t y  structures.  terminology  dis-  correspond-  r e l a t e d concepts 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  operations are, a c c o r d i n g to P i a g e t , both based  logico-mathematical principles.  The  t e r n , a set of t r a n s f o r m a t i o n r u l e s , Logico-mathematical c o n t e n t may  The  p r i n c i p l e s , once u n d e r s t o o d ,  mathematical then  a topological  symbolic, behavioural, s o c i a l , c a n be  content.  p h y s i c a l , or whatever.  discerned i n organized parts  ( e . g . , r e g u l a r phenomena, v a r i o u s s y s t e m s ) .  p r i n c i p l e i s manifested  pat-  a r e l a t i o n s h i p between symbols, e t c .  p r i n c i p l e s a r e a l w a y s embedded i n some k i n d o f  The  the environment,  be  p r i n c i p l e m i g h t be  on  i n some o r g a n i z e d  aspect  of  When a  logico-  of the  world  t h a t p a r t of 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 to 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 the s t r u c t u r e of the o r g a n i z a t i o n . One  of the i m p l i c a t i o n s of t a k i n g a s t r u c t u r a l i s t  e n v i r o n m e n t as w e l l a s  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 l e s a r e assumed t o r e s i d e i n b o t h  thought  and  w o r d s , 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 no  one  l e s s be  there to "hear"  i t (in this  a s o u n d made b y  s t r u c t u r e d w h e t h e r we  approach towards  the  case,  tree h i t t i n g  o b j e c t s of thought. i n the  f o r e s t and  appreciate i t or not.  princiIn  neverthe-  That i s , the w o r l d i s  S i n c e t h e human m i n d i s p a r t  n a t u r e , i t t o o 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 c i p l e s by w h i c h the r e s t of n a t u r e A swinging d e s c r i b e d by  1.  other  t h e r e were  " t h i n k of i t " ) there would the ground.  the  of  prin-  i s organized.  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 .  logico-mathematical principles  Its structure i s  d e r i v a b l e f r o m t h e INRC g r o u p  I n P i a g e t ' s theory both of these terms are r e l a t e d to l o g i c o - m a t h e m a t i c a l principles. 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 w o r k t o u s e t h e s e t e r m s t o mean t h e same t h i n g t h a t P i a g e t m e a n t b y them. H o w e v e r , 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 s e n s e d i s c r e p a n c i e s b e t w e e n P i a g e t ' s u s e o f t e r m s and t h e i r u s e t h r o u g h o u t this work.  14  ( P i a g e t and I n h e l d e r , Its  1956).  An ecosystem i s an o r g a n i z e d  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  t r a n s i t i v i t y and c y c l i c system.  integration.  part of the world.  principles  like  cyclic  T h e same c a n b e s a i d o f a s o c i o - e c o n o m i c  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  principle 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 " . refer  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  To  abilities  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 " . While s t r u c t u r e s a r e patterns o f o r g a n i z a t i o n which e x h i b i t the essential  characteristics of logico-mathematical  implementation  of the structures.  performances p o s s i b l e . by  the structures.  ordination,  are the processing,  logico-mathematical  Cognitive operations  arethe  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 transformation, co-  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  to the various  according  principles.  are performed 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 .  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 the person's problem s o l v i n g c o g n i t i v e a c t i v i t y more l i k e l y ,  operations  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  The o p e r a t i o n s  The o p e r a t i o n s  principles,  a set of cognitive operations.  w i t h a problem  The t a s k i s a n o r g a n i z e d  I t has a s t r u c t u r e which f o r purposes o f i n f e r e n t i a l  i d e a l l y manifests  o n l y one l o g i c o - m a t h e m a t i c a l  and has v a r i o u s  principle.  part of clarity  The p e r s o n i s a l s o  cognitive structures at h i sor her disposal.  the person b r i n g s a p a r t i c u l a r  task,  i s a cognitive operation, or  the environment.  organized  In  When  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 t h e t a s k , he o r s h e i s p e r f o r m i n g  a cognitive operation.  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 tures a v a i l a b l e t o the person, ed  the cognitive operation  t h e n we s a y t h a t t h e p e r s o n h a s n o t y e t m a s t e r -  that would lead t o task s o l u t i o n .  The p e r s o n h a s  15  not  yet acquired  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  task. 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 the p a t t e r n cognitive operations organization  and whole s o c i e t i e s  s o c i a l groups.  sophisticated  that  structures are the patterns  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  organizations other  possible, societal  of organization  possible.  of  Social  f a c e problems p r e s e n t e d by n a t u r e  and/or  The s t r u c t u r e o f t h o s e p r o b l e m s may b e m o r e o r l e s s  than the s t r u c t u r e of the s o c i a l o r g a n i z a t i o n .  Likewise, the  s o c i a l s t r u c t u r e may b e m o r e o r l e s s s o p h i s t i c a t e d t h a n t h e c o g n i t i v e tures  of various  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 .  on  them.  The M a r x i s t  t h i s premise.  assigned  notion  By f o l l o w i n g p r e s c r i b e d ,  operation  r o u t i n e procedures, by  o n some i n f o r m a t i o n  based  enacting  i n s u c h a way a s t o p e r -  w i t h o u t a n y o n e o f them  ever n e c e s s a r i l y performing the corresponding c o g n i t i v e operation same  under-  of f a l s e consciousness i s p a r t i a l l y  r o l e s , e t c . , members c a n a c t c o o p e r a t i v e l y  form an ( s o c i e t a l )  strucIndeed,  s o c i a l s t r u c t u r e s c a n e x i s t w i t h o u t a n y members o f t h e s o c i e t y f u l l y standing  make  on a l l t h e  information. 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 study have analogous  social structures  t h a t a r e commonly f o u n d i n t h e s o c i o - e c o n o m i c s y s t e m s o f  western i n d u s t r i a l i z e d social organizations  societies.  Two o f t h e m o s t common f e a t u r e 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 r c h i c a l model o f s o c i e t y has been p a r t l e a s t as f a r back as t h e m i d d l e ages. of t h e system model were i m p l i c i t  aspects.  of the western heritage Incomplete o r fragmentary  i n the s o c i a l  movement a n d o f M a r x ( P e c k h a m , 1 9 6 5 ; W i l k i n s o n ,  of western The h i e r -  since at versions  commentary o f t h e r o m a n t i c 1971).  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  Parsons view.  (1950)  The f u l l  prescope  16 of  t h e s y s t e m i c m o d e l h a s b e e n made e x p l i c i t  E a s t o n , 1965; Sztomka, 1974; M y s i o r ,  only  recently  gether i n s o c i a l organizations.  thought t o be e a s i e r  tures  implicit  structures  from the combinations  and systems a l m o s t always appear t o -  F o r the purpose of a n a l y z i n g  s o c i a l s t r u c t u r e s , however, they a r e d i s c u s s e d are  separately.  to understand are discussed  i n hierarchies are discussed  before turning  i s to clearly  their  The o n e s  first.  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  review of s o c i e t a l structures  1962;  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 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  (Boulding,  constituent that  The s o c i a l  struc-  t o t h e two of the following  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 are being s i n g l e d out f o r study v i s a v i s the c h i l d ' s  developing  understanding of society, (ii)  Structures  Implicit  i n Hierarchies  Elements 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  a c o n t i n u u m , a n d a s , ( b ) members o f d i s c r e t e c l a s s e s has  a t l e a s t one c o n t i n u u m , n a m e l y , i t s v e r t i c a l  the  base. I f the h i e r a r c h y  one  of abstractness  i s a classification  or of l o g i c a l p r i o r i t y .  may d e n o t e t e m p o r a l p r i o r i t y . reflects  sets and  i n s o f a r as t h e apex r e p r e s e n t s  classified sectors.  hierarchy  f r o m t h e apex t o  system, t h e continuum might be  authority.  the continuum  the continuum Elements  a s members o f d i s c r e t e c l a s s e s o r  a subset of elements. I n s o c i e t i e s  s t a t e s , f o r example, t h e subsets correspond t o e n t i t i e s  states, municipalities, etc. A society's  according  along  the s e t of a l l elements i n the h i e r a r c h y  each s u b o r d i n a t e element represents  l i k e provinces,  ranking  I n some s o c i a l o r g a n i z a t i o n s  c a n a l s o be c o n c e p t u a l i z e d  that are also nation  o r sets. Every  I n some h i e r a r c h i e s  d e c i s i o n making power and s u p e r v i s o r y  of h i e r a r c h i e s  as (a) p o i n t s  to public versus private sectors  economy may b e s u b -  or various  industrial  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  four consitiuent  struc-  2 tures  . I n t h i s r e s e a r c h , t h e 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  portant social structures i n a hierarchy: linear  transitivity,  correspond the  im-  (a) s e r i a t i o n o r o r d i n a t i o n ,  (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 .  t o t h e 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  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  arrangement  t h e most  transitivity  These appear,  tend to invoke the  o f e l e m e n t s as p o i n t s a l o n g a c o n t i n u u m . L o g i c a l  a n d c l a s s i n c l u s i o n , on t h e o t h e r h a n d , r e l y  (b)  on t h e d i s c r e t e  multiplication categorical  p r o p e r t i e s of elements. Seriation.  Seriation refers  companies, committees,  roles,  t o the arrangement  of elements  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  s u c c e s s i v e e l e m e n t has an a s c e n d i n g v a l u e . F o r example, tions with different  levels  (i.e. ,  of supervisory s t a f f  their resources (e.g., s a l a r i e s ,  office  space)  social  each  organiza-  a l l o c a t e a t l e a s t some o f  according to supervisory  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 tinuum. S u p e r v i s o r y r a n k m i g h t be i n d e x e d by b e i n g p e r f o r m e d by each element. F o r example, what g o a l s the o r g a n i z a t i o n w i l l might  2.  the top ranks might  a t t e m p t t o a c h i e v e . The  d e c i d e w h a t means w i l l b e u s e d  rank might  the l o g i c a l p r i o r i t y  of  then perform the tasks designed to achieve the goals.  tasks  decide  next lower  t o a c h i e v e t h o s e g o a l s . The  con-  level  bottom Elements  I t i s i m p o s s i b l e to prove that these are the only 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 v e r , the c o n c e p t o f h i e r a r c h y i s n o t a s l o g i c a l l y p r e c i s e a s 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 which u t i l i z e the concept but w h i c h a l l u s e d i f f e r e n t l a n g u a g e t o d e s c r i b e i t s f e a t u r e s a n d make d i f f e r e n t a s s u m p t i o n s a b o u t w h a t r e l a t i o n s may o b t a i n among e l e m e n t s ( 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 c o n c e p t o f h i e r a r c h y i n i t s e l f , h o w e v e r , 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 u s e d t o r e f e r t o any a r r a n g e m e n t w h i c h c a n b e r e p r e s e n t e d a s 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 s e n s e 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  along  a dimension of temporal p r i o r i t y  w i t h i n o r among l e v e l s o f r a n k . the  first  clerk to receive the tax returns  information. third  Imagine a m u n i c i p a l  either  revenue o f f i c e  where  checks the form f o r m i s s i n g  The s e c o n d c l e r k c h e c k s t h e a c c u r a c y o f c a l c u l a t i o n s .  clerk files  the form f o r f u t u r e r e f e r e n c e .  example, t h e elements a r e o r d i n a t e d  In this  i n a temporal s e r i e s  The  hypothetical corresponding  t o t h e c a r d i n a l n u m b e r s , 1 s t t o n t h , w h e r e n i s t h e number o f e l e m e n t s in  the s e r i e s . Linear Transitivity.  Linear  transitivity  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  i s a type o f s o c i a l  r e l a t i o n o f t h e same name.  c a l f o r m i t i s e x e m p l i f i e d b y t h e s t a t e m e n t "A i s g r e a t e r is  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  social the  content  t h a n C\!.  i t i s e x e m p l i f i e d by p a t t e r n s  following:  F a l s e Creek Development  In logi-  t h a n B_, a n d C_  When m a n i f e s t e d  in  o f s o c i a l o r g a n i z a t i o n as  "CPR c o r p o r a t i o n owns M a r a t h o n R e a l t y , a n d F a l s e  Development C o r p o r a t i o n  struc-  i s owned b y M a r a t h o n R e a l t y ,  Creek  t h e r e f o r e CPR owns  Corporation".  Logical Multiplication.  L o g i c a l m u l t i p l i c a t i o n as a logico-mathe-  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 , w i t h a t t r i b u t e p_ a n d t h o s e w i t h fied iL  o  r  as b e i n g n o t  matrix  - q)• (i.e.,  this simplest of  a t t r i b u t e c[.  either inside or outside  E v e r y element c a n be  classi-  o f e i t h e r s e t ( i . e . , _p o r n o t p ;  A l l e l e m e n t s c a n t h e n be l o c a t e d i n a t w o - f o l d  classification  p_ a n d _q_; p_ a n d n o t q; q_ a n d n o t p ; n o t _q_ a n d n o t p ) . o f examples, l o g i c a l m u l t i p l i c a t i o n  those elements r e p r e s e n t i n g  those  In  i s the i d e n t i f i c a t i o n  s e t i n t e r s e c t i o n ( i . e . , p_ a n d q j .  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  In socio-  considering  19 v a r i o u s i n d u s t r i e s a s e l e m e n t s i n a n a t i o n a l economy. may f i n d i n d u s t r i e s  t h a t h a v e 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_) .  plement would be p r i v a t e i n d u s t r i e s on a t t r i b u t e s  l i k e primary  (notp ) .  (q_) v e r s u s  were both p u b l i c and p r i m a r y C l a s s Inclusion. ' involving subordinate the elements  cal multiplication ing attributes classifying ments.  a subset  processing.  the a t t r i b u t e s are nested.  Like logical  (a£).  that  cases  multiplicaUnlike  logi-  classify-  o f , o r instances o f , the supraordinate examples o f A  example, c o n s i d e r p o s t a l workers  Both  relation  That i s , s u b o r d i n a t e  The e l e m e n t s a ^ a n d a2 a r e b o t h  As a s o c i o - e c o n o m i c  By  of industries  ( e . g . , a ^ a n d a 2 ) h a v e two a t t r i b u t e s e a c h .  attribute.  The com-  (e.g., Petrocan).  and s u p r a o r d i n a t e c l a s s e s .  are special  government c l e r k s  ( n o t q)  Class inclusion i s a logico-mathematical  -  s e t we  T h e s e c o n d s e t may b e b a s e d  secondary  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  tion,  In the f i r s t  groups o f people  class,  f e d e r a l government employees ( i . e . ,  exists  independently  ele-  (a-^) a n d f e d e r a l  a r e members o f a s u p r a o r d i n a t e  class A).  This s o c i a l s t r u c t u r e  o f w h e t h e r 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 . (iii)  Systemic The  logical  Structures  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 features of a hierarchy.  f a rreflect  the important  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  implicit  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 from P i a g e t and o t h e r s . As we b e g i n  t o d u s c u s s s y s t e m i c s t r u c t u r e s , h o w e v e r , we a r e m o v i n g o n t o m o r e  u n f a m i l i a r ground. be  A h i e r a r c h y i s not n e c e s s a r i l y a system although  i fcertain criteria  into waterfowl  a r e met.  and non-waterfowl  The c l a s s i f i c a t i o n o f b i r d s , with waterfowl  ducks and non-ducks i s a h i e r a r c h y .  i t can  f o r example,  further subclassified  into  I t i s n o t a s y s t e m , h o w e v e r , b e c a u s e we  20  have not  yet  dealt with  or between l e v e l s of the of  In t h i s  flow of information  the h i e r a r c h y .  feeding h a b i t s of the w a t e r f o w l  the  the  go  duck p o p u l a t i o n  population,  research  I f we  t h e n we  are  a system i s defined  as:  and/or m a t e r i a l s w i t h i n  on  t o e x a m i n e how  e f f e c t the  and/  changes i n  reproductive  t r e a t i n g the h i e r a r c h y  patterns  as  a  system.  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 formation 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 or i n d i r e c t l y , from every element (or c l a s s of elements) to every other e l e m e n t 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  channels of such i n f o r m a t i o n  feedback loops  ( L a z l o , 1972).  which receives  and  transmits  which, i n i t s l i m i t i n g  information  called  "transmission".  (A, B,  and  transmits  and  what i t r e c e i v e s . p a r t o f i t s own of  such a c y c l i c  consider ventory  accounting  C transmits  o u t p u t b a c k as  feedback as  f r o m one  t o A.  o r may  elements  t o B,  not  s t a r t i n g element e v e n t u a l l y  i n p u t , perhaps i n a l t e r e d form.  As  socio-economic  B  transform receives an  example  realm,  s e v e r a l departments, a l l of which send monthly i n -  first  clerk receives  puts i t together  year.  is a  information.  three  i f A transmits  E a c h e l e m e n t may  t o t h e company's a c c o u n t i n g the  system  element to another i s  terms a s e t of  transitivity  of  loop.  t h e name s u g g e s t s ,  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  office,  the p r e v i o u s  cyclic  as  elements, each  flow of m a t e r i a l s and/or  and/or resources  In e i t h e r case, the  d e p a r t m e n t h e a d and for  one  In logico-mathematical  a company h a v i n g reports  only  a cyclical  C) w o u l d e x e m p l i f y t o C,  r e f e r r e d to  and/or m a t e r i a l , i s a simple  Cyclic transitivity,  s o c i a l s t r u c t u r e t y p i f i e d by movement o f m a t e r i a l s  typically  A c y c l e w i t h a t l e a s t two  case, contains  Cyclic Transitivity.  The  flow are  The  first  with  office. the  the  Suppose t h a t w i t h i n  inventory  reports  report  for that  from  the  the  department  c l e r k then sends a l l t h a t i n f o r m a t i o n  to  a  21  s e c o n d c l e r k who  c a l c u l a t e s an  previous  The  it  month.  third  index  of inventory  A f o u r t h c l e r k might express  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 head.  The  i n f o r m a t i o n has  r e c e i v e d h i s own  arrangement d e s c r i b e d equal  i n complexity  this  i n f o r m a t i o n i n the  send a copy of i t back t o the  gone i n a c i r c l e  able  to a p p r e c i a t e  a b o v e , he  with  immediately  such t h a t the  the  transforms  the average r a t e f o r the  o u t p u t b a c k i n an a l t e r e d f o r m as  F o r a p e r s o n t o be  f o r the  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  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  vious year.  turnover  pre-  form of  department  department head  input.  cyclic  transitivity  in  the  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  the s o c i e t a l s t r u c t u r e b e i n g  understood.  s y s t e m s 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  Social  transitivity.  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 m u s t p e r f o r m appropriate  cognitive operations  tive operations Cyclic  Cyclic  c l a s s i n c l u s i o n i s to l i n e a r cyclic  needed to m e n t a l l y  t r a n s p i r i n g i n the ^ s o c i a l  Integration..  transitivity  transitivity.  d e a l w i t h one  circular  line,  and  tion a subordinate  cycle. , they  subroutine p r o g r a m had  relations.  transitivity  In cyclic  c y c l e are  c a l l s a subroutine,  the main program would l e a v e never been run.  The  The  Consider  subroutine  cyclic  transitivity one  In c y c l i c i n t e g r a issues  feed-  s t r u c t u r e of  a  a main program which  and w r i t e s t h e r e s u l t s . the data  and  transmitted i n  w i t h i n each o t h e r .  example.  as  c l a s s i n c l u s i o n and  element or set of elements. a familiar  transi-  transitivity  s e t o f e l e m e n t s r e c e i v e s f e e d b a c k f r o m , and  computer program p r o v i d e s reads data,  Both l i n e a r  dimension while  nested  cyclic  the  environment.  elements of the  are not  back t o , a supraordinate  simply  The  model the  i n t e g r a t i o n i s to c y c l i c  integration e n t a i l subordinate/suprordinate t h e r e i s o n l y one  a  unaltered  Without  as i f t h e  p e r f o r m s c a l c u l a t i o n s on  the  main the  22  data but without In  order  reads  t h e main program i t too would leave t h e data  t o w o r k , t h e two programs must be " i n t e g r a t e d " .  and w r i t e s data  statements  cases  unaltered.  I f t h e main program  s u c c e s s i v e l y , a s i t w o u l d i f t h e READ a n d WRITE  w e r e i n s i d e a FORTRAN D O - l o o p  f o r example, then  the executive  c o n t r o l flows i n a " c y c l e " back and f o r t h between t h e main program and t h e subroutine.  The " t r a n s m i s s i o n l i n e s " f o r t h e c y c l e w o u l d b e t h e CALL  ment a n d 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 f r o m t h e m a i n  gram, t o t h e s u b r o u t i n e , a n d b a c k a g a i n their  integration.  t r a n s f e r statements  and t h e s u b r o u t i n e according  pro-  accomplishes  Thus t h e r e l a t i o n s h i p between a m a i n p r o g r a m a n d a s u b -  routine i l l u s t r a t e s cyclic integration. control  i n a c y c l i c a l fashion  state-  With the a d d i t i o n of c o n d i t i o n a l  ( e . g . , FORTRAN I F ' s a n d GO TO's) t h e m a i n p r o g r a m  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  to contingencies.  For a socio-economic the s u p r a o r d i n a t e  example, l e t us take t h e n a t i o n a l government as  system and the telephone  company a s a s u b o r d i n a t e  The g o v e r n m e n t 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 the government  t a x revenues.  system.  a n d t h e company  gives  The company m u s t o b e y g o v e r n m e n t 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 t h e g o v e r n m e n t m u s t c r e a t e a n d / o r u p d a t e l e g i s lation  t o d e a l w i t h many c h a n g e s a n d i n n o v a t i o n s i n t h e company'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 advances). respond t o changes i n t h e p o l i c i e s response to e a r l i e r  government  Sometimes  operations  governments must  o f c o m p a n i e s t h a t t h e c o m p a n i e s h a v e made i n  regulations.  Conversely,  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 deal with e a r l i e r fies their  the social  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  structure called cyclic integration.  own e x a m p l e s o f c y c l i c i n t e g r a t i o n u s i n g  R e a d e r s may  to  exempligenerate  supraordinate/subordinate  23  p a i r s o f systems s u c h as and  i n d i v i d u a l careers,  the  f o o t b a l l team and  the the  aim  organization  of  this  Cognitive  described  p e r f o r m a n c e s , and  in this  research.  levels.  cognitive operations  i s that  t o comprehend v a r i o u s  s o c i a l e n v i r o n m e n t s can own  Theorists  be  from Freud to Piaget i n the  pattern  of  be  The  the  on.  cognitive  then the  described  and  in Piagetian  the with,  theory.  of  postulating  Although  Nevertheless, of e a r l i e r  linear  i n maturation.  To  i t s development  i t i s c l e a r from a macroscopic p e r s p e c t i v e  stages of development p r o v i d e  transitivity,  mani-  i n t e r r e l a t i o n s h i p s h a v e more commonly b e e n s e e n  s t r u c t u r e o f b e h a v i o r and  i n g t h a t mastery o v e r the  con-  1 9 7 4 ) , t h e i r manner o f  date,  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 of q u a n t i f y i n g of  that  various  and  yoked  c o u r s e o f human d e v e l o p m e n t . (Brainerd,  in  developing  i n the n a t u r a l  l i m i t e d by,  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  qualitative pattern  cognitive  structures  ordered a c q u i s i t i o n of  have a r g u e d the n e c e s s i t y  found  of  reader i s reminded  order holds,  u n d e r s t o o d t o be  i n d e v e l o p m e n t can  f e s t a t i o n and  provinces,  r e l a t e d to each o t h e r  structures  d e v e l o p m e n t a l p r o g r e s s as  stage-like progressions tinuities  i f s u c h an  are  Again,  the purpose of e s t a b l i s h i n g a case f o r the  h i s or her  so  economy  Structures  i n t h e m s e l v e s and  terms of a n t i c i p a t e d d i f f i c u l t y  child's ability  particular  s e c t i o n i s to s p e c i f y e x a c t l y what p a t t e r n s  are b e i n g s t u d i e d  under study are  i n d i v i d u a l p e r s o n a l i t i e s , the  f e d e r a l g o v e r n m e n t and  individual player  B.  The  c u l t u r e and  that  the  no  the  (Larsen,  suspect-  of s e r i a t i o n ( o r d i n 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  1977).  achievements  a n e c e s s a r y groundwork f o r  cognitive operations  to  class inclusion regularly  24  appear i n that r e s p e c t i v e order w i t h i n the stage o f concrete (e.g., Ginsberg formal  operations,  precedes c y c l i c variations us  and Opper, 1969).  Of c o u r s e t h e r e  are likely  i n t h e t i m i n g o f t h e i r appearance from c h i l d  with  t o be o c c a s i o n a l to child, but l e t  Some o f t h e s e a r g u m e n t s a r e e m p i r i c a l w h i l e  within  others  deal  t h e 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 mastery o f p a r t i c u l a r  operations. are being  W h i l e 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  examined, an a n c i l l a r y  more d e t a i l s a b o u t t h e n a t u r e w h i c h we d i s c u s s difficult  Concrete  aim of t h i s  section i s to also  o f each c o g n i t i v e s t r u c t u r e .  ordering present  The o r d e r i n  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 hypothesized  t o t h e most  least  difficult,  Stage  Seriation.  When a s k e d t o o r d e r  a s e tof sticks according  c h i l d r e n who c a n n o t 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 D u r i n g what i s a p p a r e n t l y and  transitivity  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  the major stages.  (i)  Likewise, w i t h i n the l a t e r stage of  i t c a n be a r g u e d t h a t m a s t e r y o f c y c l i c  integration.  operations  a transitional period,  e r r o r method, c o r r e c t l y o r d e r  a given  can t y p i c a l l y  the c h i l d  orderings.  can,  by a  trial  s e t o f s t i c k s b u t makes e r r o r s  when a s k e d 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 . the age o f s e v e n , t h e c h i l d  random  to length,  F i n a l l y , by  s e r i a t e without  approximately  errors or hesita-  tions . Linear Transitivity. be  subjected  to linear  Any s e t o f s t i m u l i  transitivity.  t h a t c a n be s e r i a t e d can a l s o  On t h e s i m p l e s t m a t e r i a l s a n d w i t h t h e  s i m p l e s t mode o f p r e s e n t a t i o n , m o s t s e v e n 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 mastered t h i s beginning  cognitive operation.  linear  Indeed, 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  t r a n s i t i v e operations  i f linear  t r a n s i t i v i t y problems a r e  25  presented less  using h e t e r o t r o p i c comparisons  than B ) .  I n order  to seriate,  For s u c c e s s f u l t r a n s i t i v e to C w h i l e a b r o g a t i n g  others  linear  t h e c h i l d n e e d o n l y c o m p a r e A t o B.  i n f e r e n c e t h e c h i l d must a l s o compare A  requirement  leads  ( e . g . , Formanek and G u r i a n ,  t r a n s i t i v i t y more d i f f i c u l t  1 9 7 6 ) , t h a t most c h i l d r e n w o u l d  than  ( I n h e l d e r and P i a g e t , 1964).  matrix having tives  The c h i l d  o n e empty c e l l w h i c h must b e f i l l e d  from an a r r a y o f p o s s i b l e answers.  were adapted from I n h e l d e r and P i a g e t  C.  find  seriation. The s i m p l e s t  procedure  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 t h e two-way task  than  t o t h e p r e d i c t i o n made h e r e , a n d  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 .  tion  directly  B's f o r m e r s t a t u s a s t h e o n e t h a t was t a l l e r  This additional l o g i c a l by  ( e . g . , A i s g r e a t e r t h a n B, C i s  i s presented  with a 2 x 2  u s i n g one o f f i v e  The c l a s s i n c l u s i o n  (1964).  classifica-  alterna-  tasks  used  F o r example, i n the p h y s i c a l  domain t h e s u p r a o r d i n a t e  c l a s s was "wooden b e a d s " a n d t h e two s u b o r d i n a t e  c l a s s e s were green beads  (5) and r e d beads  (2).  When a s k e d i f t h e r e w e r e  more g r e e n b e a d s o r more w o o d e n b e a d s , c h i l d r e n who h a d 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 a n s w e r e d t h a t t h e r e w e r e more g r e e n b e a d s . t h e c o m p a r i s o n b e t w e e n two s u b o r d i n a t e a subordinate  i t i s not u n t i l  argues that t h i s grouping  cation.  to Piaget  o r " o p e r a t i o n a l system".  Empiri-  t h e 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 b e -  come c o m p e t e n t wi-th t h i s g r o u p i n g  clusion operations  class.  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  ( 1 9 5 3 , p . 1 3 ) , p a r t o f t h e same g r o u p i n g cally,  confused  c l a s s e s w i t h t h e comparison between  c l a s s and the supraordinate  Logical multiplications  They  ( P i a g e t , 1953).  Kohnstamm ( 1 9 6 8 ) ,  however,  does n o t e x i s t a n d t h a t competence w i t h c l a s s i n -  develops  I n h e l d e r and P i a g e t  independently  o f competence w i t h l o g i c a l  (1964) f o u n d l o g i c a l m u l t i p l i c a t i o n  multipli-  t o b e mas-  26  tered later 1978) .  On  than c l a s s i n c l u s i o n w h i l e logical  have found the  g r o u n d s c l a s s i n c l u s i o n was  of  butes per  element, i n l o g i c a l m u l t i p l i c a t i o n the For  two.  While both operations  predicted  difficult  listed.  the  others  c l a s s i n c l u s i o n , however, the  embedded r e l a t i o n s h i p t o one  another.  same way  and  that M i l l e r , Kessel  t h o u g h t s a b o u t t h o u g h t s ....  Therefore,  on  the  bedded r e l a t i o n ,  m a s t e r e d by m o s t c h i l d r e n e a r l i e r (ii)  Systemic While the  systemic  tal as  challenging  e v e n t o 16  cyclic of  the  part  or  the about  (1978) f o u n d year  olds. embe  than c l a s s i n c l u s i o n ,  cyclic  (iii)  transitivity  linear  transitivity,  and  of  transitivity this  cyclic  and  chapter the  debated,  cyclic  integra-  systemic  i n t e g r a t i o n were  logi-  socie-  discussed  s o c i a l o r g a n i z a t i o n o f , at l e a s t most, western  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  Particular attention in this  the order  i n which these systemic  other  t o more w e l l s t u d i e d  involved understanding various f o r m a t was  i n much  i s e a s i e r t o h a n d l e t h a n an  the  s t r u c t u r e s presumably 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 the  and  other  c l a s s i n c l u s i o n h a v e b e e n much r e s e a r c h e d a n d  I n s e c t i o n A,  common f e a t u r e s  structures.  be  i n a nested  Barenboim  c o g n i t i v e s t r u c t u r e s of s e r i a t i o n ,  s t r u c t u r e s of  societies.  attri-  that l o g i c a l m u l t i p l i c a t i o n would  c o g n i t i v e s t r u c t u r e s of  t i o n have not.  t o two  Structures  c a l m u l t i p l i c a t i o n and the  more  (.1970) r e c u r s i v e t h o u g h t s  4  predicted  the  (Arlin,  a t t r i b u t e s need only  i subsume e a c h o t h e r .  assumption that a l i s t i t was  e n t a i l attending  subsumes t h e  Flavell's  t h a t t y p e o f r e c u r s i v e e m b e d d i n g t o be  t o be  a t t r i b u t e s stand  One  reverse  systemic  corresponding s o c i e t a l  section i s given  operations  to  hypothesizing  are mastered r e l a t i v e  cognitive operations.  The  systemic  aspects of p a r t i c u l a r c y c l e s .  used to p r e s e n t s u b s t a n t i v e  cognitive  information  about the  An  to  each  tasks interview  c y c l e s and  to  27  querie in two  the respondents l e v e l of understanding.  t h e two  domains i s t h e f i r s t  components o f c y c l i c  ponents of c y c l i c  The  content of the  thing described i n this section.  transitivity  are i l l u s t r a t e d .  i n t e g r a t i o n a r e a l s o examined  The  Cycles.  t e r v i e w was  T h e n , t h e two  The  The  (a b i r d ) , and a decomposer  ate the c a t e r p i l l a r . The b a c t e r i a  The  elements were a n i t r o g e n (a  (a n i t r i f y i n g b a c t e r i a ) . The  When i t d i e d  t h e b i r d was  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 (grocer).  Assuming  plant  e a t e n by  nitrifying  f o r the p l a n t . -The-elements  (WMB), t h e f l o u r m i l l ,  the  that the farmer gets 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 f o r m a commodity c y c l e . e a c h o f t h e f i v e e l e m e n t s was  The  c a t e r p i l l a r ate the p l a n t .  l e f t more n i t r o g e n i n t h e s o i l  the supermarket  mole-  caterpillar),  c y c l e u s e d i n t h e s o c i e t a l ^domain .was -the w h e a t c y c l e : ;  b a k e r y and  turns  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 -  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 .  bacteria.  com-  formal operations i n  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  The b i r d  the  l e v e l and s t a g e .  the n i t r o g e n n u t r i e n t c y c l e .  a carnivore  Next,  b e f o r e the d i s c u s s i o n  to a comparison of systemic c o g n i t i v e operations w i t h terms o f d i f f i c u l t y  cycles  For both  cycles  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  card. Cyclic Transitivity. i t y measure.  I t was  t o be a l t e r n a t e intended  to be.  T h e r e w e r e two  components t o t h e c y c l i c  n o t known b e f o r e h a n d w h e t h e r  forms o f each o t h e r ( i . e . , The  "layout"'component  highly  or not they would  out  r e q u i r e d the respondent to p l a c e  o r depended upon w h i c h o t h e r ones.  the c o r r e c t " l a y o u t " i n response to t h i s  turn  c o r r e l a t e d ) as t h e y were  i n d e x c a r d s i n d i c a t i n g e a c h e l e m e n t b e s i d e e a c h o t h e r i n s u c h a way show w h i c h o n e s n e e d e d  transitiv-  In both  as t o domains  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 d o m a i n , or  the flow of wheat/flour/bread  societal  through t h e s e r i e s o f exchanges f o r t h e  domain.  With the proper arrangement of index respondent, the i n t e r v i e w e r introduced with  the operation of c y c l i c  cards  t h e second measure o f competence  transitivity.  " t r a n s i t i v e r e c y c l i n g " component.  layed out i n front of the  T h i s m e a s u r e was c a l l e d t h e  I n t h e b i o - e c o l o g i c a l domain t h e r e s p o n -  d e n t 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 •as c a t e r p i l l a r s .  b i r d s as w e l l  The c o n c e p t 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  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 was a s k e d i f t h e same s i n g l e m o l e c u l e o f DDT  card.  explained  Then t h e r e s p o n d e n t  could ever k i l l  two b i r d s .  O p t i m a l a n s w e r s h a d t h e 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 t h e same way a s a n i t r o g e n m o l e c u l e m i g h t . initial  The m o l e c u l e n o t o n l y  element b u t a l s o passes through t h a t element  returns  to the  again.  I n t h e s o c i e t a l domain 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 v o l v e d t h e movement o f a d o l l a r b i l l the farmer c o u l d ever  through the c y c l e .  The r e s p o n d e n t was a s k e d i f  s p e n d t h e same d o l l a r b i l l  twice.  Optimal  answers  showed a n a w a r e n e s s o f t h e 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 f l o w o f wheat. t h e WMB  The f a r m e r p a y s t h e g r o c e r who p a s s e s t h e d o l l a r o n  g i v e s i t back t o the farmer t o spend  Cyclic  Integration.  F o r reasons o u t l i n e d in' the previous  former i n v o l v e s l i n k i n g  supraordinate  aspects  the elements without  of their  relations  until  again.  t r a n s i t i v i t y was p r e d i c t e d t o b e m a s t e r e d e a r l i e r The  t o the  section, cyclic  than c y c l i c i n t e g r a t i o n . attending  t o one a n o t h e r .  to the subordinate/ In cyclic integra-  t i o n , h o w e v e r , one e l e m e n t o r s e t o f e l e m e n t s i n some s e n s e s u b s u m e s elements.  The l i n k s b e t w e e n 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  other  elements  29  c a n be tion  understood  i n terms of c y c l i c  there i s a f u r t h e r requirement  distinction  i n mind.  supraordinate  By way  to keep the  of i l l u s t r a t i n g  But w i t h c y c l i c i n t e g r a -  subordinate/supraordinate  the importance of the  the s p e c i f i c  contents  of  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 tasks are  surveyed  below.  particular  dimension,  transitivity.  requirements  p r e d i c t e d t o be  the e a s i e r of the  c y c l e were the p o p u l a t i o n s the s o i l ) . The  The  Upon r e v i e w i n g  subordinate  l e v e l was  elements of the  the ecosystem of the  elements i n the s o c i e t a l  the f l o u r m i l l ,  supraordinate  The  ability on  either vival  the government.  o f e a c h e l e m e n t r e l a t i v e l y by  t h e i r v i a b i l i t y was supply  the farmers  farmers.  went b a n k r u p t .  p r o d u c t i o n quotas to prevent f l u e n c i n g the v i a b i l i t y The types  cyclic  Hence, by  inadequate  farm.  the b a k e r y ) .  f o r the f i n a n c i a l  in The  when sur-  h a r m e d i f t o o many  s u b s i d i z i n g farmers  costly overproduction,  of a l l the  nitrogen  Its positive influence  w h o l e c y c l e w o u l d be  and  by  of  imposing  t h e g o v e r n m e n t was  in-  elements. evidence  b e t w e e n t h e w h o l e s y s t e m and  r e s p o n d e d t o t h e two  components o f c y c l i c  cyclic  i t was  transitivity,  nitrogen  t h e WMB's s u b s i d i e s t o f a r m e r s  o r demand was The  taxes.  i n t e g r a t i o n s c o r e s w e r e b a s e d on  of interdependency  was  government i n f l u e n c e d the v i -  imposing  mediated through  (wheat c r o p s )  of i n d i v i d u a l  their  domain were t h e b u s i n e s s e s  the wheat c y c l e ( e . g . , the wheat farmer, l e v e l was  the  two.  ( 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  supraordinate  subordinate  t h e b i o - e c o l o g i c a l and  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  I n the b i o - e c o l o g i c a l domain, the  in  subordinate/  a l t e r n a t e m e a s u r e s w o u l d b e w i t h one  i t s parts.  i n t e g r a t i o n and,  n o t known b e f o r e h a n d how another.  of awareness of  as w i t h  These  two  cor-  the  h i g h l y c o r r e l a t e d these  30  What i s b e i n g  c a l l e d the  respondent to foresee cycle. into  For  how  "systems s y n t h e s i s "  c h a n g e s i n one  c y c l e had The  the p o t e n t i a l to a l t e r  the  populations.  ate  a whole t r o p h i c l e v e l  the  amount o f n i t r o g e n  The  w h o l e e c o s y s t e m w o u l d t h e r e b y be  standing  element c o u l d  example, i n the b i o - e c o l o g i c a l domain the  the n i t r o g e n  In the  a l t e r a t i o n s m i g h t be (i.e.,  i n the  so  drastically  e f f e c t s of  the  t u r n , would have i m p l i e d h i g h e r higher  t o be  i n f l u e n c e d by  "synthesized"  out  to e n t i r e l y  In another  and  the  and  cycle.  elements.  o f a k n o w l e d g e o f how  elimin-  reduced.  by  the  under-  flour mill.  The  farmers.  that would In these  The  of  desert.  exemplified  subsidies  subordinate  DDT  example,  permanently  s a l e s f o r wheat  taxes f o r every element i n the  t h e w h o l e c y c l e was w h o l e had  WMB  whole  equilibrium sizes  s t o c k p i l i n g o f w h e a t by  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  necessitated  the  transformed i n t o a trace was  the  the  i n t r o d u c t i o n of  carnivores; birds).  s o i l was  influence  d r a s t i c as  s o c i e t a l domain, systems s y n t h e s i s  of the  That,.in  component c h a l l e n g e d  have  cases  e f f e c t on  the  the p a r t s would  then  be i n t e r r e l a t e d . For what i s b e i n g was  presented with  The  c o r e was  one  of In  c a l l e d the  " s y s t e m s a n a l y s i s " component t h e  the problem of reducing  e l i m i n a t e d w i t h o u t the  the b i o - e c o l o g i c a l domain the the  caterpillar)  remaining elements. t h a t e a c h one  own  core.  The  top  p l a n t , b a c t e r i a and  w o u l d e v e n t u a l l y be  bread but  two  e l i m i n a t i o n of  the whole  trophic levels (i.e.,  depleted  the the  n i t r o g e n were i n t e r r e l a t e d such  i f one  were removed.  the wheat farmer.  those tasks would s t i l l  no  cycle.  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  c y c l e t h e m o s t e s s e n t i a l e l e m e n t was his  cycle to i t s e s s e n t i a l  that set of elements 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 such that  them c o u l d be  b i r d s and  the  respondent  h a v e t o be  He  In the  wheat  c o u l d h a v e made  performed.  The  elements  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 c o u l d h a v e e l i m i n a t e d any  element b e s i d e s  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  the remaining sell  set of elements  i t in his In  lated  then,  i t was  transitivity  thought  r e l a t e d p a r t s are r e l a t e d  so l o n g as  grocer  the  for in  c o u l d bake the bread  than  and  we  now  to  t h e more f a m i l i a r  the c o g n i t i v e o p e r a t i o n  the p a r t s of the c y c l e are  vice versa.  above the i n t e r r e l a t e d  cyclic  Compared t o F o r m a l ordered  that mastering  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  c o g n i t i v e demand, i t was  be more d i f f i c u l t  Having  Respondents  f u n c t i o n were accounted  t o the w h o l e , and  o f t h e w h o l e c y c l e o v e r and  (iii)  the wheat farmer  r e q u i r e s s e e i n g how  to each o t h e r w h i l e c y c l i c  additional  the bakery.  store".).  effect,  of c y c l i c  ( e . g . , "The  and  inter-  Since taking  account  e l e m e n t s seemed t o b e  predicted that c y c l i c  transitivity  the  re-  r e g a r d l e s s of  integration  an  would  domain,  Operations  t h e two  systemic  h a v e o c c a s i o n t o a s k how concrete  s t r u c t u r e s w i t h r e s p e c t to each  b o t h o f t h e m m i g h t be  s t a g e and  formal stage  ordered w i t h  other,  respect  cognitive structures  of P i a g e t ' s model. Cyclic concrete that  transitivity  stage  they are  abstract  and  cyclic  c o g n i t i v e achievements.  Systemic  Assuming that these are indeed a defense  may  be  be  cannot,  however, b e g i n by  two  distinct  postassuming  Formal operations are based  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  of t h i s assumption),  a parallel  a fifth  We  therefore formal operations.  formal logic.  for  i n t e g r a t i o n w e r e p r e d i c t e d t o be  types  of l o g i c  logic.  (see Appendix E  i t i s p o s s i b l e that systemic  operations  development d u r i n g P i a g e t ' s f o u r t h stage or t h a t they  stage unto themselves.  s e r v e some a t t e n t i o n i n t h i s  The  regard.  criteria  on  f o r i d e n t i f y i n g a stage  may de-  32  First  of a l l , the notion of a f i f t h  discussing the nature  of adult cognition.  the e x i s t e n c e o f a stage of the whole concept lenged  of stages  identifying Piaget  1977).  Third,  With  these  caveats  (1960) l i s t e d  four c r i t e r i a  of a stage  s t r u c t u r e s o f each p r e c e d i n g  Flavell  and concluded  i n mind, l e t us r e v i e w  f o ra stage.  universal invariant  t h e r e s h o u l d be e v i d e n c e  Piaget refers  (1977) a l s o l i s t s  and a b r u p t n e s s .  A full and  systemic  another.  That i s , t h e c o g n i t i v e subsequent  integration of the structures of  four stage  criteria.  Two o f them, s t r u c t u r e d ' e n -  By a b r u p t n e s s  By c o n c u r r e n c e  Flavell  leaves  sequence„but h e i n c l u d e s  Flavell  con-  ( 1 9 7 1 a ) means t h a t , " e a c h i n -  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  s h o u l d be o b s e r v e d  should f i t  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".  dividual item functioned at asymptotic,  any sense".  the c r i t e r i a  t h e r e s h o u l d be  s h o u l d be i n c l u d e d i n each  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  in  that the  Second, the stages  of hierarchization.  stage  First,  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 .  currence  chal-  suggested  s e q u e n c e w i t h r e s p e c t t o one  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  each stage.  Besides, the usefulness  stages.  a culturally  stage.  establish  W o h l w i l l (1973) has  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 . within  could ever  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 t h e o n e w h i c h was t h e  least "stage-like". for  No one s t u d y  just a vehiclef o r  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  ( e . g . , B r a i n e r d , 1978; F l a v e l l ,  which accounted  i s really  a s a n a t u r a l phenomenon.  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 one  stage  t o have been  'acquired'  F l a v e l l means t h a t a l l t h e c h i l d ' s  operations  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 .  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 would r e q u i r e another  dissertation.  logic  I n l i e u of 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 Appendix E ) . S i n c e  this  c r i t e r i o n r e q u i r e s a judgement of  r a t h e r than q u a n t i t a t i v e d i f f e r e n c e , and  the r e l e v a n t arguments are  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  are q u a l i t a t i v e l y  distinct.  In a sentence,  c l a s s i f i c a t i o n of wholes  concluded  systemic  i d e n t i f i c a t i o n of wholes w h i l e formal l o g i c 3  qualitative  that the  logic  f o c u s s e s on  philosophical two  focusses  logics  on  the comparison  the and/or  .  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 universal  4 invariant  sequence i m p l y  s c a l e w i t h r e s p e c t t o one  that, empirically another.  cluded i n the design of t h i s stage. I f the systemic w o u l d h a v e t o be The  , stages  should  form a  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 -  s t u d y as  r e p r e s e n t a t i v e s of the formal o p e r a t i o n a l  t a s k s w e r e t o become c a n d i d a t e s  for a f i f t h  c r i t e r i o n of s t r u c t u r e s d'ensemble ( l i t e r a l l y  l e v e l s w i t h i n stages  on t h e a v e r a g e .  Evidence  " s t r u c t u r e s of  t h a t would s a t i s f y  (a) t h e e x i s t e n c e o f t h e same s i z e o f a gap  difficulty  stage,  they  a G u t t m a n s t e p a b o v e 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 w h o l e .  whole"; l o o s e l y " s t r u c t u r e d wholes") i m p l i e s roughly e q u i v a l e n t  includes  Guttman  l e v e l s o f c o n c r e t e and  between the  f o r m a l t a s k s as between t h e  the  difficulty this  criterion  scalogram  systemic  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 a n d 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 w h o l e r e l a t i o n s . The t r u t h v a l u e o f f o r m a l l o g i c a l a r g u m e n t s c a n 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 . Systemic l o g i c a p p l i e s to the mental c o n s t r u c t i o n s of wholes. 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 w h o l e s a n d g o e s on t o c o m p a r e a n d c l a s s i f y them. S t a t i c w h o l e s a r e c l o s e d s y s t e m s a n d a r e a p p r e h e n d e d 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 but 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 of dynamic w h o l e s o r open s y s t e m s . Open s y s t e m s a r e c h a r a c t e r i z e d b y 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 of s t a g e s . I n a Guttman s c a l e of a b i l i t y , the 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 having passed a l l items of 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 b e t w e e n a d j a c e n t i t e m s o f a G u t t m a n s c a l e a r e G u t t m a n 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 (than  ( a ) ) g a p s among t h e d i f f i c u l t y  levels  of 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 o f t h e same s t a g e Finally,  tasks  together.  Flavell s f  c r i t e r i o n of abruptness  would r e q u i r e a short  time  s p a n 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 higher stage.  The a g e s a t w h i c h f o r m a l v e r s u s  becomes r e l e v a n t h e r e . a sudden onset  For evidence  systemic  of a f i f t h  of mastery o f the systemic  tasks a r e mastered  stage F l a v e l l would r e q u i r e  tasks.  W o h l w i l l (1973) on t h e  o t h e r hand would a l l o w f o r a g r a d u a l mastery o f t h e s y s t e m i c The concrete  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  as " p a r a l l e l "  d e v e l o p m e n t s 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  w e r e n o t met. if  logic  "ensemble".  The p a r a l l e l  the systemic  t a s k s a n d m a s t e r e d a t t h e same a g e s .  difficulty  criteria  i n t e r p r e t a t i o n would appear e s p e c i a l l y  t a s k s t u r n e d o u t t o b e o f t h e same d i f f i c u l t y  be w e a k e n e d i f t h e s y s t e m i c  The f i f t h  stage i n t e r p r e t a t i o n would greater  to a greater u n f a m i l i a r i t y with the  s u b s t a n t i v e content m a t e r i a l s used i n t h e systemic  tasks.  reason,  to familiarity  of  strong  as formal  t a s k s were more d i f f i c u l t b u t t h e i r  c o u l d be w h o l l y a t t r i b u t e d  the next  post-  s e c t i o n deals with issues related  For that  very  and domains  content.  C.  The  Domains o f C o n t e n t  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  This s e c t i o n describes' s i m i l a r i t i e s s e c t i o n i ) and then addresses  domains.  a n d d i f f e r e n c e s among d o m a i n s  the implications of d i f f e r e n t i a l  (sub-  familiarity  35 w i t h domain c o n t e n t operational (i)  tasks  including  (iii)  Comparability of The  task d i f f i c u l t y  ( i i ) comparison  and age r e l a t e d a b r u p t n e s s  of  with  formal  mastery,  Contents  content of standard P i a g e t i a n t e s t i n g procedures  comparable t o the s o c i e t a l  i s not d i r e c t l y  domain c o n t e n t , n o t o n l y b e c a u s e t h e i r  manifest  c o n t e n t s d i f f e r , b u t b e c a u s e t h e two c l a s s e s o f phenomena e n c o m p a s s e d b y t h e p h y s i c a l and s o c i e t a l principles  as w e l l .  domains e x h i b i t  different  I n terms o f m a n i f e s t  types of logico-mathematical  contents, the contents of the  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 are not. tends  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 ,  to over-represent  open*systems.  c l o s e d systems whereas t h e s o c i e t a l  I n order to extend  children's understanding  the P i a g e t i a n approach  of s o c i e t a l  chosen as an i n t e r m e d i a t e s t e p . palpable l i k e  systems,  t h e p h y s i c a l domain c o n t e n t  the s o c i e t a l  domain  domain emphasizes  to the study of  t h e b i o - e c o l o g i c a l d o m a i n was  The b i o - e c o l o g i c a l c o n t e n t  i s physically  and u n l i k e the s o c i e t a l  On t h e - o t h e r -hand t h e b i o - e c o l o g i c a l c o n t e n t like  the p h y s i c a l  domain  deals w i t h animate,  domain does, " w h i l e the " p h y s i c a l domain c o n t e n t  content. open systems is' inanimate'  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 of 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 d o m a i n , s e e A p p e n d i c i e s A, B a n d C. B r i e f l y , t h e c o n t e n t o f t h e p h y s i c a l d o m a i n 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 b e a d s o f d i f f e r e n t c o l o r s , p l a s t i c flowers of d i f f e r e n t heights, cardboard c y l i n d e r s of d i f f e r e n t h e i g h t s , a n d s o o n . The b i o - e c o l o g i c a l d o m a i n 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 concepts 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 dynamics. The e l e m e n t s i n v o l v e d w e r e 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 except 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 the l o g i c a l m u l t i p l i c a t i o n task. I n t h e s o c i e t a l domain t h e 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 c o m p a n i e d b y 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 t e r m s 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-^ inery. 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 c o m p a r e d 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 . , prime 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 a n d 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 e c o n o m i c 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 c o n c e p t s l i k e p r o f i t s , t a x a t i o n , a n d t h e l a w o f s u p p l y a n d demand i n t o a c o n 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 allows  f o r i n f e r e n c e s about  The  the d i r e c t  effects  constitutes  c a l domain i n t h a t elements  and  fish).  It is like  i t s elements  the networks  especially  which  integration.  animate  t o be  exemplar  like  the socio-economic  and  It is difficult,  systems  alive  structures,  are,  often  consequent-  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  of  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 -  o f t h e same p r i n c i p l e s . 0  Perhaps  i t i s for this  reason  f o c u s on i n a n i m a t e p h y s i c a l phenomenon  h a v e 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  systemic  might opera-  i n post-concrete cognition. Faced w i t h t h i s  shortfall,  a d e c i s i o n was  measures o f f o r m a l o p e r a t i o n s ( i . e . , of v a r i a b l e s ,  6.  are  i n t e g r a t i o n , a r e most  socio-economic  for illustrating  social  These p h y s i c a l e n t i t i t e s Systemic  physi-  (e.g., b i r d s ,  domain i n t h a t , l i k e  they form a r e open systems.  Ecosystems  which  t h e more t r a d i t i o n a l  of the task are p a l p a b l e e n t i t i e s  that Piaget's c h a r a c t e r i s t i c  tions  content  con-  Children's understanding  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  equally well suited  cyclic  judged  form open systems.  f o u n d i n open s y s t e m s . ly  the socio-economic  the primary focus of t h i s r e s e a r c h .  o f t h e b i o - e c o l o g i c a l d o m a i n was  systems,  performance.  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  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  plants,  o f c o n t e n t on  made t o i n c l u d e o n l y s t a n d a r d  i s o l a t i o n of v a r i a b l e s ,  combination  and p r o b a b i l i t y ) a s a n i d e x o f p o s t - c o n c r e t e l e v e l  think-  A l t h o u g h computer s o f t w a r e would q u a l i f y , i t i s not 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 to conclude t h a t the 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 a n h o u r , (b) i n a n i m a t e , a n d ( c ) c h a r a c t e r i z e d b y c y c l i c i n t e g r a t i o n , f o r m a n empty s e t . T h e r e 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 W a d d i n g t o n , 1976). T h e s e 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 e n 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 t o c h i l d r e n as p a r t o f a c o g n i t i v e a s s e s s m e n t t a s k .  37 ing^.  As m e n t i o n e d e a r l i e r , ' t h i s  l e v e l s between p o s t - c o n c r e t e as e v i d e n c e d  domains. the  The  o f t a s k c o n t e n t s has  I f respondents then  mains.  tasks of the  r e l e v a n c e f o r the attempt  are less  f a m i l i a r w i t h one  In the i n t e r e s t  i t i s necessary  validate  domains  to those  types  itself  content  able to d i s t i n g u i s h content  do-  related  f r o m more s e r i o u s  from the g e n e r a l p i c t u r e of c o g n i t i v e development c o n t a i n e d  Piagetian theory.  7..  societal  Such an outcome i n  the a p p l i c a b i l i t y of P i a g e t i a n theory  to  or both of these  performance d i f f e r e n c e s from d i f f e r e n c e s that might a r i s e  clearly,  l o g i c i n the  bio-ecological  t o t h e b i o - e c o l o g i c a l and  I t i s i m p o r t a n t , h o w e v e r , t o be  departures  logic,  Necessarily miss-  compare s y s t e m i c  task performance could s u f f e r .  would not v i t i a t e  systemic  gap.  the e x t e n s i o n of P i a g e t i a n theory  of content  systemic  domains.  difficulty  Issues  familiarity  of content.  societal  opportunity to d i r e c t l y  filled  Familiarity The  any  societal  domain p a r t i a l l y (ii)  t a s k s b a s e d on f o r m a l l o g i c and  i n t h e b i o - e c o l o g i c a l and  i n g , h o w e v e r , was p h y s i c a l and  d e c i s i o n allowed a comparison of  o f b e i n g a b l e t o make t h a t  in  distinction  (a) t o s p e c i f y t h e v a r i a n t o f t h e f a m i l i a r i t y  con-  I t w o u l d h a v e b e e n 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 t h e s o c i e t a l domains. That, however, w o u l d h a v e c h a n g e d t h e 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 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 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 the 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 h a v e 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 c a n be s e e n a s t h e l o w e r r u n g s o f t h e v e r t i c a l l a d d e r of 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 to P i a g e t , are the p r e r e q u i s i t e underpinnings of l a t e r , post-concrete achievements. At the p o s t - c o n c r e t e s t a g e , however, the c o g n i t i v e achievements of primary i n t e r e s t were not the formal operat i o n s b u t r a t h e r t h e 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 account f o r the c h i l d ' s u n d e r s t a n d i n g of 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 b y D e n i s K a r g b o a t t h e U.B.C. D e p a r t m e n t o f 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 the understanding of ecosystems.  38  cept t h a t i s most r e l e v a n t i n t h i s r e s e a r c h and s h i p between content  f a m i l i a r i t y and  U n f a m i l i a r i t y as F o r e i g n n e s s . with  (b) to examine the  relation-  h o r i z o n t a l de*calage a c r o s s whole domains. The  s u b j e c t ' s f a m i l i a r i t y or l a c k of i t  t e s t i n g m a t e r i a l s can p o w e r f u l l y i n f l u e n c e task performance, as s e v e r a l  c r o s s - c u l t u r a l s t u d i e s have shown ( f o r a review see G l i c k , 1975). however, many ways i n which m a t e r i a l s can be u n f a m i l i a r .  There a r e ,  G l i c k notes  cultural  d i f f e r e n c e s may  a r i s e due  o b j e c t s , or due  to d i f f e r e n c e s i n which f e a t u r e s of o b j e c t s i t i s u s u a l  note and  analyze.  to two-dimensional r e p r e s e n t a t i o n s of t h r e e  dimensional to  Used i n t h i s sense, the word " f a m i l i a r i t y " means "not  foreign".  " F a m i l i a r " m a t e r i a l s or p e r c e p t u a l / c o n c e p t u a l  indigenous  to the s u b j e c t ' s own  culture.  approaches a r e  those  Awareness of the importance of  c u l t u r a l f a m i l i a r i t y l e a d s to a g r e a t e r s e n s i t i v i t y to the p o s s i b l e e f f e c t s of f i n e r degrees of f o r e i g n n e s s .  Of p a r t i c u l a r importance i n the  r e s e a r c h i s the p o s s i b i l i t y t h a t the a d u l t world  of p o l i t i c s and  might be somewhat l i k e a f o r e i g n c u l t u r e to c h i l d r e n and  that  present economics  consequently  developmental c l a i m s about c h i l d r e n ' s a b i l i t i e s to comprehend such might e a s i l y be confounded w i t h  content  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  familiarity. U n f a m i l i a r i t y as M e a n i n g l e s s n e s s . i n the sense of c u l t u r a l f o r e i g n n e s s . l o o s e s some of i t s c r i s p n e s s when we mental d i f f e r e n c e s .  Thus f a r we The  have d e a l t w i t h  meaning of  familiarity  f a m i l i a ' r i t y , however,  move from c u l t u r a l d i f f e r e n c e s to  I t then becomes n e c e s s a r y  to speak i n terms of  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  develop-  continuous sense of  the term comes from t r a d i t i o n a l v e r b a l l e a r n i n g s t u d i e s where the more f a m i l i a r a s t i m u l u s i s , the q u i c k e r i t can be r e c o g n i z e d w i t h another s t i m u l u s p r i o r "exposure" or  can be r e l e a r n e d . "acquaintanceship".  or the q u i c k e r i t s a s s o c i a t i o n  T h i s i s f a m i l i a r i t y i n the sense of  39 At  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  familiarity  as  k n o w i n g t h i n g s a b o u t 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 importantly related  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  context,  p e r h a p s what i t s m e t a p h o r i c a l a n d / o r 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. is  familiarity  into  i n the sense of "meaningfulness",  t h e c o n t e x t o f o t h e r k n o w l e d g e i s one  to the concepts  development can be the world.  o f k n o w l e d g e and  l o o s e l y d e s c r i b e d as  In t h i s broad  f e r e n t from the e x p l o r e . Any  A s t i m u l u s t h a t c a n be  the concept  understanding. the process  meaning, f a m i l i a r i t y  i s s u e of s o c i a l understanding  attempt  familiarity  w h i c h m u s t now  to c o n t r o l f o r or assess  In this  ceases  t o be  which t h i s  importantly  The  in this  t a s k s f r o m o t h e r more f a m i l i a r to v e r i f y  a result, i t  d o m a i n t a s k s m i g h t be more content  and  (b) more d i f f i c u l t  t u r f :• m i g h t f a i l  tasks i n the l e s s f a m i l i a r s o c i e t a l come m i g h t a p p e a r t o f a l s i f y  societal an  difficult  domains. T h i s has i m p l i c a t i o n s  then i t i s p o s s i b l e t h a t respondents  t a s k s on more f a m i l i a r  of the  the g e n e r a l i z a b i l i t y of P i a g e t i a n theory  f a m i l i a r i n terms of content  in  sense would  s o c i e t y leads to  s o c i e t a l domain. I f the s o c i e t a l domain t a s k s a r e found  rates,  to  acquaintanceship  p r o p o s i t i o n that the content  e x p e c t a t i o n t h a t a l l of the s o c i e t a l  cess  dif-  r e s e a r c h s e t out  familiarity  d o m a i n t a s k s m i g h t b e m o r e f o r e i g n t o c h i l d r e n i n any  f o r the attempt  with  considered.  H o r i z o n t a l Decalage.  than  is  sense c o g n i t i v e  of f a m i l i a r i z a t i o n  i n the e a r l i e r sense of foreignness or be  placed  of f a m i l i a r i t y  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 h o l e . As is  This  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 " , linked  and,  who  structurally  domain. A t  first  t o be b o t h  to  the  (a)  less  i n terms of o v e r a l l  suc-  pass formal o p e r a t i o n a l l e s s complex glance  this  "concrete" type of  the P i a g e t i a n premise of a discontinuous  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 ,  such  out-  shift  "between-stage"  40 discontinuity  f o r s o c i e t a l content might s t i l l  a t an o l d e r a g e .  The  stage  domain owing t o e i t h e r  t r a n s i t i o n m i g h t s i m p l y be  it  such evidence  c o u l d be  found  this  t h e b i o - e c o l o g i c a l and  (iii)  Familiarity Apart  theory  and  Task  from a s s i s t i n g  to other content  particular,  of both  one  content  only i n the s o c i e t a l  of these  c o g n i t i v e o p e r a t i o n s and  familiarity  the r e l a t i v e  importance  t h e same l o g i c a l  of l o g i c a l  m e n t s . What r e m a i n e d t o be t i o n s w o u l d p r o v e t o be  comparisons  requirements  be  cases where the c o n t e n t s  (i.e.,  could  involved  logical require-  the formal  s e t s o f 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 determined  was  a developmentally  whether or not later  of  involved i n  r e s o l v e d i n t h i s manner i s t h e  o p e r a t i o n s a r e more a d v a n c e d t h a n  that both  complexity  d i f f e r e d i n terms of the f a m i l i a r i t y  i s s u e t h a t c o u l d be  of whether the systemic  of P i a g e t i a n  formal operations.'In  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  expected  rather  could also allow a  f o r both kinds of t a s k s . F i r s t ,  t h e i r c o n t e n t s . S e c o n d , t h e r e may  I t was  the  c o n t e n t s w o u l d be i m p l i c a t e d  domains, data about f a m i l i a r i t y  could assess  important  domain  s o c i e t a l domains e q u a l l y , then  i n the e v a l u a t i o n of the a p p l i c a b i l i t y  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  m e n t s . An  the  Difficulty  be made b e t w e e n t a s k s t h a t h a d  two  (b)  societal  of u n f a m i l i a r content,  comparison between s y s t e m i c  versus  i n the  g r e a t e r d i f f i c u l t y w o u l d a p p e a r more f o r m a l o r s t r u c t u r a l  than simply a matter  occur  to the n o n p a l p a b i l i t y of the c o n t e n t s . I f i t were  a n i m a t e , open s y s t e m s n a t u r e and  or  simply  of i t s content.  of decalage were observed  attributed  i n both  delayed  (a) the f o r e i g n n e s s o f i t s c o n t e n t  purely v e r b a l , non-physical nature If  be p r e s e n t , b u t  operations. achieve-  the systemic  achievement than  matter  opera-  formal  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 accounted  t h e d a t a on  ness f a c i l i t a t e s  the f a m i l i a r i t y  of task contents  an i n f e r e n c e o f t h e p r e s e n c e the matter  s o c i e t a l content  lish  o f how  ( i v ) Age The tered  priority  Second, the f a m i l i a r i t y  difficulty  and  bio-ecological  data might help  factors  that i n f l u e n c e performance  operations on  l e v e l of a t a s k i s always  r e l a t i v e to other tasks  I t i s n o t an a b s o l u t e l e v e l .  one w o u l d p a s s ) .  With  adminis-  W i t h a sample of of equal  a s a m p l e o f 11 t o 15 y e a r o l d s  w o u l d show l i t t l e v a r i a n c e .  In the present  covered  (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  a wide range o f ages  was  study  l e v e l of tasks w i t h heterogeneous a b i l i t y  to maximize the v a r i a n c e i n the d i f f i c u l t y Although  the d i f f i c u l t y  t h i s s t u d y t h e age ences i n d i f f i c u l t y  of mastery levels.  i n terms of d i f f i c u l t y t h a t one  the sample of  level,  of data  levels.  The  t a s k s were found  t a s k i s m a s t e r e d a t a l a t e r age  on  intention  level*data. focus i n  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  t h e r e c o u l d b e no  tasks  respondents  l e v e l d a t a were the c e n t r a l a n a l y t i c a l  Where two  dif-  the  same f o r m a l o p e r a t i o n a l t a s k s w o u l d 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  the d i f f i c u l t y  estab-  of those o p e r a t i o n s ,  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 w o u l d a p p e a r t o be ( i . e . , no  thereby  Level  t o t h e same r e s p o n d e n t s .  ficulty  i t could  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  to assess mastery  and D i f f i c u l t y  foreign-  This allows for  g e n e r a l i z a b l e P i a g e t i a n theory i s to  of the content r e l a t e d  the tasks designed  a c r o s s domains.  First,  or absence of h o r i z o n t a l decalage  i n general.  the developmental  independently  i n terms of  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 w a y s .  index a constant f a c t o r of task d i f f i c u l t y  and  f a m i l i a r content have been  for.  I n sum,  clarifies  less  t o be v e r y  assurance  from  t h a n t h e o t h e r by most  differ-  different  that data per children.  se  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 of the d i f f i c u l t y  level  the interpretation  data.  D. H y p o t h e s e s  In  the attempt  t o extend  domains o f c o n t e n t , t h i s of a n a l y s i s ,  the P i a g e t i a n approach t o r e l a t i v e l y  study attempts  t o show ( a ) o n t h e m i c r o s c o p i c  that the order i n which v a r i o u s operations a r e mastered  t h e same a c c r o s s d o m a i n s , a n d ( B ) o n t h e m a c r o s c o p i c the 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 ization  (e.g., stages)  study.  understand  p r e s u m a b l y be p e r f o r m i n g operations.  remains  i n modes o f c o g n i t i v e  organ-  These p o i n t 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  I n understanding  such  systems respondents  would  c o g n i t i v e operations a t l e a s t as d i f f i c u l t as formal  The e x a c t d i f f i c u l t y  o f these  systemic  cognitive operations 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 remains t o be d e t e r m i n e d . same t i m e related  factors i n accounting The attempt  translates into The  f o r the observed t o extend  a l l the hypotheses a r e independent,  section  ( i n subsection  (ii)),  ( i ) ) . Each h y p o t h e s i s  ( i . e . operative)  l e v e l s of the systemic  and m i c r o s c o p i c a s p e c t s  Before  of the f i r s t  operdomains •  hypothesis.  study deal w i t h the i s s u e s  l e v e l s of the systemic  r e l a t i o n s h i p w i t h one a n o t h e r . amined  complexity  difficulty  hypotheses i n t h i s  to the d i f f i c u l t y  Although  logical  t h e P i a g e t i a n approach t o f u r t h e r content  the macroscopic  second-and t h i r d  related  At the  some a t t e n t i o n m u s t b e 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  ( i . e . f i g u r a t i v e ) factors versus  ations.  that  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 m a i n f o c u s o f  The c e n t r a l f o c u s open systems.  level  level of analysis,  a l s o r e m a i n t h e same a c r o s s d o m a i n s .  once e s t a b l i s h e d , p r e p a r e this  unexplored  they  the nature  cognitive operations. a l s o stand i n a  contingent  of that relationship  the hypotheses themselves  w i l l be l i s t e d  i sex( i n sub-  i s e x a m i n e d i n more d e t a i l a l o n g w i t h i t s  43  corresponding (i)  List The  " n u l l hypothesis"  i n subsection  (iii).  of Hypotheses hypotheses of t h i s  study  a r e as f o l l o w s :  First. 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 determined  by a  a n a l y s i s w i l l b e t h e same a c r o s s a l l d o m a i n s . T h e d i f f i c u l t y e a s i e s t t o most d i f f i c u l t , seriation, In  linear  f o r the concrete  transitivity,  o r d e r i n g , from  t a s k s w i l l be as  logical multiplication,  class  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  difficult and  transitivity  inclusion. b e more  t a s k s w i l l b o t h b e more  than 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  t a s k s w i l l b o t h b e more d i f f i c u l t Macroscopic: cult  follows:  than a l l of the concrete o p e r a t i o n a l t a s k s . I n the b i o - e c o l o g i c a l  s o c i e t a l domains t h e c y c l i c  cult  the  stage  scalogram  than both  of the c y c l i c  Whatever o r d e r i n g s a r e observed  least d i f f i c u l t  post-concrete  staged  integration  transitivity  w i t h i n s t a g e s , t h e most  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  diffi-  difficult  tasks. diffi-  than  t a s k i n t h e same d o m a i n a n d t h e r e  w i l l b e n o G u t t m a n s t e p s b e t w e e n 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  found  i n a l l three content  domains w i t h o u t  exception.  Second. At  least  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 ,  t h e b i o - e c o l o g i c a l a n d t h e s o c i e t a l d o m a i n s , b e more d i f f i c u l t  i n both than the  The t e r m " n u l l h y p o t h e s i s " i s u s e d 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 context of 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 the a s s u 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 w o r k t h e t e r m i s used 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 which would p r e v a i l w e r e no e v i d e n c e f o u n d 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 ^ tained i n a proposed hypothesis."  44 most d i f f i c u l t to  f o r m a l o p e r a t i o n a l t a s k by  the d i f f e r e n c e i n d i f f i c u l t y  t i o n a l t a s k and  between the l e a s t d i f f i c u l t  t h e most d i f f i c u l t  t a s k ( s ) w i l l be  formal  concrete operational task.  t h e s t e p between t h e most d i f f i c u l t systemic  a margin t h a t i s comparable  f o r m a l t a s k and  t h e more  opera-  Moreover, difficult  a Guttman s t e p .  Third. The  difficulty  l e v e l o f t h e most d i f f i c u l 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 ( i i ) A Contingent Strictly o f one  hypothesis) s t a g e and  task(s) w i l l  of t a s k content  the three hypotheses of t h i s  levels  to  be  this  c o u l d f e r r e t out  strict  the i n f l u e n c e of content  (third hypothesis)  o f t h e same d i f f i c u l t y  (second  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  g e n e r a l i z e to t h e b i o - e c o l o g i c a l o r the s o c i e t a l domains  levels  independent  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 the  sequence p a t t e r n s found  difficulty  variables,  study are  I t i s p o s s i b l e to l o c a t e the d i f f i c u l t y  of the systemic  L i k e w i s e , one  not  Succession  speaking,  another.  systemic  ( f i r s t hypothesis). on  even i f the systemic  systemic  task  tasks are  observed  l e v e l s as the f o r m a l o p e r a t i o n a l t a s k s .  independence, however, t h e r e i s the p o s s i b i l i t y  Despite  of a l l three  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 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 the systemic  of a f i f t h stage of c o g n i t i v e development. c o u l d n o t be tensive.  three hypotheses of t h i s study  survive.  I f those  s t u d y no m a t t e r  stage how  ex-  d i r e c t e d a t the f i f t h  the f i n d i n g s of the present  study.  stage  The  c o u l d be v i e w e d a s t e s t s o f t h e p r e c o n d i t i o n s  f o r p o s i t i n g a f i f t h stage.  provides a t e s t of the l e a s t to  e x i s t e n c e of a f i f t h  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  c o u l d be p r e - e m p t e d b y  hypothesis.  operations are representatives  Nevertheless, future research e x p l i c i t l y  hypothesis  required  The  not  From t h i s p e r s p e c t i v e t h e f i r s t  s t r i n g e n t requirements  c o n d i t i o n s w e r e met  f o r a f i f t h stage  the second h y p o t h e s i s  hypothesis hypothesis  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 to  be met  o f the 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  i n order f o r a f i f t h  stage hypothesis  second s e t of p r e r e q u i s i t e s were found c o u l d l i k e w i s e be  construed  t i o n s t h a t w o u l d h a v e t o be could  stand or f a l l  demonstrated.  independently  The ize  Null first  Although  when c o n s i d e r e d  to the f i f t h  a r e j e c t i o n of the n u l l hypothesis The  to o b t a i n then the t h i r d  as a s u c c e s s i v e l y m o r e r e f i n e d  of each s u c c e s s i v e h y p o t h e s i s  (iii)  to remain v i a b l e .  If  this  hypothesis  s e t s of  condi-  each of the three  individually,  the  hypotheses  relevance  stage notion i s contingent  f o r each' p r e c e d i n g  upon  hypothesis,  Hypotheses n u l l hypothesis  i s t h a t the P i a g e t i a n a p p r o a c h does not  to the b i o - e c o l o g i c a l or the s o c i e t a l domains.  The  vast bulk of P i a g e t i a n  t h e o r y i s b a s e d 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  of the  inanimate  physical world.  T h e r e i s no  to  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  understanding  assurance  general-  as i s t h e case w i t h s o c i e t a l r e a l i t y . m i g h t be  ranked  discontinuities  m i g h t n o t a p p e a r o r m i g h t be n u l l hypothesis  the f i r s t  evidence  predictive hypothesis  n u l l hypothesis  s t a g e s , as we  extended world  the c o g n i t i v e operations l e v e l and  l e v e l s f r o m one  less Guttman-like.  I f the f i r s t o f any  s o c i e t a l domains. P i a g e t i a n type  in difficulty  of P i a g e t i a n theory applying w e l l  s o c i e t a l domains. h a v e no  Specifically,  i n an u n p r e d i c t a b l e o r d e r b a s e d on d i f f i c u l t y  more m a c r o s c o p i c  ample e v i d e n c e  t h a t t h e same t h e o r y c a n be  stage  the  to  In o p p o s i t i o n to the  another  first  states that there w i l l  be  i n t h e B i o - e c o l o g i c a l and c a n n o t Be  r e j e c t e d then  we  know them, i n t h e B i o - e c o l o g i c a l a n d / o r  That a u t o m a t i c a l l y r u l e s out  the p o s s i B i l i t y  of a  fifth  stage.  Cognitive operations of a f i f t h o f B e i n g more d i f f i c u l t  s t a g e w o u l d have t o meet t h e p r e r e q u i s i t e  than formal o p e r a t i o n s .  Given  that there are P i a g e t i a n  46 stages, the second n u l l hypothesis stages already discovered. at  T h e r e i s no  t h e same l e v e l o f d i f f i c u l t y  aspect  a s s e r t s that there are only those P i a g e t i a n fifth  stage.  The  as t h e f o r m a l o p e r a t i o n s a n d  of the f o u r t h stage of c o g n i t i v e development.  t h e s i s a n t i c i p a t e s t h a t on i n g s , a t l e a s t one  systemic operations  the B a s i s of d i f f i c u l t y  of the systemic  The  are therefore  o p e r a t i o n s w i l l Be  I f that p r e d i c t i o n proves  difficulty, Given  candidates  correct,  for a fifth  t h e n , on  l o c a t e d aBout as f a r a p a r t  the B a s i s of t h e i r  s t a g e would have Been  r e q u i r e t h a t i t Be ment t a s k s .  The  stage  a r e s u l t of the greater o p e r a t i v e d i f f i c u l t y  greater d i f f i c u l t y  of the tasks a s s e s s i n g the systemic  c o u l d Be w h o l l y a c c o u n t e d t h e n i t w o u l d Be  related  f o r By  unparsimonious  factors.  the g r e a t e r d i f f i c u l t y  then f u r t h e r analyses assess  the extent  for a fifth  to which the c r i t e r i a  stage  fifth  stage candidates  for  the t h i r d  for  a fifth  among t h e m .  and  stage  of the task  f o r a stage have Been  content, stage. cannot  form a separate  f o u r t h stages r e s p e c t i v e l y .  them,  introduced satisfied.  o p e r a t i o n B e i n g proposed as  t h e n i t w o u l d make s e n s e t o p u t  should  the  cognitive operations  a d d i t i o n a l d a t a c a n Be  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 The  shown t h a t  o f some s y s t e m i c o p e r a t i o n s  c a n Be p e r f o r m e d and  assesssuch  s i d e e f f e c t s of the t a s k s used to a s s e s s  F o r e x a m p l e , i f t h e r e w e r e m o r e t h a n one candidate  of the  to p o s t u l a t e the e x i s t e n c e of a f i f t h  the 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  Be w r i t t e n o f f a s a r t i f a c t u a l  I f i t c o u l d Be  formal  would  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 h a n d , a t t r i B u t e s to content  to  greater  identified.  i n t e r p r e t a t i o n of that g r e a t e r d i f f i c u l t y  greater d i f f i c u l t y  If  opera-  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  operations, a f i f t h  hypo-  Guttman s c a l e o r d e r -  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 tions.  another  second p r e d i c t i v e  l e v e l s and  are  a  the s t r u c t u r e  a cluster  analysis.  c l u s t e r , as s h o u l d  W i t h more t h a n one  the  tasks  candidate  i t w o u l d a l s o Be p o s s i b l e t o c h e c k f o r n o n - G u t t m a n  steps  47  •III. A.  METHOD Measures  B r i e f l y s t a t e d , t h e r e were t h r e e domains o f c o n t e n t i n w h i c h t h e c o g n i t i v e o p e r a t i o n s were p r e s e n t e d .  These were (a) s t a n d a r d 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 o b j e c t s (see Appendix A ) , (b) b i o e c o l o g i c a l c o n t e n t r e p r e s e n t e d 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 c o n t e n t a l s o r e p r e s e n t e d i n d r a w i n g s and words (see Appendix C) . W i t h i n a l l t h r e e domains t h e r e were tasks"*" a s s e s s i n g t h e 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 itivity  ( 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 .  I n 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 t h e proposed c o g n i t i v e o p e r a t i o n s o f (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 A p r e n d i x D f o r s c o r i n g d e t a i l s ) .  For reasons already d i s c u s s e d ,  t h e r e was no p h y s i c a l domain e q u i v a l e n t t o these measures so i n s t e a d measures were t a k e n o f t h e f o r m a l 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 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 b a b i l i t y and i s o l a t i o n o f 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  description  of a l l t h e measures w i t h s e l e c t e d r e f e r e n c e m a t e r i a l s c o n c e r n i n g t h e i r use i n other research.  1.  Some o f these s i m p l e r c o g n i t i v e o p e r a t i o n s measured ( e . g . , s e r i a t i o n ) were so elementary t h a t t h e r e might appear t o be v e r y l i t t l e a c r o s s domain v a r i a t i o n i n t h e d e s i g n o f t h e t a s k s meant t o a s s e s s them. That i s , t h e v a r i a t i o n s i n t a s k c o n t e n t may appear t r i v i a l compared t o the c o n s i s t e n c i e s i n t a s k s t r u c t u r e . T h i s was an u n a v o i d a b l e s i d e e f f e c t of i n s u r i n g a c r o s s domain c o n s i s t e n c y 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 In  all  Tasks  t h r e e d o m a i n s t h e s e r i a t i o n t a s k was b a s e d o n 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 . , F o r m a n e k a n d G u r i a n , 1 9 7 6 ) . 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 responses from concrete o p e r a t i o n a l responses 137-138).  into the series.  seriated,  t o p l a c e an a d d i t i o n a l  The b i o - e c o l o g i c a l v e r s i o n  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 w e r e . t r e e s w e r e shown b u t r e s p o n d e n t s w e r e t o l d  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 . on i n d i v i d u a l to  index cards.  an i n v i s i b l e dimension  (crowns).  the i n t e r object  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 cardboard c y c l i n d e r s .  the  pre-operational  ( G i n s b e r g and Opper, 1969;  I f a n d when t h e o b j e c t s h a v e b e e n c o r r e c t l y  polation variation involves asking the c h i l d  The  entailed  Only t h e crown o f  that the depth of the roots  The t r e e s were a l l hand  drawn  T h u s , t h e s e r i a t i o n was t o b e p e r f o r m e d a c c o r d i n g ( r o o t s ) t h a t was r e p r e s e n t e d b y a v i s i b l e o n e  S i n c e t h e s o c i e t a l d o m a i n d i m e n s i o n o f s e r i a t i o n was t o b e  invisible,  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 for  purposes  o f comparison.  The " o b j e c t s " t o be s e r i a t e d  v e r s i o n were p e o p l e ' s r i g h t s . all  Respondents were t o l d  money h a d t h e r i g h t  t o use i t f i r s t .  s h o w i n g how many $ 1 0 0 b i l l s to use  i n the s o c i e t a l  domain  t h a t seven f a r m e r s had  c o n t r i b u t e d d i f f e r e n t a m o u n t s o f money t o j o i n t l y b u y a t r a c t o r .  two f a r m e r s b o t h w a n t e d t o u s e i t a t o n c e ,  domain  Where  t h e o n e who h a d p u t i n t h e m o s t  F o r e a c h f a r m e r t h e r e was a n i n d e x c a r d  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 w e r e  asked  u s e t h e i n d e x c a r d s t o q u e u e t h e f a r m e r s o n a d a y when t h e y a l l w a n t e d t o 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  transitivity  tasks followed  the standard procedures  49 i n v e s t i g a t e d by  G l i c k and  f e r e n t h e i g h t s and  Wapner ( 1 9 6 8 ) .  d i f f e r e n t numbers o f eggs. In the s o c i a l content  three d i f f e r e n t  They w e r e d e p i c t e d g r a p h i c a l l y on  by  t h r e e p a p e r mache d o l l s ,  dress appropriate to t h e i r r o l e s .  much e a c h o n e ,  species of b i r d s which  difIn  the  layed  index  cards.  domain t h r e e o c c u p a t i o n a l r o l e s (prime 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  how  c y l i n d e r s of  c o l o r s were employed i n the p h y s i c a l domain t a s k .  b i o - e c o l o g i c a l d o m a i n i t was  wearing  Three cardboard  "had  to say  The  a l l t h e same  dimension of comparison  about what the laws would  was  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 d o m a i n s was t h e two-way c l a s s i f i c a t i o n t a s k  size,  ( I n h e l d e r and P i a g e t , 1 9 6 4 ) .  assessed  The  by  intersecting  d i m e n s i o n s i n the 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 q u a r e s ) and card.  One  color (red, yellow).  of the  f o u r c e l l s was  A  t w o f o l d m a t r i x was  empty.  The  c h i l d was  presented  on an  card would " f i t  i n t h e empty c e l l .  the s o c i a l domain  stimuli  b i o - e c o l o g i c a l and  f o r the m a t r i c e s were t y p e w r i t t e n words.  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 , eating).  The  b i r d ) and  diet  I n h e l d e r and  Piaget's  f o r use w i t h c o n t e n t superordinate  the  bio-  (meat-eating,  plant-  versus  flour. (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  from the t h r e e domains.  c l a s s was  five  best"  intersecting  I n the s o c i a l domain the c h o i c e s were between p r o d u c e r s  consumers of wheat v e r s u s  index  asked which of the  a l t e r n a t i v e answers d i s p l a y e d at the bottom of the In both"the  (stars,  For  the p h y s i c a l domain  wooden b e a d s w i t h c o l o r a s t h e  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 d o m a i n was  subclasses.  " b i r d s " and  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 d u c k s and  crows.  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 a n  index card.  elements of the s u p r a o r d i n a t e  s o c i a l domain.  c l a s s i n the  adapted  the  the  The  subclasses  These were  So w e r e t h e The  supra-  index  type-  particular card  50 d i s p l a y e d n o u n p h r a s e s f o r e a c h o f t h e members o f t h e w h e a t m a r k e t i n g  board.  Some w e r e p r o d u c e r r e p r e s e n t a t i v e s ; some w e r e c o n s u m e r r e p r e s e n t a t i v e s . A l l were government (ii)  appointees,  The F o r m a l T a s k s The c o m b i n a t i o n  a v e r s i o n by S i l l s logical  o f v a r i a b l e s p r o c e d u r e was a d a p t e d By A r l i n  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  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  C o l o r l e s s Chemical Bodies"  task.  button  atop  electrical  three buttons the box.  switches  (1978) f r o m  (1958) " c o m b i n a t i o n  The c h e m i c a l s  o f C o l o r e d and  a r e replaced by f i v e  a s m a l l b l a c k box.  push  O n l y one c o m b i n a t i o n  pushed s i m u l t a n e o u s l y would 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  One b u t t o n was n o t w i r e d  r a t h e r than c l o s e d , t h e c i r c u i t  of atop  ( 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 ,  (the analogue o f t h e n e u t r a l i z i n g  The m e a s u r e o f c o m p r e h e n s i o n o f p r o b a b i l i t y was A r l i n ' s  chemical).  (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 116-130). Bowl.  (1975;  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 m i x e d i n a  Respondents estimated  twice without  the p r o B a B i l i t y o f drawing a p a r t i c u l a r  color  replacement.  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 B y K u h n a n d Ho 0-977) w i t h minor adaptations by Chandler,  S i e g a l and Boyes (1980) and t h e a u t h o r .  R e s p o n d e n t s w e r e 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 , s e v e n r o s e s a n d seven l e a f y p l a n t s . were b e i n g  They were t o l d  fed to the plants.  each p l a n t t o r e p r e s e n t were t a l l e r and  than others.  efficient  comBination  t o imagine that three types  Plastic vials with lettered  the p l a n t food Being  l a b e l s stood  fed to that plant.  Respondents were asked t o i d e n t i f y o f p l a n t foods  of plant  Beside  Some p l a n t s  t h e most  t o produce t a l l p l a n t s .  foods  effective  51 (iii)  The  Systemic  Tasks  Cyclic transitivity  and  cyclic  format d e v i s e d f o r t h i s study. a n t was  asked what would  standardized probes  i n t e g r a t i o n were a s s e s s e d i n an  A s i t u a t i o n was  happen n e x t .  and w h a t e v e r  cycles  (Kargbo,  1979).  about  The  T h i s was  then the  f o l l o w e d by more  reduce  I n the b i o - e c o l o g i c a l domain  the systemic r e l a t i o n s i m p l i c i t  interviews,  i n nutrient  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 the s y s t e m i c  r e l a t i o n s i n the 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 of the Canadian industry.  Specifically,  i t i n v o l v e d ' t h e wheat commodity c y c l e from  f a r m e r , t o the wheat m a r k e t i n g b o a r d , the r e t a i l e r , back to the (iv)  to the f l o u r m i l l ,  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  w i t h the m a t e r i a l s and/or  For the c o n c r e t e t a s k s the f a m i l i a r i t y "Do  does?").  The  post-concrete f a m i l i a r i t y  sell  familiar  the  i n the task.  do y o u  assessments  tell  how  deep a  Do y o u know w h a t  he  took  the  For example, f a m i l i a r i t y w i t h the concept  a s s e s s e d b y a s k i n g , " I f t h e g r o c e r b o u g h t b r e a d a t 80<;/loaf,  i t f o r more t h a n 80<:,  or  80C?"  For reasons d i s c u s s e d i n the i n t r o d u c t i o n ,  i t was  tinguish familiarity interdependent.  tree's  w e r e more c o n c e p t u a l  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 a s s e s s m e n t s  form of p r e l i m i n a r y problems. p r o f i t was  to  items were l e s s c o n c e p t u a l (e.g.,  "Have y o u e v e r h e a r d o f a j u d g e b e f o r e ?  and more e x t e n s i v e .  he  concepts b e i n g used  y o u know w h a t t h e s e b e a d s a r e made o f ? " ; "How  r o o t s go?"'  the  farmer. f o r Systemic  was  wheat  to the bakery,  F a m i l i a r i t y Assessments  respondent  respond-  specific  a d d i t i o n a l probes were needed t o  ambiguity or confusion i n responses. t h e respondents were asked  d e s c r i b e d and  interview  l e s s t h a n 80<;,  important to  from o p e r a t i v e u n d e r s t a n d i n g even though  I t o b v i o u s l y would  n o t do  to f a m i l i a r i z e  of would  dis-  t h e y may  be  s u b j e c t s w i t h the  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 assessed  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  the  task.  Conversely,  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 of competence w i t h a p a r t i c u l a r o p e r a t i o n w o u l d be  u n j u s t i f i e d when t h e r e  d e n t s knew e n o u g h a b o u t t h e apply  c o n s t i t u e n t elements of the  that p a r t i c u l a r cognitive operation meaningfully  These c o n s i d e r a t i o n s suggested the of understanding etc.  i s a reasonable  of  cognitive  doubt t h a t  t a s k t o be i n ' some  respon-  able  then i n t r o d u c i n g the  to  context.  s t r a t e g y o f i d e n t i f y i n g a minimum  (or " f a m i l i a r i t y with")  f o r e a c h t a s k and  the  level  the m a t e r i a l s , concepts,  premises,  task with, i n s t r u c t i o n s designed  2 to provide of t h i s  that l e v e l of understanding  s t r a t e g y a l l o w s one  unfamiliarity  5,  c o m p l e t e d g r a d e 12  7,  at each grade l e v e l ,  8-7;  g r a d e 5,  port-secondary,  elementary school the and  9,  and  The  12-5;  use  l e v e l of the  task  g r a d e 9 and  An  T h e r e w e r e 8 m a l e s and  8  females  a d d i t i o n a l 8 m a l e s and  8  females  academic year. i n years g r a d e 9,  g r a d e 3, 11  5,  and  and 14-7;  The  mean a g e s o f  months, were: grade 11,  grade  3,  16-10; f i r s t  7 respondents were from  respondents attended  respond-  year  an  a secondary  school,  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 w e r e e i t h e r f u l l - t i m e members o f t h e w o r k  f o r c e or post-secondary students. metropolitan  2.  the  the"familiarity/  the o v e r a l l d i f f i c u l t y  11.  expressed  g r a d e 7,  18-11.  by  Respondents  the previous  ents  10-8;  i n f l u e n c e of  s u b j e c t s were t e s t e d .  i n e a c h o f g r a d e s 3, had  on  i n f o r m a t i o n gained  respondents. B.  A t o t a l o f 96  The  t o gauge t h e  of the task contents  f o r the whole sample of  .  A l l schools were i n the  greater Vancouver  area.  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 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 g o o d  introexample.  53 The elementary and secondary s c h o o l s t u d e n t s were randomly  selected  from a p o o l o f p o t e n t i a l respondents t h a t remained a f t e r t h e f o l l o w i n g cons t r a i n t s has been met.  F i r s t , t h e s t u d e n t had t o be E n g l i s h s p e a k i n g , b u t  E n g l i s h d i d n o t have t o be t h e s t u d e n t ' s n a t i v e language.' had t o v e r b a l l y agree t o v o l u n t a r y p a r t i c i p a t i o n .  Second, t h e s t u d e n t  T h i r d , t h e number o f males  and females had t o be e q u a l a t each grade l e v e l . F o u r t h , t h e s t u d e n t ' s ' p a r t i c i p a t i o n had t o have been approved t h r o u g h t h e s t a n d a r d c h a n n e l s f o r o b t a i n i n g p e r m i s s i o n t o conduct r e s e a r c h i n s c h o o l s . An attempt was made t o match t h e sample o f f i r s t y e a r p o s t - s e c o n d a r y respondents t o t h e p o p u l a t i o n o f g r a d u a t e s from t h e secondary s c h o o l t h e p r e v i o u s academic y e a r .  The c h a r a c t e r i s t i c on w h i c h t h e m a t c h i n g  attempt  was made was f u l l time e d u c a t i o n a l o r o c c u p a t i o n a l s t a t u s i n t h e f i r s t p o s t secondary y e a r . year.  S c h o o l r e c o r d s were a v a i l a b l e f o r g r a d u a t e s o f t h e p r e v i o u s  The r e c o r d s i n c l u d e d t h e s t u d e n t s ' 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 u c a t i o n a l and/or o c c u p a t i o n a l a c t i v i t i e s f o r t h e i r f i r s t year.  post-secondary  E x c l u d i n g those who gave no c l e a r i n d i c a t i o n o f what they would be  d o i n g , 47% o f t h e s t u d e n t s a n t i c i p a t e d becoming f u l l - t i m e members o f t h e work force.  Fourty-two p e r c e n t 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 o r t e c h -  n i c a l school.  Eleven percent a n t i c i p a t e d attending a u n i v e r s i t y .  The p r o -  p o r t i o n o f f i r s t y e a r p o s t - s e c o n d a r y respondents i n t h i s study who were  full-  time members o f t h e work f o r c e i s e s p e c i a l l y l o w by comparison t o t h e e s t i m a t e s o b t a i n e d from t h e secondary s c h o o l g r a d u a t e s .  A good d e a l o f time and e f f o r t  was expended t o a m e l i o r a t e t h i s c o n d i t i o n b u t t o l i t t l e a v a i l .  The p r o p o r t i o n s  o b t a i n e d i n t h i s s t u d y were 25% f u l l - t i m e members o f t h e work f o r c e , 37.5% a t t e n 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% a t t e n d i n g a university.  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. 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  campus o f D o u g l a s C o l l e g e . work f o r c e were r e c r u i t e d who h a d e l i g i b l e  friends  The r e s p o n d e n t s a t t e n d i n g a c o m m u n i t y Westminster  The r e s p o n d e n t s who w e r e f u l l - t i m e members o f t h e e i t h e r through the p a r t i c i p a t i n g u n i v e r s i t y  students  Ctwo r e s p o n d e n t s were o b t a i n e d b y t h i s means) o r  through the author's'personal f r i e n d s ,  r e l a t i v e s , a n d a c q u a i n t a n c e s Ctwo more  respondents).  C.  Procedure  This section i s divided into  two p a r t s :  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 .  procedures f o r c o l l e c t i n g the  A f t e r describing the data  collection  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  discussed. (i)  Data For  to  Collection 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  55 m i n u t e s .  strictly  These s e s s i o n s were r e f e r r e d  speaking, part of  interviewing.  t o as " i n t e r v i e w s " even  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  W i t h t h e e l e m e n t a r y and secondary  views were conducted  i n offices  i n the school.  to  I n the elementary school the to the  I n the secondary s c h o o l groups of 4 t o 6 s t u d e n t s were  t h e m a i n o f f i c e when d a i l y a n n o u n c e m e n t s w e r e made.  s t u d y was b r i e f l y  than  school students the i n t e r -  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 i n t e r v i e w room.  though,  e x p l a i n e d t o them and t h e y w e r e a s k e d  A t that time the to volunteer.  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 t h e m t o come t o t h e i n t e r v i e w r o o m the  approval of t h e i r teacher'for that c l a s s time p e r i o d .  p a r e n t s had n o t d i s a l l o w e d  called  If pending  S t u d e n t s whose  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  from  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 , f i r s t year post-secondary students  With the  t h e u n i v e r s i t y s t u d e n t s and t h e community  c o l l e g e s t u d e n t s were i n t e r v i e w e d i n P s y c h o l o g y Department r e s e a r c h  rooms.  Two o f t h e w o r k i n g ' r e s p o n d e n t s were a l s o i n t e r v i e w e d i n a U.B.C. P s y c h o l o g y Department r e s e a r c h room.  One was i n t e r v i e w e d i n h e r own home and one was  i n t e r v i e w e d a t t h e home o f a mutual  acquaintance.  The i n t e r v i e w s themselves c o n s i s t e d o f 19 t a s k s .  These were 12 c o n c r e t e  o p e r a t i o n a l t a s k s (3 domains x 4 c o g n i t i v e o p e r a t i o n s ) , 3 f o r m a l t a s k s , and 4 s y s t e m i c  operational  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 ) .  The o r d e r o f t a s k p r e s e n t a t i o n was Concrete  Standard Domain (Appendix A., S e c t i o n s (i) to ( i v ) )  B i o l o g i c a l Domain (Appendix B, Sections ( i ) to (iv))  S o c i a l Domain (Appendix C, Sections ( i ) tio ( i v ) )  Formal  Appendix A, S e c t i o n (v)  1.  Seriation  2.  Linear  3.  Logical Multiplication  4.  Glass I n c l u s i o n  5.  Seration  6.  Linear  7.  Logical Multiplication  8.  Glass I n c l u s i o n  9.  Seriation  Transitivity  Transitivity  10.  Linear  Transitivity  11.  Logical Multiplication  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  Systemic  B i o l o g i c a l Domain (Appendix B, S e c t i o n (v) and Appendix D)  15.  I s o l a t i o n of Variables  16.  Cyclic Transitivity  17.  Cyclic Integration  S o c i a l Domain (Appendix C. S e c t i o n (v) and Appendix D)  18.  Cyclic Transitivity  19.  Cyclic Integration  Owing t o s c h e d u l i n g d i f f i c u l t i e s f o u r o f t h e e l e m e n t a r y s c h o o l received the systemic  students  t a s k s , as a b l o c k , b e f o r e t h e c o n c r e t e and f o r m a l b l o c k s . 3  The  o r d e r o f t a s k p r e s e n t a t i o n w i t h i n b l o c k s was always t h e same . The  d e t a i l s o f how each o f these t a s k s were a d m i n i s t e r e d and s c o r e d  are presented  i n the appendicies  i n d i c a t e d above.  o f responses on t h e c o n c r e t e and f o r m a l t a s k s . tasks were tape r e c o r d e d  W r i t t e n r e c o r d s were made  Responses on t h e s y s t e m i c  and some were a l s o w r i t t e n .  The t a s k s covered  a  v a s t range o f a b i l i t i e s w i t h some b e i n g c h a l l e n g i n g t o 8 y e a r o l d s and o t h e r s b e i n g c h a l l e n g i n g t o 18 y e a r o l d s .  S i n c e t h e s e r i e s o f t a s k s were  i n an o r d e r r o u g h l y t h o u g h t , f o r t h e o r e t i c a l r e a s o n s ,  presented  t o 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 t h a t t h e most d i a g n o s t i c phases o f the i n t e r v i e w f o r p a r t i c u l a r r e s p o n s e s would g r a d u a l l y s h i f t f r o m t h e e a r l i e r to t h e l a t e r t a s k s as t h e t e s t i n g proceeded from t h e youngest t o t h e o l d e s t respondents.  There a r e advantages and d i s a d v a n t a g e s  on an a p r i o r i b a s i s . "experimenter"  to ordering presentation  The danger i n making t h e p r e s u p p o s i t i o n I s t h a t  e x p e c t a n c y , 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 t o i n s u r i n g t h e expected 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 .  The advantage  i s t h a t s t e p s can be taken t o a v o i d l o o s i n g r a p p o r t w i t h t h e respondent. B e f o r e d e a l i n g w i t h t h e nexus between o r d e r o f t a s k p r e s e n t a t i o n and r e s p o n d ent r a p p o r t we w i l l r e v i e w t h e measures adopted t o guard a g a i n s t e x p e r i m e n t e r expectancies 3.  i n f l u e n c i n g the r e s u l t s .  F u l l c o u n t e r b a l a n c i n g o f o r d e r o f t a s k p r e s e n t a t i o n would have r e q u i r e d over a m i l l i o n respondents i n o r d e r t o have one respondent p e r o r d e r . F u l l r a n d o m i z a t i o n o f o r d e r o f p r e s e n t a t i o n would have extended t h e d u r a t i o n o f each s e s s i o n Beyond t h a t p e r m i t t e d by b o t h t h e s c h o o l a u t h o r i t i e s and t h e a t t e n t i o n spans o f t h e c h i l d r e n .  57 First,  i n the elementary  a v a i l a b l e as an a s s i s t a n t . and  The  f o r m a l o p e r a t i o n a l t a s k s and  views. in  s c h o o l , a Ph.D.  The  The  second  the author administered the systemic kept  t h e c o m m u n i c a t i o n o f any  step taken to guard  expectancies.  against experimenter  t a s k s beyond the supposed d i f f i c u l t y  task.  I t was  n o t assumed t h e f i r s t  sarily  s i g n a l e d a s t r i n g of f a i l u r e s  expectancy  l e v e l of t h e i r f i r s t  S i n c e one  of the prime  i t was  to avoid  (a) o v e r w h e l m i n g t h e y o u n g e r r e s p o n d e n t s and  (b) i n s u l t i n g  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 . complex c y c l i c in and  grades  3 and  0'Brian  hension  i n t e g r a t i o n items  The  t o be  responses  of  succeeded this policy  Patterson,  or monosyllabic  a n y w a y , i t was cyclic  decided  3 to 5 respondents  The  responding"  been  leaving  E s p e c i a l l y w i t h the grade 3 c h i l d r e n , the d i f f i c u l t  justification  None o f t h e  f o r b r i n g i n g them so c l o s e t o s u c h  they  implementation  i n e a c h grade had  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 of the i n t e r v i e w , but little  and  i n t e g r a t i o n items unless  i n t e g r a t i o n items l e d to q u i t e despondent demeanours.  be  Cosgrove,  t h a t they would  i n t e r v i e w e d ) made a m a r k e d 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 t h e i n t e r v i e w room.  young  i n d i c a n t s o f non-compre-  at the s i m p l e r , q u a s i - p r e r e q u i s i t e items. ( a f t e r the f i r s t  prob-  three to f i v e students interviewed  Since t h e i r non-responding  n o t b e 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 had  with  m o s t r o b u s t i n d i c a n t s a r e more h a n d movements  coded as " f a i l i n g "  con-  When p r e s e n t e d w i t h - t h e m o r e  (1980) have documented r e l i a b l e n o n v e r b a l  longer reaction times. had  the f i r s t  neces-  respondents,  the i n t e l l i g e n c e of  5 became e i t h e r " f i d g e t y " o r u n r e s p o n s i v e .  in children.  with  f a i l u r e a f t e r a s t r i n g of successes to follow.  the  unsuccessful  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  lems f a r beyond t h e i r a b i l i t i e s  was  w o u l d be p r e s e n t e d  cerns i n a b i l i t y important  inter-  t o a minimum a t t h a t p o i n t  adoption of the general r u l e that a l l respondents all  was  a s s i s t a n t administered the concrete o p e r a t i o n a l  c o m m u n i c a t i o n b e t w e e n t h e m was  order to minimize  candidate i n psychology  cyclic  children  t h e r e seemed emotions.  to  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 with a seriation  t a s k . The t e n d e n c y 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 adolescents concrete  the " c h i l d i s h "  l e v e l of the task. I n p i l o t  w i t h p r o b l e m s t h a t do c h a l l e n g e  the only concrete  staged  task presented  classified  among t h e f i f t e e n three  few grade 9 s t u d e n t s  i n t e r e s t and r a p p o r t  task.  Likewise,  o n l y two f a i l e d  two o f  m i g h t h a v e f a i l e d e v e n more  concrete  t h e b e n e f i t s i n terms o f respondent  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  that  information,  Scoring concrete  scoring c r i t e r i a  and f o r m a l  tasks were scored  u p o n a d m i n i s t r a t i o n . The  f o ra l l tasks are described i n the appendicies  h e a d i n g f o r e a c h t a s k . The s y s t e m i c the procedures described be  o n l y one o f t h e s e v e n  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 -  t a s k s had such t a s k s been p r e s e n t e d ,  The  i n grade 9 o r  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  formal o p e r a t i o n a l grade 9 students  mains t h a t a very  Data  I n view  f o r this resides i nthe  t h a t i n g r a d e 7, w h e r e a l l t a s k s w e r e p r e s e n t e d ,  students  (ii)  their intellects.  to students  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  staged  with  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  of t h i s ,  the  interviews  t e n d e d 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  are f i n a l l y presented  finding  o l d i s presented  r e f e r r e d to here,  follows i s a brief  t a s k s were s c o r e d  l a t e r according to  i n A p p e n d i x D. T h e j u d g e s o r " s c o r e r s " , a s t h e y  scored  only the c y c l i c  summary o f t h e t r a i n i n g a n d s c o r i n g  the i n t e r v i e w were t r a n s c r i b e d verbatim. tasks  will  i n t e g r a t i o n i n t e r v i e w s . What procedures.  When a l l t h e d a t a h a d b e e n c o l l e c t e d , t h e t a p e r e c o r d e d  transitivity  under the  The a u t h o r  ( s e e A p p e n d i x D ) . The c y c l i c  scored  sections of  the c y c l i c  integration sections of the  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 i n d e p e n d e n t l y r a t e d by two female s c o r e r s ^ . I t was i m p o s s i b l e t o t e l l how l o n g i t would t a k e t h e t r a i n e e s t o r e a c h t h e 90% c r i t e r i o n o f agreement t h a t had been p r e v i o u s l y chosen as a g o a l o f t h e training.  As i t t u r n e d o u t , t h e s c o r e r s agreed w i t h e a c h o t h e r on 81.2% o f  the items by t h e time they had s c o r e d 1/5 o f t h e d a t a .  They s t a y e d between  83.2% and 86.4% f o r t h e r e m a i n i n g f o u r f i f t h s and f o r a r e s c o r i n g o f t h e f i r s t fifth.  The o v e r a l l agreement r a t e f o r t h e 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 s p a r e grade 11 p r o t o c o l and two f i c t i c i o u s p r o t o c o l s , t h e s c o r e r s and a u t h o r t h e n met a f t e r each s u c c e s s i v e 20 p r o t o c o l s had been scored"*. W i t h i n each " b a t c h " o f 20 p r o t o c o l s t h e respondents were a r r a n g e d i n a second random o r d e r .  The o r d e r i n w h i c h t h e respondents had been i n t e r -  viewed was o n l y random w i t h i n grade l e v e l s .  The o r d e r i n w h i c h t h e s c o r e r s  r e c e i v e d t h e p r o t o c o l s was random a c r o s s t h e whole sample.  There were s i x  of these " r e l i a b i l i t y check" meetings a t a r a t e o f a p p r o x i m a t e l y two p e r week. At each o f t h e r e l i a b i l i t y check meetings s p e c i f i c i t e m s o f disagreement discussed.  were  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 s c o r e s was a m a j o r i t y agreement.  I n 80% o f t h e c a s e s , however, spontaneous u n a n i m i t y was a c h i e v e d .  4..  One was a 25 y e a r o l d t e a c h e r and t h e o t h e r was a 20 y e a r o l d p s y c h o l o g y major. They were p a i d from a d i s c r e t i o n a r y g r a n t awarded by t h e E d u c a t i o n a l Research I n s t i t u t e o f B r i t i s h Columbia. The s c o r e r s made t h e i r r a t i n g s from the p r o t o c o l s . T h i s added c l e r i c a l s t e p had two advantages over h a v i n g t h e s c o r e r s make t h e i r r a t i n g s d i r e c t l y from a u d i o tapes t h e m s e l v e s . First, i t reduced t h e p o s s i b i l i t y o f a r t i f a c t u a l c o n t a m i n a t i o n o f t h e s c o r e s on t h e 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 t h e age o f t h e r e s p o n d e n t s . The s c o r e r s might have been prone t o a s s i g n lower s c o r e s t o younger respondents and h i g h e r s c o r e s t o o l d e r respondents on a t 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 o f responses i n t o p r o t o c o l s was an attempt t o m i n i m i z e t h e o p p o r t u n i t y f o r such a r t i f a c t s . Second, many o f t h e audio tapes were f l a w e d by h i g h l e v e l s o f background n o i s e . I f s c o r e r s had had t o decode s i g n a l s a g a i n s t such h i g h n o i s e l e v e l s , t h e i r t a s k would have been immensely more cumbersome and time consuming.  5 .  One b a t c h o f p r o t o c o l s c o n t a i n e d o n l y 16 p r o t o c o l s s i n c e t h e t o t a l number o f respondents was 4 s h o r t o f 100.  60 IV.  RESULTS  As m e n t i o n e d 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 , study a r e arranged'such hypotheses  that a failure  automatically implies a failure  A t l e a s t o n e o f t h e two l e v e l s n u l l hypothesis-must second  to reject  ( i . e . , macroscopic  hypotheses  null  hypotheses.  n u l l h y p o t h e s i s were n o t  h y p o t h e s i s would n o t have been  A s i t t u r n s o u t , t h e phenomena p r e d i c t e d b y t h e f i r s t were observed.  testing the third  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  hypothesis.  The o r g a n i z a t i o n o f t h i s  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 . reviewed  and second  through t o  chapter r e f l e c t s the  The f i r s t  hypothesis  a n d 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 .  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 . is  later  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  unrejected.  is  null  vs. microscopic) of the f i r s t  L i k e w i s e , i f t h e second  t h e phenomenon d e a l t w i t h b y t h e t h i r d  observed.  earlier  of this  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  h y p o t h e s i s a r e met.  rejected  to reject  t h e hypotheses  That i s f o l -  Then t h e second  hypothesis  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 -  tive  evaluation are discussed.  presented  the third  A f t e r those s t a t i s t i c a l  hypothesis i s reviewed.  Again,  a n a l y s e s have been  the s t a t i s t i c a l  approaches  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  basic data i n t h i s  study were dichotomous s c o r e s .  commented u p o n t h e r e l a t i v e l y  undeveloped  state of the statisticians  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 t h e s e s s u c h a s t h o s e common i n d e v e l o p m e n t a l  c l a r i t y of the results i n this  have  art with  a n a l y s e s , e s p e c i a l l y f o r hypo-  psychology  a r e common ( e . g . , W o h l w i l l , 1 9 7 3 ; F r o m a n & H u b e r t , relative  Many a u t h o r s  where o r d e r  1980).  predictions  Fortunately, the  study coupled w i t h the o r d i n a l  nature  61  o f t h e p r e d i c t i o n s make i t e a s y t o c i r c u m v e n t lacuna.  The  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 a n d  ( 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 f i n d i n g s w i t h respect to the f i r s t  that warranted  more d e t a i l e d a t t e n t i o n .  c o g n i t i v e o p e r a t i o n s were of extremely  hypothesis  The  s e c t i o n B.  composite scores f o r the  diverse d i f f i c u l t y  levels.  s c o r e s and  f o r h y p o t h e s e s t h r e e and  s e c t i o n F a l l of the r e s u l t s are  A.  will  included peculiarities systemic  Therefore  reanalysed  in  S e c t i o n C c o n t a i n s the r e s u l t s f o r the second h y p o t h e s i s .  E show t h e a n a l y s e s  The  parametric  case) i n a p p r o p r i a t e .  t h e y w e r e decomposed i n t o t h e component s y s t e m i c  D and  that  T h i s i s a s i t u a t i o n i n which the dichotomous data, the o r d i n a l p r e d i c -  t i o n s , and analyses  t h e d i f f i c u l t i e s posed by  four respectively.  In  summarized.  F i r s t Hypothesis  w i t h Composite Systemic  b a s i c t h r u s t of the f i r s t hypothesis  h a v e t h e same r e l a t i o n s h i p s  T h a t i s , one  Sections  t o one  need not d r a s t i c a l l y  Scores  i s that the c o g n i t i v e o p e r a t i o n s  another  r e g a r d l e s s of content  domain.  reformulate P i a g e t i a n theory i n order  to  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 content. The  There w i l l  be  cognitive operations w i l l  sequential order. predictions. The  still  One  a concrete still  s t a g e and  a post-concrete  b e m a s t e r e d i n p r e t t y much t h e  More s p e c i f i c a l l y ,  the f i r s t  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  seriation,  linear transitivity,  be  same  h y p o t h e s i s makes two  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  orderings of c o g n i t i v e operations w i l l  stage.  v e r s i o n of the difficulty  t h e same a c r o s s d o m a i n s  logical multiplication,  class  related  (i.e.,  inclusion,  other.  62 cyclic  transitivity*  hypothesis  cyclic  integration''').  T h e more m a c r o s c o p i c v e r s i o n o f  o n e c o m p l e m e n t s 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 d o m a i n s w h i l e p r e d i c t i n g t h a t i n no d o m a i n w i l l t a s k s o f d i f f e r e n t  stages be m i s o r d e r e d .  Stated  d i f f e r e n t way, t h e s e c o n d 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 p r e d i c t s t h a t , whatever d i f f i c u l t y all will  d i f f i c u l t postconcrete  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  vice versa. ficulty  The n u l l  hypothesis,  also.in  t h a t a l l t a s k s w i l l b e o f t h e same s t a g e  post-concrete (i)  stage  i n difficulty  r a n k i n g s Between c o n c r e t e  t h e whole sample.  stage  t a s k s and  ordering are the frequencies Scalogram a n a l y s i s (Guttman,  o r d e r i n g s as a p r e l i m i n a r y step  s c a l e p r o p e r t i e s o f a s e t of items  vectors correspond  i n gauging t h e Guttman  ( i n t h i s case the "items" 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 to the three content  i n t h e u p p e r r e g i o n o f t h e g r a p h c a n Be s a i d  1.  a c r o s s domains, and (b)  i n s o f a r a s t h e r e w i l l b e no s i g n i f i -  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  yields difficulty  vertical  task, but not  Orderings  of passes on each t a s k a c r o s s 1950)  task  t a s k s i n any domain,  Scalogram D i f f i c u l t y The  stage  observed,  two p a r t s , s t a t e s ( a ) t h a t t h e d i f -  orderings of the task w i l l vary haphazardly  cant d i s c o n t i n u i t i e s  one  o r d e r i n g o f t a s k s may b e e m p i r i c a l l y  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  in a  each t a s k .  domains.  The t h r e e  The t a s k s  falling  t o B e more d i f f i c u l t t h a n  those  S i n c e no p h y s i c a l d o m a i n 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 a n d 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 complete range of tasks 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 d o m a i n s . H o w e v e r , 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 o p 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 s u p p o s e d 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 formal o p e r a t i o n a l t a s k s . Therefore three formal 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 Figure  1  KEY S LT LM C Prob Iso CV CyTr Cylh  = = = = = = = = =  Scalogram d i f f i c u l t y orderings 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.  Seriation Linear Transitivity Logical Multiplication Class Inclusion Probability I s l o a t i o n of Variables Combination of Variables Cyclic Transitivity Cyclic Integration  100  9.0  •  80  r  Percentage Failing (Difficulty)  sical  n . n ecological 1 0  Domains  Societal  64 i n t h e lower r e g i o n .  I n f i g u r e 1 i t can be seen t h a t t h e 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 o f t a s k s was o b t a i n 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. I n t h e p h y s i c a l domain, however, c e r t a i n 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 were m i s o r d e r e d .  T h i s was m a i n l y a r e s u l t o f t h e l i n e a r t r a n s i t i v i t y t a s k  b e i n g more d i f f i c u l t than t h e l o g i c a l m u l t i p l i c a t i o n and t h e c l a s s tasks.  The l a t t e r two were t i e d w i t h each o t h e r .  inclusion  The s e r i a t i o n t a s k s i n a l l  domains were t h e e a s i e s t , so much so t h a t t h e r e were no cases o f f a i l u r e s a t t h a t c o g n i t i v e o p e r a t i o n i n e i t h e r t h e p h y s i c a l o r t h e b i o - e c o l o g i c a l domain. O v e r a l l , t h e t a s k s conformed t o t h e 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 s a c r o s s domains. The  scalogram r e s u l t s a l s o p r o v i d e 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 t o  the macroscopic  v e r s i o n of the f i r s t hypothesis.  The m a c r o s c o p i c  version  amounted t o a p r e d i c t i o n o f 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 w i t h i n each domain.  rankings  The v i s u a l i m p r e s s i o n g i v e n by f i g u r e 1 i s t h a t t h e r e  a r e s t a g e - l i k e gaps and they appear i n every domain a t a p p r o x i m a t e l y t h e same places.  The c o n c r e t e o p e r a t i o n a l t a s k s a l l f a l l between t h e 0% t o 18.8%  failure level.  The f o r m a l o p e r a t i o n a l t a s k s span a range comparable t o t h a t  covered by t h e c o n c r e t e t a s k s (approx. 15 t o 19 p e r c e n t a g e  points).  The two  c y c l i c t r a n s i t i v i t y s c o r e s encompass t h e f o r m a l o p e r a t i o n a l s c o r e s and appear to be about t h e same d i s t a n c e from t h e c o n c r e t e s c o r e s as t h e f o r m a l s c o r e s are.  The d i s t a n c e from t h e h i g h e s t c o n c r e t e t a s k ( 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) t o t h e l o w e s t f o r m a l o p e r a t i o n a l t a s k i s 21.8 p e r c e n t a g e points.  The d i s t a n c e t o t h e l o w e s t s y s t e m i c  s o c i e t a l domain) t a s k i s 17.7 p e r c e n t a g e  (i.e., cyclic  points.  transitivity,  Therefore the distance that  s e p a r a t e s 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 from t h e l e a s t  difficult  p o s t - c o n c r e t e stage t a s k s i s a p p r o x i m a t e l y 17.7 to. 21.-8 -percentage p o i n t s ; That i s r o u g h l y the-same r a n g e covered ' by a l l the: t a s k s i n a - s i n g l e s t a g e 1  65 (i.e.,  15 t o 19 p e r c e n t a g e p o i n t s ) .  there are at l e a s t post-concrete. all  two s e p a r a t e  On t h e f a c e o f i t ,  stages  These data p r e d i s p o s e  can be e s t i m a t e d  two d i f f e r e n t  While the c y c l i c  Moreover, given t h e assumption  transitivity  sized  gap" between  tasks f a l l  t a s k was 21.8 p e r c e n t a g e p o i n t s m o r e d i f f i c u l t  highest concrete separates concrete  that tasks  i n roughly  t h e same  than  difficulty  cyclic integration  t h e most d i f f i c u l t  formal  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 a s t h a t b e t w e e n t h e t a s k and t h e lowest  the c y c l i c  formal task.  Since a stage  i n t e g r a t i o n tasks from the b u l k o f the other  t a s k s , i t make s e n s e 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  gration constituting a possible f i f t h (ii)  that  17.7 t o 21.8 p e r c e n t a g e p o i n t s .  range as t h e formal 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  operational task.  that  and t h 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  stages, a "stage  t o be a p p r o x i m a t e l y  i tappears  i n a l l domains, t h e c o n c r e t e  t h e t a s k s a r e f r o m t h e same s t a g e .  the d a t a do r e f l e c t  then,  s i z e d gap post-  of c y c l i c  inte-  stage o f c o g n i t i v e development,  Guttman S t e p s The  information presented  t h e r e was i n t h e d i f f i c u l t y t h e mean o r d e r i n g , t h e n most d i f f i c u l t  o n f i g u r e 1 d o e s n o t i n d i c a t e how much v a r i a n c e  l e v e l data.  I f t h e r e w e r e no r e s p o n d e n t s  the increase 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  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  t h e c o m p a r i s o n . b e t w e e n two t a s k s f o r m s a G u t t m a n s t e p p r a c t i c a l l y t h e r e s p o n d e n t s who p a s s e d t h e m o r e d i f f i c u l t ficult  violating  a l l of-„  task a l s o passed the l e s s  dif-  t a s k b u t n o t n e a r l y a s 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  passed the harder  task.  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  of equivalence  between t h e adjacent  ing or f a i l i n g  either.  degrees  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 pass-  W i t h non-Guttman s t e p s t h e r e . w i l l  tend  t o b e a s many  66 respondents versa.  who passed  The macroscopic  t h e h a r d e r t a s k b u t f a i l e d t h e e a s i e r one as v i c e part of the f i r s t hypothesis p r e d i c t s that there  s h o u l d be non-Guttman s t e p s between a d j a c e n t c o n c r e t e s t a g e t a s k s , a Guttman s t e p between t h e most d i f f i c u l t c o n c r e t e t a s k and 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 , and non-Guttman s t e p s between a d j a c e n t p o s t - c o n c r e t e t a s k s , (iii)  Converging  Techniques  There i s no one s t a t i s t i c w h i c h a d e q u a t e l y i n f o r m s us about t h e Guttmanl i k e n a t u r e o f each step i n t h e d i f f i c u l t y o r d e r i n g . s e v e r a l approaches w h i c h g i v e p a r t i a l i n f o r m a t i o n . statistics  There a r e , however,  By u s i n g a l l o f t h e s e  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 t o e v a l u a t e t h e second h y p o t h e s i s .  I t must be emphasized, however,  t h a t t h e n a t u r e o f t h i s p r o b i n g does n o t a l l o w any s i g n i f i c a n c e  testing.  The r e s u l t s a r e r e p o r t e d i n terms o f degree o f a s s o c i a t i o n o r d i f f e r e n c e b e tween and among t a s k s .  The h y p o t h e s i s does n o t and cannot s t a n d o r f a l l on  the r e s u l t s o f any one o f these s t a t i s t i c a l a n a l y s e s .  The f i n a l d e c i s i o n on  the second h y p o t h e s i s i s e n t i r e l y dependent upon t h e composite p i c t u r e p r o v i d e d 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 G u t t m a n - l i k e n a t u r e o f t h e d i f f i c u l t y o r d e r i n g s i n each domain were examined by drawing t o g e t h e r t h e r e s u l t s o f s e v e r a l s t a t i s t i c s . based as i t i s on p e r c e n t a g e s p r o v i d e d some i n f o r m a t i o n .  o f respondents  Figure 1,  p a s s i n g each t a s k , has a l r e a d y  Guttman's 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 f o r  scalogram a n a l y s e s c o n t r i b u t e s i n f o r m a t i o n about t h e Guttman s c a l e q u a l i t i e s o f t h e whole sequence o f t a s k s i n each domain.  Looking at s p e c i f i c  w i t h i n sequences, 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 respondents 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 a r e reported.  steps  following  Using t e s t s f o r  the s i g n i f i c a n c e o f d i f f e r e n c e s between p r o p o r t i o n s , z^ s c o r e s a r e o b t a i n e d  67 which, used f o r d e s c r i p t i o n o n l y , p r o v i d e a more r e f i n e d index of the Guttman nature  of the r e l a t i o n s h i p between a d j a c e n t  tasks.  With each of the above mentioned s t a t i s t i c s t h e r e a r e s t r e n g t h s , weaknesses and"general o p e r a t i n g 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 . T h i s i s undertaken as each of these  s t a t i s t i c s i s i n t r o d u c e d and brought to  b e a r upon a p a r t i c u l a r h y p o t h e s i s .  Hopefully, t h i s s e r i a l presentation  c o n t r i b u t e to c l a r i t y by  s t a y i n g c l o s e to the data and  debate about the p r o s and (iv)  will  avoiding a contextless  cons of v a r i o u s s t a t i s t i c a l a l t e r n a t i v e s ,  Reproducibility Coefficient 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 t h a t  i n f o r m a t i o n about the o v e r a l l Guttman-like q u a l i t i e s of an ordered items.  I t g i v e s no  steps.  Coombs, Dawes, and  f i c i e n t o f 0.90  gives set of  i n f o r m a t i o n about which s t e p s i n the o r d e r i n g a r e Guttman  i s "good".  Tversky  (1970) s t a t e t h a t a r e p r o d u c i b i l i t y  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  coefthe  t a s k s i n f i g u r e 1, ordered  together  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 0.958, (b) b i o l o g i c a l 0.942, and  s o c i a l 0.950. i n g s do,  Therefore  i r r e s p e c t i v e o f domain, i s 0.918.  t h i s c r i t e r i o n t e l l s us t h a t the observed t a s k  i n f a c t , c o n s t i t u t e Guttman s c a l e s .  p r e c i s e l y what we want to know. s e r i a t i o n t a s k and  The  the most d i f f i c u l t  the magnitude of the r e p r o d u c i b i l i t y  The  is in itself The  tasks.  Therefore  c y c l i c i n t e g r a t i o n t a s k c o n t r i b u t e s to coefficient.  The  hypothesis  under  I t deals only with  Guttman's c o e f f i c i e n t of  reproducibility  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 " . (MMR)  The  consider-  steps  reproducibility  purposes.  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 w i t h  reproducibility  order-  problem i s t h a t t h i s i s not  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 p r e s e n t  c o e f f i c i e n t of minimum m a r g i n a l  (c)  huge Guttman step between the e a s i e s t  a t i o n does not d e a l w i t h t h a t huge Guttman s t e p . between a d j a c e n t  The  the  to produce a more u s e f u l  c o e f f i c i e n t of minimum  index  marginal  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 t h a t c o u l d  68 have been o b t a i n e d  given t h e p r o p o r t i o n o f respondents  each o f t h e items. on i n d i v i d u a l  items.  I t i s a f f e c t e d by c e i l i n g  effects  -  p a s s i n g and f a i l i n g and extreme skews  When t h e MMR i s s u b t r a c t e d f r o m ' o n e ' ( i . e .  1-MMR  =  t h e " 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 m e a s u r e o f t h e r a n g e 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 . from the 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  the result  When t h e MMR i s s u b t r a c t e d i s a measure o f t h e "percent  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 over level of prodiction. sures.  The c o e f f i c i e n t  D i v i d i n g the percent  of 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  a b o v e .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 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. scalability  and' c u m u l a t i v e  i n the.data.  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)  We do n o t know t h a t t h e y  s c a l e s b u t one f a l s i f i c a t i o n Two o t h e r d e s c r i p t i v e is  consider-  to three correlated but d i s t i n c t  u s t h a t , W i t h i n d o m a i n s , t h e t a s k s may f o r m  scales.  (Nie, H u l l ,  T h i s i s a s one w o u l d e x p e c t  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, a n d ( c ) s o c i e t a l  cumulative  " s h o u l d be w e l l  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  i n g t h a t these a r e t h r e e domains c o r r e s p o n d i n g  criterion tells  yields  533)".  t o g e t h e r i r r e s p e c t i v e o f d o m a i n i s 0.585.  dimensions  base  o f t h e s e mea-  i m p r o v e m e n t b y t h e r e c i p r o c a l o f t h e MMR  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 .  The  uses both  t h e MMR  t e s t has been  0.714.  This  undimensional,  do f o r m u n d i m e n s i o n a l ,  cumulative  passed.  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  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  hypothesis.  First,  i n subsection  ( v ) , we e x a m i n e t h e f r e q u e n c i e s a n d 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 the  easier  Second, i n  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 harder  subsection  task.  ( v i ) , we l o o k a t t h e d i f f e r e n c e s b e t w e e n 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 concerning  the use  task of a p a i r w h i l e f a i l i n g  of each s t a t i s t i c  the other.  Particulars  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  is  first  introduced. (v)  Frequencies The  and  Proportions  information presented  i n f i g u r e 1 s t r o n g l y suggests  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  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 d o m a i n i s p a r a l l e l e d by tween c o n c r e t e domains. a r e as  t a s k s and  systemic  What r e m a i n s t o b e  c l e a n c u t as  t h e gap  t h e b i o - e c o l o g i c a l and  between the c o n c r e t e  latter and  steps from concrete  a r e l e s s Guttman i n c h a r a c t e r than the p r e d i c t i o n s of p a r a l l e l  formal  a similar  t a s k s i n t h e b i o - e c o l o g i c a l and  shown i s t h a t t h e s e  societal  that the w e l l  the corresponding  sequencing  two  gap  be-  societal  s t a g e - l i k e gaps  the formal tasks. to post-concrete  If  stages  p h y s i c a l domain step  a c r o s s domains are l e s s  than  then  fully  supported. Table  I i s presented  i n t h r e e p a r t s , , one  f o r each content  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 failing  the other.  orderings.  The  (most d i f f i c u l t )  t o t h e p h y s i c a l d o m a i n ( t a b l e I , p a r t A) was adjacent  to the l e a s t d i f f i c u l t  N o t e t h a t a s one two  reads  t a s k s where the  r e s p o n d e n t s who (i.e.  the  concrete  linear  to r i g h t  operational task It is  (i.e. probability).  to r i g h t  f o r these  respondents,  these  of  operational tasks  c o n t r a s t , t h e b o t t o m t h r e e r o w s show d a t a  passed formal o p e r a t i o n a l tasks.  quency data from l e f t  while  difficulty  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 the group  By  The  i t i s a t the j u n c t u r e between  passed each of the s u c c e s s i v e concrete  had  i n the  transitivity.  formal operational task  from l e f t  top f o u r rows).  r e s p o n d e n t s who  task of a p a i r  This includes p a i r s that are adjacent  h i g h e s t ranked  domain.  When one  reads  t h e r e i s no  the  for fre-  dramatic  Table Frequencies  and p r o p o r t i o n s  I  of respondents p a s s i n g one task o f a p a i r w h i l e  P a r t A:  Total Passes  Logical Multiplication  Class Inclusion  other.  Task  Linear Transitivity  , ^  M  1  r o t , a b : L  . -  Seriation  96  Logical Multiplication  91  Class Inclusion  91  4 .044  Linear Transitivity  84  4 .048  3 .036  Probability  57  0 .000  0 .000  1 .018  Isolation of V a r i a b l e s  52  0 .000  0 .000  0 .000  2 .038  Combination of V a r i a b l e s  43  0 .000  1 .023  3 .070  4 .093  5 .052  the  P h y s i c a l Domain Failed  Passed Task  failing  L : L t  y  o  Isolation variables  Combination of V a r i a b l e s  f  5 .052  12 .125  39 .406  44 .458  53 .552  4 .044  11 .121  34 .374  39 .429  48 .527  10 .110  34 .374  39 .429  49 .538  28 .333  32 .381  44 .524  7 .123  18 .316 15 .288  6 .140  Table I  P a r t B:  Bio-ecological Failed  Passed Task  Total Passes  Seriation  96  Linear Transitivity  88  Logical Multiplication  87  Class Inclusion  :  7  8  Linear Transitivity 8 .083  (cont'd)  Logical Multiplication  Domain  Task  Class Inclusion  Cyclic Transitivity  Cyclic Integrat:  9 '.092  18 .188  61 .635  74 .771  7 .080  13 .148  53 .602  66 .750  15 .172  52 .598  65 .747  43 .551  57 .731  6 .069 3 .038  6 .077  Cyclic Transitivity  35  0 .000  0 .000  0 .000  Cyclic Integration  22  0 .000  0 .000  1 .045  20 .571 7 .318  I—  1  Table I  P a r t C:  (cont'd)  S o c i e t a l Domain F a i l e d Task  Passed Task Seriation  Total Passes 92  Linear Transitivity 8 .087  Logical Class Multiplication Inclusion  Cyclic Transitivity  Cyclic Integrat:  ... • 9 .098  14 .152  32 .348  82 .891  7 .082  10 .118  27 .318  75 .882  11 .131  26 .310  74 .881  26 .325  70 .875  Linear Multiplication  85  Logical Multiplication  84  6 .071  Class Inclusion  80  5 .063  7 .087  Cyclic Transitivity  61  3 .049  3 .049  7 .115  Cyclic Integration  10  0 .000  0 .000  0 .000  51 .836 0 .000  73 increase i n f a i l u r e is  crossed.  f r e q u e n c i e s as the c o n c r e t e  This pattern r e f l e c t s  to post-concrete  juncture  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 formal operational stage. 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 the n o n - t r a d i t i o n a l content  and t h e s y s t e m i c p o s t - c o n c r e t e  operations.  b i o - e c o l o g i c a l d o m a i n f r e q u e n c i e s a r e shown o n p a r t B o f t a b l e 1. to  post-concrete discontinuity  it  i s e v e n more p r o n o u n c e d .  failure for  frequency  the hardest  concrete  task.  task.  concrete  societal  cyclic  tasks than  societal cyclic  t a s k i s 43 r e s p o n d e n t s  particularly of c y c l i c  transitivity  transitivity  of t h i s chapter,  failure  overall  than  The r e a s o n  domain  for this  r a t e s a r e c l o s e r t o those f o r  f o r the s o c i e t a l c y c l i c  integration task.  t a s k was a l w a y s p r e s e n t e d  Perhaps the c y c l i c  i s a c t u a l l y a concrete  after  transitivity  i m p r e s s i o n g i v e n by a l e f t  The  the bio-ecological  operations are  P e r h a p s one o f t h e components stage operation.  In section B  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 a n e x a m i n a t i o n  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 The  more d i f f i c u l t  B)  task..  susceptible to practice effects.  transitivity  than  gap seems t o h a v e s o m e t h i n g t o do w i t h o n e  transitivity  t o those  v e r s i o n o f t h e same t a s k .  higher  This r a t e drops c o n s i d e r a b l y i n the s o c i e t a l  a t t e n u a t i o n o f t h e between stage  The  In fact,  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  ( 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 .  task, the s o c i e t a l c y c l i c  concrete  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  however, t h e e a s i e s t p o s t - c o n c r e t e the hardest  The  The  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 here.  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  concrete  with  of the  operations.  to r i g h t reading of the frequency  tables i s that the stage-like d i s c o n t i n u i t i e s  i n difficulty  levels of tasks  74 are found t o be  a c r o s s a l l domains.  The  societal cyclic  a somewhat i n t e r m e d i a t e c a s e b u t  notions of stages s o c i e t a l content On  can  s a f e l y be  overall  transitivity  i t appears t h a t the P i a g e t i a n  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  the  domains.  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  from the top l e f t represent  to the bottom r i g h t .  The  e n t r i e s below t h i s  f r e q u e n c i e s \ of cases where respondents  of the p a i r but  failed  t h e e a s i e r one.  passed  These are cases  failed  concrete  t a s k s have the lowest  Guttman s t e p between c o n c r e t e  frequencies.  o p e r a t i o n s and  formal  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 .  w o r d s , i t i s more p r o b a b l e  that a respondent would pass a harder  p a s s a f o r m a l t a s k and  fail  a concrete  task.  tasks  This indicates a  formal operations.  e a s i e r one  task  o f non-Guttman p a t t e r n s .  c i e s o f non-Guttman cases  t a s k , f o r example, w h i l e f a i l i n g an  running  diagonal  the harder  I n the p h y s i c a l domain the c e l l s a t the i n t e r s e c t i o n of passed and  t a s k seems  The  frequen-  In  other  concrete  t h a n i t i s t h a t he  o r she  L i k e w i s e , t h e r e w e r e more  would cases  o f n o n - G u t t m a n p e r f o r m a n c e among t h e f o r m a l t a s k s when p a i r e d w i t h e a c h o t h e r . Looking  a c r o s s d o m a i n s , a g a i n , we  Piagetian task contents and,  see  t h a t the p a t t e r n found  i s repeated w i t h . b i o - e c o l o g i c a l contents  to a l e s s e r extent, w i t h s o c i e t a l contents  domain the c y c l i c clearly  data w i t h the systemic  transitivity  s c o r e s g r o u p e d by  the i n t e r p r e t a t i o n of t h i s  (part  In the  B)  societal  task.  the a n a l y s i s of  components i s i n t e n d e d  to help  i n t a b l e I show t h e same p a t t e r n o f  There are d i s c o n t i n u i t i e s  i n a l l domains and  Again,  the clarify  finding.  proportions presented  as t h e f r e q u e n c i e s . stages  (part C).  traditional  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 m o r e  than does the c y c l i c  The  with  in difficulty  i n a l l domains the evidence  levels  results across  f o r Guttman s t e p s i s  75 stronger across  stages  proportions over  t h a n w i t h i n s t a g e s . The a d v a n t a g e o f c o n s i d e r i n g  frequencies  i s that t h e p r o p o r t i o n s take i n t o account  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 facilitates I mainly  task of the p a i r being  considered.  how  This  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  f o rt h e i r relevance  to the analyses  presented  i n the next  subsection  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 ) . (vi)  Z Scores  f o r Proportions  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 a n 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 c o n cept  s o f a r a s i s p o s s i b l e . A t t h e same t i m e o n e m o r e s t a t i s t i c a l  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 domain p a t t e r n s i n d i f f i c u l t y to  take  groupings.  i n t o account the v a r i a b i l i t y  hypothesis  approach  dealing with  across  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  i n t h e number o f r e s p o n d e n t s  passing  t h e " p a s s e d " member o f e a c h " p a s s ; 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 " p a s s . • • " A / f a i l B" p a i r w i t h t h e " p a s s A" p a i r .  I t m u s t b e r e i t e r a t e d , h o w e v e r , 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  are presented  The c l o s e s t we c a n come t o s i g n i f i c a n c e unequivocal  cases  the s t a t i s t i c s  f o r purely d e s c r i p t i v e purposes. testing  i s to s e t out c r i t e r i a f o r  o f a Guttman s t e p and a non-Guttman s t e p . I n ambiguous  are reported  b e made t o u s e t h o s e  cases  f o r t h e s a k e 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 i n determining  can be i n d e x e d  being  (Bruning  will  by z s c o r e s  produced 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 respondents or f a i l i n g o r d i n a l l y adjacent  cases  the f a t e of the hypotheses.  The d e g r e e t o w h i c h a s t e p i s a G u t t m a n s t e p  scores  B/fail  t a s k s w i t h i n d o m a i n s . The f o r m u l a  passing  f o r t h e z:  & K i r i t z , 1 9 6 8 ) h a s t h e d i f f e r e n c e b e t w e e n t h e two p r o p o r t i o n s  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 of 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 of ' d i s c o n f i r m a t i o n f o r both  tasks.  T h e y 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 e a c h 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 tasks,  then  the step  w o u l d n o t be  from A  a Guttman s t e p  passing A while f a i l i n g w h i l e f a i l i n g A. while failing  The  the other  q u e s t i o n i s , how T h e r e a r e no  does not  B w e r e much t h e same a s  s t e p w o u l d be  the  step  the p r o p o r t i o n p a s s i n g  the converse  not  failed  proportion.  w i l l be  i t , b e c a u s e A w o u l d be  f r o m t h e most d i f f i c u l t  decided  i t w o u l d be  confidence  applied.  b a c k e d up b y y e a r s  On  who  allowed.  interval.  o f r e s e a r c h , i t can be concrete  that  significance  Instead, a v a i l a b l e  f o r m a l o p e r a t i o n a l t a s k was  o p e r a t i o n a l task to the l e a s t I f i t i s not as  a  task.  The  the  difficult  statistically  i t n e e d s t o be  sample of respondents.  the p r o b a b i l i t y  theoretical  s a f e l y assumed t h a t  purpose of 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 to the present  or  i n a p p r o p r i a t e to r e t r e a t to  p e r f e c t G u t t m a n 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  The  be  A  easier  the b a s i s of w e l l accepted  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 .  o p e r a t i o n a l t a s k was  Those  f o r d e c i d i n g when a z s c o r e d o e s  Also, having  inappropriate here,  tasks administered  B  much?  t r a d i t i o n a l c r i t e r i o n o f a 95%  statements  task)  a Guttman s t e p i f the p r o p o r t i o n p a s s i n g  conventional c r i t e r i a  theoretical criteria  adjacent  simultaneously  A c e r t a i n amount o f e r r o r m u s t , o f c o u r s e ,  r e f l e c t a Guttman s t e p .  t e s t i n g w o u l d be  B a r e two  i f the p r o p o r t i o n of respondents  B w e r e much g r e a t e r t h a n  than B f o r everyone.  I f A and  ( 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  p a s s e d B w o u l d h a v e a l s o p a s s e d A,  The  task.  The  for  levels for least  the  the  difficult  most d i f f i c u l t  concrete  the c l a s s i n c l u s i o n t a s k i n the b i o - e c o l o g i c a l domain.  p r o p o r t i o n of respondents passing 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.  inclusion while  failing  two  ( B r u n i n g and  proportions  The  proportion'passing bio-ecological class  p r o b a b i l i t y was Kintz,  1968,  0.308. The p . 1 9 9 ) was  d i f f e r e n c e between thesez = 5.822. I t m i g h t  be  argued, however, t h a t t h i s b i o - e c o l o g i c a l content  z underestimates  might have added t o the d i f f i c u l t y  s i o n task. In that case f i g u r a t i v e some g a p s as  t h e s i z e o f t h e d i f f e r e n c e . The  f a c t o r s a l o n e w o u l d be  s t a g e - l i k e or Guttman-like,  Therefore  of the  class  l e a d i n g us  adopted. I n s t e a d of t a k i n g the d i f f e r e n c e between the p r o p o r t i o n  and  failing  t h r e e d o m a i n s , i t was  t a s k and  decided  the highest concrete  to r e p l a c e the  latter  c r e t e t a s k i n t h e p h y s i c a l d o m a i n o n l y . T h a t was transitivity  task. This  restriction  accord w i t h the supporting  of  task w i t h the highest  the p h y s i c a l domain  the con-  linear  t o p h y s i c a l d o m a i n t a s k s i s a l s o more i n  t h e o r y and  l a r g e l y b a s e d on  passing  t a s k f r o m any  research  that j u s t i f y  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 r e s e a r c h was  t o deem  a more s t r i n g e n t c r i t e r i o n  was  the p r o b a b i l i t y  inclu-  choosing  the  con^  Guttman s t e p .  tasks containing p h y s i c a l content.  The  The  p r o p o r t i o n of respondents passing 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  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 t h e s e p r o p o r t i o n s was  z =  proportion passing  0.333. The  7.663. A l l z s c o r e s  linear  d i f f e r e n c e between  that are equal  to or  greater 2  than +  7.663 w i l l  consequently  A t t h e o t h e r end, G u t t m a n s t e p . One  be  taken  might use  b a b l y be 2.  a fair  as  non-  the assumption  that  a r e non-Guttman s t e p s . Given  that  b a s e d on  the average z f o r d i f f e r e n c e s between adjacent  the c r i t e r i o n  estimate  Guttman s t e p s . example of a  p o s s i b l e c r i t e r i o n m i g h t be  tasks w i t h i n stages  unequivocal  t h e r e i s a need f o r an u n e q u i v o c a l  t h e s t e p b e t w e e n t a s k s o f t h e same s t a g e a s s u m p t i o n , one  t o be  but  f o r a non-Guttman s t e p . That would  s i n c e the aim  Since the o l d e r respondents d i d y o u n g e r ones d i d not r e c e i v e a l s e r v a t i v e l y b i a s e d . The g r a d e 7 z f o r a Guttman s t e p c a l c u l a t e d t e r i o n o f z = 7.663, t h e r e f o r e ,  i s t o have an u n e q u i v o c a l  : pro-  criterion,  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 l systemic t a s k s , t h i s c r i t e r i o n i s cons t u d e n t s w e r e g i v e n a l l t a s k s . The c r i t e r i o n on t h e i r d a t a a l o n e i s z = 1.214. The crii s very stringent.-  78  a more s t r i n g e n t c r i t e r i o n would be d e s i r a b l e . to  A second p o s s i b i l i t y would be  take the z f o r the s m a l l e s t step w i t h i n a s t a g e .  In.the p h y s i c a l domain  the s m a l l e s t 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 . f a c t , these two t a s k s were t i e d i n terms of d i f f i c u l t y l e v e l . the s m a l l e s t s t e p i n the p h y s i c a l domain was no step a t a l l . be the most u n e q u i v o c a l to  find.  of  respondents  was  That means t h a t T h i s seems to  example of a non-Guttman step t h a t one c o u l d  I t i s not o n l y a non-Guttman step-,' i t i s a non-step.  0.044.  passed  expect  The p r o p o r t i o n  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 class  The same p r o p o r t i o n of respondents  In  inclusion  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 s c o r e f o r the d i f f e r e n c e between these p r o p o r t i o n s was z =  2.380.  are taken to b e - u n e q u i v o c a l i a t e scores  (between  2.380  T h e r e f o r e , z s c o r e s e q u a l to o r l e s s than c a s e s ' o f non-Guttman s t e p s . and  7.663)  Again,  2.380  the intermed-  a r e c a t e g o r i z e d as ambiguous  cases  ("?") and l e f t a t t h a t . T a b l e I I shows the z s c o r e s f o r a l l the s t e p s by domain o f content.-» These a r e on the d i a g o n a l s .  F o r the standard domain the o n l y u n e q u i v o c a l l y  Guttman step i s between the c o n c r e t e t a s k s and the f o r m a l t a s k s . of  Within  those stages t h e r e i s one c l e a r non-Guttman step and one ambiguous  each  case.  In the b i o l o g i c a l domain c l e a r Guttman s t e p s s e p a r a t e the c o n c r e t e t a s k s from all  the systemic  tasks.  There i s a non-Guttman step between l i n e a r t r a n s -  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 o t h e r s t e p s a r e ambiguous.  I n the  s o c i e t a l domain the d i a g o n a l c o n t a i n s two non-Guttman s t e p s between c o n c r e t e stage t a s k s and one ambiguous case.  The c y c l i c t r a n s i t i v i t y t a s k i s o n l y an  ambiguous step a p a r t from any of the c o n c r e t e t a s k s except (i.e.  seriation).  the e a s i e s t one  The c y c l i c i n t e g r a t i o n t a s k was a Guttman step more d i f f i c u l t  than a l l the o t h e r t a s k s i n the s o c i e t a l domain i n c l u d i n g the c y c l i c t r a n s itivity  task.  Table I I Z scores  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 respondents p a s s i n g while  f a i l i n g the other.  P a r t A:  P h y s i c a l Domain  Less D i f f i c u l t More Difficult Task of P a i r  Seriation*  Class Inclusion  Logical Multiplication  one t a s k o f a p a i r  Class Inclusion  Task o f P a i r  Linear Transitivity  Probability  Insolation of V a r i a b l e s  2.380 (NC)  Linear Transitivity  -  2.489  2.698  (?)  (?)  Probability  -  9.396 (G)  9.396 (G)  7.663 (G)  Isolation of V a r i a b l e s  -  10.356 (G)  10.356 (G)  9.148 (G)  2.315 (NG)  Combination of Variables  -  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 = N o n - G u t t m a n s t e p G = Guttman step  (*2.380)  (^7.663)  ? = ambiguous s t e p  ( b e t w e e n 2.380 a n d 7.663) VO  Table I I  P a r t B:  (cont'd)  Bio-ecological  Less D i f f i c u l t  Task o f  Domain Pair  More Difficult Task o f P a i r  Seriation* e  o  n  Linear Transitivity  Logical Multiplication  0.378 (NG)  Class Inclusion  3.488  (?)  Logical Multiplication  Class Inclusion  Cyclic Transitivity  2.653  (?)  Cyclic . Transitivity  13.648  13.463  CG)  CG)  Cyclic Integration  18.166  17.946  13.985  2.813  (G)  CG)  CG)  (?)  11.783  (G)  Table I I  P a r t C:  Societal  Less D i f f i c u l t More Difficult Task o f P a i r  Linear oeriacxon T r a n s i t i v i t y  Logical Multiplica  (cont'd)  Domain  Task o f P a i r  Class iclusion  Cyclic Transitivity  Linear Transitivity  3.316 (?)  Logical Multiplication  3.604 (?)  0.377 (NG)  Class Inclusion  4.259 (?)  1.758 (NG)  1.265 (NG)  Cyclic Transitivity  8.317 (G)  6.319 (?)  6.142  4.407  (?)  C?)  28.921 (G)  26.693 (G)  26.374 CG)  25.100  19.029  CG)  CG)  Cyclic Integration  82 To The  summarize, the f i r s t  s t a g e s and  domains.  The  finding  further attention.  t h a t the s o c i e t a l c y c l i c stage  t a s k s and  In the next  The  F i r s t Hypothesis  systemic  the c y c l i c  c h i l d ' s developing understanding  the  data. new  t a s k was  intermed-  integration task  deserves  s c o r e s are grouped  to provide a f i n e r  w i t h Component 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  by  i n t h e two  transitivity  s e c t i o n the systemic  c o n s t i t u e n t components i n an a t t e m p t  B.  g e n e r a l l y supported  d i s c o n t i n u o u s g a p s b e t w e e n them w e r e f o u n d  i a t e between the concrete  their  h y p o t h e s i s was  grained  by  analysis.  Scores  the upper reaches  of s o c i a l o r g a n i z a t i o n s .  While  of  the  the 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 the ontogeny o f t h a t unders t a n d i n g , the systemic fathom the nature us  c o g n i t i v e o p e r a t i o n s i n themselves  of that understanding  take a c l o s e r look at those Since the systemic  a r e an attempt  when i t i s d e v e l o p e d .  Therefore l e t  tasks.  t a s k s were newly d e v i s e d f o r t h i s  scope f o r t h e i r refinement.  The  r e p o r t i n g of d e t a i l e d  study,  there  item analyses  remains  leading  t o improved v e r s i o n s o f the t a s k i s an u n d e r t a k i n g  f o r another  study.  now,  t h a t can be  attempted  h o w e v e r , t h e r e a r e some i m m e d i a t e r e f i n e m e n t s  order to sharpen our understanding entail.  S p e c i f i c a l l y , both  s c o r e s c a n be  (i)  their  and  in  cognitive operations  the c y c l i c  integration  w h i c h seem t o  reflect  Components  cognitive operations. i n two w a y s .  For  cognitive operations,  scores f o r the systemic  tionalized  transitivity  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  Cyclic Transitivity The  of what t h e s e s y s t e m i c  the c y c l i c  the mastery of q u i t e d i f f e r e n t  to  t a s k s were b a s e d on w o r k i n g  For c y c l i c  First,  transitivity  definitions  t h e d e f i n i t i o n was  i n the " l a y o u t " procedure  respondents  of opera-  were .  83 p r e s e n t e d w i t h "five c a r d s , each showing  a p i c t u r e o f an element  i n the c y c l e .  The respondent was asked t o arrange the p i c t u r e s b e s i d e one another i n a way t h a t would show how they were r e l a t e d . depending  The wording'of  the r e q u e s t v a r i e d  on the content o f the c y c l e b u t s u c c e s s f u l performance  v o l v e d a r r a n g i n g t h e cards i n a c i r c l e .  Second,  always i n -  the " r e c y c l i n g " procedure  i n v o l v e d the respondent i n e x p l a i n i n g how a commodity c o u l d pass through the same element  twice.  I n 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 .  C o r r e c t e x p l a n a t i o n s had the com-  modity moving around t h e c i r c l e from one a d j a c e n t element procedure presupposed  t o the n e x t .  t h a t respondents had the c o r r e c t c i r c u l a r ' arrangement  of cards d i s p l a y e d i n f r o n t o f them.  Thus an u n d e r s t a n d i n g o f the r e l a t i o n s  u n d e r l y i n g the " l a y o u t " was a p r e r e q u i s i t e f o r the " t r a n s i t i v e component.  This  recycling"  S i n c e i t was not known a p r i o r i whether these two procedures would  be o f e q u a l d i f f i c u l t y ,  i t was d e c i d e d t h a t t h e i r s c o r e s would be combined i n  o r d e r t o have an o v e r a l l p i c t u r e o f the respondents a b i l i t y w i t h the 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 (see Appendix scores).  D f o r s c o r i n g r u l e s and r u l e s f o r combining  Below, these two components a r e t r e a t e d s e p a r a t e l y i n a r e a n a l y s i s  of the d a t a . (ii)  C y c l i c I n t e g r a t i o n Components In the c y c l i c i n t e g r a t i o n t a s k the c y c l e used i n t h e c y c l i c  t a s k remained  transitivity  d i s p l a y e d on c a r d s i n f r o n t o f t h e respondent b u t the c y c l e  i t s e l f was c o n s t r u e d as one o f t h r e e l e v e l s o f o r g a n i z a t i o n .  The elements o f  the c y c l e were t h e s u b o r d i n a t e l e v e l and the f o r c e s which i n t e g r a t e d the c y c l e a c r o s s time and changing c i r c u m s t a n c e s were t h e s u p r a o r d i n a t e l e v e l . component t h a t i s b e i n g c a l l e d "systems  The  a n a l y s i s " i n v o l v e d the a b i l i t y t o  e x p l a i n the impact o f c y c l i c p r o c e s s e s on i n d i v i d u a l elements o f the c y c l e .  84 The o t h e r 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 s c o r e i s b e i n g r e f e r r e d to as "systems s y n t h e s i s " .  Systems s y n t h e s i s i n v o l v e d e x p l a i n i n g how t h e n a t u r e  of t h e c y c l e i t s e l f would change under t h e impact o f s u p r a o r d i n a t e f o r c e s . There were no g r a p h i c r e p r e s e n t a t i o n s o f t h e s u p r a o r d i n a t e l e v e l .  Rather,  i t had t o be i n f e r r e d , d i s c o v e r e d o r " s y n t h e s i z e d " out o f t h e a v a i l a b l e knowledge about t h e c y c l e and i t s p a r t s . combinations  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  o f t h e s c o r e s f o r systems a n a l y s i s and systems s y n 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  rules).  The c o m b i n a t i o n o f component s c o r e s 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 s c o r e s was based on t h e assumption t h a t t h e components measured a s p e c t s o f t h e same c o g n i t i v e o p e r a t i o n .  T h i s a s s u m p t i o n can be v e r i f i e d by  r e a n a l y s i n g t h e d a t a w h i l e s u b s t i t u t i n g two component s c o r e s f o r each o f t h e f o u r composite s y s t e m i c s c o r e s . F i r s t , a s c a l o g r a m a n a l y s i s i s examined t o see how d i f f i c u l t t h e components were r e l a t i v e t o o t h e r t a s k s and t o each o t h e r . s c o r e s i s reviewed  Then a t a b l e o f z  t o see how w e l l t h e f i r s t h y p o t h e s i s f a r e d w i t h t h e com-  ponent s c o r e s . (iii)  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 a r e shown i n f i g u r e 2 .  most n o t a b l e r e v e l a t i o n i s t h e r e l a t i v e e a s i n e s s o f t h e c y c l i c layout procedure,  e s p e c i a l l y i n t h e s o c i e t a l domain.  The  transitivity  T a b l e I I I shows t h e z  s c o r e s f o r p a i r w i s e comparisons o f t h e component s c o r e s w i t h each o t h e r and with the other tasks.  The z s c o r e s f o r t h e s o c i e t a l domain c y c l i c  transitivity  l a y o u t procedure w i t h each o f t h e f o u r c o n c r e t e t a s k s shows t h a t i n no case i s i t an unambiguous Guttman s t e p a p a r t . procedure  T h i s was n o t t r u e f o r t h e l a y o u t  i n t h e b i o - e c o l o g i c a l domain n o r f o r any o t h e r component s c o r e .  85 Figure Scalogram  difficulty  2  o r d e r i n g s w i t h component s y s t e m i c and (b) a c r o s s domains.  scores  (a) by  domain,  KEY  s =  LT LM C Prob Iso CV  = = = = = =  Seriation Linear Transitivity Logical Multiplication Class Inclusion Probability I s o l a t i o n of Variables Combination of Variables  L a y = L a y o u t Component o f Cyclic Transitivity SyAn = S y s t e m s A n a l y s i s Component o f Cyclic Integration S y S y = S y s t e m s S y n t h e s i s Component o f Cyclic Integration TRec = T r a n s i t i v e R e c y c l i n g Component of C y c l i c T r a n s i t i v i t y  Table I I I , Part A B i o - e c o l o g i c a l d o m a i n "L_ s c o r e s f o r d i f f e r e n c e s b e t w e e n p r o p o r t i o n s 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 More Difficult Task o f P a i r  Less D i f f i c u l t Seriation  Linear" Transitivity  Logical Multiplication  —  0.378 (NG)  Class Inclusion  —  3.488 (?)  Layout Procedure  of respondents passing s c o r e s i n components  Task o f P a i r  Logical Multiplication  Class Inclusion  Layout Procedure  Systems Analysis  Systems  2.653 (?)  12.161 (G)  11.984 (G)  9.041 (G)  S y s t e m s .'. Analysis  _  13.383 (G)  13.200 (G)  10.671 (G)  0.889 (NG)  Systems Synthesis  —  14.491 (G)  14.301 (G)  10.671 (G)  1.894 (NG)  0.936 (NG)  Transitive Recycling  _  17.711 (G)  17.495 (G)  15.541 (G)  4.632  3.084 (?)  (?)  2.319 (NG)  00 ON  Table I I I , Part 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 Less D i f f i c u l t More Difficult Task o f P a i r  Seriation  Linear Transitivity  Task o f P a i r  Logical Multiplication  Class Inclusion  Layout Procedure  Systems Analysis  Linear Transitivity  3.316  Logical Multiplication  3.604  Class Inclusion  4.259  (?)  1.758 (NG)  1.265 (NG)  Layout Procedure  7.238  4.930  4.738  3.174  (?)  (?)  (?)  (?)  15.248 (G)  11.803 (G)  12.592 (G)  10.998 (G)  8.811 (G)  16.926 (G)  15.511 (G)  15.308 (G)  13.067 (G)  10.665 (G)  1.015 (NG)  19.045 (G)  17.505. (G)  17.284 (G)  14.357 •• (G)  11* 89.4 • (G)  1.534 (NG)  i  S y s t e m s ',:. .'. -: ?. Analysis Transitive Recycling Systems Synthesis  Systems Synthesis  (?) (?)  0.377 (NG)  1.005 (NG)  00  88 These r e s u l t s p a r a l l e l score.  Apparently  s c o r e t h a t was  The  i t was  pulling  from the c y c l i c  those  obtained w i t h the composite c y c l i c  t h e l a y o u t component o f t h e c y c l i c  transitivity  transitivity  t h a t o p e r a t i o n t o w a r d s t h e c o n c r e t e t a s k s and  integration  task.  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 are  0.5868,  ably lower  than these obtained u s i n g the composite scores f o r the  tasks  (i.e.physical  p h y s i c a l domain had  (c) s o c i e t a l  0.838,  no  bio-ecological  systemic  s c o r e s t h e b i o - e c o l o g i c a l and for being undimensional c o e f f i c i e n t s may post-systemic  0.5436.  (a) p h y s i c a l ; 0 . 8 3 8 ,  ecological  and  and  partially  (b) b i o -  These c o e f f i c i e n t s are  0.696,  societal  t a s k s so i t i s t h e same.  consider-  systemic  0.714). With  The  component  t h e s o c i e t a l d o m a i n s f a l l b e l o w t h e 0.6  cumulative reflect  scales.  The  the r e l a t i v e l y  drop i n the  criterion  scalability  greater weight  that  the  t a s k s h a v e when t h e t a s k s f o r t h e d o m a i n i n c l u d e c o m p o n e n t  scores r a t h e r than composite scores. Since there are 4 concrete item t o t a l .  away  Therefore  There are 2 composite scores per  t a s k s , the composites  the systemic  tasks a f f e c t  a r e one  third  domain.  of the s i x  the s c a l a b i l i t y  coefficients  more when t h e y a r e r e p o r t e d a s c o m p o n e n t s t h a n when t h e y a r e r e p o r t e d  as  composites. Even though the "percent minimum m a r g i n a l  i m p r o v e m e n t " v a l u e s s t a y e d a b o u t t h e same,  reproducibility  c o e f f i c i e n t s w e r e l o w e r when t h e  c o n t a i n e d c o m p o n e n t s c o r e s t h a n when t h e y means t h e r e was patterns.  contained  more p o s s i b l e v a r i a t i o n t o be  domains  composite scores.  accounted  f o r by  the  This  the o r d e r i n g  H o w e v e r , t h e r e w e r e 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.  the z s c o r e s i n the bottom r i g h t  This i s consistent with  c o r n e r s o f p a r t s A and  B of Table  III.  The  89 i m p l i c a t i o n i s that there i s considerable misordering of the systemic components amongst t h e m s e l v e s Across ficulty  Domain S c o r e s .  i n both  domains.  The r i g h t m o s t  c o l u m n i n f i g u r e 2 shows t h e d i f -  o r d e r i n g o f t h e c o m p o n e n t s when we c o l l a p s e a c r o s s d o m a i n s .  " a c r o s s domain" o r d e r i n g i s b a s e d on a c r o s s domain s c o r e s . component  s c o r e s were produced by c o u n t i n g s i m u l t a n e o u s  as p a s s e s on t h e a c r o s s domain s c o r e . had  been a f a i l ,  This  The a c r o s s  passes of both  I f t h e component  domain domains  s c o r e f o r one domain  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  across  d o m a i n c o l u m n 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 c l u m p e d t o g e t h e r b e l o w t h e systemic  scores.  Table  t a s k s and t h e s y s t e m i c  I V shows t h e z s c o r e s f o r t h e s t e p s b e t w e e n t h e f o r m a l component  tasks.  c l e a r G u t t m a n s t e p more d i f f i c u l t t h a n m a r k e d w i t h a "G"  ( f o r Guttman s t e p )  Those s y s t e m i c  tasks which are a  two o u t o f t h e t h r e e f o r m a l t a s k s a r e  i n the step column.  Those t h a t a r e c l e a r  n o n - G u t t m a n 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 m a r k e d w i t h a n , "NG"  ( f o r non-Guttman s t e p ) .  The o v e r a l l  Q u e s t i o n marks i n d i c a t e t h e ambiguous  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 operational tasks.  t r a n s i t i v e r e c y c l i n g and s y s t e m s s y n t h e s i s f r o m t h e f o r m a l 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  mental maturity required to master the systemic t h e n i t c o u l d be a r g u e d t h a t t h o s e stage of c o g n i t i v e development. the f i f t h how w e l l  cases.  systemic  cognitive operations involved  operations constitute a  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  stage question c o n c l u s i v e l y but f u r t h e r analyses t h e d a t a meet some o f t h e c r i t e r i a  develop-  f o r a stage  could  fifth to s e t t l e  establish  interpretation.  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. 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)).  The  A further  90 Table  IV  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 . 3 8 0 < ? < 7.663  Probability  Isolation of V a r i a b l e s  -  -2.315  Probability Isolation of Variables  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 Bio-ecological  Overall Step Type*  Formal Tasks  Combination of V a r i a b l e s -4.064  NG  -2.545  NG  2.545  NG  Components  Layout  3.943  2.493  0.415  NG  9.669  7.794  6.013  G  5.046  4.141  1.672  6.991  5.547  2.234  -3.010  -4.936  -5.953  Transitive Recycling  8.720  7.69.9  3.042  Systems Analysis  6.040  4.004  2.371  Systems Synthesis  9.915  7.984  4.357  4.115  2.812  0.605  11.730  10.682  7.522  5.716  4.802  2.314  10.875  8.643  4.997  Transitive Recycling Systems Analysis Systems Synthesis S o c i a l Components Layout  Across  Domain  Layout Transitive Recycling Systems Analysis Systems Synthesis  Scores  *The o v e r a l l s t e p t y p e f o r e a c h c o m p o n e n t 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 b y w h a t e v e r s t e p t y p e two o u t o f t h r e e o f t h e Z s c o r e s h a p p e n t o b e 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.  The  Second  Hypothesis  second h y p o t h e s i s s t a t e s t h a t the systemic o p e r a t i o n s , or a t l e a s t  some of t h e i r components r e p r e s e n t a f i f t h s t a g e of c o g n i t i v e development above f o r m a l o p e r a t i o n s .  The  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 s t h a t the  systemic  o p e r a t i o n s and a l l of t h e i r components a r e a l t e r n a t e forms of a d u l t c o g n i t i o n , e q u a l i n d i f f i c u l t y to f o r m a l o p e r a t i o n s . h y p o t h e s i s amounts to an attempt  The q u a n t i t a t i v e t e s t i n g o f  this  to l o c a t e the d i f f i c u l t y l e v e l s of the  s y s t e m i c t a s k s i n r e l a t i o n to those f o r the f o r m a l o p e r a t i o n s .  Do  they  cluster  t o g e t h e r o r i s the d i f f e r e n c e i n . t h e i r d i f f i c u l t y l e v e l s enough to s e t a t l e a s t some s y s t e m i c components a p a r t from the f o r m a l o p e r a t i o n a l c l u s t e r ?  As  the t e r m i n o l o g y used i n p h r a s i n g the problem s u g g e s t s , the most a p p r o p r i a t e statistic (i)  to a s s e s s the second  hypothesis i s c l u s t e r  analysis,  C l u s t e r A n a l y s i s of Components C l u s t e r a n a l y s i s i s o f t e n r e f e r r e d to as an analogue of f a c t o r  f o r dichotomous d a t a . by Ward (1963).  The  c l u s t e r i n g a l g o r i t h m used was  an a g l o m e r a t i v e  I t produces a dendrogram which, a t one end,  of the n items e n t e r e d a r e most s i m i l a r and,  component s y s t e m i c s c o r e s .  a t the o t h e r end,  shows which of  The  last  two  c l u s t e r s t o be f o r c e d t o g e t h e r by  the remaining  by f o r c i n g these two  the g r e a t e s t e r r o r produced  Figure 3  by t h i s a n a l y s i s on a l l the c o n c r e t e , f o r m a l , and  a l g o r i t h m are the c o n c r e t e t a s k s and The e r r o r produced  one  i n d i c a t e s which  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 . shows the dendrogram produced  analysis  f o r m a l and  c l u s t e r s i n t o one  the  systemic t a s k s .  c l u s t e r i s by f a r  by any j o i n i n g o p e r a t i o n i n the e n t i r e  analysis.  T h i s dramatic r i s e i n the e r r o r term, however, must be i n t e r p r e t e d w i t h 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 Figure o o o  Cluster Anlysis  *  3  Dendrogram w i t h S c o r e s by Domain and S c o r e s b y Component  Systemic  D o m a i n Code o o  The l a s t c a p i t a l l e t t e r i n each abbreviated task l a b e l ( s e e KEY f o r F i g u r e s 1 a n d 2) i n d i c a t e s t h e domain. A = P h y s i c a l B = Bio-ecological C = Societal  •  CN  O O  CM*  »  vo.  oo« ON»  —* <  •—I  O CM ON . CO P-  3  O H  M  0 3  CJ  CO  CJ  pq H  t-1  CJ H  i-l  < H  n4  CJ  s i-l  a  u u  PQ  >>  <J  <!  H  o  o >, cO CO l-J  <!  > CJ  pq  e  <l  pq  o a)  pq  CJ  CO  o cu  !>.  CJ  CJ  <  CO  q  Sy  cu  TR  °. ,  i—i  Sy  4J •H U CO 60 O  o m o  TR  o e  •H  o, CM  Sy  w  Pr  u a u u  >N >N  CO  93 a dendrogram w i t h l a r g e changes i n l e v e l , e s p e c i a l l y going from two one group. two  T h i s would p r o b a b l y l e a d the i n v e s t i g a t o r to i n f e r the presence  groups."  E v e r i t t made these comments i n comparing ward's method w i t h  s i n g l e l i n k a g e method and and d i s a d v a n t a g e s .  The  the c e n t r o i d method.  i n v e s t i g a t o r can a v o i d b e i n g m i s l e d i f the  i n i n t e r p r e t i n g the r e s u l t s .  of  the  Each method has i t s advantages  o p e r a t i n g c h a r a c t e r i s t i c s of each a l g o r i t h m a r e kept i n mind and account  groups to  distorting  taken  into  With Ward's method i t i s important  to  remember t h a t the e r r o r term f o r the l a s t j o i n i n g w i l l be u n u s u a l l y h i g h and may  obscure  e q u a l l y important  d i f f e r e n c e s between the groups j o i n e d i n going  3 from 3 to 2  groups.  Scores by Domain.  The  l o g r i t h m i c graph of e r r o r terms shown a l o n g  the o r d i n a t e of f i g u r e 3 i s designed f o r the d i s t o r t i o n .  to g i v e an approximate v i s u a l  The h i g h e r the e r r o r r a t e and  the s t e e p e r the s l o p e the  more d i s s i m i l a r are the groups b e i n g j o i n e d i n t h a t s t e p . a n a l y s i s the c o n c r e t e v e r s u s non-concrete The  groupings  correction  In the p r e s e n t  are the most d i f f e r e n t ,  d i f f e r e n c e t h a t s e p a r a t e s them i s not p r o p o r t i o n a t e l y as l a r g e as the e r r o r  term would i n d i c a t e .  The  d i f f e r e n c e i s p r o b a b l y more comparable to t h a t  s e p a r a t i n g the c l u s t e r s j o i n e d i n the second  l a s t grouping.  That i s , the c o n c r e t e  t a s k s are not much f u r t h e r from the o t h e r t a s k s than the predominantly  formal  o p e r a t i o n a l c l u s t e r i s from the systemic t a s k s . While  the z s c o r e s i n d i c a t e d t h a t the top c l u s t e r was  f o r m a l c l u s t e r , t h i s c l u s t e r a n a l y s i s showed the r e v e r s e .  3.  s m a l l e r than The ambiguous  the cases  I t i s a c t u a l l y the l a s t 5% + 3% of the j o i n i n g s which are s u b j e c t to the d i s t o r t i o n i n e r r o r terms. In the p r e s e n t case, w i t h 17 items, the d i s t o r t i o n o n l y takes n o t i c e a b l e 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 g r o u p s ) .  94 were grouped upwards.  The  f a c t t h a t they s p l i t away from the f o r m a l  and j o i n e d the top systemic  t a s k s o n l y emphasizes how  tasks  ambiguous these  cases  are. A c r o s s Domain S c o r e s .  Some of the ambiguity  the a c r o s s domain s c o r e s i n t o a c l u s t e r a n a l y s i s .  can be reduced  by e n t e r i n g  F i g u r e 4 shows the dendrogram  produced by the c l u s t e r a n a l y s i s on the a c r o s s domain s c o r e s .  From t h i s  per-  s p e c t i v e , the i m p r e s s i o n gained from the z s c o r e s i s c o r r o b o r a t e d .  The  t r a n s i t i v i t y r e c y c l i n g s c o r e and  separate  the systems s y n t h e s i s s c o r e form a  c l u s t e r above f o r m a l o p e r a t i o n s i n d i f f i c u l t y . these two  To s i m p l i f y the d i s c u s s i o n of  s c o r e s we w i l l r e f e r to them as the "upper s y s t e m i c " s c o r e s or t a s k s ,  as the case may  be.  last joining s t i l l e r r o r terms.  Even w i t h the l o g a r i t h m i c s c a l i n g , the e r r o r term f o r the appears d i s p r o p o r t i o n a t e l y l a r g e r e l a t i v e to the  A l s o the systemic c l u s t e r would appear more d i s t i n c t  f o r m a l c l u s t e r i f the lower  systemic  scores  (systems a n a l y s i s and  component) were not i n c l u d e d i n the a n a l y s i s . i f we  cyclic  a r e mainly  i n t e r e s t e d i n s e e i n g how  from the the l a y o u t  D e l e t i n g those s c o r e s makes sense  f a r and upper systemic  are from the s t a n d a r d f o r m a l o p e r a t i o n s a l o n e .  earlier  It i s , after a l l ,  operations the  three  s t a n d a r d f o r m a l o p e r a t i o n s by themselves which g i v e us the b e s t e s t i m a t e of where f o r m a l o p e r a t i o n s f a l l  r e l a t i v e to systemic o p e r a t i o n s .  a d d i t i o n a l c l u s t e r a n a l y s e s are p r e s e n t e d gap between f o r m a l o p e r a t i o n s and  Therefore,  i n o r d e r to gauge the s i z e of  the d i s t i n c t i v e upper systemic  two  the  operations.  F i g u r e 5 shows the dendrogram f o r a c l u s t e r a n a l y s i s of a c r o s s domain scores.  The  c o n c r e t e o p e r a t i o n a l s c o r e s were coded as " p a s s e s " i f two  the t h r e e examples of t h a t c o g n i t i v e o p e r a t i o n had been passed.  out of  The  l o g r i t h m i c a l l y s c a l e d e r r o r term i n c r e a s e s on the o r d i n a t e show t h a t the i n c r e a s e  Figure  95  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  C o d i n g o f A c r o s s Domain S c o r e s ST p a s s = LT p a s s = p a s s 2/3 o f l i n e a r t r a n s i t i v i t y tasks MT p a s s = p a s s 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 tasks CT p a s s = p a s s 2/3 o f c l a s s i n c l u s i o r tasks Lay p a s s i n one domain and n o t l e s s than a 2 - l e v e l f a i l i n the other. S y A n p a s s = same a s L a y p a s s S y S y p a s s = same a s L a y p a s s TRec p a s s = same a s L a y p a s s  H CO  H HJ  H  >~, o  CO  CO  O  U  P-l  > CJ  fi < CO  CO CO  CJ  Pi  Figure 5  o o m  C l u s t e r A n a l y s i s Dendrogram Scores w i t h Lower S y s t e m i c ( s e e F i g u r e 2 f o r KEY a n d C o d i n g o f A c r o s s Domain  o n A c r o s s Domain Scores Deleted Figure 4 f o r Scores)  o o  CM  O O  O m  o CM  oo«  H co  y  •H •£  <4-l  | f  o  •u  0)  o u o u 60  tJ w  s  3 53  co  P-  o  H  H C_>  o u  o  CO H  >  CO CO  97  caused by j o i n i n g the systemic o p e r a t i o n s w i t h the f o r m a l o p e r a t i o n s i s f a i r l y comparable to t h a t caused by j o i n i n g the c o n c r e t e o p e r a t i o n s w i t h the Summary S c o r e s . c o n c r e t e and submitted  F i n a l l y , i n o r d e r to get the broadest  f o r m a l stage s c o r e s were reduced  overview, the  to one number each and were  to a c l u s t e r a n a l y s i s a l o n g w i t h the s c o r e s f o r the lowest of  upper s y s t e m i c components ( i . e . , expect  a c r o s s domain systems s y n t h e s i s ) .  a f a i r l y even s i z e d e r r o r term i n c r e a s e a c r o s s the two  the s y s t e m i c  i n f i g u r e 6.  Numerically,  We  formal  T h i s i s p r e c i s e l y what i s shown  (67.5) was  o n l y 1.5  e r r o r u n i t s more than  i n c r e a s e i n e r r o r f o r the j o i n i n g of the l a t t e r two w i t h the c o n c r e t e two  i n c r e a s e s were v i r t u a l l y  identical.  the i m p r e s s i o n g i v e n by T a b l e I I I p a r t s B and found  among the upper systemic  from the formal t a s k s and  should  the i n c r e a s e i n e r r o r f o r the j o i n i n g of the  s c o r e w i t h the s y s t e m i c s c o r e  The  the  j o i n i n g s only i f  s c o r e were as f a r from the f o r m a l stage s c o r e as the  stage s c o r e i s from the c o n c r e t e stage s c o r e .  (66.5).  rest.  These r e s u l t s  the  score  corroborate  C where non-Guttman s t e p s were  t a s k s , w h i l e Guttman s t e p s s e p a r a t e d  (see T a b l e I V ) .  formal  them  The p a t t e r n s d i s p l a y e d on t h r e e t a b l e s  i n t h i s c l u s t e r a n a l y s i s a r e c o n s i s t e n t w i t h the s t r u c t u r e s d'ensemble  c r i t e r i o n f o r a stage.  These a n a l y s e s i n d i c a t e t h a t i t i s u n q u e s t i o n a b l y  i b l e to c o n s i d e r systems s y n t h e s i s and  plaus-  t r a n s i t i v e r e c y c l i n g as c o g n i t i v e opera-  t i o n s b e l o n g i n g to a f i f t h stage of c o g n i t i v e development.  The next s e c t i o n  r e p o r t s the a v a i l a b l e d a t a which c o n t r i b u t e to an e v a l u a t i o n of the " f i f t h stage"  interpretation.  D.  T r a n s i t i v e r e c y c l i n g and  Third  Hypothesis  systems s y n t h e s i s are the two  c o g n i t i v e opera-  98 Figure 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 Score A c r o s s Domains  o o  CM  cn cn  o o  O  o CM  0) i-l o  U  cd  U o  o  !-i  60| S-I 1-1  W  S-i  cu  £0 3  Z  CU  S-i O  CO  cu  3  a  o u  o  3 O  c_>  CU  60  cd CO  Sc  te Sc  m o  iH cfl  6  o  PM  CU  60  CO 4J CO  ain  r—1  g o  Q  CO CO CO  o  S-i  a  <  e cu  4-1 CO  >,  CO  CO •H CO CU 4J  3  >N CO  99 t i o n s which a r e b e i n g c o n s i d e r e d as c a n d i d a t e s f o r a f i f t h f o u r component t a s k s c o r e s i n d e x i n g mastery been shown to be the most d i f f i c u l t The  4  The  o f these c o g n i t i v e o p e r a t i o n s have  t a s k s used  i n this  study.  t h i r d h y p o t h e s i s i s t h a t the g r e a t e r d i f f i c u l t y o f the upper s y s t e m i c  t a s k s i s due  to t h e i r greater s t r u c t u r a l complexity.  needed t o s o l v e them b e l o n g to a f i f t h is  stage.  stage.  The  That i s , the o p e r a t i o n s  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 :".  t h a t the g r e a t e r d i f f i c u l t y o f these t a s k s i s w h o l l y a t t r i b u t a b l e t o non-  s t r u c t u r a l content r e l a t e d f a c t o r s .  The  fifth  stage i n t e r p r e t a t i o n would be  weakened i f i t c o u l d be shown t h a t a t l e a s t p a r t of the g r e a t e r d i f f i c u l t y  of  the 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 to f a c t o r s o t h e r than the g r e a t e r d i f f i c u l t y of the c o g n i t i v e o p e r a t i o n s they r e q u i r e .  T h i s s e c t i o n examines  the d a t a a v a i l a b l e on the f a m i l i a r i t y o f the t a s k 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 t a s k s . (i)  U n f a m i l i a r i t y v s . Complexity  as Reasons f o r D i f f i c u l t y  If  to the study of systemic o p e r a t i o n s as w e l l  P i a g e t ' s approach  extends  as the study o f s o c i a l u n d e r s t a n d i n g then the u n i v e r s a l i s t f l a v o r o f h i s t h e o r y should be v i n d i c a t e d w i t h the upper s y s t e m i c t a s k s .  That would r e q u i r e evidence  t h a t competence w i t h the upper systemic o p e r a t i o n s would be m a n i f e s t e d across v a r i a t i o n s i n content.  Large d i f f e r e n c e s i n how  familiar  respondents  were w i t h v a r i o u s c o n t e n t s 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 l e v e l s o f the t a s k s .  difficulty  I f , on the o t h e r hand, t h e r e were evidence t h a t t a s k p e r "  formance v a r i e d a l o n g w i t h the f a m i l i a r i t y of the content then have been d i s c o v e r e d t o P i a g e t ' s u n i v e r s a l i s t approach,  4.  evenly  and  (a) a l i m i t would  (b) the  difficulty  A s t a g e , of c o u r s e , i s a whole group of c o g n i t i v e o p e r a t i o n s t h a t form a " s t r u c t u r e d whole" (e.g., I n h e l d e r and P i a g e t , 1958). Two c o g n i t i v e operat i o n s would not l i k e l y c o n s t i t u t e a stage i n themselves but they may be r e p r e s e n t a t i v e s of a s t a g e .  100  of the upper s y s t e m i c t a s k s c o u l d be a t t r i b u t e d to f a c t o r s o t h e r than subsumptive power of the 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 . s u g g e s t i v e evidence a g a i n s t a f i f t h  stage  the  That would amount to  interpretation.  In t h i s s e c t i o n the f a m i l i a r i t y data are compared w i t h the t a s k ance d a t a i n an attempt  to d i s c e r n whether o r not t h e r e are grounds f o r b e l i e v i n g  t h a t s u c c e s s f u l t a s k performance on the most d i f f i c u l t  systemic tasks r e q u i r e d  a n y t h i n g over and above f a m i l i a r i t y w i t h c o n t e n t s o f those t a s k s . arguments are m a r s h a l l e d i n support of the n u l l h y p o t h e s i s . are p r e s e n t e d to show how content produced  perform-  Two  First,  main  data  d i f f e r e n c e s i n f a m i l i a r i t y w i t h whole domains of  no c o r r e l a t e d d i f f e r e n c e s i n performance on t a s k s .  Second,  the complementary case i s made t h a t when f a m i l i a r i t y w i t h content i s h e l d c o n s t a n t and  i t i s the s t r u c t u r a l c o m p l e x i t y of the t a s k t h a t i s v a r i e d ,  c o r r e s p o n d i n g changes i n t a s k performance are (ii)  V a r y i n g F a m i l i a r i t y With Constant  observed,  Complexity  In. the c o n c r e t e stage performance on a l l t a s k s f e l l ' w i t h i n a  fairly  c o n s i s t e n t range r e g a r d l e s s of the f a m i l i a r i t y of the t a s k c o n t e n t . 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 paralellism  in their d i f f i c u l t y  the s o c i e t a l t a s k s was  s o c i e t a l t a s k s showed a s t r i k i n g degree of  l e v e l s d e s p i t e the f a c t t h a t the content of  c o n s i d e r a b l y l e s s f a m i l i a r to the sample as a whole.  T a b l e V, p a r t A shows the f r e q u e n c i e s of respondents  f a m i l i a r w i t h the  of each o f the c o n c r e t e stage t a s k s i n each of the t h r e e domains. f a m i l i a r i t y r a t e f o r the b i o - e c o l o g i c a l domain v a r i e s between 0 and ents.  More  The  contents un-  10  By c o n t r a s t the u n f a m i l i a r i t y r a t e f o r the s o c i e t a l domain ranges  24 to 56 respondents.  While  respondfrom  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  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 . , f o u r respondents)  there  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 b e t w e e n 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  Linear Transitivity  Seriation Frequency of Pass FamiliTask a r i t y Physical  Bio-ecological  Societal  96  96  92  96  96  70  Z  Frequency of. P a s s FamiliTask a r i t y  0.0 (NG)  84  0.0 (NG)  88  -7.135  85  (?)  96  93  Logical Multiplication  Z  Frequency of Pass FamiliTask a r i t y  Frequency o f _Pass . FamiliTask a r i t y  Z  5.071 (?)  91  95  3.226  91  96  3.203 (?)  2.714  87  86  -0.247 (NG)  78  91  5.310  -7.578  80  (?)  72  Z  Class Inclusion  -3.706 (?)  84  55  (?)  (?)  (?) 40 - 1 0 . 1 9 8 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 assessments Fami1iar i t i e s  Tasks  Frequency c Passes  Layout Procedure  41  Transitive Recycling  23  Cyclic Transitivity  35  Systems Analysis  36  Systems .Synthesis  32  Cyclic Integration  22  Nitrogen Molecule  Bacteria  44 0.715  67 6.285  (NG)  6.920 (?)  2.675  Reproduction  Starvation  59  65  C?)  13.122 (G)  8.251  (?)  CG)  2.121 (NG)  6.297 (?)  4.548 (?)  6.749.  2.879  8.19-4  6,378  7.864  CG).  C?)  CGi  9.660  8.408  11.505  CG)  CG)  (?)  5.822 (?)  (G)  (?)  KEY Nitrogen = f a m i l i a r i t y with Molecule Bacteria = familiarity with Reproduction = f a m i l i a r i t y w i t h reproduction Starvation = familiarity with in a population  concept o f n i t r o g e n molecule bacteria concept of p o p u l a t i o n concept of s t a r v a t i o n  Table V  3  Part 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 Familiarity Frequency of P a s s e s  Task Layout Procedure  67  WMB  FM  domain t a s k s and f a m i l i a r i t y  Assessment  Bakery  29 -8.670 (G)  81 4.398 (> ?  assessments  Profits  92 7.238 (?)  73  Taxes  S/D  78  46  Own Wheat 77 3.237 (?)  Transitive Recycling  27  0.282 (NG)  14.697 (G)  16.926 •(G)  13.878 (G)  Cyclic Transitivity  61  -8.310 (G)  5.940 (?)  8.818 (G)  5.535 (?)  Systems Analysis  32  -0.612 (NG)  13.154 (G)  15.248 (G)  9.840 (G)  10.671 (G)  3.049 (?)  12.381 (G)  Systems Synthesis  22  1.045 (NG)  16.620 (G)  19.045 (G)  14.840 (G)  15.954 (G)  4.439 (?)  15.732 (G)  Cyclic Integration  10  2.732 ' (?)  25.418 (G)  28.921 (G)  22.867 (G)  24.462 (G)  7.041 (?)  24.143 (G)  KEY  G = G u t t m a n s t e p (-7'.663.0 NG  ?  = non-Guttman s t e p = ambiguous s t e p  (=2.380)  (between 2.380 a n d 7.6.63.) :  WMB FM Bakery Profits Taxes S/D Own Wheat  = = = = = =  familiarity familiarity familiarity familiarity familiarity familiarity  with with with with with with  t h e wheat m a r k e t i n g b o a r d the flour m i l l the bakery concept of p r o f i t s concept of taxes l a w o f s u p p l y a n d demand  = Introductory item f o r transitive recycling 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 w h e a t 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 t a s k s and t h e s u c c e s s r a t e s f o r b i o - e c o l o g i c a l tasks. form.  The z s c o r e s on p a r t A o f t a b l e V t e l l t h e same s t o r y i n a more s y n o p t i c The z s c o r e s a r e 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 .  p o r t i o n r e p r e s e n t s those respondents who f a i l e d t h e t a s k .  The f i r s t  pro-  who were f a m i l i a r w i t h t h e c o n t e n t s b u t  The second p r o p o r t i o n r e p r e s e n t s respondents  the t a s k b u t were u n f a m i l i a r w i t h t h e c o n t e n t .  who  passed  When t h e d i f f e r e n c e between  these two p r o p o r t i o n s y i e l d s a n e g a t i v e z s c o r e then t h e t a s k was passed by more p e o p l e than were f a m i l i a r w i t h i t s c o n t e n t s .  P o s i t i v e z s c o r e s a r i s e when  more p e o p l e a r e f a m i l i a r w i t h t h e c o n t e n t s than a r e c a p a b l e o f s u c c e e d i n g on the t a s k .  Z s c o r e s i n t h e 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 o f t a s k s u c c e s s and r a t e s o f f a m i l i a r i t y w i t h t a s k c o n t e n t . N e g a t i v e z s c o r e s o f t h e Guttman s t e p magnitude i n d i c a t e t h a t respondents a whole were q u i t e u n a c q u a i n t e d performed q u i t e w e l l on i t .  as  w i t h the contents of the task but nevertheless  Such i s t h e case f o r t h e s o c i e t a l domain.  s c o r e s a r e a l l n e g a t i v e and w i t h i n o r c l o s e t o t h e Guttman s t e p range. s i t u a t i o n i s r e v e r s e d f o r t h e b i o - e c o l o g i c a l domain.  The z The  Two o f t h e z s c o r e s a r e  non-Guttman and t h e o t h e r two a r e ambiguous range p o s i t i v e .  The c o n t r a s t be-  tween t h e l a r g e n e g a t i v e z s c o r e s f o r t h e s o c i e t a l domain and t h e near z e r o t o moderately  p o s i t i v e z s c o r e s i n t h e b i o - e c o l o g i c a l domain i n d i c a t e s once a g a i n  t h a t t h e c o n t e n t o f t h e s o c i e t a l domain was much l e s s f a m i l i a r t o respondents as a whole.  Y e t t h i s u n f a m i l i a r i t y was n o t accompanied by any decrement i n  s u c c e s s r a t e s on t h e t a s k . s o c i e t a l domain t a s k s .  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  Thus one p o t e n t i a l source o f c o r r o b o r a t i v e e v i d e n c e  f o r a c o n t e n t r e l a t e d i n t e r p r e t a 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 components has been  abrogated.  Of more d i r e c t r e l e v a n c e are,the' d a t a f o r t h e upper s y s t e m i c components  105.  themselves.  Here a g a i n , d i f f e r e n c e s i n the f a m i l i a r i t y of t a s k c o n t e n t a r e not  accompanied by s i m i l a r d i f f e r e n c e s i n t a s k performance. shows the d a t a f o r the b i o - e c o l o g i c a l domain.  Part B of table V  The columns a r e headed by  f o u r most important content items i n the b i o - e c o l o g i c a l interview."' show both the s y s t e m i c components and  the composite  The  the rows  systemic operations.  Part  C o f t a b l e V shows the comparable d a t a f o r the s o c i e t a l s y s t e m i c s c o r e s .  For  b o t h domains the most important f a m i l i a r i t y items to note are the ones t h a t were most u n f a m i l i a r .  These items s e t the l i m i t s on the sample's  w i t h the r e s p e c t i v e systems under c o n s i d e r a t i o n . the b i o - e c o l o g i c a l domain was f a m i l i a r w i t h t h a t concept. was  these two t e n t was  The most u n f a m i l i a r i t e m i n  the n i t r o g e n m o l e c u l e .  Only 44 respondents were  In the s o c i e t a l domain the most u n f a m i l i a r i t e m  the wheat marketing board  t h i s item.  familiarity  (WMB).  Only 29 respondents were f a m i l i a r w i t h  An i n s p e c t i o n o f the f a m i l i a r i t y r a t e s w i t h s p e c i a l emphasis on items i n d i c a t e s t h a t , as w i t h the c o n c r e t e t a s k s , the s o c i e t a l  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 c o n t e n t .  s u c c e s s f u l t a s k performance  A l s o , the r a t e of  on the upper systemic components was  r o u g h l y w i t h i n the same range  (22 to 32 p a s s e s ) .  p a t t e r n , however, s u c c e s s f u l t a s k performance  con-  again  U n l i k e the c o n c r e t e stage  i n both domains was  than f a m i l i a r i t y w i t h the most u n f a m i l i a r content i t e m s .  l e s s frequent  Hence, t h e r e a r e no  5.  The d e t a i l s o f the f a m i l i a r i t y assessments are g i v e n i n A p p e n d i c i e s A, and C a l o n g w i t h procedures f o r t a s k a d m i n i s t r a t i o n .  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 t a s k s , 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 m a t e r i a l s used i n both the l a y o u t and the r e c y c l i n g p r o c e d u r e s . L i k e w i s e w i t h 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 s y n t h e t i c components used the same m a t e r i a l s and c o n c e p t s . Hence, the same s e t o f f a m i l i a r i t y assessments a p p l y t o b o t h components. S i n c e the s y s t e m i c t a s k s were arranged such t h a t i n f o r m a t i o n gained i n p r i o r t a s k s c o n t i n u e d to be o f r e l e v a n c e f o r l a t e r t a s k s comparisons a r e r e p o r t e d between a l l s y s t e m i c f a m i l i a r i t i e s and a l l s y s t e m i c t a s k s .  B,  106 negative  z scores f o r comparisons of the upper systemic  most u n f a m i l i a r c o n t e n t  items.  Nevertheless,  among t h e z s c o r e s i s t h e same a s  domain.  than  stage.  those  Specifically,  i n the  i s not  accompanied by  a task performance d e f i c i t  Hence t h e g r e a t e r u n f a m i l i a r i t y to account  of the systemic  the upper systemic  tasks i n both  of the  of s i m i l a r  task content  f o r the b u l k of the g r e a t e r systemic  the  bio-ecological  T h i s means t h a t o n c e 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  content  the  the p a t t e r n of d i f f e r e n c e s  i n the concrete  s o c i e t a l domain z s c o r e s are a g a i n lower  components w i t h  societal magnitude.'  does not  task d i f f i c u l t y .  domains a p p a r e n t l y depends on  appear  Success  factors  on  over  Q ...  and  above f a m i l i a r i t y In the  away f r o m (i.e., was  Cor u n f a m i l i a r i t y ) w i t h t h e i r  s o c i e t a l domain the l a y o u t procedure  the  familiarity  score f o r the l e a s t  the wheat m a r k e t i n g  less  familiar,  e c o l o g i c a l domain.  s o c i e t a l ) was  see  does f a l l  familiar  t a b l e V,  t a s k p e r f o r m a n c e was  part C).  a Guttman  evidence  step  element i n the c y c l e Although, the  more s u c c e s s f u l t h a n  T h i s w o u l d seem t o b e  the l a y o u t procedure. domain of content  board;  contents.  i n the b i o -  for a practice effect  Even though o r d e r of p r e s e n t a t i o n i s confounded  i t was  more n o v e l .  known t h a t t h e c o n t e n t Despite  a c r o s s the whole sample s t i l l  i n the second domain  that countervaling factor,  i m p r o v e d on  element  with  with (I.e.,  performance  t h e l a y o u t component o f  cyclic  transitivity.  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 the above comparisons. With the present 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 bles. 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 b e c a u s e 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 w h o l e r a n g e o f a b i l i t y l e v e l s i n the sample. . •  8.  At the i n d i v i d u a l level..of/-analysis t h i s c o n c l u s i o n i s a l s o upheld. For exa m p l e , 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 s y s t e m s s y n t h e s i s , 13 ( 5 9 % ) w e r e u n f a m i l i a r w i t h t h e WMB. N o r was f a m i l i a r i t y w i t h t h e m o s t 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 t h e 29 r e s p o n d e n t s who w e r e 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 s y s t e m s s y n t h e s i s .  : 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 a r e  s i d e r e d t o g e t h e r , however, the f i f t h stage i d e a appears back to the scalogram it  t h a t produced  f i g u r e 2 and  stronger.  107  con-  Referring  the z s c o r e s on t a b l e  IV,  can be seen t h a t the upper s y s t e m i c s c o r e s a r e of more or l e s s the same  difficulty  l e v e l r e g a r d l e s s 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  societal  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 s y s t e m i c t a s k s v e r y substantially.  In the next s u b s e c t i o n we  c o n s i d e r cases where the  content  i s h e l d c o n s t a n t but performance n e v e r t h e l e s s v a r i e s , (iii)  V a r y i n g O p e r a t i o n s w i t h Constant  Content  The above c o n c l u s i o n i s c o r r o b o r a t e d by the d a t a f o r the lower components. caused  I f l e s s f a m i l i a r content o f the s y s t e m i c i n t e r v i e w s r e a l l y  d e t r i m e n t s i n t a s k performance then the d e t r i m e n t  j u s t as e v i d e n t i n the lower s y s t e m i c t a s k s as the upper. used  systemic  the same c y c l e s w i t h the same elements.  should have been Both s e t s of t a s k s  Y e t d e s p i t e 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 t a s k c o n t e n t s w i t h i n domains the upper components were more d i f f i c u l t .  T h i s suggests a g a i n t h a t the g r e a t e r d i f f i c u l t y of the upper  s y s t e m i c components cannot be w r i t t e n 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 i t e m of i n t e r e s t from T a b l e V, C i s the r i g h t m o s t column l a b e l e d "Own Wheat". T h i s was an i t e m used to i n t r o d u c e 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 a b l e t o t r a c e the t r a i l o f the wheat around the c y c l e , back t o the farmer i n the form of b r e a d . The a c t u a l t r a n s i t i v e r e c y c l i n g i t e m r e q u i r e d 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 a l o n g e x a c t l y the same p a t h but i n the o p p o s i t e d i r e c t i o n . Only about 25% of the respondents c o u l d do t h i s . The two items were a l a r g e Guttman s t e p a p a r t (z = 13.878). On the f a c e of i t , the two items seem l o g i c a l l y e q u i v a l e n t . The obvious e x i s t e n c e of p s y c h o l o g i c a l d i f f e r e n c e s between them impels us t o 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 Overall,  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  greater d i f f i c u l t y  of the upper systemic  tasks i s not,  a t t r i b u t a b l e to the u n f a m i l i a r i t y of t h e i r  contents.  i n t e r p r e t a t i o n of t h e i r greater d i f f i c u l t y  remains  E.  In this issue.  Age  section ancillary  Flavell  of Mastery  data  Thus a f i f t h  preceding  final  " i n " a s t a g e was  consolidation.  t o t h e s e d i f f e r i n g v i e w s o f how Table  stage  viable.  Data  are r e p o r t e d that, are, r e l e v a n t ' t o ; the-stage  (1971a) posed a b r u p t n e s s  spent  of t r a n s i t i o n c r i t e r i o n  for  t o age  the  a model wherein  most  a c t u a l l y a long gradual t r a n s i t i o n period  Table VI  d a t a t h a t i s r e l e v a n t .-.v:- -  shows age  long a t r a n s i t i o n p e r i o d might  last.  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 o n  scores related  The  f o r the most p a r t ,  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 W o h l w . i l l ' : ,(1973) s u g g e s t e d of the time  rejected.  of mastery f o r formal versus  systemic  various  logic.  The  scores  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 intended  to c l a s s i f y  respondents  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  T h i s measure o f f o r m a l o p e r a t i o n a l stage a t t a i n m e n t not  the respondent passed  tasks.  at l e a s t  two  For the purposes of comparison,  f o r o v e r a l l mastery of systemic assigns a "pass" four tasks:  t o t h o s e who  logic.  out  simply i n d i c a t e s whether  summary s c o r e was  systems s y n t h e s i s . component s c o r e s and  or  calculated  T h i s "summary s y s t e m s t h i n k i n g at l e a s t  three of the  1) b i o l o g i c a l d o m a i n t r a n s i t i v e r e c y c l i n g ,  transitive recycling,  pre-formal.  of the three formal o p e r a t i o n a l  a similar  have passed  score  following  2) s o c i a l  domain  3) b i o l o g i c a l d o m a i n s y s t e m s s y n t h e s i s , 4) s o c i a l  I n a d d i t i o n t a b l e VI p r e s e n t s a l l the a c r o s s domain a l l o f t h e component s c o r e s by  domain.  score"  domain systemic  109 T a b l e VI Age  p r o f i l e f o r pass es on f o r m a l and systemic s c o r e s 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. Grade Systemic  III  Familiarities  Nitrogen Molecule Wheat M a r k e t i n g Board Summary  8  10- . V  12  14  16  18  VII  IX  XI  XII]  Number out o f s i x t e e n / g r a d e pas S i n g  0 0  0 0  3 6  11 4  14 7  16 12  0  0  6  15  16  16  A  n  A  u  6  3  9  1 0 0  0 0 1  9 6 5  14 15 7  16 16 14  16 15 15  0 0 0 4 0 1 0 0  1 0 1 5 0 3 1 0  7 1 5 12 2 11 6 0  10 5 8 16 8 16 10 5  11 7 9. 16 8 15 11 3  12 10 12 14 a 15 12 7  1 0 0 1 0 0 1 0  2 1 1 1 1 0 1 0  4 2 1 6 0 0 3 0  5 8 4 5 8 2 5 7  10 10 7 9 7 5 11 8  14 11 9 10 6 3 13 8  Scores  Formal Stage Summary Systems T h i n k i n g Score  U  U  Formal Tasks Probability I s o l a t i o n of Variables Combination o f V a r i a b l e s  Cyclic  Transitivity  B i o - e c o l o g i c a l : layout Bio-ecological: recycling B i o - e c o l o g i c a l : combined S o c i a l : layout Social: recycling S o c i a l : combined A c r o s s Domain: l a y o u t *Across Domain: r e c y c l i n g Cyclic Integration Bio-ecological: sy.analysis Bio-ecological: sy.synthesis B i o - e c o l o g i c a l : combined Social: sy.analysis Social: sy.synthesis S o c i a l : combined A c r o s s Domain: a n a l y s i s *Across Domain: s y n t h e s i s  *Best  i n d i c a t o r s o f age p r o f i l e s f o r top systemic  scores  110 As expected, Successes  the 8 and  10 y e a r o l d s r a r e l y succeeded on any o f the t a s k s .  on the f o r m a l o p e r a t i o n a l t a s k s s t a r t a p p e a r i n g a t age 12 but i t  i s not u n t i l age  14 t h a t the m a j o r i t y of the respondents  pass the m a j o r i t y  of the f o r m a l o p e r a t i o n a l t a s k 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 the f r e q u e n c i e s f o r the systemic  i n t a b l e VI i s t h a t systemic abstract thinking. At age  t h i n k i n g l a g s about two  Successes  s t a r t appearing  y e a r s behind  scores  formal  i n some numbers around age  14.  16 s e v e r a l = of-: the s c o r e s show s u c c e s s f u l performance f o r the m a j o r i t y  of the respondents.  At no age  f r e q u e n c i e s of success  l e v e l , however, does any  systemic  s c o r e show  t h a t match those f o r the f o r m a l stage s c o r e .  Most  s t r i k i n g i n t h a t r e g a r d i s the a c r o s s domain t r a n s i t i v e r e c y c l i n g s c o r e . not know a t what age, tion. age  i f ever, the m a j o r i t y becomes competent w i t h t h i s  There a r e h i g h f a i l u r e r a t e s on systemic  groups.  abruptness  The  s c o r e s throughout  do  opera-  the o l d e r  t r a n s i t i o n i n t o the f o r m a l stage appears to s a t i s f y  criterion.  We  Flavell's  The mastery of the upper s y s t e m i c t a s k s i s more i n  l i n e w i t h the p a t t e r n of g r a d u a l t r a n s i t i o n t h a t W o h l w i l l suggests * as a c h a r a c t e r i s t i c of P i a g e t i a n s t a g e s .  The  c o n t r a s t may  be a f u n c t i o n of the i n h e r e n t  d i f f i c u l t y of the o p e r a t i o n s chosen to r e p r e s e n t each " s t a g e " . t a s k s used i n t h i s study might be r e l a t i v e l y easy  The  formal  compared to o t h e r  formal  t a s k s which might show a more g r a d u a l t r a n s i t i o n p a t t e r n .  F.  Summary of R e s u l t s  ... In a c c o r d w i t h the p r e d i c t i o n  made , i n the f i r s t .hypothesis,., the P i a g e t i a n  approach -appearechtq " g e n e r a l l z e T ^ e l l ^ t o ^ t l i & c - b ^ x e c e l o g i c a l - and  Ill s o c i e t a l content domains. supported  f o r two  t h e s i s and  The p r e d i c t i o n made by the second h y p o t h e s i s  subcomponents of the systemic o p e r a t i o n s .  The  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  operational tasks.  The d i f f e r e n c e was  was  systems syn-  than the f o r m a l  of a stage s i z e d 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 l a y o u t component  tended to f a l l  towards the c o n c r e t e stage c l u s t e r i n terms of  l e v e l and  difficulty  the systems a n a l y s i s component f e l l w i t h i n the same range of  f i c u l t y as the f o r m a l o p e r a t i o n a l t a s k s .  dif-  Under the t h i r d h y p o t h e s i s the r e s -  pondents' r e l a t i v e f a m i l i a r i t y w i t h the c o n t e n t of t a s k s was  examined.  The  g r e a t e r d i f f i c u l t y of the upper s y s t e m i c 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 n o v e l c o n t e n t of the t a s k s a s s e s s i n g them.  The  s y s t e m i c t a s k s and  approximately each age  t h e i r subcomponents were found  to be mastered  two y e a r s l a t e r than the f o r m a l o p e r a t i o n a l t a s k s but w i t h i n  l e v e l the f r e q u e n c i e s of success on the s y s t e m i c t a s k s were g e n e r a l l y  lower than those f o r the f o r m a l o p e r a t i o n a l t a s k s .  I t appears t h a t the upper  systemic t a s k s r e p r e s e n t a f i f t h s t a g e of c o g n i t i v e development a l t h o u g h 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 r u l e d  out.  the  "V.  DISCUSSION  T h i s c h a p t e r b e g i n s w i t h a review of the r e s u l t s c o r r e s p o n d i n g t o of  the t h r e e hypotheses  and then proceeds  each  to an examination o f the i s s u e s  r e l a t e d to the i n t e r p r e t a t i o n o f the r e s u l t s .  A.  The Three Hypotheses  The r e c u r r i n g theme o f t h i s s e c t i o n concerns the r e l a t i v e d i f f i c u l t y the "upper s y s t e m i c " t a s k s and the m e r i t s of evoking a f i f t h development i n an e f f o r t to account  for. t h i s f a c t .  The  stage o f c o g n i t i v e  f i r s t hypothesis deals  w i t h groundwork t h a t i s p r e r e q u i s i t e to an examination of t h i s i s s u e . second  In the  s u b s e c t i o n ( i i ) the f i n d i n g s w i t h r e g a r d to the second h y p o t h e s i s a r e  e v a l u a t e d a g a i n s t the s t r u c t u r e s d'ensemble and for  of  the Guttman s c a l e  i d e n t i f y i n g a stage o f c o g n i t i v e development.  criteria  In the t h i r d s u b s e c t i o n  the content r e 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 d i s c u s s e d w i t h r e f e r e n c e to the age d a t a . f i n a l s u b s e c t i o n the evidence f o r and a g a i n s t the stage v e r s u s  In the  parallel  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:  E x t e n d i n g P i a g e t i a n Theory  B e f o r e an examination c o u l d be undertaken  i t was  of 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 o r g a n i z a t i o n n e c e s s a r y to f i r s t  i d e n t i f y and document some of  the 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 i n u n d e r s t a n d i n g such open systems. requirement  This  l e d to the use o f h i t h e r t o seldom s t u d i e d types of c o n t e n t s i n the  assessment t a s k s ( i . e . , c o n t e n t s more o f t e n c o n t a i n i n g open systems).  Before  these content domains c o u l d be used to i n t r o d u c e n o v e l c o g n i t i v e o p e r a t i o n s , i t was  n e c e s s a r y to demonstrate  t h a t the more t h o r o u g h l y 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 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 c o n t e n t s .  113 The  f i r s t hypothesis,>which s t a t e s t h a t P i a g e t ' s account  development i n the impersonal s o c i e t a l c o n t e n t , was  sphere  of c o g n i t i v e  can Be extended to B i o - e c o l o g i c a l and  g e n e r a l l y supported.  were examined from two v i e w i n g d i s t a n c e s .  Data B e a r i n g upon t h i s These macroscopic  and  hypothesis  microscopic  a n a l y s e s are B r i e f l y summarized Below. M i c r o s c o p i c L e v e l of A n a l y s i s .  At t h i s l e v e l i t was  p r e d i c t e d t h a t the  d i f f i c u l t y o r d e r i n g s of e q u i v a l e n t t a s k s would Be the same a c r o s s a l l domains. S p e c i f i c a l l y , i t was ficult  p r e d i c t e d t h a t the o r d e r of these t a s k s , from l e a s t  to most d i f f i c u l t , would Be as f o l l o w s :  logical multiplication^ gration. and  first  observed  cyclic  inte-  i n Both the B i o - e c o l o g i c a l  For reasons o u t l i n e d e a r l i e r , measures of o n l y  the  f o u r of these c o g n i t i v e o p e r a t i o n s w e r e . p o t e n t i a l l y a v a i l a B l e w i t h i n  the p h y s i c a l domain. i n c l u s i o n t a s k was and  transitivity,  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 , and  T h i s i s e x a c t l y the o r d e r t h a t was  s o c i e t a l domains.  seriation, linear  dif-  Contrary  to e x p e c t a t i o n s , the p h y s i c a l domain c l a s s  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  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 t a s k .  task Somewhat  p a r a d o x i c a l l y , then, the o r d e r o f d i f f i c u l t y p r e d i c t i o n s Based upon P i a g e t i a n t h e o r y were more a c c u r a t e i n the n o v e l B i o - e c o l o g i c a l and than i n the more f a m i l i a r s t a n d a r d p h y s i c a l domain. o f the c l a s s i n c l u s i o n and f u n c t i o n o f sampling  The  simple  demonstrated the  expected  l o g i c a l m u l t i p l i c a t i o n , But not c l a s s i n c l u s i o n .  m i s o r d e r i n g 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 c u r r e n t r e s e a r c h was  equivalency  i t might Be assumed t h a t w i t h a l a r g e r  numBer of s u B j e c t s , i n d i v i d u a l s might have emerged who  The  oBserved  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 c o u l d be a  p e c u l i a r i t i e s ' and  p a t t e r n of u n d e r s t a n d i n g  s o c i e t a l domains  designed  of these t a s k s were and why  The  to e x p l a i n away, however.  to determine what the d i f f i c u l t y  they d i d or d i d not conform to t h e i r  orderings  hypothesized  ino r d e r i n g i s n o t r e a d i l y apparent  from these data.  however, s u p p o r t i n g data were o b t a i n e d predicted by hypothesis expectations.  This single d i f f i c u l t y  aside,  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  o n e . 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  From t h i s e v i d e n c e  t h e same r e a s o n i n g d e v e l o p e d  i t seems r e a s o n a b l y  by P i a g e t t o account  safe to conclude  that  f o r the order of 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 d o m a i n may be--extended t o t h e b i o - e c o l o g i c a l a n d s o c i e t a l domains as w e l l . Before  t u r n i n g to the macroscopic  level  i n o r d e r t o s e e 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 theory apply domains, t h e matter  o f stages  of stages  a concrete  staged  as s t r u c t u r e d wholes.  systemic  S t r u c t u r e d Wholes. change q u i t e r e a d i l y  tation,  The d i f f i c u l t y  from person  to person,  f r o m mode o f p r e s e n t a t i o n t o mode Moreover, i t appears that  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 another  on second  operation's  linked  presen-  difficulty  to the novelty of  content.  i n c o n s i s t e n c i e s observed  a c r o s s domains i m p l y t h a t a t t h e most  grained l e v e l o f a n a l y s i s the stages r e a l l y " s t r u c t u r e d wholes" as P i a g e t has claimed  if  each  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 .  o f o n e c o g n i t i v e o p e r a t i o n may b e r e d u c e d  the m a t e r i a l s and/or  1958).  that the p o s s i b i l i t y of  orderings of cognitive operations  may b e 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  The  t o be d e a l t w i t h i s  operational task i s discussed.  cognitive operation i s d i f f e r e n t i a l l y difficulty  The f i r s t After  o f p r e s e n t a t i o n and from domain t o domain.  The  content  a s 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  regard t o the stage o f concrete operations. the matter  to the novel  fine  a r e s t r u c t u r e s d'ensemble o r  they a r e (e.g., I n h e l d e r and P i a g e t ,  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 present, d a t a . w o u l d n o t have a r i s e n  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 . , b y v i r t u e o f t h e i r common s t a g e ) . o p e r a t i o n may whole.  The  i d i o s y n c r a s i e s of each c o g n i t i v e  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  from the s t r u c t u r e d  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  they are taken out  o f t h a t c o n t e x t and  t h e n compared w i t h e a c h o t h e r .  As  a  whole stage of o p e r a t i o n s , however, the c o n c r e t e o p e r a t i o n s are p r e d i c t a b l e . Specifically,  they are a l l mastered i n middle  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 evidence present  childhood.  another  The  impetus t o compare  comes f r o m e a r l i e r e m p i r i c a l  that they are ordered w i t h i n the stage of concrete o p e r a t i o n s . d a t a , by  a l s o c o m p a r i n g them a c r o s s d i v e r s e c o n t e n t  t h a t the e a r l i e r evidence of task content.  o f s y s t e m a t i c o r d e r i n g s was  d o m a i n s , shows  s o m e t h i n g o f an  That i s , a l l the assessment t a s k s tended  Formanek and  entities  Content areas  ( e . g . , e c o n o m i c s i t u s e s ) c a n o n l y be  yield different be  Gurian, 1976).  t e m p e r e d by  orderings. o n l y a few  that deal with  inanimate Kohnstamm,  non-physical  r e p r e s e n t e d v e r b a l l y and  they  s e q u e n c e s . .The w o r k o n 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 the present  evidence  P e r h a p s b e c a u s e i t was tasks of s i m i l a r  "structured wholes." ings w i t h i n stages.  t h a t changes i n content l e s s focused  content,  That i s not  the present  t o say  on  can change  data support  the of  the i d e a of  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 f e x t e n s i v e e n o u g h c o m p a r i s o n s a r e made among such  search f o r such o v e r a l l w i t h i n - s t a g e orderings,however,  much m o r e e l a b o r a t e u n d e r t a k i n g .  may  must  the r e l a t i v e d i f f i c u l t y  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 s a m p l e s o f r e s p o n d e n t s , The  artifact  t o employ  p h y s i c a l o b j e c t s a s t e s t i n g m a t e r i a l s ( e . g . , G l i c k and W a p n e r , 1 9 6 8 ; 1968;  The  A greater s e n s i t i v i t y  concrete  o r d e r i n g s do  emerge.  i s now  seen as  to type of  content  a  is required. Macroscopic  L e v e l of A n a l y s i s .  At  t h i s l e v e l of a n a l y s i s the  first  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.  This  116  i s p r e c i s e l y what was.observed w i t h the e x c e p t i o n of the s o c i e t a l transitivity  task.  cyclic  That e x c e p t i o n i s d i s c u s s e d i n more d e t a i l below.  the c e n t r a l P i a g e t i a n n o t i o n of a d i s c o n t i n u i t y between c o n c r e t e and concrete  thought was  difficulty  supported  l e v e l data.  Given  by the a p p r o p r i a t e c o r r e s p o n d i n g  Generally, post-  p a t t e r n i n the  the support p r o v i d e d by these m a c r o s c o p i c  and  m i c r o s c o p i c a n a l y s e s , the g e n e r a l P i a g e t i a n approach would appear to a p p l y q u i t e w e l l 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  c o n f i d e n t t h a t t h e r e were no major hidden  confounds v i t i a t i n g the  comparisons  t h a t were to be made between the systemic  o p e r a t i o n a l t a s k s and  the  formal  operational tasks. Before t a s k s and  the d i s c u s s i o n goes on to the comparisons between the  the f o r m a l t a s k s t h e r e i s one more i s s u e t h a t must be mentioned.  That i s the i n t e r p r e t a t i o n of the u n u s u a l l y low d i f f i c u l t y l a y o u t components of c y c l i c Concrete domain  l a y o u t procedure may  I t was  suggested  e a r l i e r t h a t the s o c i e t a l  have been e x t r a o r d i n a r i l y easy owing to a  I t i s a l s o p o s s i b l e t h a t the l a y o u t procedure may  c o n c r e t e stage example of a s y s t e m i c the d i f f i c u l t y  l e v e l s f o r the  transitivity.;  Stage Systerns L o g i c ?  practice effect.  i t y and  systemic  operation.  be a  F u t u r e r e s e a r c h c o u l d compare  l e v e l s o b t a i n e d a c r o s s f a c t o r i a l v a r i a t i o n s of element  o r d e r of p r e s e n t a t i o n ( p r a c t i c e ) w i t h a s m a l l e r range of  respondents.  For example, Kates and K'atz (1977) s t u d i e d u n i n s t r u c t e d u n d e r s t a n d i n g hydrologic  (water) c y c l e i n 3, 4, and  5 year o l d s .  i z a t i o n e n t a i l e d i n the l a y o u t procedure,  familiar-  of  the  With the p r e t e s t f a m i l i a r -  a l l the elements of the water c y c l e  would be f a m i l i a r enough to c o n c r e t e o p e r a t i o n a l and  e a r l y formal o p e r a t i o n a l  c h i l d r e n to i n f o r m us b e t t e r about the e a r l i e s t appearance of mastery over type of o p e r a t i o n .  this  . 117  (ii)  Second H y p o t h e s i s : The  second  Upper Systemic  h y p o t h e s i s was  Tasks  supported by the d i f f i c u l t y l e v e l d a t a .  t h e s i s two p r e d i c t e d t h a t t h e r e would be a gap  in difficulty  same s i z e between a t l e a s t some s y s t e m i c components and f o r m a l o p e r a t i o n a l t a s k as t h e r e was t a s k and  the most d i f f i c u l t  t h a t the gap  the most  difficult formal  T h i s amounted to a p r e d i c t i o n  i n terms of d i f f i c u l t y l e v e l s Between the f o r m a l t a s k s and  upper s y s t e m i c components would B e a stage s i z e d gap. p r e d i c t e d t h a t the d i f f i c u l t y f i f t h stage.  l e v e l s of the  Between the l e a s t d i f f i c u l t  concrete task.  Hypo-  the  In o t h e r words, i t was  l e v e l s data would suggest  the p o s s i b i l i t y of a  S i n c e the c o r r o b o r a t i o n of the o v e r a l l f i r s t h y p o t h e s i s p r e -  c l u d e s an i n t e r p r e t a t i o n of the 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 of the upper systemic t a s k s i n terms of confounding d i s c r e t e n e s s of s t a g e s , any observed  content r e l a t e d d i f f e r e n c e s i n the  g r e a t e r d i f f i c u l t y i s a l l the more r e a s o n -  a b l y i n t e r p r e t e d as a f u n c t i o n of the g r e a t e r s t r u c t u r a l c o m p l e x i t y form r e l a t e d d i f f i c u l t y ) of the upper s y s t e m i c components. the Guttman step a n a l y s e s p o r t i o n s ) and  The  (i.e.,  r e s u l t s of  ( i . e . , z s c o r e s f o r the d i f f e r e n c e s between p r o -  the c l u s t e r a n a l y s e s show t h a t the systems s y n t h e s i s and  t i v e r e c y c l i n g components were indeed a stage s i z e d gap more d i f f i c u l t the f o r m a l o p e r a t i o n a l t a s k s .  The  transithan  t h i r d h y p o t h e s i s dealt', w i t h a content  r e l a t e d a l t e r n a t i v e t o a f i f t h stage i n t e r p r e t a t i o n .  B e f o r e 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 t h a t c o n t e x t , the argument f o r i t s reasonableness The  i s d i s c u s s e d i n d e t a i l w i t h r e s p e c t t o the second  hypothesis.  second h y p o t h e s i s e n t a i l e d analyses' w h i c h were r e l e v a n t t o the s t r u c t u r e s  d'ensembleo cr±tex;ton:-(P,iaget.;.;i$60| F l a v e l l , 1971a) f o r - i d e n t i f y i n g a stage  and  .to. -the- c r i t e r i o n : - t h a t s t a g e s form q Guttman scale, (i.. e; P i a g e t ' s (I960) sequence  ;  118 and h i e r a r c h y c r i t e r i a ) . s t r u c t u r e s d'ensemble. analyses. step  The upper systemic t a s k s d i d indeed appear to be They c l u s t e r e d e x c l u s i v e l y t o g e t h e r i n the  cluster  They were s e p a r a t e d from each o t h e r i n d i f f i c u l t y by non-Guttman  ( i . e . p a s s i n g t r a n s i t i v e r e c y c l i n g and  as common as the r e v e r s e ) .  f a i l i n g systems s y n t h e s i s was  about  A l s o , the s c a l a b i l i t y c o e f f i c i e n t s i n d i c a t e d t h a t  the s y s t e m i c components were not u n i d i m e r i s i o n a l and  c u m u l a t i v e amongst  The  also s a t i s f i e d with respect  c r i t e r i o n t h a t stages form a Guttman s c a l e was  to the upper systemic t a s k s . The  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  gave u n e q u i v o c a l evidence of t h i s . concurrence  criteria  s u b s e c t i o n A, The difficult  themselves.  Evidence r e l e v a n t t o the abruptness  and  ( F l a v e l l , 1971a) f o r i d e n t i f y i n g s t a g e s i s examined i n  (IV) of t h i s c h a p t e r  ("Age  Related  Criteria").  systems a n a l y s i s and layout'component w e r e ^ n o t acSuttmanr-stepmore :  than the most d i f f i c u l t  formal o p e r a t i o n .  Strictly  n e i t h e r c o r r o b o r a t e s nor d e t r a c t s from n e i t h e r the f i f t h stage nor the p a r a l l e l i n t e r p r e t a t i o n . domain l a y o u t component was does suggest  speaking  interpretation  N e v e r t h e l e s s the f a c t t h a t the  so c l o s e to the most d i f f i c u l t  societal  concrete operation  t h a t c o n c r e t e staged s y s t e m i c o p e r a t i o n s might e x i s t .  o p e r a t i o n s were found, formal operations.  this  I f such  s y s t e m i c o p e r a t i o n s would be p a r a l l e l to more than  They would be a whole c l a s s of l o g i c a l o p e r a t i o n s  i n g a l o n g w i t h those exemplars o f , and p r e c u r s o r s o f , f o r m a l l o g i c a l  just  developoperations  s t u d i e d by P i a g e t and h i s c o l l e g u e s . (iii)  T h i r d Hypothesis; The  G r e a t e r Content  Difficulty  t h i r d h y p o t h e s i s p r e d i c t e d t h a t the d i f f i c u l t y of the most  s y s t e m i c t a s k s would not be w h o l l y a t t r i b u t a b l e to any of t a s k content p e c u l i a r to those t a s k s .  The  difficult  greater u n f a m i l i a r i t y  z s c o r e s f o r the d i f f e r e n c e s  —  .11-9 between t h e p r o p o r t i o n s o f respondents p a s s i n g 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  the familiarity  o f passes on both p r e c l u d e  straightforward a t t r i b u t i o n of the greater d i f f i c u l t y tasks  to content  fifth  stage To  ( s e e t a b l e s V and V I ) .  o f t h e upper  With these  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  d e c i d e what e f f e c t c o n t e n t  necessary A priori  difficulty  assessments  systemic  results the  falsification  attempt.  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  to d i s t i n g u i s h the content  any  from the r e q u i r e d operative  i t i s  knowledge.  i t seemed t h a t ' 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 a n d t h e w h e a t c y c l e  would 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 order  to apply  those  contents.  the operations  of c y c l i c  E m p i r i c a l l y , however, i t turned  mastered t h e t a s k s even without The  transitivity  complete i n i t i a l  s y s t e m s s y n t h e s i s c o m p o n e n t s seemed a p r i o r i  with  t h e concepts 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  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 , i n t h e s o c i a l domain.  Again,  and systems a n a l y s i s t o  o u t t h a t some r e s p o n d e n t s f a m i l i a r i t y w i t h those to require further on t h e p o p u l a t i o n  elements.  familiarity l e v e l i nthe  t a x e s , and supply/demand r e l a t i o n s h i p s  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 m a s t e r e d t h e s y s t e m s s y n t h e s i s t a s k s w e r e 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 content.  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 lower  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 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 v a r i a t i o n s i n content  familiarity  across  very  difficult  i n both.  A l l o f these  t o argue t h a t the greater d i f f i c u l t y  Finally, the  f i n d i n g s make  o f t h e upper  tasks i s a t t r i b u t a b l e i n large part to the greater d i f f i c u l t y T h i s does n o t prove t h a t content  that  d o m a i n s was n o t a c c o m p a n i e d b y a s  large v a r i a t i o n s i n the d i f f i c u l t y of the tasks. it  systemic  systemic  of their  d i f f i c u l t y never i n f l u e n c e s task  contents.  difficulty  f o r the upper s y s t e m i c t a s k s .  Nor  does i t prove  t h a t the upper s y s t e m i c  r e q u i r e d more s o p h i s t i c a t e d c o g n i t i v e o p e r a t i o n s . n a t i o n s t h a t cannot The  There may  tasks  be a l t e r n a t i v e e x p l a -  be a s s e s s e d w i t h ..the data a t hand but none s p r i n g t o .mind.  i n t e r p r e t a t i o n t h a t the t a s k s were more d i f f i c u l t because the c o g n i t i v e  o p e r a t i o n s they r e q u i r e d were more d i f f i c u l t (iv)  Age The  remains v i a b l e ,  Related. C r i t e r i a d a t a p r e s e n t e d on T a b l e V I were not connected w i t h any h y p o t h e s i s b u t  they a r e r e l e v a n t to the abruptness f o r i d e n t i f y i n g stages.  and concurrence  criteria  (Flavell,  1971a)  These d a t a i n d i c a t e d t h a t the mastery o f v a r i o u s  systemic operations i s concurrent  (with the noted e x c e p t i o n of the l a y o u t  component of c y c l i c t r a n s i t i v i t y ) but not a b r u p t .  The  concurrence  criterion  i s a c t u a l l y subsumed by P i a g e t ' s i n t e r p r e t a t i o n of the s t r u c t u r e s 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 s t r u c t u r e s d'ensemble c r i t e r i o n but supplemented i t w i t h the concurrence  criterion.  Therefore  the  data a l r e a d y d i s c u s s e d i n c o n n e c t i o n w i t h s t r u c t u r e s d'ensemble (see s u b s e c t i o n A(ii);  "Second H y p o t h e s i s " )  are these age d a t a .  a r e more r e l e v a n t t o the concurrence  criteria  than  The age d a t a do not i n d i c a t e whether or not the mastery  o c c u r r e d as c o n c u r r e n t l y w i t h i n i n d i v i d u a l s as i t d i d among i n d i v i d u a l s w i t h i n age  groups.  The  z s c o r e s between the upper s y s t e m i c t a s k s , however, do  i n d i c a t e concurrence w i t h i n i n d i v i d u a l s . The abruptness  c r i t e r i o n , r e q u i r e s t h a t the t r a n s i t i o n i n t o the next  s t a g e be s h o r t i n d u r a t i o n .  The age d a t a have b e a r i n g on t h i s requirement  the l e v e l of groups of same aged peers but not a t the l e v e l of the I f the t r a n s i t i o n appear abrupt a c r o s s i n d e p e n d e n t l y i t was  likely  higher  individual.  sampled age groups  to have been abrupt f o r the i n d i v i d u a l s a l s o .  at  then  I f , however, the  121 c r o s s - s e c t i o n a l d a t a shows a g r a d u a l r i s e a c r o s s age of  mastery then i t remains i m p o s s i b l e to determine  u a l s undergo the t r a n s i t i o n a b r u p t l y . T a b l e VI showed an abrupt  The  groups i n the  frequency:  whether o r not the  individ-  c r o s s - s e c t i o n a l data reported i n  t r a n s i t i o n i n t o the f o r m a l o p e r a t i o n a l stage but  a g r a d u a l l y i n c r e a s i n g frequency of mastery over the upper s y s t e m i c t a s k s . In  f a c t , the frequency  f o r successes on the upper s y s t e m i c components  never  goes as h i g h a t any of the ages sampled as the f r e q u e n c i e s f o r the f o r m a l tasks.  Perhaps the upper systemic o p e r a t i o n s do not blossom i n the m a j o r i t y  u n t i l an age beyond the o l d e s t sampled h e r e . simply not a l l t h a t common i n a d u l t s . not r e q u i r e t h a t a f i f t h  c r i t e r i a f o r i d e n t i f y i n g stages  do  stage would have t o be a c q u i r e d by a l l a d u l t s .  The v i a b i l i t y of the f i f t h abruptness  The  Perhaps s y s t e m i c t h i n k i n g i s  stage i n t e r p r e t a t i o n remains u n a f f e c t e d by  c r i t e r i o n mainly because t h e r e are. no r e l e v a n t d a t a  the  available.  Even i f a p p r o p r i a t e d a t a were o b t a i n e d t h a t showed a g r a d u a l mastery of the upper s y s t e m i c t a s k s , the f i f t h Wohlwill  (1973) argued  d i t i o n f o r a stage.  stage i n t e r p r e t a t i o n might s t i l l s u r v i v e .  t h a t abruptness  Flavell  of t r a n s i t i o n i s not a n e c e s s a r y  (1977) commented t h a t W o h l w i l l ' s more dynamic  n o t i o n of a stage seemed u n c o n v i n c i n g . of  stages may  F l a v e l l ' s view i s t h a t the whole i d e a  have to be abandoned s i n c e attempts  d i l u t i o n of the concept  con-  to save i t l e a d to s u c h a  t h a t i t ceases to be u s e f u l .  c o r r e c t but what i s a t i s s u e here i s the  F l a v e l l may  w e l l be  e x t e n t to which the upper  systemic  t a s k s meet stage c r i t e r i a a t l e a s t as w e l l as do o t h e r t a s k s i n o t h e r P i a g e t i a n stages. if  None of P i a g e t ' s s t a g e s may  the upper s y s t e m i c c l u s t e r i s any  be v e r y s t a g e - l i k e but we want to know l e s s s t a g e - l i k e than the o t h e r s .  122 (v)  Summary All  three hypotheses were c o r r o b o r a t e d .  ( t r a n s i t i v e r e c y c l i n g and being do  The  evaluated w i t h the present  upper systemic  operations  s y s t e m s s y n t h e s i s ) seem t o meet t h e c r i t e r i a  r e p r e s e n t a t i v e s of a f i f t h  f o r other stages.  The  stage  abruptness data.  a t l e a s t as w e l l as o t h e r  operations  of t r a n s i t i o n c r i t e r i o n ' c o u l d not  The  to s p e c u l a t e t h a t the upper  o p e r a t i o n s were merely 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 of a  B.  In this attention.  The  i s s u e i s f a r from  I n t e r p r e t a t i o n s of Systemic  typical  settled.  Difficulty  Levels  F i r s t , however, the next  subsection  t h a t m u s t be b o r n e i n m i n d when  interpreting  results. Interpretive. Caveats This i s not  intended  t o be  i n t e r p r e t a t i o n of the f i n d i n g s .  an e x h a u s t i v e The  f o l l o w s here are  t h e most i m p o r t a n t  list  method and  s e v e r a l comments o n p o s s i b l e a r t i f a c t s a n d caveats  Sample.  The  age  p r o f i l e data  of the f a c t o r s c o n s t r a i n i n g  r e s u l t s chapters  sources  contain  of u n r e l i a b i l i t y .  t o b e a r i n m i n d a s one  .various i n t e r p r e t a t i o n s of the g r e a t e r d i f f i c u l t y  was  systemic  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 ,  e x a m i n e s some o f t h e l i m i t a t i o n s  (i)  also  s e c t i o n , t h e p a r a l l e l d e v e l o p m e n t i n t e r p r e t a t i o n i s g i v e n more  c o g n i t i v e development are c o n s i d e r e d .  the  be  p a r a l l e l development 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 e v e n t h o u g h i t r e q u i r e s one  e a s i e r set of o p e r a t i o n s .  for  show t h a t n o t  What  considers  of the upper systemic e v e n among t h e 18 y e a r  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  mastered the  tasks. olds  upper  123 systemic  tasks.  formed.  I t w o u l d be i n t e r e s t i n g  mastery o f those age  We do n o t k n o w how e v e n o l d e r r e s p o n d e n t s m i g h t h a v e to search  f o r the earliest  t a s k s was m o r e o r l e s s u n i v e r s a l .  group b u t from t h e p r e s e n t  age group a t w h i c h  T h e r e m i g h t be no s u c h  sample o f ages i t i s i m p o s s i b l e  way o r t h e o t h e r .  Also, although  group t o t h e o t h e r  a g e groups^'dlii t e r m s o f p r o j e c t e d  per-  t o know o n e  a n a t t e m p t was made t o m a t c h t h e 18 y e a r o l d educational/occupational  s t a t u s u p o n 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 m a t c h was f a r f r o m p e r f e c t . t h e 18 y e a r  o l d group would have c o n t a i n e d  o r who w i s h e d t o b e f u l l Task D e f i n i t i o n s .  i s whether o r not the systemic i n t e g r a t i o n should  a m a j o r i t y o f r e s p o n d e n t s who w e r e  t i m e members o f t h e l a b o u r To some e x t e n t  this  operations  be d i s p e n s e d  Ideally  force.  i s a semantic problem.  of c y c l i c  question  t r a n s i t i v i t y and c y c l i c  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  g r o u n d s i t seems j u s t i f i a b l e  The  t o group t h e l a y o u t  component  scores.  On l o g i c a l  together  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 g r o u p t h e s y s t e m s  a n a l y s i s component w i t h t h e s y s t e m s s y n t h e s i s component. culty  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, those  on e m p i r i c a l g r o u n d s . same s y s t e m i c  The d i f f i c u l t y  problem f o r future theory contributions of this  of these  g r o u p i n g s c a n be  Perhaps the s a f e s t procedure i s  Future  concepts.  taken  research w i l l  have t o be  The i d e n t i f i c a t i o n o f t h i s  and r e s e a r c h c a n be s e e n a s one o f t h e h e u r i s t i c  study.  Meanwhile, a measure o f c i r c u m s p e c t i o n  o r d e r when i n t e r p r e t i n g a n y o f t h e c o m p o s i t e s c o r e s is  questioned  T h a t i s t o r e p o r t t h e r e s u l t s b y com-  ponents as w e l l as by composite o p e r a t i o n . based on f u r t h e r r e f i n e m e n t  Now t h a t t h e d i f f i -  l e v e l s between t h e components o f t h e  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 .  t h e one t h a t h a s been f o l l o w e d h e r e .  component  reported here.  i s i n This  issue  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, w h e r e t h e p o s s i b l e v a r i a t i o n i n  " 124 :  the . l o g i G o - m a t h e m a t i c a l are  forms o f c y c l i c  transitivity  and c y c l i c i n t e g r a t i o n  considered, A partially  scores  r e l a t e d problem concerns the composition  themselves.  obtained.  Future  Appendix D d e t a i l s the items  o f t h e component  from which these  r e s e a r c h o u g h t t o i n c l u d e some a n a l y s e s  used here along w i t h whatever n o v e l items  devised.  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  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 .  were  of the internal  consistency o f the items In t h i s regard  scores  c a n be  assessment  The n i t r o g e n c y c l e and t h e  w h e a t 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 h a n d b u t t h e e x amination  o f a d d i t i o n a l c y c l e s would 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  reliability can  and v a l i d i t y  of the assessment procedures.  A g a i n , no one  study  s e t t l e a q u e s t i o n as broad as e i t h e r t h e e x i s t e n c e o f a developmental  or the existence of a p a r a l l e l Task A d m i n i s t r a t i o n .  chapter. issue.  type o f l o g i c .  Most o f t h e i s s u e s s u r r o u n d i n g  which t h e t a s k s were presented  stage  the f i x e d order i n  have a l r e a d y been d i s c u s s e d  i n t h e method  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 o n e f u r t h e r 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  the 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 m i g h t h a v e 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  less ing  than o p t i m a l l y on those v e r y this possibility.  or l e s s steady  First  tasks.  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  performance decrement.  T h i s was n o t t h e c a s e .  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 of the s o c i e t a l systemic actually  superior.  T h e r e a r e some g r o u n d s f o r d i s c o u n t -  The b i o - e c o l o g i c a l  t a s k s were p r e s e n t e d  b e f o r e any  t a s k s b u t p e r f o r m a n c e o n some o f t h e l a t t e r  was  The s o c i e t a l s y s t e m s a n a l y s i s c o m p o n e n t a n d , e s p e c i a l l y ,  t h e l a y o u t c o m p o n e n t w e r e much e a s i e r t h a n  t h e upper systemic  tasks i nthe  125 b i o - e c o l o g i c a l domain.  To the e x t e n t t h a t f a t i g u e might have  shortened  a t t e n t i o n spans, the e f f e c t would p r o b a b l y have been most pronounced among younger respondents.  Although  the r e l a t i v e e a s i n e s s of the lower  t a s k s i n the s o c i e t a l domain argues a g a i n s t any not known how  T h e r e f o r e one  r e s e a r c h to circumvent ness and  t h a t t h i s caveat  t a s k s had  respon-  they been p r e s e n t e d  ought to remain.undecided on t h i s i s s u e .  Were f u t u r e  the p o s s i b i l i t y o f a f a t i g u e e f f e c t , the r e l a t i v e  i n f r e q u e n c y of mastery of the systemic  t a s k s might d i s a p p e a r .  lateNote  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 . upper systemic  such i n t e r p r e t a t i o n i t i s  much b e t t e r performance, e s p e c i a l l y t h a t of the younger  dents, might have been on those l o w e r . s y s t e m i c earlier.  systemic  t a s k s are a r t i f i c i a l l y  I f the d i f f i c u l t y l e v e l s f o r the  i n f l a t e d then the case f o r 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 s t r o n g e r . Statistics.  The most obvious problem w i t h the s t a t i s t i c a l a n a l y s e s i s  the n o v e l t y of u s i n g 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 . s t a t i s t i c was  not designed  normal d i s t r i b u t i o n .  f o r t h i s use.  I t was  meant to be r e l a t e d to the  In a d a p t i n g the z s c o r e f o r use i n i n d e x i n g the Guttman  l i k e n a t u r e o f s t e p s between a d j a c e n t  t a s k s g r e a t p a i n s were taken to a v o i d  any  r e f e r e n c e to the normal d i s t r i b u t i o n and a s s o c i a t e d c o n f i d e n c e  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  Perhaps i t s g r e a t e s t shortcoming character. Hubert  i s g i v e n i n the r e s u l t s  intervals. chapter.  as i t has been used here i s i t s cumbersome  A more e l e g a n t technique has been r e c e n t l y p u b l i s h e d by Froman and  (1980).  A s i d e from i t s n o v e l t y , however, t h a t technique appears to be  s u i t e d f o r more f i n e g r a i n e d a n a l y s e s of o r d e r hypotheses than was for  This  the o v e r a l l f i r s t h y p o t h e s i s .  appropriate  Froman and Hubert's t e c h n i q u e would r e q u i r e  p r i o r s p e c i f i c a t i o n of the p r e c i s e s i z e of gaps between t a s k s w i t h i n stages  i2.6 and  w i t h i n content  difficulty. to  the  two  For  domains as w e l l as  the purpose of j u s t i f y i n g  novel  content  domains t h e i r  I t w o u l d be more a p p r o p r i a t e  present  the e x t e n s i o n  technique  age  to the  s t r u e t u r e s d'enseiiib 1 e c r i t e r i o n .  i n w h i c h t a s k s may  cases w i t h  l e v e l of a n a l y s i s .  may  a c t u a l l y obscure r e a l l o n g i t u d i n a l orders  as  independence.  to  A l s o , B a r t and  • t h e c h i l d m u s t m a s t e r one  more a d v a n c e d t a s k s a n d  tasks before and  themselves.  A i r a s i a n ' s r e l a t i o n of by  proceeding.  A i r a s i a n ' s m e t h o d was  individ-  "independence"  construing joint-necessity to d i s t i n g u i s h between  or another task before  used to assess  t a s k s were s t r u c t u r e s d'ensemble.  One  the extent  m i g h t be m i s l e d  a  proceeding both  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 w h e r e  being  the  Only  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 This  re-  are used to c o n s t r u c t  In t h e i r system i t i s impossible  s i t u a t i o n wherein  "fail/pass"  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  ual  Bart  to w h i c h a group  into postulating  of  two  "independent" s e t s of t a s k s where a c t u a l l y r e l a t i o n s of j o i n t n e c e s s i t y were in effect. in  T h a t s h o r t c o m i n g was  the present  function (ii)  study.  not  shared  by  the  statistics  They were l e s s s o p h i s t i c a t e d but  they  t h a t were used served  their  However,  the  adequately,  Piaget's Parallel Position So  f a r the  fifth  stage  the  That method,  h a v e b e e n m a s t e r e d by  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  longitudinal observation  respondents  method m i g h t have been u s e d w i t h  s p o n d e n t s e v e n t h o u g h t h e r e s p o n d e n t s , whose d a t a o r d e r i n g may  theory  seems i n a p p r o p r i a t e l y s p e c i f i c .  however, uses p a i r w i s e comparisons of " p a s s / f a i l " case to approximate the order  of  range.  A i r a s i a n ' s (1974) o r d e r i n g  data with regard  orders  of P i a g e t i a n  f o r s t u d i e s w i t h l a r g e r samples of  w i t h i n a much more r e s t r i c t e d B a r t and  s p e c i f i c a t i o n of corresponding  v  i n t e r p r e t a t i o n remains v i a b l e .  127 same c a n b e s a i d o f t h e p a r a l l e l d e v e l o p m e n t i n t e r p r e t a t i o n .  In fact  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 b y P i a g e t , a l b e i t b e f o r e t h e evidence  from the present  study had been obtained. P i a g e t holds  t h a t no  f u r t h e r q u a l i t a t i v e developments occur 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 m o r e 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 mal  operations progresses  t o P i a g e t , development beyond  i n terms o f h i g h e r and h i g h e r orders o f  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 ,  may b e 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 cedes t h a t h i s work has focused  for-  concatena-  however, t h a t  t h a t he has i d e n t i f i e d .  on f o r m a l l o g i c and t h a t l e s s  He  formally  there conlogi-  c a l o p e r a t i o n s o r w h o l e c l a s s e s o f o p e r a t i o n s may y e t b e d i s c o v e r e d . F r o m 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  f r o m 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 an a s p e c t  of post-concrete  i n d i v i d u a l s may s p e c i a l i z e For  different represent  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 d e v e l o p m e n t . Some i n one t y p e o f p o s t - c o n c r e t e  t h e w h o l e s p e c i e s , h o w e v e r , t h e two t y p e s  mental  this  logic or the other.  constitute "parallel"  develop-  paths.  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 not r u l e d out by the f a c t of  the g r e a t e r d i f f i c u l t y  of the upper systemic  tasks. Within the structural  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 difficulty  one  c o g n i t i v e operation to another.  i n t e r p r e t a t i o n would  for  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 m u s t b e remem-  bered  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  used i n t h i s by  evidence  than  The " p a r a l l e l "  study. Therefore t h a t some s y s t e m i c  the p a r a l l e l  operations besides  from allow  t h e ones  i n t e r p r e t a t i o n i s not diminished  o p e r a t i o n s a r e a G u t t m a n s t e p more  difficult  some f o r m a l o p e r a t i o n s b e c a u s e p o s s i b l y j u s t a s many r e v e r s e c a s e s  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 tasks  level  exist.  concrete operational  (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 weight; M i l l e r ,  Schwartz and  128 Stewart,  1973) a n d t h e l e s s d i f f i c u l t  tween s t a g e s  c o u l d b e made t o a p p e a r n o n - G u t t m a n . I f t h i s  t h e gap i n d i f f i c u l t y it  l e v e l s between t h e t h i r d  c o u l d a l s o be a r r a n g e d  fifth  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-  t h a t t h e whole concept  w i t h the a c t u a l course (iii)  and f o u r t h s t a g e s ,  i n t e r p r e t a t i o n gains by d e f a u l t  of stages  i s found  observed  (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  on t h e s y s t e m i c  span d i f f e r e n c e s  for the less  than abrupt age  c o m p o n e n t s . She a r g u e s t h a t p u r e  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 vironment  t o be i n c o n s i s t e n t  Position.  i n p r e f e r r e d types o f l o g i c which would account profile  presumably  o f development,  Labouvie-Vief's P a r a l l e l Labouvie-Vief  c a n b e done f o r  f o r t h e gap b e t w e e n t h e f o u r t h a n d p r o p o s e d  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  to the extent  1  a n d t h a t t h e more p r a g m a t i c  formal  i n a c u l t u r e ' s adaptation t o i t s en-  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  serving accumulated c u l t u r a l a r t i f a c t s  con-  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 b e a d v a n t a g e o u s t o have a d u l t s capable  of both  types  of l o g i c a l  thinking. Also, the generation  r e l a t e d s p e c i a l i z a t i o n i n each type o f l o g i c would enhance t h e p o p u l a t i o n ' s adaptiveness  b y s e t t i n g up a h o m e o s t a t i c  v a l u e , v i s a v i s a s t a b l e o r changing  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  environment, of the c u l t u r a l  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. H e n c e , a l t h o u g h ability  t o perform  systemic  the teen^aged respondents this  type o f l o g i c .  type o f l o g i c  i t was f o u n d  o p e r a t i o n s was a v a i l a b l e a t a g e 14, v e r y  i n this  study  showed s i g h s o f b e i n g  On t h e o t h e r h a n d , a l m o s t  that suited  knowledge  the socio-biological  that the few o f  specialists i n  a l l o f them e x c e l l e d a t t h e cultural function of their  129 1 age group. (iv) Stages and One way a fifth in  Paradigms  to d i s c o u n t the non-abrupt age p r o f i l e d a t a and thereby  strengthen  stage i n t e r p r e t a t i o n , would be to argue t h a t the f i f t h stage l o g i c i s  the p r o c e s s o f b e i n g c r e a t e d i n our c u l t u r e .  I f adult cognitive structures  are assumed t o be a product o f the s t r u c t u r e s a v a i l a b l e i n the p a r t i c u l a r c u l t u r e then the v e r y f a c t of c u l t u r a l e v o l u t i o n guarantees new  s e t s of c o g n i t i v e o p e r a t i o n s among the a d u l t members of t h a t c u l t u r e .  Systemic  o p e r a t i o n s may  Hence one would expect  be p a r t and p a r c e l of a " c u l t u r a l paradigm t h e i r p r e v a l e n c e t o be low but i n c r e a s i n g .  v a l a n c e o f s u c c e s s f u l use of s y s t e m i c l o g i c was dents i n t h i s study.  shift". The  low f o r the teen-aged  prerespon-  Long term f o l l o w up s t u d i e s would be r e q u i r e d t o d e t e r -  mine whether o r not a c u l t u r a l paradigm s h i f t is  the emergence of  i s underway.  s t i l l a chance t h a t perhaps a t around ages 18 to 21  m a j o r i t y ) o r perhaps 27 to 30 would come t o supercede  I f i t i s , there  ( common ages of  (see G i l l i g a n and Murphy, 1979)  systemic  f o r m a l l o g i c i n a c u l t u r e where s y s t e m i c l o g i c  logic was  w e l l accepted among a d u l t s .  1.  By way of adding t e x t u r e t o L a b o u v i e - V i e f s t h e s i s I would l i k e to r e l a t e two p i e c e s of a n e c d o t a l i n f o r m a t i o n o b t a i n e d from secondary s c h o o l t e a c h e r s . An e c o l o g y t e a c h e r t o l d me t h a t the grade 11 s t u d e n t s who he found to be more adept i n u n d e r s t a n d i n g e c o l o g i c a l systems a l s o tended t o be those who were more c o n s e r v a t i o n minded. C o n s e r v i n g , of c o u r s e , i s t h e c u l t u r a l r o l e t h a t L a b o u v i e - V i e f notes i s the s p e c i a l t y of o l d e r persons, those who use more pragmatic l o g i c . A h i s t o r y t e a c h e r made a s i m i l a r o b s e r v a t i o n w i t h r e g a r d t o u n d e r s t a n d i n g s o c i a l systems. He noted t h a t h i s grade 12 s t u d e n t s who were more adept a t t h i s were those who had more p r a c t i c a l e x p e r i e n c e i n political activity. F u r t h e r , he f e l t t h a t the s t u d e n t s who were more " b o o k i s h " , i n h i s words, were l e s s q u i c k to see the s y s t e m i c n a t u r e of s o c i e t a l o r g a n i z a t i o n . A g a i n , t h i s c o r r o b o r a t e s the e q u a t i o n of s y s t e m i c t h i n k i n g w i t h l o n g t e r m > a c t i v i t i e s aimed a t m a i n t a i n i n g a h e r i t a g e and s e r v i n g a s t r u c t u r e to which one has made a p e r s o n a l commitment. As L a b o u v i e V i e f (1980, p.153) s t a t e s , " T h i s c o n s c i o u s commitment to one pathway and the d e l i b e r a t e d i s r e g a r d of o t h e r 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 a d u l t c o g n i t i v e m a t u r i t y . " 1  13.0 One  c o u l d , 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 m o d i f i e d v e r s i o n  of the "paradigm s h i f t " argument.  The m o d i f i e d paradigm s h i f t approach would  a g a i n assume t h a t 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; was  Buss, 1977;  R i e g e l , 1976;  L u r i a , 1979)  but would not assume t h a t one  u n i v e r s a l l y s u p e r i o r t o , o r subsumptive o f , a n o t h e r .  form  R a t h e r , t h e form o f  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 m a t t e r of a d a p t a t i o n t o a p a r t i c u l a r environment and/or n i c h e . taneously.  L a b o u v i e - V i e f ' s t h e s i s c o u l d be a s s e r t e d s i m u l -  I n 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  t h a t our c u l t u r e must adapt i t s e l f to a v e r y q u i c k l y changing  environment.  A n o t h e r v a r i a n t i s t h a t our c u l t u r e has chosen t h e a d a p t a t i o n s t r a t e g y ( n i c h e ) o f b e i n g v e r y q u i c k l y changeable, n e c e s s i t a t e emphasizing  very f l e x i b l e .  I n e i t h e r c a s e , t h a t would  f o r m a l l o g i c and s u p p r e s s i n g s y s t e m i c l o g i c as  the  p r e f e r r e d a d u l t form o f c o g n i t i o n . Hence, the appearance 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 might be a l i t t l e d e l a y e d as deserved  i n the age p r o f i l e d a t a .  A l s o , the m a j o r i t y o f persons would never develop a f u l l f a c i l i t y w i t h , o r c o n s o l i d a t i o n o f , the s y s t e m i c s t r u c t u r e s e x a c t l y because they would be t u r a l l y , non-preferred. In  cul-  A g a i n , 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 d a t a .  summary t h e n , i t i s i m p o s s i b l e , g i v e n o n l y the p r e s e n t d a t a t o d e c i d e  whether t h e upper s y s t e m i c o p e r a t i o n s develop i n p a r a l l e l w i t h f o r m a l o p e r a t i o n s o r a r e 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 s t a g e . u n c e r t a i n t y may  To a c e r t a i n e x t e n t the  be a r e f l e c t i o n o f the a m b i g u i t y t h a t e x i s t s i n the  t u r e on P i a g e t ' s f i r s t f o u r s t a g e s .  litera-  I n any c a s e , w i t h r e g a r d t o the more  fundamental i s s u e o f e l u c i d a t i n g the n a t u r e o f a d u l t c o g n i t i o n , the p r e s e n t s t u d y s e r v e s t o emphasize the importance  of systemic o p e r a t i o n s .  V.  The  specific  I m p l i c a t i o n s f o r Three Areas  of  Study  c o n t e n t s of the 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 m o r e for  other areas.  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  d e v e l o p m e n t , s o c i a l d e v e l o p m e n t , and  A.  The and of  theory i n the areas of  social  psychology.  r e s u l t s reported here r a i s e a host of questions f o r f u t u r e theory The  p o s t u l a t i o n of a d i f f e r e n t  i s perhaps the most f a r r e a c h i n g n o t i o n .  f o r m a l and  systemic l o g i c  Logico-mathematical  cannot  be  analyses w i l l  fully  be  The  required simply to i d e n t i f y  a b s e n c e o f e a c h i n any p a r t i c u l a r  case.  to  s e t t l e questions of developmental  p r i o r i t y versus  of  development.  Systemic  l o g i c bears  t h a t s e v e r a l a u t h o r s have suggested h o w e v e r , seems t o be  systemic l o g i c  similarities  way  be  I n h e l d e r , 1956;  does i n d e e d  develop  to the type of  needed  thinking  t y p i f i e s mature a d u l t c o g n i t i o n .  It also, based  an e u c l i d i a n c o n c e p t i o n  P i a g e t , I n h e l d e r and  Szeminska,  i n p a r a l l e l with formal l o g i c  c h i l d h o o d and  presence  s i m u l t a n e i t y at a l l stages  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  have p r e c u r s o r s i n middle in  between  the  Empirical studies w i l l  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 claims precede ( P i a g e t and  relationship  type  e l u c i d a t e d w i t h o u t more work.  or  space  cognitive  C o g n i t i v e Development  r e s e a r c h i n c o g n i t i v e development. logic  interest  early adolescence,  1960).  examination  Future  research  are to look f o r , t h i s section begins w i t h  of the c h a r a c t e r i s t i c s of mature a d u l t  cognition.  If  then i t would  c o n c r e t e stage c o g n i t i v e development might l o o k f o r those p r e c u r s o r s . o f c l a r i f y i n g w h a t i t i s we  of  By an  132. (i)  C o r r o b o r a t i v e Work bri A d u l t C o g n i t i o n While  the p r e s e n t r e s e a r c h was  i n p r o g r e s s , s e v e r a l a r t i c l e s have ap-  peared on v a r i o u s a s p e c t s of a d u l t c o g n i t i o n .  I n the realm of moral  ment, Gibbs  theory as a two-phase model.  (1979) r e c o n c e p t u a l i z e d Kohlberg's  develop-  For the present, d i s c u s s i o n the r e l e v a n t aspect of Gibbs' r e c o n c e p t u a l i z a t i o n i s h i s f o u r t h and l a s t  stage d u r i n g the p r e - e x i s t e n t i a l , p r e - a d u l t phase.  H i s f o u r t h stage i s c a l l e d the "systems" s t a g e .  Gibbs, a f t e r an  apology  f o r the s k e t c h i n e s s of h i s d e s c r i p t i o n s of the stages d e s c r i b e s the systems stage as f o l l o w s : Evidence  f o r a f o u r t h stage i s apparent  realm, a l t h o u g h such a d i s t i n c t i o n may c o g n i t i v e realm  p r i m a r i l y i n the s o c i o m o r a l a l s o be helpful:'.in the  (e.g., Wyatt and G e i s , 1978).  logico-  Over the course of the  a d o l e s c e n t y e a r s , t h e r e i s a p r o g r e s s i v e a b i l i t y t o d i s c e r n the systema t i c arrangements which are n e c e s s a r y hypothetical  to form a v i a b l e s o c i e t y , r e a l or  (see A d e l s o n and O ' N e i l , 1966;  t h e i r seminal s t u d i e s , A d e l s o n to a p p r e c i a t e law and  A d e l s o n e t a l . , 1969).  et a l . found  In  t h a t the a d o l e s c e n t comes  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 a u t h o r i t y (stage 3 ) , but more.broadly i n terms of s o c i a l f u n c t i o n s and Thus, t h e r e i s an  'expansion'  (Selman, 1976,  p. 307)  in  practices.  second-order  t h i n k i n g such t h a t an o v e r a l l p e r s p e c t i v e i s a p p l i e d not o n l y to f a c e t o - f a c e r e l a t i o n s h i p s , but a l s o t o complex s o c i a l systems as r e p r e s e n t e d by modern s o c i e t y Although understanding  ( c f . Edwards, 1975,  the p r e s e n t study was  i n press).  not concerned  (Gibbs, 1979,  To be f a i r ,  independently  There seems t o be a consensus  emerging t h a t (a) s o c i e t y i s b e s t d e s c r i b e d as a system, and i n g of s o c i e t y r e q u i r e s s y s t e m i c  102)"  w i t h the moral a s p e c t s of  s o c i a l systems, i t i s i n t e r e s t i n g t h a t Gibbs should  c h a r a c t e r i z e t h i n k i n g about s o c i e t y as s y s t e m i c .  p.  Cb) and  understand-  thought.  the l a t t e r comment a c t u a l l y r e q u i r e s q u a l i f i c a t i o n .  Piaget  133 ( 1 9 7 2 ) d i d come t o s t r e s s t h a t t h e r e w e r e some p r o b l e m s c r e a t e d b y 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 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  analysis.  development i n t e r p r e t a t i o n ,  In his Piaget  states: We c o u l d , t h e r e f o r e , f o r m u l a t e  the following hypothesis:  i fthe formal  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 a p p e a r i n a l l c h i l d r e n o f 1 4 - 1 5 years  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 b e 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.  According  to this  h o w e v e r , we w o u l d h a v e t o a d m i t t h a t o n l y i n d i v i d u a l s  interpretation,  t a l e n t e d from the  p o i n t o f v i e w o f l o g i c , m a t h e m a t i c s a n d p h y s i c s w o u l d manage t o c o n struct  such  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 ,  i n d i v i d u a l s would be i n c a p a b l e o f doing s o .  artistic  I n t h i s case  and p r a c t i c a l i t would not  be a p r o b l e m o f u n d e r - d e v e l o p m e n t c o m p a r e d t o n o r m a l d e v e l o p m e n t b u t more s i m p l y a g r o w i n g  diversification  i n individuals,  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 b e t w e e n 15 a n d 2 0 y e a r s , t h a n a t 7-10 y e a r s .  I n other words, our  f o u r t h p e r i o d c a n no l o n g e r b e c h a r a c t e r i z e d a s a p r o p e r  stage, but  w o u l d a l r e a d y seem t o b e a s t r u c t u r a l a d v a n c e m e n t i n t h e d i r e c t i o n o f specialization. Boswell's  ( P i a g e t , 1972, p. 9 ) "  (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' a n d 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 b y l i f e - s p a n r e s e a r c h "showing differences across professional specializations 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., Dennis,  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 .  i n t h e ages a t w h i c h c r e a t i v e 1966).  Mathematicians  Natural scientists,  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 approximate o r d e r . course,  i s t h e epitome o f formal a b s t r a c t i o n .  incomprehensible  without  tend  artists, Mathematics, of  H i s t o r y , on t h e o t h e r hand, i s  a r i c h base of c o n t e x t u a l d e t a i l s out o f which the  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  fifth  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  thinking.  As  m e n t i o n e d 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 b y d i a l e c t i c a l l o g i c found  support  i s considerable.  Basseches claimed  f o r , "the idea of a p o s t - f o r m a l - o p e r a t i o n a l stage of 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 (ii)  Post-Concrete The  Diversification  r e s u l t s of the present  order to avoid confusing adolescent o p e r a t i o n a l thought  i n particular,  c o n t r i b u t e t o t h e growing  thought  than j u s t  and a d u l t thought I prefer to refer  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 " stage. 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 Post-concrete  tion of a b i l i t i e s . gross b i f u r c a t i o n , The  parellel  with Boswell's  thought  The p r e s e n t  thinking."  t  study  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  operations.  consensus  formal operations. i n general from  Post-concrete  i s c h a r a c t e r i z e d by a growing  study has found  evidence  thought  diversifica-  s u g g e s t i n g o n l y one logic.  i n t e r p r e t a t i o n of the r e s u l t s of the present  f i n d i n g s and L a b o u v i e - V i e f ' s arguments suggest  study  to Piaget's but broader.  ment m o v i n g a l o n g i n p a r a l l e l w i t h t h e d e v e l o p m e n t o f a b s t r a c t l o g i c . (1972) a l s o c o n s i d e r e d  along  an o v e r a l l  T h i s expanded v i e w o f c o g n i t i v e development sees a d d i t i o n a l l i n e s o f  this  expanded v i e w .  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 a g e i n d i v i d u a l s become more f r o m one a n o t h e r  formal  to the f o u r t h stage of  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  later writings Piaget  In  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  view 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  sophisticated  t o have  i n s o f a r a s some l o g i c a l a b i l i t i e s  The  developIn over-  different  g e t more e l a b o r a t e d a n 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 " , h o w e v e r ,  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 (iii)  abilities.^  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 One  i n t e r e s t i n g f e a t u r e of the upper s y s t e m i c t a s k s i s t h a t t h e i r empha-  s i s on feedback l o o p s and dynamic i n t e r r e l a t e d n e s s a l l o w s the p e r s o n u s i n g these o p e r a t i o n s t o d i s c o v e r h i d d e n , 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 e v e n t s .  W i t h f o r m a l 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 , o r t h e i r i d e n t i t i e s a r e r e c o v e r a b l e , through i t i e s of thought, formed upon them.  r e g a r d l e s s o f whatever t r a n s f o r m i n g o p e r a t i o n s may  reversibilbe  per-  W i t h systems l o g i c the elements a r e c o n s t a n t l y changing  each o t h e r s ' 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 b e s t  term t o d e s c r i b e the c y c l e of c o n t i n u o u s mutual i n f l u e n c e c h a r a c t e r i s t i c o f systems o p e r a t i n g a c c o r d i n g to the 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 d e n t i t i e s of the elements i n v o l v e d a r e not f i x e d . the use. o f systemicT l o g i c may  Hence,  make, i t e a s i e r , i n " some s i tuatiohs.-,to. d i s c o v e r  unexpected i n t e r a c t i o n s o r phenomena. with Arlin's  They e v o l v e .  The  I n t h i s sense s y s t e m i c l o g i c  (1975) c a n d i d a t e f o r a f i f t h s t a g e , "problem f i n d i n g " .  overlaps Arlin  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 " , w h i c h i s seen as a hallmark o f f o r m a l l o g i c . a l s o generates  n o v e l and u n t r i e d s o l u t i o n s .  i t can be seen how  1.  But L a b o u v i e - V i e f  (1980) n o t e s t h a t f o r m a l l o g i c I f the t e r m i n o l o g y i s a d j u s t e d ,  b o t h forms o f l o g i c can b o t h promote and i n h i b i t  creativity.  The more advanced s y s t e m i c o p e r a t i o n s a r e s t i l l b e i n g a r t i c u l a t e d by mathe m a t i c i a n s and p h i l o s o p h e r s . The p r i n c i p l e s o f G e n e r a l Systems Theory seem the most l i k e l y c a n d i d a t e s h e r e . P r i n c i p l e s s u c h 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 a r e a few examples. F o r r e s e a r c h e r s i n t e r e s t e d i n t a k i n g up t h i s q u e s t , von B e r t a l a n f f y (1968), K l i r (1972), and Weinberg 0-975) p r o v i d e good i n t r o d u c t i o n s . A l s o , J a n t s c h and Waddington (1976) have compiled a panoramic sampling o f the a p p l i c a t i o n s o f these p r i n c i p l e s i n v a r i o u s s c i e n c e s  136 Problem s o l v i n g c o u l d a l s o be c a l l e d " s o l u t i o n f i n d i n g " . out L a b o u v i e - V i e f ' s phrase b r i n g s out  p o i n t about the c r e a t i v i t y of f o r m a l  i t s foreclosing properties.  c r e a t i v e s i d e of systemic new  invention.  reasons f o r not  On  logic.  New  l o g i c j u s t as  attempting  new  C y c l i c T r a n s i t i v i t y and  s o l u t i o n s we  The  any n o t i o n about how  cornered,  the Feedback Concept.  Jaquette's  considered  an element r e c e i v e s i t s own (1977) s t a g e ,  theory  of s o c i a l p e r s p e c t i v e  the  consider-  At the next phase i n Selman see two  b a s i c f e a t u r e s of feedback c o u l d be read  the l a y o u t procedure through the simultaneous a p p r e c i a t i o n of an i n p u t as i t s output and  taking,  s o l v e d by  framework the c h i l d can d e a l w i t h m u t u a l i t i e s and The  In  cannot see them a l l at once.  i n g the l i n k s between elements s u c c e s s i v e l y o n l y .  spectives simultaneously.  the  solved without i t .  output back as i n p u t .  the c y c l i c t r a n s i t i v i t y l a y o u t procedure c o u l d be  Jaquette's  concept of  s u c c e s s i v e l y w i t h o u t ever e n t e r t a i n i n g  stage 3 c h i l d can see a l l the p e r s p e c t i v e s but  and  to  C r e a t i v i t y i s a m u l t i f a c e t e d phenomenon and  l a y o u t p r o c e d u r e , however, c o u l d be  A d j a c e n t elements c o u l d be  Likewise,  the  can see the i n h i b i t o r y r o l e i t  r e c y c l i n g component c l e a r l y r e q u i r e s an u n d e r s t a n d i n g of  feedback concept.  Selman and  1  d e f i n i t i o n s of problems are the key  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 The  Arlin s  "Problem f i n d i n g " suggests  t h a n k f u l l y n e i t h e r form of l o g i c seems to have i t  feedback.  brings  the o t h e r hand, i f problem f i n d i n g i s taken to mean f i n d i n g  plays i n creative exploration.  (iv)  That l a b e l  of i t s output as i t s i n p u t .  perinto  element's  T h i s l e v e l of s o p h i s t i c a -  t i o n , however, would not be n e c e s s a r y to produce a c o r r e c t answer f o r the layout procedure. puts with  I n a two  element c y c l e , the e q u a t i o n  o f one  elements o u t -  i t s l a t e r i n p u t s amounts to s o l v i n g the l a y o u t 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 o p e r a t i o n .  Perhaps the l a y o u t component, w i t h  a more f a m i l i a r c o n t e n t , would prove to be a t a s k s i m u l a t i n g the o p e r a t i o n s u n d e r l y i n g Selman and J a q u e t t e ' s  second stage  what u n d e r l i e s t h e i r t h i r d stage  (mutual p e r s p e c t i v e s ) might be the  t i o n of t r a n s i t i v e r e c y c l i n g .  (self-reflection).  Likewise, opera-  F u t u r e r e s e a r c h i n the a r e a of s o c i a l p e r s p e c t i v e  2 t a k i n g might examine the r e l e v a n c e of t h i s systemic  cognitive operation.  Conversely,  f u t u r e r e s e a r c h on c y c l i c  t r a n s i t i v i t y might examine the  of r e d u c i n g  (or i n c r e a s i n g ) the number of elements i n the c y c l e .  effects  A  two  element c y c l e would be a c l o s e r analogue of the p e r s p e c t i v e t a k i n g problem. One  of the most c u r i o u s f i n d i n g s w i t h r e s p e c t to c y c l i c  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 s e c t i o n . item  (see t a b l e V ) , which a s s e s s e d  The  transitivity  i n t r o d u c t o r y "Own  the a b i l i t y of respondents  was Wheat"  to t r a c e the  commodity flow i n the d i r e c t i o n o p p o s i t e to t h a t of the d o l l a r f l o w , not i n t e n d e d to measure a b i l i t y w i t h 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 .  was None-  t h e l e s s , as the data came i n , the i t e m began to appear more and more interesting. am  The  "own  wheat" i t e m was  s e r e n d i p i t o u s l y c o n s t r u c t e d to be  exact m i r r o r image o f the "same d o l l a r t w i c e " i t e m from which the  t r a n s i t i v e r e c y c l i n g s c o r e s were o b t a i n e d . the wheat went from the farmer  to the WMB  The first  o n l y l o g i c a l d i f f e r e n c e was  that  ( l e t us c a l l t h i s the c l o c k -  wise d i r e c t i o n ) w h i l e the d o l l a r went from the farmer  2.  social  to the g r o c e r y s t o r e  I f i t proved f r u i t f u l , t h i s l i n e of r e a s o n i n g might l e a d f u t u r e i n v e s t i g a t o r s to the next l o g i c a l q u e s t i o n : what more s o p h i s t i c a t e d v e r s i o n 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 J a q u e t t e ' s f o u r t h stage ( s o c i a l and c o n v e n t i o n a l system)? At f i r s t g l a n c e i t appears t h a t the f o u r t h stage ( s o c i a l and c o n v e n t i o n a l system)? A t f i r s t g l a n c e i t appears t h a t the f o u r t h stage moves away from any s o r t of t r a n s i t i v e o p e r a t i o n t o 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 p a r t s of an i n t e g r a t e d whole. T h i s sounds l i k e systems s y n t h e s i s .  1:38 first  (counterclockwise d i r e c t i o n ) .  S u r p r i s i n g l y , the c l o c k w i s e i t e m was much  e a s i e r than the c o u n t e r c l o c k w i s e i t e m .  I f we l o o k c l o s e r a t the n a t u r e o f what  i s b e i n g c y c l e d we see t h a t t r a c i n g bread around the wheat c y c l e i s e a s i e r 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 w i t h o u t  the r e c i p r o c a l movement o f money.  They might have more t r o u b l e t h i n k i n g o f money moving w i t h o u t movement o f goods.  than  the r e c i p r o c a l  I f so then the movement o f 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 o n l y one t h i n g moves i n o n l y one d i r e c t i o n .  The  movement o f 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 t h e r e must be goods moving i n the opposite d i r e c t i o n .  T h i s i n t e r p r e t a t i o n i s consonant w i t h the f i n d i n g s o f  F u r t h , e t a l . (1979) t h a t c h i l d r e n understand b e f o r e they understand any  t h a t you get food from t h e g r o c e r  t h a t you have t o g i v e the g r o c e r money i n r e t u r n .  In  case f u t u r e r e s e a r c h ought t o examine the d i f f e r e n c e s between more c l e a r l y  c o n s t r u c t e d cases o f 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  recycling.  Another p o s s i b l e i n t e r p r e t a t i o n o f the d i f f e r e n c e has t o do w i t h what happens t o the r e c y c l e d commodity when the farmer r e c e i v e s i t . going around the c y c l e because t h e farmer e a t s , i t .  The bread  The "same d o l l a r  stops  twice"  item, on the o t h e r hand, makes s p e c i f i c r e f e r e n c e t o t h e r e l e a s e o f the r e c y c l e d commodity f o r 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 o f t i m e s .  The w h e a t / f l o u r / b r e a d  travels  i n a s i n g l e c i r c l e ; t h e d o l l a r t r a v e l s around t h e c i r c l e an i n d e f i n i t e number of times, g i v i n g the i m p r e s s i o n o f a s p i r a l motion. examine the importance  F u t u r e r e s e a r c h might a l s o  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  transitivity.  139 (v)  C y c l i c I n t e g r a t i o n and The  ability while  I t s Components.  systems a n a l y s i s s e c t i o n s of the i n t e r v i e w s assessed to decompose the whole c y c l e , i n t o i t s m i n i m a l l y  still  preserving i t s i n t e g r i t y .  the  respondent's  e s s e n t i a l subcycles  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 d i s p l a y i n g a r e a l i z a t i o n t h a t the c a r n i v o r e s and c o u l d be  e l i m i n a t e d without e l i m i n a t i n g the r e m a i n i n g elements but  of the t h r e e r e m a i n i n g elements  (producers,  herbivores  t h a t none  decomposers, n u t r i e n t s ) c o u l d  be  e l i m i n a t e d w i t h o u t d e s t r o y i n g the whole c y c l e . The  systems a n a l y s i s o p e r a t i o n  seems to be a systemic  i s o l a t i o n of v a r i a b l e s o p e r a t i o n i n f o r m a l  logic.  analogue of  the  Some systems t h e o r i s t s con-  s i d e r the phrase "systems a n a l y s i s " to be a c o n t r a d i c t i o n i n terms s i n c e a n a l y s i s per  se e n t a i l s u n t a n g l i n g  the complex web  of  interconnectedness.  Perhaps i t i s f o r t h a t v e r y r e a s o n t h a t the term "systems a n a l y s i s has r e f e r to the study of more c l o s e d systems, n o t a b l y 1950's and  e a r l y 1960's, systems t h e o r y was  computers.  D u r i n g the  theory  B e r t a l a n f f y and  Conrad Waddington), t r i e d  i n t o a r e a s concerned w i t h  biologists  to expand systems  s y n t h e s i s , c o - e v o l u t i o n and  emergence.  l a t t e r t h r u s t seems to r e q u i r e the type of t h i n k i n g t h a t the systems component has  This  synthesis  tapped.  As o r i g i n a l l y c o n c e i v e d ,  c y c l i c i n t e g r a t i o n was  t i v i t y i n s o f a r as the s u b o r d i n a t e mutually  late  synonymous w i t h systems a n a l y s i s .  L a t e r systems t h e o r i s t s , concerned w i t h more open systems (e.g., l i k e Ludwig von  come to  i n f l u e n c e one  of the i n f l u e n c e flows the top to the bottom.  (bottom) and  to subsume c y c l i c  supraordinate  (top)  levels  another through b i d i r e c t i o n a l feedback l o o p s . from the bottom to the top and The  transi-  Part  p a r t of i t f l o w s  systems s y n t h e s i s qomponent captured  more of  from the  i4:o f l a v o r o f what c y c l i c i n t e g r a t i o n was i n t e n d e d t o be than d i d the systems a n a l y s i s component.  The systems s y n t h e s i s s e c t i o n d e a l t d i r e c t l y w i t h t h e  flow o f i n f l u e n c e from the s u b o r d i n a t e l e v e l t o the s u p r a o r d i n a t e l e v e l (see f i g u r e 7, p a r t A ) . There i s need f o r f u r t h e r l o g i c o - m a t h e m a t i c a l refinement o f the c y c l i c i n t e g r a t i o n c o n s t r u c t b e f o r e what was i n t e n d e d by i t can be more e f f e c t i v e l y assessed.  I s systems s y n t h e s i s t o be c o n s i d e r e d the bottom t o top component  of a l a r g e r grouping o f o p e r a t i o n s to be c a l l e d c y c l i c i n t e g r a t i o n ? I f so, shouldn't t h e r e a l s o be some o p e r a t i o n i n c l u d e d i n t h e grouping t h a t t r e a t s the s u b o r d i n a t e l e v e l by each s i n g l e element and t r a c e s t h e i r on the m u l t i p l e f a c e t s o f t h e s u p r a o r d i n a t e l e v e l  effects  (see f i g u r e 7, p a r t B)?  Or should we c o n s i d e r i n t e g r a t i o n to be a type o f m u l t i p l e c o n c a t e n a t i o n involving transitive recycling?  I f s o , then b o t h the s u p r a o r d i n a t e and  the s u b o r d i n a t e l e v e l s would be t r e a t e d by s i n g l e elements (see f i g u r e 7, part C). The  same q u e s t i o n s c o u l d be posed i n r e v e r s e when d e a l i n g w i t h the top to  bottom p a r t o f c y c l i c i n t e g r a t i o n .  O b v i o u s l y , t h e r e i s much room f o r f u t u r e  work a t the most advanced l e v e l s o f s y s t e m i c t h i n k i n g .  B.  The  S o c i a l Development  i m p l i c a t i o n s o f t h i s r e a s e a r c h f o r s o c i a l development i n the sense  of u n d e r s t a n d i n g  i n t e r p e r s o n a l i n t e r a c t i o n were mentioned i n s e c t i o n A ( i v )  of t h i s c h a p t e r i n c o n n e c t i o n w i t h Selman and J a q u e t t e ' s of s o c i a l p e r s p e c t i v e t a k i n g .  (1977) stage t h e o r y  The p r e s e n t s e c t i o n d e a l s e x c l u s i v e l y w i t h  social  development i n the sense o f i n t e r a c t i o n between the i n d i v i d u a l and s o c i e t y .  Figure Some p o s s i b l e  forms of bottom to top  Many t o one: systems s y n t h e s i s  single entity  B.  7  processes i n c y c l i c  One t o m a n y : l i k e M a r x ' s "internal relations"  multiple entities  Supraordinate Level  integration.  T r a n s i t i v e form: takes representative entities from both populations  multiple treated  if  entities singly  .-0*  •Subordinate Level  multiple entities (e.g., a population)  single entity ( e . g . , an i n d i v i d u a l )  multiple treated  entities singly  In  terms of the development of u n d e r s t a n d i n g  of s o c i a l  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 w o r d w o u l d be child's progress. 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  gation. to  The: p i o n e e r w o r k o f F u r t h  Now  unearth  slight to  r e p o r t the r e s u l t s .  As  seem t o go of s o c i a l  through  determined  It  With  of concrete o p e r a t i o n s .  f r o m t h e r e s e a r c h d o n e up  that the f i r s t  The  l a s t two  t o how,  towards an a d u l t  to which but  children understanding  t r e a t e d as a h y p o t h e s i s  t o a more  two  rather study  detailed  phases appear d u r i n g the  seem t o a p p e a r d u r i n g t h 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  through  the appearance of phases W i t h i n stages  the stages  stage  post-concrete  i n t h e same s e q u e n c e  i s s u b j e c t t o a g r e a t d e a l more  t h e i r appearance between  stages,  Ordination The  is  level)  hypothesis.  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 than (i)  individual  t h e m o s t u s e f u l l e v e l on  t h a t i n m i n d , l e t us p r o c e e d  of t h i s "four phases"  i s being suggested  stage.  attempted  T h i s i s an a r e a where the f i n d i n g s o f the p r e s e n t  are of h e u r i s t i c value. examination  study  of o p e r a t i o n s .  T h i s p r o p o s i t i o n s h o u l d be  than a c o n c l u s i o n .  investi-  S i n c e some o f t h e  f o u r phases i n t h e i r progress  systems.  the present  others  Instead, the f i n d i n g s are described at a grosser  the l e v e l of groupings  f a r a s c a n be  stage of  have  the  (1979) and  ( i n terms of d i f f i c u l t y  changes i n c o n t e n t , perhaps t h a t i s not  more s t a b l e l e v e l ,  but  at that i n i t i a l  the 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 .  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  "mathematize",  (1977), Jahoda  t h a t s e v e r a l s t u d i e s have accumulated,  s y s t e m s , we  first  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 a b o u t s o c i a l o r g a n i z a t i o n  t h a t some p e o p l e  the people  a r e more i m p o r t a n t  at the top, the people  This realization i s reflected "first  come f i r s t  t h a n , o r "come b e f o r e " o t h e r s .  i n the middle,  and  the people  There  at the  i n everything from t h e i r understanding  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 e a c h  of  are  bottom. the  other.  143 (ii)  Hierarchy The  understanding  u s u a l l y develops  of n e s t e d c l a s s i f i c a t i o n s and whole-part  a little  a permanent apparatus  later.  T h i s i s when government s t a r t s to be seen as  o f power, a s t a t e s t r u c t u r e .  o f t e n speak of the government as "he", 1971;  E a s t o n and Dennis,  1969).  and  P r i o r to t h a t  children  "he" has p e r s o n a l power ( C o n n e l l ,  The u n d e r s t a n d i n g  o r d e r i n g a l s o extends to g e o - p o l i t i c a l areas r e a l i z e that being a Vancouverite  relationships  of h i e r a r c h i c a l  (Jahoda,  1964).  does not p r e c l u d e one  social  C h i l d r e n b e g i n to  from b e i n g a B r i t i s h  Columbian and a Canadian a t the same time. (iii)  Systems A n a l y s i s The  a b i l i t y to m e n t a l l y remove elements from a s o c i a l feedback loop  d e s t r o y i n g the c y c l e i t s e l f would appear to emerge e a r l y i n the stage.  post-concrete  A d e l s o n and h i s c o l l e a g u e s (Adelson, Green and O ' N e i l , 1969;  O ' N e i l , 1966;  Adelson,  1970)  has  commented on the extremely  without  Adelson  draconian  and  a u t h o r i t a r i a n approach t h a t a d o l e s c e n t s o f t e n take to s o c i a l o r d e r .  Perhaps  t h i s i s a n a t u r a l r e s u l t of b e i n g a b l e to c o g n i t i v e l y remove (e.g.,  execute,  outlaw, ban)  the elements t h a t a c u r s o r y c a u s a l a n a l y s i s i d e n t i f i e s as the p r e -  c i p i t a t i n g causes of the d i s o r d e r (e.g., lawbreakers, parties).  The  for  The  the  changes t h a t are seen as p o s s i b l e i n v o l v e changes  the p a r t s of the system, not the whole system. how  unions, o p p o s i t i o n  a d o l e s c e n t r e l y i n g s o l e l y on systems a n a l y s i s s t a r t s b y ' t a k i n g  s o c i a l system as a g i v e n . in  and  There i s l i t t l e a p p r e c i a t i o n  the whole e v o l v e s i n t o something e l s e when one  of i t s interdependent  p a r t s i s changed. (iv)  Systems S y n t h e s i s W i t h the mastery of systems s y n t h e s i s the a d o l e s c e n t 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 a c t i o n s and i n t e r a c t i o n s of the p a r t s a c r o s s time. a c r o s s p e r s o n a l and  Systems s y n t h e s i s a l l o w s the a d o l e s c e n t  societal levels.  to r e l a t e ; . e f f e c t s  For example, s e e i n g the i n t e r r e l a t e d n e s s  -144 between p e r s o n a l  finances  systems s y n t h e s i s .  and the n a t i o n a l economy was counted as evidence o f  The amount o f taxes p a i d a r e r e l a t e d b o t h t o how much one  earns and how much the government-spends.  L i k e w i s e , government e x p e n d i t u r e s  are r e l a t e d t o how much t h e government charges i n taxes and how much the n a t i o n a l currency w i l l l e v e l s of finance,  fetch internationally.  the p e r s o n a l  Note here t h a t t h e r e a r e two  and the n a t i o n a l .  f a c t o r s on the same h o r i z o n t a l l e v e l .  Each l e v e l i s a f f e c t e d by  Discretionary personal  income f o r an i n d i v i d -  u a l o r p r o f i t s f o r a b u s i n e s s a r e a f f e c t e d by b o t h gross income and c o s t .  The  b a l a n c e o f a n a t i o n a l budget i s a f f e c t e d by t h e v a l u e o f the c u r r e n c y and t h a t i n t u r n r e l a t e s t o the governments " p r o d u c t i v i t y " i n terms o f f o r e 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 l o o p s t h a t o p e r a t e on each r e s p e c t i v e  agreements, e t c .  l e v e l alone.  Those a r e the feeback  But the f i n a n c i a l  picture  f o r each l e v e l i s a l s o i n f l u e n c e d by feedback l o o p s t h a t o p e r a t e a c r o s s l e v e l s . The by  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 b u s i n e s s ' s p r o f i t s a r e i n f l u e n c e d taxes and government e x p e n d i t u r e s .  conversely  i n f l u e n c e d by the amount o f goods and s e r v i c e s produced .by the  individuals  (GNP p r i v a t e s e c t o r ) .  influences across the p o i n t . involves  The b a l a n c e o f the n a t i o n a l budget i s  There a r e , o f c o u r s e , innumerable o t h e r  l e v e l s too but the ones c i t e d here a r e s u f f i c i e n t t o make  The p o i n t  i s t h a t systems s y n t h e s i s  applied  t r a c i n g t h e l i n e s o f mutual i n f l u e n c e a c r o s s  to s o c i e t a l a f f a i r s  l e v e l s of organization.  These v e r t i c a l feedback l o o p s p r o v i d e c o n t r o l i n f o r m a t i o n organization feedback loop  simultaneously. i f the WMB  f o r both l e v e l s of  The wheat c y c l e c o u l d be t r e a t e d as a h o r i z o n t a l  i s c o n c e i v e d as a type o f w h o l e s a l e r . Such a con-  c e p t i o n would i n d i c a t e a f a i l u r e to p e r c e i v e between t a x p a y e r and government.  the h i e r a r c h i c a l arrangement  The c o n c r e t e o p e r a t i o n a l  achievement o f  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 t h i n k i n g .  When the  . 145 respondent  gave responses  v e r t i c a l feedback  d i s p l a y i n g an a p p r e c i a t i o n o f the WMB's r o l e i n t h e  l o o p , as w e l l as the h o r i z o n t a l l o o p , then a pass was  scored on systems s y n t h e s i s . In  g e n e r a l then t h e c h a r t o f development i n 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 e t y s t a r t s with understanding With the advent  s o c i a l o r d e r i n g , then s o c i a l  hierarchies.  o f t h e p o s t - c o n c r e t e stage systems a n a l y s i s becomes p o s s i b l e .  Systems s y n t h e s i s might become p o s s i b l e a t 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 o f s o c i e t a l knowledge. s y s t e m i c l o g i c i s s i m p l y n e g l e c t e d by the c u l t u r e 1977b) and so the use o f i t s more d i f f i c u l t  Perhaps  (Buck-Morss, 1975; Buss,  forms (e.g., systems s y n t h e s i s )  has n o t become p r e v a l e n t among a d o l e s c e n t s . Perhaps by t h e i r i n t e r a c t i v e n a t u r e , feedback thoroughly without  i n t e r a c t i o n o f some s o r t .  l o o p s cannot be apprehended  P a r t a k i n g o f the i n t e r a c t i o n s  t h a t these l o o p s d e s c r i b e would a t l e a s t h e l p one t o a c q u i r e a broader of  f a c t s about the system.  I n s o f a r as u n d e r s t a n d i n g  feedback  i n t e r a c t i n g w i t h them s y s t e m i c t h i n k i n g i s more pragmatic systemic understanding  loops r e q u i r e s  i n nature.  If a  o f s o c i e t y c a r r i e d w i t h i t a heavy p r e r e q u i s i t e o f  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 , of  base  i t would be no wonder t h a t o n l y a m i n o r i t y  the o l d e s t a d o l e s c e n t s i n t h i s study e v i n c e d a mastery o f systems s y n t h e s i s .  C. ''Social  Psychology  The p r e s e n t study takes a step towards c o r r e c t i n g some o f s o c i a l psychology's "the c r i s i s  shortcomings literature".  i d e n t i f i e d by c r i t i c s I n the c r i s i s  i n what has come t o be c a l l e d  l i t e r a t u r e s e v e r a l a u t h o r s have  criti-  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 p s y c h o l o g y (PSP) t o i s o l a t e from developments and,  (a) o u t s i d e N o r t h America  (b) i n o t h e r d i s c i p l i n e s  CSherif,  itself  ( S m i t h , 1978; S i l v e r m a n , 1977),  1977).  I n the s o c i o l o g i c a l wing o f  s o c i a l p s y c h o l o g y (SSP) t h e r e has been concern o v e r an o p p o s i t e t r e n d .  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 r e s e a r c h tends t o be p r e s e n t e d and l a b e l e d as b e l o n g i n g t o a s u b s t a n t i v e s u b f i e l d o f s o c i o l o g y thus p r o m o t i n g t h e d i s s i p a t i o n of SSP is this:  ( L i s k a , 1977; H e w i t t , 1977).  S t a r k l y s t a t e d , the s i t u a t i o n  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  s o c i a l p s y c h o l o g y 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 w h i l e t h o s e who  a r e committed  t o the d i s c i p l i n e tend-towards  Both responses a r e u n h e a l t h y f o r the; d i s c i p l i n e . (i)  from  itself  isolationism.  •  Towards an I n t e r a c t i v e Framework I t needn't be one o r the o t h e r .  There i s another a l t e r n a t i v e .  Social  p s y c h o l o g y s t a n d s a t the i n t e r s t i c e between the c o m p l e x i t y of the p e r s o n and the c o m p l e x i t y o f s o c i e t y .  The t a s k o f u n d e r s t a n d i n g how  Yet i t  one a n o t h e r i s an u n i q u e l y s o c i a l p s y c h o l o g i c a l problem. r e c u r s i n a l l branches o f s o c i a l s c i e n c e .  s c i e n c e and s o c i o l o g y as w e l l as p s y c h o l o g y .  p s y c h o l o g i s t s a r e i n an e x c e l l e n t p o s i t i o n t o f i l l generalists.  geography,  history,  the r o l e of s o c i a l science  I n o r d e r t o make t h i s type of c o n t r i b u t i o n , however, t h e r e must  (1944) made a f r u i t f u l c o n t r i b u t i o n a l o n g those l i n e s .  G.H.  Mead  I t l e d t o a good d e a l  e m p i r i c a l r e s e a r c h on v a r i o u s a s p e c t s of t h e t o p i c but t h a t r e s e a r c h has  become d i f f u s e .  that  For t h i s reason, s o c i a l  be a g e n e r a l framework f o r s t u d y i n g p e r s o n - s o c i e t y i n t e r a c t i o n .  of  i s a problem  The n a t u r e o f p e r s o n - s o c i e t y i n t e r -  a c t i o n i s o f v i t a l importance i n a n t h r o p o l o g y , economics, political  the two r e l a t e . . t o  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  that w i l l  integrate, a l l  the d i v e r s i t y  of i n s i g h t s  mulated w i t h regard to person-society i n t e r a c t i o n Svendsen,  t h e o r i e s about  t h e r e a r e no a d e q u a t e  i n such, a framework  t h e o r i e s about  w o u l d be  and  opinion  the processes that c h a r a c t e r i z e  the  (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 isomorphic  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  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  described  p r e s e n t r e s e a r c h i s an a t t e m p t  move t o w a r d s t h e k i n d o f i n t e g r a t i v e f r a m e w o r k  than B o u t i l i e r ,  to  e_t a l . a n d  called for.  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  He  and  the s o c i a l system  the d e s c r i p t i o n of b o t h systems  t e r m s . That i s , t h e p e r s o n and  S.L.  Roed,  the person-system but i n the author's  i n t e r a c t i o n of those systems. DiRenzo  DiRenzo  (Boutilier,  1980). There a r e s a t i s f a c t o r y "theories about  satisfactory  t h a t have a c c u -  R u b e n s t i e n ( c i t e d by Payne,  (Neisser,  1 9 8 0 ) . The  psychologist,  1 9 6 8 ) , a t t e m p t e d an a l t e r n a t i v e  sought a theory which would view the i n d i v i d u a l  i n an a c t i v e e n v i r o n m e n t .  soviet  a s an a c t i v e  approach. participator  S i n c e open systems must, by d e f i n i t i o n ,  remain  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 the p e r s o n and  the s o c i a l environment  p r o m i s e s t o p r o v i d e a framework  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 the person's c o g n i t i v e modeling of the environment 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  for theories theory of  i s a g o o d e x a m p l e o f how  to d e s c r i b i n g  the person  system.  P i a g e t c o n s t r u e s t h e 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 reality.  I n s e v e r a l p l a c e s one  active social 1977;  system  Sztompka,  1978;  B o u l d i n g , 1962; E a s t o n , 1965; M y s i o r ,  t a s k , t h e n , was  to extend P i a g e t  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 t e m . I t was p r o v i d e the framework  of  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 of the  (e.g., B a l l ,  197'4). The  an  needed t o (a) i n t e g r a t e  t o b e a r upon t h e  hoped t h a t t h i s would h e l p  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 t h e s o c i o - c u l t u r a l c o n t e x t t o bear upon t h e s t u d y o f t h e 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 u n d e r s t o o d 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 u n d e r s t a n d those a s p e c t s of ing  s o c i e t y t h a t they a r e i n f l u e n c i n g ( i . e . , a c t i v e person) o r t h a t a r e i n f l u e n c them ( i . e . , a c t i v e s o c i a l system).  F o r example, l o c u s o f c o n t r o l w i t h  respect to society, e s p e c i a l l y p o l i t i c s , (Lao, 1970; C o l l i n s , 1974).  i s a s u b f a c t o r o f t h e I-E s c a l e  The analogous c o n s t r u c t i n s o c i o l o g i c a l  p s y c h o l o g y i s a l i e n a t i o n (Seeman, 1959).  social  S c a l e s c o r e s on t h e p o l i t i c a l  control  f a c t o r do n o t t e l l us i f a persons f e e l i n g s o f p o w e r l e s s n e s s , f o r example, a r e a r e s u l t o f a l a c k o f u n d e r s t a n d i n g o f t h e p o l i t i c a l system o r r e a l disenfranchisement or both.  The p r e s e n t study p r o v i d e s a means o f d e s c r i b i n g  t h e person's l e v e l o f u n d e r s t a n d i n g o f t h e p o l i t i c a l system i n more d e t a i l . A c c o r d i n g t o P i a g e t ( e . g . , 1970) u n d e r s t a n d i n g advances through a c t i o n w i t h a p a r t i c u l a r environment.  inter-  E x t e n d i n g t h i s p r i n c i p l e t o t h e under-  s t a n d i n g o f s o c i a l systems, we s h o u l d expect a m i c r o g e n e t i c r e c a p i t u l a t i o n (Werner, 1948) o f t h e o n t o g e n e t i c sequence found i n t h i s s t u d y .  Each time  a p e r s o n e n t e r s a new o r g a n i z a t i o n , f o r example, t h e i r u n d e r s t a n d i n g o f the o r g a n i z a t i o n s h o u l d p r o g r e s s t h r o u g h t h e phases d e s c r i b e d 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 o f u n d e r s t a n d i n g 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 , l o w e r l e v e l s o f u n d e r s t a n d i n g w i l l be found w i t h r e s p e c t to t h o s e a s p e c t s o f s o c i e t y t h a t they i n t e r a c t w i t h l e s s .  F o r example, m e d i c a l  d o c t o r s might have a v e r y poor u n d e r s t a n d i n g o f the r e l a t i o n s h i p w e l f a r e a g e n c i e s and t h e i r c l i e n t s .  between  E x t e n d i n g t h i s i d e a , we might even be  a b l e t o c h a r a c t e r i z e p e o p l e s g e n e r a l v i e w s o f s o c i e t y as b e i n g b u i l t  around  t h o s e a s p e c t s o f i t w i t h w h i c h they have t h e more f r e q u e n t and/or i m p o r t a n t interactions.  Thus we would p r e d i c t t h a t t h e c o r e c y c l e s i n a l a w y e r ' s v i e w  149 of s o c i e t y would i n v o l v e  government and l e g i s l a t i o n .  housewife's view o f s o c i e t y may  involve  The c e n t r a l c y c l e s  the v a r i o u s phases  marriage, through c h i l d r e a r i n g , t o grandparenthood.  of family  in a  life  from  Members o f i n d u s t r i a l  l a b o r 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 c y c l e t h a t makes s o c i e t y m e a n i n g f u l to them.  Rokeach (1973) has  t h a t d i f f e r e n t o c c u p a t i o n a l groups have d i f f e r e n t s e t s o f v a l u e s . s o c i a l , and economic v a l u e o r i e n t a t i o n s may group's  through some p a r t i c u l a r feedback l o o p .  Kohn (1969) f i n d s t h a t working middle c l a s s p e o p l e .  For example,  I n terms o f f i n a n c i a l s e c u r i t y , obedience g e t s workers Workers and management  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 n e g a t i v e  feedback  f o r the workers.  In g e n e r a l then, v a l u e s and a t t i t u d e s may  f i c a n t l y r e l a t e d t o , and perhaps, that  outcomes i n  c l a s s people v a l u e obedience much more than do  more o f what they want than autonomy o r d i s o b e d i e n c e . are  Political,  w e l l a r i s e from i n d i v i d u a l s ' and  u n d e r s t a n d i n g s o f what moves do and do not produce d e s i r e d  i n t e r a c t i o n with society  found  generated by, the types o f feedback  be s i g n i loops  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 w i t h v a r i o u s a s p e c t s of  society. (ii)  Towards S p e c i f l y i n g the S t r u c t u r e of the S o c i a l For  some time now  s o c i a l p s y c h o l o g i s t s have emphasized  s o c i a l s i t u a t i o n " to c o n t r o l b e h a v i o r . Zimbardo's p r i s o n c l a s s i c examples.  study  Situation  The Milgram  the power of "the  (1963) obedience study and  (Zimbardo, Haney, Banks, and J a f f e , 1972)  The work on b y s t a n d e r i n t e r v e n t i o n  are  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 b e h a v i o r . yet,  As  however, no system has been d e v i s e d f o r a n a l y s i n g o r c l a s s i f y i n g s o c i a l  situations.  Perhaps  the l e v e l s of u n d e r s t a n d i n g s o c i e t y p r e s e n t e d i n t h i s study  150 would help  do  t h a t by  c o n s t r u c t i o n of in  the present  of "the  the  situation.  study  situation"  p r o v i d i n g a framework f o r d e s c r i b i n g the i n d i v i d u a l ' s The  could help  are  salient  (1973)  the person  situation  actionism Endler  leaves  and  the  (1976),  Magnusson  (P<—*S).  framework p r e s e n t e d be  the  Note that subject  find  salient  i s very  does, accepting  a u t i s t i c a l l y , without i n the  any  Reese  trait  s i t u a t i o n s can describe  be  The  situation  t h o s e where the  own  one  upon the  the  w i l l vary  the  Perhaps t h i s other.  other  by  the  i n t e r a c t i o n could  c o n s t r u a l of  the  situation  form of  p o s s i b l e form.  i s construed  of  sit-  (a)  the  Few,  exactly  and  (b)  they  social  reality  subjects  from person to person.  This  i f any,  is  social  Unless s o c i a l psychologists take  inter-  of  facilitated  Extended to the understanding only  of  (1977a),  Buss  f u n c t i o n s of each  s i d e of  can  f o r d i f f e r e n t people,  the  produce c o n s i s t e n t r e s u l t s w i l l  more o r l e s s t h e  P e r s o n a l i t y v a r i a b l e s are poor p r e d i c t o r s of behavior situation.  function  to what s u b j e c t s o r anyone e l s e say  interactions that w i l l  situation  inter-  h i s verbal reports purely at face value,  content  one  features  advocate a form  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 . have o n l y  discussed  That form of  from d e f i n i n g the  t h e p o s s i b l e f o r m s t h a t a s i t u a t i o n may  o n l y p e r s o n by  a joint  (P,S).  C1973)  subject's  the P i a g e t i a n approach promises to i d e n t i f y  where the  as  s i t u a t i o n unsolved.  situational  different  reference  situation.  phenomenal s i t u a t i o n .  v e r s i o n of  t y p e o f i n t e r a c t i o n i s m w o u l d be  here because the  this  (B)  the person are  s p e c i f i e d i n terms t h a t r e l a t e to the  uation. as  O v e r t o n and  s i t u a t i o n and  This  The  such that B = f  the problem of d e f i n i n g the  i n t e r a c t i o n i s m where the such t h a t  (S)  sees behavior  perspectives  s p e c i f y j u s t what  to d i f f e r e n t persons.  Bowers  and  and  social psychologists  a c t i o n i s m a d v o c a t e d by (P)  phases r e p o r t e d ,  same way  i n the Milgram  by  everyone.  obedience  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 ,  P e r s o n a l i t y v a r i a b l e s m i g h t 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 t h e form o f t h e 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 , s y s tems a n a l y t i c , systems s y n t h e t i c ) B e i n g p e r c e i v e d By t h e s u b j e c t were examined.  '1-52  D.  CONCLUSIONS  P i a g e t s o r g i n a l n o t i o n o f stages as s t r u c t u r e d wholes f a r e s q u i t e w e l l 1  when the t a s k s used to t e s t the n o t i o n a r e 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 c o n t e n t and when a wide range o f a b i l i t y l e v e l s a r e sampled.  The  g e n e r a l P i a g e t i a n approach seems to g e n e r a l i z e q u i t e 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 c o n t e n t .  The observed  d i f f i c u l t y o r d e r i n g s and stage  d i s c o n t i n u i t i e s were g e n e r a l l y as p r e d i c t e d .  related  The s y s t e m i c t a s k s , which appeared  o n l y i n the two open systems domains, were t h e r e f o r e not l i k e l y to have been confounded w i t h any abnormal c o n t e n t r e l a t e d  artifacts.  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 s t r u c t u r e s i d e n t i f i e d examined  i n t h i s study turned out to be composed o f f o u r q u i t e d i s t i n c t  components difficult  which a r 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 i r own  more d i f f i c u l t difficult  right.  The most  o p e r a t i o n s f o r 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 s y n t h e s i s component.  These upper systemic t a s k s were as much  than the f o r m a l o p e r a t i o n s as the f o r m a l o p e r a t i o n s were more  than the c o n c r e t e o p e r a t i o n s .  Moreover, the gap i n d i f f i c u l t y  was a Guttman s t e p but t h e r e were no Guttman steps among the upper tasks.  and  The g r e a t e r d i f f i c u l t y of the upper systemic  systemic  t a s k s c o u l d not be  c l e a r l y a t t r i b u t e d to the more u n f a m i l i a r n a t u r e of t h e i r c o n t e n t s . r e s u l t s r a i s e d the p o s s i b i l i t y  levels  These  t h a t these t a s k s might a s s e s s o p e r a t i o n s r e -  p r e s e n t a t i v e of a f i f t h stage o f c o g n i t i v e development. The upper systemic except  concurrence  abruptness  t a s k s 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  ( f o r which t h e r e were no r e l e v a n t data a v a i l a b l e ) and  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 y e a r s o l d e r than those b e g i n n i n g t o master  the f o r m a l o p e r a t i o n s .  The m a j o r i t y o f respondents  mastered the systemic components;,  a t a l l age l e v e l s  never  whereas from age 14 onward the v a s t m a j o r i t y  had mastered t h e f o r m a l o p e r a t i o n s .  I t was noted  are not i n c o m p a t i b l e w i t h stage i n t e r p r e t a t i o n s . on t h e upper systemic t a s k s might be observed  t h a t g r a d u a l stage I t was suggested  transitions  that success  t o Be more f r e q u e n t were f u t u r e  r e s e a r c h t o sample o l d e r 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 t h a t systemic o p e r a t i o n s develop i n p a r a l l e l w i t h f o r m a l o p e r a t i o n s as a complementary a s p e c t o f c o g n i t i v e d i v e r s i f i c a t i o n i n the p o s t - c o n c r e t e stage.  A r e l a t e d s u g g e s t i o n was p u t forward  and systemic l o g i c a r e complementary and  t o the e f f e c t t h a t f o r m a l l o g i c  develop  c o n c r e t e stage as w e l l as the p o s t - c o n c r e t e stage  i n p a r a l l e l throughout the  Cand  perhaps even  through-  out a l l s t a g e s ) . 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 e t y was d e s c r i b e d as going t h r o u g h two  stages w i t h two o v e r l a p p i n g phases w i t h i n each s t a g e .  According to t h i s  d e s c r i p t i o n , i n the c o n c r e t e s t a g e , 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 t u r e s would become comprehensible  to the c h i l d .  struc-  E a r l y i n the post-concrete  stage the a d o l e s c e n t would be a b l e t o use systems a n a l y s i s t o make s o c i e t a l r e a l i t y meaningful.  L a t e r , systems s y n t h e s i s would emerge as a c o n c e p t u a l  tool.  T h i s r e s e a r c h was designed t o a l l o w ample scope f o r e x p l o r a t i o n and discovery. raised.  Q u i t e a few d i s c o v e r i e s were made and even more q u e s t i o n s were  Perhaps the most important  the e x i s t e n c e o f a second  outcome was the e m p i r i c a l v i n d i c a t i o n o f  type o f l o g i c .  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New Y o r k : W i l e y , 1970.  P e r s o n a l i t y and S o c i a l Systems (2nd  ed.)  S i l l s , Thomas, and H e r r o n , J . Duddley,. Study o f an e l e c t r o n i c a n a l o g to the c o m b i n a t i o n s o f c h e m i c a l b o d i e s P i a g e t i a n t a s k . The J o u r n a l of G e n e t i c P s y c h o l o g y , 1976, 129, 267-272. S i l v e r m a n , I r w i n . Why s o c i a l p s y c h o l o g y f a i l s . 1977, 18, 353-358.  Canadian P s y c h o l o g i c a l Review,  S m i t h , R.J. The f u t u r e o f an i l l u s i o n : American s o c i a l p s y c h o l o g y . and S o c i a l P s y c h o l o g y B u l l e t i n , 1978, 4_, 172-176. S u t t o n , D.B., 1973.  and Harmon, N.P.  Ecology:  Sztompka, P i o t r . System arid F u n c t i o n : Academic P r e s s , 1974. von B e r t a l a n f f y , Ludwig.  S e l e c t e d Concepts.  Personality  New Y o r k :  Towards a Theory o f S o c i e t y .  G e n e r a l System Theory.  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Zimbardo, Inc.1972 (Tape r e c o r d i n g ) .  •161  APPENDIX A;  P h y s i c a l Domain Tasks  The methods f o r a s s e s s i n g mastery over each o f the e i g h t c o g n i t i v e o p e r a t i o n s i n the standard domain i s d e s c r i b e d h e r e i n . F o r each c o g n i t i v e o p e r a t i o n the source of the t a s k and m i s c e l l a n e o u s background i n f o r m a t i o n i s g i v e n i n the i n t r o d u c t i o n . Then the m a t e r i a l s a r e d e s c r i b e d b e f o r e the q u e s t i o n s a s s e s s i n g the respondent's f a m i l i a r t i t y w i t h them a r e p r e s e n t e d . The i n s t r u c t i o n s and probes to be d i r e c t e d towards the respondent appear next and are f o l l o w e d by a d e s c r i p t i o n o f the s c o r i n g procedures and c r i t e r i a . S i n c e P i a g e t was not e s p e c i a l l y concerned w i t h s t u d y i n g the u n d e r s t a n d i n g of open systems, t h e r e a r e no standard P i a g e t i a n t a s k 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 n s t e a d , the p h y s i c a l domain c o n t a i n e d 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 t h a t a c t e d as markers i n the scalogram a n a l y s e s . They made i t p o s s i b l e t o l o c a t e the d i f f i c u l t y l e v e l s o f the systemic t a s k s w i t h respect to formal operations.  A. (i)  Seriation  Int roduction  The standard s e r i a t i o n t a s k , 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) was used. The respondents were a l s o r e q u i r e d to i n t e r p o l a t e an element i n t o the s e r i e s . The i n t e r p o l a t i o n requirement h e l p e d to d i s t i n g u i s h stage I I responses from stage I I I responses (Ginsberg and Opper, 1969, pp. 137-138). (ii)  Procedure Materials.  -Seven cardboard c y c l i n d e r s t h a t stand on end, a l l one c o l o r ( r e d ) , r a n g i n g i n h e i g h t from 2" t o 8". -One  interpolation cylinder 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 c y c l i n d e r s were p l a c e d s t a n d i n g on end i n a random a r r a y i n f r o n t o f the respondent. The respondent was asked, "Can you t e l l me what these t h i n g s a r e ? " and, i f n o t a l r e a d y answered by the respondent, "Do you know what they a r e made o f ? " Pass:  Tubes, Cardboard.  Fail:  Other, Don't know, No  response.  Instructions. P a r t A: The respondent was asked t o arrange the c y l i n d e r s i n o r d e r . S i z e was not mentioned i n o r d e r t o t e s t whether the respondent s e r i a t e d spontneously.  •162  P a r t B: The respondent was t o l d to arrange the c y l i n d e r s going from the " s m a l l e s t to the l a r g e s t " , or from the " l i t t l e s t to the b i g g e s t " i f t h i s had not a l r e a d y been done. P a r t C: I f the c y l i n d e r s were s e r i 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 t o , "Put i t i n the r i g h t p l a c e w i t h the r e s t . " (iii)  Scoring  The responses were c l a s s i f i e d i n t o t h r e e s t a g e s . 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 f o r the purpose of dichotomous s c o r i n g . I (Fail): The l a r g e and s m a l l .  c h i l d o f t e n d i v i d e s the o b j e c t s i n t o two  groups s u c h as  II ( F a i l ) : The c h i l d sometimes d i v i d e s - the o b j e c t s i n t o t h r e e groups: s m a l l , medium, and l a r g e . C o r r e c t s e r i a t i o n sometimes o c c u r s a f t e r c o n s i d e r a b l e u n s y s t e m a t i c t r i a l and e r r o r . In stage IT the I n t e r p o l a t e d o b j e c t i s m i s p l a c e d . III  (Pass):  The  c h i l d i s a b l e to s e r i a t e a l l e i g h t o b j e c t s c o r r e c t l y .  B. (i)  Linear  Transitivity  Introduction  F o l l o w i n g the standard procedure ( C l i c k and Wapner, 1968). f o r d e t e r m i n i n g the a b i l i t y to 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 we used 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 dimension. The o b j e c t s were cardboard c y l i n d e r s v a r y i n g i n h e i g h t , each one a d i f f e r e n t c o l o r . The c y l i n d e r s were p r e s e n t e d i n p a i r s w i t h the c y l i n d e r of i n t e r m e d i a t e l e n g t h b e i n g a member of b o t h p a i r s . The respondent memorized the r e l a t i o n s between the members o f b o t h p a i r s (e.g., s h o r t e r than) and the d e s i g n a t i o n s 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 p r e s e n t e d h e t e r o tropically. In h e t e r o t r o p i c p r e s e n t a t i o n 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 l o n g e r than B" and "C i s s h o r t e r than B " ) . G l i c k and Wapner found h e t e r o t r o p i c 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 w i t h t h i s p r o c e d u r e . H e t e r o t r o p i c r e l a t i o n s were used because they f o c u s a t t e n t i o n on the b i v o c a l n a t u r e of the i n t e r m e d i a t e element. (ii)  Procedure Materials.  -Three cardboard c y l i n d e r s (A,B,C) v a r y i n g i n length, and Color  Length  A.  Red  9'ii  B.  White  6 II  C.  Blue  3 ii  color.  163 F a m i l i a r i t y Assessment. The c y l i n d e r s were p r e s e n t e d 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 t h a t he/she would be shown two p a i r s o f c y l i n d e r s ( o r " t u b e s " ) and would than Be a s k e d , "Which was t h e t a l l e s t ? " and "Which one was t h e s h o r t e s t ? " The c h i l d was asked t o name t h e c o l o r o f each c y l i n d e r as i t was p r e s e n t e d . The w h i t e 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 t h e r e d c y l i n d e r ( A ) . The r e d one was t o t h e c h i l d ' s r i g h t v i s a v i s t h e w h i t e one. The cylinders;.were then removed from s i g h t and t h e 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 p r o c e d u r e was r e p e a t e d f o r t h e second p a i r w i t h t h e w h i t e c y l i n d e r B e i n g d i s p l a y e d t o t h e s u b j e c t ' s l e f t v i s a V i s t h e B l u e one and t h e B l u e one B e i n g p r e s e n t e d f i r s t . I n s t r u c t i o n s . . When t h e i n v e s t i g a t o r was c e r t a i n t h a t t h e c h i l d rememBered the c o l o r s o f a l l t h r e e c y l i n d e r s , he a s k e d , "Which one was t h e t a l l e s t ? " and "How c a n y o u t e l l t h a t ? " f o l l o w e d By, "Which one was t h e sho;rtest?"and "How can you t e l l t h a t ? " (iii)  Scoring I  (fail):  I n c o r r e c t c h o i c e f o r one o r B o t h  endpoints.  I I ( F a i l ) : C o r r e c t c h o i c e o f e n d p o i n t s But i n c o r r e c t e x p l a n t i o n f o r c h o i c e (e.g.,, t a u t o l o g y ; t e m p o r a l o r d e r as h e i g h t p r e d i c t o r ) III  (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.  (1)  Logical Multiplication  Introduction  The l o g i c a l m u l t i p l i c a t i o n o f c l a s s e s i s t h e o p e r a t i o n u n d e r l y i n g m u l t i p l e classification. I t a l s o u n d e r l i e s t h e concept o f t h e " g r e 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 t o i n l o g i c as t h e " i n t e r s e c t i o n " o f s e t s o f " c o n j u n c t i o n " ( G o r o v i t z and W i l l i a m s , 1969) i n t r u t h t a B l e s , s y m B o l i z e d By t h e o p e r a t o r " f l " . 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 mastery 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 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 , 1964).  164  (ii)  Procedure  Materials. -A t w o - f o l d m a t r i x w i t h (a) y e l l o w shapes i n the l e f t and r e d shapes i n the r i g h t column, and (b) s t a r shapes on the top row 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  - R i g h t top c e l l :  red  - L e f t bottom c e l l : - R i g h t bottom c e l l : a r e d square)  column and  star  star  yellow  square  BLANK (.to be f i l l e d by respondent  w i t h c o r r e c t e n t r y of  -Below the m a t r i x was a row of f i v e a l t e r n a t i v e s t h a t may 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  be s e l e c t e d f o r the  circle  F a m i l a r i t y Assessment. The i n v e s t i g a t o r p o i n t e d to each o b j e c t i n the m a t r i x and asked the repondent what i t was. I f shape o r c o l o r were not ment i o n e d , the i n v e s t i g a t o r asked what shape or c o l o r e a c h o b j e c t was. Pass:  C o r r e c t shape and  color.  Instructions. The i n v e s t i g a t o r then p o i n t e d t o each o b j e c t i n the m a t r i x from column to column, s a y i n g "OK, so here i s a y e l l o w s t a r . Here i s a r e d star. Here i s a y e l l o w square. Which of these ( p o i n t s to row of f i v e a l t e r n a t i v e s a t bottom) goes b e s t here ( p o i n t s to b l a n k c e l l ) w i t h t h i s y e l l o w s t a r , t h i s r e d s t a r and t h i s y e l l o w square?" Respondents' e x p l a n a t i o n s were recorded. "Can of (iii)  a n y t h i n g e l s e f o i n t h i s empty p l a c e j u s t as w e l l as your c h o i c e __?"  Scoring I II III  (Fail): (Fail):  Incorrect choice Correct shoice; incorrect  explanation  (Pass): Correct choice; correct explanation  '-16'5 D. (i)  Class Inclusion  Introduction  The o p e r a t i o n o f c l a s s i n c l u s i o n r e q u i r e s a combined u n d e r s t a n d i n g o f 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 r e f e r r e d t o i n l o g i c as the " u n i o n " o f s e t s o f " i n c l u s i v e d i s j u n c t i o n " i n t r u t h t a b l e s ( G o r o v i t z and W i l l i a m s , 1 9 6 9 ) , symbolized by the o p e r a t o r " U " . I n c l u s i o n r e l a t i o n s a r e i m p l i c i t i n t h e concept o f " 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 I n h e l d e r and P i a g e t ( 1 9 6 4 ) . The "whole" c l a s s was the c o n s t r u c t i o n m a t e r i a l (wood) and t h e " p a r t " c l a s s was the c o l o r (red vs_. g r e e n ) . (ii)  Procedure M a t e r i a l s . -Seven wooden beads, f i v e green and two r e d , 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 h e r e ? " I f the s u b j e c t f a i l e d t o mention c o l o r the i n v e s t i g a t o r asked what c o l o r t h e o b j e c t s were. L i k e w i s e , i f c o n s t r u c t i o n m a t e r i a l (wood) was not mentioned, a prompt was g i v e n f o r t h a t . I n s t r u c t i o n s . When the respondent had a f f i r m e d these premises,,.. the i n v e s t i g a t o r asked "Are t h e r e more wooden beads i n t h i s bowl o f more geen beads?" While r e c o r d i n g the responses the 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 took away a l l o f the green beads would t h e r e be any beads l e f t i n the bowl? I f I took away a l l the wooden beads would t h e r e be any beads l e f t i n the bowl? Which a r e t h e r e more o f i n t h i s bowl, green beads or wooden beads?" (Iii)  Scoring I II  (Fail):  More o f the p a r t c l a s s than the whole c l a s s .  (Pass):  More o f the whole c l a s s than the p a r t  E. (i)  class.  Combination o f V a r i a b l e s  Introduction  T h i s v e r s i o n o f the problem was adapted by A r l i n ( 1 9 7 8 ) from a v e r s i o n by S i l l s and Herron ( 1 9 7 6 ) which 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 of I n h e l d e r and P i a g e t ' s ( 1 9 5 8 ) "Combination o f C o l o r e d and C o l o r l e s s Chemical Bodies" task. The b a s i c i d e a was f o r the respondent to engage i n a s y s t e m a t i c s e a r c h f o r t h e r i g h t combination o f v a r i a b l e s t h a t would produce t h e d e s i r e d outcome.  16-6 (ii)  Procedure  Materials. A b l a c k box (10 cm. x 5h cm. x 4 cm.) w i t h a row of 5 numbered momentary push b u t t o n s and a r e d i n d i c a t o r l i g h t on the t o p . The d e p r e s s i o n of t h r e e b u t t o n s s i m u l t a n e o u s l y turned on the l i g h t . A f o u r t h button turned i t o f f a g a i n . The f i f t h b u t t o n was not w i r e d to the b a t t e r y . Instructions. The i n v e s t i g a t o r p l a c e d an index c a r d between the f i v e b u t t o n s and the l i g h t such t h a t the respondent c o u l d not see which b u t t o n s were b e i n g depressed but c o u l d 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 p r e s s i n g down on some o f these b u t t o n s . Would you l i k e to t r y to make the l i g h t go on by f i n d i n g the b u t t o n s to push?" The i n v e s t i g a t o r r e c o r d e d the attempts o f the respondent t o i l l u m i n a t e the l i g h t , n o t i n g which b u t t o n s were p r e s s e d i n which sequence. The respondent was then asked why he/she pushed the b o t t o n s which had been attempted. The repondent was encouraged t o cont i n u e t r y i n g and was p e r m i t t e d to l o o k a t the numbers which the i n v e s t i g a t o r had w r i t t e n down r e p r e s e n t i n g each o f the respondent's t r i e s . I f the r e s p o n dent was s u c c e s s f u l i n t u r n i n g on the r e d l i g h t he/she was asked "What would you do to f i n d any o t h e r p o s s i b l e combinations of b u t t o n s which might a l s o t u r n on the l i g h t ? " (iii)  Scoring  The s c o r i n g was the same as t h a t used f o r the P i a g e t i a n "Combination o f C o l o r e d and C o l o r l e s s Chemicals" t a s k ( I n h e l d e r and P i a g e t , 1958; 110-122). Fail Concrete I I A and 2 x 2  (1-2 p o i n t s ) : Empirical associations, precausal explanations t r i a l s o f p a i r s of b u t t o n s .  Concrete I I B (3-5 p o i n t s ) : M u l t i p l i c a t i v e o p e r a t i o n s w i t h the t r i a l e r r o r i n t r o d u c t i o n o f n x n. combinations.  and  Pass Formal I I I A  (6-8 p o i n t s ) :  Formation o f s y s t e m a t i c 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 , p r o o f s appear i n a more s y s t e m a t i c f a s h i o n .  F. (i)  the  P r o b a b i l i t y i n Random Drawing  Introduction  T h i s t a s k was A r l i n ' s (1978) s t a n d a r d i z a t i o n o f the l e s s s t r u c t u r e d procedure 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). With each c h i l d  167  P i a g e t and I n h e l d e r changed the number and c o l o r of items to be drawn. This more standard v e r s i o n 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 a c r o s s c h i l d r e n and' s i m p l i f i e d the p r o c e d u r e s f o r the i n v e s t i g a t o r . (ii)  Procedure Materials,  -box --beads:  6 yellow,  6 green, 6 r e d  Instructions. The beads were c o u n t e d * i n t o the box i n f r o n t of the c h i l d . The i n v e s t i g a t o r s a i d , "What do you t h i n k are your chances of drawing a r e d bead on your f i r s t r e a c h i n t o t h i s box? Why do you t h i n k so? I f the c h i l d d i d not understand the q u e s t i o n , the q u e s t i o n was rephrased to: "How many t u r n s do you t h i n k you w i l l need to take b e f o r e you w i l l get a r e d 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 t h i n k a r e your chances of -getting another ... (the c o l o r the c h i l d had drawn was.named) bead on your second turn? Why do you t h i n k t h a t ? " (iii)  Scoring I  (Fail)  II  for  (Pass)  Absence of s y s t e m a t i c  B e g i n n i n g s of q u a n t i f i e d p r o b a b i l i t y  (e.g. 1/3  for f i r s t  I I I (Pass) S u c c e s s f u l q u a n t i f i c a t i o n a g a i n a f t e r each drawing second draw).  G. (i)  probability.  (e.g.  draw). 5/17  I s o l a t i o n of V a r i a b l e s  Introduction  T h i s t a s k was d e v i s e d by Kuhn and Ho (19.77) w i t h minor a d a p t a t i o n s by Chandler, S i e g e l and Boyes (1980). The b a s i c i d e a was to show the respondent two a r r a y s of outcomes w i t h the i n p u t s t h a t produced each. In the f i r s t a r r a y the respondent had to d i s c e r n which two i n p u t v a r i a b l e s were e q u a l l y e f f i c a c i o u s i n i n d e p e n d e n t l y p r o d u c i n g an outcome. I n the second a r r a y , the des i r e d ;outcome c o u l d o n l y have been o b t a i n e d through the use of two p a r t i c u l a r i n p u t s c o n j o i n t l y . The repondent had to d i s c e r n how the outcome was achieved. (ii)  Procedure Materials.  -Empty v i a l s w i t h p l a n t food l a b e l s -Plastic  plants  168  First  array:  LEAFY PLANTS  Second  P l a n t Food L a b e l  Height of Plant  no food  3"  a  3"  b  6"  c  6"  ab  6"  ac  6"  be  6"  abc  6"  no food  3"  1  3"  2  6"  3  6"  1.2  6"  1.3  6"  2,3  9"  1,2,3  9"  array:  FLOWERY PLANTS  Instructions.» One a r r a y a t a time was p l a c e d i n f r o n t o f 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 o f p l a n t food. The types we used on each p l a n t a r e shown by the b o t t l e s i n f r o n t o f each p l a n t . A l l these p l a n t s were s t a r t e d a t the same time. We're s t a r t i n g a new p l a n t and we have t o d e c i d e which would make the t a l l e s t p l a n t . (INDICATE PLANTS AND FOOD INDIVIDUALLY AND STRESS THE HEIGHT). Now we don't want t o use any more food than we have t o , because i t s v e r y e x p e n s i v e . Now, t h i n k about i t f o r a minute and t e l l me what you t h i n k we should feed the new p l a n t we're s t a r t i n g i n o r d e r t o make i t grow t a l l . " When the s u b j e c t had responded the i n v e s t i g a t o r asked, "Why do you t h i n k t h a t would be the b e s t t h i n g t o make t h e new p l a n t grow t a l l e s t ? " Then the i n v e s t i g a t o r asked "Does a,b,c,/l,2,3) (ONE AT A TIME) have a n y t h i n g t o do w i t h how the ( l e a f y / f l o w e r y ) p l a n t s t u r n o u t ? " The procedure was r e p e a t e d f o r the second a r r a y and then the s u b j e c t was asked t o compare both a r r a y s as f o l l o w s : "Now, the p l a n t foods we're u s i n g on t h e s e p l a n t s a r e t h e same foods we're u s i n g on t h e f l o w e r y p l a n t s . A i s a. B i s b, (3 i s c_. Do the p l a n t foods work d i f f e r e n t l y on the two types o f p l a n t s ? Does t h e type o f p l a n t make any d i f f e r e n c e to how the p l a n t food work?" I f the s u b j e c t d i d not e x p l a i n h i s / h e r answer the f o l l o w i n g probes were g i v e n : "How can you t e l l t h a t ? " "What i s the d i f f e r e n c e ? "  169 (iii)  Scoring The s c o r i n g was the same as t h a t used by Kuhn and Ho  (1977);  Fail I C o n c r e t e : Reasons s o l e l y on the b a s i s of i s o l a t e d i n s t a n c e s , i g n o r e s i n s t a n c e s c o n t r a d i c t o r y to own c o n c l u s i o n s , makes l o g i c a l e r r o r o f false inclusion. I I Emergent Formal. Begins to l o g i c a l l y e x c l u d e the i n o p e r a t i v e 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 e s c l u d e s the i n o p e r a t i v e v a r i a b l e and i n c l u d e s o p e r a t i v e 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 ( a l t e r n a t i v e i n f i r s t a r r a y ; a d d i t i v e i n second).  Pass IV E a r l y f o r m a l .  Comprehends  e i t h e r a l t e r n a t i v e o r a d d i 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 a d d i t i v e causes.  170 APPENDIX B:  B i o - e c o l o g i c a l Domain Tasks  Except f o r t h e s y s t e m i c 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 t a s k s used. The t a s k s a r e from t h e same s o u r c e s as those i n Appendix A. For t h 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 and c l a s s i n c l u s i o n t a s k s t h e s c o r i n g i s i d e n t i c a l t o t h