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The concept of equilibration in Piaget’s theory of cognitive development Sutton, Margaret Ruth 1978

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THE CONCEPT OF  EQUILIBRATION  I N P I A G E T ' S THEORY COGNITIVE  OF  DEVELOPMENT by  MARGARET RUTH B.A., S e a t t l e  SUTTON  University,  THESIS SUBMITTED I N P A R T I A L  1974  FULFILLMENT  THE R E Q U I R E M E N T S FOR THE DEGREE  OF  M A S T E R OF A R T S  in THE F A C U L T Y  OF GRADUATE  STUDIES  (FOUNDATIONS OF E D U C A T I O N )  We  accept to  this  thesis  the required  as  conforming  standard  THE U N I V E R S I T Y OF B R I T I S H C O L U M B I A April,  1978  Margaret Ruth Sutton  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y I  in p a r t i a l  the U n i v e r s i t y  s h a l l make i t  freely  f u l f i l m e n t o f the of B r i t i s h  available  for  requirements f o r  Columbia, I agree  that  reference and study.  f u r t h e r 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 o f t h i s  thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  representatives.  It  this thesis for financial  i s understood that copying or p u b l i c a t i o n gain s h a l l  written permission.  Depa rtment The U n i v e r s i t y  o f B r i t i s h Columbia  2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  not be allowed without my  ABSTRACT Many p h i l o s o p h e r s meaning and/or Piaget's here  a)  from other, the  o f c o g n i t i v e development.  similar  particular  concepts  character  self-regulation  allows  between b i o l o g i c a l  theory  and  a synopsis  and  model o f o r g a n i c  the  criteria  that  as a mechanism o f  c)  that  concept i n Piaget's  are a presentation o f the problem, theory  structures.  by which  Nine,  i ti s concluded  of genetic Chapter  equilibration  Chapters  equilibration  concept i n Piaget's  b)  t o account f o r the differences  a fruitful  of Piaget's  which  theory  Piaget  theory  development.  C h a p t e r s One t o T h r e e  the  of equilibration  i s therefore  concept.  i n Piaget's  i s distinct  and c o g n i t i v e s t r u c t u r e s and  of cognitive  fruitful  I t i s argued  the concept of e q u i l i b r a t i o n  equilibration  the  function of the concept o f e q u i l i b r a t i o n i n  theory  that  and p s y c h o l o g i s t s have questioned  plays  S i x to Eight  lays out  examine  theory.  that equilibration  are discussed.  Five  c o u l d be s a i d  i n Piaget's  theory,  epistemology  i s a  a n d some g e n e r a l  t o be a the role  In Chapter fruitful points  about  LEAF i i i  OMITTED IN PAGE NUMBERING.  iv  ACKNOWLE DGEMEN TS  I would Drs.  like  Jerrold  t o t h a n k my t h e s i s Coombs, L e R o i  Gaalen E r i c k s o n as w e l l  committee,  Daniels, and  as o t h e r  faculty  members, p a r t i c u l a r l y D r . P a t r i c i a for  their  c r i t i c i s m s and suggestions.  Warm t h a n k s  also  t o t h e many  members, e s p e c i a l l y  Shirley  and  Andy G i n g e r a ,  and  encouragement throughout  process,  Arlin,  department Packinson  who h a v e p r o v i d e d  the writing  and t o S h e i l a g h C r a n d a l l ,  assistance  i npreparing  counsel  the final  for her copy.  T A B L E OF L I S T OF C H A R T S ' ' I.  II.  IV.  2 2 4  '  5 7 8  a) b)  9 14  Properties of Structures Functioning of a Structure  A P P L I C A T I O N OF S T R U C T U R A L I S M DEVELOPMENT  TO  COGNITIVE 15  Structuralist Explanation of Cognitive Development T r a n s i t i o n From B i o l o g i c a l t o C o g n i t i v e Functioning  E Q U I L I B R A T I O N AS A HYPOTHETICAL  CONSTRUCT  Meaning Fruitfulness  , 16 17 19 20 21  B I O L O G I C A L AND C O G N I T I V E S E L F - R E G U L A T I O N  22  a) b)  24 27  S e l f - r e g u l a t i o n by F u n c t i o n i n g Regulation and C o g n i t i v e S t r u c t u r e s  C O N S T R U C T I O N OF C O G N I T I V E  STRUCTURES  Meaning o f Cognitive E q u i l i b r a t i o n Mechanisms o f S e l f - r e g u l a t i o n  A C C O U N T I N G FOR C O G N I T I V E DEVELOPMENT BY THE CONCEPT OF E Q U I L I B R A T I O N a) b)  IX.  F a c t o r s o f Development Equilibration  Construction of Logico-mathematicalStructures Language o f E q u i l i b r a t i o n  31 34 37 43 44 47  F R U I T F U L N E S S OF THE CONCEPT OF E Q U I L I B R A T I O N  49  a) b)  50  E q u i l i b r a t i o n and P i a g e t ' s Organic Model V e r i f i c a b i l i t y o f the Concept o f Equilibration  FOOTNOTES BIBLIOGRAPHY  e  COGNITIVE  STRUCTURALISM  a) b) VIII.  Questions Concerning E q u i l i b r a t i o n Methods o f Approach  O V E R V I E W OF P I A G E T ' S THEORY OF DEVELOPMENT  a) b)  VII.  g  a  a) b)  b)  VI.  P  1  a)  V.  '  STATEMENT OF THE P R O B L E M  a) b) III.  '  CONTENTS  54  L I S T OF CHARTS Page CHART 1  39  CHART 2  40  1  I.  S T A T E M E N T OF  "Equilibration" prominent easy  laws"  2  of  PROBLEM  i s a word which  i n P i a g e t ' s work.  to t e l l  speaks  THE  from h i s works  "equilibration  , "equilibration  has  At  become  increasingly  t h e same t i m e ,  i t i s not  j u s t what e q u i l i b r a t i o n  factors  o f action"" ", 3  and  He  "equilibration  1  processes"  i s .  the  "mechanism  have  commented  of  4 equilibration".  Various  psychologists  equilibration, equilibration  also as  and  philosophers  i n diverse  "...a  terms.  regulatory  and  Furth  speaks  organizing  upon  of  factor  5 within  evolutionary  equilibration reconstruction that to  govern  be  development"-.  considered  o f how  directed  we  as  think  thinking."  Mischel  proposes  "...an a n a l y s i s  or  i n accordance with 6 Elkind,  in his  that  rational the  norms  introduction  S i x P s y c h o l o g i c a l S t u d i e s , says that: The p r i n c i p l e o f e q u i l i b r a t i o n w h i c h r e g u l a t e s the i n t e r a c t i o n o f s o c i a l and m a t u r a t i o n a l factors is essentially dialectical i n nature.'  Perhaps  the questions  summed u p b y  Flavell,  surrounding equilibration when he  are  best  says:  I am e v e n u n c l e a r a s t o e x a c t l y w h a t p h e n o m e n o n g e q u i l i b r a t i o n i s and i s n o t supposed t o d e n o t e .  2  a)  Questions  Since  equilibration  theory, its by  Concerning  there  meaning.  several questions  The  first  'equilibration'?"  or  m e n t , we concept  also  f o r these  Method of  to  equilibration  describe  will  question  Related  because, i t w i l l  explain  b)  i s a hypothetical construct  are  w a n t t o k n o w how And  Equilibration  be  certain ask  i s defined  calls  concept of  by  for believing  bration  are  derived  then,  i t i s a part.  cognitive  we  also  i n Piaget's  equilibration of  theory.  i s meant  cognitive  the  role  theory  i s to  genetic  that  from  theory  to  develop-  is a  dependent  of which  epistemology".  equilibration  reasons  Equilibration,  the  "genetic  development provided  terms o f  question,  mean  fruitful  Approach  i n terms o f  in  examining  purposes.  It  which  this  whether e q u i l i b r a t i o n  is a particularly  the  Piaget's  i s "What d o e s P i a g e t  features  Equilibration  which Piaget  involved i n  operates  argued,  in  to  The the  isolated  account  development.  For  i t plays this  the  equili-  body.  from the  i n Piaget's  reason,  of  of  Further,  theory  I t s m e a n i n g m u s t somehow be which  part,  purpose  i s a mechanism of  theoretical  c a n n o t be  i t is a  epistemology.  there  the  add  concept.  of  clarified account  Chapters  Two  of  through  3  Four w i l l  be devoted t o a b r i e f e x p o s i t i o n  theory o f cognitive overview, In  Chapter  Piaget of  focusing Three  development.  look  means b y a s t r u c t u r e .  structuralism applied  development,  In  would  mean  Piaget's  differs  from other  reasons  f o rbelieving  i n Chapter  whether theory.  about  account  Here  o n e s t a b l i s h i n g how  regulatory i tdoes  look  cognitive  are seen  equili-.  i n the d i f f e r -  and b i o l o g i c a l s t r u c t u r e s .  a t d i f f e r e n t mechanisms o f  are constructed.  f o rthe construction  Finally,  equili-  mechanisms, and t h e  a t t h e way i n w h i c h In Chapter Eight,  a p a r t i c u l a r mechanism o f the s o r t  accounts  we  t o do s o .  and i n Chapter Seven,  structures  structures.  i s explaining  structures  S i x we w i l l  self-regulation,  a s k how  part  that  between c o g n i t i v e  describes  development.  Determining the f r u i t f u l n e s s of  bration  will  be an  concept i n  i n large  cognitive  Chapter Four w i l l  what  f o r e q u i l i b r a t i o n t o be a f r u i t f u l  depends  So,  asking  o f what i t  bration  ences  development.  to the question  theory.  turn  be an  at structuralism,  a n d how h e p u r p o r t s  C h a p t e r F i v e , we w i l l  of cognitive  to cognitive  want t o e s t a b l i s h what P i a g e t  Piaget's  C h a p t e r Two w i l l  on t h e f a c t o r s  we w i l l  of  of  that  we  Piaget :  logico-mathematical  i n C h a p t e r N i n e , we w i l l  the concept o f e q u i l i b r a t i o n i s f r u i t f u l  discuss to  Piaget's  4  II.  OVERVIEW OF PIAGET'S THEORY OF COGNITIVE DEVELOPMENT  According subject  to Piaget's  passes  theory  through three  of cognitive levels  sensori-motor, pre-operational, before  reaching  thinking.  the f i n a l  By " s t a g e "  stage,  Piaget  development, the  of cognitive  and c o n c r e t e o f formal  puts  forth  thing a stage o f c o g n i t i v e  operational  -  operational  does n o t means g r o u p s o f a c t i o n  c h a r a c t e r i z e d by some theme, as does F r e u d , Rather, Piaget  development -  three  conditions  f o r example. f o r c a l l i n g some-  development:  . . . f i r s t , the s e r i e s of actions i s constant... second, each s t a g e i s d e t e r m i n e d n o t m e r e l y by a dominant p r o p e r t y , b u t by a whole s t r u c t u r e w h i c h characterizes a l l further actions that belong to t h i s stage t h i r d . . . these s t r u c t u r e s o f f e r a process o f i n t e g r a t i o n s u c h t h a t e a c h one i s p r e p a r e d b y t h e p r e c e d i n g one and i n t e g r a t e d i n t o t h e one t h a t f o l l o w s . The  first  condition  invariable, can is  vary that  says t h a t  although  according  the order  t h e age a t w h i c h e a c h s t a g e  to the i n d i v i d u a l .  The s e c o n d  a s t a g e c o n s t i t u t e a s t r u c t u r e d whole  a d i s c u s s i o n , below, o f P i a g e t ' s The  o f the stages i s  third  condition  gives  i s attained condition  ( t h e r e w i l l be  meaning o f " s t r u c t u r e " ) .  Piaget's  definition  o f development.  D e v e l o p m e n t i s more t h a n a change f r o m one o r g a n i z a t i o n t o  5  another;  the  structure, before with for  c h a n g e m u s t be  so  i t .  that  Each  biological  the  new  stage  there  structure  that  of  children's  stages  of  c h i l d r e n go  of  that  the  order  by  other  have been c o r r a b o r a t e d  Factors  Piaget  has  of  Cognitive  named f o u r  ence,  and  necessitated experience nature, people. objects  by  the  refers  Included  Maturation  experience the  w o u l d be  ment, i . e . the  the  of  that  proceeds observation  cognitive  stages  does not  vary,  cognitive  physical experience, i s the and  of  such  actions  space.  individual  intersubjective  experiof  development code.  are as  Physical  less  individual  common t o a l l manipulation  Social experience  with  world.  social unfolding  a more o r  experiences  movement t h r o u g h  i n t e r a c t i o n of  case  His  determine  individual's genetic  to  conditions  researchers.  s t r u c t u r e s , i . e . growth  t h o u g h many o f  and  these  next,  Development  equilibration.  predetermined  of  stages  factors which  development; maturation,  makes t h e  defines.  particular  went  observational  development, which  s o r t t h a t he  through  d e v e l o p m e n t , and  Piaget  previous  f o r the  initial  I n h i s many  cognitive  the  the  the  a l l that  condition  providing  thought,  of  includes  i s a necessary  organization  i s a process  through  the  re-organization  sensori-motor structures,  studies  a)  a  her  social  of is  environ-  6  These in  first  sum, do n o t e x p l a i n  cognitive culty mine to  three' f a c t o r s ,  There  o f s e p a r a t i n g them f r o m their  unique  e.g.,  alone  advances  Even  can account  o f development.  unlikely  explanations f o ra process  cognitive they  development,  relate  t o each  contributions  Because  experiences  factors  taken  factors  o f each  The  make  them  to a l l individuals.  together are to explain  fail  t h e q u e s t i o n o f how  t o account  their respective  They  intrinsic  the effects  "equilibration"  P i a g e t has  equilibration. of the other  and t o account f o r Equilibration  of internal  of experience  account  factor,  t o human l i f e ,  are process  f o r cognitive  the roles  development,  development.  existence of internal  ment which  individual  common  us t o determine  i n cognitive  argues,are  determine  differences,  The v a r i e t i e s o f  there i s s t i l l  the pattern o f cognitive  hereditary.  that  to the process.  Equilibration: enables  Piaget  possible  formalization/  other, i . e . , determining  the c l a s s i c a l  factors  to deter-  I t i s unlikely  development, P i a g e t p o s t u l a t e s a fourth  three  and  forindividual  and s o c i a l  i fa l l three  i n order  i f i t were  i n technology  physical  And,  and i n v a r i a n c e o f  each.other,  n o t be a n s w e r e d .  i n t h e speed  independently o r  i s to begin with the d i f f i -  contributions.  question would  maturation  either  the universality  development.  do s o , t h r o u g h  the  taken  and i n t h a t regulation,  on c o g n i t i v e  observed.  sense, which  development.  regulations of the sort  f o rthe particular  processes,  process  d e f i n e d as o f develop-  7  b)  Equilibration  Equilibration  i s a process  Equilibrium  is a  in  system,  Piaget's  cular  kind  of  s t a t e of are  are  understood  i n terms of  formation of  by  and  regulation.  mechanism which  In order  to  One  of  Piaget  the  cognition or  cally  and  The  internal  equilibration  m u s t know w h a t P i a g e t  k n o w i n g , and he  and  points  out a  regulates  considers  or  that  action.  the  receptor  of  cognitive  t o be  cognition.  i t is active.  empirical links  activity  On  between the  organism i s  biologi-  environmental  asks:  B u t a r e we t o b e l i e v e t h a t a n o r g a n i s m w h i c h i s a c t i v e a t every s t a g e of growth s h o u l d , upon reaching the apex of i t s development, become^ a mere s l a v i s h i m i t a t o r o f i t s s u r r o u n d i n g s ? -•'  We  do  not  merely  receive  or  react  to our  of  regulatory  cognition i s that  conceptual  and  mechanisms  development.  cognitive  parti-  processes  determines  both  plane,  states.  formation  internal  a c t i v e , never simply  stimuli,  of  c h a r a c t e r i s t i c s of  claims  empirical  processes  g u i d e d by  a  properly  E q u i l i b r a t i o n i s the  u n d e r s t a n d how  d e v e l o p m e n t , we  They are  are  are  balanced,  characteristics,  dynamic.  in their  maintenance  somehow  Structures  /Among o t h e r  their  than  equilibrium.  What a r e  structures.  definition  rather  achieving  balance.  organization.  structures  maintenance,  of  environment,  we  8  interact with  On  i t ,• c o g n i t i v e l y as w e l l  the conceptual  thing  always  level,  implies  Piaget  activity  knowledge  i s connected with  or  happening  i s t o make  action  schemata".^"'""  activity to  such  assimilating Cognition some  new  that  t o know  sort:  some-  "...any  an a c t i o n . . . t o  c a n mean  piece  know an  anything  from  the cover from a hidden  of cognitive organization,  information  i s always  object  into pre-existing  a c t i v e because  knowing  a  an  physical  object, such  as  schemata.  always  involves  type o f o r g a n i z a t i o n .  Equilibration  regulates  First,  i tdetermines  takes,  a t each  organization Second,  structural activity  the form  that  stage of cognitive  i n turn  determines  e q u i l i b r a t i o n regulates  activity in  Action  activity  biologically-.  use o f i t by a s s i m i l a t i o n i n t o  as removing  the mental  claims  o f some  of  as  on the s t r u c t u r e s .  Chaper  Six.  In both  cognitive  III.  Piaget  organization  development.  the activity  The f o r m o f possible.  the effects of s t r u c t u r a l  This  point w i l l  be  elaborated  cases, regulation i s a process of  establishingja balance between repeating action,  i n two ways.  o r s t r u c t u r e , and  an e x t a n t  form o f  modifying structure. s  STRUCTURALISM  sees  cognitive  development,  t h e n , as a p r o c e s s o f  9  structural  development.  He  the  source o f a model w i t h  The  applicability  points:  1)  activity  which  that  t h a t we  point  will  A  structure  of  originate  such  of  in biological  i n Chapter Four  an o r g a n i c  cognition. two  cognitive  structures  and  as  r e s t s on  structures  at the properties  and  2)  activity. (b).  In  The this  functioning  of  model.  Structures  i s a dynamic  remains  to understand  to organic  t a k e n up  look  based on  Properties  but which  be  structures  model t o c o g n i t i o n  are analogous  c h a p t e r , we. w i l l structures  which  can i d e n t i f y  these structures  latter  a)  of this  uses b i o l o g i c a l  entity,  organized  whose components  throughout such  can  changes.  change, Piaget  says:  We s h a l l d e f i n e s t r u c t u r e i n t h e b r o a d e s t p o s s i b l e sense as a system which p r e s e n t s the laws o r p r o p e r t i e s o f a t o t a l i t y s e e n a s a s y s t e m . 12 The  three  properties  formation  and  Wholeness  refers  relationship do  of structures  trans-  self-regulation.  n o t t o t h e sum  of the parts  n o t make a s q u a r e ; f o u r  right  are wholeness,  angles at their  with  of the p a r t s , each  other.  equal line  e n d p o i n t s do.  segments a r e not n e c e s s a r i l y  related  Four  segments The  but  to  the  line  segments  joined  particular  to the structure  at  line of  a  10  square.  I t i s their  equality  of length  tute  is  of a  which  define  determine  consti-  a r e t h e "laws o f  square.  misleading i n that  structures,  to point out that  a structure.  structural  Piaget  systems.  :The  i t i s the laws o f c o m p o s i t i o n  These laws o f c o m p o s i t i o n n o t o n l y  the r e l a t i o n s h i p  the whole  other, i . e . ,  angles, that  These r e l a t i o n s h i p s  speaking of "larger" i s used  each  at right  example o f a square i s s l i g h t l y  example  on  and j o i n i n g  the structure.  composition"  The  relationship with  of the parts,  as such o v e r a l l  properties  but:  "...they confer  distinct  from the  13 properties  of the elements".  integers, which confers as  individual structure simply  are necessarily  on i n t e g e r s  reciprocity,  Piaget  as a whole  which  integers, consists  i t s elements, wholeness  "Wholeness"  thus  i s primarily  from  laws o f c o m p o s i t i o n t o cope w i t h  a structure  i s more o r l e s s  structure  also  o r changes  Thus r a t h e r  i s i n a state  such  the properties  o r oddness.  contrasted  the  structure.  properties,  of  Since a than  i s a property o f the laws.  wholeness  upon i t ,  ordering  of composition, rather  The  "intrusions"  of a structure  This  structural  as evenness  o f i t s laws  t h e example o f  ordered.  are distinct such  uses  to "aggregation".  includes  the a b i l i t y  of  o r compensate f o r  i n the environment  than being complete "adequate"  of the  or incomplete,  or "stable".  o f e q u i l i b r i u m when, w i t h o u t  A trans-  11  formation against it  The  of  intrusions.  i s always  a property  structures  into  Besides perty  the  historical  the  not  relationship to  of  this  number, and  created,  the  irrational processes. sitional mation;  can  By  change.  rational  Since  the  into  this For  which  can  number.  The  numbers can  a  pro-  P i a g e t means  that  that within this never  falsified  "untransformed"  an  i f we  organic or  treat  organic  model,  incorporate  isosceles  right  number s y s t e m  can-  i s not  relationship  compositional  now  of  acids.  example,  this  the  that  a piece  something which  express  the  themselves.  numbers c a n n o t an  i t  means  amino  rational  relationship,  Piaget  s t r u c t u r e s have  hypotenuse of  numbers, e.g.,  are  environment.  First,  simply  a c i d s , and  number s y s t e m change w i t h  laws the  the  irrational  Note  since  portions of  "transforms"  themselves.  i t s sides.  incorporate  entire  This  environment,  system of  rational  the  senses.  development o f mathematics on  the  itself  dynamic,  from the  "transform"  fatty  the  composition  that  triangle  related  activity.  carbohydrates,  laws of  see  i n two  d i g e s t i v e system  transforming  maintain  structures i s transformation.  structural  the  the  we  disturbances  o f s t r u c t u r e s to  transforming  of  i t can  incorporate e x t e r n a l elements  example,  bread  of  laws,  e q u i l i b r i u m m u s t be  t o new  transformation  e n v i r o n m e n t by  For  This  subject  second property  speaks of is  i t s compositional  laws  a is  of  i n t r o d u c t i o n of incorporate model,  destroyed  the  infinite compo-  in transfor-  l a w s become a s u b s e t  of  the  "new"  12  laws of  These by  composition.  two  senses  of  transformation  d e f i n i t i o n of the laws  composition  determine  are conceptually  of composition.  the kinds  of elements  incorporated  into  also  the p o t e n t i a l f o r t h e i r  contain  The  the s t r u c t u r e .  The  related  laws  which  of  can  laws o f c o m p o s i t i o n transformation.  T h e s e l a w s m u s t o f t h e i r v e r y n a t u r e be s t r u c t u r i n g . . . a s t r u c t u r e ' s laws are defined ' i m p l i c i t l y ' i . e . , as g o v e r n i n g t h e t r a n s formations of the system which they s t r u c t u r e . Because laws is  the mechanism  is implicit  called  The  idea  infinite talk  of self-transforming regress.  therefore  It  of  compositional transformation  Life  from which  determines  does n o t l e a d  cognitive  property that  to  an  must e x i s t i n o r d e r implies  and  the  c o n s t i t u t i n g the laws o f are  even  structures,  determined organism,  structures  to  organization,  In the case o f c o g n i t i v e  the s t r u c t u r e  i s the t h i r d  which  laws.  structure.  as  laws  Some s t r u c t u r e  takes the b i o l o g i c a l l y  genotype, tion  kind  of  1 4  self-transformation.  of compositional  Piaget  f o r transformation  to the laws, t h i s  be  compos-  formed.  of structures, s e l f - r e g u l a t i o n ,  changes  i n a structure  development,  rather  t h a n some h a p h a z a r d  formations.  Self-regulation, Piaget  constitute  series of  trans-  states, entails  self-  13 maintenance that  "the  beyond  and  closure.  Together,  transformations  the  system but  inherent  these  properties  provide  i n a structure never  always engender elements  that  lead  belong  15 to  i t and  all  preserve  conservative.  including  by  are  brings serve  laws". the  the  taken  of  the  b r a i n has  o v e r by  the  environmental  wholeness of For  a  the  structure i s  example, where  hemisphere.  circuits  into  f o r the  organization of  development of  tures.  Transformation  tions;  self-regulation  play  the  left  i t s  func-  The  brain  i n order  provides  a  structure,  to  con--;  and  the  p o t e n t i a l f o r new  incorporates By  more a d a p t i v e  these  new  the  existing  structure.  into  the  original  structure, self-regulation  f o r e x a m p l e , an  individual  numbers t h a t r e m a i n e d  self-regulation  new  into  If,  intrusions,  b e e n d a m a g e d , some o f right  of  functioning.  maintaining  provides  face  time,  p r e v i o u s l y unused total  Self-regulation is first  self-regulation.  hemisphere of tions  In  decay over  maintained  By  xts  structures  is constructive.  a system of  independent from a  construc-  constructions  r e i n t e g r a t i n g new  acquired  struc-  system of  irrational rational  ,.y'  numbers, the although  we  could  constructed. old,  the  number s y s t e m w o u l d  For  certainly the  new  o l d s t r u c t u r e m u s t be  regulation  reorganized  i s c o n s t r u c t i v e beyond  with  a new  structures.  regulating transformations,  structures  that  have undergone  s t r u c t u r e t o be  encompass p r o p e r t i e s o f b o t h  In  say  not  differentiated  the  development,  s t r u c t u r e had incorporated to enable This  limits  of  self-regulation substructures.  i s how  been  into  the  i t to self-  transformation. constructs  14  b)  Functioning of a  Piaget  describes  Structure  f u n c t i o n i n terms o f the i n h e r e n t  tendency of a s t r u c t u r e .  action  F o r example:  F u n c t i o n i s the a c t i o n e x e r t e d by t h e f u n c t i o n i n g o f a s u b s t r u c t u r e on t h a t o f a t o t a l s t r u c t u r e , w h e t h e r t h e l a t t e r be i t s e l f a s u b s t r u c t u r e c o n t a i n i n g the former o f the s t r u c t u r e of the e n t i r e organism. ± 0  There  a r e two m a j o r c a t e g o r i e s o f o r g a n i c  tation,  w h i c h c a n be  dation,  and o r g a n i z a t i o n .  for is  by r e p e t i t i o n called  The  lungs,  organism,  respond  need.  repeating  compensate  bringing  i t into  assimilation, sated  The  and  adap-  accommo-  i s compensated  pattern or substructure,  disturbance  i s subsumed  by  this the  I n h a l i n g i s an example o f a b i o l o g i c a l a s s i m i l a t o r y  function.  lungs  assimilation  When a d i s t u r b a n c e  o f an e x t a n t  assimilation.  structure.  By  divided into  functions:  which are a substructure of the  to a disturbance, the coordinated  i n this  case,  where  Accommodation  a disturbance  f o r by a l t e r a t i o n  internal  action of inhaling,  f o r lack of oxygen i n the blood the system.  an  total  stream  the by  i s the reverse  t o t h e s t r u c t u r e i s compen-  i n a substructure.  I t w o u l d be  nice  to  say t h a t e x h a l i n g i s an example o f accommodation, b u t i t  is  not.  in  response  Accommodation  i s a change  to the environment.  of  i n assimilation  Piaget provides  an  structures example:  15  . . . i n an i n f a n t o f f i v e o r s i x months o l d , t h e s e i z i n g o f t h i n g s by b o t h h a n d s i s an a s s i m i l a t i o n schemata, but the s t r e t c h i n g out or b r i n g i n g nearer o f t h e h a n d s a c c o r d i n g t o w h e t h e r an o b j e c t , i s n e a r o r f a r i s an a c c o m m o d a t i o n o f t h a t schema.17  The  second  category  organization.  of  organic  Whereas a d a p t a t i o n  Structure's-environment, the  structure  types of  Adaptation face  of  functioning  are  maintain  environmental  intrusions.  disturbances.  reintegration  IV.  of  Discussion pervades  of  These "internal :  The  new  on  original  i s the  organizing  an  Piaget's  An  works.  In  accommodation m u s t be  structure, or  by are  constructs either  lost.  This  function.  S T R U C T U R A L I S M TO  organizing  the  functions  disturbances"  substructure  i n t o the  A P P L I C A T I O N OF  Organization  in  when i t i s t h r e a t e n e d  accommodations.  substructure.  reintegrated  the  operate  structural integrity  internal  new  functions  on  mechanisms of s e l f - r e g u l a t i o n .  structural organization  a  operate  f u n c t i o n may b e s a i d t o b e t h e a c t i o n by the f u n c t i o n i n g o f a s u b s t r u c t u r e on t h e t o t a l s t r u c t u r e . . . o r g a n i z a t i o n as a i s the a c t i o n of t h e . e n t i r e functioning of the substructures.18^  functions  aftermath  functions  organization  maintain  the  is called  itself:  ...of a exerted that of function on t h a t Both  functioning  function this  COGNITIVE  raises  case,  a  i t is  DEVELOPMENT  question "Which  which comes  16  first, In  organization  more g e n e r a l  product of  terms,  same t i m e ,  be  is  formation  the  functioning  in  are  In  which  a  the  of  new  which  can  area of  aspects  be  and  the  result.  account  for  the  universal  the  In  the  second  are  At  the  structure. activity  constructive.  of  If  this  i s d e t e r m i n e d by Since  the  func-  particular  determinant of  way  the  constructed.  of  Cognitive  Development  development, Piaget of  In  wishes  logico-mathematical  the  and  m u s t be first  explained,  c a s e , we  c a s e , w h a t m u s t be of  to  structures.  wish  i n v a r i a n t sequence of  special structural properties  structures.  cannot,  functioning.  i n the  i s a key  construction  process  ment.  structure.  conserves  i s 'that,  a  of  there  prior structures.  regulates  construction this  a product  exist without or  functions?"  structures  s e l f - r e g u l a t i o n , the  cognitive  of  a  structures  (temporally)  function  the  without  functions of  i s , "Are  a l l apparent that  S t r u c t u r a l i s t Explanation  explain Two  of  organizing  functions  cease to  mechanisms of  structures  a)  are  essential hypothesis structure,  tions  or  above a l l , m a i n t a i n s  conserving  or  question  functioning  structures  Functioning,  so,  the  It is first  definition,  Piaget's  structures,  functioning,  structures?" by  of  accounted  the to develop-  for  are  logico-mathematical  17  These q u e s t i o n s functioning ter  of  i n terms of  mechanism of  manner t o ,  and  functioning  The to  surpassing  key  to  the  cognitive  Initial  Functional creating  b)  that  i t due  structures  development.  functioning and  can  be  differences and  internal  thought from  differences  regulatory  of to  organizing  the  biological  the  of  new  from  structures"." biological  of  functions.  functioning.  upon p r i o r  which  whose  in turn  structures,  provide  functioning.  his  a metaphor by Cognitive  structures:  generalization  elaborates  like  organization,  continuity  provides  in  activity  elaboration  the  i s the  specialized  develop  an  specialized structures  more t h a n  of  the  organization  that  i n terms  from, b i o l o g i c a l  argument f o r  maintains  explained  structures  T r a n s i t i o n From B i o l o g i c a l  Piaget is  cognitive  generalization  increasingly  charac-  functioning.  constitutes  biological  that  distinct  These s i m i l a r i t i e s  continously  extends  hypothesis The  to  equilibration,  that  "...intelligence  while  Cognitive  cognitive  claims  be  its similarities  by  the  structures.  t h o u g h t can  functioning.  explained  Piaget  new  functioning.  biological are  c o n n e c t e d by  constructs  operational  cognitive of  are  to  Cognitive  model of which  Functioning  biological  to  functioning,  understand he  functioning cognitive  maintains,  is  an  18  extension  of biological  functioning.  I n The O r i g i n s  of  20 Intelligence, cognitive  Piaget  structures,  regulations.  traces  from r e f l e x e s programmed by  Repetition  and c o o r d i n a t i o n  form schemata f o rh a b i t s . functioning, cognitive" Piaget  defines  that  are  cognitive  f o r formation  of  "truly  increased.  activity  as i n t e n t i o n a l a c t i o n ,  t o draw a c l e a r l i n e  forms o f i n t e n t i o n a l a c t i o n  functioning  are r e f i n e d by  d i s t i n g u i s h e s b e t w e e n means a n d e n d s .  i ti s d i f f i c u l t  first  biological  of reflex  As t h e s e h a b i t s  the p o s s i b i l i t i e s  structures  action which  the development o f the  He  states  between p r i m i t i v e  and b i o l o g i c a l l y  determined  actions but: I n p r a c t i c e , we c a n a c k n o w l e d g e . . . t h a t i n t e n t i o n a l a d a p t a t i o n b e g i n s as soon as t h e c h i l d transcentds the l e v e l o f simple c o r p o r a l a c t i v i t i e s (sucking, l i s t e n i n g and making sounds, l o o k i n g and grasping) and a c t s upon t h i n g s and uses t h e i n t e r r e l a t i o n s h i p s of o b j e c t s . 2 1  In h i s accounts o f the t r a n s i t i o n functioning, e.g., why  i to c c u r s ,  series the  h e f o c u s e s m o r e o n how  describing  stated,  from b i o l o g i c a l  the transition  e.g., what cause  this  transition  occurs,  i n structuralist  terms,  the transition.  Briefly  the i n c r e a s i n g l y complex adaptations, of functions  to cognitive  t o a t t a i n one e n d , " b r i n g  d i f f e r e n c e b e t w e e n means a n d e n d s .  providing  than  a  attention to"  19  A series of increasingly functioning  lead  to the "bursting  creation of structures or  complex adaptations  which  g e n e t i c a l l y determined,  structures  of cognition  of  self-regulation.  or  replace  of  of instinct",  instinctive which  a r e not m a i n t a i n e d by  functioning.  Instead,  i s the  programmed, the  a r e m a i n t a i n e d by i n t e r n a l mechanisms  Cognitive  functioning  biological functioning,  does n o t  destroy  but extends i t :  What v a n i s h e s w i t h t h e b u r s t i n g o f i n s t i n c t i s e x c l u s i v e l y the c e n t r a l o r median p a r t , that i s , t h e programmed r e g u l a t i o n , w h e r e a s t h e o t h e r two realities persist: the source of organization and t h e r e s u l t a n t s o f i n d i v i d u a l o r p h e n o t y p i c . adjustment. T h u s i n t e l l i g e n c e d o e s i n h e r i t somet h i n g from i n s t i n c t a l t h o u g h i t r e j e c t s i t s method o f programmed r e g u l a t i o n i n f a v o u r o f c o n s t r u c t i v e autoregulations. 2  2  The mechanism o f c o n s t r u c t i v e  autoregulation,  i s what  Piaget  calls equilibration.  V.  In  EQUILIBRATION  light  general  AS A H Y P O T H E T I C A L CONSTRUCT  of the previous  we  definition of equilibration:  mechanism o f c o g n i t i v e self-regulatory organization, its  sections,  early  c a n now  and c o n s t r u c t s  new  a  e q u i l i b r a t i o n i s the  self-regulation.  mechanism, i tb o t h  formulate  As a s t r u c t u r a l  conserves  structural  structures.  While  i t has  origins i n biological functioning, equilibration  must t r a n s c e n d  the limits  of merely  regulating  structures.  20  o f c o g n i t i v e \st"rucjbures„;;must b e c a p a b l e  Functioning only is,  responding the notion  structures within  o f growth o r t h e c o n s t r u c t i o n  c a n n o t be l i m i t e d t o t h e i n n a t e  g e n e t i c a l l y given  case w i t h  biological  from b i o l o g i c a l biological the  to the environment, but adapting  structures  structures.  differences  to i t .  That  of cognitive  potential  themselves,  contained  as i s t h e  So, e q u i l i b r a t i o n d i f f e r s  autoregulations.  autoregulations  of not  The d i f f e r e n c e s  between  and e q u i l i b r a t i o n c a n be seen by  between b i o l o g i c a l  Because e q u i l i b r a t i o n c o n s t r u c t s necessary  pattern  of cognitive  stability  of logico-mathematical  and c o g n i t i v e  structures,  development, structures  structures.  i texplains  the  and t h e unique among  organic  structures.  a)  Meaning  This of  definition  concepts  tures is  o f e q u i l i b r a t i o n i s based on the r e l a t i o n s h i p  i n Piaget's  have a property  model o f o r g a n i c  development.  of self-regulation.  Self-regulation  m a i n t a i n e d by mechanisms o f r e g u l a t i o n , o r  mechanisms.  Since  regulatory  d i f f e r e n c t types o f s t r u c t u r e have d i f f e r e n t  mechanisms o f r e g u l a t i o n , c o g n i t i v e  regulatory  differ  The d e f i n i t i o n  very  Piaget in  from b i o l o g i c a l  general  at this  mechanisms.  point.  mechanisms i s , however,  To s a y m o r e s p e c i f i c a l l y  means b y e q u i l i b r a t i o n , i t i s n e c e s s a r y  more d e t a i l  Struc-  what  t o examine  the d i f f e r e n c e s between c o g n i t i v e  and  biological  21  structures,  b)  and  equilibration  theory,  cognitive  construct  a fruitful  theory.  concept second  By  could  internally  or procedures  or retrodict  first  type of  definition  of  s a i d t o be  fruitful  f o r examining  aspects of  fruitfulness the  concepts  self-regulation.  and  together  The  been  useful The suggest  development.  theory  conto  addressed.  organic  model  of  a specialized  equilibration  l e s s a b s t r a c t concepts, such  s t r u c t u r a l .change.  in  development.  already  mechanism o f  three  a fruitful  Piaget's  cognitive structures require  of  theory.  c o u l d be  i n Piaget's  of  fruitful  cognitive  cognitive  has  the  are  i s f o r i t to  development,  holds  There  coherent  equilibration  of  equilibration  i s t h a t i t i s a n e c e s s a r y and  i t c o u l d be  i n which  Piaget's  the meaning  theory.  be  in  f o r some f e a t u r e s  i s f o r i t s p o s t u l a t i o n to enable  predict  The  first  i n which  t h i r d way  struct  i n Piaget's  equilibration The  experiments The  functioning,  purpose  i t i s p e r t i n e n t to ask whether  f o r p r o v i d i n g an way  The  Thus, i n examining  construct  i n which  f o r a purpose. i s to account  development.  equilibration,  ways  i s a hypothetical construct  i t i s postulated  equilibration  the  biological  Fruitfulness  Since  is  between c o g n i t i v e and  as  construct  functioning  22  Piaget  does not  fruitfulness.  deal  i n depth  Most of the  with  h i s work on  on  specifying  To  d a t e , most o f h i s procedures  ment have o n l y ment as  note,  exact  nature  of  second  the  of  the  f o r examining  c o n s t r u c t i o n s , and  the work of  of  concentrates  equilibration  p a r t i c u l a r mechanism o f  however,  form  equilibration  depended upon u n d e r s t a n d i n g  a series  specifying  the  mechanisms.  cognitive cognitive  have not  develop-  develop-  depended  construction.  some o f h i s a s s o c i a t e s i n  upon  He  does  this  23 regard. at  They have  particular  equilibrated" It  i s the  the  according  third  form of  development. of  this  type  f o l l o w i n g pages.  equilibration  retrodict, be  or  noted  i s connected  T h a t i s , we  necessary  f o r the model developed  In  B I O L O G I C A L AND  Chapter  bration rides  We  One  t o be  the  must ask  COGNITIVE  i t was  to the  be  classical  "dis-  most to  estab-  Piaget's  for, cognitive  question of first  type  fruit-  of  whether e q u i l i b r a t i o n by  ex-  self-regulating  fruit-  is  Piaget.  SELF-REGULATION  shown t h a t P i a g e t c o n s i d e r e d  a distinct  three  account  place  equilibration.  wish  allows  t h a t the  fulness.  VI.  of  f r u i t f u l n e s s which w i l l  form of  I t should  takes  when a s u b j e c t w o u l d be  to Piaget's d e f i n i t i o n  i n the  to p r e d i c t and  fulness  l e a r n i n g which  point that postulating a particular  mechanism i n the theory  a t the  p o i n t s i n time  plicitly-examined lish  looked  factor  of  factors  equili-  development which of  maturation,  over-  social  23  experience  and  postulated  because  alone  to  Piaget For  account  argues,  this  three  organic a  the  experience. classical  for cognitive  cannot e x p l a i n  r e a s o n , he  factor which  The  physical  concludes  coordinates  classical  factors  development  good analogy  the  are  development. how  formal  that  are  T h e y do  by  there  m u s t be  concerning  is plausible  t r a n s i t i o n from b i o l o g i c a l f u n c t i o n i n g  model,  the. s t r u c t u r e s ally  the  gical  simultaneously and  structures  structures.  of  biological/.model,  i n turn  determine theory,  we  the  to  gives  credence  cognitive operations,  account  cognitive  for  upon  of  to  the However:,  functioning, differ  the  especi-  from b i o l o -  from b i o l o g i c a l differences  development.  By  analogy  e q u i l i b r a t i o n i s a mechanism of  develops  role which  " e q u i l i b r a t i o n " plays a)  development.  In in  what s e l f - r e g u l a t o r y  to  internal  from b i o l o g i c a l f u n c t i o n i n g ,  cognitive  know  the  cognitive  i t .  determines  need to  comprehen-  explanation to  the  cognitive  and  E q u i l i b r a t i o n must d i f f e r  b e t w e e n b i o l o g i c a l and  which  by  formal  i n order  regulation, which  an  further elaborates  constructed  autoregulation,  the  provided  of  provides  That i s ,  direct  This  has  formed.  fourth  which  Further,  biological  Piaget  a  subsumed i n t o a model  development.  model  are  and  three.  observations  this  not,  operations  sive.  functioning.  insufficient  (biological functioning)  account of  development given  factors  other  for cognitive  interpretative  Equilibration is  and  order  to  Piaget's mechanisms  24  are  and  b)  how e q u i l i b r a t i o n d i f f e r s  from b i o l o g i c a l  autoregulations.  a)  Self-regulation  Self-regulation  by  Functioning  i s given  as a p r o p e r t y  system were n o t s e l f - r e g u l a t i n g form, o r dead is  or dying.  i t would  be e i t h e r  an  n o t t h e same a s a m e c h a n i s m o f s e l f - r e g u l a t i o n .  Functions,  i n Piaget's  theory,  conserved by functioning,  structural  I f a inorganic  But the property o r s e l f - r e g u l a t i o n  can be any number o f mechanisms w h i c h  is  of structures.  account  There  f o r the property.  are autoregulators.  Structure  by s t r u c t u r a l a c t i v i t y .  s e l f - r e g u l a t i o n , there  can also  be  Besides  functional  self-regulation:  S t r u c t u r a l r e g u l a t i o n i s t h a t w h i c h o c c u r s when the m o d i f i c a t i o n brought-about i s e i t h e r a n a t o m i c a l • o r h i s t o l o g i c a l , whereas, f u n c t i o n a l r e g u l a t i o n h a s an i n f l u e n c e o n l y o n t h e e x e r c i s e o f p h y s i o l o g i c a l r e a c t i o n o f t h e organs.24  Although it  functional  regulation  does so by r e g u l a t i o n  ultimately  of functioning,  conserves n o t by  structure,  structural  compens a t i o n .  Functions,  and groups  of functions  form one t y p e o f a u t o r e g u l a t o r y conserve require  structure. specialized  linked  i n feed-back  mechanism.  Regulation of functions substructures,  These  regulators  themselves  o r "organs" o f  systems,,  would  regulation.  25  Piaget  points  biological the  internal lators, second the  process  system.  c l e a r example o f a  i s a functional regulator i s  Through the nervous  o f the body a r e r e g u l a t e d or external  as c o n c e i v e d (or higher)  theory  Piaget  the only  structure which  nervous  functions  out that  i n Piaget's  order  to give  describes  disturbances.  i n response  theory,  the genesis  structures, structures  from  are  behaviour.  of functional regulators  as  a  and r e i n t e g r a t i o n o f  structure.  are constructed  of functional regulation which  from the nervous  regu-:-  to enable  a c c o u n t o f human  the o r i g i n a l  he m a i n t a i n s ,  to either  themselves  functions, postulated  a fruitful  various  Most f u n c t i o n a l  of increasing differentiation  substructures  system,  Cognitive as s p e c i a l i z e d are  differentiated  system:  C o g n i t i v e p r o c e s s e s seem, t h e n , t o be a t one and t h e same t i m e t h e o u t c o m e o f o r g a n i c autoregulation, r e f l e c t i n g i t se s s e n t i a l mechanisms, and t h e most h i g h l y d i f f e r e n t i a t e d organs o f t h i s r e g u l a t i o n . a t t h e c o r e o f i n t e r a c t i o n s w i t h t h e e n v i r o n m e n t . . . 25  Cognitive  structures  functioning,  are  of  freed  biological  Logico-mathematical  structures of functioning.  The  of functioning requires  autoregulation,  autoregulation.  from p h y s i c a l s t r u c t u r e , are  cognitive structures.  structures  from  and e s p e c i a l l y from f u n c t i o n i n g as  Autoregulations, into  are extrapolated  which Piaget  coordination  coordinated  structures of  these  a s p e c i a l i z e d mechanism  calls  equilibration.  26  Just in  as the nervous  system  their interaction with  regulates  cognitive  environment. Piaget  calls  cognitive,  activity  intentional  Equilibration,  ture.  nervous  is a distinct  i s simply  Piaget  has  structural similar  discussed and  properties  all  kinds  functions structure. comparing  n o t as  of  function  We  can  There  distinct  detail  that  define  them as  ask  than  struc-  exception now  since  whether  equiliwhether  of the nervous  the problems  i s , i n s o f a r as  they  structures.  They  can be  exerted  distinguished  t h e i r laws of composition,  and  in  are  have  Similarly,  functions,  the type of a c t i o n  system.  Involved  A l l structures  can have p a r a l l e l  by  from  since upon  a r e , however, ways o f d i s t i n g u i s h i n g  structures.  t h e i r elements,  functioning.  rather  regulations  sense,  of structures are defined  functioning  from most b i o l o g i c a l  f u n c t i o n a l comparison.  which  Regulated  functioning.  h o w e v e r , i s one  i n great  i n a general  are  s e l f - r e g u l a t o r y mechanism, o r  an e x t e n s i o n  the  of  system,  i s a functional regulator.  bration it  regulates  the  affects  from b i o l o g i c a l  then, i s d i s t i n c t  because . i t  The  i n turn  the  environment  exchanges".  because  i s "behavioural",  regulation  it  an e x c h a n g e ,  action, but  the  and when t h e s e e x c h a n g e s  the environment, which  Cognitive  i n i t s interaction with  interaction with  "exchanges",  involves  functions  the environment, e q u i l i b r a t i o n  functioning  Functional  biological  they are c a l l e d "behavioural  functioning affects  regulates  on by  the  the  and basis  different  27  types o f laws o f c o m p o s i t i o n . differ,  their functioning  And, i n s o f a r  i s distinct  as  structures  from that  of other  structures.  b)  Regulation  Cognitive  structures  differences ment.  of Cognitive  differ  increasing  with  One o f t h e c h i e f  biological  structures  functioning,  i s seen  Structures  from b i o l o g i c a l s t r u c t u r e s , the each  stage of cognitive  differences  and thus,  between c o g n i t i v e  cognitive  i n the d i f f e r e n t environments  Since a l ltypes o f regulated  exchanges w i t h  the environment,  different structures .  structures The by  i s relatively  environment  externally introduced  essentially  stable:  functioning are  well-defined,  and s t a b l e  f o r example,  for  c a n be  The is  over  time.  affected  elements, b u t remains nonetheless  t h e r e s t o f t h e body.  than the i n t e r n a l organs.  changing i t s environment  itself  indi-  of biological  The  nervous  s y s t e m , o f c o u r s e , o p e r a t e s i n a much more f l u i d environment  i n which  d i f f e r e n t environments  The e n v i r o n m e n t  of the l i v e r ,  and  and b i o l o g i c a l  they operate.  cate  develop-  Still,  and complex  i t s potential  i s l i m i t e d , so t h e environment  i s limited.  environment of cognitive constantly  expanding..  structures,  The c o g n i t i v e  motor s t a g e o p e r a t e s i n an e n v i r o n m e n t  on t h e o t h e r hand, subject  defined  i n the sensoriby b i o l o g i c a l  28  functioning, action  instinct,  a c c o r d e d by  differentiation the  the in the is  this  abstracted the  subject  creates  the  young c h i l d  The  the  and  operates  things  formal and  objects,  the  a physical action.  and  sense,  makes i t d i f f i c u l t Second,  the  as  to  identify  are  through exchanges w i t h  built  structures  the  d e f i n i n g the  exchanges modifying  and  objects  of  these  actions. as  b u i l d i n g new  as  objects be  is  of  not  non-physical,  This a  there  properties  of  course  schema. enormous  cognitive structures. environment,  environment at  indicates  First,  numbers, or  the  "content"  cognitive  expanding environment i n d i c a t e s the  f o r development of  content,  her.  something  potential  form  non-material  a v a r i e t y of  Schema can  "internalized"  is  environment  cognitive subject  manipulation  necessarily i n this  the  about c o g n i t i v e s t r u c t u r e s . o b j e c t s , such  content,  include  from  the  essentially  ( s c h e m a ) , and  operational stage,  removed  an  i n development,  to  i s a f f e c t e d by  temporally  non-material  material  action  expands  expanding environment of  several  f o r m and  Later  between  differentiation  f r o m m a t e r i a l o b j e c t s , and  affects,  spatially  that of  subject/object  manipulated.  This  distinction  and  a d i s a s s o c i a t i o n of  subject In  possibilities for  a marked  case meaning a p a t t e r n of  objects.  are  of  object being  which  The  alone  animal.  beginning  the  subject/object differentiation.  environment of  instinctual  h a b i t and  that point,  Structures the and  s t r u c t u r e s , which  existing the open  29  up  new  for  possibilities  action  i s an  structures. exciting, to  a  A  but  action.  Third,  enormous menace t o  relatively  stable  i t does pose o n l y  structure's  cognitive  be  resolved.  For  a l l structures, i n the  The  subject  of  produce  sing  i n order  not  functioning.  Each of  identified  Piaget  z a t i o n of  by  cognitive  the  development i d e n t i f i e d is  stable  to  an  stages of an  structures. by  Piaget,  extent unique  cognitive  not  be  means  very  threats  problems  to  conserving  intrusion.  Cognitive  intrusions, require  t o be  represents  of  expanding  generates  environmental  actively  potential  number o f  complex and  self-conservation face  very  stability  limited  structures, which organization  the  the  e n v i r o n m e n t may a  organization.  e n v i r o n m e n t of' the  organization  for  destroyed cognitive  by  fact,  the  their  stable  final  organi-  stage  logico-mathematical  among o r g a n i c  own  development  increasingly  In  increa-  of  thought,  structures:  We s u g g e s t t h a t t h e . e q u i l i b r i u m . . . w h i c h i s brought a b o u t by l o g i c o - m a t h e m a t i c a l s t r u c t u r e s c o n s t i t u t e s a s t a t e - m o b i l e . a n d d y n a m i c , a n d , a t t h e same t i m e s t a b l e - a s p i r e d t o u n s u c c e s s f u l l y b y thesuccession of forms, at l e a s t where b e h a v i o u r forms are concerned, throughout the course of the e v o l u t i o n of organized c r e a t u r e s ?7  Not face  only of  selves form of  do an  they  cognitive  structures  conserve organization  expanding environment, but achieve  a highly  organization.  stable,  i n so though  conserving always  in  the  them-  dynamic,  30  In  the  final  formal  stage  of  operational  structures  cognitive  thought,  is their  the  complete  development, striking  the  stage  feature  reversibility.  of  of  cognitive  Operations  are:  A c t i o n s c h a r a c t e r i z e d by t h e i r v e r y g r e a t g e n e r a l i t y . . . they are also reversible...(and) are never i s o l a t e d but capable of b e i n g coordinated i n t o o v e r a l l systems.28  An  action  beads be  upon an  into  the  "undone";  "beads"  to  class of  the  the  object,  Logico-mathematical are  highly  stable  as  beads,  objects  classes  such  can  of  and  blue  i s r e v e r s i b l e because  be  "red  combining red  returned beads"  from  and  the  "blue  s t r u c t u r e s , whose f u n c t i o n s  i t  class  can of  beads". are  operations,  because:  ...an o p e r a t i o n i s a " p e r f e c t " r e g u l a t i o n . What t h i s means i s t h a t an o p e r a t i o n a l s y s t e m i s one w h i c h e x c l u d e s e r r o r s b e f o r e t h e y a r e made, b e c a u s e e v e r y o p e r a t i o n has i t s i n v e r s e i n the s y s t e m . . . o r , to put i t d i f f e r e n t l y , because every o p e r a t i o n i s r e v e r s i b l e , an ' e r r o n e o u s r e s u l t ' i s s i m p l y n o t an e l e m e n t o f t h e s y s t e m ( i f +n-n^0, t h e n n ^ n ) . 29  Logico-mathematical expanding  environment because  Intrusions  upon them are  compositional are  structures  laws of  Piaget  argues  requires  that  the  autoregulations  stable  they  form  i n the  "closed  face  or  structure.  of  an  systems".  d e a l t with-,;-without t h r e a t  the  either assimilated  are  Environmental  to  the elements  rejected.  development of distinct  such  stable  from b i o l o g i c a l  structures autoregulations.  31  Biological the  autoregulations  structures  mathematical once  By  biological the  New  change  comparing  in i t s  serves would  structure yield  deduces  the  structures  and  e q u i l i b r a t i o n from  of structuralism.  The  differences  implies  a  In p a r t i c u l a r , the s t a b i l i t y  which  e x i s t i n an e x p a n d i n g  regulation The  property  functioning,  that  of  regulation  of  is  con-  What  would  be  functions  this  of  enviroment,  so c o g n i t i v e  a d d i t i o n a l mechanism by which  a  i s not structures  functional  obtained.  C O N S T R U C T I O N OF  there  than functioning  functions.  COGNITIVE  STRUCTURES  i s a s p e c i a l mechanism o f c o g n i t i v e  i t i s a functional  comparisions of if  conserved,  than does b i o l o g i c a l f u n c t i o n i n g .  better  of  regulation  and  Logico-  a f o r m o f s e l f - r e g u l a t i o n w h i c h more c o m p l e t e l y  must have an  That  Piaget  i n functioning.  intrinsic  VII.  i s subsumed by  and b i o l o g i c a l s t r u c t u r e s  structures,  regulator an  over time.  compositionalllaws.  framework  between c o g n i t i v e  implies  t o decay  structure;  certain characteristics of cognitive  conceptual  cognitive  conserve  however, are p e r f e c t l y  information  structures,  difference  subject  structures,  formed.  without  are s t i l l  incompletely  cognitive  logico-mathematical  regulator,  and  regulation,  i s indicated  biological structures.  structures  by But  show c h a r a c t e r i s t i c s o f  32  functional  regulation, the question  remains:  . . . i f i ti s t h e s t r u c t u r e s which e x p l a i n e q u i l i b r a t i o n , o r i fon t h e c o n t r a r y t h e s t r u c t u r e s can be i n t e r p r e t e d as t h e p r o d u c t o r r e s u l t o f a process o f e q u i l i b r a t i o n . 3 0 Unless the is  creation of logico-mathematical not a very  the  examining  these  Piaget's that  i n Piaget's  explanatory  equilibration's  s t r u c u t r e s are indeed  evidence  there  Piaget's  f o rthis,  role  theory.  To  address  u s e f u l n e s s , we  must  i n the construction  are distinct  i s i s s a f e enough  thought, these  vary.  has been m o d i f i e d  sensori-motor  are sub-periods  consists i n observations  seen a t d i f f e r e n t  has been observed  across  o f c o g n i t i v e development.  thought,  and formal o p e r a t i o n a l thought.  stages  presence  i s h i s observation  and order  cultural  over  time,  t o name t h e t h r e e m a j o r p e r i o d s o f  development:  periods, there  patterns  stages  to believe  c o n s t r u c t e d i n some m a n n e r .  o f course,  enumeration o f stages  cognitive  It  structures, "equilibration"  c o g n i t i v e s t r u c t u r e s , t h e r e must be r e a s o n  that  the  concept  contributes to  a t t h e mechanisms o f s t r u c t u r a l c o n s t r u c t i o n .  Before  but  fruitful  issue of equilibration's  look  of  i t c a n b e shown t h a t e q u i l i b r a t i o n  pre-operational  Within  each o f  and stages. of distinctive  points i n a child's  Evidence action  development.  b y P i a g e t , a n d m a n y o t h e r s ?\hat  o f succession o f the stages  barriers,  though  of  the  i s constant  t h e speed o f s u c c e s s i o n  may  33  Each (or of  stage  represents  "equilibrated state" the equilibrium).  cerning  cognitive  construction or  a more o r l e s s p e r m a n e n t - t o emphasize  Piaget's  increasingly stable  the active  nature  fundamental hypothesis  development i s that  of "progressively  equilibrium  con-  i t i s a process of 32  adequate e q u i l i b r a t i o n " ,  structures.  This  process of  construction: . . . i n b e i n g c o n s t a n t l y r e g u l a t e d by e q u i l i b r a t i o n r e q u i r e m e n t s , (a s e l f - r e g u l a t i o n whose c o n d i t i o n s become t h e more s t r i n g e n t as i t s t e e r s t o w a r d a n e q u i l i b r i u m t h a t i s . m o b i l e a n d s t a b l e a t t h e same time), f i n a l l y y i e l d s a n e c e s s i t y that i s a nontemporal, because r e v e r s i b l e , . law?^  So,  equilibration itself  directs  In  the pattern  order  the course of cognitive  special attention.  cognitive  equilibrium.)  constructing is  and  development.  stable  functioning insufficient  look  points  i n what  The s e c o n d  general,  between e q u i l i b r a t i o n and o t h e r  Piaget  to construct  maintains  sense  point  mechanisms i n  a t the regulations  a n d why  two  i s the meaning o f  structures,  stable?  the nature of regulatory  H e r e we w i l l  i n fact,  development,  The f i r s t  more o r l e s s  the differences  which  , I fe q u i l i b r a t i o n i s a process o f  increasingly  a structure  concerns  of cognitive  a process  t o decide whether e q u i l i b r a t i o n does,  determine deserve  i s a process;  regulators.  produced by b i o l o g i c a l that  they  logico-mathematical  alone are structures.  34  a)  Meaning of. C o g n i t i v e  Cognitive  structures  The  type  first  of  can  '34. e q u i l i b r a t e d i n d i f f e r e n t ways.  be  equilibrium  lation  and  is  functioning  the  Equilibrium  accommodation. of  a  i s a balance  between  Assimilation, i t will  s c h e m a t o  assimi-  be  incorporate  recalled, outside  ,35  elements  compatible with  accommodation i s the to  deal  the  with  total  For be  to  example, subject  the  a  the  there  ability  of  The  bring  this  second  of  objects  i t i s an  objects  the  To  conserve  the  be  accommodation.  the  mouth  taking  into  these  could  account accom-  schema upon w h i c h extension mouth.  require  e q u i l i b r a t i o n as i s one  of  the  Instead,  random t r i a l i t relates of  to  they  each  and a  balance  assimilating  each  schemata.  cognitive  equilibrium  Various  from each other,  and  This  i n Piaget's  case  in  I f each of  to  schema  accommodation must  systematic  accommodation  between s u b s t r u c t u r e s .  i s the  assimilation  i n t o the  action would  process  form of  no  and  environment.  which  object.  w o u l d be  to  accommodation to  an  assimilated  a s s i m i l a t i o n and  The  an  schema, each  schema f o r p u t t i n g  weight of  performance of error.  a  of  the  structure.of  modations were not  child's  of  of  into itself,  t o many a c c o m m o d a t i o n s , e . g . ,  shape or  were based,  modification  a particularity  structure  assimilated  i t s nature  only  be  i s an  schema can  brought  to  observations  equilibrium  exist  independently  play i n d i v i d u a l l y . of  conservation  35  notions  (or lack  thereof)  i n pre-operational  child  at this  water  a f t e r i t has been poured, because  higher,  stage might sometimes  or that  there  thought.  say that  i s l e s s because  the water  a s s i m i l a t i o n o f t h e two s c h e m a t a ,  continuous  quantity  bration  between substructures  i s more level i s  i ti s thinner.  reciprocal  i s constructed.  there  A  By  conservation  The p r o c e s s  i s one o f mutual  of  of  equili-  intercoordina-  tion.  The  third  form of e q u i l i b r a t i o n e s t a b l i s h e s  connections between s t r u c t u r e s process,  the substructures  reciprocally  and s u b s t r u c t u r e s .  created  intercoordinated  hierarchical  with  has been e s t a b l i s h e d  such a s t r u c t u r e intrusion tional  their total  i s compensated  equilibrium  objects  i t and i t s  i s a closed  an e n v i r o n m e n t a l  f o rwithout  change  i s not a "balance"  o f e q u a l w e i g h t on a s c a l e .  anced, instead,  are the "forces"  onment and accommodating because  structure.  system.  When  intrusion, the i n the composi-  laws o f t h e s t r u c t u r e .  Cognitive two  meets w i t h  this  by accommodation a r e  A s t r u c t u r e where a l l relationships.-between substructures  In  the subject  was i n a s t a t e  to i t .  i s active.  of cognitive  would be temporary,  that  between  What  i s being  bal-  of assimilating the envirThe e q u i l i b r i u m i s d y n a m i c I f we  said  equilibrium,  and would  like  that  this  a  subject  equilibrium  "...consist of a s e t of probable  36  compensations o f e x t e r n a l  i n t r u s i o n s by t h e a c t i v i t y  of the  , . .. „. 36 subject .  Compensations a r e formed and  a r e o f two  through  the functioning of  schemata,  types:  ...the compensations by i n v e r s i o n w h i c h are /• c a n c e l l a t i o n s - o f t h e d i s t u r b a n c e / , a n d t h e - , c o m p e n s a t i o n s by. r e c i p r o c i t y , . w h i c h a r e . m o d i f i c a t i o n s o f t h e schema t o accommodate i t t o t h e i n i t i a l l y d i s t u r b i n g element.3 7 1  1  Hammering both  a nail  1  s t r a i g h t into a piece  types of compensations.  compensates  f o r a blow which  inversion.  Reciprocity  her  p o s i t i o n o r reach,  force  Striking  o f wood  can  the n a i l  h a s b e n t i t down.  i s involved  involve  on the This  i s  when t h e s u b j e c t  to h i t the n a i l  with  side  adjusts  the most d i r e c t  possible.  "Reversibility"  i s the s t r u c t u r a l counterpart  to compensations.  I t , .too-, h a s t h e t w o f o r m s o f i n v e r s i o n a n d r e c i p r o c i t y . Logico-mathematical because procity, For  they  structures  are structures  are completely  not only  reversible  o f i n v e r s i o n and  reci-  b u t o f t h e r e c i p r o c a l i n t e r c o o r d i n a t i o n o f them.  example,  the arithmetic  operations,  of  i n v e r s i o n and r e c i p r o c i t y , a l l o w  in  an a l g e b r a i c  statement:  by t h e  us t o d e f i n e  coordination a variable  37  3x:.+ 2 = 7 (3x + 2 ) - 2 = 7 - 2 (3x)(1/3) = (5)(1/3) • x = 5/3  (-2 i s t h e r e c i p r o c a l o f 2) ( 1 / 3 i s t h e i n v e r s e o f 3)  Thus, s t r u c t u r a l r e v e r s i b i l i t y  refers  connections of a structure which be  "transformed"  original  b)  into other  this  really The  point,  Chart  i s that 1).  functioning. property  form.  they  and  there  functions.  are i n a hierarchical relationship,  Compensatory mechanisms a r e mechanisms, which  I n each case,  constructed  are.constructed  t h e p r i o r mechanism  of the next higher  mechanism i n an  from contains incomplete  effect of  reg-  mechanisms have t h e  e f f e c t o f s t r u c t u r a l compensation..  t h e v a r i e t y o f names b y w h i c h  mechanisms, e.g., compensatory  a  to their  regulations  hierarchical relationship explains,  excuse,  i n i t to  Regulation  s t r u c t u r e , and r e g u l a t o r y  secondary  and  and back  That i s , f u n c t i o n i n g has the secondary  ulating  This  elements  one m i g h t w e l l wonder what d i f f e r e n c e  from regulatory  the  elements  i s between compensations,  answer  (see  allow  state.  Mechanisms o f  At  to the internal  regulatory  functions  Piaget  regulations  f o rregulations.  refinement of functions;  though  compensations  i t does n o t  calls  these  f o r compensations, Regulations  are a  are  refinement  38  of  regulations.  organization specific  see  that  leads  case,  to the construction  alone  accounts  conservation  requires  struction  of structures  to  Whether they  by  brings  different  us t o a c r u c i a l  from  functioning, sations. a  o r i s i t simply  "regulator  extension  leads  to the  question:  the regulations  of regulations", itself.  of organic  Is  inherent  c a n be  qualitatively  and d e v e l o p s  Thus i t i s b o t h  different  a lead  part  on t h e  functioning.  equilibration  i n biological  an e x t e n s i o n  regulations.  and  to compensations.  The answer'.is -both y e s a n d no.  functioning  the con-  do o r n o t d e p e n d s i n t h e g r e a t e s t which  greater  Not a l l functions  nor a l l regulations  nature of the disturbance  This  there  to  the  adds s t i l l  regulation  of course,  schema(s).  and t h a t  2 represents  functioning,  At each step,  regulations,  construction,  Chart  con-  I t i s not d i f f i c u l t  and compensations  f o r construction.  t o the o r i g i n a l  of increasingly  f o r a c e r t a i n amount o f  potential  compensation.  to preserve  conservation.  ( i ,e . , a c c o m m o d a t i o n s . ) .  presence of regulations  return  the l i f e - d r i v e  mechanisms o f s t r u c t u r a l  Functioning struction  In each  o f , e.g.,  compen-  Equilibration i s from  biological  a conceptual  and  actual  However, i t i s a l s o  from other organic  regulations.  39  CHART I  m e c h a n i s m o f k—  EQUILIBRATION Reciprocal Assimilation  mechanism o f f -  I  m e c h a n i s m o f <—  >  C O M P E N S A T I O N Reciprocity  Inversion  .Property of  R E G U L A T I O N Positive Feedback  mechanism of  Negative Feedback F U N C T I O N I N G  Assimilation  Accommodation  .Property of  CHART I I  S T R U C T U R A L CONSTRUCTION THROUGH F U N C T I O N I N G  -<u>.  Environmental Intrusion  Equislibration Compensation by Inversion'  >ration  <—>/s 'V <T  Regulation by Positive Feedback  Compensation byReciprocity  Regulation by Negative Feedback Assimilation  Accommodation  *See Page  42  41  The  d i f f e r e n c e between  lies  i n the disturbances  functioning  operates Biological  structures  i n their  Cognitive  accommodation the  which i tregulates.  r e g u l a t o r y mechanisms  regulators Biologically-  regulate  r e l a t i o n s h i p to this environment.  structures are subject  accommodation  and other  on t h e p h y s i c a l environment o f the  organism.  The  equilibration  to internal  disturbances.  of a cognitive structure, unlike the  of a biological  structure, creates  not only  s t r u c t u r e o f accommodation, b u t a second, complementary  structure.  In  t h e c a s e o f an accommodation  the  immediate organic  leading to a compensation,  requirement  i s that  S', b e a s s i m i l a t e d t o t h e o r i g i n a l lation tion  of S  1  as a subclass  of a subclass  the accommodation,  s t r u c t u r e , S.  of S implicitly  o f t h e same o r d e r ,  entails  S" = S n o n S .  form o f e q u i l i b r a t i o n  or resolution of internal  thus  f o r the second and t h i r d  it  creates  creates  a second substructure  Equilibration gni  _  S" ,  As  i I I^ s  types,  can look  classificatory  as  since S . 1  a new s t r u c t u r e , S, S',  e s t a b l i s h e s a l l connections between  substructures, but the boundaries  cular  first  disturbances,  p^fi r e c i p r o c a l a s s i m i l a t i o n b e t w e e n  a n e x a m p l e , we  construcThe  o f t h e same o r d e r  of the second form creates  e t c . , not only  1  its  S  t h e need  The a s s i m i -  S and  o f S.  a t t h e accommodation  structure.  S",  Imagine t h a t  of a  a child  partiknows  42  t h a t dogs first and  and cats  time,  are animals.  and i d e n t i f i e s  has eyes.  created  ture  and l i v e  created  reciprocal structure  the  of their  i n t e r s e c t i o n , "things  In this  class/subclass  R e f e r r i n g back by  lead  the beginning require  conservation i t s form.  construction, will  The  creates  a  move a n d h a v e  establishes  r e l a t i o n s h i p s b e t w e e n S"', a n d S' a n d S".  new s t r u c t u r e s w h i c h  determine  (S").  which  to equilibration of  t o C h a r t 2, i t c a n b e s e e n  i ti s o n l y  Structural  which  case, that e q u i l i b r a t i o n  functioning i s inadequate to resolve  Indeed,  to S i s "things  i n the water".  These c o n s t r u c t i o n s  struc-  f o r m , b e t w e e n t h e new s t r u c t u r e a n d t h e t w o s u b -  structures. the  live  which  w h i c h move a n d  The complementary 1  i t moves  The s t r u c t u r e  a s s i m i l a t i o n o f t h e s e two s u b s t r u c t u r e s  (S"').  third  and don't  i s "things  i s "things  i n the water".  f o r the  because  on t h e l a n d " .  by the a s s i m i l a t i o n o f S  move a n d h a v e e y e s  eyes".  and l i v e  structure(s)  by the accommodation(s)  have eyes  a fish  i tas an a n i m a l ,  The o r i g i n a l  move a n d h a v e e y e s ,  She s e e s  conservation  internal  o f a l lthree  forms.  c o n s t r u c t i o n , b u t does n o t  Compensation  determines  the form o f  b u t d o e s n o t d e t e r m i n e h o w t h e new  be i n t e g r a t e d  disturbances.  o f them, as i t c r e a t e s t h e  equilibration  implies  that  into the original  structure.  constructions  43  VIII.  By  A C C O U N T I N G FOR C O G N I T I V E D E V E L O P M E N T WITH THE OF E Q U I L I B R A T I O N  contrasting  cognitive  cognitive  regulations  and  establishes  that  regulation.  structures  and b i o l o g i c a l s t r u c t u r e s ,  and b i o l o g i c a l r e g u l a t i o n s ,  equilibration i s a distinct  These  CONCEPT  arguments  tell  Piaget  form o f  self-  us what e q u i l i b r a t i o n means,  a n d how e q u i l i b r a t i o n i s n e c e s s a r y f o r t h e i n t e r n a l  consistency  of  whether  Piaget's  the  theory.  However, i ti s s t i l l  concept o f e q u i l i b r a t i o n increases  theory does  to explain  cognitive  not clear  the ability  development.  n o t add t o t h e theory's explanation,  o f .Piaget's  I fequilibration i t s usefulness  i s  questionable.  Equilibration  i s meant t o e x p l a i n  been observed;about c o g n i t i v e through stage  a s e r i e s o f stages,  certain things  development:  and that  that  which  i t proceeds  the structures  a r e i n c r e a s i n g l y r e v e r s i b l e , and therefore  have  o f each  complete.  B a s e d o n C h a p t e r s O n e a n d Two, we c a n s e e w h y e q u i l i b r a t i o n explains  ..cognitive  how i t d o e s  so.  equilibration necessary  the  varying  cognitive  a t the kind  methods.  language  equilibration.  and t o a c e r t a i n  However, i n o r d e r  explains  t o look  structuralist  development,  Piaget  u n d e r s t a n d how  development,  o f explanation  We w i l l  that  to fully  also  extent,  i twill yielded  be by  t r y t o make s e n s e o f  u s e s when he t a l k s  about  44  a)  Construction  The  primary  entail  The  the  of  This  differs,  late  construction  the  structures  the  to  an  can  ask  s t i l l  pattern  and  the  the  by  p o s i t i v e or  environment.  j u s t how  Piaget  outcome of  the  the  i s that a l l  constructed regulatory  are  the deter-  mechanism. a  regulatory  reciprocal assimilation. mechanisms, which  negative  feed-back.  reguEach  disturbances  structure, rather  This  based  than i t s  much s a i d , h o w e v e r ,  purports  cognitive  for  s t r u c t u r e s , and  accommodation creates  i n t e r n a l relations of  relations  so  from r e g u l a t o r y by  of  e q u i l i b r a t i o n as  i t regulates  e.g.,  a s s i m i l a t i o n of on  construction  s p e c i a l c h a r a c t e r i s t i c of that  structures  the  c h a r a c t e r i s t i c s of  mechanism i s  Structures  e q u i l i b r a t i o n accounts  logico-mathematical  characteristics m i n e d by  Logico-mathematical  r e a s o n why  development of regulations  of  to  we  account  for  the  development w i t h  the  concept  of e q u i l i b r a t i o n .  To  begin with,  does not  p r o c e e d by  he  asserts,  at  play  an  account of  bilistic  Piaget's way  cannot deal  i n cognitive  laws.  explanation of  simple  cognitive  causal  adequately with  development.  cognitive  of  laws. the  the  E q u i l i b r a t i o n mechanism,  Such  dynamic  R a t h e r , he  development on  development accounts, processes  formulates  basis  of  therefore:  proba-  45  ...do not y i e l d simple causal (laws), but s t a t i s t i c a l ( l a w s ) , w h i c h s h o u l d be interp r e t e d i n an ' i m p e r s o n a l ' , or n e u t r a l , manner, f o r e x a m p l e , i n t h e way t h a t we c a l l o n the p r i n c i p l e s of 'least action' i n a n a l y t i c mec h a n i c s , t o ' d e s c r i b e ' t h e p a t h o f an a t o m as being t h a t which corresponds to the ' l e a s t a c t i o n * i n the passage from the p o i n t of d e p a r t u r e to t h e e n d - p o i n t ( o f t h e m o t i o n ) .38  T h u s , we of  of  of  for  the  s t r u c t u r e s " , but  "the  construction  providing  increasing  of  " e q u i l i b r a t i o n causes  logico-mathematical  process  the  say  logico-mathematical  tion  By  would not  an  structures  g o v e r n e d by  explanation  probabilities,  ' s e l e c t i o n ' of  the  of  particular  cognitive  actual  particularly'.-by fulfilling) bration,  development on  system  the  The  contain  a  basis  accommodations.  the  successful  for  range possibilities  functioning,"';  (i.e.,  Each coordination,  set of  of  probability for  i s ' i n c r e a s e d through  a. new  to  f r o m among t h e  regulations  a s s i m i l a t i o n of  determines  corresponds  e q u i l i b r a t i o n mechanisms".  regulations.  coordinations  construct  " . . . e q u i l i b r a t i o n ... a c c o u n t s  possibles...".39 organic initial  that  construction  need-  or  reequili-  probabilities.  40 In  his  e a r l i e r w o r k on  probabilistic field The  of  first  equilibration,  m o d e l b a s e d on  four  Piaget  presents  dimensions of e q u i l i b r a t i o n :  a p p l i c a t i o n , m o b i l i t y , permanence, and cognitive coordinations,,  functioning,  i s the  a  arising  e q u i l i b r a t i o n of  from  stability. biological  schemata across  their  46  field This  of application coordination  equilibration, disturbances e.g.  (the objects  then provides  (one w h i c h  crosses  coordination  on l e n g t h ,  fields)  of  volume.  In this  of  the d i a l e c t i c a l  I n h i s more r e c e n t dialectical  account,  processes  fashion,  with  to the  has attempted  i n development,  . ,  the  conservation t h e name  rather  to  than  explain to  explain  I n The D e v e l o p m e n t o f T h o u g h t ^ 1  functional  affirmations  are completely  reversible.  a s s i m i l a t i n g accommodations,  creating  (negative  (positive feedback),  and a f f i r m a t i o n s  Piaget  development based on t h e c o -  of functional negations  synthesized,  Internal  e q u i l i b r a t i o n i s simply  works, Piaget  a model o f c o g n i t i v e  negations  mobile  and so on.  on width,  leading  ordination  of  f o ra  process.  d e v e l o p m e n t by them.  which  refer).  i n dialectical  centration  of these eventually  they  the p o s s i b i l i t y  a r i s e and a r e r e s o l v e d  centration  presents  to which  feedback) into  structures  E q u i l i b r a t i o n , o r the process i s the: m e c h a n i s m b y  of particular structures  structures  and  which are  comprised of r e c i p r o c a l  relations.  In  this  raises  account,  as i n h i s e a r l i e r  the p o s s i b i l i t y  ment o f d i a l e c t i c a l existence for  accounts, each e q u i l i b r a t i o n  f o r new d i s t u r b a n c e s .  Unlike  state-  processes, however, p o s t u l a t i n g the  o f a mechanism o f r e c i p r o c a l a s s i m i l a t i o n  the form which  a  the e q u i l i b r a t i o n  takes:  accounts  47  C o n s t r u c t i o n , i n b e i n g c o n s t a n t l y r e g u l a t e d by e q u i l i b r a t i o n r e q u i r e m e n t s , (a s e l f - r e g u l a t i o n whose c o n d i t i o n s become t h e more s t r i n g e n t as i t s t e e r s t o w a r d an e q u i l i b r i u m t h a t i s m o b i l e a n d s t a b l e a t t h e same t i m e ) , f i n a l l y y i e l d s a n e c e s s i t y that i s a non-temporal, because r e v e r s i b l e , l a w . 42 A mechanism o f r e c i p r o c a l a s s i m i l a t i o n , then, the of  construction of structures with logico-mathematical  the s p e c i a l c h a r a c t e r i s t i c s  structures.  To f u r t h e r e l u c i d a t e i t s e x p l a n a t o r y principles  The u n c e r t a i n t y  g o v e r n s w h a t c a n be known a b o u t sub-atomic p a r t i c l e sense type  that  b)  the speed  a necessary  Similarly,  of cognitive  equilibration principle i n  i s a  "law" which  and p o s i t i o n o f a  I t i s a law i n the feature  of a certain  equilibration  describes  development.  Language o f E q u i l i b r a t i o n  Also are  i tdescribes  features  principle  a t any one t i m e .  of observation.  necessary  nature,  c a n be l i k e n e d t o t h e u n c e r t a i n t y  modern p h y s i c s .  accounts f o r  like  the uncertainty  implicit  part  i n that which  f o r the difficulties  principle,  they explain. people often  t o make s e n s e o f P i a g e t ' s  theory.  Piaget  i n language  often  i s simply shifts  careless  as he u s e s  equilibration This  "laws"  accounts i n  e n c o u n t e r when  To a c e r t a i n use.  a number o f s i m i l a r  trying  extent,  His terms  terminology t o convey  48  roughly of  t h e same c o n c e p t .  understanding  This  c a n compound  the problem  an a l r e a d y  difficult  theory.  A prime example o f P i a g e t ' s  confusing  language  ment o f v a r i o u s able  use o f the terms  times,  o f "(the)  process",  and  needlessly or  attributes  to equilibration,  so c o n s t r u c t e d .  equilibration  "equilibration  confusing  laws".  Although there  at various  "equilibration i t may  i s no  particular  called  interchange-  speaks, :  to the reader,  c a n be r i g h t l y  and  m e c h a n i s m ^ s ) ",  contradiction involved i n this  Equilibration  He  i s h i s assign-  be  inconsistency  practice.  a mechanism, process  or  law.  One  meaning o f "mechanism"  i s t h e " a g e n c y o r means by  which  43 an  effect  i s produced".'  equilibration  t o be s u c h  Piaget a  certainly  intends f o r  phenomenon:  E q u i l i b r a t i o n would thus e x p l a i n the process o f t r a n s i t i o n from p r e l o g i c a l to the l o c a l mathematical s t r u c t u r e s , and, hence, t h e f o r m a t i o n and above a l l completion of these structures.44  The by  process which  such e f f e c t s  r e q u i r e d by laws  are produced.  i s the mechanism  The: r e g u l a t i o n s mechanisms  the construction of structures.  and p l u r a l  c a n be  equilibrations  the character o f e q u i l i b r a t i o n  governing  singular which  of progressive  forms, e q u i l i b r a t i o n  a c t i n g on any number  i s a  are  As f o r mechanism  of structures  simultaneously.  49  IX.  Now it for  F R U I T F U L N E S S OF T H E CONCEPT  that  we k n o w w h a t P i a g e t  differs  of cognitive  EQUILIBRATION  m e a n s b y " e q u i l i b r a t i o n " , how  from s i m i l a r concepts,  i t t o e x p l a i n , we  theory  OF  and what Piaget  can ask what  development.  intends  i tcontributes  to  O r , i n o t h e r w o r d s , we  to  ask " I s e q u i l i b r a t i o n a f r u i t f u l  As  a s p e c i a l mechanism o f i n t e r n a l r e g u l a t i o n , which  cognitive of  functioning,  regulation  functioning the  organic  model.  theory?"  regulates  other  Since  want  mechanisms  i t regulates  by r e c i p r o c a l a s s i m i l a t i o n o f accommodations  original  structure,  e q u i l i b r a t i o n constructs  whose laws o f c o m p o s i t i o n  elements o f the s t r u c t u r e .  are  stable  t o an extent unique  their functioning  These  "reversible"  among o r g a n i c  does not. m o d i f y  into  structures  are reversible connections  the  because  concept i n the  equilibration i s unlike  i n Piaget's  Piaget's  between  structures  structures,  their  compositional  laws.  If  we  accept Piaget's  framework of the  model o f o r g a n i c  f o rexamining  cognition,  self-regulation i s conceptually differences  On t h e s e  between c o g n i t i v e  grounds,  equilibration  functioning  some s p e c i a l required  as an a p t  mechanism  to account f o r  and b i o l o g i c a l s t r u c t u r e s .  the concept o f e q u i l i b r a t i o n i s u s e f u l ;  holds  t h e model  together.  50  Piaget,  however, intends  more t o h i s a c c o u n t model.  for equilibration  than  simply  Postulating a special  maintains,  of  c o g n i t i v e development, proceeding of  stages,  structures.  and  This  can  c o u l d be  of  I t i s not  has  the  are  concept  of  t h a t he  the  recourse  reading  ask to  a  describes.  about the  account  to  plausibility  i n general.  Equili-  implied  through  s t r u c t u r e s , are  P i a g e t , one  model.  the  this We  theory  question of  the  paper  them-  i s often  e x p l a i n e d anything beyond h i s  of Piaget's  r e l e v a n t to  sort  purpose of  a/few, p o i n t s c o n c e r n i n g  invariant  claim, i t i s fair  a b s t r a c t concept,  Thus, on  an  explanation  logico-mathematical  whose b a s i c elements,  abstract.  justification  through  made w i t h o u t  Piaget's  w o n d e r i n g w h e t h e r he itself.  the  is a particularly  complex theory  selves  this  the  internal regulation,  a probabilistic  lead to questions  and/or usefulness  a  to  mechanism of  question  bration  to provide  culminating i n  In regard  w h e t h e r hiiis a c c o u n t particular  us  coherence of  mechanism of  he  series  allows  internal  to contribute  to  left model  provide  w i l l , however, look  i n g e n e r a l , as fruitfulness  these of  at points  the  equilibration.  a)  Equilibration  To  b e g i n w i t h , we  equilibration  and  and  want  Piaget's Organic  to ask  whether  the:..reversibility of  Model  the  relationship  between  logico-mathematical  51  structures  i s merely  structures  simply  equilibration,  tautological.  "look  or  i s there  mechanisms c o n t r i b u t e replies, as  possible  that  are  acceptance  of  of  this  to  T h e s e two the as  the  two  this  of  Piaget  and  e x p e r i m e n t show as  clearly  point  To  can  c o n s t r u c t e d . . . " .45  best  most p e o p l e  radical  i n the  i s due  that  fact,  there  of  of  are  m i n d as  is  cognitive the  children's  widespread  to  Piaget's  conceptions  prevailing epistemological  concepts  Piaget  understood  today,  idea In  be  i n l a r g e measure  studies  i n some  non-contradiction,  equilibration  them?  stands  both  of  which  form.  stands o f f e r opposing  world.  that  empiricist associationism,  day  i m p r e s s e d upon the  say  by  formation  this  idea  and  fundamental  vable  to  regulated  s t r u c t u r e s are  began h i s  were i n n a t e i s m survive  reason  are  somehow.constructed.  When h e  the world,  they  these  the  context;-..  s u r p r i s i n g or  structures  work.  logical  i n s i s t e n c e on  a historical  nothing  to  "...observation  Piaget's in  like"  T h a t i s , do  and  simple  cognition.  e i t h e r given necessary  counters  both  explanations  These concepts, a priori,  features  of  these views,  or the  they  such are  obser-  saying:  . . . t h e k n o w l e d g e o f t h e e n v i r o n m e n t w h i c h i s so a d m i r a b l y a t t a i n e d by t h e human m i n d i s o n l y so a t t a i n e d by v i r t u e o f an e x t e n s i o n o f t h e o r g a n i z a t i o n ' s s t r u c t u r e s i n t o the u n i v e r s e as a whole. 4 6  for  52  If  anything,  Piaget  is  generally  considered  pains in  to point  biological  the  process  But, add  the structures  organization,  to Piaget's  However, as he  Insofar  takes  o f c o g n i t i o n may b e  but this  latent  i n no way a c c o u n t s f o r  construction.  the concept of e q u i l i b r a t i o n  account o f the construction  o r could  he  this  a s we  of cognitive  a c c o u n t b e made w i t h o u t  equili-  take h i s account t o be a d e s c r i p t i o n  t h e s e r i e s o f stages o f development, t h e answer i s t h a t p a r t i c u l a r mechanism he d e s c r i b e s  refer  i t s nature  i n the s t r i c t  equilibration theory.  of cognitive  development p e r se  sense o f " p r e d i c t i o n " , the concept o f  i s not necessary  Functioning,  increasingly  likely.  predict  each  that  at this  state of cognitive i n t o a new  Piaget's development, stage  E q u i l i b r a t i o n i s not necessary to  stage w i l l  likelihood  f o rprediction to  of structures  n o t as y e t p r o v i d e d  particular  b u t do n o t  i n detail.  makes a r e o r g a n i z a t i o n  stage.  i s not necessary.  t o e q u i l i b r a t i o n as an important process,  specify  has  a form o f innateism;  a Kantian.  I n d e e d , h i s many s t u d i e s  So,  toward  w e ^ c a n ! s t i l l a s k , does  bration?  the  out,  of their  structures,  of  leans  be o b t a i n e d .  a framework  Likewise,  Piaget  f o rpredicting the  o f an i n d i v i d u a l ' s a t t a i n i n g a  higher  53  There tion are to  i s , however, more t o P i a g e t ' s of  stages.  Besides  determining  c o n s t r u c t e d ..in a p a r t i c u l a r determine  regard, theory are  how  this  retrodict,  constructed.  of o r g a n i z a t i o n (stage) of  the  next,  fact of  provides  i t does n o t  tell  us  place.  concept.  o r e x p l a i n t h e way the  the  predic-  sequence, P i a g e t i s  is a fruitful  Although  than  that cognitive structures  c o n s t r u c t i o n takes  equilibration to  theory  attempting  In  this  I t allows  the  i n which structures attaining  the  possibility  how  the  one  level  for  attainment  organization is  attained: I f t h e n o v e l t y t o be c o n s t r u e d i s s u g g e s t e d by t h e p r e c e d i n g c o m p l e t i o n s , i s i t riot p r e d e t e r m i n e d ? The r e p l y i s t h a t t h e w o r l d o f p o s s i b i l i t i e s i s never complete, nor, consequently, given i n a d v a n c e d :  Equilibration, can  by  e x p l a i n why  i t s particular  character of r e g u l a t i o n ,  c o g n i t i v e s t r u c t u r e s are  c o n s t r u c t e d as  they  are.  T h u s , by and  outcome o f  fruitful that of may  enabling Piaget's  to r e t r o d i c t  the  c o g n i t i v e development, e q u i l i b r a t i o n  concept  retrodiction  equilibration, yield  theory  i n the  theory.  i s not such  particular  as  I t should  a c l o s e d book. those  predictive  mentioned  be  course is  noted,  Experimental i n Chapter  hypotheses.  a  too, studies Five,  54  b)  In  Verifleability of Equilibration  conclusion, there  I f we a r e a s k e d bration than  i s one f u r t h e r p o i n t  t o accept  mechanisms h e l p  a retrodictive  hypothesis,  this  hypothesis  likely,  the equilibration but only  they  The  hypothesis  48 opposed.  But even these  of inadequacies,  highly flexible;  into  Most  structuralist modified, modifications  not inconsistencies per se.  i n which  i t i s imbedded a r e  a g o o d many a n a m o l o u s  c o u l d be i n c o r p o r a t e d  to ask  cannot be proven t o be  o f i t s a c t i o n s might be  concept and t h e framework  both  equili-  or falsified.  . I f one remains w i t h i n  were by P i a g e t h i m s e l f .  were t h e r e s u l t  that  i ti s appropriate  c a n be v e r i f i e d  methods, t h e p a r t i c u l a r s as  that the hypothesis  considered.  f o r m c o g n i t i v e s t r u c t u r e s may b e m o r e  whether  false,  t o be  the theory  observations  without  radically  changing i t .  One. c o u l d people  simply  do.  deny  Piaget  challenges.  t h e .entire model, which,  apparently  Besides  enjoys  h i s frequent  responding  arguments  forms o f a s s o c i a t i o n i s m and i n n a t e i s m , times  to behaviourists  learning.theorists. on  t h e same t h e m e :  made f r o m  these  These statements  many  t o such  against  he speaks  needs-reductionists  He i s a b l e  i n fact,  simple  at various and  social-  are a l l variations  t o account f o r observations  perspectives, while  account f o r a l l of h i sobservations,  they  are inadequate  and o f t e n , he  to  claims,  55  for  their  own.  Approaching  equilibration  both  generated by s t r u c t u r a l i s m ,  from w i t h i n  a n d f r o m w i t h o u t i t , we  u p a g a i n s t t h e same  question:  With  equilibration,  the concept.of  psychology fiability grounds of  into  for rejecting  an a l t e r n a t i v e  evidence this  than  to occur  this  a  theory which  concepts  the  level  of  i s able to account The o n l y o b v i o u s  which  itself,  formalization  subsumes  stands  as i n c l u d i n g  construction within  falsionly,  theory i s the existence  i s t o come u p w i t h a f o r m a l i z a t i o n on a concept  account?  brought  w o r l d where  a plausible  regard, equilibration  scientific  P i a g e t has  come  The p r i m a r y , a n d p e r h a p s  the p r e v i o u s one.  processes based In  Is there a better  t h e modern s c i e n t i f i c  becomes v e r y hazy.  left  the model  f o r more way f o r of  cognitive  equilibration.  out with other  the p o s s i b i l i t y  modern  f o r such  and t h e r e f o r e e x c l u d i n g i t a t  56  FOOTNOTES 1.  J e a n P i a g e t , The C h i l d a n d R e a l i t y , V i k i n g P r e s s , 1973), p . 146.  (New Y o r k :  2.  Jean Piaget, S t r u c t u r a l i s m , 1973), p. 59.  3.  Ibid,,  4.  Jean P i a g e t , B i o l o g y and Knowledge, (Chicago: U n i v e r s i t y o f C h i c a g o P r e s s , 1971) p . 1 2 .  5.  H a n s G. F u r t h , Prentice Hall,  6.  Theodore M i s c h e l , "Piaget: C o g n i t i v e C o n f l i c t and Motivation", i n C o g n i t i v e Development and Epistemology, e d . b y T. M i s c h e l , (New Y o r k : A c a d e m i c P r e s s , 1 9 7 1 ) , p. 3 3 2 .  (New Y o r k :  Harper  & Row,  p. 90.  P i a g e t and Knowledge, 1965), p. 1870.  (New  Jersey:  :  7.  Jean Piaget, S i x Psychological R a n d o m H o u s e , 1 9 6 7 ) , p . 6.  Studies,  (New Y o r k :  8.  J o h n F l a v e l l , " C o m m e n t s o n B e i l i n ' s 'The D e v e l o p m e n t o f P h y s i c a l C o n c e p t s ' , " o p . c i t . , T. M i s c h e l , p . 1 2 6 .  9.  Op. c i t . , P i a g e t ,  10.  Ibid.,  11.  Jean P i a g e t , Psychology and Epistemology, V i k i n g P r e s s , 1971), p. 67.  12.  Op.  13.  Ibid.,  14 .  I b i d . , p.' 1 0 .  15.  Ibid'.,  16.  Op.  17.  J e a n P i a g e t , The P s y c h o l o g y o f t h e C h i l d , B a s i c B o o k s , 1 9 6 7 ) , p. 1 1 .  18.  Op.  (1971), p. 17.  p. 32.  c i t . ,Piaget,  ( 1 9 7 3 ) , p.  (New Y o r k :  6.  p. 24.  p . 14 ^  c i t . ,Piaget,  c i t . ,Piaget,  (1971), p. 141.  (1971), p. 148.  (New Y o r k :  57  19.  Op.  Sit.,  (1970), p.  114.  20.  Jean Piaget, The Origins of Intelligence i n Children, (New York: International University Press, 1 9 5 2 ) .  21.  Ibid,,, :P: 148.  22.  Op.  23.  Jean Piaget, The Development of Thought, (New The Viking Press, 1 9 7 7 ) , p. 39.  24.  Op.  25.  Ibid., p. 26.  26.  Cf. Structuralism, and Biology, and Knowledge, pp.  27.  Op.--cit , P i a g e t ( 1 9 7 1 ) , p. 356.  28.  Op.  c i t . , Piaget,  (1967), p.  96.-  29.  Op.  c i t . , Piaget,  (1970), p.  15.'  30.  Jean Piaget, Logique et E q u i l i b r e , (Paris: Universitaires France, 1 9 5 7 ) , p. 43. Translated by present author.  31.  Cf. Inhelder and others, Etudes L'epistemologie Genetique.  32.  Op.  cat.,  Piaget,  (1977), p.  4.  33.  Op.  c i t . , Piaget,  (1970), p.  67.  34.  "Equilibrated" i s the achievement-word corresponding to the task-word, " e q u i l i b r a t i o n " . " E q u i l i b r a t i o n " i t s e l f i s sometimes used as an achievement word.  35.  Op.'cit., Piaget,  36.  Ibid., p. 19.  37 .  Ibid., p. 26.  c i t . , Piaget, X1971), p.  c i t . , Piaget,  (1971), p.  366.  York:  30.  54-60.  v  (1977),  p.  O P - c i t . , Piaget,  (1957),  Translated by present author.  39.  Op.  c i t . , Piaget,  (1970), p.  40.  Op.  c_it. , Piaget,  ( 1 9 5 7 ) , pp.  3 8  '  7.  113. 38-40.  58  41.  Op. c i t . , P i a g e t ,  (1977).  42.  Op. c i t . , P i a g e t ,  43.  Random House C o l l e g e D i c t i o n a r y , H o u s e P r e s s , 1 9 7 2 ) , p . 8 2 9 , #2.  44.  Op. c i t . , P i a g e t ,  (1967),  p. 105.  45.  Op. c i t . , P i a g e t ,  (1970),  p. 62.  46.  Op. c i t . , P i a g e t ,  (1971),  p. 338.  47.  Op. c i t . , P i a g e t ,  (1977),  p. 182.  4 8.  C f . Thomas K u h n , The S t r u c t u r e o f S c i e n t i f i c Revolutions, (Chicago: The U n i v e r s i t y o f C h i c a g o P r e s s , 1962).  49.  Jean P i a g e t ,  50.  Op. c i t . , P i a g e t ,  (1971)),  p p . 45-49 .  51.  Op. c i t . , P i a g e t ,  (1971),  p. 368.  (1970),  Introduction  p . 67 (New Y o r k :  to Furth,  op. c i t .  Random  59  BIBLIOGRAPHY  F l a v e l l , J o h n H. " C o m m e n t s o n B e i l i n ' s 'The D e v e l o p m e n t o f P h y s i c a l C o n c e p t s ' " , (pp. 121-128) i n C o g n i t i v e D e v e l o p m e n t and E p i s t e m o l o g y . e d . T. M i s c h e l , New Y o r k : Academic Press, 1971. 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New  and E p i s t e m o l o g y : Towards York: Viking Press, 1971.  a  of  60  Piaget, Jean. Random H o u s e ,  Six Psychological 196 7. Structuralism.  Studies.  Piaget, 1970.  Jean.  New  York:  Piaget, Child.  J e a n and B a r b e l I n h e i d e r . The New Y o r k : B a s i c B o o k s , 1969.  New  York:  Harper  and  P s y c h o l o g y Of  Row, the  

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