UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Transitivity, identity conservation and equivalence conservation of a solid continuous quantity Humphrey, Gary Keith 1975

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1976_A8 H84.pdf [ 3.57MB ]
Metadata
JSON: 831-1.0093773.json
JSON-LD: 831-1.0093773-ld.json
RDF/XML (Pretty): 831-1.0093773-rdf.xml
RDF/JSON: 831-1.0093773-rdf.json
Turtle: 831-1.0093773-turtle.txt
N-Triples: 831-1.0093773-rdf-ntriples.txt
Original Record: 831-1.0093773-source.json
Full Text
831-1.0093773-fulltext.txt
Citation
831-1.0093773.ris

Full Text

TRANSITIVITY, IDENTITY CONSERVATION AND EQUIVALENCE CONSERVATION OF A SOLID CONTINUOUS QUANTITY  by  GARY KEITH HUMPHREY B.A. (Hons.) U n i v e r s i t y  o f New Brunswick, 1972  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS  i n the Department of Psychology  We a c c e p t t h i s t h e s i s as conforming t o t h e required  THE  standard  UNIVERSITY OF BRITISH COLUMBIA December, 1975  In p r e s e n t i n g  this  thesis  an a d v a n c e d d e g r e e the L i b r a r y I further for  agree  scholarly  by h i s of  shall  at  the U n i v e r s i t y  make  it.freely  that permission  written  thesis  for  It  financial  of  British  2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date  X)jUtj .30  Jf  7S~  of  Columbia,  British for  gain  Columbia  shall  the  requirements  reference copying of  I agree and this  that  not  copying or  for  that  study. thesis  t h e Head o f my D e p a r t m e n t  by  is understood  of  The U n i v e r s i t y  of  for extensive  permission.  Department  fulfilment  available  p u r p o s e s may be g r a n t e d  representatives.  this  in p a r t i a l  or  publication  be a l l o w e d w i t h o u t my  ABSTRACT  An i n v e s t i g a t i o n i n t o the d i s t i n c t i o n between i d e n t i t y and  equivalence  the content  c o n s e r v a t i o n , as p r e s e n t e d  area of s o l i d continuous  by E l k i n d (1967) was  quantity.  One  examined i n  group of s u b j e c t s  r e c e i v e d the t a s k s as o u t l i n e d by E l k i n d (Group I) w h i l e another s u b j e c t s r e c e i v e d m o d i f i e d v e r s i o n s o f the t a s k s t a s k was  presented  at two  to  continuous  q u a n t i t y was  group of  Each  conservation  extreme.  In  examined i n r e l a t i o n s h i p  conservation.  The and  (Group I I ) .  l e v e l s of t r a n s f o r m a t i o n ; moderate and  a d d i t i o n t r a n s i t i v i t y of s o l i d  conservation  Grade two  assigned  sample c o n s i s t e d of 144 students.  s u b j e c t s ; 48 K i n d e r g a r t e n ,  Grade  one  H a l f of the s u b j e c t s w i t h i n each grade l e v e l were  to Group I , the o t h e r h a l f was  assigned  to Group I I .  Within  each  group h a l f of the c h i l d r e n were male and h a l f were female.  An a n a l y s i s of v a r i a n c e performed on the c o n s e r v a t i o n i n d i c a t e d t h a t i d e n t i t y and e q u i v a l e n c e The  main e f f e c t s of Group and Age  Sex x Grade was  significant.  judgment p l u s e x p l a n a t i o n was  The  c o n s e r v a t i o n were of equal  were s i g n i f i c a n t and  d i f f e r e n t procedures;  difficulty.  the i n t e r a c t i o n of  c r i t e r i o n f a c t o r of judgment o n l y v s .  found  to have a s i g n i f i c a n t e f f e c t , w i t h more  t r i a l s passed w i t h a judgment o n l y c r i t e r i o n . two  tasks  Data were s c o r e d a c c o r d i n g  to  oneyprocedure r e q u i r e d t h a t s u b j e c t s be c o n s i s t e n t  i n t h e i r answers i n each phase of the t a s k i n o r d e r  to r e c e i v e non-zero s c o r e s .  T h i s procedure employed a t h r e e - p o i n t s c a l e w i t h v a l u e s of 0, 1, and  2.  The  other procedure used a s c a l e w i t h v a l u e s r a n g i n g from 0 to 6 i n c l u s i v e . S u b j e c t s were g i v e n a p o i n t f o r each of the s i x q u e s t i o n s answered  correctly  i n the c o n s e r v a t i o n t a s k s , r e g a r d l e s s of the c o n s i s t e n c y of the answers. method w i t h  the 0, 1, and  2 s c a l e showed that' i d e n t i t y and  equivalence  The  conservation 0-6 that  were e q u a l l y  d i f f i c u l t , w h i l e the method which employed  s c a l e showed t h a t i d e n t i t y was the  of the  Furthermore i t was  from an a p p l i c a t i o n of the  l e v e l of concept  An tasks.  The  transitivity  0-6  shown t h a t  a n a l y s i s of v a r i a n c e  was  main e f f e c t s f o r Group and  in  s c a l e s c o r e s which  s c a l e were an ambiguous r e f l e c t i o n  performed on Age  the  The  implications  equivalence conservation  (1967) a n a l y s i s .  transitivity  were s i g n i f i c a n t .  t a s k s were s i g n i f i c a n t l y e a s i e r than a l l  of i d e n t i t y and  shown  attainment.  t a s k s at a l l grade l e v e l s .  Elkind's  I t was  l a t t e r method y i e l d e d these r e s u l t s because of an a r t i f a c t  the q u e s t i o n s asked. resulted  e a s i e r than e q u i v a l e n c e .  the  conservation  of t h i s and  were d i s c u s s e d  The  the  co-occurrence  i n r e l a t i o n to  T a b l e of Contents  Abstract T a b l e of Contents List  of T a b l e s  Acknowledgement Introduction  i i iv v vi 1  Method  11  Results  18  Discussion  44  Footnotes  59  References  60  Appendix A  63  V  List  of Tables  Table 1  2 3  4  5  6 7 8 9 10 11 12 13  14  15  16  Page Frequency and Percentage o f S u b j e c t s P a s s i n g t h e C o n s e r v a t i o n Tasks when a C r i t e r i o n o f Judgment Only was used.  19  Summary o f Group x Sex x Grade x Task Type x L e v e l of Transformation A n a l y s i s of Variance  21  Frequency and Percentage o f S u b j e c t s P a s s i n g t h e C o n s e r v a t i o n Tasks when a C r i t e r i o n o f Judgment P l u s E x p l a n a t i o n was Used.  23  Number o f S u b j e c t s P a s s i n g I d e n t i t y and E q u i v a l e n c e Tasks a t each Grade L e v e l when a C r i t e r i o n o f Judgment Only was Used.  26  Number o f S u b j e c t s P a s s i n g I d e n t i t y and E q u i v a l e n c e Tasks a t each Grade L e v e l when a C r i t e r i o n o f Judgment P l u s E x p l a n a t i o n was used.  27  Frequency and Percentage o f S u b j e c t s g i v i n g Adequate E x p l a n a t i o n s f o r a l l I d e n t i t y C o n s e r v a t i o n Tasks.  29  Frequency and Percentage o f S u b j e c t s g i v i n g Adequate Explanations f o r a l l Equivalence Conservation Tasks.  30  Frequency and Percentage o f S u b j e c t s g i v i n g Adequate E x p l a n a t i o n s f o r a l l C o n s e r v a t i o n Tasks.  31  Frequency and Percentage o f Tasks on which Obtained the S p e c i f i e d V a l u e s .  33  Number and Percentage T r a n s i t i v i t y Tasks.  Subjects  of S u b j e c t s P a s s i n g the Four 35  Summary o f Group x Sex x Grade x Type of T r a n s i t i v i t y Task A n a l y s i s o f V a r i a n c e .  37  Number and Percentage of S u b j e c t s P a s s i n g Only the S p e c i f i e d Number o f T r a n s i t i v i t y Tasks.  38  Number and Percentage o f S u b j e c t s P a s s i n g and F a i l i n g T r a n s i t i v i t y Tasks and I d e n t i t y C o n s e r v a t i o n Tasks ( C r i t e r i o n o f Judgment O n l y ) .  41  Number and Percentage of S u b j e c t s P a s s i n g and F a i l i n g T r a n s i t i v i t y Tasks and E q u i v a l e n c e C o n s e r v a t i o n Tasks ( C r i t e r i o n of Judgment O n l y ) .  42  Number and Percentage of S u b j e c t s P a s s i n g and F a i l i n g T r a n s i t i v i t y Tasks and A l l C o n s e r v a t i o n Tasks ( C r i t e r i o n o f Judgment O n l y ) .  43  P o s s i b l e P a t t e r n s o f Responding  54  Acknowledgement s  The author would l i k e to express his gratitude to Dr. Lou Moran and Dr. Tannis Williams for providing assistance and encouragement throughout  the project.  Tim McTiernan  Thanks are also due to Dr. Ralph Hakstian and  for advice on s t a t i s t i c a l techniques.  The author also  wishes to acknowledge the cooperation and assistance of the Vancouver School Board and the p r i n c i p a l s and teachers of G r e n f e l l and Bruce Elementary  Schools.  1.  INTRODUCTION  The  t r a d i t i o n a l c o n s e r v a t i o n t a s k was  c h i l d r e n understand  d e v i s e d to a s s e s s whether  t h a t p e r c e p t u a l deformations  of o b j e c t s do not produce  changes i n the q u a n t i t a t i v e p r o p e r t i e s of the o b j e c t s ( P i a g e t , P i a g e t and I n h e l d e r , 1974).  F o r example a b a l l of c l a y may  shape changed to t h a t of a f l a t d i s c ,  or "pancake", but  1952;  have i t s  this  leaves  q u a n t i t a t i v e p r o p e r t i e s of the o b j e c t , such as i t s mass, weight, or volume, unchanged.  In the t r a d i t i o n a l format f o r a s s e s s i n g c o n s e r v a t i o n a c h i l d i s first  shown two  o b j e c t s (e.g., A and  perceptually similar.  One  B)  that are q u a n t i t a t i v e l y  of the o b j e c t s  a perceptual transformation  (e.g., B)  (e.g., to B"'') .  and  i s then s u b j e c t e d  to  F i n a l l y the c h i l d i s asked to  make some q u a n t i t a t i v e comparison between the s t a n d a r d o r untransformed o b j e c t and  the transformed  o b j e c t ( e . g . , between A and B"*") .  c o n c r e t e terms a c h i l d might be p r e s e n t e d w i t h two i n s i z e , shape and  q u a n t i t y of c l a y .  changed to t h a t of a pancake.  The  The  I n more  clay balls  shape of one  identical  of the b a l l s i s  c h i l d i s then asked such q u e s t i o n s  Is t h e r e the same amount of c l a y i n the pancake as t h e r e i s i n the Does one have more c l a y ?  The  answers g i v e n to q u e s t i o n s  determine whether the c h i l d i s s a i d  Elkind  The  ball?  type  conserve.  (1967) p o i n t e d to c e r t a i n m e t h o d o l o g i c a l  t r a d i t i o n a l conservation task. understanding  to  of t h i s  as:  t a s k was  designed  problems i n the  to a s s e s s c h i l d r e n ' s  o f the i n v a r i a n c e of q u a n t i t a t i v e p r o p e r t i e s of o b j e c t s  across i r r e l e v a n t  perceptual transformations.  Success on the t a s k  imply  t h a t the i n v a r i a n c e i s understood,  not.  However a c c o r d i n g to E l k i n d ' s a n a l y s i s a c h i l d c o u l d f a i l  should  whereas f a i l u r e should mean i t i s the  task  2.  for  reasons o t h e r  than a f a i l u r e t o grasp t h e q u a n t i t a t i v e i n v a r i a n c e o f  objects i n this s i t u a t i o n .  A=B  A schematic example o f t h e t a s k  follows:  (The o b j e c t s a r e i n i t i a l l y e q u a l on a l l q u a n t i t a t i v e and p e r c e p t u a l dimensions)  B-^B"*" (Object B has i t s shape changed t o B"'") A?B^  The simple  (The c h i l d i s q u e s t i o n e d about t h e q u a n t i t a t i v e r e l a t i o n s h i p h o l d i n g between A and B^)  first  deductive  statement, A=B, can be viewed as the f i r s t argument.  premise i n a  The second statement can a l s o be thought o f as  a premise i n an argument such t h a t B=B^ on t h e r e l e v a n t q u a n t i t a t i v e dimension.  F i n a l l y g i v e n A=B and B=B^ then i t n e c e s s a r i l y f o l l o w s  A=B"'", hence t h e l a s t  statement can be seen as a c o n c l u s i o n .  c o u l d f a i l t h e t a s k because they f o r g o t t h e f i r s t b e l i e v e that the relevant q u a n t i t a t i v e property was  changed t o B"'".  that  Children  premise, o r because they  o f B changed when i t s shape  Even i f c h i l d r e n remember t h a t A=B and understand  B=B"'", they may n o t be a b l e t o c o o r d i n a t e  t h i s information  that  to reach the  c o n c l u s i o n t h a t A=B"'' (see E l k i n d , 1967).  That c h i l d r e n f a i l the t a s k because they f o r g e t t h e i n i t i a l e q u a l i t y o f A and B seems u n l i k e l y i n view o f B r y a n t ' s (1974) Bryant  observations.  (1974) p o i n t s out t h a t Bruner, e t a l (1966) have shown t h a t c h i l d r e n  who would n o r m a l l y display before  f a i l conservation  the transformation.  number c o n s e r v a t i o n  t a s k s Bryant  t a s k s remember t h e appearance o f t h e A l s o , using a task very  s i m i l a r to  (1972) demonstrated that c h i l d r e n who d i d  p o o r l y on these tasks performed w e l l i n a c o n t r o l c o n d i t i o n which r e q u i r e d t h a t they remember what t h e r e l a t i o n s between two rows o f counters before  a perceptual  transformation.  were  3.  A more l i k e l y reason  f o r f a i l u r e on the t r a d i t i o n a l  task,  a c c o r d i n g to E l k i n d ' s a n a l y s i s , i s that c h i l d r e n do not understand B=B"'".  T h i s , E l k i n d c l a i m s , i s r e a l l y what the t a s k was  but does so ambiguously.  I f the c h i l d r e n succeed  i n f e r r e d t h a t they understand reasons and  that  B=B"S  B"*".  on the t a s k i t can  occur f o r  technique  be  employed  t h a t q u a n t i t a t i v e p r o p e r t i e s of  s i n g l e o b j e c t s remain the same a f t e r p e r c e p t u a l t r a n s f o r m a t i o n s .  A  would be shown a s i n g l e o b j e c t , the shape of the o b j e c t would then changed and  finally  a f t e r the t r a n s f o r m a t i o n  same amount of c l a y i n t h i s pancake as t h e r e was E l k i n d has  when i t was  shaped  The  transform-  t r a d i t i o n a l t a s k measures what E l k i n d  to E l k i n d ' s a n a l y s i s a c h i l d must have the concept  to succeed  t h e r e may  like  conservation.  i d e n t i t y , as w e l l as the a b i l i t y i n order  the  r e f e r r e d to the r e c o g n i t i o n t h a t q u a n t i t a t i v e  a t i o n s as i d e n t i t y c o n s e r v a t i o n .  According  be  (e.g., I s t h e r e  p r o p e r t i e s of s i n g l e o b j e c t s remain i n v a r i a n t a c r o s s p e r c e p t u a l  c a l l s equivalence  child  the c h i l d would make a judgment about some q u a n t i t a t i v e  r e l a t i o n h o l d i n g b e f o r e and  a ball?).  be  of the r e l a t i o n between B  E l k i n d proposed t h a t a much more d i r e c t  to a s s e s s whether c h i l d r e n understand  d e v i s e d to a s s e s s ,  however f a i l u r e may  o t h e r than the c h i l d ' s u n d e r s t a n d i n g  that  to reason  of  i n a simple d e d u c t i v e manner,  on the t r a d i t i o n a l t a s k format.  be a developmental l a g between i d e n t i t y and  He  suggested  equivalence  that conser-  v a t i o n with i d e n t i t y conservation being a p r i o r c o g n i t i v e a c q u i s i t i o n . Hooper (1969b, p. 236)  argued s i m i l a r l y ; " s i n c e e q u i v a l e n c e  r e q u i r e s the a d d i t i o n a l d e d u c t i o n achievement than  identity  Hooper's study  conservation  sequence, i t should be a l a t e r c o g n i t i v e  conservation."  (1969b) was  one  of the f i r s t p u b l i s h e d r e p o r t s  4.  to provide evidence which showed that i d e n t i t y conservation occurs p r i o r to equivalence conservation.  Identity and equivalence conservation were  assessed i n the content area of discontinuous quantity ( i . e . , small seeds placed i n glass beakers).  Ninety-six subjects of mean ages 6, 7, and 8  years were used i n a between subjects design.  Hooper (1969b, p. 248)  concluded that " i d e n t i t y conservation may be viewed as a necessary but not s u f f i c i e n t prerequisite for adequate equivalence conservation performance. Further evidence that i d e n t i t y conservation precedes equivalence conservation in the area of discontinuous quantity was obtained by Hooper (1969a) i n a study of low socio-economic-status  subjects aged 5 1/2 to 6 1/2 years.  Schwarty and Scholnick (1970) investigated i d e n t i t y and equivalence conservation i n 40 children of nursery and kindergarten age.  Glasses equal  in diameter and d i f f e r i n g i n diameter were p a r t i a l l y f i l l e d with candies. Subjects were required to make d i r e c t comparisons, i d e n t i t y judgments and equivalence judgments both when the containers had the same diameter and when they d i f f e r e d .  When the glasses were of equal diameter there were no  s i g n i f i c a n t differences among i d e n t i t y judgments, equivalence judgments and direct comparisons.  However, when the containers d i f f e r e d i n diameter  i d e n t i t y judgments were easier than both equivalence judgments and d i r e c t comparisons.  Papalia and Hooper (1971) worked with 60 subjects at ages 4, 5 and 6 years.  Each subject was given a battery of tasks designed to measure  q u a l i t a t i v e i d e n t i t y , quantitative i d e n t i t y and equivalence conservation of discontinuous quantity and number.  I t should be noted that q u a l i t a t i v e  i d e n t i t y d i f f e r s from the notion of i d e n t i t y ( i . e . , quantitative) developed by Elkind.  Qualitative i d e n t i t y refers to a c h i l d ' s recognition that i t i s  5. the same c l a y even though i t s shape has been changed; t h i s does not mean t h a t the c h i l d n e c e s s a r i l y b e l i e v e s t h a t i t i s the same amount. depends upon the concept 1975;  of q u a n t i t a t i v e i d e n t i t y  Hooper, 1969b; P a p a l i a and Hooper, 1971,  i d e n t i t y concepts were found  to develop  c o n c e p t s , which i n t u r n developed a r e a of d i s c o n t i n u o u s q u a n t i t y .  latter  (see B r a i n e r d and Hooper,  P i a g e t , 1968).  Qualitative  p r i o r to q u a n t i t a t i v e i d e n t i t y  p r i o r to e q u i v a l e n c e concepts There was  i n the  no c o n c l u s i v e evidence  the o r d e r of emergence of the v a r i o u s number  E l k i n d and S c h o e n f e l d  The  regarding  concepts.  (1972) used 22 f o u r year o l d s and  22 s i x  year o l d s to i n v e s t i g a t e the problem i n the content areas of l e n g t h , l i q u i d , mass and number. was  T h e i r g e n e r a l c o n c l u s i o n was  e a s i e r than e q u i v a l e n c e c o n s e r v a t i o n but  that i d e n t i t y  conservation  the d i f f e r e n c e was  most  pronounced i n the; younger c h i l d r e n .  B r a i n e r d and Hooper (1975) i n v e s t i g a t e d the i d e n t i t y i s s u e w i t h 60 f o u r year o l d s , 60 s i x year o l d s and s u b j e c t s were g i v e n i d e n t i t y and e q u i v a l e n c e l e n g t h and weight.  I d e n t i t y was  e s p e c i a l l y a t the lower  age  60 e i g h t year o l d s .  t a s k s i n the content areas  a c q u i r e d p r i o r to e q u i v a l e n c e  levels.  equivalence  of  conservation,  In a s i m i l a r study T o n i o l o and Hooper  (1975) i n v e s t i g a t e d the i d e n t i t y - e q u i v a l e n c e i s s u e i n the content areas l e n g t h and w e i g h t .  All  of  I n a d d i t i o n to t h e t a s k s from the B r a i n e r d and Hooper  (1975) study t a s k s measuring t r a n s i t i v i t y of l e n g t h and weight were g i v e n t o 60 f o u r y e a r o l d s , 60 s i x y e a r o l d s and supported  60 e i g h t y e a r o l d s .  the n o t i o n t h a t i d e n t i t y i s a c q u i r e d p r i o r to  The  results  equivalence  conservation.  The  r e s u l t s o f o t h e r s t u d i e s have f a i l e d to p r o v i d e support f o r  the developmental  p r i o r i t y of i d e n t i t y over e q u i v a l e n c e  conservation.  6. Northman and Gruen (1970) d i d n o t o b t a i n the h y p o t h e s i z e d liquid  q u a n t i t y i n 60 second and t h i r d g r a d e r s .  presented  Moynahan and G l i c k (1972)  96 k i n d e r g a r t e n and f i r s t - g r a d e c h i l d r e n w i t h  equivalence  t a s k s i n v o l v i n g number, l e n g t h , continuous  I d e n t i t y preceded e q u i v a l e n c e  sequence f o r  i d e n t i t y and q u a n t i t y and weight.  o n l y under l e n g t h t r a n s f o r m a t i o n s .  number, q u a n t i t y and weight t a s k s i d e n t i t y and e q u i v a l e n c e were found  to co-occur.  Murray  (1970) f a i l e d  On the  conservation  to f i n d the developmental  sequence w i t h 33 k i n d e r g a r t e n and f i r s t - g r a d e s u b j e c t s i n the content areas o f weight and number.  F i n a l l y , Koshinsky and H a l l  (1973) used 72  k i n d e r g a r t e n and second-grade s u b j e c t s i n an experiment r e p l i c a t i n g Hooper's study  (1969b) w i t h  They f a i l e d  the e x c e p t i o n t h a t a w i t h i n s u b j e c t d e s i g n was used.  t o f i n d the sequence.  As noted  above, a c c o r d i n g t o E l k i n d ' s a n a l y s i s , the main  f o r f a i l u r e on the e q u i v a l e n c e concept  o r the i n a b i l i t y  (1972) have suggested  t a s k s would be the l a c k of t h e i d e n t i t y  t o make t r a n s i t i v e i n f e r e n c e s .  t h a t the reason  sequence i s t h a t the a b i l i t y  Moynahan and G l i c k  f o r t h e i r n o t f i n d i n g evidence  t h a t the i d e n t i t y and e q u i v a l e n c e  t a s k s were of equal d i f f i c u l t y , even though the e q u i v a l e n c e  the a b i l i t y  and Trabasso  S i m i l a r l y , Northman and Gruen (1970) proposed t h a t  f o r i d e n t i t y c o n s e r v a t i o n , hence i d e n t i t y and  tasks are of equal d i f f i c u l t y .  F u r t h e r , the r e s e a r c h o f Bryant  (1971) i m p l i e s t h a t c h i l d r e n as young as f o u r y e a r s o f age,  which i s below the u s u a l age f o r attainment  o f c o n s e r v a t i o n , can make  t r a n s i t i v e inferences i n v o l v i n g length provided support.  t a s k has an  t o make t r a n s i t i v e i n f e r e n c e s o c c u r s a t about t h e same time as  the o p e r a t i o n s n e c e s s a r y equivalence  o f the  t o make t r a n s i t i v e i n f e r e n c e s was so r e a d i l y  a v a i l a b l e t o the s u b j e c t s i n t h e i r study  i n f e r e n c e requirement.  reasons  they a r e g i v e n memory  7. Brainerd  (1973) has reviewed P i a g e t ' s t h e o r e t i c a l  r e g a r d i n g the o r d e r o f emergence o f t r a n s i t i v i t y , conservation  ( i . e . , equivalence).  position  c l a s s i f i c a t i o n and  A c c o r d i n g t o B r a i n e r d i t i s not a t a l l  c l e a r what p r e d i c t i o n s s h o u l d be d e r i v e d from the v a r i o u s statements made by P i a g e t c o n c e r n i n g t r a n s i t i v i t y  and c o n s e r v a t i o n .  H i s w r i t i n g s can be  i n t e r p r e t e d as p r e d i c t i n g t h a t (a) c o n s e r v a t i o n and t r a n s i t i v i t y emerge s y n c h r o n o u s l y developmentally.  o r , (b) c o n s e r v a t i o n s h o u l d precede  should  transitivity  B r a i n e r d has a l s o reviewed t h e c o n t r a d i c t o r y r e s u l t s  c o n c e r n i n g t h e o r d e r o f emergence o f these two concepts. a t t e n t i o n t o the m e t h o d o l o g i c a l i n s e n s i t i v i t i e s  He draws  i n many o f the t r a n s i t i v i t y  t a s k s used t o assess the order o f emergence o f these two c o n c e p t s . d a t a support  H i s own  t h e o r d e r o f emergence as b e i n g t r a n s i t i v i t y p r i o r t o conser-  vation.  If i t i s true that t r a n s i t i v i t y  emerges p r i o r t o e q u i v a l e n c e  c o n s e r v a t i o n i n a l l or most content a r e a s , then p r o v i d e d t h a t E l k i n d ' s a n a l y s i s i s a c c e p t e d , s e v e r a l q u e s t i o n s r e g a r d i n g t h e r e s u l t s o f the s t u d i e s supporting the p r i o r i t y raised.  o f i d e n t i t y over e q u i v a l e n c e c o n s e r v a t i o n can be  The problems a r e concerned w i t h the order o f a c q u i s i t i o n o f  transitivity  and i d e n t i t y c o n s e r v a t i o n .  The s p e c i f i c  problem which formed  the b a s i s o f the p r e s e n t study was the o r d e r o f a c q u i s i t i o n o f t r a n s i t i v i t y , i d e n t i t y c o n s e r v a t i o n and e q u i v a l e n c e c o n s e r v a t i o n .  I t was reasoned t h a t i f  t r a n s i t i v i t y p r e c e d e s e q u i v a l e n c e c o n s e r v a t i o n as B r a i n e r d (1973) i n d i c a t e s and  i f i d e n t i t y precedes e q u i v a l e n c e c o n s e r v a t i o n then t r a n s i t i v i t y would  develop p r i o r t o , c o n c u r r e n t w i t h , o r a f t e r i d e n t i t y c o n s e r v a t i o n . were found  that t r a n s i t i v i t y  develops p r i o r t o or c o n c u r r e n t w i t h  c o n s e r v a t i o n then i t would be n e c e s s a r y conservation i s a l a t e r  If i t identity  t o q u e s t i o n whether e q u i v a l e n c e  c o g n i t i v e a c q u i s i t i o n than i d e n t i t y c o n s e r v a t i o n ,  8. for  a c c o r d i n g to E l k i n d ' s a n a l y s i s (1967) i t i s the l a c k of the  reasoning  a b i l i t y which accounts  equivalence  task.  questioned.  f o r f a i l u r e on the t r a d i t i o n a l  I f , however, t h i s i s p r e s e n t  pass i d e n t i t y and  fail  as a s k i l l  Indeed the o n l y o r d e r of emergence t h a t would be  p r i o r to e q u i v a l e n c e  the evidence which suggests  t h a t the r e a s o n  conservation.  f o r f a i l u r e on t h e e q u i v a l e n c e  may  by e m p i r i c a l  There may t a s k s and  transitivity  to form  transitive  on a l l t h r e e t a s k s  this  tasks.  f o r a s u b j e c t to pass i d e n t i t y  According  to P i a g e t a v e r y  f a c t o r i n the assessment of c o n s e r v a t i o n i s t h a t of p e r c e p t u a l P i a g e t b e l i e v e s t h a t f o r c o n s e r v a t i o n to be assessed  important conflict.  properly there  should  be a c o n f l i c t between the s u b j e c t ' s immediate p e r c e p t u a l e x p e r i e n c e s his  i n t e l l e c t u a l operations.  other.  t h a t one  o b j e c t may  Inhelder  sufficiently  correctly  they  from  the  understand  the same amount to b e g i n w i t h , they s t i l l have the  same amount i f only the shape of one and  look  appear q u a n t i t a t i v e l y d i f f e r e n t  However, i f the c h i l d r e n a r e r e a s o n i n g  t h a t i f the o b j e c t s had  and  Thus i n the t r a d i t i o n a l assessment format  the o b j e c t s , a f t e r a p e r c e p t u a l t r a n s f o r m a t i o n , may different  task  evidence.  however be o t h e r reasons  f a i l equivalence  develops  t a s k , when the i d e n t i t y  i f a l l s u b j e c t s have been assessed  be supported  congruent  Then i t c o u l d be argued  has been passed s u c c e s s f u l l y , i s the l a c k of the a b i l i t y i n f e r e n c e s and  who  seriously  identity  i s t h a t i d e n t i t y c o n s e r v a t i o n precedes  which i n t u r n precedes e q u i v a l e n c e  or  i n subjects  e q u i v a l e n c e E l k i n d ' s a n a l y s i s should be  w i t h E l k i n d ' s a n a l y s i s and  transitive  (1974, p. 10)  of the o b j e c t s has been changed.  Piaget  s t a t e "the problem of c o n s e r v a t i o n r e f l e c t s a  c o n f l i c t between d i r e c t e x p e r i e n c e  or p e r c e p t i o n s and  rational  operations".  It  i s c l e a r that t h i s c o n f l i c t  s h o u l d be p r e s e n t w i t h i n the t a s k  in  o r d e r to p r o v i d e a measure of c o n s e r v a t i o n as P i a g e t c o n c e i v e s  situation it.  In  9.  another two  p l a c e he s t a t e s "the d i r e c t and  i d e n t i c a l g l a s s e s , one r e m a i n i n g  p. 533).  The  from a s i n g l e r e c e p t o r i n t o  as such may  the e q u i v a l e n c e  remove a source task.  and  untransformed  stimulus  of d i f f i c u l t y encountered by s u b j e c t s i n  T h i s c o u l d a l s o account f o r the d i f f e r e n c e between  the developmental a c q u i s i t i o n of i d e n t i t y and e q u i v a l e n c e  The  others"  i d e n t i t y t a s k , as d e s c r i b e d p r e v i o u s l y , removes  t h i s p e r c e p t u a l c o n f l i c t between the transformed and  conservation.  r o l e of p e r c e p t u a l c o n f l i c t has been f u r t h e r emphasized  P i a g e t i n the case of c h i l d r e n i n a t r a n s i t i o n a l stage of acquisition.  from  untouched as a means of comparison i s  not the same t h i n g as p o u r i n g a l i q u i d ( P i a g e t , 1967,  immediate p o u r i n g of a l i q u i d  by  conservation  A s m a l l p e r c e p t u a l change i n the transformed  o b j e c t may  not  produce the same amount of p e r c e p t u a l c o n f l i c t as would a more extreme transformation.  P i a g e t and  Inhelder  (1974, p. 12)  s t a t e , i n the c o n t e x t  d i s c u s s i n g c h i l d r e n i n a t r a n s i t i o n a l s t a t e of c o n s e r v a t i o n that " i n small s c a l e transformations  as the deformations  acquisition  the c h i l d ' s mind can surmount  p e r c e p t i b l e appearances thanks to a grasp  the  of the o p e r a t i o n s , but as soon  go beyond a c e r t a i n l i m i t , d i r e c t  p r e v a i l over o p e r a t i o n a l i n t e l l i g e n c e and  of  i n t u i t i o n comes to  conservation i s again c a l l e d  into  question".  The p r e s e n t  study was  importance of the l o g i c a l  undertaken to d e l i n e a t e the  ( a c c o r d i n g to E l k i n d ' s a n a l y s i s ) and  components i n the s o l u t i o n of i d e n t i t y and The  o r d e r of emergence of t r a n s i t i v i t y ,  v a t i o n was  assessed  i d e n t i t y and  i n the content  equivalence  to E l k i n d ' s a n a l y s i s , and  relative  equivalence  i d e n t i t y and  a r e a of continuous  t a s k s were p r e s e n t e d  perceptual  conservation  equivalence  tasks.  conser-  s o l i d quantity.  as o u t l i n e d above w i t h  i n a d d i t i o n a m o d i f i e d v e r s i o n of each t a s k  The regard was  10. given.  Thus there were two i d e n t i t y  tasks, one with perceptual c o n f l i c t  absent and one with this c o n f l i c t present.  Similarly there were two  equivalence tasks, one with the c o n f l i c t absent and one with i t present. Each of the conservation tasks was administered under a "moderate" and an "extreme" degree of perceptual transformation.  11.  METHOD Sub.j e c t s  S u b j e c t s were drawn from k i n d e r g a r t e n , f i r s t in  s c h o o l s l o c a t e d i n a b r o a d l y lower middle  were 24 males and 24 females and  two f i r s t  and second  grade  c l a s s neighbourhood.  a t each grade l e v e l .  There  Four k i n d e r g a r t e n e r s  graders had t o be r e p l a c e d because o f f a i l u r e on t h e p r e t e s t .  The mean ages f o r the K i n d e r g a r t e n , Grade one and Grade two groups were 5 y e a r s , 11 months (S.D.= 4 months), 6 y e a r s , 10 months (S.D.= 4 months), and  7 y e a r s , 10 months (S.D.= 5 months) r e s p e c t i v e l y .  A t o t a l o f 144 s u b j e c t s  completed the study.  Materials  Blue c l a y b a l l s ;  ( p l a y dough) were used t o a s s e s s c o n s e r v a t i o n and  both b l u e and r e d b a l l s o f c l a y were used t o assess t r a n s i t i v i t y . b a l l s and y e l l o w b a l l s were used i n the p r e t e s t . d i s p l a y e d approximately  White  The m a t e r i a l s were  i n t h e c e n t e r o f a sheet o f white cardboard  cm. which was on a s m a l l r e c t a n g u l a r wooden t a b l e .  81 x 61  Two s m a l l p l a s t i c bowls  one y e l l o w and one r e d , were a l s o used i n t h e t r a n s i t i v i t y t a s k s .  Only  those m a t e r i a l s i n use d u r i n g any p a r t i c u l a r t a s k were i n the s u b j e c t ' s sight.  Procedure  Each c h i l d was taken i n d i v i d u a l l y  t o the e x p e r i m e n t a l  room and was  s e a t e d a t t h e s m a l l r e c t a n g u l a r t a b l e o p p o s i t e the experimenter. experimenter  The  d e s c r i b e d t h e s i t u a t i o n as a game i n which some q u e s t i o n s about  c l a y b a l l s would be asked.  12. In a d d i t i o n to the e q u i v a l e n c e t a s k o u t l i n e d by E l k i n d  (1967) , a  m o d i f i c a t i o n of the e q u i v a l e n c e t a s k s i m i l a r to Hooper's (1969b) e q u i v a l e n c e I t a s k was  used.  established.  In t h i s t a s k the i n i t i a l  Then p r i o r to any  the s t a n d a r d s t i m u l u s was  e q u a l i t y of the two  c o n s e r v a t i o n q u e s t i o n s or  objects  transformations  removed from the s u b j e c t ' s s i g h t .  T h i s made the  t a s k comparable to the i d e n t i t y t a s k d e s c r i b e d above i n terms of both memory requirements Although  removed the l o g i c a l requirements t a s k s s h o u l d have been the same.  (as c o n c e i v e d by P i a g e t )  f o r the proper The  t r a d i t i o n a l t a s k was  the m o d i f i e d t a s k as e q u i v a l e n c e  a l s o i n c l u d e d i n the p r e s e n t study.  comparison o b j e c t which was  was  r e f e r r e d to as  B.  c o n f l i c t s i n c e t h e r e were two  In t h i s m o d i f i e d t a s k a standard  i n the s u b j e c t ' s view d u r i n g the course  of  The m o d i f i e d t a s k i n t r o d u c e d p e r c e p t u a l  o b j e c t s , one  formed, i n the s u b j e c t ' s f i e l d of view. i d e n t i c a l to the t r a d i t i o n a l  transformed  the o t h e r  ( e q u i v a l e n c e A) c o n s e r v a t i o n t a s k .  f o r proper  r e f e r r e d t o as i d e n t i t y B and t h e  t a s k d e s c r i b e d by E l k i n d as i d e n t i t y  identity  A.  Each of the c o n s e r v a t i o n t a s k s was t r a n s f o r m a t i o n , moderate and  However  other  t a s k i t s h o u l d not have r e q u i r e d the d e d u c t i v e a b i l i t y The m o d i f i e d t a s k was  untrans-  T h i s made the t a s k p e r c e p t u a l l y  s i n c e the q u e s t i o n s asked were the same as those asked i n the  solution.  (1967)  A l l q u e s t i o n s asked were i d e n t i c a l to those asked  i n the o t h e r i d e n t i t y c o n d i t i o n .  identity  equivalence  q u a n t i t a t i v e l y and p e r c e p t u a l l y i d e n t i c a l to  the o b j e c t to be transformed the t a s k p r e s e n t a t i o n .  was  s o l u t i o n of the two  A m o d i f i c a t i o n o f the i d e n t i t y t a s k as o u t l i n e d by E l k i n d was  the  and the p e r c e p t u a l i n f o r m a t i o n a v a i l a b l e to the s u b j e c t .  the source of p e r c e p t u a l c o n f l i c t  e q u i v a l e n c e A and  was  extreme.  b a l l used i n a l l c o n s e r v a t i o n t a s k s was  The  p r e s e n t e d under two  l e v e l s of  c r o s s s e c t i o n a l diameter of the  4.45  cm.  Under the moderate  13. t r a n s f o r m a t i o n t h e b a l l was f l a t t e n e d changing 6.35  cm.;  t h i s was r e f e r r e d t o as a " f a t c o o k i e " .  i n t o a "pancake" w i t h a diameter transformation. preceded  t h e diameter  of approximately  to approximately  The b a l l was p r e s s e d 14 cm. under the extreme  In a l l c o n s e r v a t i o n t a s k s t h e moderate t r a n s f o r m a t i o n  t h e extreme.  Four t a s k s were g i v e n t o each s u b j e c t t o a s s e s s t h e i r a b i l i t y to form t r a n s i t i v e i n f e r e n c e s .  The t a s k s can be d e s c r i b e d i n schematic  form  u s i n g t h e symbol ">" to stand f o r more c l a y and "=" to stand f o r the same amount o f c l a y .  Each o f t h e t a s k s i n v o l v e d t h r e e b a l l s o f c l a y and can be  s c h e m a t i c a l l y r e p r e s e n t e d as f o l l o w s : and  (D) A>B>C.  and Y o u n i s s  (A) A=B=C, (B) A>B=C, and (C) A=B>C,  These t a s k s were s i m i l a r t o some o f t h e tasks used by Murray  (1968), Y o u n i s s  and Murray (1970) and B r a i n e r d  (1973).  In a d d i t i o n t o t h e t a s k s d e s c r i b e d above a p r e t e s t was g i v e n t o each s u b j e c t i n o r d e r t o a s s e s s u n d e r s t a n d i n g  o f t h e r e l a t i o n a l terms more,  l e s s and same amount.  The  c h i l d r e n were d i v i d e d i n t o two groups:  p r e t e s t , the four t r a n s i t i v i t y  Group I r e c e i v e d the  t a s k s and i d e n t i t y A and e q u i v a l e n c e A under  b o t h t h e moderate and extreme t r a n s f o r m a t i o n s .  Group I I r e c e i v e d t h e p r e t e s t ,  the f o u r t r a n s i t i v i t y t a s k s and i d e n t i t y B and e q u i v a l e n c e B under both of t r a n s f o r m a t i o n . tivity  levels  The o r d e r i n which t h e i d e n t i t y , e q u i v a l e n c e and t r a n s i -  t a s k s o c c u r r e d was f u l l y randomized a c r o s s s u b j e c t s .  Pretest  There were f o u r d i f f e r e n t  tasks i n the p r e t e s t .  d i f f e r i n g i n s i z e were used i n each o f t h e f i r s t  Two b a l l s o f c l a y  two p r e s e n t a t i o n s .  The  degree o f d i f f e r e n c e i n t h e amount o f c l a y between the.two b a l l s was l e s s i n  14.  the second presentation than i n the f i r s t . questions:  Subjects were asked the following  (1) Do these two b a l l s of clay have the same amount of clay, do  they each have just as much?  (2) Does one have more clay? (3) Which one  has more clay? (The subject was instructed to point.)  (4) Does one have  less clay? (5) Which one has less clay?  The t h i r d part of the pretest involved three b a l l s of clay d i f f e r i n g in size.  The questions asked were: (1) Do these three b a l l s a l l have the  same amount of clay, do they each have just as much? (2) Does one b a l l have more clay than the other two? (3) Which one? (4) Does one b a l l have less clay than the other two? (5) Which one?  The fourth part of the pretest involved four b a l l s of clay, two d i f f e r i n g i n size and two i d e n t i c a l .  The only question asked of the subject  was: (1) Which two of these four b a l l s look l i k e they have the same amount of clay? Conservation  Tasks  Each of the conservation tasks included three phases: prediction, judgment and explanation.  (See Brainerd & Brainerd, 1972; Brainerd & Hooper,  1975; and Elkind, 196L)  Identity A.  One blue b a l l of clay was placed on the white card-  board i n front of the subject.  In the prediction phase the experimenter  asked the following questions:  (1) I f I press this b a l l into the shape of  a f a t cookie  (pancake) w i l l i t have the same amount of clay as i t has now?  (2) W i l l i t have more clay than i t has now? (3) W i l l i t have less clay than i t has now?  In the judgment phase the b a l l was transformed and the subject  was asked: (1) Does this f a t cookie  (pancake) have the same amount of clay  15. as i t had when i t was than i t had b e f o r e ?  shaped l i k e a b a l l ?  (2) Does i t have more c l a y  (3) Does i t have l e s s c l a y now  than i t had  now  before?  (The o r d e r of the q u e s t i o n s i n v o l v i n g the terms more, l e s s and  same was  randomized f o r the p r e d i c t i o n and judgment phase of a l l c o n s e r v a t i o n t a s k s . ) Finally  the c h i l d was  by answering How  asked  the q u e s t i o n s :  do you know i t has  I d e n t i t y B.  do you  say i t has  the q u a n t i t a t i v e  e s t a b l i s h e d by h a v i n g the c h i l d agree  the same amount of c l a y .  those asked  equivalence  t h a t the  two  A l l of the q u e s t i o n s were i d e n t i c a l to  i n the i d e n t i t y A t a s k .  E q u i v a l e n c e A.  Two  b a l l s were p l a c e d on t h e w h i t e cardboard  t h e i r i n i t i a l q u a n t i t a t i v e e q u i v a l e n c e was  c h i l d agree  i d e n t i c a l to that  c l a y b a l l s were i n the s u b j e c t ' s  A l s o , b e f o r e the q u e s t i o n s were asked  b a l l s had  (more, l e s s o r the same)?  (more, l e s s , or the same)?  f o r the f a c t t h a t two  of the two b a l l s was  and  Why  The p r e s e n t a t i o n of t h i s t a s k was  of i d e n t i t y A except view.  to e x p l a i n h i s / h e r answer to the judgment phase  t h a t the two b a l l s had  d i c t i o n phase the experimenter  e s t a b l i s h e d by h a v i n g  the same amount of c l a y .  asked:  (E p o i n t e d  this ball  to standard) have the same amount of c l a y as the f a t c o o k i e  the  In the p r e -  (1) I f I p r e s s t h i s b a l l  to one of the b a l l s ) i n t o a f a t c o o k i e (pancake) w i l l  sheet  (E p o i n t e d  (pancake)?  (2) W i l l one of them have more c l a y ? (3) W i l l one of them have l e s s c l a y ? Then i n the judgment phase one b a l l was q u e s t i o n s were asked:  (1) Do  transformed  the b a l l and  and  the f a t c o o k i e  the f o l l o w i n g (pancake) have  the same amount of c l a y ? (2) Does one have more? (3) Does one have l e s s ? Finally  the c h i l d r e n were r e q u i r e d t o e x p l a i n t h e i r responses  the q u e s t i o n s :  Why  do you say t h a t one has  by  answering  (more, l e s s or the same amount)?  16.  E q u i v a l e n c e B. sheet and  their  initial  phase began one b a l l was q u e s t i o n s were asked to  the b a l l behind  Two  b a l l s were p l a c e d on the white  e q u i v a l e n c e was  established.  cardboard  B e f o r e the  p l a c e d out of s i g h t behind a s c r e e n .  as i n e q u i v a l e n c e A except  prediction  The  same  t h a t r e f e r e n c e was  made  the s c r e e n when n e c e s s a r y .  Transitivity. then t o l d  Two  The  c h i l d was  had  the same amount ( i n cases  balls  A and B were f i r s t  t h a t one b a l l (A) and  p l a c e d on the  (E p o i n t e d t o A which was (C) of the t r a n s i t i v i t y  table.  always  tasks  d e s c r i b e d above) or more ( i n the cases of (B) and  (D) d e s c r i b e d above)  than the o t h e r b a l l B which was  red b a l l  always b l u e .  put under a s m a l l y e l l o w or red bowl. p l a c e d on the t a b l e and amount  ( i n cases  (A) and  the c h i l d was  The  Another red b a l l told  (B) or more than C ( i n cases  then p l a c e d under the o t h e r bowl and B was f o l l o w i n g q u e s t i o n s were then asked:  (C) was  (C) and  (1) Do  the b a l l s  one?  (3) Which one?  The q u e s t i o n s were asked  then  (D)).  under the  the same C  was  The two  as much?  (4) Does one have l e s s ?  i n different  then  (B) had  removed from s i g h t .  bowls have the same amount of c l a y , do they each have j u s t (2) Does one have more?  (A) was  t h a t the b l u e b a l l  red)  (5) Which  orders.  Scoring  Pretest. their  S u b j e c t s were g i v e n a s c o r e of 1 or 0 depending on  answers t o each of the q u e s t i o n s asked  d u r i n g the p r e t e s t .  t h e r e were 16 q u e s t i o n s i n t o t a l the maximum s c o r e was who  s c o r e d 15 or 16 were a l l o w e d to proceed  i n the  16.  study.  Since  Only s u b j e c t s  17. Conservation. and  Three q u e s t i o n s were asked i n t h e p r e d i c t i o n phase  t h r e e q u e s t i o n s were asked i n t h e judgment phase.  c o r r e c t on a l l t h r e e q u e s t i o n s s c o r e o f 1, s i m i l a r l y  I f a c h i l d was  i n t h e p r e d i c t i o n phase he/she was g i v e n a  i f a c h i l d was c o r r e c t on a l l t h r e e q u e s t i o n s  judgment phase he/she was g i v e n a s c o r e o f 1.  These s c o r e s c o u l d then be  added t o g i v e a composite s c o r e f o r both phases. on both phases o b t a i n e d  i n the  C h i l d r e n who were c o r r e c t  a s c o r e of 2, c h i l d r e n c o r r e c t on o n l y one phase  o b t a i n e d a s c o r e o f 1, and c h i l d r e n i n c o r r e c t on b o t h phases were g i v e n a s c o r e o f 0.  When c h i l d r e n ' s s c o r e s depended o n l y on t h e p r e d i c t i o n and  judgment phases t h e s c o r e s were s a i d  t o be based on a judgment o n l y  criterion.  When a judgment p l u s e x p l a n a t i o n c r i t e r i o n was used a c h i l d was g i v e n a s c o r e o f 2 i f he/she was c o r r e c t on b o t h p r e d i c t i o n and judgment phases and gave an e x p l a n a t i o n which c o u l d be p l a c e d i n an a c c e p t a b l e c a t e g o r y (see Appendix A ) .  I f a c h i l d was c o r r e c t on both t h e p r e d i c t i o n and judgment  phases, b u t gave an inadequate A l l e x p l a n a t i o n s were tape  Transitivity. all  questions  e x p l a n a t i o n he/she r e c e i v e d a s c o r e o f 1.  recorded.  C h i l d r e n were g i v e n a s c o r e o f 1 i f they  c o r r e c t l y ; otherwise  they r e c e i v e d a s c o r e o f 0.  answered  18. Results  Conservation  The  frequency  and p e r c e n t a g e of s u b j e c t s p a s s i n g the v a r i o u s  c o n s e r v a t i o n t a s k s on the b a s i s of a judgment o n l y c r i t e r i o n i s g i v e n i n T a b l e 1.  I t i s apparent t h a t w h i l e v e r y few K i n d e r g a r t e n  s u b j e c t s passed  the t a s k s c o n s i d e r a b l y more Grade 1 and Grade 2 c h i l d r e n were s u c c e s s f u l . It  i s a l s o e v i d e n t from T a b l e 1 t h a t c h i l d r e n r e c e i v i n g the i d e n t i t y  as o u t l i n e d by E l k i n d (1967) and  the t r a d i t i o n a l c o n s e r v a t i o n t a s k  task  (Group  I) performed b e t t e r on a l l c o n s e r v a t i o n t a s k s than those c h i l d r e n who r e c e i v e d the m o d i f i e d  tasks  (Group I I ) .  There was  very l i t t l e d i f f e r e n c e  i n the number of s u b j e c t s p a s s i n g i d e n t i t y t a s k s and w i t h i n each group.  Twenty-seven s u b j e c t s i n Group I passed the  task under both l e v e l s of t r a n s f o r m a t i o n and t a s k s under both l e v e l s of t r a n s f o r m a t i o n . both  equivalence  i d e n t i t y t a s k s and  Conservation  27 passed the  tasks identity  equivalence  In Group. I I 13 s u b j e c t s passed  16 passed b o t h e q u i v a l e n c e  tasks.  t a s k s c o r e s were s u b j e c t e d to a 2x2x3x2x2 a n a l y s i s  of v a r i a n c e i n which the v a r i a b l e s were Group (Group I , Group I I ) , Sex, Age  ( K i n d e r g a r t e n , Grade 1, Grade 2 ) , Task Type ( I d e n t i t y , E q u i v a l e n c e )  and T r a n s f o r m a t i o n  level  (Moderate, Extreme).  As can be seen from T a b l e  2 the o n l y main e f f e c t s to r e a c h s i g n i f i c a n c e were Group (F=6.02; df=l,132, _p_<.025) and Age i n Group I was Duncan's New  (F=11.92; df.=2,132; £.<.001).  The mean s c o r e f o r c h i l d r e n  s i g n i f i c a n t l y g r e a t e r than the mean s c o r e f o r Group I I .  M u l t i p l e Range S t a t i s t i c  i n d i c a t e d t h a t o n l y the d i f f e r e n c e  between the s c o r e s of c h i l d r e n i n k i n d e r g a r t e n and significant  (p_<.05).  significance.  No  Grade 2 were  o t h e r age d i f f e r e n c e s reached  statistically  statistical  TABLE 1 Frequency and Percentage of S u b j e c t s P a s s i n g the C o n s e r v a t i o n Tasks when a C r i t e r i o n o f Judgment Only was Used.  IDENTITY Moderate Group I Kindergarten Males Females Combined  No  %  2 (16.7) 1 ( 8.3) 3 (12.5)  EQUIVALENCE  Extreme No  %  2 (16.7) 1 ( 8.3) 3 (12.5)  Moderate No  %  1 ( 8.3) 3 (25.0) 4 (16.7)  Extreme No  %  2 (16.7) 2 (16.7) 4 (16.7)  IDENTITY  EQUIVALENCE  Moderate & Extreme  Moderate & Extreme  No,  %  2 (16.7) 0 ( 0.0) 2 ( 8.3)  No  %  1 ( 8.3) 1 ( 8.3) 2 ( 8.3)  Grade 1 Males Females Combined  8 (66.7) 7 (58.3) 15 (62.5)  9 (75.0) 7 (58.3) 16 (66.7)  8 (66.7) 6 (50.0) 14 (58.3)  8 (66.7) 7 (58.3) 15 (62.5)  8 (66.7) 7 (58.3) 15 (62.5)  8 (66.7) 6 (50.0) 14 (58.3)  Grade 2 Males Females Combined  4 (33.3) 7 (58.3) 11 (45.8)  5 (41.7) 8 (66.7) 13 (54.2)  5 (41.7) 7 (58.3) 12 (50.0)  4 (33.3) 9 (75.0) 13 (54.2)  4 (33.3) 6 (50.0) 10 (41.7)  4 (33.3) 7 (58.3) 11 (45.8)  Group I T o t a l Males Females Combined  14 (38.9) 15 (41.7) 29 (40.3)  16 (44.4) 16 (44.4) 32 (44.4)  14 (38.9) 16 (44.4) 30 (41.7)  14 (38.9) 18 (50.0) 32 (44.4)  14 (38.9) 13 (36.1) 27 (37.5)  13 (36.1) 14 (38.9) 27 (37.5)  TABLE 1  (cont'd)  IDENTITY  EQUIVALENCE  Moderate  Extreme  No.  No  %  Group I I  %  Moderate No  Extreme  %  No  %  IDENTITY  EQUIVALENCE  Moderate & Extreme  Moderate & Extreme  No  %  No,  %  Kindergarten Males Females Combined  1 ( 8.3) 0 ( 0.0) 1 ( 4.2)  2 (16.7) 0 ( 0.0) 2 ( 8.3)  0 ( 0.0) 0 (0.0) 0 ( 0.0)  1 ( 8.3) 2 (16.7) 3 (12.5)  1 ( 8.3) 0 ( 0.0) 1 ( 4.2)  0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  Grade 1 Males Females Combined  2 (16.7) 3 (25.0) 5 (20.8)  3 (25.0) 2 (16.7) 5 (20.8)  3 (25.0) 2 (16.7) 5 (20.8)  3 (25.0) 2 (16.7) 5 (20.8)  2 (16.7) 2 (16.7) 4 (16.7)  3 (25.0) 1 ( 8.3) 4 (16.7)  Grade 2 Males Females Combined  3 (25.0) 5 (41.7) 8 (33.3)  4 (33.3) 7 (58.3) 11 (45.8)  4 (33.3) 8 (66.7) 12 (50.0)  4 (33.3) 9 (75.0) 13 (54.2)  3 (25.0) 5 (41.7) 8 (33.3)  4 (33.3) 8 (66.7) 12 (50.0)  Group I I T o t a l Males Females Combined  6 (16.7) 8 (22.2) 14 (19.4)  9 (25.0) 9 (25.0) 18 (25.0)  7 (19.4) 10 (27.8) 17 (23.6)  8 (22.2) 13 (36.1) 21 (29.2)  6 (16.7) 7 (19.4) 13 (18.1)  7 (19.4) 9 (25.0) 16 (22.2)  T o t a l Sample Males Females Combined  20 (27.8) 23 (31.9) 43 (29.9)  25 (34.7) 25 (34.7) 50 (34.7)  21 (29.2) 24 (33.3) 45 (31.3)  22 (30.6) 31 (43.1) 53 (36.8)  20 (27.8) 20 (27.8) 40 (27.8)  20 (27.8) 23 (31.9) 43 (29.9)  Group I - Received the I d e n t i t y Task as O u t l i n e d by E l k i n d (1967) and the T r a d i t i o n a l C o n s e r v a t i o n Task r e f e r r e d t o as the E q u i v a l e n c e Task by E l k i n d . Group I I - Received  the M o d i f i e d I d e n t i t y and E q u i v a l e n c e  Tasks.  O  21. TABLE 2  Summary o f Group x Sex x Grade x Task Type x L e v e l o f Transformation A n a l y s i s of Variance  Source Between  DF Subjects  Group (A) Sex (B) Grade (C) AB AC BC ABC E r r o r Between Within  MS  1 1 2 1 2 2 2 132  14.38 1.09 28.44 0.14 6.48 8.72 0.13 2.39  2 2 4 4 132 1 1 1 2 1 2 2 2 132 2 2 4 132  0.64 0.20 0.95 0.26 0.23 0.43 0.17 0.17 0.11 0.43 0.21 0.14 0.30 0.13 0.29 0.27 0.57 0.14  6.02 ** 0.45 11.92 **** 0.06 2.72 3.65 * 0.05  Subjects  Task Type D(A) BD(A) CD(A) BCD(A) D x SS w/in gps. L e v e l of T r a n s . F AF BF CF ABF ACF BCF ABCF F x SS w/in gps. FD(A) BFD(A) BCFD(A) FD(A) x SS w/in gps. (  0.28 0.87 0.41 1.09 0.33 0.01 0.01 0.82 0.33 1.62 1.06 2.34 0.21 1.87 0.40  * ** ****  P<.05 P<.025 p<.001  22. The o n l y i n t e r a c t i o n t o r e a c h s i g n i f i c a n c e was the i n t e r a c t i o n of Sex x Grade (F=3.65; dF=2,132; p_<.05). t h a t the mean f o r g i r l s for g i r l s  test  indicated  i n Grade 2 was s i g n i f i c a n t l y g r e a t e r than the mean  i n Kindergarten  (p_<.01).  The d i f f e r e n c e between boys i n K i n d e r -  g a r t e n and boys i n Grade 1 was s i g n i f i c a n t New M u l t i p l e Range S t a t i s t i c . failed  A Newman K u e l s  (p_<.05) a c c o r d i n g t o Duncan's  Duncan's t e s t was used when the d i f f e r e n c e  t o read s t a t i s t i c a l s i g n i f i c a n c e a c c o r d i n g t o t h e Neuman Kuels  The frequence  test.  and p e r c e n t a g e o f s u b j e c t s who passed t h e v a r i o u s  c o n s e r v a t i o n t a s k s w i t h a c r i t e r i o n o f judgment p l u s - e x p l a n a t i o n i s shown i n T a b l e 3.  Group I can be seen to have performed b e t t e r than Group I I .  A l s o , fewer c h i l d r e n i n K i n d e r g a r t e n  than i n Grade 1 o r Grade 2 passed the  tasks when a judgment p l u s e x p l a n a t i o n c r i t e r i o n was used. of T a b l e s  A comparison  1 and 3 r e v e a l s t h a t when e x p l a n a t i o n s were i n c l u d e d i n the  c r i t e r i o n fewer s u b j e c t s passed a l l c o n s e r v a t i o n t a s k s than when a c r i t e r i o n of judgment o n l y was used.  With a c r i t e r i o n o f judgment o n l y , 40 s u b j e c t s  i n b o t h groups, passed t h e i d e n t i t y t a s k s under b o t h l e v e l s o f t r a n s f o r m a t i o n and  43 s u b j e c t s passed both e q u i v a l e n c e  tasks.  However w i t h a c r i t e r i o n o f  judgment p l u s e x p l a n a t i o n o n l y 28 s u b j e c t s passed both 33 passed both e q u i v a l e n c e included c r i t e r i o n  tasks.  i d e n t i t y t a s k s and  An a d d i t i o n a l a n a l y s i s o f v a r i a n c e which  (judgment o n l y v s . judgment p l u s e x p l a n a t i o n )  as a  f a c t o r i n d i c a t e d t h a t the judgment p l u s e x p l a n a t i o n c r i t e r i o n r e s u l t e d i n significantly  lower s c o r e s on the c o n s e r v a t i o n t a s k s  (F=30.73;  df=1,132;  p_<.001).  The number o f s u b j e c t s p a s s i n g i d e n t i t y t a s k s and e q u i v a l e n c e t a s k s w i t h a c r i t e r i o n o f judgment only i s p r e s e n t e d  i n T a b l e 4 and w i t h  TABLE 3 Frequency and Percentage o f S u b j e c t s P a s s i n g t h e C o n s e r v a t i o n Tasks When a C r i t e r i o n o f Judgment P l u s E x p l a n a t i o n was Used IDENTITY Moderate No, I Group I Kindergarten Males Females Combined  %  1 ( 8.3) 0 (0.0) 1 ( 4.2)  EQUIVALENCE  Extreme No  %  1 ( 8.3) 1 ( 8.3) 2 ( 8.3)  Moderate No,  %  1 ( 8.3) 2 (16.7) 3 (12.5)  Extreme No,  %  2 (16.7) 1 ( 8.3) 3 (12.5)  IDENTITY  EQUIVALENCE  Moderate & Extreme  Moderate & Extreme  No.  %  1 ( 8.3) 0 ( 0.0) 1 ( 4.2)  No,  %  1 ( 8.3) 1 ( 8.3) 2 ( 8.3)  Grade 1 Males Females Comb i n e d  6 (50.0) 4 (33.3) 10 (41.7)  7 (58.3) 4 (33.3) 11 (45.8)  8 (66.7) 4 (33.3) 12(50.0)  7 (58.3) 5 (41.7) 12 (50.0)  5 (41.7) 4 (33.3) 9 (37.5)  7 (58.3) 4 (33.3) 11 (45.8)  Grade 2 Males Females Combined  3 (25.0) 6 (50.0) 9 (37.5)  5 (41.7) 7 (58.3) 12 (50.0)  4 (33.3) 7 (58.3) 11 (45.8)  3 (25.0) 9 (75.0) 12 (50.0)  3 (25.0) 5 (41.7) 8 (33.3)  3 (25.0) 7 (58.3) 10 (41.7)  Group I T o t a l Males Females Combined  10 (27.8) 10 (27.8) 20 (27.8)  13 (36.1) 12 (33.3) 25 (34.7)  13 (36.1) 13 (36.1) 26 (36.1)  12 (33.3) 15 (41.7) 27 (37.5)  9 (25.0) 9 (25.0) 18 (25.0)  11 (30.6) 12 (33.3) 23 (31.9)  TABLE 3 (cont'd)  Moderate  Extreme  No.  No  Group I I  %  Moderate No  %  Extreme No  %  Moderate & Extreme No  %  Moderate & Extreme No  %  Kindergarten Males Females Combined  1 ( 0 ( 1 (  8.3) 0.0) 4.2)  2 (16.7) 0 ( 0.0) 2 ( 8.3)  0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  1 ( 8.3) 1 ( 8.3) 2 ( 8.3)  1 ( 8.3) 0 ( 0.0) 1 ( 4.2)  0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  Grade 1 Males Females Combined  2 (16.7) 3 (25.0) 5 (20.8)  3 (25.0) 1 0=8.3) 4 (16.7)  2 (16.7) 1 ( 8.3) 3 (12.5)  2 (16.7) 1 ( 8.3) 3 (12.5)  2 (16.7) 1 ( 8.3) 3 (12.5)  2 (16.7) 0 ( 0.0) 2 ( 8.3)  Grade 2 Males Females Combined  3 (25.0) 4 (33.3) 7 (29.2)  4 (33.3) 3 (25.0) 7 (29.2)  3 (25.0) 5 (41.7) 8 (33.3)  3 (25.0) 6 (50.0) 9 (37.5)  3 (25.0) 3 (25.0) 6 (25.0)  3 (25.0) 5 (41.7) 8 (33.3)  Group I I T o t a l Males Females Combined  6 (16.7) 7 (19.4) 13 (18.1)  9 (25.0) -4 :(n.i) 13 (18.1)  5 (13.9) 6 (16.7) 11 (15.2)  6 (16.7) 8 (22.2) 14 (19.4)  6 (16.7) 4 (11.1) 10 (13.9)  5 (13.9) 5 (13.9) 10 (13.9)  T o t a l Sample Males Females Combined  16 (22.2) 17 (23.6) 33 (22.9)  22 (30.5) 16 (22.2) 38 (26.4)  18 (25.0) 19 (26.4) 37 (25.7)  18 (25.0) 23 (31.9) 41 (28.5)  15 (20.8) 13 (18.1) 28 (19.4)  16 (22.2) 17 (23.6) 33 (22.9)  25. a c r i t e r i o n o f judgment p l u s e x p l a n a t i o n i n T a b l e 5. a comparison o f T a b l e s  I t i s evident  4 and 5 t h a t more s u b j e c t s passed both  from  tasks  with  a c r i t e r i o n o f judgment o n l y than w i t h a c r i t e r i o n o f judgment p l u s ation.  Thirty-five  s u b j e c t s passed both  identity  and e q u i v a l e n c e  the moderate l e v e l o f t r a n s f o r m a t i o n w i t h a c r i t e r i o n o f judgment w h i l e 25 passed w i t h a c r i t e r i o n o f judgment p l u s e x p l a n a t i o n . extreme l e v e l 44 s u b j e c t s passed both  tasks at only,  At the  t a s k s w i t h a c r i t e r i o n o f judgment  o n l y and 34 passed w i t h a c r i t e r i o n o f judgment p l u s e x p l a n a t i o n . both  levels  explan-  When  o f t r a n s f o r m a t i o n a r e combined i t can be seen t h a t 35 s u b j e c t s  passed a l l tasks w i t h a c r i t e r i o n o f judgment o n l y and 23 s u b j e c t s passed w i t h a c r i t e r i o n o f judgment p l u s  explanation.  Three s u b j e c t s passed b o t h i d e n t i t y equivalence both  t a s k s and 3 s u b j e c t s passed both e q u i v a l e n c e  identity  T a b l e 4. identity  both  t a s k s and f a i l e d  tasks w i t h a c r i t e r i o n o f judgment o n l y as i s e v i d e n t  An examination  o f T a b l e 5 shows t h a t 2 s u b j e c t s passed  t a s k s and f a i l e d both e q u i v a l e n c e  equivalence  t a s k s and f a i l e d  t a s k s and f a i l e d both i d e n t i t y  plus explanation.  both  tasks w i t h a c r i t e r i o n o f judgment  I t can a l s o be seen from T a b l e 4 t h a t 14 s u b j e c t s passed  f a i l e d the c o r r e s p o n d i n g  e i t h e r the moderate but  both  t a s k s and 1 s u b j e c t passed  e i t h e r t h e moderate (8 s u b j e c t s ) o r extreme (6 s u b j e c t s ) i d e n t i t y but  from  equivalence  tasks,  t a s k s , w h i l e 21 s u b j e c t s passed  (13 s u b j e c t s ) o r extreme (8 s u b j e c t s ) e q u i v a l e n c e  f a i l e d the c o r r e s p o n d i n g  identity  tasks.  tasks  With a c r i t e r i o n o f judgment  p l u s e x p l a n a t i o n , as i n T a b l e 5, 13 s u b j e c t s passed e i t h e r the moderate (8 s u b j e c t s ) o r extreme (5 s u b j e c t s ) i d e n t i t y sponding e q u i v a l e n c e  t a s k s and 19 s u b j e c t s passed e i t h e r the moderate (12  s u b j e c t s ) o r extreme (7 s u b j e c t s ) e q u i v a l e n c e sponding i d e n t i t y  t a s k s but f a i l e d t h e c o r r e -  tasks.  t a s k s and f a i l e d the c o r r e -  26TABLE 4 Number o f S u b j e c t s P a s s i n g I d e n t i t y and E q u i v a l e n c e Tasks at Each Grade L e v e l when a C r i t e r i o n o f Judgment Only was Used.  Passed  M  Both  E  M&E  F a i l e d Both  M  E  M&E  Passed  Ident.  Passed  Equiv.  F a i l e d Equiv.  Failed  Ident.  M  M  E  M&E  E  M&E  Group I Kindergarten  1  Grade 1  14  14  14  Grade 2  9  12  Group I Total  24  29  3  1  18 20  18  2  8  8  1  2  1  0  0  0  9  10 10  10  2  1  1  3  1  0  24  37 38  36  5  3  2  6  2  0  23 20  20  0  1  0  0  2  0  9  0  0  3  1  0  Group I I Kindergarten  1  Grade 1  2  4  2  16 18  16  3  1  1  3  Grade 2  8  10  8  12 10  10  0  1  0  4  3  2  Group I I Total  11  15  11  51 48  46  3  3  1  7  6  3  Total Sample  35  44  35  88 86  82  8  6  3  13  8  3  1  1  M = Moderate L e v e l o f T r a n s f o r m a t i o n E = Extreme L e v e l of T r a n s f o r m a t i o n  1  1  27. TABLE 5  Number of S u b j e c t s P a s s i n g  Identity  and E q u i v a l e n c e Tasks a t Each Grade L e v e l When a C r i t e r i o n of Judgment P l u s E x p l a n a t i o n was  Used.  Passed Both  F a i l e d Both  Passed I d e n t . F a i l e d Equiv.  Passed Failed  M  E  M&E  M  M  E  M&E  M  E  m  Kindergarten  1  2  1  21 21  20  0  0  0  2  1  0  Grade 1  9  11  8  11 12  11  1  0  0  3  1  l  Grade 2  7  10  7  11 10  10  2  2  1  4  2  0  Group I Total  17  23  16  43 43  41  3  2  1  9  4  1  1 0  23 21  21  1  0  1  0  1  17 20  17  4  1  1  2  0  0  0  1  0  1  2  0  2  12  E  M&E  Equiv. Ident.  Group I  Group I I Kindergarten  0  Grade 1  1 3  Grade 2  7  7  6  16 14  14  Group I I Total  8  11  7  56 55  52  Total Sample •  25  34  23  99 98  93  8  1  0  5  28.  The explanations  frequency  and  on i d e n t i t y  p e r c e n t a g e of s u b j e c t s g i v i n g adequate  conservation, equivalence  c o n s e r v a t i o n t a s k s are g i v e n i n T a b l e s  6,  7 and  c o n s e r v a t i o n and a l l  8 respectively.  c l a s s i f i c a t i o n scheme f o r the v a r i o u s types of e x p l a n a t i o n s i n Appendix A. explanations  i s described  I t can be seen from the t a b l e s that the number of adequate  g i v e n by Grade 2 s u b j e c t s was  by Grade 1 s u b j e c t s which i n t u r n was Kindergarten  The  subjects.  s u b t r a c t i o n and  g r e a t e r than the number g i v e n  g r e a t e r than  the number g i v e n  by  I t can be seen from T a b l e 8 t h a t the a d d i t i o n -  statement of o p e r a t i o n s  67% of the e x p l a n a t i o n s  c a t e g o r i e s account f o r  g i v e n by K i n d e r g a r t e n  approximately  s u b j e c t s on a l l t a s k s .  c a t e g o r i e s used by Grade 1 s u b j e c t s account f o r 88.3%  of t h e i r  responses;  a d d i t i o n - s u b t r a c t i o n , statement of o p e r a t i o n s , r e f e r e n c e to p r e v i o u s and  inversion.  one  category"  account f o r 91.8%  However the "more than one composite e x p l a n a t i o n s  category"  account f o r o n l y 9.6%  of the second g r a d e r s '  category  and  explanations.  i s composed t o t a l l y  from the other f o u r c a t e g o r i e s .  of r e c i p r o c i t y , sameness (same s t i m u l u s )  The  of  three categories  sameness (same q u a n t i t y )  of the e x p l a n a t i o n s o v e r a l l .  The  category  of  never used.  Comparison of T a b l e s  6 and  7 r e v e a l s t h a t the c a t e g o r i e s of s t a t e -  ment of o p e r a t i o n s , r e f e r e n c e to p r e v i o u s s t a t e , and more f r e q u e n t l y on e q u i v a l e n c e s u b t r a c t i o n c a t e g o r y was equivalence  state  These same f o u r c a t e g o r i e s p l u s the use of the "more than  category  compensation was  Four  tasks.  i n v e r s i o n were used  t a s k s than on i d e n t i t y t a s k s .  used more f r e q u e n t l y on i d e n t i t y  The a d d i t i o n -  tasks than  on  TABLE 6 Frequency and Percentage of S u b j e c t s G i v i n g Adequate E x p l a n a t i o n s f o r a l l I d e n t i t y C o n s e r v a t i o n Tasks  KDG. No. %  Group I GR. 1 No. %  GR. 2 No. %  KDG. No.  Group I I GR. 1 % No. %  GR. No.  2 %  Group I and Group I I KDG. GR. 1 GR. 2 No. % No. % No. %  Total No.  %  Addition Subtration  2 (50.0) 8 (38.1) 3 ( 1 1 . 5 ) 2 ( 6 6 . 7 )  3 (27.3) 4 (22.2) 4 (57.1)11 (34.4) 7 (15.9) 22  Statement of Operations  0  (0.0) 9 (42.9)10 ( 3 8 . 5 ) 0  (0.0)  3 (27.3) 5 (27.8) 0  (0.0)12 (37.5)15 (34.1) 27 (32.5)  Reference to Previous state  0  (0.0) 0  (0.0) 2 ( 7.7) 0  (0.0)  3 (27.3) 4 (22.2) 0  (0.0) 3  (9.4) 6 (13.6)  9 (10.8)  Inversion  0  (0.0) 1  (4.8) 1 ( 3.8)0  (0.0)  0 ( 0.0)  1  (5.6) 0  (0.0) 1  (3.1) 2  (4.5)  3  (3.6)  Reciprocity  0  (0.0) 0  (0.0) 0 ( 0.0) 0  (0.0)  1 ( 9.1)  0  (0.0) 0  (0.0) 1  (3.1) 0  (0.0)  1  (1.2)  Compensation  0  (0.0) 0  (0.0) 0 ( 0.0) 0  (0.0)  0 ( 0.0)  0  (0.0) 0  (0.0) 0  (0.0) 0  (0.0)  0  (0.0)  Sameness (same s t i m u l u s )  2 (50.0) 1  (4.8) 0 ( 0.0) 0  (0.0)  1 ( 9.1)  0  (0.0) 2 (28.6) 2  (6.3) 0  (0.0)  4  (4.8)  Sameness (same q u a n t i t y )  0  (0.0) 2  (9.5) 5 (19.2)0  (0.0)  0 ( 0.0)  0  (0.0) 0  (6.3) 5 (11.4)  7  0  (0.0) 0  (0.0) 4 (19.2) 1 (33.3)  0 ( 0.0)  4 (22.2) 1 (14.3) 0  More than one c a t e g o r y No. and % of Explanations  (0.0) 2  (26.5)  (8. 4)  (0.0) 9 (20.5) 10 (12.0)  4(100.0) 2L(100.0)26(100.0) 3(100.0) 11(100.0)18(100,0) 7(100.0^2.(100.0X44.(100._0.) . 83(100.0)  TABLE 7 Frequency and Percentage of Subjects Giving Adequate Explanations for a l l Equivalence Conservation Tasks  GROUP I KDG. No.  %  GR. 1 No. %  GR. 2 No. %  KDG. No.  '  GROUP I I  %  GR. 1 No. %  GROUP I AND GROUP I I GR. 2 No. %  KDG. No. %  GR. 1 No. %  GR. 2 No. %  TOTAL  No. %  AdditionSubtraction  2 (28.6) 6 (25.0) 3 (12.0) 1 (25.0) 1 (10.0) 3 (17.6) 3 (27.3) 7 (20.6) 6 (14.3)16 (18.4)  Statement of Operations  2 (28.6) 7 (29.2) 9 (36.0) 3 (75.0) 5 (50.0) 6 (35.3) 5 (45.5)12 (35.3)15 (35v7)32 (36.8)  Reference to Previous state  2 (28.6) 5 (20.8) 5 (20.0) 0 ( 0.0) 3 (30.0) 6 (35.3) 2 (18.2) 8 (23.5)11 (26.2)21 (24.1)  Inversion  0 ( 0.0) 3 (12.5) 2 ( 8.0) 0 ( 0.0) 1 (10.0) 1 ( 5.9) 0 ( 0.0) 4 (11.8) 3 ( 7.1) 7 (16.7)  Reciprocity  0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  Compensation  0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  Sameness (same stimulus)  0 ( 0.0) 1 ( 4.2) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 1 ( 2.9) 0 ( 0.0) 1 ( 2.4) o  Sameness (same quantity)  1 (14.3) 2 ( 8.3) 2 ( 8.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 1 ( 9.1) 2 ( 5.9) 2 ( 4.8) 5 (11.9)  More than one category  0 ( 0.0) 0 ( 0.0) 4 (16.0) 0 ( 0.0) 0 ( 0.0) 1 ( 5.9) 0 ( 0.0) 0 ( 0.0) 5 (11.9) 5 (11.9)  No. and % of Explanations  7(100.0)24(100.0)25(100.0) 4(100.0)10(100.0)17(100.0)11(100.0)34(100.0)42(100.0)87(100.0)  TABLE 8 Frequency and Percentage of S u b j e c t s G i v i n g Adequate E x p l a n a t i o n s f o r a l l C o n s e r v a t i o n Tasks GROUP I KDG. No.  %  GR. 1 No. %  GROUP I I GR. 2 No. %  KDG. No. %  GR. 1 No. %  GROUP I GR. 2 No. %  KDG. No.  %  AND  GROUP I I  GR. 1 GR. 2 No. % No. %  TOTAL No. %  Addition Subtraction  4 (36.4)14 (31.2) 6 (11.8) 3 (42.9) 4 (18.2) 7 (20.6) 7 (38.9)18 (26.9)13 (15.3)38  (22.4)  Statement o f Operations  2 (18.2)16 (35.6)19 (37.3)23 (42.9) 8 (36.4)11 (32.4) 5 (27.8)24 (35.9)30 (35.3)59  (34.7)  Reference t o Previous state  2 (18.2) 5 (11.1) 7 (13.8) 0 ( 0.0) 6 (27.3)10 (29.5) 2 (11.1)11 (16.5)17 (20.0)30  (17.6)  Inversion  0 ( 0.0) 4 ( 8.9) 3 ( 5.9) 0 ( 0.0) 2 ( 9.1) 1 ( 3.0) 0 ( 0.0) 6 ( 9.0) 4 ( 4.7)10 ( 5.9)  Reciprocity  0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 1 ( 4.6) 0 ( 0.0) 0 ( 0.0  Compensation  0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  Sameness (same s t i m u l u s )  2 (18.2) 2 ( 4.4) 0 ( 0.0) 0 ( 0.0) 1 ( 4.6) 0 ( 0.0) 2 (11.1) 3 ( 4.5) 0 ( 0.0) 5 ( 2.9)  Sameness (same q u a n t i t y )  1 ( 9.1) 4 ( 8.9) 7 (13.8) 0 ( 0.0) 0 ( 0.0) 0 ( 0.0) 1 ( 5.6) 4 ( 6.0) 7 ( 8.3)12 ( 7.1)  More than one c a t e g o r y  0 ( 0.0) 0 ( 0.0) 9 (17.7) 1 (14.3) 0 ( 0.0) 5 (14.7) 1 ( 5.6) 0 ( 0.0)14 (16.5)15 ( 8.8)  No. and % o f Explanations  11(100.0)45(100.0)51(100.0)  1 ( 1.5) 0 ( 0.0) 1 ( 0.6)  7(100.0)22(100.0)34(100.0)18(100.0)67(100.0)85(100.0)170(L00.0)  32. S c o r i n g w i t h a 0-6  The  scale  frequency and p e r c e n t a g e of s u b j e c t s s c o r i n g from 0-6  the v a r i o u s c o n s e r v a t i o n t a s k s i s g i v e n i n T a b l e 9.  The  s c o r e s were  d e r i v e d by a s s i g n i n g s u b j e c t s a 1 f o r each c o r r e c t answer i n v o l v i n g r e l a t i o n a l terms "same", "more" and and judgment phases.  " l e s s " used i n both the  T h i s i s the s c o r i n g scheme employed by  and Hooper (1975) and T o n i o l o and Hooper (1975). an 0 f o r each i n c o r r e c t answer.  57  on 124  possible.  (44.3%) of the e q u i v a l e n c e  the e q u i v a l e n c e  32  (11.1%) of the t a s k s and  conservation tasks.  26  (9.0%)  conservation.  (4.5%) of both the i d e n t i t y and  There were 16  r e c e i v e d a s c o r e of 5.  On  equivalence  14  the e q u i v a l e n c e  conservation tasks subjects a s c o r e of 5 on 5 (1.7%) t a s k s . perfectly  c o n s e r v a t i o n t a s k s were answered p e r f e c t l y .  An a d d i t i o n a l a n a l y s i s of v a r i a n c e performed on the d a t a w i t h a 0-6  on  (4.9%) t a s k s on which s u b j e c t s  (32.3%) i d e n t i t y c o n s e r v a t i o n t a s k s were answered  (34.7%) e q u i v a l e n c e  Subjects  (5.6%) i d e n t i t y c o n s e r v a t i o n t a s k s  r e c e i v e d a s c o r e of 4 on 5 (1.7%) t a s k s and  100  the  There were  a s c o r e of 2 on 9 (3.1%) of the t a s k s .  w h i c h v s u b j e c t s r e c e i v e d a s c o r e of 4, and  Ninety-three  of  be  c o n s e r v a t i o n t a s k s s u b j e c t s r e c e i v e d a s c o r e of 1 on  r e c e i v e d a s c o r e of 3 on 13  and  (24%)  tasks.  t a s k s on which s u b j e c t s r e c e i v e d a s c o r e of 2 on i d e n t i t y  in a l l ,  As can  (19.8%) t a s k s on which s u b j e c t s r e c e i v e d a s c o r e of 1 and  On  Brainerd  S u b j e c t s were g i v e n  seen from the t a b l e , s u b j e c t s r e c e i v e d a s c o r e of 0 on 69 i d e n t i t y t a s k s and  the  prediction  S i n c e t h e r e were s i x q u e s t i o n s  e x c l u d i n g e x p l a n a t i o n s , a maximum s c o r e of 6 was  on  s c a l e i n the manner p r e s e n t e d  performance on the e q u i v a l e n c e  t a s k s was  scored  i n Table 9 indicated that s i g n i f i c a n t l y b e t t e r than p e r f o r m -  TABLE 9 Frequency and Percentage of Tasks On Which S u b j e c t s Obtained the S p e c i f i e d Values Score Obtained Group I I d e n t i t y Moderate  0 No.  1 %  No.  2 %  No.  3 %  %  No.  5 %  13 (18.1)  11 (15.3)  19 (26.4)  7 ( 9.7)  6 ( 8.3)  2 ( 2.8)  4 ( 5.6)  I d e n t i t y Moderate  15 (20.8)  21 (29.2)  6 ( 8.3)  7 ( 9.7)  I d e n t i t y Extreme  22 (30.6)  18  (25.0)  6 ( 8.3)  Total for Identity  69 (24.0)  57 (19.8)  E q u i v a l e n c e Moderate  24 (33.3)  E q u i v a l e n c e Extreme  I d e n t i t y Extreme  1  8 (11.1)  No.  4  2 ( 2.8)  1  5 ( 6.9)  No. 1 1  6 %  4 ( 5.6)  No.  %  '29 (40.3)  2 ( 2.8)  32  (44.4)  7 ( 9.7)  2 ( 2.8)  14  (19.4)  2 ( 2.8)  0 ( 0.0)  6.( 8.3)  18 (25.0)  26 ( 9.0)  13 ( 4.5)  16 ( 5.6)  14 ( 4.9)  93 (32.3)  11 (15.3)  1 ( 1.4)  5 ( 6.9)  0 ( 0.0)  1 ( 1.4)  30  (41.7)  30 (41.7)  3 ( 4.2)  3 ( 4.2)  2 ( 2.8)  1 ( 1.4)  1 ( 1.4)  32  (44.4)  E q u i v a l e n c e Moderate  31 (43.1)  11 (15.3)  3 ( 4.2)  5 ( 6.9)  3 ( 4.2)  2 ( 2.8)  17  (24.6)  E q u i v a l e n c e Extreme  39 (54.2)  7 ( 9.7)  2 ( 2.8)  1 ( 1.4)  1 ( 1.4)  9 ( 3.1)  13 ( 4.5)  5 ( 1.7)  Group I I  Group I  Group I I  T o t a l f o r Equivalence  124  (44.3)  32  (11.1)  1 ( 1.4) 5 ( 1.7)  21 (29.2) 100  (34.7)  34. ance on i d e n t i t y t a s k s  (F=8.85; dF=l,132; p_<.01).  Transitivity  The  g e n e r a l performance p a t t e r n on the t r a n s i t i v i t y tasks f o r  each grade w i t h i n each group i s p r e s e n t e d of  s u b j e c t s who  i n T a b l e 10.  The  t o t a l number  passed each t a s k v a r i e d l i t t l e among the f o u r t a s k s .  C o n s i d e r i n g the t o t a l sample 76 s u b j e c t s passed t a s k A, 84 passed t a s k C, and  77 s u b j e c t s passed t a s k D.  74 passed t a s k  W i t h i n group t o t a l s  B, on  each of the f o u r t a s k s were v e r y s i m i l a r , however more s u b j e c t s i n Group I passed t a s k s A, B and D and more i n Group I I passed t a s k  Transitivity  C.  t a s k s were s u b j e c t e d to a 2x2x3x4 a n a l y s i s of  v a r i a n c e i n which the v a r i a b l e s were Group (Group I , Group I I ) , Sex, ( K i n d e r g a r t e n , Grade 1, Grade 2 ) , and Task Type (A, B, C, and D). be  Age  As  can  seen from T a b l e 11 the o n l y main e f f e c t s to r e a c h s i g n i f i c a n c e were the  main e f f e c t s f o r group (F=6.84; dF=l,132; p_<.01) and jK.001)"'". Kuels  Group I performed s i g n i f i c a n t l y b e t t e r than Group I I .  Newman  t e s t s performed on the grade means showed t h a t Grade 2 c h i l d r e n  scored s i g n i f i c a n t l y garten  grade (F=22.30; dF=2,132;  (p_<.01), who  The  h i g h e r than c h i l d r e n i n Grade 1 (p_<.01) and d i d not  frequency  differ.  and p e r c e n t a g e of s u b j e c t s p a s s i n g  numbers of t r a n s i t i v i t y t a s k s i s g i v e n i n T a b l e 12. t a b l e o n l y a v e r y s m a l l percentage transitivity  tasks.  Kinder-  The  As can be  seen from the  (4.2% of the t o t a l sample) f a i l e d a l l  At the o t h e r extreme o n l y 11.1%  passed a l l t r a n s i t i v i t y t a s k s .  specified  of the t o t a l  p e r c e n t a g e of s u b j e c t s who  number of t a s k s between these extremes decreases  from 95% who  sample  passed a passed 1  35. \ TABLE 10 Number and P e r c e n t a g e o f S u b j e c t s P a s s i n g t h e Four T r a n s i t i v i t y  Task A Task Schema  A==B=C No.  Ir  Tasks  Task B  Task C  Task D  A>B=C  A==B>C  A> B>C  No.  %  No.  Group I Kindergarten Males Females Combined  3 5 8  Grade 1 Males Females Combined  %  No.  %  (25. 0) 8 (41. 7) 6 (33. 3) 14  (66. 7) 7 (50. 0) 8 (58. 3) 15  (58. 3) 3 (66. 7) 9 (62. 5) 12  (25. 0) (75. 0) (50. 0)  10 6 16  (83. 3) (50. 0) (66. 7)  3 5 8  (25. 0) 3 (41. 7) 7 (33. 3) 10  (25. 0) 7 (58. 3) 7 (41. 7) 14  (58. 3) (58. 3) (58. 3)  Grade 2 Males Females Combined  7 11 18  (58. 3) 12 (91. 7) 9 (75. 0) 21  (100. 0) 9 (75. 0) 7 (87. 5) 16  (75. 0) 9 (58. 3) 9 (66. 7) 18  (75. 0) (75. 0) (75. 0)  Group 1 T o t a l Males Females Combined  20 22 42  (55. 6) 23 (61. 1) 20 (58. 3) 43  (63. 9) 19 (55. 6) 22 (59. 7) 41  (52. 8) 19 (61. 1) 25 (56. 9) 44  (52. 8) (69. 4) (61. 1)  36.  TABLE 10  (cont'd)  Group I I  T  a  s  k  A  T  a  s  k  B  T  a  s  k  Task D  c  Kindergarten Males Females Combined  5 2 7  (41 .7) (16 .7) (29 • 2)  4 4 8  (33 .3) 4 (33,.3) 8 (33,.3) 12  (33 .3) (66 .7) (50 .0)  2 3 5  (16 • 7) (25 .0) (20 • 8)  Grade 1 Males Females Comb i n e d  6 3 9  (50 .0) (25 • 0) (37 .5)  4 5 9  (33..3) 6 (41.• 7) 7 (37.• 5) 13  (50,.0) 5 (58,.3) 8 (54..2) 13  (41,.7) (66,.7) (54, • 2)  •  Grade 2 Males Females Combined  9 9 18  (75 • 0) 9 (75 .0) 5 (75 • 0) 14  (75. 0) 9 (41. 7) 9 (58. 3) 18  (75.• 0) 7 (75. 0) 8 (75.• 0) 15  (58..3) (66..7) (62. 5)  Group I I T o t a l Males Females Combined  20 14 34  (55,• 6) 17 (38,.9) 14 (47,.2) 31  (47. 2) 19 (38. 9). 24 (43. 1) 43  (52. 8) 14 (66. 7) 19 (59. 7) 33  (38. 9) (52. 8) (45. 8)  T o t a l Sample Males Females Comb i n e d  40 36 76  (55, .6) 40 (50..0) 34 (52. .8) 74  (55. 6) 38 (47. 2) 46 (51. 4) 84  (52. 8) 33 (63. 9) 44 (58. 3) 77  (45. 8) (61. 1) (53. 5)  37. TABLE 11 Summary o f Group x Sex x Grade x Type o f T r a n s i t i v i t y Task A n a l y s i s o f V a r i a n c e  SOURCE  DF  MS  1 1 2 1 2 2 2 132  1.46 0.85 4.76 0.14 0.23 0.17 0.68 0.21  3 3 3 6 3 6 6 6 396  0.13 0.28 0.57 0.45 0.20 0.29 0.41 0.30 0.23  F  Between subj e c t s  Group (A) Sex (B) Grade (C) AB AC BC ABC E r r o r Between  6.84 *** 0.40 22.30 «.*** 0.66 1.08 0.79 0.32 i  Within subjects  Task Type (D) AD BD CD ABD ACD BCD ABCD Error Within  0.58 1.25 2.50 1.97 0.86 1.28 1.81 1.34  *** P<.01 **** p<.001  38. TABLE 12 Number and P e r c e n t a g e o f S u b j e c t s  Passing  Only the S p e c i f i e d Number o f T r a n s i t i v i t y Tasks  0 Tasks  One or Two o r More Tasks More Tasks  Three o r Four Tasks More Tasks  No.  No.  No.  %  %  No.  %  %  No.  %  Group I Kindergarten Males Females Combined  0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  12(100.0) 12(100.0) 24(100.0)  6 (50.0) 9 (75!0) 15 (62.5)  3 (25.0) 4 (33.3) 7 (29.2)  0 ( 0.0) 3 (25.0) 3 (12.5)  2 (16.7) 5 (41.7) 8 (33.3)  1 ( 8.3) 1 ( 8.3) 2 ( 8.3)  Grade 1 Males Females Combined  1 ( 8.3) ?. 1 ( 8.3) 2 ( 8.3)  11 (91.7) 8 (66.7) 10 (83.3) 8 (66.7) 21 (87.5) 16 (66.7)  Grade 2 Males Females Combined  0 ( 0.0) 0 ( 0.0) '0 ( 0.0)  12(100.0) 12(100.0) 24(100.0)  11 (91.7) 12(100.0) . 23 (95.8)  9 (75.0) 10 (83.3) 19 (79.2)  35 (97. 2) 34 (94. 4) 69 (95. 8)  25 (69 .4) 29 (80 .6) 54 (75 • 0)  15 (41.• 7) 6 (16,.7) 19 (52.• 8) 6 (16,.7) 34 (47.• 2) 12 (16,.7)  Group I T o t a l Males Females Combined  1 ( 2,.8)'! 1 ( 2..8) 2 ( 2,.8)  5 (41.7) 2 (16.7) 7 (29.2)  39. T a b l e 12  (cont'd)  0 Tasks  One or Two or More Tasks More Tasks  Three or Four Tasks More Tasks  No.  No.  No.  %  %  No.  %  %  No.  %  Group I I Kindergarten Males Females Combined  2 (16. 7) 1 ( 8.3) 3 (12. 5)  10 (83.3) 11 (91.7) 21 (87.5)  4 (33.3) 5 (41.7) 9 (37.5)  .2 (16.7) 0 ( 0.0) 2 ( 8.3)  Grade 1 Males Females Combined  1 ( 8.3) 0 ( 0.0) 1 ( 4.2)  11 (91.7) 12(100.0) 23 (95.8)  8 (66.7) 8 (66.7) 16 (66.7)  2 (16.7) 3 (25.0) 5 (20.8)  rade 2 Males Females Combined  0 ( Q.0) 0 ( 0.0) 0 ( 0.0)  12(100.0) 12(100.0) 24(100.0)  12(100.0) 10 (83.3) 22 (91.7)  8 (66.7) 7 (58.3) 15 (62.5)  2 (16.7) 2 (16.7) 4 (16.7)  Group I I Total Males Females Combined  3 ( 4.2) 1 ( 1.4) 4 ( 2.8)  33 (91.7) 35 (97.2) 68 (94.4)  24 (66. 7) 23 (63. 9) 47 (65. 3)  12 (33.3) 10 (27.8) 22 (30.6)  2 ( 5 .6) 2 ( 5 • 6) 4 ( 5 .6)  T o t a l Sample Males Females Combined  4 ( 5. 6) 2 ( 2. 8) 6 ( 4. 2)  68 (94. 4) 49 (68.1) 69 (95. 8) 52 (72.2) 137 (95. 1) 101 (70.1)  27 (37.5) 29 (40.3) 56 (38.9)  0 ( 0.0) 0 ( 0.0) 0 ( 0.0)  0 ( 0 ( 0 (  0.0) 0.0) 0.0)  8 (11.1) 8 (11.1) 16 (11.1)  40. or more, t o 70.1% who passed 2 or more, t o 38.9% who passed 3 o r more.  The  d e c l i n e i n t h e number o f s u b j e c t s who passed 1 or more to t h e number who passed 3 o r more was l e s s i n the case o f Grade 2 than i n K i n d e r g a r t e n o r Grade 1.  The frequency transitivity equivalence Tables  and p e r c e n t a g e o f s u b j e c t s who passed o r f a i l e d  t a s k s and passed o r f a i l e d  i d e n t i t y conservation  c o n s e r v a t i o n tasks and a l l c o n s e r v a t i o n t a s k s a r e g i v e n i n  13, 14, and 15 r e s p e c t i v e l y .  The o v e r a l l r e s u l t s i n d i c a t e t h a t  many more s u b j e c t s passed t r a n s i t i v i t y than f a i l e d t r a n s i t i v i t y  t a s k s and f a i l e d  number who passed 2 o r more t a s k s .  failed  conservation  t a s k s b u t passed c o n s e r v a t i o n t a s k s .  number o f s u b j e c t s who passed 2, 3 or 4 t r a n s i t i v i t y  who f a i l e d  tasks,  2, 3 o r 4 t r a n s i t i v i t y  2 o r more t r a n s i t i v i t y  tasks  Summing the  tasks y i e l d s the  S i m i l a r l y summing t h e number of s u b j e c t s t a s k s g i v e s t h e number of s u b j e c t s who  tasks.  When t h i s i s done i t can be seen from  T a b l e 13 t h a t 65 s u b j e c t s (45.1%) passed 2 or more t r a n s i t i v i t y  t a s k s but  f a i l e d t h e i d e n t i t y c o n s e r v a t i o n t a s k s , but o n l y 15 s u b j e c t s  (10.4%) f a i l e d  2 or more t r a n s i t i v i t y  The comparable  t a s k s and passed t h e i d e n t i t y t a s k s .  f i g u r e s from T a b l e 14 a r e 64 s u b j e c t s  (44.4%) who passed 2 o r more  t a s k s and f a i l e d the e q u i v a l e n c e  c o n s e r v a t i o n t a s k s and 20 s u b j e c t s  who f a i l e d 2 o r more t r a n s i t i v i t y  t a s k s but passed the e q u i v a l e n c e  conservation tasks.  An examination  transitivity (13.9%)  o f T a b l e 15 shows t h a t 70 s u b j e c t s  (48.6%) passed 2 or more t r a n s i t i v i t y  t a s k s and f a i l e d both  c o n s e r v a t i o n t a s k , w h i l e only 13 s u b j e c t s  types o f  (9.0%) passed both types o f  c o n s e r v a t i o n t a s k and f a i l e d 2 o r more t r a n s i t i v i t y  tasks.  TABLE 13 Number and Percentage pf S u b j e c t s P a s s i n g and F a i l i n g T r a n s i t i v i t y and I d e n t i t y C o n s e r v a t i o n Tasks.  No. o f T r a n s i t i v i t y Tasks  (Criterion  Number o f s u b j e c t s p a s s i n g t h e conser^ v a t i o n t a s k s but f a i l i n g the s p e c i f i e d number o f T r a n s i t i v i t y t a s k s . 0 1 2 3 4 No. % No. % No. % No, % No. %  o f Judgment  Tasks  Only).  Number o f s u b j e c t s f a i l i n g the c o n s e r v a t i o n t a s k s but p a s s i n g the s p e c i f i e d number o f T r a n s i t i v i t y t a s k s . 0 2 1 3 4 No. % No. % No. % % No. % No.  Group I Kindergarten  0 (0.0)  1 (4.2) . 0 (0.0)  1 (4.2)  0 (0.0)  0 (0.0)  9(37.5)  7(29.2)  3(12 .5)  3(12.5)  Grade 1  2 (8.3)  5(20.8)  5(20.8)  3(12.5)  0 (0.0)  2 (8.3)  3(12.5)  3(12.5)  1 (4 .2)  0 (0.0)  Grade 2  4(16.1)  6(25.0)  0 (0.0)  0 (0.0)  0 (0.0)  0 (0.0)  1 (4.2)  4(16.7)  6(25 .0)  3(12.5)  Total  6 (8.3) 12(16.7)  5 (6.9)  4 (5.6)  0 (0.0)  2 (2.8)  13(18.1) 14(19.4) 10(13 .9)  6 (8.3)  Kindergarten  0 (0.0)  1 (4.2)  0 (0.0)  0 (0.0)  0 (0.0)  3(12.5) 12(50.0)  7(29.2)  1 (4 .2)  0 (0.0)  Grade 1  0 (0.0)  1 (4.2)  2 (8.3)  1 (4.2)  0 (0.0)  1 (4.2)  6(25.0)  9(37.5)  4(16 .7)  0 (0.0)  Grade 2  3(12.5)  2 (8.3)  3(12.5)  0 (0.0)  0 (0.0)  0 (0.0)  2 (8.3)  4(16.7)  9(37 .5)  1 (4.2)  Total  3 (4.2)  4 (5.6)  5 (6.9)  1 (1.4)  0 (0.0)  4 (5.6)  20(27.8) 20(27.8) 14(19 .4)  1 (1.4)  9 (6.3) 16(11.1) 10 (6.9)  5 (3.5)  0 (0.0)  6 (4.2)  33(22.9) 34(23.6) 24(16 • 7) 7 (4.9)  Group I I  Total  Sample  TABLE 14 Number and Percentage o f S u b j e c t s P a s s i n g and F a i l i n g and E q u i v a l e n c e C o n s e r v a t i o n Tasks ( C r i t e r i o n  No. o f t r a n s i t i v i t y tasks Group I Kindergarten  Transitivity  o f Judgment  Tasks  Only).  Number of s u b j e c t s p a s s i n g the conserv a t i o n t a s k s but f a i l i n g the s p e c i f i e d number o f t r a n s i t i v i t y t a s k s  Number o f s u b j e c t s f a i l i n g t h e c o n s e r v a t i o n t a s k s but p a s s i n g t h e s p e c i f i e d number o f t r a n s i t i v i t y t a s k s  0  0  No.  1 %  No.  2 %  No.  3 %  No,  4  %  No,  %  No.  1 %  No.  2 %  No.  3 %  No.  4  %  No.  %  0 (0.0)  0 (0.0)  1 (4.2)  1 (4.2)  0 (0.0)  0 (0.0)  9(37.5)  6(25.0)  4(16. 7)  3(12.5)  Grade 1  2 (8.3)  4(16.7)  5(20.8)  3(12.5)  0 (0.0)  2 (8.3)  3(12.5)  3(12.5)  2 (8.3)  0 (0.0)  Grade 2  4(16.7)  5(20.8)  2 (8.3)  0 (0.0)  0 (0.0)  0 (0.0)  1 (4.2)  2 (8.3)  7(29. 2)  3(12.5)  Total  6 (8.3)  9(12.5)  8(11.1)  4 (5.6)  0 (0.0)  2 (2.8) 13(18.1) 11(15.3) 13(18. 1)  6 (8.3)  Kindergarten  0 (0.0)  0 (0.0)  0 (0.0)  0 (0.0)  0 (0.0)  3(12.5) 12(50.0)  Grade 1  0 (0.0)  1 (4.2)  1 (4.2)  1 (4.2)  1 (4.2)  Grade 2  3(12.5)  4(16.7)  4(16.7)  1 (4.2)  Total  3 (4.2)  5 (6.9)  5 (6.9)  T o t a l Sample  9 (6.3) 14 (977) 13 (9.0)  Group I I 7(29.2)  2 (8.3)  0 (0.0)  0 (0.0)  6(25.0) 10(41.7)  4(16. 7)  0 (0.0)  0 (0.0)  0 (0.0)  1 (4.2)  7(29. 2)  1 (4.2)  2 (2.8)  1 (1.4)  3 (4.2) 19(26.4) 20(27.8) 13(18. 1)  1 (1.4)  6 (4.2)  1 (0.7)  5 (3.5) 32(22.2) 31(21.5) 26(18. 1)  7 (4.9)  3(12.5)  TABLE 15 Number and Percentage of Subjects P a s s i n g and F a i l i n g T r a n s i t i v i t y and  a l l C o n s e r v a t i o n Tasks ( C r i t e r i o n  Number o f s u b j e c t s p a s s i n g the conserv a t i o n t a s k s but f a i l i n g the s p e c i f i e d number o f t r a n s i t i v i t y t a s k s . No. o f T r a n s i t i v i t y Tasks  0 No.  1 %  No.  2 %  No.  3 %  No,  No,  of Judgment Only) Number o f s u b j e c t s f a i l i n g t h e conserv a t i o n t a s k s b u t p a s s i n g the s p e c i f i e d number of t r a n s i t i v i t y t a s k s .  4  %  Tasks  0  %  No.  1 %  No.  2  %  No.  3 %  No.  4 %  No.  %  Group I Kindergarten  0 (0.0)  0 (0.0)  0 (0.0)  1 (4.2)  0 (0.0)  0 (0.0)  9(37. 5)  7(29.2)  4(16.7)  3(12.5)  Grade 1  2 (8.3)  4(16.7)  5(20.8)  3(12.5)  0 (0.0)  2 (8.3)  3(12. 5)  3(12.5)  2 (8.3)  0 (0.0)  Grade 2  4(16.7)  5(20.8)  0 (0.0)  0 (0.0)  0 (0.0)  0 (0.0)  1 (4.2)  4(16.7)  7(29.2)  3(12.5)  Total  6 (8.3)  9(12.5)  5 (6.9)  4. (5.6)  0 (0.0)  2 (2.8) 13(18. 1) 14(19.4) 13(18.1)  6 (8.3)  Kindergarten  0 (0.0)  0 (0.0)  0 (0.0)  0 (0.0)  0 (0.0)  3(12.5) 12(50. 0)  Grade 1 .  0 (0.0)  1 (4.2)  1 (4.2)  0 (0.0)  0 (0.0)  Grade 2  3(12.5)  2 (8.3)  3(12.5)  0 (0.0)  Total  3 (4.2)  3 (4.2)  4 (5.6)  9 (6.3) 12 (8.3)  9 (6.3)  Group I I  Total  Sample  7(29.2)  2 (8.3)  0 (0.0)  1 (4.2)  7(29. 2) 10(41.7)  4(16.7)  0 (0.0)  0 (0.0)  0 (0.0)  2 (8.3)  9(37.5)  1 (4.2)  0 (0.0)  0 (0.0)  4 (5.6) 21(29. 2) 21(29.2) 15(20.8)  1 (4.0)  4 (2.8)  0 (0.0)  6 (4.2) 34(23. 6) 35(24.3) 28(19.4)  7 (4.9)  4(16.7)  44. Discussion  Conservation  Taken t o g e t h e r the r e s u l t s agreement w i t h the r e s u l t s  study a r e i n g e n e r a l  o f s t u d i e s which i n d i c a t e t h a t  c o n s e r v a t i o n and e q u i v a l e n c e sense.  o f the p r e s e n t  c o n s e r v a t i o n co-occur  identity  i n a developmental  Performance on i d e n t i t y c o n s e r v a t i o n t a s k s was not s i g n i f i c a n t l y  different  from performance on e q u i v a l e n c e  very l i t t l e  conservation tasks.  d i f f e r e n c e i n t h e number o f s u b j e c t s who passed  c o n s e r v a t i o n t a s k s and e q u i v a l e n c e  There was  identity  c o n s e r v a t i o n t a s k s w i t h i n each group.  A l s o o f importance i s t h e f a c t t h a t t h e r e were n o t more s u b j e c t s who passed i d e n t i t y  c o n s e r v a t i o n t a s k s and f a i l e d e q u i v a l e n c e  t a s k s than t h e number who passed e q u i v a l e n c e failed  i d e n t i t y conservation tasks.  Kindergarten  c o n s e r v a t i o n t a s k s and  S i g n i f i c a n t l y more Grade 2 than  s u b j e c t s passed the c o n s e r v a t i o n t a s k s .  g a r t e n s u b j e c t s passed e i t h e r  identity  identity  The This result one  s u b j e c t s who passed  c o n s e r v a t i o n t a s k s and f a i l e d e q u i v a l e n c e  conservation tasks.  e f f e c t o f t h e two l e v e l s o f t r a n s f o r m a t i o n was i n s i g n i f i c a n t .  i s i n agreement w i t h o t h e r s t u d i e s which have used more  l e v e l of t r a n s f o r m a t i o n .  found  Very few K i n d e r -  c o n s e r v a t i o n or e q u i v a l e n c e  c o n s e r v a t i o n t a s k s and t h e r e were no K i n d e r g a r t e n both  conservation  Hooper (1969a) and Koshinsky and H a l l  t h a t v a r y i n g the l e v e l o f t r a n s f o r m a t i o n o f d i s c o n t i n u o u s  i n g l a s s c y l i n d e r s d i d not have a s i g n i f i c a n t e f f e c t . c o n t r a d i c t P i a g e t and I n h e l d e r ' s l e v e l o f t r a n s f o r m a t i o n , although  than (1973)  objects  T h i s would seem to  (1974) view of the importance o f t h e i t i s a l s o p o s s i b l e t h a t the d i f f e r e n t i a l  45. between the moderate and  The (1967) and  extreme was  not g r e a t enough.  group which r e c e i v e d the i d e n t i t y t a s k o u t l i n e d by E l k i n d  the t r a d i t i o n a l c o n s e r v a t i o n t a s k s  (Group I) performed  c o n s i s t e n t l y b e t t e r than the group which r e c e i v e d the m o d i f i c a t i o n (Group I I ) for a l l conservation tasks.  I t i s p o s s i b l e , however, t h a t t h i s r e s u l t e d  from some o v e r a l l d i f f e r e n c e i n the a b i l i t y of the groups r a t h e r than d i f f e r e n t i a l e f f e c t s of the t a s k s . f a c t t h a t Group I I a l s o was  T h i s i n t e r p r e t a t i o n i s based on  i n f e r i o r i n performance on the  t a s k s even though they were the same t a s k s a d m i n i s t e r e d  the  the  transitivity  to Group I .  It  i s not c l e a r what f a c t o r s c o u l d account f o r the s u p e r i o r performance of Group I s i n c e many p r e c a u t i o n s were taken groups was  done randomly.  c l a s s e s , w i t h the r e s u l t  t h a t s u b j e c t s i n d i f f e r e n t c l a s s e s at the same to be p l a c e d i n Group I  random t e s t i n g a c r o s s time of day  not be t e s t e d at any  s i n g l e time p e r i o d .  s u c c e s s f u l on the t r a n s i t i v i t y t a s k s was administered  b e f o r e any  T h i s was  treatment  :as i n Group I I .  to ensure t h a t one  The  group would  number of s u b j e c t s who  equivalence  were  the same whether the t a s k s were  c o n s e r v a t i o n t a s k s , between c o n s e r v a t i o n  ( i . e . , between i d e n t i t y and tasks.  the  S u b j e c t s were chosen randomly from t h e i r  grade l e v e l were e q u a l l y l i k e l y There was  to i n s u r e t h a t assignment to  t a s k s ) o r a f t e r the  tasks  conservation  t r u e w i t h i n each group, hence a d i f f e r e n t i a l m u l t i p l e  interference effect  (Campbell and  S t a n l e y , 1963;  p. 6) cannot  account f o r the d i f f e r e n c e between groups.  The most f r e q u e n t e x p l a n a t i o n c a t e g o r i e s used when j u s t i f y i n g responses were a d d i t i o n - s u b t r a c t i o n , statement of o p e r a t i o n s , to p r e v i o u s s t a t e and more than one  category.  reference  T o n i o l o and Hooper (1975)  46. found  t h a t a d d i t i o n - s u b t r a c t i o n was  category.  the s i n g l e most f r e q u e n t l y used  In the p r e s e n t study the statement  of o p e r a t i o n s  category  was used most f r e q u e n t l y w i t h the a d d i t i o n - s u b t r a c t i o n c a t e g o r y b e i n g the second most f r e q u e n t l y used  category.  Hooper  (1969a) and T o n i o l o  and Hooper (1975) found t h a t a d d i t i o n - s u b t r a c t i o n was  the c a t e g o r y most  f r e q u e n t l y used on i d e n t i t y c o n s e r v a t i o n , whereas P a p a l i a and Hooper (1971) found  t h a t r e f e r e n c e to the p r e v i o u s s t a t e was used most f r e q u e n t l y .  The most f r e q u e n t l y used  c a t e g o r y on the e q u i v a l e n c e t a s k s was r e f e r e n c e  to the p r e v i o u s s t a t e i n both the Hooper (1971) s t u d i e s .  T o n i o l o and Hooper  was the most f r e q u e n t l y used study statement  (1969a) and P a p a l i a and Hooper  (1975) found t h a t a d d i t i o n - s u b t r a c t i o n  c a t e g o r y on e q u i v a l e n c e t a s k s .  o f o p e r a t i o n s was  the most f r e q u e n t l y used  In the p r e s e n t c a t e g o r y on  both types of t a s k s .  The second most f r e q u e n t l y used e x p l a n a t i o n c a t e g o r y f o r i d e n t i t y tasks d i f f e r e d  from t h a t used  f o r equivalence tasks.  The statement  of  o p e r a t i o n s c a t e g o r y was most f r e q u e n t f o r i d e n t i t y t a s k s and the r e f e r e n c e to p r e v i o u s s t a t e c a t e g o r y was most f r e q u e n t f o r e q u i v a l e n c e t a s k s . i s i n agreement w i t h T o n i o l o and Hooper (1975) who of r e s u l t s w i t h the second most f r e q u e n t l y used  found  This  the same p a t t e r n  c a t e g o r y f o r the d i f f e r e n t  conservation tasks.  In agreement w i t h Hooper T o n i o l o and Hooper  (1969a), P a p a l i a and Hooper  (1975) the p r e s e n t study i n d i c a t e s t h a t i n v e r s i o n and  r e c i p r o c i t y a r e c a t e g o r i e s t h a t a r e used v e r y i n f r e q u e n t l y . of compensation was never used  type.  The c a t e g o r y  i n the p r e s e n t study, which i s i n agreement  w i t h the r e s u l t s o f T o n i o l o and Hooper (1975) , who e x p l a n a t i o n of t h i s  (1971) and  o b t a i n e d o n l y one  47. A comparison of T a b l e s and  14 supports  Brainerd's  1 and  3, T a b l e s  4 and  5, and T a b l e s  13  (1973) c o n t e n t i o n t h a t a judgment p l u s  e x p l a n a t i o n c r i t e r i o n i s much more s t r i n g e n t than a judgment o n l y  criterion.  The number of s u b j e c t s c o n s i d e r e d to have passed the c o n s e r v a t i o n  tasks  w i t h a c r i t e r i o n of judgment p l u s e x p l a n a t i o n i s c o n s i s t e n t l y l e s s the number who  passed w i t h a c r i t e r i o n of judgment o n l y .  than  These r e s u l t s  a r e i n agreement w i t h those of B r a i n e r d and Hooper (1975) and T o n i o l o Hooper (1975) i n t h a t the c r i t e r i o n chosen a f f e c t e d performance on c o n s e r v a t i o n t a s k s to a s t a t i s t i c a l l y  It  i s important  which support equivalence  the  degree.  at t h i s p o i n t to d i s c u s s two  recent studies  the t h e s i s t h a t i d e n t i t y c o n s e r v a t i o n i s a c q u i r e d p r i o r  conservation.  and Hooper (1975) p r e s e n t  Both B r a i n e r d and Hooper (1975) and evidence  Toniolo  c o n s e r v a t i o n of l e n g t h and  s t u d i e s were v e r y s i m i l a r to the p r e s e n t  one  and hence  weight. deserve  c l o s e d i s c u s s i o n p a r t i c u l a r l y s i n c e i t i s p o s s i b l e t h a t the r e s u l t s these s t u d i e s are  to  to show t h a t i d e n t i t y c o n s e r v a t i o n of  l e n g t h and weight precede e q u i v a l e n c e These two  significant  and  of  artifactual.  In both s t u d i e s a s c o r i n g technique 0 to 6 on the c o n s e r v a t i o n t a s k s was  used.  which a s s i g n e d v a l u e s  from  Three q u e s t i o n s were asked i n  the p r e d i c t i o n phase employing the terms "more", " l e s s " and  "same" and  t h r e e q u e s t i o n s employing these same t h r e e r e l a t i o n a l terms were asked i n the judgment phase.  Three terms were employed i n each phase i n o r d e r  i n s u r e t h a t c h i l d r e n had  to both  i n o r d e r to be c o r r e c t .  Rothenberg  agree and d i s a g r e e w i t h the experimenter (1969) has  r e p o r t e d on a tendency f o r  c h i l d r e n to agree w i t h what an experimenter says more f r e q u e n t l y than disagree.  Each time one  to  of the q u e s t i o n s was  they  answered c o r r e c t l y a s c o r e  48. of  1 was a s s i g n e d and each i n c o r r e c t response  was s c o r e d 0.  Since  there  were s i x q u e s t i o n s on each t a s k a maximum s c o r e o f 6 was p o s s i b l e and a l l v a l u e s between 0 and 6 c o u l d be o b t a i n e d .  I t i s v e r y important  to note  t h a t t h e r e was a d i f f e r e n c e between  the q u e s t i o n s employed i n i d e n t i t y c o n s e r v a t i o n t a s k s and e q u i v a l e n c e conservation tasks.  T h i s d i f f e r e n c e may account  f o r t h e supposed  develop-  mental p r i o r i t y o f i d e n t i t y c o n s e r v a t i o n over e q u i v a l e n c e c o n s e r v a t i o n . To i l l u s t r a t e  l e t us assume t h a t t h e r e i s a s u b j e c t who  consistently  b e l i e v e s t h a t a p e r c e p t u a l t r a n s f o r m a t i o n changes t h e r e l e v a n t q u a n t i t a t i v e f e a t u r e o f a c l a y b a l l c a u s i n g i t t o weigh more.  The same p o i n t would  apply to s u b j e c t s who c o n s i s t e n t l y b e l i e v e t h a t an o b j e c t weighs l e s s . The  f o l l o w i n g q u e s t i o n s a r e taken from t h e c o n s e r v a t i o n o f weight  tasks  employed by T o n i o l o and Hooper (1975) :  I d e n t i t y Format  1.  Prediction:  the t a b l e 8 - 1 0 a.  P l a c i n g t h e green  clay b a l l  i n c h e s from t h e S^ t h e E asks I f I were t o r o l l  i n the middle o f  the f o l l o w i n g q u e s t i o n s :  this clay b a l l  i n t o a hotdog would the  p i e c e o f c l a y s t i l l have t h e same weight? Yes  '  No b.  Q  I f I were t o r o l l  I don't know this clay b a l l  No response i n t o a hotdog would the  p i e c e o f c l a y weigh more? Yes  Q  No c.  I don't know  I f I were t o r o l l  this clay b a l l  No response i n t o a hotdog would the  p i e c e o f c l a y weigh l e s s ? Yes  No  1  I don't know  No  response  49. 2.  Deformation:  The E then r o l l s the b a l l i n t o a hotdog, and  asks the f o l l o w i n g q u e s t i o n s : a. Yes  No b.  Yes  Does t h i s p i e c e o f c l a y weigh the same as b e f o r e ?  0  0  I don't know  Does t h i s p i e c e of c l a y weigh more than b e f o r e ? No  c. Yes  No response  I don't know  No response  Does t h i s p i e c e o f c l a y weigh l e s s than b e f o r e ? No  1  I don't know  No response  E q u i v a l e n c e Format  1.  Prediction:  T a k i n g t h e b a l l s from t h e S and p l a c i n g  on the t a b l e s i d e - b y - s i d e 8 - 1 0 following  the  i n c h e s from t h e S, the E asks the  questions while pointing a.  No b.  t o one o f the s t i m u l i :  I f I were t o f l a t t e n t h i s c l a y b a l l i n t o a pancake,  two p i e c e s o f c l a y s t i l l  Yes  them  would  have the same weight?  0  I don't know  No response  I f I were t o f l a t t e n t h i s c l a y b a l l i n t o a pancake would  one o f the p i e c e s o f c l a y weigh more? Yes  0  No c.  I don't know  I f I were t o f l a t t e n t h i s c l a y b a l l i n t o a pancake would  one o f t h e p i e c e s o f c l a y weigh Yes  0  No  2.  No response  less? I don't know  Deformation:  No response  The E then f l a t t e n s t h e c l a y b a l l i n t o a  pancake and asks t h e f o l l o w i n g q u e s t i o n s : a. Yes  Do these two p i e c e s o f c l a y weigh t h e same as b e f o r e ? No  0  I don't know  No response  50. b. Yes  0  of the p i e c e s weigh more than  No c.  Yes  Does one  0  before?  I don't know  Does one  No  of the p i e c e s weigh l e s s than  No  response  before?  I don't know  No  response  N o t i c e t h a t the c h i l d would r e c e i v e a s c o r e of 2 f o r these answers on the i d e n t i t y t a s k .  T h i s i s because the c h i l d b e l i e v e s t h a t the  w i l l have more c l a y when i t i s r o l l e d  i n t o a hotdog.  p r e d i c t i o n and judgment  phase when asked i f the b a l l  (deformation)  Consequently i n the  have l e s s when i t i s a hotdog the c h i l d answers "no" i t w i l l have more. because, i n one  ball  will  f o r he/she b e l i e v e s  However a s c o r e of 1 w i l l be g i v e n f o r each phase  sense, the answer i s c o r r e c t i t w i l l not have l e s s .  analogous q u e s t i o n s  i n the e q u i v a l e n c e  t a s k do not  l e a d to such s c o r e s .  When the s u b j e c t i s asked i n the p r e d i c t i o n phase i f one l e s s he/she r e p l i e s t h a t one w i l l , ment phase the s u b j e c t w i l l  Scores o b t a i n e d  i . e . , the b a l l .  r e p l y t h a t one  The  object w i l l  S i m i l a r l y i n the  o b j e c t has  have judg-  less.  i n t h i s manner, employed the 0-6  s c a l e , were  s u b j e c t e d to an a n a l y s i s of v a r i a n c e by B r a i n e r d and Hooper (1975) and by T o n i o l o and Hooper (1975).  A statistically  tween i d e n t i t y c o n s e r v a t i o n and  equivalence  s i g n i f i c a n t d i f f e r e n c e be-  c o n s e r v a t i o n was  a t t r i b u t e d to the developmental p r i o r i t y of the i d e n t i t y concept  over the e q u i v a l e n c e  c o n s e r v a t i o n concept.  My  obtained  conservation  preceding a n a l y s i s  which shows that s c o r e s on i d e n t i t y c o n s e r v a t i o n t a s k s would be than s c o r e s on e q u i v a l e n c e  It  t a s k s suggests  t h a t the  i n the a n a l y s i s of v a r i a n c e are  i s important  greater  c o n s e r v a t i o n t a s k s because of the d i f f e r e n c e s  i n q u e s t i o n s employed on the two d i f f e r e n c e s obtained  and  significant  artifactual.  to note t h a t the d i f f e r e n c e s observed  i n the  51. T o n i o l o and Hooper (1975) study between i d e n t i t y c o n s e r v a t i o n  and  e q u i v a l e n c e c o n s e r v a t i o n were much l e s s pronounced when a dichotomous pass/ fail  c r i t e r i o n was  have passed  used.  According  a t a s k i f they were c o r r e c t on a l l q u e s t i o n s i n b o t h  p r e d i c t i o n and judgment phases. counted  to t h i s c r i t e r i o n s u b j e c t s were s a i d to  as a f a i l u r e .  Any  o t h e r p a t t e r n of responses  P r e s c h o o l , k i n d e r g a r t e n and  the was  t h i r d grade s u b j e c t s  were a s s e s s e d and when an a n a l y s i s of v a r i a n c e of the s c o r e s o b t a i n e d a 0-6 X.  s c a l e was  Equivalence  done a s i g n i f i c a n t main e f f e c t was  o b t a i n e d f o r the I d e n t i t y  f a c t o r i n b o t h l e n g t h and weight measures.  Grade L e v e l x C o n s e r v a t i o n Task Type i n t e r a c t i o n was when the p a s s / f a i l c r i t e r i o n was sample weight cases equivalence  with  A  significant  also obtained.  used, o n l y the k i n d e r g a r t e n and  i n d i c a t e d t h a t i d e n t i t y c o n s e r v a t i o n was  However  total  e a s i e r than  conservation.  U n f o r t u n a t e l y the same k i n d s of q u e s t i o n s were used f o r the c o n s e r v a t i o n t a s k s i n the p r e s e n t study as i n B r a i n e r d and Hooper and T o n i o l o and Hooper (1975) , as were s e v e r a l of the o t h e r p r e s c r i p t i o n s of B r a i n e r d and Hooper (1975). used i n the p r e s e n t studies.  scale.  However the s c o r i n g t e c h n i q u e  A t h r e e - p o i n t s c a l e w i t h v a l u e s of 0, 1 and  To  methodological  study o b v i a t e s the c r i t i c i s m s d i r e c t e d a t the o t h e r  s c a l e r e f l e c t s the l e v e l of concept 0-6  attainment  2 was  employed.  more c l e a r l y  This  than does a  i l l u s t r a t e l e t us assume t h a t t h e r e are two h y p o t h e t i c a l  s u b j e c t s X and Y who  both o b t a i n s c o r e s of 3 u s i n g the 0-6  scale.  n u m e r i c a l magnitudes a c c u r a t e l y r e f l e c t a s u b j e c t ' s l e v e l of attainment  (1975)  then s u b j e c t X and  I f these  concept  s u b j e c t Y s h o u l d be c o n s i d e r e d to be a t the  same l e v e l of c o n c e p t u a l development on the p a r t i c u l a r however, t h a t the d i s t r i b u t i o n of s c o r e s f o r the 0-6  task.  Suppose,  s c a l e i s as f o l l o w s :  52.  Prediction Same Sub.  X  1  Sub.  Y  1  More 1  Judgment Less  Same  1  0  0  On the s c o r i n g technique  More  Total Less  0  0  0  3  0  1  1  3  used i n the p r e s e n t  study  the s c o r e s  would be as f o l l o w s :  Prediction  Judgment Same  Sub.  X  Sub.  Y  0  0  More  0  0  0  1  Total Less  0  On t h e 0-6 s c o r i n g scheme s u b j e c t X and Y would be judged i n terms o f concept a t t a i n m e n t , s u b j e c t X shows a h i g h e r  equal  however, on t h e 0, 1, 2 s c o r i n g scheme  l e v e l o f concept attainment  than s u b j e c t Y.  The  0, 1, 2 s c o r i n g scheme demands t h a t s u b j e c t s be c o n s i s t e n t i n t h e i r answers w i t h i n each phase i n o r d e r i s done because t h e q u e s t i o n s not  independent.  to o b t a i n scores o t h e r  than 0.  This  i n v o l v i n g t h e t h r e e r e l a t i o n a l terms a r e  Given t h a t a s u b j e c t b e l i e v e s a transformed  object to  have the same amount o f c l a y as b e f o r e t h e t r a n s f o r m a t i o n he/she  should  a l s o b e l i e v e t h a t i t does n o t have more or l e s s , i n o r d e r t o be c o n s i s t e n t . This c o n s t r a i n t of consistency  i n responding  0-6 s c a l e as s u b j e c t s can o b t a i n p a r t v a l u e s  i s absent i n the case o f the f o r t h e i r answers.  i l l u s t r a t e , t h e importance o f t h i s c o n s i s t e n c y  To  c o n s t r a i n t , consider a l l  53.  p o s s i b l e p a t t e r n s of respondings conservation task. example i s concerned  to one phase of the  An example i s p r e s e n t e d w i t h o n l y one  can range from 0 to 3 i n c l u s i v e . to  the l e f t  i n T a b l e 16.  Since  phase of the c o n s e r v a t i o n t a s k s c o r e s Only  two  p a t t e r n s of r e s p o n d i n g ,  first  of  What t h i s means w i l l become c l e a r e r  l e t us c o n s i d e r another  numerals are a s s i g n e d to responses.  type of example, one  i n which  In many types of mental measurement  s i t u a t i o n s p a r t - v a l u e s are a s s i g n e d to a s u b j e c t ' s responses q u e s t i o n s a r e answered i n c o r r e c t l y .  may  those  A l l s i x o t h e r p o s s i b l e p a t t e r n s , to the r i g h t  the d o t t e d l i n e , are i n c o n s i s t e n t .  to  this  of the d o t t e d l i n e , can be c o n s i d e r e d to be c o n s i s t e n t  p a t t e r n s of responses.  below, but  equivalence  i f some  For i n s t a n c e , i f a s u b j e c t i s asked  d e f i n e the meaning o f 10 words and  gives 7 acceptable d e f i n i t i o n s ,  a s s i g n the number 7 to those r e s p o n s e s .  the words have been a s s i g n e d e q u a l weights.  we  Assuming, of c o u r s e , t h a t Another s u b j e c t who  a p p r o p r i a t e d e f i n i t i o n s would be a s s i g n e d a s c o r e of 5.  We  can  (based on the r e l a t i v e magnitude of the numerals a s s i g n e d to the  gave 5 say responses)  t h a t the s u b j e c t s c o r i n g 7 performed b e t t e r ( i . e . , gave more c o r r e c t d e f i n i t i o n s ) than the s u b j e c t s c o r i n g 5.  Furthermore, a l l o t h e r s u b j e c t s  can be ordered a c c o r d i n g l y .  Now  c o n s i d e r what happens i n the c o n s e r v a t i o n s i t u a t i o n s o u t l i n e d  above i n T a b l e 16.  Three of the i n c o n s i s t e n t p a t t e r n s of responding  be a s s i g n e d a 1 and  t h r e e w i l l be a s s i g n e d a 2.  will  F o l l o w i n g the l o g i c of  the p r e v i o u s example, i t would appear, w i t h i n an o r d e r of e r r o r , t h a t the t h r e e p a t t e r n s a s s i g n e d a 2 would evidence development which would i n t u r n be concept  the same l e v e l of  conceptual  c o n s i d e r e d to show more evidence  than p a t t e r n s b e i n g a s s i g n e d a 1.  There i s one  important  of. the  difference,  TABLE 16. P o s s i b l e P a t t e r n s of Responding  More  N  Y  '  N  N  N  Y  Less  N  Y  J  Y  Y  N  N  3  0  J  1  2  2  2  Assigned  Y = Yes  Score  N = No  55. however, between the c o n s e r v a t i o n s i t u a t i o n definitions.  The  three questions  and  the example of word  asked i n the c o n s e r v a t i o n  r e l a t i o n a l terms which are dependent on each o t h e r a c o n s i s t e n t response p a t t e r n . dependent i n the same sense. first  i n order  t a s k employ to l e a d to  However, the word d e f i n i t i o n s  are  not  To make t h i s p o i n t c l e a r e r , c o n s i d e r  the  p a t t e r n of responses to the r i g h t  of the d o t t e d l i n e i n T a b l e  A s u b j e c t g i v i n g t h i s s e t of responses would say t h a t both b a l l s not  the same weight, one  weigh l e s s .  C l e a r l y t h i s subject i s being  a s s e r t i n g t h a t mutually object.  b a l l does not weigh more and  b a l l does  e x c l u s i v e p r o p o s i t i o n s are h o l d i n g about the same  i n c o n s i s t e n t are of t h i s n a t u r e .  Even those  which have been l a b e l e d  s u b j e c t s which have been  a 2 have been i n c o n s i s t e n t i n t h i s manner, but  are supposedly r e l a t i v e l y c l o s e to having problem w i t h  these  subjects  the concept i n q u e s t i o n .  questions  correctly  but how  can  t h i s be  interpreted?  The  independent i n the sense t h a t answers can stand on t h e i r  without  r e f e r e n c e to the o t h e r answers.  Moreover, s i n c e a  ( i n a broad sense) i s b e i n g measured c o n s i s t e n c y  one  answered  are not  skill  The  the assignment of a l l of these p a r t - v a l u e s i s t h a t i n  sense the s u b j e c t i s p a r t i a l l y c o r r e c t i n t h a t he/she has or two  are  i n c o n s i s t e n t s i n c e he/she i s  In f a c t , a l l of the p a t t e r n s of responding  assigned  one  16.  one  questions own  reasoning  i n reasoning  is  important.  The  c r i t i c i s m s of the B r a i n e r d and Hooper (1975) and  and Hooper (1975) s t u d i e s can be  summarized as f o l l o w s .  s h o u l d be taken to i n s u r e t h a t the q u e s t i o n s e q u i v a l e n t i n terms of d i f f i c u l t y .  Greater  on each of the t a s k s  I t i s a l s o important  should be s t r u c t u r e d so t h a t answers can be  Toniolo  scored  t h a t the  care are questions  i n an unambiguous  56. manner.  The s c a l e of 0-6 l e a d s to an ambiguous r e f l e c t i o n o f t h e l e v e l  of concept  attainment  l a r g e l y because o f the d i f f i c u l t y  s c o r e v a l u e s o f 1 through  5.  i n interpreting  The p r e s e n t method o f s c o r i n g u s i n g a 0, 1,  2 s c a l e i s , u n f o r t u n a t e l y , o n l y s l i g h t l y more r e f i n e d than a p a s s / f a i l c r i t e r i o n , b u t i t i s not open t o t h e problems o f i n t e r p r e t a t i o n t h a t occur w i t h t h e 0-6 t e c h n i q u e .  The  importance o f these c r i t i c i s m s can be a p p r e c i a t e d when t h e  d a t a from t h e p r e s e n t study a r e s c o r e d w i t h t h e 0-6 s c a l e .  There were  many more s u b j e c t s who o b t a i n e d s c o r e s o f 1 o r 2 on t h e i d e n t i t y than on t h e e q u i v a l e n c e t a s k s . equivalence  tasks  The d i f f e r e n c e between i d e n t i t y and  t a s k s was a l s o s t a t i s t i c a l l y  s i g n i f i c a n t when an a n a l y s i s o f  v a r i a n c e o f s c o r e s o b t a i n e d w i t h t h i s a:ale was r u n . %  Transitivity  Subjects i n Kindergarten  and Grade 1 performed e q u a l l y w e l l on  the t r a n s i t i v i t y t a s k s , w h i l e s u b j e c t s i n Grade 2 performed b e t t e r than b o t h K i n d e r g a r t e n and Grade 1 s u b j e c t s .  As on t h e c o n s e r v a t i o n t a s k s  Group I performed b e t t e r than Group I I on t h e t r a n s i t i v i t y  tasks.  There was no d i f f e r e n c e i n performance on t h e v a r i o u s tasks.  A study by Murray and Y o u n i s s  transitivity  (1969) has i n d i c a t e d t h a t some  t r a n s i t i v i t y paradigms a r e e a s i e r than o t h e r s .  They p r e s e n t e d  tasks of  the form A>B=C, A=B>C and A>B>C t o K i n d e r g a r t e n , Grade 1 and Grade 2 children.  They found  t h a t t h e A>B>C paradigm was e a s i e r than e i t h e r o f  the o t h e r two paradigms, however t h e A>B=C, and A=B>C forms o f t h e t a s k d i d not d i f f e r s i g n i f i c a n t l y .  T h e i r tasks d i f f e r e d  from those used i n  57. the p r e s e n t  study  of l e n g t h was  i n t h a t none of the o b j e c t s were h i d d e n and  investigated.  Almost a l l of the s u b j e c t s i n the p r e s e n t more of the t r a n s i t i v i t y 2 or more t a s k s . conservation and  failed  tasks.  t a s k s , w h i l e v e r y few tasks.  study  passed 1 or  A l a r g e p r o p o r t i o n of s u b j e c t s passed  Many s u b j e c t s passed t r a n s i t i v i t y  transitivity  of B r a i n e r d  transitivity  t a s k s , but  s u b j e c t s passed c o n s e r v a t i o n  tasks  These r e s u l t s are i n agreement w i t h  (1973) and T o n i o l o and Hooper (1975) r e g a r d i n g  of t r a n s i t i v i t y and  failed  the  those .  acquisition  conservation.  Conclusion  The  r e s u l t s of the p r e s e n t  study  and  those  Hooper (1975) c a s t c o n s i d e r a b l e doubt on E l k i n d ' s the r o l e of t r a n s i t i v i t y  of T o n i o l o  and  (1967) a n a l y s i s about  i n the t y p i c a l c o n s e r v a t i o n  task.  Transitivity,  as a mental o p e r a t i o n , develops p r i o r to b o t h i d e n t i t y c o n s e r v a t i o n equivalence  c o n s e r v a t i o n , at l e a s t i n the content  areas  of s o l i d  and  continuous  q u a n t i t y , l e n g t h and weight, hence the absence of t h i s concept cannot i n v o l v e d i n an e x p l a n a t i o n of f a i l u r e on the t r a d i t i o n a l t a s k .  T h i s would  o n l y be the case, however, i f i t i s shown t h a t i d e n t i t y precede conservation  developmentally.  i d e n t i t y and  equivalence  I f , however, as the p r e s e n t  conservation  co-occur  s t i l l h o l d t r u e i n the sense t h a t t r a n s i t i v i t y proper who  tasks.  It is difficult  e m p i r i c a l l y unless  to see how  equivalence  study  indicates,  then E l k i n d ' s a n a l y s i s c o u l d i s indeed  s o l u t i o n of the t r a d i t i o n a l c o n s e r v a t i o n  pass i d e n t i t y t a s k s have the concept, they  be  t a s k but  important  f o r the  since a l l subjects  can a l s o pass  equivalence  E l k i n d ' s a n a l y s i s c o u l d be i n v e s t i g a t e d  a p a r t i c u l a r content  area was  found i n which s u b j e c t s  58. do not have t r a n s i t i v i t y , but can pass i d e n t i t y c o n s e r v a t i o n t a s k s . s u b j e c t s passed i d e n t i t y t a s k s but t h i s would support  the a n a l y s i s .  t a s k s and passed e q u i v a l e n c e the a n a l y s i s . found  area.  identity  study and  area w i l l  those of  (1971), B r a i n e r d '(1973) , and T o n i o l o and Hooper  be  Bryant  (1975)  to be a r e l a t i v e l y p r i m i t i v e o p e r a t i o n which  p r i o r to c o n s e r v a t i o n .  were found  tasks  c o n s e r v a t i o n t a s k s t h i s would c o n t r a d i c t  I t i s h i g h l y u n l i k e l y t h a t such a content  which show t r a n s i t i v i t y develops  conservation  I f , however s u b j e c t s passed  c o n s i d e r i n g the r e s u l t s of the p r e s e n t  and Trabasso  i t was  f a i l e d equivalence  If  Moreover even i f such a content  area  E l k i n d ' s o r i g i n a l a n a l y s i s would be c o n s i d e r a b l y weakened as  meant to apply  to a l l c o n s e r v a t i o n t a s k s i r r e s p e c t i v e of  content  59. Footnotes  *These e f f e c t s s h o u l d be t r e a t e d w i t h c a u t i o n (0,1) length Feldt  was used i n the a n a l y s i s .  I n an a n a l y s i s  scale"  o f t h e e f f e c t s o f the  o f a s c o r e s c a l e on the s i g n i f i c a n c e l e v e l o f the F - t e s t Hsu and (1969) p o i n t  out t h a t when a two-point s c a l e i s i n v o l v e d  s i z e o f 50 o r more s h o u l d be used. the  s i n c e a "two-point  However s i n c e  a sample  the group e f f e c t i s  r e s u l t o f a sample s i z e of 72 and t h e grade e f f e c t a sample s i z e o f  48 t h i s p r e s c r i p t i o n has n o t been s e r i o u s l y v i o l a t e d .  Further,  considering  unlikely  the r o b u s t n e s s o f t h e e f f e c t s i t i s h i g h l y  these f a c t o r s d i d not have a s i g n i f i c a n t  2 This  that  influence.  c l a s s i f i c a t i o n scheme has been adopted from T o n i o l o and Hooper  (1975).  60. References  B r a i n e r d , C.J. Judgments and e x p l a n a t i o n s as c r i t e r i a f o r t h e p r e s e n c e of c o g n i t i v e s t r u c t u r e s . P s y c h o l o g i c a l B u l l e t i n , 1973, _7_9» 172-179. (a) B r a i n e r d , C . J . Order o f a c q u i s i t i o n o f t r a n s i t i v i t y , c o n s e r v a t i o n , and c l a s s - i n c l u s i o n o f l e n g t h and weight. Developmental P s y c h o l o g y , 1973, 8, 105-116.(b) B r a i n e r d , C . J . & B r a i n e r d , S.H. Order o f a c q u i s i t i o n o f number and l i q u i d quantity conservation. C h i l d Development, 1972, 43, 1401-1406. B r a i n e r d , C . J . & Hooper, F.H. A m e t h o d o l o g i c a l a n a l y s i s o f developmental s t u d i e s o f i d e n t i t y c o n s e r v a t i o n and e q u i v a l e n c e c o n s e r v a t i o n . P s y c h o l o g i c a l B u l l e t i n , 1975, j52_, i n p r e s s . Bruner, J.S., O l v e r , R.R., G r e e n f i e l d , P.M. e t a l . growth. New York: John W i l e y , 1966.  Studies i n c o g n i t i v e  B r y a n t , P.E. P e r c e p t i o n and u n d e r s t a n d i n g i n young c h i l d r e n : An e x p e r i m e n t a l approach. New York: B a s i c Books, Inc. 1974. Bryant, P.E.- The U n d e r s t a n d i n g o f i n v a r i a n c e by v e r y young c h i l d r e n . Canadian J o u r n a l o f P s y c h o l o g y , 1972, 26, 78-96. B r y a n t , P.E. & T r a b a s s o , T. T r a n s i t i v e i n f e r e n c e s and memory i n young children. N a t u r e , 1971, 232, 456-458. Campbell, D.T. & S t a n l e y , J.C. E x p e r i m e n t a l and Q u a s i - e x p e r i m e n t a l f o r Research. C h i c a g o : Rand M c N a l l y , 1963.  Designs  E l k i n d , D. C h i l d r e n ' s d i s c o v e r y o f the c o n s e r v a t i o n o f mass, weight, and volume: P i a g e t r e p l i c a t i o n study I I . The J o u r n a l o f G e n e t i c P s y c h o l o g y , 1961, 98, 219-2271. E l k i n d , D. P i a g e t ' s 38, 15-27.  conservation  problems.  C h i l d Development, 1967,  E l k i n d , D. & S c h o e f e l d , E. I d e n t i t y and e q u i v a l e n c e c o n s e r v a t i o n a t two age l e v e l s . Developmental P s y c h o l o g y , 1972, 6_, 529-533. F l a v e l l , J.H. Stage r e l a t e d p r o p e r t i e s o f c o g n i t i v e development. C o g n i t i v e P s y c h o l o g y , 1971, 2, 421-453. Furby, L. Cumulative l e a r n i n g and c o g n i t i v e development: E l a b o r a t i o n and i m p l i c a t i o n s o f a p r e t h e o r e t i c a l model. Human Development, 1972, 15, 265-286. H a l f o r d , G.S. A c q u i s i t i o n o f c o n s e r v a t i o n . J77, 302-316.  P s y c h o l o g i c a l Review, 1970,  61. Hooper, F.H. P i a g e t ' s c o n s e r v a t i o n t a s k s : The l o g i c a l and developmental p r i o r i t y o f i d e n t i t y c o n s e r v a t i o n . J o u r n a l of E x p e r i m e n t a l C h i l d Psychology, 1969, 8, 234-249. (a) Hooper, F.H. The A p p a l a c h i a n c h i l d ' s i n t e l l e c t u a l c a p a b i l i t i e s — d e p r i v a t i o n or d i v e r s i t y . 1969 Yearbook of the J o u r n a l of Negro E d u c a t i o n , 1969, 224-235. (b) Hsu,  T. & F e l d t , L.S. The e f f e c t of l i m i t a t i o n s on the number of c r i t e r i o n s c o r e v a l u e s on the s i g n i f i c a n c e l e v e l of the F - t e s t . American E d u c a t i o n a l Research J o u r n a l , 1969, 6_, 515-527.  K o s h i n s k y , C. & H a l l , A.E. The developmental r e l a t i o n s h i p between i d e n t i t y and e q u i v a l e n c e c o n s e r v a t i o n . J o u r n a l of E x p e r i m e n t a l C h i l d Psychology, 1973, 15, 419-424. Moynahan, E. & G l i c k , J . R e l a t i o n between i d e n t i t y c o n s e r v a t i o n and e q u i v a l e n c e c o n s e r v a t i o n w i t h i n f o u r c o n c e p t u a l domains. Developmental Psychology, 1972, 6, 247-251. Murray, J.P. & Y o u n i s s , J . Achievement of i n f e r e n t i a l t r a n s i t i v i t y and i t s r e l a t i o n to s e r i a l o r d e r i n g . C h i l d Development, 1968, 39(4) , 1259-1268. Murray, F.B. Stimulus mode and the c o n s e r v a t i o n o f weight and J o u r n a l of E d u c a t i o n a l Psychology, 1970, 61, 287-291.  number.  Northman, G. & Gruen, C. R e l a t i o n s h i p between i d e n t i t y and e q u i v a l e n c e conservation. Developmental P s y c h o l o g y , 1970, ^ ( 2 ) , 311. P a p a l i a , D.E. & Hooper, F.H. A developmental comparison of i d e n t i t y and equivalence conservations. J o u r n a l of E x p e r i m e n t a l C h i l d Psychology, 1971, 12, 347-361. Piaget, J . 1965.  The  c h i l d ' s conception  P i a g e t , J . C o g n i t i o n s and Psychology, 1967, 12,  of number.  conservations: 530-533.  New  Two  P i a g e t , J . On the development of memory and C l a r k U n i v e r s i t y P r e s s , 1968.  York:  views.  identity.  Norton L i b r a r y ,  Contemporary  B a r r e , Mass.:  P i a g e t , J . & I n h e l d e r , B. The c h i l d ' s c o n s t r u c t i o n of q u a n t i t i e s : C o n s e r v a t i o n and atomism. London: Routledge & Kegan P a u l , 1974. Rothenberg, B.B. C o n s e r v a t i o n of number among f o u r and f i v e - y e a r - o l d children: Some m e t h o d o l o g i c a l c o n s i d e r a t i o n s . C h i l d Development, 1969, 40, 383-406.  62. Schwartz, M.M. & S c h o l n i c k , E.K. Scalogram a n a l y s i s of l o g i c a l and p e r c e p t u a l components of c o n s e r v a t i o n of d i s c o n t i n u o u s q u a n t i t y . C h i l d Development, 1970, 41, 695-705. T o n i o l o , T. & Hooper, F.H. M i c r o - a n a l y s i s of l o g i c a l r e a s o n i n g relationships: C o n s e r v a t i o n and t r a n s i t i v i t y . T e c h n i c a l Report No. 326. Madison: W i s c o n s i n Research and Development Center for Cognitive Learning, 1975. Y o u n i s s , J . & Murray, J.P. solutions controlled. 169-175.  T r a n s i t i v e inferences with n o n - t r a n s i t i v e Developmental P s y c h o l o g y , 1970, 2^(2),  63. Appendix A*"  Explanation Categories  1)  f o r Conservation  Addition-Subtraction:  n o t h i n g has been added to or s u b t r a c t e d from  the transformed 2)  Tasks  stimulus.  Statement o f O p e r a t i o n s :  a s s e r t i o n t h a t t h e t r a n s f o r m a t i o n d i d not  a f f e c t the quantity i n question. Example: You j u s t 3)  Reference t o P r e v i o u s  f l a t t e n e d i t down ( i t ' s s t i l l  State:  standard  s t i m u l u s and  the same amount). transformed  s t i m u l u s have the same amount because the standard and  stimulus  comparison s t i m u l u s had the same amount b e f o r e t t h e  transformation. Example:  They ( t h e o b j e c t s ) were the same amount b e f o r e , so  they a r e s t i l l 4)  Inversion:  the same now.  when o b j e c t can be r e t u r n e d t o i t s s t a t e p r i o r t o t r a n s -  formation. Example:  You can r o l l  i t back i n t o a b a l l and i t w i l l have  the same amount. 5)  Reciprocity:  when s t a n d a r d  transformed Example:  s t i m u l u s can be made t o resemble t h e  stimulus.  You can f l a t t e n t h a t  ( t h e standard) and they  will  have the same amount. 6)  Compensation:  one dimension o f the transformed  by t h e o t h e r Example:  stimulus  i s compensated  dimension.  The pancake i s b i g g e r around, but i t i s a l s o  flatter.  Sameness (same stimulus):  assertion that stimulus as a whole entity  is the same piece of clay. Example:  I t i s s t i l l just the same clay as before.  Sameness (same quantity):  assertion that the stimulus has the same  amount as before. Example:  I t s t i l l has just the same amount of clay.  More than one category:  use of two or more of the above categories  in a composite explanation. Example of 1) and 2 ) : take any away.  You just flattened i t down, you didn't  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0093773/manifest

Comment

Related Items