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