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An analysis of children’s ideas of heat phenomena 1975

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AN ANALYSIS OF CHILDREN'S IDEAS OF HEAT PHENOMENA by Gaalen L. E r i c k s o n B. Ed., 1964, M. Sc., 1966, U n i v e r s i t y of A l b e r t a A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF EDUCATION i n the Department of Education We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1975 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . CV. O. CvV \' Department o f fc_ C C Cv \ \ D H The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date ABSTRACT This study was d i r e c t e d towards the r e s o l u t i o n of t h r e e , i n t e r - dependent problems: 1) the i d e n t i f i c a t i o n of ' t y p i c a l ' b e l i e f s about heat phenomena h e l d by c h i l d r e n ; 2) the development of a method f o r examining the o r g a n i z a t i o n of these b e l i e f s ; and 3) the a p p l i c a t i o n of the r e s u l t s to a classroom s i t u a t i o n . U n d e r l y i n g these.problems was the fundamental assumption that knowledge of c h i l d r e n ' s i n t e l l e c t u a l commitments i s an important p r e - cursor to the systematic development of i n s t r u c t i o n a l s t r a t e g i e s . Some recent s t u d i e s have suggested that a discrepancy between students' ex- i s t i n g commitments and those portrayed by the c u r r i c u l a r m a t e r i a l s may be the source' of s i g n i f i c a n t " l e a r n i n g d i f f i c u l t i e s " encountered i n the science classroom. The methods of study used were i n p a r t d e s c r i p t i v e and i n p a r t e m p i r i c a l . In the f i r s t p a r t , i n t e r v i e w dataware c o l l e c t e d and analyzed while the second p a r t i n v o l v e d the c o n s t r u c t i o n of a type of instrument f o r i d e n t i f y i n g conceptual p r o f i l e s of i n d i v d u a l c h i l d r e n and groups of c h i l d r e n . The Conceptual P r o f i l e Instrument (C.P.I.) c o n s i s t e d of statements about heat obtained from the i n t e r v i e w data, r e p r e s e n t i n g ' t y p i c a l ' c h i l d r e n ' s i d e a s , along w i t h statements r e p r e s e n t i n g the k i n e t i c and c a l o r i c t h e o r i e s of heat. C h i l d r e n were r e q u i r e d to respond to each statement on a set of b i p o l a r s c a l e s r e p r e s e n t i n g b e l i e f and f a m i l i a r i t y dimensions. The r e s u l t s of the i n t e r v i e w data were summarized i n terms of a number of ideas about heat c a l l e d a " C h i l d r e n ' s P e r s p e c t i v e . " I t was concluded that most c h i l d r e n possess some genuine b e l i e f s about heat and temperature. These b e l i e f s were hypothesized to be based at l e a s t i n p a r t upon common-sense i n t u i t i o n s developed from everyday experience. For example, the temperature of an obj e c t was thought to be r e l a t e d to the amount of heat possessed by that o b j e c t and so many c h i l d r e n concluded that the temperature of an obj e c t depended, i n p a r t , upon i t s s i z e . "Heat", and f r e q u e n t l y " c o l d " , were g e n e r a l l y conceived to be a type of s u b t l e substance ( o f t e n r e f e r r e d to as fumes or rays) capable of p e n e t r a t i n g most o b j e c t s . Heat was thus considered to be an a c t i v e e x t e r n a l agent accounting f o r the ex p a n s i o n - c o n t r a c t i o n and m e l t i n g - f r e e z i n g behaviour e x h i b i t e d by many substances. A n a l y s i s of the r e s u l t s obtained from a d m i n i s t e r i n g the C.P.I, to twelve c l a s s e s of grade 5, 7 and 9 students provided evidence f o r three c l e a r l y d i s t i n g u i s h a b l e b e l i e f p a t t e r n s about heat phenomena. The b e l i e f p a t t e r n s corresponded to the ' b u i l t - i n ' k i n e t i c , c a l o r i c and c h i l d r e n ' s p e r s p e c t i v e s . These p a t t e r n s were termed "Model Conceptual P r o f i l e s " i n the study. These P r o f i l e s were i n t e r p r e t e d i n terms of d i f f e r e n t l e v e l s of understanding of heat phenomena. One Model Con- c e p t u a l P r o f i l e appeared to represent a more a b s t r a c t view of heat as manifested by higher r a t i n g s of the k i n e t i c and c a l o r i c statements. Another was i n t e r p r e t e d to represent a more concrete, common-sense view p o i n t , w h i l e the t h i r d was thought to represent a type of t r a n s i - t i o n a l l e v e l . Two ways of a p p l y i n g the r e s u l t s of the study to a classroom s i t u a - t i o n were disc u s s e d : an i n t e r p r e t i v e use of the p r o f i l e s and an a p p l i c a t i v e use. A set of p o t e n t i a l teaching maneuvers, cross-referenced to a p a r t i - c u l a r Model Conceptual P r o f i l e were proposed. i i TABLE OF CONTENTS Page A b s t r a c t i L i s t of Tables v i i L i s t of Figur e s v i i i Acknowledgements i x Chapter One The Problem 1.00 I n t r o d u c t i o n 1 1.10 The General Problem 2 1.11 The S p e c i f i c Problems 3 1.20 Methods of Study 4 1.30 E d u c a t i o n a l S i g n i f i c a n c e of the Study . . . . 5 1.40 L i m i t a t i o n s of the Study 7 Two Context of the Study 2.00 E d u c a t i o n a l Context of the Problem 14 2.01 R e l a t i o n s h i p to Curriculum Problems i n Science Education 14 2.02 R e l a t i o n s h i p to Teaching-Learning Problems i n Science Education 17 2.03 Review of Studies Related to the Problem . 19 2.10 P s y c h o l o g i c a l Context of the Study . . . . . . 21 2.11 R e l a t i o n s h i p to S t r u c t u r a l A n a l y s i s . . . . 21 2.12 R e l a t i o n s h i p to P i a g e t ' s S t r u c t u r e s of I n t e l l i g e n c e 22 2.13 R e l a t i o n s h i p to Witz and Easley's Deep St r u c t u r e s 24 i i i Chapter Page 2.14 The Concept of S t r u c t u r e Used i n the Present Study . 27 Three Method of C o l l e c t i n g and A n a l y z i n g the I n t e r v i e w Data 3.00 The P r e l i m i n a r y Work 33 3.10 A D e s c r i p t i o n of the Formal Interviews . . . 33 3.11 The Subjects 33 3.12 The Tasks 34 3.13 The Format of the I n t e r v i e w 37 3.20 A n a l y s i s of the I n t e r v i e w Data 39 3.21 D e f i n i t i o n of an Idea 41 3.22 I d e n t i f i c a t i o n of Ideas 4 1 3.23 C o n s t r u c t i o n of Conceptual I n v e n t o r i e s . . . 46 3.24 An example of a Conceptual Inventory . . . . 46 3.25 A C h i l d r e n ' s P e r s p e c t i v e of Heat 49 Four Method of Obtaining Conceptual P r o f i l e s 4.00 I n t r o d u c t i o n . . 53 4.10 A Model f o r S t r u c t u r a l A n a l y s i s 53 4.20 Development of the Conceptual P r o f i l e Instrument 57 4.21 O p e r a t i o n a l i z i n g the A t t r i b u t e 57 4.22 Method of Assessing P s y c h o l o g i c a l R e l a - t i o n s h i p 58 4.23 A l t e r a t i o n s i n the Standard Semantic D i f f e r e n t i a l Format . . . 61 4:24 C o n s t r u c t i o n of the Conceptual P r o f i l e Instrument 64 i v Chapter Page 4.30 A d m i n i s t r a t i o n of the Conceptual P r o f i l e Instrument 65 4.31 D e s c r i p t i o n of the Subjects 65 4.32 D e s c r i p t i o n of A d m i n i s t r a t i o n Procedures 66 4.33 D e s c r i p t i o n of the Demonstrations and Statements 66 4.40 A n a l y s i s of the Instrument Data . . . . . . 72 4.41 A n a l y s i s of the Scale D i m e n s i o n a l i t y . . . 73 4.42 A n a l y s i s of Statement D i m e n s i o n a l i t y . . . 76 4.50 The A n a l y s i s of Model Conceptual P r o f i l e s . . 83 Fi v e R e s u l t s of the Conceptual P r o f i l e A n a l y s i s 5.00 Model Conceptual P r o f i l e s f o r the B e l i e f - S c o r e s . 89 5.10 Model Conceptual P r o f i l e s f o r the F a m i l i a r i t y - S c o r e s 91 5.20 I n t e r p r e t a t i o n of the Model Conceptual P r o f i l e s 99 5.21 The B e l i e f P r o f i l e s . . . 99 5.22 The F a m i l i a r i t y P r o f i l e s 108 S i x I l l u s t r a t i v e A p p l i c a t i o n s of the Study 6.00 Two Way of Applying the Study . . . . . . . 112 6.10 I l l u s t r a t i o n of an I n t e r p r e t i v e Use of the Study 1 1 3 6.20 I l l u s t r a t i o n of an A p p l i c a t i v e Use of the Study 1 1 5 6.21 Problems of Designing Teaching S t r a t e g i e s • ^ 5 6.22 An Example of an A p p l i c a t i v e Use .• • • • •• 1 ^ v Chapter Page Seven Conclusions and Recommendations 7.00 Overview of the Study . . . . . . . . . . . . 127 7.10 Conclusions of the Study 128 7.20 Recommendations f o r Further Research . . . 131 B i b l i o g r a p h y 1 3 7 LIST OF TABLES Table Page 4-1 Rotated P r i n c i p a l Component-Loadings f o r I n t e r - S c a l e C o r r e l a t i o n M a t r i x 75 4-2 Rotated P r i n c i p a l Component-Loadings f o r Inter-Statement C o r r e l a t i o n M a t r i x of B e l i e f - S c o r e s ( S i x Components Rotated) 78 4-3 Rotated P r i n c i p a l Component-Loadings f o r Inter-Statement C o r r e l a t i o n M a t r i x of B e l i e f - S c o r e s (Four Components Rotated) . . . . . . . 79 4- 4 Rotated P r i n c i p a l Component-Loadings f o r Inter-Statement C o r r e l a t i o n M a t r i x of F a m i l i a r i t y - S c o r e s (Four Components Rotated) 81 5- 1 The 16 Eigenvalues from the P r i n c i p a l F a c t o r A n a l y s i s of the I n t e r - P r o f H e C o r r e l a t i o n M a t r i x of B e l i e f - S c o r e s 90 5-2 The Largest S i x Eigenvalues Obtained by F a c t o r i n g the D-Matrices f o r Each of the Three Shape F a m i l i e s o f B e l i e f - S c o r e s 91 5-3 A L i s t of the Statements i n Each Viewpoint Used i n the P r o f i l e A n a l y s i s of the B e l i e f - Scores 95 5-4 The Eigenvalues from the P r i n c i p a l F a c t o r A n a l y s i s of the I n t e r - P r o f i l e C o r r e l a t i o n M a t r i x of F a m i l i a r i t y - S c o r e s 96 5- 5 Model Conceptual P r o f i l e Membership by Grade L e v e l 107 6- 1 A L i s t of the Statements i n Each Viewpoint Used i n the P r o f i l e A n a l y s i s of the B e l i e f - Scores 119 6-2 L i s t of P o s s i b l e Teaching Maneuvers to Accompany Model Conceptual P r o f i l e Two 122 v i i LIST OF FIGURES Figure Page 4- 1 A Reproduction of a S i n g l e Page from the Conceptual P r o f i l e Instrument 68 5- 1 Model Conceptual P r o f i l e 1 ( B e l i e f - S c o r e s ) . . . 92 5-2 Model Conceptual P r o f i l e 2 ( B e l i e f - S c o r e s ) . . . 93 5-3 Model Conceptual P r o f i l e 3 ( B e l i e f - S c o r e s ) . . . 94 5-4 Model Conceptual P r o f i l e 4 ( F a m i l i a r i t y - Scores) • . • 97 5- 5 Model Conceptual P r o f i l e 5 ( F a m i l i a r i t y - Scores) 98 6- 1 An I n d i v i d u a l P r o f i l e of B e l i e f - S c o r e s f o r a Grade 7 Subject 120 6-2 Model Conceptual P r o f i l e 2 120 v i i i ACKNOWLEDGEMENTS I would l i k e to express my g r a t i t u d e to a number of people who have been i n s t r u m e n t a l i n a s s i s t i n g me, i n a number of d i f f e r e n t ways, to complete t h i s d i s s e r t a t i o n . I am deeply indebted to Walter B o l d t , my t h e s i s a d v i s e r , who was always a v a i l a b l e to provide me w i t h the necessary i n t e l l e c t u a l and emotional support. In a d d i t i o n , I would l i k e to thank the members of my committee — Harry Cannon, J u l i Conry, J e r r y Coombs, Roi D a n i e l s , Steve F o s t e r , and Steve S t r a k e r — who have c o n t r i b u t e d to the t h e s i s through many c l a r i f y i n g d i s c u s s i o n s and h e l p f u l comments on a d r a f t copy. A l s o I would l i k e to thank Dave W i l l i a m s and Derek Wilson f o r agreeing to serve as e x t e r n a l members of the examination committee. My t y p i s t , Esther McDonald, o f t e n responded h e r o i c a l l y to the many demands I've made on her. F i n a l l y I would l i k e to thank my w i f e , Lynda, f o r the much needed support that she has provided over the years from conception to completion o f the t h e s i s . Her c o n t r i b u t i o n as companion and c r i t i c was g r e a t l y valued. i x CHAPTER ONE THE PROBLEM 1.00 I n t r o d u c t i o n The purpose of the study i s to f i n d answers to three broad questions concerning i n s t r u c t i o n i n s c i e n c e : 1) How can c h i l d r e n ' s b e l i e f s and i n t u i t i o n s about n a t u r a l phenomena be i d e n t i f i e d ? 2) How can these b e l i e f s be represented i n a meaningful way? 3) How can these r e p r e s e n t a t i o n s be used to advantage by the teacher i n classroom p r a c t i c e ? Since the t h i r d q u e s t i o n concerning e d u c a t i o n a l a p p l i c a b i l i t y placed c e r t a i n c o n s t r a i n t s upon the methods used to answer the f i r s t two q u e s t i o n s , a l l of the questions ought to be t r e a t e d as i n t e r - dependent r a t h e r than separate research q u e s t i o n s . As an i n t r o d u c t i o n to the d i s s e r t a t i o n the f i r s t chapter c o n t a i n s an o u t l i n e of the nature of the problem and i t s e d u c a t i o n a l s i g n i f i c a n c e . A b r i e f d i s c u s s i o n of the methods used and the l i m i t a t i o n s of the study are a l s o i n c l u d e d i n t h i s chapter. The second chapter c o n t a i n s a d i s - c ussion to embed the study i n a broader e d u c a t i o n a l and methodological context. Previous work r e l a t i n g to the problem i s examined and the r e s u l t i n g s y n t h e s i s of methods designed f o r the study i s d e s c r i b e d . The f i r s t q u e s t i o n above, concerning the i d e n t i f i c a t i o n of c h i l d r e n ' s b e l i e f s , i s addressed i n Chapter Three. I t provides a d e s c r i p t i o n of the s p e c i f i c methods used to gather i n t e r v i e w data and an i l l u s t r a t i o n of the a n a l y t i c a l scheme used to process these data. A d i s c u s s i o n of the r e s u l t s i s a l s o i n c l u d e d i n t h i s chapter. 2 Chapter Four contains a d e s c r i p t i o n of a classroom instrument (based i n p a r t upon the i n t e r v i e w data) that was designed to answer the second question — the development of a method f o r o b t a i n i n g a represen- t a t i o n of c h i l d r e n ' s b e l i e f s . This chapter includes a d i s c u s s i o n of the s t a t i s t i c a l techniques used to analyze the data obtained from adminis- t e r i n g the instrument to a sample of s c h o o l c h i l d r e n . The r e s u l t s of the a n a l y s i s are presented i n Chapter F i v e . The l a s t q u e stion posed above i s addressed i n Chapter S i x . An a p p l i c a t i o n of the study to an e d u c a t i o n a l s e t t i n g i s discussed and the chapter concludes w i t h a sample i l l u s t r a t i o n of how the classroom instrument might be u t i l i z e d by a teacher. The f i n a l chapter c o n s i s t s of the major conclusions of the study and a l i s t of recommendations f o r f u r t h e r research i n the area. 1.10 The General Problem There i s widespread agreement, spanning the e n t i r e spectrum of e d u c a t i o n a l o r t h o d o x i e s , t h a t knowledge of what the l e a r n e r b r i n g s to the l e a r n i n g s i t u a t i o n i s an important component i n planning any edu- c a t i o n a l program. The b e h a v i o r i s t s have long endorsed the n o t i o n of a s s e s s i n g 'entry b e h a v i o r s ' , but only w i t h the r e d i s c o v e r y of P i a g e t d i d support f o r t h i s p o s i t i o n extend to the l e f t wing of s c h o o l reform — the open education movement. Perhaps the most emphatic statement of t h i s p o s i t i o n i s made by Ausubel (1968) who introduced h i s book, Edu c a t i o n a l Psychology: A C o g n i t i v e View, w i t h the f o l l o w i n g statement: I f I had to reduce a l l the e d u c a t i o n a l psychology to j u s t one p r i n c i p l e , I would say t h i s : The most important s i n g l e f a c t o r i n f l u e n c i n g l e a r n i n g i s what the l e a r n e r already knows. A s c e r t a i n t h i s and teach him a c c o r d i n g l y . 3 Given t h i s r a r e i n s t a n c e of agreement across wide s e c t i o n s of the e d u c a t i o n a l community i t i s indeed s u r p r i s i n g how l i t t l e r e s e a r c h has been d i r e c t e d towards the problem of a s c e r t a i n i n g what the l e a r n e r already knows. Those few c u r r i c u l a t h a t have attempted to i n c o r p o r a t e t h i s p o i n t of view i n t o t h e i r program ( f o r example, "The Science Curriculum Improvement Study" and "Science 5/13") have g e n e r a l l y been content to simply p o i n t out the match between t h e i r m a t e r i a l s and P i a g e t ' s somewhat e l u s i v e stages of development. While t h i s may represent a reasonable beginning, much more work i s needed on the i d e n t i f i c a t i o n of the b e l i e f s and commitments of c h i l d r e n at v a r i o u s age l e v e l s and then i n t e g r a t i n g t h i s knowledge i n t o the c u r r i c u l a r process. The general problem of the study i s to i d e n t i f y the substance and s t r u c t u r e of c h i l d r e n ' s ideas about heat and temperature and to e x p l o r e the u s e f u l n e s s of t h i s knowledge f o r a p p l i c a t i o n i n a classroom s e t t i n g . I t i s being hypothesized that c h i l d r e n do possess a somewhat systematic set of b e l i e f s and i n t u i t i o n s which can be represented i n such a way as to have p o t e n t i a l e d u c a t i o n a l a p p l i c a t i o n . 1.11 The S p e c i f i c Problems The general problem d e s c r i b e d above can be c o n v e n i e n t l y sub- d i v i d e d i n t o three s p e c i f i c problems which are addressed i n the d i s s e r - t a t i o n . These s p e c i f i c problems: a) To i d e n t i f y the s u b s t a n t i v e b e l i e f s about heat and temperature h e l d by c h i l d r e n aged eleven to f i f t e e n . b) To map out a set of p o s s i b l e s t r u c t u r a l r e l a t i o n s h i p s b e t w e e n these b e l i e f s . 4 c) To suggest and i l l u s t r a t e ways i n which knowledge obtained from a) and b) could be used by a teacher i n a classroom s e t t i n g . These s p e c i f i c problems correspond to three somewhat d i s t i n c t phases i n the study. Hence the major purpose of Phase One i s d i r e c t e d towards i d e n t i f y i n g the s a l i e n t b e l i e f s expressed by c h i l d r e n about heat phenomena, w h i l e Phase Two d e s c r i b e s one method f o r r e p r e s e n t i n g the s t r u c t u r a l r e l a t i o n s h i p s of these b e l i e f s . Phase Three i s devoted to e x p l o r i n g the e d u c a t i o n a l v a l u e of the f i r s t two phases. Each of these phases w i l l be elaborated upon i n the f o l l o w i n g s e c t i o n on methods. 1.20 Methods of Study Phase One c o n s i s t e d of a s e r i e s of r e l a t i v e l y open-ended i n t e r - views w i t h c h i l d r e n ranging i n age from s i x to t h i r t e e n y e a r s . T h i s phase culminated i n the v i d e o - t a p i n g of ten in-depth i n t e r v i e w s w i t h twelve year o l d s . The a n a l y s i s of these i n t e r v i e w s provided c o n s i d e r a b l e evidence concerning the s u b s t a n t i v e ideas about heat and temperature h e l d by c h i l d r e n o f t h i s age. Although some attempt was made to develop an a p p r o p r i a t e category system that would r e a d i l y y i e l d some i n d i c a t i o n of s t r u c t u r a l r e l a t i o n s h i p s , i t became evident t h a t p a t t e r n s of t h i s s o r t could b e s t be detected w i t h a s e m a n t i c - d i f f e r e n t i a l type of instrument. Adoption of t h i s instrument a l s o made i t p o s s i b l e to o b t a i n data r e a d i l y from l a r g e groups of c h i l d r e n . The subsequent development, a d m i n i s t r a t i o n , and a n a l y s i s of r e s u l t s of such an instrument c o n s t i t u t e d Phase Two of the study. This instrument c o n s i s t e d of twenty-nine statements about heat; w i t h each statement 4 5 r e q u i r i n g the c h i l d to make s i x d i f f e r e n t judgments along a seven-point s c a l e u s i n g the f o l l o w i n g s c a l e s : agree-disagree, c l e a r - c o n f u s i n g , e a s y - d i f f i c u l t , t r u e - f a l s e , f a m i l i a r - u n f a m i l i a r , and l i k e my ideas-un- l i k e my i d e a s . These statements were created so as to sample three d i f f e r e n t p o i n t s of view — the present s c i e n t i f i c theory, the K i n e t i c Viewpoint; i t s predecessor, the C a l o r i c V i e w p o i n t ; and a C h i l d r e n ' s Viewpoint that evolved from the i n t e r v i e w data. In order to make some of the statements more concrete and meaningful f o r the younger c h i l d r e n , s e v e r a l demonstrations, d i r e c t l y r e l a t e d to the statements, were performed f o r each c l a s s . The subsequent a n a l y s i s of these data provided the major source of evidence regarding the s t r u c t u r a l r e l a t i o n s e x i s t i n g among the ideas h e l d by the c h i l d r e n and the extent to which these s t r u c t u r e s resemble the three b u i l t - i n V iewpoints. In c o n t r a s t to the previous two phases, the l a s t phase, d e a l i n g w i t h s p e c i f i c problem c ) , was s p e c u l a t i v e i n nature. Using the r e s u l t s from the i n t e r v i e w and q u e s t i o n n a i r e data as g u i d e l i n e s , s e v e r a l p o t e n t i a l classroom a p p l i c a t i o n s were i d e n t i f i e d and d i s c u s s e d . 1.30 E d u c a t i o n a l S i g n i f i c a n c e of the Study Heat was s e l e c t e d as the area of i n v e s t i g a t i o n f o r the f o l l o w i n g reasons: 1) i t i s a t o p i c g e n e r a l l y found throughout the e n t i r e s c h o o l science c u r r i c u l u m ranging from p r i m i t i v e i n v e s t i g a t i o n s i n thermometry i n the primary grades to r a t h e r s o p h i s t i c a t e d experiments of heat t r a n s - f e r i n high s c h o o l ; 2) most c h i l d r e n have an o p p o r t u n i t y , commencing w i t h the a c q u i s i t i o n of language, to formulate an i n t u i t i v e s et of b e l i e f s about the nature of hotness and coldness; 3) i t i s an area that 6 i s c o n s p i c i o u s l y absent from the s t u d i e s of c h i l d r e n ' s conceptions c a r r i e d out by P i a g e t and o t h e r s . The r e s u l t s of an i n v e s t i g a t i o n i n t o c h i l d r e n ' s ideas about heat and temperature can be a p p l i e d to problems of e d u c a t i o n a l p r a c t i c e i n two broad ways. The f i r s t , and more con- c r e t e a p p l i c a t i o n , i s the c r e a t i o n of i n s t r u c t i o n a l packages based upon knowledge obtained from the study. Such a package might be as formal as the development of a d i a g n o s t i c instrument complete w i t h a set of u n i t s on heat aimed at the d i f f e r e n t l e v e l s of understanding i d e n t i f i e d i n the study. A second way i n which the study can make a s i g n i f i c a n t c o n t r i b u t i o n to e d u c a t i o n a l p r a c t i c e i s by p r o v i d i n g the teacher w i t h a well-documented and r i c h d e s c r i p t i o n of the many ideas t h a t c h i l d r e n use to t r y and ac- count f o r s i t u a t i o n s i n v o l v i n g heat phenomena. I n c o n t r a s t to the more formal a p p l i c a t i o n discussed above, the teacher would be u s i n g t h i s know- ledge i n a more i n f o r m a l , or i n t e r p r e t i v e manner to make i n t e l l i g i b l e the c h i l d r e n ' s e x i s t i n g set of b e l i e f s about heat. By a c t i n g upon t h i s background knowledge, the teacher can respond to given s i t u a t i o n s i n such a way as to m a i n t a i n the b a s i c i n t e g r i t y of the c h i l d ' s attempts to ac- count f o r or e x p l a i n the phenomena observed. As w i t h most claims about the e d u c a t i o n a l s i g n i f i c a n c e of a study there are s e v e r a l p r e s u p p o s i t i o n s a s s o c i a t e d w i t h the above two c o n s i d e r a - t i o n s . Obviously, i n the f i r s t i n s t a n c e i t i s assumed that there w i l l be some homogeneity among the ideas h e l d by c h i l d r e n at p a r t i c u l a r age l e v e l s . I f t h i s assumption i s tenable then c u r r i c u l a r m a t e r i a l s could be developed that would u t i l i z e the knowledge obtained about c h i l d r e n ' s 7 ideas as the primary b a s i s f o r i n s t r u c t i o n . The i n t e r p r e t i v e use of knowledge, as d i s c u s s e d above, a l s o con- t a i n s some hidden premises. In order to act upon t h i s type of t a c i t knowledge i t i s being assumed th a t the teacher has a f a i r l y w e l l - d e f i n e d i n s t r u c t i o n a l problem to s o l v e , o r , i n other words, a c l e a r v i s i o n of the e d u c a t i o n a l goal being sought. In the present i n s t a n c e the broad, over- a r c h i n g goal would be something a k i n to "the c u l t i v a t i o n of the i n q u i r i n g mind" whereby the teacher would be seeking to n u r t u r e those s i t u a t i o n s which he judged to be s u p p o r t i v e of t h i s g o a l . 1.40 L i m i t a t i o n s of the Study Because each of the three phases of the study d e a l t w i t h somewhat unique problems the l i m i t a t i o n s of each phase w i l l be d i scussed s e p a r a t e l y . The c r i t e r i a used to assess the r e l i a b i l i t y and v a l i d i t y of the r e s u l t s of Phase One depart somewhat from standard p r a c t i c e s i n e d u c a t i o n a l research. The u s u a l concerns ar e : 1) the low r e l i a b i l i t y of an un- s t r u c t u r e d i n t e r v i e w ; 2) the s m a l l s i z e and p o s s i b l e b i a s i n the sample; 3) the v a l i d i t y of the i n f e r e n t i a l statements about c h i l d r e n ' s ideas of heat and temperature. But here the major c o n s i d e r a t i o n f o r the Phase One procedures was one of i d e n t i f y i n g genuine b e l i e f s , o r , as P i a g e t c a l l s them — " l i b e r a t e d convictions".''" For t h i s task the u n s t r u c t u r e d i n t e r v i e w was judged to be a more s e n s i t i v e and p r o d u c t i v e method than a more standardized procedure. However, as these data on c h i l d r e n ' s ideas were used to develop the instrument f o r Phase Two, the r e a l v a l u e of t h i s method can o n l y be determined to the extent t h a t the data t h a t i t produces hold up under f u r t h e r e m p i r i c a l s c r u t i n y . An o p p o r t u n i t y 8 fo r t h i s extended s c r u t i n y was a f f o r d e d i n Phase two where the c h i l - dren's ideas were incorp o r a t e d i n t o the classroom instrument that was developed. The subsequent a n a l y s i s of these data provided some evidence about the e x i s t e n c e o f the hypothesized s t r u c t u r e of c h i l d r e n ' s i d e a s . In g eneral there are two major concerns i n the measurement of a c o n s t r u c t , such as the hypothesized "viewpoints of heat" h e l d by c h i l - dren. The f i r s t i s the r e l i a b i l i t y of the instrument and the second i s the v a l i d i t y of the procedures used. One estimate of r e l i a b i l i t y f o r an instrument i s the t e s t - r e t e s t procedure. I n the present study the instrument was administered i n a classroom s e t t i n g but under c o n d i t i o n s i n which i t was not f e a s i b l e to r e t u r n on another day to r e t e s t the same c h i l d r e n . There are f o r t u n a t e l y , other ways of a s s e s s i n g r e l i a b i l i t y . The i n t e r n a l c o n s i s t e n c y of a q u e s t i o n n a i r e i s o f t e n i n t e r p r e t e d as a measure of r e l i a b i l i t y . In the present a n a l y s i s two separate estimates of response c o n s i s t e n c y are c a l c u l a t e d : the p a t t e r n s of response to the s i x s c a l e s used i n the instrument and the c l u s t e r i n g of the statements r e p r e s e n t a t i v e of a p a r t i c u l a r heat viewpoint. The s t a t i s t i c a l a n a l y s i s of the data, which i s discussed f u l l y i n Chapter Four, i n d i c a t e d that both of these estimates are reasonably h i g h , thus p r o v i d i n g some degree of confidence i n the q u e s t i o n n a i r e . I n a d d i t i o n , an item a n a l y s i s of the instrument reported i n Appendix D, was performed and the r e s u l t s g e n e r a l l y s u b s t a n t i a t e d t h i s c l a i m . In t u r n i n g to the i s s u e of v a l i d i t y , K e r l i n g e r (1973) provides an o u t l i n e of the three major types: content v a l i d i t y , c o n s t r u c t v a l i d i t y , and c r i t e r i o n - r e l a t e d v a l i d i t y . Each of these w i l l be d i s - cussed as i t r e l a t e d to t h i s study. Content v a l i d i t y attempts to assess "the r e p r e s e n t a t i v e n e s s or 9 sampling adequacy of the content of a measuring instrument." ( K e r l i n g e r , 1973, p. 458) Since the instrument was cons t r u c t e d to con- t a i n r e p r e s e n t a t i v e items from three d i f f e r e n t viewpoints of heat the question of content v a l i d i t y a r i s e s . How r e p r e s e n t a t i v e and accurate was the sampling of items from each of these domains? An attempt was made to assess the accuracy of the items sampled from two of the view- p o i n t s (the C a l o r i c Theory and the K i n e t i c Theory) by checking them w i t h three judges who were knowledgeable i n these areas. The items from the Ch i l d r e n ' s Viewpoint were s e l e c t e d on the b a s i s of how f r e q u e n t l y they occurred i n the i n t e r v i e w data and t h e i r relevance to the demonstrations performed during the a d m i n i s t r a t i o n of the instrument. The adequacy w i t h which each of these domains was sampled cannot be a s c e r t a i n e d w i t h - out f u r t h e r e m p i r i c a l s t u d i e s . While c o n s t r u c t v a l i d i t y i s perhaps the most important form of v a l i d i t y , as K e r l i n g e r suggests, i t i s a l s o the most d i f f i c u l t to assess. I t i s concerned w i t h questions such as: What does a score on t h i s instrument mean i n some t h e o r e t i c a l sense? What f a c t o r s or c o n s t r u c t s might account f o r the observed r e s u l t s ? and so on. In K e r l i n g e r ' s words the i n t e r e s t i s focused "more on the property being measured than on the t e s t i t s e l f . " ( K e r l i n g e r , 1973, p. 461) The t h e o r e t i c a l i n s p i r a t i o n f o r the present study i s to be found i n the w r i t i n g s of P i a g e t and s e v e r a l recent papers by Witz and Eas l e y . While the techniques used i n Phase Two d i f f e r from t h e i r approaches, the 'property' under s u r v e i l l a n c e — the s t r u c t u r a l c h a r a c t e r i s t i c s of c h i l d r e n ' s thought — i s common ground. The e m p i r i c a l r e s u l t s of t h i s study might w e l l be i n t e r p r e t e d as evidence 10 i n favor of the type of c o g n i t i v e o r g a n i z a t i o n that i s so c h a r a c t e r i s t i c of t h e i r t h e o r e t i c a l p e r s p e c t i v e . T h i s p e r s p e c t i v e w i l l be d i s c u s s e d i n Chapter Two. The q u e s t i o n of c r i t e r i o n - r e l a t e d or p r e d i c t i v e v a l i d i t y i s not addressed i n t h i s study as the only e x t e r n a l v a r i a b l e being considered — the grade of the s u b j e c t — i s of no r e a l i n t e r e s t as an o b j e c t of p r e d i c t i o n . While i t i s expected that there w i l l be a s h i f t towards the more s o p h i s t i c a t e d K i n e t i c Viewpoint as the s u b j e c t s i n c r e a s e i n age, i t i s i m p o s s i b l e , a t present, to determine whether i t would be a genuine developmental trend ( i n the P i a g e t i a n t r a d i t i o n ) or simply an environmental e f f e c t due to increased exposure to the a d u l t view. To d i g r e s s b r i e f l y to d i s c u s s a r e l a t e d p o i n t , the author b e l i e v e s , as i n d i c a t e d e a r l i e r , t h a t too l i t t l e e d u c a t i o n a l research ever f i n d s i t s way i n t o a c t u a l classroom p r a c t i c e . One way to draw more a t t e n t i o n to t h i s i s s u e might be to s p e c i f y a v a l i d i t y index which i n d i c a t e d the degree to which a p a r t i c u l a r study f u l f i l l e d some c r i t e r i o n of e d u c a t i o n a l a p p l i c a b i l i t y or s i g n i f i c a n c e . This index, which might be c a l l e d peda- g o g i c a l v a l i d i t y , would be an important member of the g e n e r a l c l a s s of r e s u l t s considered under c r i t e r i o n - r e l a t e d v a l i d i t y . T h i s leads to a d i s c u s s i o n of the l i m i t a t i o n s f o r the T h i r d Phase of the.study — the proposed a p p l i c a t i o n s f o r classroom use. Because the major purpose of t h i s r e s e a r c h was d i r e c t e d toward s o l v i n g the pro- blems emanating from the f i r s t two phases, most of the f o r e g o i n g com.-*- ments a r e s p e c u l a t i v e i n nature. The d e c i s i o n to proceed w i t h Phase Two, the development and a n a l y s i s 11 of the instrument data, was made l a r g e l y because i t was b e l i e v e d that both the instrument and the type of data c o l l e c t e d would prove to be of more immediate v a l u e to the classroom teacher than would an el a b o r a t e method f o r a n a l y z i n g i n t e r v i e w data. The f i r s t l i m i t a t i o n , then, centers around the s t r e n g t h of the procedures developed i n Phase Two. F i r s t , the instrument would have to be developed u s i n g a much l a r g e r and more r e p r e s e n t a t i v e sample of c h i l d r e n . And second, the instrument would have to be s i m p l i f i e d both i n terms of i t s l e n g t h and the methods f o r computing the r e s u l t s f o r a c h i l d or a c l a s s of c h i l d r e n . A second l i m i t a t i o n i s to be found i n terms of the development and e f f e c t i v e use of the c u r r i c u l a r packages to accompany the instrument. I t w i l l r e q u i r e c o n s i d e r a b l e e f f o r t to develop m a t e r i a l s and a c t i v i t i e s t hat can be cro s s - r e f e r e n c e d to performance on the instrument. The task of o r i e n t i n g teachers to i t s e f f e c t i v e use i s an even more important i s s u e that w i l l have to be addressed. There are at present very few teachers t r a i n e d i n the mode of i n d i v i d u a l i z e d or even s m a l l group i n s t r u c t i o n based upon a set of w e l l d efined d i a g n o s t i c procedures. A f i n a l h u r d l e i n the path of implementing the r e s u l t s i s that the techniques suggested above presuppose a somewhat d i f f e r e n t r a t i o n a l e f o r a s c i e n c e program than i s now being p r a c t i c e d i n the sc h o o l s . As t h i s i s s u e w i l l be r a i s e d again i n Chapter Two, s u f f i c e i t to say at t h i s p o i n t that teachers w i l l have to be convinced that the r e o r i e n t a - t i o n of goals can be j u s t i f i e d and i s a t t a i n a b l e i n a classroom s e t t i n g . Perhaps the e a s i e s t way to o b t a i n an o v e r a l l p e r s p e c t i v e of the study and i t s c o n s t i t u e n t procedures i s by examining the f l o w c h a r t which f o l l o w s . 12 FLOWCHART OF THE STUDY Operation P i l o t I n terviews Phase of Study F i n a l Interviews C h a r a c t e r i s t i c s 1. 9 uns t r u c t u r e d i n t e r v i e w s w i t h c h i l d r e n aged 6 to 13 10 s e m i - s t r u c t - ured i n t e r v i e w s w i t h c h i l d r e n aged 12 Function To provide informa- t i o n of c h i l d r e n ' s ideas and e s t a b l i s h a set o f i n t e r v i e w procedures f o r step 2 To gather data on the s u b s t a n t i v e aspects of c h i l - dren's b e l i e f s about heat Conceptual 3. Summary of Ideas 3. To provide input f o r Inventory 1 expressed by i n d i - C h i l d r e n ' s Viewpoint v i d u a l c h i l d r e n i n the c o n s t r u c t i o n of classroom instrument Development of Classroom 2 Instrument 4. C r e a t i o n , of 29 statements r e p r e - s e n t i n g three Heat Viewpoints ( K i n e t i c , C a l o r i c and C h i l d r e n 4. To e s t a b l i s h e v i - ence of c o g n i t i v e o r g a n i z a t i o n i n c h i l d r e n ' s ideas about heat Administer Classroom Instrument 5. Given to 276 sub j e c t s i n grades 5, 7, and 9 5. To gather data f o r s t r u c t u r a l a n a l y s i s of c h i l d r e n ' s ideas A n a l y s i s of Instrument Data 6. Factor a n a l y s i s of s c a l e s and statements. Guertin's P r o f i l e A n a l y s i s To check r e l i a b i l i t y and v a l i d i t y of the instrument. To gen- erate model p r o f i l e s f o r grouping of c h i l d r e n E d u c a t i o n a l A p p l i c a t i o n s 3 7. Examination of model p r o f i l e s f o r 'point of view' of heat i l l u s t r a t e d 7. To develop, p r o f i l e s f o r d i a g n o s t i c and i n s t r u c t i o n a l procedures 13 NOTES FOR CHAPTER ONE 1. An eloquent j u s t i f i c a t i o n of a non-standardized i n t e r v i e w t e c h - nique (Piaget r e f e r s to i t as a " c l i n i c a l method") i s given i n the f i r s t chapter of P i a g s t ' s (1969) The C h i l d ' s Conception of the World. In t h i s chapter he o u t l i n e s and c h a r a c t e r i z e s f i v e p o t e n t i a l types of responses made by the c h i l d i n an i n t e r v i e w s i t u a t i o n : answers a t random, romancing, suggested c o n v i c t i o n , spontaneous c o n v i c t i o n and l i b e r a t e d c o n v i c t i o n . The responses of i n t e r e s t to the a n a l y s t are those i n the l a s t two c a t e g o r i e s . 14 CHAPTER TWO CONTEXT OF THE STUDY In an e x t e n s i v e , c r i t i c a l review of e d u c a t i o n a l research encom- passing the past twenty years, Averch et a l . (1972) concluded t h a t only l i m i t e d improvement of present e d u c a t i o n a l p r a c t i c e s can be ex- pected through expanding the c u r r e n t base of e d u c a t i o n a l r e s e a r c h . Rather, more e f f o r t ought to be d i r e c t e d towards i n v e s t i g a t i n g c u r r e n t e d u c a t i o n a l reforms. This study, i n f o c u s i n g upon i n s t r u c t i o n a l d i f - f i c u l t i e s emanating from recent c u r r i c u l a r reforms i n science education, represents such an e f f o r t . To gain an o v e r a l l p e r s p e c t i v e of the study t h i s chapter w i l l examine i s s u e s r e l a t e d to the e d u c a t i o n a l , psycholo- g i c a l and p h i l o s o p h i c a l aspects of the problem. 2.00 E d u c a t i o n a l Context of the Problem 2.01 R e l a t i o n s h i p to Curriculum Problems i n Science Education The past f i f t e e n years have witnessed an unprecedented growth of new science c u r r i c u l a . Emerging from these numerous p r o j e c t s have been two trends: an increased emphasis upon the processes of s c i e n c e i n s t e a d of the products, and secondly, a tendency to u t i l i z e student i n q u i r y as the predominant method of i n s t r u c t i o n . Proponents of the new programs have e x t o l l e d the v i r t u e s of f o c u s i n g upon the methods used i n o b t a i n i n g s c i e n t i f i c knowledge r a t h e r than com- m i t t i n g to memory a body of f a c t s which w i l l soon be f o r g o t t e n or obso- l e t e . The implementation of t h i s "process" philosophy has v a r i e d s i g - n i f i c a n t l y among the d i f f e r e n t programs. On one extreme, authors of Science: A Process Approach have i d e n t i f i e d and defined t h i r t e e n 15 processes, ranging from simple l i k e 'observation' and ' c l a s s i f i c a t i o n ' to more complex ones l i k e ' d e f i n i n g o p e r a t i o n a l l y ' and 'experimenting'. Authors of other p r o j e c t s l i k e the Elementary Science Study and N u f f i e l d J u n i o r Science have been content to use a much more i n f o r m a l approach whereby the c h i l d i s engaged i n wide-ranging i n v e s t i g a t i o n s of n a t u r a l phenomena w i t h the e x p e c t a t i o n that he w i l l develop these 'process s k i l l s ' i n the course of h i s i n q u i r y . T his s o - c a l l e d "process approach" has had such an impact upon science education that i t has prompted the authors of one textbook on elementary science i n s t r u c t i o n to comment: Of the many goals proposed and adopted f o r teaching elementary school s c i e n c e , those goals a s s o c i a t e d w i t h p r o c e s s - o r i e n t e d science seem to be most r e l e v a n t f o r the next twenty years. In p a r t i c u l a r the goal of the c u l t i v a t i o n of the i n q u i r i n g mind, i s s t r e s s e d because i t represents a whole p h i l o s o p h i c a l s t y l e of t h i n k i n g about what science i s , how i t should be taught, and what c u r r i c u l a r s t r u c t u r e (or l a c k of s t r u c t u r e ) i s a p p r o p r i a t e . (Kuslan and Stone, 1972, p. 179) As i n d i c a t e d by the above q u o t a t i o n the adoption of an o v e r a r c h i n g g o a l such as "the c u l t i v a t i o n of the i n q u i r i n g mind" a l s o suggests a c e r t a i n s t y l e of teaching. The s t y l e , adopted by most of the new c u r r i c u l a , has been l a b e l l e d the " i n q u i r y approach." The i m p l i c i t assumption i s that i f we are attempting to teach students the s k i l l s of s c i e n t i f i c i n q u i r y , then, l i k e other s k i l l s t hat we teach, an o p p o r t u n i t y must be a f f o r d e d the students to p r a c t i c e those s k i l l s . T his trend of student i n q u i r y , or ' s c i e n c i n g ' as i t has been c a l l e d by some, has been f u r - ther buoyed up by a r e d i s c o v e r y of P i a g e t ' s work on the i n t e l l e c t u a l development of the c h i l d . The cornerstone of P i a g e t ' s p o s i t i o n — 16 that the a c t i v e c h i l d , through i n t e r a c t i o n w i t h h i s environment, i s c o n s t a n t l y engaged i n the business of r e s t r u c t u r i n g h i s own thought processes — i s a very a t t r a c t i v e t h e o r e t i c a l foundation f o r c u r r i c u l a adopting an inquiry-based mode of i n s t r u c t i o n . However, i n emphasizing student i n q u i r y w i t h i n a p r o c e s s - o r i e n t e d program, c u r r i c u l u m developers have t a c i t l y assumed t h a t the s u b t l e r e g u l a r i t i e s of nature, apparent to the s c i e n t i s t , can be 'discovered' by an i n q u i r i n g c h i l d . While the c h i l d may indeed be l i k e a s c i e n t i s t i n some important r e s p e c t s , there i s an ever i n c r e a s i n g body of psycho- l o g i c a l l i t e r a t u r e , to be discussed i n S e c t i o n 2.10, which concludes that c h i l d r e n see the world from very d i f f e r e n t p e r s p e c t i v e s than t h a t of a d u l t s i n g e n e r a l , and s c i e n t i s t s i n p a r t i c u l a r . Thus perhaps the r e a l u t i l i t y of the ' c h i l d as a s c i e n t i s t ' metaphor i s not t h a t i t sug- gests one can s i m p l i f y or reduce the complex body of s c i e n t i f i c knowledge and methods i n t o p e d a g o g i c a l l y d i g e s t i b l e programs, as has been done to date. Rather, i t i s to view both c h i l d and s c i e n t i s t as engaged i n the same b a s i c a c t i v i t y of attempting to p e r c e i v e some sense of order i n t h e i r world — only a t d i f f e r e n t l e v e l s of a b s t r a c t i o n . Bohm (1965) has e f f e c t i v e l y argued t h i s p o i n t i n an appendix to h i s book on s p e c i a l r e l a t i v i t y . H i s t h e s i s i s that the process of p e r c e p t i o n does not d i f f e r s i g n i f i c a n t l y between the c h i l d and the a d u l t . Rather, the s o p h i s t i c a t e d conceptual c o n s t r u c t i o n , "embodying, i n e f f e c t , a hypothesis t h a t accounts f o r the i n v a r i a n t f e a t u r e s that have been found i n [past] experiences" (Bohm, 1965, p. 217), of the a d u l t s c i e n t i s t i s a n a t u r a l e x t e n s i o n of the c h i l d ' s p e r c e p t u a l process, only a t a higher l e v e l of a b s t r a c t i o n . 17 The i m p l i c a t i o n s of such a p o s i t i o n f o r the development of science c u r r i c u l a seem c l e a r . Instead of attempting to package the a b s t r a c t p e r c e p t i o n s of the w o r l d , based upon many years of accumulated experience, c u r r i c u l u m development ought to proceed from the simple and more concrete phenomena a s s o c i a t e d w i t h the c h i l d ' s world toward the more powerful and s o p h i s t i c a t e d conceptions of the a d u l t world. This type of r e o r g a n i z a t i o n e n t a i l s the e v o l u t i o n of c u r r i c u l a i n an upward d i r e c t i o n from the c h i l d ' s own ideas and ways of t h i n k i n g , i n s t e a d of the present downward d i r e c t i o n from e s t a b l i s h e d , a d u l t frameworks of methods and knowledge. Such an approach, however, i s not without problems. Among the most prominent would be the need f o r teachers to become more adept at i d e n t i f y i n g and diagnosing the c h i l d ' s p e r s p e c t i v e of the sub- j e c t matter being s t u d i e d . 2.02 R e l a t i o n s h i p to Teaching-Learning Problems i n Science Education A n t i c i p a t i n g a p o s s i b l e r e o r i e n t a t i o n i n c u r r i c u l a r emphasis, such as that d i s c u s s e d above, researchers at the U n i v e r s i t y of I l l i n o i s have conducted a number of e x p l o r a t o r y s t u d i e s i n t o some of the b a s i c t e a c h i n g - l e a r n i n g problems that might accompany such an approach. For example, Hanson (1970) found t h a t beginning teachers tended to r e j e c t any a l t e r - n a t i v e t h e o r i e s (that i s , d i f f e r e n t from the p r e v a i l i n g s c i e n t i f i c theory being 'taught' by the teacher) h e l d by the c h i l d r e n . These teachers e i t h e r ignored any a l t e r n a t i v e theory put forward by the s t u - dents or e l s e attempted to persuade them to change t h e i r minds. Ashen- f e l t e r (1970) and C r a i g (1971) a l s o worked on the problem of teachers' i n s e n s i t i v i t y to the i n t e l l e c t u a l commitments of t h e i r students. In the 18 l a t t e r study by C r a i g , an attempt was made to "create f o r a group of beginning science teachers an environment i n which these teachers could become more s e n s i t i v e to and more f a m i l i a r w i t h h i g h s c h o o l student i d e a s . " ( C r a i g , 1971, p. 1) The r e s u l t s of these s t u d i e s , which i n d i c a t e d t h a t beginning teachers are i n s e n s i t i v e to (and i n some cases i n t o l e r a n t of) student perceptions of s c i e n t i f i c phenomena, poin t out the need f o r a r e v i s i o n of our present t e a c h e r - t r a i n i n g pro- grams. As i t now stands the students are being encouraged to i n q u i r e i n t o some phenomenon, and i n so doing they formulate something a k i n to Bohm's " i n n e r c o n s t r u c t i o n " . But any attempts to f o r m a l i z e or make these i n n e r thoughts e x p l i c i t are met w i t h r e s i s t a n c e by the teacher. Hence the students e i t h e r experience f r u s t r a t i o n as they attempt to accommodate to the u n f a m i l i a r ideas s e t f o r t h by the teacher, or pas- s i v e l y acquiesce to a viewpoint they do not r e a l l y understand or accept. N e i t h e r of these outcomes i s compatible w i t h the s t a t e d goals of the new s c i e n c e c u r r i c u l a . E a r l i e r , Hawkins (1965), i n amuch p u b l i c i z e d a r t i c l e e n t i t l e d "Messing About i n Science", a l s o recognized the attendant t e a c h i n g - l e a r n i n g problems inherent i n an inquiry-based approach. He suggested that educators must l e a r n to recognize and c u l t i v a t e that very powerful s t y l e of l e a r n i n g which i s r e s p o n s i b l e f o r "most of what c h i l d r e n have already l e a r n e d , the r o o t s of t h e i r moral, i n t e l l e c t u a l and e s t h e t i c development." (Hawkins, 1965, p. 7) But, as i s i l l u s t r a t e d by the I l l i n o i s s t u d i e s , t h i s l e a r n i n g s t y l e (which Hawkins c a l l s "messing about") and the ideas i t produces, are most o f t e n a l i e n to teachers who are 19 steeped i n the a d u l t t r a d i t i o n s of s c i e n t i f i c knowledge. Sensing t h i s gap between the teacher and c h i l d , Hawkins c a l l s upon c u r r i c u l u m de- s i g n e r s to a s s i s t the teacher by d e s i g n i n g m a t e r i a l s and a c t i v i t i e s w i t h a r i c h v a r i e t y of a l t e r n a t i v e pathways f o r the c h i l d to choose. In so doing he assumed that the c h i l d , w i t h a s s i s t a n c e from the t e a - cher, w i l l be f r e e to pursue those avenues of i n q u i r y which are most appr o p r i a t e to h i s present i n t e r e s t s and i n t e l l e c t u a l c a p a b i l i t i e s . Hawkins has thus mapped out a somewhat i n f o r m a l s t r a t e g y f o r meeting the d i v e r g e n t e x p e r i e n t i a l backgrounds that e x i s t between teacher and c h i l d , and a l s o to a l e s s e r extent between d i f f e r e n t c h i l d r e n . The assumption from which t h i s study stems i s t h a t a p r e l i m i n a r y step of g a t h e r i n g data about the substance and s t r u c t u r e of c h i l d r e n ' s b e l i e f s would g r e a t l y f a c i l i t a t e any approach to the above problem; whether i t be the development of the type of m a t e r i a l s envisaged by Hawkins or some other more formal approach. 2.03 Review of Studies Related to the Problem W r i t t e n accounts of the ideas h e l d by c h i l d r e n date back a t l e a s t as f a r as the l a t e 18th Century w i t h the c a r e f u l observations made by P e s t a l o z z i on h i s own c h i l d . But the f i r s t s et of l a r g e s c a l e s t u d i e s of c h i l d r e n ' s i n t e l l e c t u a l commitments was reported i n G. Stanley H a l l ' s The Content of C h i l d r e n ' s Minds on E n t e r i n g School (1883). Ever s i n c e , there have been numerous i n v e s t i g a t i o n s probing i n t o the world of the c h i l d , the purposes of which have ranged from i d e n t i f y i n g the expressed i n t e r e s t s of c h i l d r e n to c h a r t i n g c h i l d r e n ' s behavior w i t h the use of s o p h i s t i c a t e d category systems. This l a t t e r type of study, which i n v o l v e s 20 c l a s s i f y i n g some type of v e r b a l response, u s u a l l y generated by an i n t e r - view s i t u a t i o n , has been very p r e v a l e n t i n the area of science education. The e a r l y , p i o n e e r i n g s t u d i e s examined the development of c a u s a l reason- i n g i n the c h i l d . ^ But soon i n v e s t i g a t i o n s of t h i s nature spread to other areas of i n t e r e s t to the science educator. Thus there were a number of s t u d i e s probing i n t o the c h i l d ' s conception of n a t u r a l pheno- mena (e.g., Oakes, 1947; K i n g , 1960; and Inbody, 1964) and s e v e r a l d i r e c t e d at more s p e c i f i c s k i l l s such as the c h i l d ' s a b i l i t y to formulate hypotheses ( A t k i n , 1958) or to c o n s t r u c t models to account f o r observed p h y s i c a l phenomena (Anderson, 1965; P e l l a and Z i e g l e r , 1967). While a l l of the above s t u d i e s have c o n t r i b u t e d to our knowledge of the mechanics of c h i l d thought, they s t i l l have had l i t t l e a p p r e c i a b l e e f f e c t upon e d u c a t i o n a l p r a c t i c e . S e v e r a l c o n j e c t u r e s might be forwarded to account f o r t h i s l a c k of i n f l u e n c e . One i s that many of the above mentioned s t u d i e s are fragmentary i n nature — each one surveying a number of t o p i c s ranging from c h i l d r e n ' s ideas about the o r i g i n of g e o l o g i c a l f e a t u r e s , to e l e c t r i c i t y and magnetism, to t h e i r understanding of l i v i n g o b j e c t s . For example, Oakes (1947) employed 17 experiments and 15 questions to examine c h i l d r e n ' s e x p l a n a t i o n s of 19 d i f f e r e n t areas of n a t u r a l phenomena; w h i l e King (1960) had 70 questions ranging over 5 broad t o p i c areas. A second reason f o r the l a c k of e d u c a t i o n a l e f f e c t might be a t - t r i b u t e d to a f a i l u r e on the part of the authors to address s e r i o u s e d u c a t i o n a l i s s u e s w i t h i n the bounds of t h e i r study proper, thus l e a v i n g 2 the implementation of t h e i r r e s u l t s to o t h e r s . 21 The author of the present study has attempted to meet the f i r s t shortcoming ( i n terms of e d u c a t i o n a l a p p l i c a b i l i t y ) of most previous s t u d i e s by f o c u s i n g upon c h i l d r e n ' s conceptions of heat. By l i m i t i n g the area of i n v e s t i g a t i o n to a s i n g l e t o p i c i t was f e l t t hat two out- comes could be accomplished: 1) to generate a t l e a s t some t e n t a t i v e hypotheses about c h i l d r e n ' s ideas of heat; and 2) to provide an ex- ample of a p o s s i b l e method f o r c h a r t i n g other areas of i n t e r e s t to educators. The second shortcoming, l i s t e d above, was approached by proceeding beyond the stage of simply i d e n t i f y i n g and c a t e g o r i z i n g c h i l d r e n ' s views. As described i n Chapter One, the method employed i n Phase One to summa- r i z e the s u b s t a n t i v e aspects of c h i l d r e n ' s b e l i e f s about heat c o n s i s t e d of a type of c a t e g o r i z a t i o n procedure. However, t h i s l e v e l of a n a l y s i s , which i s the p o i n t of t e r m i n a t i o n f o r most of the above-mentioned 3 s t u d i e s , was judged to be i n s u f f i c i e n t i n depth and scope f o r meeting any s e r i o u s e d u c a t i o n a l problems. Hence the d e c i s i o n was made to t r y to examine the data f o r some evidence of a type of o r g a n i z a t i o n or s t r u c t u r e that might be of value to both the c u r r i c u l u m w r i t e r and the classroom teacher. 2.10 P s y c h o l o g i c a l Context of the Study 2.11 R e l a t i o n s h i p to S t r u c t u r a l A n a l y s i s Since the c u r r e n t language of education i s r e p l e t e w i t h v a r i o u s usages of the word ' s t r u c t u r e ' ( f o r example, frequent r e f e r e n c e s are made t o : the " s t r u c t u r e of knowledge", the " s t r u c t u r e of the c u r r i c u l u m " , a " s t r u c t u r e d l e s s o n p l a n " , and so on), at t h i s p o i n t i t i s a d v i s a b l e 22 to s p e c i f y what i s intended by the phrase, 'the s t r u c t u r e of c h i l d r e n ' s b e l i e f s ' . A standard d i c t i o n a r y d e f i n i t i o n of s t r u c t u r e i s : " t h a t which i s c o n s t r u c t e d ; a combination of r e l a t e d p a r t s . " 4 The focus i n the present study i s upon the manner i n which the p a r t s (that i s , the c h i l d r e n ' s ideas) are organized i n t o some meaningful whole. The systematic study of the o r g a n i z a t i o n of a s e t of ideas h e l d by a c h i l d i s a much more demanding task than simply enumerating or c a t e g o r i z i n g the ideas according to t h e i r substance, as discussed e a r l i e r . I t i s g e n e r a l l y not f e a s i b l e to simply ask c h i l d r e n (nor a d u l t s f o r that matter) to d e s c r i b e d i r e c t l y the o r g a n i z a t i o n of t h e i r i d e a s , or the p o s s i b l e r e l a t i o n s h i p s between these i d e a s , w i t h regards to some p h y s i - c a l phenomena. Hence the problem becomes one of attempting to develop a s u i t a b l e method f o r f o r m a l l y r e p r e s e n t i n g those ideas by means of some t h e o r e t i c a l framework. G e n e r a l l y t h i s f o r m a l i z a t i o n procedure i s a r e s u l t of t h e o r i z i n g which f u n c t i o n s i n such a way as to t r y to r e c o n s t r u c t the 'mental space' of the s u b j e c t i n terms of a set of t h e o r e t i c a l c o n s t r u c t s . 2.12 R e l a t i o n s h i p to P i a g e t ' s S t r u c t u r e s of I n t e l l i g e n c e Undoubtedly the most prominent t h e o r e t i c i a n concerned w i t h a s t r u c t u r a l a n a l y s i s of c h i l d r e n ' s thought i s P i a g e t . Because h i s w r i t i n g s have s t r o n g l y i n f l u e n c e d the conception, and to a l e s s e r extent the methods of the present study a b r i e f account of h i s t h e o r e t i c a l p o s i t i o n (as i t i n f l u e n c e s h i s s t r u c t u r a l a n a l y s i s ) would seem warranted. Although P i a g e t professes to be a genetic e p i s t e m o l o g i s t — that i s , one who seeks to e x p l a i n knowledge "on the b a s i s of i t s h i s t o r y , i t s 23 so c i o g e n e s i s , and e s p e c i a l l y the p s y c h o l o g i c a l o r i g i n s of the notio n s and operations upon which i t i s based" ( P i a g e t , 1971a, p. 1) — he i s best known f o r h i s comprehensive s t u d i e s of c h i l d r e n ' s i n t e l l e c t u a l development. In h i s d e s i r e to d e s c r i b e the way i n which the thought processes of the c h i l d g r a d u a l l y e v o l v e , through a s e r i e s of c l o s e r approximations to the perceived r e a l i t y of the a d u l t w o r l d , he has attempted to wed p s y c h o l o g i c a l i n v e s t i g a t i o n w i t h a type of l o g i c a l f o r m a l i z a t i o n . The r e s u l t of t h i s union i s the s t r u c t u r a l a n a l y s i s which has become p r e v a l e n t i n P i a g e t ' s w r i t i n g s . As a f i r s t approxima- t i o n one might d e s c r i b e t h i s type of a n a l y s i s as an attempt to represent mental processes i n terms of t h e o r e t i c a l e n t i t i e s which can p r o p e r l y be c a l l e d c o g n i t i v e s t r u c t u r e s . P i a g e t claims the d i s t i n g u i s h i n g f e a t u r e s of these p s y c h o l o g i c a l s t r u c t u r e s , i n a d d i t i o n to other t h e o r e t i c a l s t r u c t u r e s p o s i t e d i n f i e l d s l i k e mathematics, l i n g u i s t i c s and anthro- pology, are based upon a system of transformations and the laws governing these t r a n s f o r m a t i o n s . ( P i a g e t , 1971b) Hence i n P i a g e t ' s d e s c r i p t i o n mental growth i s d e r i v e d from a number of suc c e s s i v e t r a n s f o r m a t i o n s producing the developmental stages. The elemental c o n s t i t u e n t s i n t h i s process, as w e l l as the determining f a c t o r f o r s o r t i n g out the l e v e l of i n t e l l e c t u a l development, are the o p e r a t i o n a l s t r u c t u r e s . For example, the k i n d of o p e r a t i o n a l s t r u c t u r e s that appear at the 'stage of concrete o p e r a t i o n s ' are those p e r t a i n i n g t o : c l a s s i n c l u s i o n and c l a s s i f i c a t i o n , s e r i a t i o n and o r d e r i n g , and correspondence. According to P i a g e t these s t r u c t u r e s do not j u s t u n f o l d i n a g e n e t i c a l l y predetermined sense; they must be constructed by the c h i l d through i n t e r a c t i n g w i t h concrete, 24 p h y s i c a l o b j e c t s and then, a t l a t e r stages of development, m e n t a l l y a c t i n g upon and transforming the r e a l i t y p erceived by the c h i l d . Or, i n P i a g e t ' s words: From the most elementary sensorimotor a c t i o n s (such as pushing and p u l l i n g ) to the most s o p h i s - t i c a t e d i n t e l l e c t u a l o p e r a t i o n s , which are i n t e - r i o r i z e d a c t i o n s , c a r r i e d out mentally (e.g., j o i n i n g together, p u t t i n g i n o r d e r , p u t t i n g i n t o one-to-one correspondence), knowledge i s c o n s t a n t l y l i n k e d w i t h a c t i o n s or o p e r a t i o n s , that i s , w i t h t r a n s f o r m a t i o n s . ( P i a g e t , 1970, p. 704) ( I t a l i c s h i s ) 2.13 R e l a t i o n s h i p to Witz and Easley's Deep S t r u c t u r e s Witz and Easley (1971) have r e c e n t l y pointed out the l i m i t a t i o n s of r e l y i n g s o l e l y upon o p e r a t i o n a l s t r u c t u r e s as the t h e o r e t i c a l b a s i s f o r e x p l a i n i n g s p e c i f i c p a t t e r n s of behavior. They argue that opera- t i o n a l s t r u c t u r e s , i n themselves, are i n s u f f i c i e n t f o r i n t e r p r e t i n g why c h i l d r e n r e a c t i n c h a r a c t e r i s t i c ways towards c e r t a i n p h y s i c a l systems. Their s o l u t i o n i s to propose a new type of c o g n i t i v e s t r u c t u r e which they e n t i t l e d " p h y s i c a l deep s t r u c t u r e " . While P i a g e t recognized the i n f l u e n c e of what he c a l l e d p h y s i c a l knowledge or experience, he d i d not accord i t the f u l l s t r u c t u r a l s t a t u s as have Witz and E a s l e y . To place t h i s i s s u e i n proper p e r s p e c t i v e i t must be remembered that Piaget i s i n t e r e s t e d i n d e s c r i b i n g normative trends and mechanisms w h i l e Witz and Easley admit that they are more concerned w i t h making sense out of the a c t i o n s of a p a r t i c u l a r c h i l d i n t e r a c t i n g w i t h a p a r t i c u l a r set of m a t e r i a l s . To quote Witz and E a s l e y : When the c h i l d i s i n t e r a c t i n g w i t h a p a r t i c u l a r p h y s i c a l system, or when he contemplates one, a [ p h y s i c a l deep s t r u c t u r e ] comes i n t o p l a y , gives r i s e to what appears i n i n t r o s p e c t i o n as i n t u i t i v e 25 f e e l i n g s of weight, momentum, i n e r t i a , e t c . , and s t r o n g l y i n f l u e n c e s h i s e x t e r n a l l y observable behavior. (Witz and E a s l e y , 1971, p. 2) To i d e n t i f y a p h y s i c a l deep s t r u c t u r e , then, the a n a l y s t must c a r e f u l l y observe a c h i l d i n t e r a c t i n g w i t h a p h y s i c a l system ( f o r ex- ample, a pendulum) and c o n s t r u c t i n f e r e n c e s about the nature of the p h y s i c a l deep s t r u c t u r e s from the c h i l d ' s a c t i o n s and d i s c u s s i o n w i t h the i n t e r v i e w e r . I d e a l l y , the i n t e r v i e w e r ought to be capable of f o r m u l a t i n g these hypotheses and checking them out d u r i n g the i n t e r - view i n s t e a d of r e l y i n g upon a post hoc r e c o n s t r u c t i o n from t r a n s c r i p t data. Thus, on f i r s t view one might conceive of p h y s i c a l deep s t r u c t u r e as a sub-species of c o g n i t i v e s t r u c t u r e a c t i n g as a type of general data base to be manipulated and transformed by the o p e r a t i o n a l s t r u c t u r e s . 5 In t h i s sense both c o n s t r u c t s are necessary i f one i s attempting to ex- p l a i n any complex, c o g n i t i v e a c t i o n . The e d u c a t i o n a l i m p l i c a t i o n s of mapping out the c o n t e n t - o r i e n t e d , p h y s i c a l deep s t r u c t u r e s would appear to be more s i g n i f i c a n t than simply c o n s i d e r i n g o p e r a t i o n a l s t r u c t u r e s . Previous attempts to modify or ac- c e l e r a t e o p e r a t i o n a l development have met e i t h e r w i t h l i t t l e or o nly short-term success. P i a g e t , when d i s c u s s i n g the i s s u e of a c c e l e r a t i o n of o p e r a t i o n a l s t r u c t u r e s , i s quick to p o i n t out t h a t there are two n o n - a c c e s s i b l e , b i o l o g i c a l f a c t o r s which r e g u l a t e the development of s t r u c t u r e s — maturation and e q u i l i b r a t i o n — and so any i n s t r u c t i o n a l program w i l l be l i m i t e d by these two f a c t o r s . ( P i a g e t , 1964) On the other hand p h y s i c a l deep s t r u c t u r e s , as Witz and Easley point out, are 26 t h e o r e t i c a l c o n s t r u c t s that attempt to account f o r c h i l d r e n ' s charac- t e r i s t i c ways of d e a l i n g w i t h p h y s i c a l systems and would t h e r e f o r e seem to be more responsive to the type of experience provided i n the c l a s s - room. I n other words, because they have a strong content component, exposure to c o n t e n t - o r i e n t e d experiences would i n c r e a s e the l i k e l i h o o d of b r i n g i n g about a change i n these s t r u c t u r e s . I t would seem that i f ' t y p i c a l ' p h y s i c a l deep s t r u c t u r e p a t t e r n s c o u l d be i d e n t i f i e d and mapped out f o r s p e c i f i c groups of c h i l d r e n , then at l e a s t two d i s t i n c t e d u c a t i o n a l gains would accrue. The f i r s t e d u c a t i o n a l a p p l i c a t i o n c o u l d be d i r e c t e d towards the p r o d u c t i o n of c u r r i c u l a r packages f o r use by the classroom teacher. Such a package might c o n t a i n a d i a g n o s t i c instrument, f o r i d e n t i f y i n g the p a t t e r n of p h y s i c a l deep s t r u c t u r e s of "a p a r t i c u l a r group of c h i l d r e n , along w i t h a number of p o t e n t i a l t e a c h i n g s t r a t e g i e s matched to t h a t p a t t e r n . Of course, the pedagogical b a s i s f o r such a matching procedure would depend upon the overarching goals f o r s c i e n c e i n s t r u c - t i o n i n the s c h o o l s . For example, i f the aim was to f i n d the most e f - f i c i e n t route f o r i n i t i a t i n g the c h i l d i n t o a more a d u l t way of per- c e i v i n g the w o r l d , then the s t r a t e g i e s would take on a very d i f f e r e n t appearance from other aims such as f o s t e r i n g i n t e l l e c t u a l c u r i o s i t y or developing an a p p r e c i a t i o n of our environment. More w i l l be s a i d of these p o s s i b l e t e a c h i n g s t r a t e g i e s i n Chapter S i x . A second b e n e f i c i a l e f f e c t would r e s u l t from making a v a i l a b l e to teachers the knowledge obtained about the o r g a n i z a t i o n of c h i l d r e n ' s p h y s i c a l i n t u i t i o n s or deep s t r u c t u r e s . By possessing such knowledge 27 i t i s hoped that the teachers' perceptions of the i n s t r u c t i o n a l t a sk w i l l be a l t e r e d i n such a way that the b a s i c i n t e g r i t y of the c h i l d ' s b e l i e f s and p r i m i t i v e methods of 'inquiry w i l l be respected. While t h i s second e f f e c t i s much more tenuous i n nature, Broudy et a l . (1964) have argued that t h i s type of i n t e r p r e t i v e use of knowledge may be as powerful as the more conv e n t i o n a l a p p l i c a t i v e usage. 2.14 The Concept of S t r u c t u r e Used i n the Present Study The task f o r the present study, as o u t l i n e d i n Chapter One, i s to i d e n t i f y the substance and s t r u c t u r e of c h i l d r e n ' s ideas about heat. A l - though Witz and Easley's t h e o r e t i c a l conception of p h y s i c a l deep s t r u c t u r e s would appear to be a u s e f u l c o n s t r u c t f o r examining the o r g a n i z a t i o n of c h i l d r e n ' s b e l i e f s about heat phenomena,there are s e v e r a l drawbacks i n c o n s i d e r i n g t h e i r approach f o r t h i s study. The f i r s t i s an inadequate a r t i c u l a t i o n of a s e t of procedures to a s s i s t others i n the i d e n t i f i c a t i o n of p h y s i c a l deep s t r u c t u r e s . As w i t h P i a g e t , they have s e l e c t e d only those passages from s e v e r a l d i f f e r e n t t r a n s c r i p t s a p p r o p r i a t e to i l l u s - t r a t e the p o i n t of t h e o r e t i c a l contact being discussed at the time. A second reason i s th a t t h e i r approach a l s o presupposes some knowledge of c h i l d r e n ' s understanding of heat, so as to o r i e n t both the i n t e r v i e w e r and the a n a l y s t — a c o n d i t i o n which could not be s a t i s f i e d due to the l a c k of work i n the area of c h i l d r e n ' s b e l i e f s about heat. But, per- haps the most compelling reason f o r not usi n g t h e i r approach i s to be found i n one of the s t a t e d aims of t h i s study: the a p p l i c a t i o n of the r e s u l t s of t h i s study to a c t u a l classroom s i t u a t i o n s . In t h i s regard a concise and standardized instrument, based upon the i n t e r v i e w data, 28 would appear to be much more u s e f u l than a somewhat a b s t r a c t d i s c u s s i o n o u t l i n i n g the p o t e n t i a l o r g a n i z a t i o n of b e l i e f s manifested by a c h i l d , or a s m all group of c h i l d r e n . Hence a search was i n i t i a t e d f o r an a l t e r n a t i v e to the P i a g e t i a n type of a n a l y s i s f o r i n v e s t i g a t i n g the s t r u c t u r a l c h a r a c t e r i s t i c s of c h i l d r e n ' s ideas about heat phenomena. I t was hoped t h a t a model could be found that would r e t a i n the content o r i e n t a t i o n of the p h y s i c a l deep s t r u c t u r e s , and yet meet the two o b j e c t i o n s r a i s e d above. A promising approach f o r r e v e a l i n g some aspects of the p o t e n t i a l o r g a n i z a t i o n of c h i l d r e n ' s b e l i e f s i s t h a t of m u l t i d i m e n s i o n a l a n a l y s i s . There are two inter-dependent i s s u e s t h a t must be addressed b e f o r e an a n a l y s i s of t h i s nature can be c a r r i e d out. D e c i s i o n s must be made w i t h regards to the methods to be employed f o r the c o l l e c t i o n of the data and the type of s t a t i s t i c a l model t h a t i s to be used to analyze the data. The task i n the present study, then, was one of f i r s t , t r a n s - l a t i n g the s u b s t a n t i v e b e l i e f s , gathered i n Phase One from the i n t e r - view data, i n t o a format that a l l o w s other c h i l d r e n to respond to those b e l i e f s and second, choosing some s u i t a b l e a n a l y t i c a l model. The f i r s t attempt at approaching the above i s s u e s was i n s p i r e d by a r e p o r t w r i t t e n by M i l l e r et a l . (1967) e n t i t l e d , Elementary School Teachers' Viewpoints of Classroom Teaching and L e a r n i n g . In t h i s r e p o r t they o u t l i n e d a technique, c a l l e d Latent P a r t i t i o n A n a l y s i s , which r e l i e d upon data obtained by s o r t i n g a l a r g e number of cards ( g e n e r a l l y around 150) i n t o p i l e s which were s i m i l a r i n some r e s p e c t . Each card contained 29 a d e s c r i p t i o n of some classroom-relevant behavior i n which a teacher might engage. Those cards which the s u b j e c t perceived to be a s s o c i a t e d w i t h the same type of behavior were placed i n t o the same p i l e — which was subsequently c a l l e d a "manifest category." By comparing these c a t e - g o r i e s over a number of s u b j e c t s f o r t h e i r commonalities a number of l a t e n t c a t e g o r i e s emerge. Hence the c l a i m that t h i s procedure i s tapping i n some manner, a l a t e n t c o g n i t i v e s t r u c t u r e that i s r e s p o n s i b l e f o r o r g a n i z i n g the s u b j e c t s ' perceptions i n the manner observed. Although the technique i s capable of producing the k i n d of s t r u c - t u r a l a n a l y s i s that i s d e s i r e d , the somewhat s o p h i s t i c a t e d s o r t i n g p r o- cedures proved to be too d i f f i c u l t f o r the seven d i f f e r e n t c h i l d r e n who t r i e d to s o r t statements about heat and temperature. Furthermore, i t would be extremely d i f f i c u l t to a d m i n i s t e r t h i s type of s o r t i n g task to a whole c l a s s at a time — a d e s i r a b l e f e a t u r e both f o r sampling l a r g e numbers of c h i l d r e n and f o r adapting the q u e s t i o n n a i r e f o r even- t u a l classroom use. T a y l o r ' s (1966) study, e n t i t l e d The Mapping of Concepts, provided some u s e f u l a l t e r n a t i v e s to the s o r t i n g techniques d e s c r i b e d above f o r the g a t h e r i n g of data s u i t a b l e f o r the a n a l y s i s of s t r u c t u r a l r e l a t i o n - s h i p s . A l l of the methods of c o l l e c t i n g judgmental data t h a t he d i s - cusses — r a t i o judgment, paired-comparison, category s o r t , and semantic d i f f e r e n t i a l — are s u i t a b l e f o r use w i t h a m u l t i d i m e n s i o n a l a n a l y s i s model. A f t e r a review of the l i t e r a t u r e concerning these techniques, i t was decided t h a t the method that would best meet the requirements of the study ( t h a t i s , i t would be simple enough f o r an eleven-year o l d to comprehend and could be presented to a l a r g e group of c h i l d r e n ) was that 3Q of the semantic d i f f e r e n t i a l , o r some simple v a r i a t i o n of t h i s t e c h - nique (Osgood et a l . , 1957). Subsequent p i l o t runs w i t h s m a l l groups of c h i l d r e n and f i n a l l y w i t h an e n t i r e c l a s s o f grade f i v e c h i l d r e n i n d i c a t e d that a m o d i f i e d s e m a n t i c - d i f f e r e n t i a l instrument d i d indeed meet these requirements. The data generated by the use of t h i s instrument could be analyzed us i n g s e v e r a l d i f f e r e n t s t a t i s t i c a l models. The model s e l e c t e d was the f a c t o r - a n a l y t i c model because i t was judged to b e t t e r s a t i s f y the par- t i c u l a r needs of t h i s study, o u t l i n e d i n the preceeding two chapters. Both the measuring instrument and the f a c t o r - a n a l y t i c model are d e s c r i b e d i n d e t a i l i n Chapter Four. In summary, the procedures that are used i n the study to a s c e r t a i n the ' s t r u c t u r e of c h i l d r e n ' s b e l i e f s ' about heat e n t a i l the measurement of the perceived p s y c h o l o g i c a l a s s o c i a t i o n s between a number of s t a t e - ments drawn from three d i f f e r e n t P e r s p e c t i v e s of heat. T h i s measure was obtained by a s k i n g a c l a s s o f c h i l d r e n to judge a s e t of statements about heat u s i n g s i x c r i t e r i a (the s c a l e s on the instrument) as t h e i r b a s i s f o r judgment. Using an a p p r o p r i a t e f a c t o r - a n a l y t i c technique, i t was p o s s i b l e to assess the number of r e l e v a n t dimensions b e i n g used by the s u b j e c t s i n making the judgments. As the instrument was c o n s t r u c t e d w i t h statements u s i n g three d i f f e r i n g heat P e r s p e c t i v e s , i t was hypo- t h e s i z e d that one ought to be a b l e to i d e n t i f y these as somewhat separate dimensions. The study showed t h a t i t was p o s s i b l e to i d e n t i f y the extent to which a c h i l d , or a group of c h i l d r e n , subscribed to a p a r t i c u l a r p o i n t of view r e g a r d i n g heat phenomena ( t h a t i s , how h e a v i l y weighted 31 t h e i r judgments were on a given dimension). The c o l l e c t i o n of the data and the techniques used to determine the s t r u c t u r e of the c h i l - dren's judgments are discussed i n Chapter Four. 32 NOTES FOR CHAPTER TWO 1. Some examples of these e a r l y s t u d i e s on c a u s a l reasoning i n the c h i l d are: P i a g e t (1930), Issacs (1930), Keen (1934) and Huang's (1943) comprehensive review a r t i c l e . 2. A notable exception to t h i s trend was the work of Gerald C r a i g who went on to develop a very s u c c e s s f u l program based upon h i s s t u d i e s of c h i l d r e n ' s i n t e r e s t s and t h e i r r e l a t i o n s h i p to the p r e v a i l i n g s c i e n - t i f i c ideas of the day. 3. P i a g e t i s o b v i o u s l y to be excepted from t h i s c l a i m as he has always been i n t e r e s t e d i n c a r r y i n g h i s a n a l y s i s much beyond the c a t e g o r i z a t i o n stage. 4. Funk and Wagnalls Standard D i c t i o n a r y (1962). 5. Although t h i s p o i n t i s not addressed by Witz and Easley i n t h e i r paper, Easley (1969).has argued i n an e a r l i e r paper that P i a g e t ' s con- c e p t i o n of the o p e r a t i o n a l s t r u c t u r e s ( t h a t u n d e r l i e the development o f l o g i c a l t h i n k i n g i n the c h i l d ) can best be i n t e r p r e t e d as f u n c t i o n i n g i n a generative c a p a c i t y f o r the c h i l d . That i s , the c h i l d u t i l i z e s these s t r u c t u r e s , such as P i a g e t ' s famous INRC group, to c r e a t e a num- ber of p o t e n t i a l hypotheses when faced w i t h a problem s i t u a t i o n , as op- posed to u s i n g them to t e s t the v a l i d i t y of the p r o p o s i t i o n . The p h y s i c a l deep s t r u c t u r e s could then be c o n c e p t u a l i z e d as the content- o r i e n t e d product of these d e l i b e r a t i o n s by the c h i l d when i n t e r a c t i n g w i t h some p h y s i c a l system. For example, most c h i l d r e n b e l i e v e that the weight of the pendulum bob i s a determining v a r i a b l e i n how long i t takes to complete one swing. However, as the c h i l d works w i t h the system he i d e n t i f i e s other v a r i a b l e s , such as l e n g t h of s t r i n g , shape of bob, and amplitude of the swing. Once these v a r i a b l e s become known then the o p e r a t i o n a l s t r u c t u r e s enable him to generate other p o t e n t i a l hypotheses ( i n theory, a l l of the p o s s i b l e elements of the v a r i o u s combinations of v a r i a b l e s ) r e g a r d i n g the mechanism of the pendulum. As these new hypo- theses are examined e m p i r i c a l l y they may d i s p l a c e the c h i l d ' s e x i s t i n g n otions thus c r e a t i n g a new, or a l t e r e d p h y s i c a l deep s t r u c t u r e . 33 CHAPTER THREE METHOD OF COLLECTING AND ANALYZING THE INTERVIEW DATA 3.00 The P r e l i m i n a r y Work The p r e l i m i n a r y approach to Phase One of the study i n v o l v e d work- i n g w i t h s e v e r a l s m a l l groups of 11 and 12 y e a r - o l d c h i l d r e n who v i s i t e d The U n i v e r s i t y of B r i t i s h Columbia Campus. 1 E x p l o r a t o r y experiments and d i s c u s s i o n s concerned w i t h heat and temperature were conducted w i t h these groups. F o l l o w i n g these s e s s i o n s a d d i t i o n a l i n f o r m a l , i n d i v i d u a l i n t e r v i e w s were conducted w i t h elementary school c h i l d r e n ranging i n age from 6 to 13 years. The author's work w i t h these c h i l d r e n served as a type of p i l o t study p r o v i d i n g c l u e s concerning the types of ex- periments and demonstrations that are of i n t e r e s t to c h i l d r e n . They a l s o provided some i n d i c a t i o n of t y p i c a l p a t t e r n s of response to c e r t a i n questions and to the m a t e r i a l s themselves. Out of these s e s s i o n s , which spanned a p e r i o d of two months, emerged the tasks t h a t were f i n a l l y chosen f o r the formal i n t e r v i e w s . These t a s k s , which w i l l be d e s c r i b e d i n d e t a i l i n S e c t i o n 3.22, c o n s i s t e d of f i v e d i f f e r e n t s e t s of e x p e r i - ments or demonstrations r e l a t i n g to some aspect of heat phenomena. 3.10 A D e s c r i p t i o n of the Formal Int e r v i e w s 3.11 The Subjects While the ages of the c h i l d r e n used i n the p i l o t i n t e r v i e w s v a r i e d from 6 to 13, a d e c i s i o n was made to use only 12 y e a r - o l d c h i l d r e n f o r the f i n a l i n t e r v i e w s . T h i s d e c i s i o n was based on s e v e r a l c o n s i d e r a t i o n s : (1) most of the younger c h i l d r e n i n t e r v i e w e d i n the p i l o t s e s sions ap- peared to e i t h e r have given l i t t l e thought to the subject of heat or e l s e 34 had some d i f f i c u l t y i n expressing t h e i r i d e a s ; (2) c h i l d r e n o l d e r than 12 have o f t e n been introduced to a d u l t t h e o r i e s of heat i n a school s e t t i n g , thus, i n t e r f e r i n g w i t h the i n t e n t of the study — to examine c h i l d r e n ' s ideas of heat; (3) f i n a l l y , 12 i s about the age at which a c h i l d i s beginning to reason i n a more a b s t r a c t , t h e o r e t i c a l manner and i t was hoped that some of these more t h e o r e t i c a l commitments could be i d e n t i f i e d i n the i n t e r v i e w . The ten c h i l d r e n i n t e r v i e w e d ( f i v e boys and f i v e g i r l s ) were s e l e c t e d from two elementary schools i n the C i t y of Vancouver. There was a c o n s i d e r a b l e amount of d i v e r s i t y among the s u b j e c t s i n t h e i r s o c i o - economic background and l e v e l s of achievement i n s c h o o l . This was d e t e r - mined from i n f o r m a l conversations w i t h the c h i l d r e n p r i o r to and a f t e r the i n t e r v i e w , and by assurances from the teachers that the c h i l d r e n represented a wide range of a b i l i t i e s . The l a t t e r judgment by the teachers appeared to be s u b s t a n t i a t e d by the v a r y i n g responses to the i n t e r v i e w s i t u a t i o n . Some of the c h i l d r e n attempted to provide a f u l l , r i c h d e s c r i p t i o n of t h e i r ideas w h i l e others were content to respond to many of the questions posed by the i n v e s t i g a t o r w i t h very b r i e f , o f t e n non-commital answers. 3.12 The Tasks This s e c t i o n w i l l o u t l i n e the f i v e tasks used to engage the s u b j e c t s i n d i s c u s s i o n s of t h e i r ideas about heat phenomena. In a d d i t i o n , the s e c t i o n w i l l i n c l u d e a b r i e f d e s c r i p t i o n of the p h y s i c a l apparatus used and an abbreviated d i s c u s s i o n of the general types of questions accom- panying each task. The c r i t e r i a used f o r task s e l e c t i o n were: the 35 inherent i n t e r e s t or appeal of the task to the c h i l d and the degree of d i v e r s i t y i n heat phenomena i l l u s t r a t e d i n the t a s k s . The apparatus f o r the f i r s t task c o n s i s t e d of a 125 ml. E r l e n - meyer f l a s k c o n t a i n i n g water coloured by red food c o l o u r i n g . A one- hole stopper c o n t a i n i n g a 30 cm. c a p i l l a r y tube was i n s e r t e d i n t o the 2 f l a s k u n t i l a column of 'red l i q u i d ' rose up p a r t way i n t o the tube. Each c h i l d was shown t h i s apparatus and was asked to examine i t . I f no promising questions emerged from t h i s i n i t i a l encounter, the i n v e s t i - gator asked the c h i l d i f he could t h i n k of some way to lower the l e v e l of l i q u i d i n the tube. E v e n t u a l l y a l l of the s u b j e c t s ended up immersing the f l a s k i n beakers of c o l d and hot water, although a number of other i d i o s y n c r a t i c methods were a l s o used to t r y t o : a f f e c t the l i q u i d l e v e l . Questions such as: Why d i d the l i q u i d change as i t did? Would other l i q u i d s r e a c t i n a s i m i l a r fashion? What happens to the h o t / c o l d water when t h i s j a r i s immersed i n i t ? were posed at a p p r o p r i a t e moments whi l e the c h i l d was h a n d l i n g the m a t e r i a l s . The second task c o n s i s t e d of p l a c i n g e i g h t d i f f e r e n t o b j e c t s , a l l cube shaped, i n an aluminium t r a y on a hot p l a t e and observing the r e s u l t . The o b j e c t s c o n s i s t e d o f : two metal cubes (copper and aluminium), wood, sugar, wax, b u t t e r , i c e , and a mothball.. Before p l a c i n g the t r a y on the hot p l a t e , the c h i l d examined each of the cubes, u s u a l l y attempting to i d e n t i f y or name each cube. I f the q u e s t i o n d i d not a r i s e spontaneously the i n v e s t i g a t o r asked the c h i l d what would happen when the t r a y was placed on the hot p l a t e . Other questions r a i s e d by e i t h e r the c h i l d r e n or the i n v e s t i g a t o r r e l a t e d to the nature of the m e l t i n g process, and 36 why some substances melt more q u i c k l y and e a s i e r than o t h e r s . When time permitted a r e l a t e d experiment of comparing the m e l t i n g r a t e of i c e cubes i n water and i n a i r was performed. This m e l t i n g r a c e , staged between an i c e cube i n a i r at 70° F. and one i n about 200 ml. of water at 50° F. was of i n t e r e s t to most of the c h i l d r e n . The obvious q u e s t i o n as to why i t melted f a s t e r i n the water drew a l a r g e v a r i e t y of responses. A t h i r d task c o n s i s t e d of mixing water at d i f f e r e n t i n i t i a l tempe- r a t u r e s i n a s p e c i a l l y c onstructed p l e x i g l a s s c o n t a i n e r of dimensions 8 inches by 4 inches by 4 inches. A removable b a r r i e r i n the middle a l - lowed water at d i f f e r e n t temperatures to be poured i n each s i d e without mixing. The b a r r i e r could then be removed to mix the water i f d e s i r e d . The i n v e s t i g a t o r f i r s t posed questions concerning the t r a n s f e r of heat through the b a r r i e r before i t was removed. Then the c h i l d was asked to p r e d i c t the f i n a l temperature when the water a t two d i f f e r e n t tempe- r a t u r e s was mixed by removing the b a r r i e r . T his apparatus was a l s o used to i n v e s t i g a t e an i n t e r e s t i n g d i s - covery made by the i n v e s t i g a t o r d u r i n g the p i l o t s e s s i o n s . A f t e r ob- s e r v i n g a s i m i l a r p a t t e r n of responses made by c h i l d r e n aged 6 to 10 i t became apparent that one c r i t e r i o n used by some c h i l d r e n f o r ju d g i n g the temperature of water was the 'amount of water present'. Thus the apparatus was used to a l t e r the amounts of water at the same temperature to f u r t h e r explore the nature and prevalence of t h i s b e l i e f . A f o u r t h task i n v o l v e d h e a t i n g d i f f e r e n t s i z e d metal and g l a s s rods w i t h a candle flame to see which one would heat up the q u i c k e s t . Three p i n s , embedded i n wax, were placed along the rods to t r a c e the 37 progress of the c o n t e s t . The questions that accompanied t h i s experiment were: Why does the opposite end (to that being heated by the candle) of the rod get hot? Why do some rods get hot f a s t e r than others? One question f r e q u e n t l y asked by the c h i l d r e n about the experiment was: How i s heat able to move along the rod? While the i n v e s t i g a t o r pur- sued t h i s type of q u e s t i o n , u s i n g the c h i l d ' s own language where pos- s i b l e , he was c a r e f u l not to i n i t i a t e questions of t h i s nature which might suggest heat to be a type of m a t e r i a l substance. The f i n a l task proved to be the most d i f f i c u l t f o r the c h i l d r e n to comprehend. The b a s i c apparatus was designed to i l l u s t r a t e the ex- pansion of a s o l i d when heated. I t c o n s i s t e d of a 12-inch h o r i z o n t a l metal rod anchored at one end of a wooden frame (by d r i l l i n g a s m a l l hole i n the rod and i n s e r t i n g i t i n t o a s m a l l n a i l p r o t r u d i n g up from the frame). The other end of the rod r e s t e d upon a l o n g , s t r a i g h t p i n attached to a cardboard d i a l 4 inches i n diameter. When the rod was heated by two candles the l i n e a r expansion of the rod caused the p i n to t u r n . The motion of the p i n was t r a n s l a t e d to the l a r g e d i a l , which contained numbers th a t could be read by us i n g a reference p o i n t attached to the frame. A diagram of t h i s apparatus i s provided i n Appendix B. While the c h i l d r e n were very f a s c i n a t e d by the motion of the d i a l o n l y two c h i l d r e n were able to provide a somewhat reasonable e x p l a n a t i o n of what was o c c u r r i n g . Most of them simply shrugged t h e i r shoulders and s a i d something l i k e : "Well I guess the heat i s doing i t somehow, but I don't know how." 3.13 The Format of the I n t e r v i e w As standard procedure f o r the i n t e r v i e w s , the i n v e s t i g a t o r would 38 meet each c h i l d a t h i s or her school and d r i v e the c h i l d to The Uni v e r - s i t y of B r i t i s h Columbia f o r the i n t e r v i e w . This system allowed the i n v e s t i g a t o r to chat i n f o r m a l l y w i t h the c h i l d f o r 10 to 20 minutes before a c t u a l l y i n i t i a t i n g the i n t e r v i e w . An o p p o r t u n i t y was thus pro- vided to assure the c h i l d r e n that i t was not a ' t e s t i n g type' of s i t u a - t i o n , but one that they would enjoy. I t was a l s o p o s s i b l e to gather some simple b i o g r a p h i c a l data d u r i n g these d i s c u s s i o n s . The c h i l d was t o l d that the i n v e s t i g a t o r was t r y i n g to develop a new science course f o r t h e i r grade l e v e l , and so he was i n t e r e s t e d i n t h e i r ideas r e g a r d i n g the experiments about heat and temperature. The time r e q u i r e d to com- p l e t e the e n t i r e i n t e r v i e w s e s s i o n ranged from 40 to 70 minutes, w i t h most of the c h i l d r e n t a k i n g about 60 minutes. The room used f o r the i n t e r v i e w s was equipped w i t h one-way m i r r o r s and microphones. A one-inch Sony videotape recorder and camera were placed behind the m i r r o r , however, each c h i l d was informed of i t s pre- sence and was asked f o r permission to record the i n t e r v i e w . A diagram of the a c t u a l p h y s i c a l l a y o u t i s given i n Appendix B, The model adopted f o r conducting the i n t e r v i e w s resembled that of P i a g e t ' s " c l i n i c a l method". ( P i a g e t , 1969) E f f e c t i v e use of t h i s technique r e q u i r e s the i n t e r v i e w e r t o : ... u n i t e two o f t e n incompatible q u a l i t i e s ; he must know how to observe, that i s to say, to l e t the c h i l d t a l k f r e e l y , without ever checking or s i d e - t r a c k i n g h i s u t t e r a n c e , and at the same time he must c o n s t a n t l y be a l e r t f o r something d e f i n i t i v e , at every moment he must have some working h y p o t h e s i s , some theory, t r u e or f a l s e , which he i s seeking to check. ( P i a g e t , 1969, p. 9) In keeping w i t h t h i s technique no formal i n t e r v i e w schedule of 39 questions was used. Rather, the i n v e s t i g a t o r attempted f i r s t to get the c h i l d i n v o l v e d i n some aspect of the task. Having e s t a b l i s h e d some avenue of i n q u i r y or i n t e r e s t , open-ended questions were posed, u s i n g the c h i l d ' s own language where a p p r o p r i a t e . The "working hypotheses" that guided some of the qu e s t i o n i n g during the i n t e r v i e w s were l a r g e l y based upon the r e s u l t s from the p i l o t s e s s i o n s . For example, the n o t i o n that heat was a 's o r t of i n v i s i b l e substance, something l i k e a i r ' per- vaded many of the p i l o t i n t e r v i e w s . Although the i n v e s t i g a t o r was a l e r t to t h i s p o t e n t i a l view of heat, to the p o i n t of g e t t i n g the c h i l - dren to t r y and c l a r i f y and expand upon t h e i r i d e a s , he a l s o attempted to 'check out' other b e l i e f s which appeared to be d i s c r e p a n t w i t h t h i s substance n o t i o n of heat. A c a r e f u l s c r u t i n y of the t r a n s c r i p t s from the i n t e r v i e w s i n d i c a t e d that w h i l e a number of o p p o r t u n i t i e s f o r checking out some of these b e l i e f s were missed, some evidence of genuine b e l i e f s , or " l i b e r a t e d and spontaneous c o n v i c t i o n s " as P i a g e t c a l l s them, could be found. These b e l i e f s are the s u b j e c t of d i s c u s s i o n i n the f o l l o w i n g s e c t i o n . 3.20 A n a l y s i s of the In t e r v i e w Data There are a number of d i f f e r e n t methods f o r a n a l y z i n g q u a l i t a t i v e 3 data such as these generated by the i n t e r v i e w s d e s c r i b e d above. They range from the very "f r e e - w h e e l i n g " type of a n a l y s i s employed by P i a g e t and h i s co-workers to the more standardized methods such as those found i n books by Barker (1963) or Raush and Willems (1969). I n P i a g e t ' s method, the i n t e r v i e w data are i n v a r i a b l y analyzed i n terms of a p r o g r e s s i o n of developmental stages, but systematic p r e s e n t a t i o n 40 of the i n t e r v i e w s i s not attempted. This may be d i r e c t l y a t t r i b u t e d to h i s o v e r a l l t h e o r e t i c a l p e r s p e c t i v e , o u t l i n e d b r i e f l y i n Chapter Two. However, P i a g e t ' s i n f o r m a l method of r e p o r t i n g and s u b s t a n t i a t i n g h i s research claims has long been a s u b j e c t of controversy. Many other i n v e s t i g a t o r s have t r i e d to ' o b j e c t i f y ' h i s procedures e i t h e r by dev- e l o p i n g standardized instruments ( f o r example, Goldschmid and B e n t l e r , 1968; Tuddenham, 1922; and Green, Ford and Flamer, 1971) or attempting to be more e x p l i c i t i n the manner of a n a l y s i s and subsequent r e p o r t i n g of the i n t e r v i e w data. (Knifong, 1971) In c o n t r a s t to P i a g e t ' s techniques of s e l e c t i n g and c l a s s i f y i n g o n l y a few r e l e v a n t passages from an i n t e r v i e w , another frequent mode of a n a l y s i s i s to d i v i d e the e n t i r e t r a n s c r i p t i n t o segments according to some w e l l d e f i n e d c r i t e r i o n . T h i s c r i t e r i o n may be as a r b i t r a r y as the passage of a given amount of time ( F l a n d e r s , 1970) o r , i t may be based upon the d e f i n i t i o n of some meaningful u n i t of behavior ( f o r example, Smith et a l . (1962) A Study of the L o g i c of Teaching). The b a s i s f o r the method used i n the present study i s given by Witz (1970) i n a paper e n t i t l e d " A n a l y s i s of Frameworks i n Young C h i l - dren." Witz o u t l i n e d a method to " . . . d e s c r i b e and document mental s t r u c t u r e s which a c h i l d has, and which are s p e c i f i c to the c h i l d , without adopting a preconceived system of behavior c a t e g o r i e s . " (Witz, 1970, p. 1) The Frameworks, which are the end products of h i s a n a l y s i s , are constructed by f i r s t i d e n t i f y i n g a set of ideas expressed by the c h i l d t h a t seem connected and are somewhat s t a b l e — t h a t i s , extend over a p e r i o d of time. Once i n i t i a l l y i d e n t i f i e d , the a n a l y s t can 41 modify the framework, as necessary, w h i l e examining the remainder of the t r a n s c r i p t . An attempt i s made at a l l times to use the c h i l d ' s own language where p o s s i b l e i n d e s c r i b i n g the framework. Instead of c o n s t r u c t i n g frameworks, which are conceived to be r e p r e s e n t a t i v e of the u n d e r l y i n g mental s t r u c t u r e s possessed by the c h i l d , the present a n a l y s i s i s confined simply to i s o l a t i n g those b e l i e f s or c o n v i c t i o n s which appeared to be used by the c h i l d i n a s i t u a t i o n i n v o l v i n g heat and temperature phenomena. The u n i t of a n a l y s i s used f o r examining the i n t e r v i e w data, which i s c a l l e d an "Idea", thus represents a l e v e l of a n a l y s i s which i s more task s p e c i f i c and consequently l a c k s the d i r e c t t h e o r e t i c a l import of a framework. 3.21 D e f i n i t i o n of an Idea An Idea i s d e f i n e d as: an attempt by the c h i l d to e x p l a i n or i n some way account f o r a problem s i t u a t i o n that was i d e n t i f i e d i n the course of the i n t e r v i e w . While the i n v e s t i g a t o r most o f t e n i n i t i a t e d the problem s i t u a t i o n w i t h one or more questions r e l a t e d to some aspect of the task being considered, i t was a l s o p o s s i b l e f o r the s u b j e c t to i n i t i a t e the problem s i t u a t i o n w h i l e i n t e r a c t i n g w i t h the experimental m a t e r i a l s . 3.22 I d e n t i f i c a t i o n of Ideas The procedure used to i d e n t i f y Ideas i n the t r a n s c r i p t began w i t h an attempt by the a n a l y s t to recognize a p o t e n t i a l problem s i t u a t i o n . Considerable care was e x e r c i s e d to determine whether t h i s was indeed a genuine problem s i t u a t i o n f o r the c h i l d or whether i t was a r t i f i c i a l l y imposed upon the c h i l d by the i n t e r v i e w e r . That i s , the a n a l y s t t r i e d 42 d i s t i n g u i s h between those responses where the c h i l d d i d not understand the nature of the que s t i o n ( s ) being asked and so answered at random simply to s a t i s f y the i n v e s t i g a t o r , and those responses which were an accurate r e f l e c t i o n of the c h i l d ' s thoughts about the s i t u a t i o n . Using the c h i l d ' s own language where p o s s i b l e , the a n a l y s t then attempted to formulate the Idea used by the c h i l d to account f o r the problem s i t - u a t i o n . In many instances these i n i t i a l f o r m u l a t i o n s were a l t e r e d l a t e r i n the t r a n s c r i p t when the c h i l d e i t h e r embellished the b a s i c Idea i n some way or perhaps even changed i t completely. The f o l l o w i n g b r i e f excerpt from a t r a n s c r i p t should serve to i l l u s t r a t e the type of a n a l y s i s d escribed above. A Sample Analysis for Identifying Ideas Analyst's Remarks Excerpts from the Interview Transcript Analyst's summary of an Idea i s in (Explanatory comments in brackets) BOLD PRINT L ~ interviewer S_ = subject) Formulation of the liquid expansion problem by Interviewer. Subject seems familiar with the expansion of objects when heated, however, he ob- viously hasn't thought too much about the mechanism of expansion and so tries a familiar process — condensation. While this might qualify as an Idea, he doesn't pursue the notion of condensation further and so i t i s not included. While I pushed S to go a l i t t l e further with his explanation, i t i s obvious that I did not in any way suggest the notion of cells or particles to S_. Hence the c e l l notion seems to be genuine. It is uncertain at this point whether the ce l l s are related in any way to his i n i t i a l condensation hypothesis or not. I: Why do you suppose that liquid goes up when we put i t in hot water and down when we put i t in (S interrupts) S: It expands. (3 second pause) It might condense or something and the condensation might l i f t i t up some, the water that's in the tube. And probably the water when i t ' s in the tube might start bubbling or something. I: Now let's try i t step by step. (I picks up apparatus and motions as i f to put i t in the hot water beaker) As soon as we put i t i n the hot water what do you think might happen inside, say? If you could see what's hap- pening inside what do you think might have taken place? S: The ce l l s might be expanding. I: Now by expanding what do you think i s happening? S: It's getting larger. I: What i s getting larger? S: The water. (S_ points to the colored l i q u i d in the expansion container) I* Okay, the water. And* then what? I t i s noteworthy that S_ q u i c k l y returned to h i s c e l l i dea even though he had an oppo r t u n i t y to d i v e r t the d i s c u s s i o n away. From h i s u n c e r t a i n t y "Well I guess..." one might i n f e r that he had not thought of t h i s idea b e f o r e . On the molar l e v e l he knew substances expanded, and on the molecular l e v e l he was f a m i l i a r w i t h the no t i o n of c e l l s . But i t may w e l l be the f i r s t time that he had connected the two together. Hence the Idea might be expressed: THE WATER GOES UP IN THE TUBE BECAUSE THE WATER GETS LARGER WHEN IT IS HEATED DUE TO THE EXPANDING OF THE CELLS IN THE WATER. WHEN THE WATER COOLS THE CELLS CONTRACT AND THE WATER GOES BACK DOWN AGAIN. S: I t goes up when i t i s heated, j u s t by the heat of my hand. (S_ i s holding the apparatus i n h i s hand) Look a t t h a t ! I t doesn't take very long. I : That's very i n t e r e s t i n g . Are you sure you're not f o r c i n g i t out w i t h your hand? S: No. (5 second pause) Well I guess the c e l l s would expand. I : Okay, r i g h t , we were going to...the c e l l s would expand and then what? S: The water has to be forced out somewhere and t h i s (S_ p o i n t s to the tube) i s the only e x i t f o r i t . I ; And when i t cools down? S: I t co n t r a c t s and goes back to the bottom l i k e a thermometer. I : You t h i n k t h a t ' s how a thermometer works huh? S: Yes. Well l i k e some thermometers are made of colored water aren't they? I : Could be. I'm not sure. I don't break t h e r - mometers that o f t e n so,...Now what do you thi n k makes i t expand? S: Well the heat. I : And where i s the heat coming from? S: The hot water. I : The heat comes from the hot water. And how does i t get from the hot water? Another Idea is being suggested here which is developed more f u l l y later i n the transcript. WHEN A COOLER OBJECT (the expansion flask) IS PLACED IN CONTACT WITH A HOTTER OBJECT, (the hot water) THE TWO OBJECTS EVENTUALLY REACH THE SAME HOTNESS (temperature). Through the glass. (S_ laughs) And then where does i t go? The heat penetrates the water in here. (S points to the expansion container) If you l e f t i t i n there (the hot water beaker) long enough, in the boiling hot water, i t would get just as hot inside here, (the expansion container) 46 3.23 Construction of Conceptual Inventories By looking at the entire set of Ideas held by a child one can get a much better global perspective of the child's understanding of heat and temperature phenomena. In an endeavor to simplify this over- a l l summarization procedure i t was decided to organize the Ideas into a number of content-oriented categories to form a Conceptual Inventory. These categories were based upon those topics most often found i n science textbooks and elementary science programs dealing with heat and temperature. The following set of categories was adopted for constructing a Conceptual Inventory for each child interviewed: A. NATURE OF HEAT 1.0 Composition of Heat 2.0 Movement of Heat 3.0 Effects of Heat 4.0 Source of Heat 5.0 Matter and Heat B. NATURE OF TEMPERATURE 6.0 Description of Temperature 7.0 Change of Temperature 8.0 Temperature and Heat 3.24 An Example of a Conceptual Inventory The following example of a Conceptual Inventory should serve to better i l l u s t r a t e the nature of the Conceptual Inventory and i l l u s t r a t e the wide range of Ideas identified in a single interview. This Conceptual 47 Inventory of Ron's Ideas corresponds w i t h a f u l l t r a n s c r i p t of h i s i n t e r v i e w i n Appendix A. Ron was 12 years 9 months and was i n grade s i x . L i k e most of the other c h i l d r e n he could not remember i f he had ever s t u d i e d 'heat' i n s c h o o l . A Conceptual Inventory f o r Ron (Numbers i n Brackets r e f e r to t r a n s c r i p t page i n Appendix A) A. NATURE OF HEAT 1.0 Composition of Heat 1.1 Heat i s l i k e a wave th a t r i s e s up from the road. I t looks l i k e fumes. (p. 147) 1.2 Hot substances c o n t a i n fumes, and when they c o o l down these fumes escape g r a d u a l l y i n t o the a i r (p. 152) 1.3 There are two types of heat — hot heat and c o l d heat. (p. 155) 1.31 The c o l d heat i s more powerful and moves f a s t e r than the hot heat. (p. 156) 1.32 Cold heat might look d i f f e r e n t from hot heat, but I don't know what i t would look l i k e . (p. 156) 2.0 Movement of Heat 2.1 The movement of heat occurs by p a s s i n g through o b j e c t s i n a stepwise manner. (p. 146) 2.2 Heat passes from a hot o b j e c t to a c o l d e r one when they are touching. (p. 146) 2.3 The whole metal rod heats up because the heat keeps moving from one p a r t of the rod to the next u n t i l the whole rod i s hot. (p. 167) 2.4 Heat t r a v e l s f a s t e r i n a s m a l l e r rod because i t doesn't have as much rod to get the heat t o . (p. 167) 2.41 Heat t r a v e l s through a l l substances. (p. 167) 48 3.0 E f f e c t s of Heat 3.1 The l i q u i d i n the tube goes up because water r i s e s when i t gets hot. (p. 149) 3.11 When you heat something i t gets bubbles i n i t , and the bubbles take up space. So t h a t ' s why the water i n the tube r i s e s . (p.171) 3.2 Some things l i k e i c e and suger cubes melt because they c o n t a i n a i r bubbles. (p. 161) 3.3 The d i a l (on the l i n e a r expansion apparatus) moves because the rod i s m e l t i n g and s t r e t c h i n g . When i t co o l s o f f i t s h r i n k s . (p. 170) 4.0 Sources of Heat 4.1 Heat comes from any o b j e c t t h a t i s hot. (p. 146) 5.0 Heat and Matter 5.1 E v e r y t h i n g c o n t a i n s a i r bubbles. Some of the bubbles might c o n t a i n hot a i r and some c o l d a i r . (p. 156) B. NATURE OF TEMPERATURE 6.0 D e s c r i p t i o n of Temperature 6.1 The temperature of an o b j e c t i s based on the amount of heat (fumes) i t c o n t a i n s . (p. 151) 6.2 A small i c e cube has the same temperature as a l a r g e i c e cube. (p. 163) 7.0 Change of Temperature 7.1 When a c o l d o b j e c t meets a hot ob j e c t the c o l d o b j e c t get warmer and the hot o b j e c t gets c o l d e r . A f t e r awhile they reach the same same temperature, (p. 147) 7.2 An ob j e c t c o o l s when i t gives o f f some of i t s heat as fumes. (p. 152) 8.0 Temperature and Heat (Ron doesn't r e a l l y make a d i s t i n c t i o n between heat and temperature and appears to equate the two on s e v e r a l occasions as i s sug- gested i n 6.1) 49 3.25 A C h i l d r e n ' s P e r s p e c t i v e of Heat The f i n a l step of the a n a l y s i s of the i n t e r v i e w data i n v o l v e d an attempt to e x t r a c t the commonalities from a l l ten Conceptual Invento- r i e s and c o n s t r u c t a composite p i c t u r e of the c h i l d r e n ' s Ideas. This composite s t r u c t u r e was c a l l e d a C h i l d r e n ' s P e r s p e c t i v e of heat. The g u i d e l i n e s employed to develop the P e r s p e c t i v e c o n s i s t e d of examining a l l ten I n v e n t o r i e s f o r Ideas which occurred more than once; preference was given to those which appeared i n three or more d i f f e - r e n t I n v e n t o r i e s . The C h i l d r e n ' s P e r s p e c t i v e , then, c o n s i s t s of a s e r i e s of Ideas judged to be r e p r e s e n t a t i v e of those c h i l d r e n who were interv i e w e d i n the study. An attempt of t h i s nature — to d i s t i l l the essence of ten i n t e r - views i n t o a l i m i t e d set of statements — i s s u b j e c t to severe l i m i t a - t i o n s and open to c r i t i c i s m w i t h regard to the r a t h e r l a r g e i n f e r e n t i a l leap t h a t must be made. However, as i t was intended to s u b j e c t t h i s P e r s p e c t i v e to an e m p i r i c a l check i n Phase Two of the study, t h i s pro- cedure does not d i f f e r s i g n i f i c a n t l y from the t h e o r i z i n g process i n other f i e l d s of i n q u i r y . Ron's i n t e r v i e w was s e l e c t e d to i l l u s t r a t e the Conceptual Inven- t o r y because h i s Ideas were reasonably t y p i c a l of a l l of the c h i l d r e n . Thus h i s Inventory w i l l a l s o be used to i l l u s t r a t e b r i e f l y the type of statements used to c o n s t r u c t the C h i l d r e n ' s P e r s p e c t i v e of heat. I n examining the Ideas expressed i n Ron's Inventory one can r e a d i l y d e t e c t a tendency to p e r c e i v e heat as a type of m a t e r i a l sub- stance that has p r o p e r t i e s that we g e n e r a l l y a t t r i b u t e to matter. For 50 example, he f r e q u e n t l y d i s c u s s e s heat i n terms of "fumes" that are capable of " t r a n s f e r r i n g i n t o or out of an o b j e c t " . In f a c t at one p o i n t , to account f o r the h e a t i n g and c o o l i n g of an o b j e c t , he t a l k e d about 'hot heat' and 'cold heat' — c l e a r l y a s u b s t a n t i a l , two-compo- nent view of heat embodying a type of p o s i t i v e and negative q u a l i t y . In a d d i t i o n to t h i s n o t i o n , most of the other c h i l d r e n a t t r i b u t e d to heat an a d d i t i v e - s u b t r a c t i v e property where the temperature of the obje c t could be changed e i t h e r by adding or s u b t r a c t i n g heat from the o b j e c t . In one p a r t i c u l a r task, which c o n s i s t e d of h e a t i n g d i f f e r e n t types of cubes over a hot p l a t e , more than h a l f of the c h i l d r e n ac- counted f o r the o b s e r v a t i o n that the metals heated up before the wood or sugar by s t a t i n g that "the metals could a t t r a c t the heat b e t t e r than the other o b j e c t . " While t h i s l a t t e r e x p l a n a t i o n i s v i r t u a l l y i d e n t i c a l w i t h a view of heat p r e v a l e n t i n the l a t e 18th and e a r l y 19th C e n t u r i e s (the c a l o r i c theory of h e a t ) , i t was f e l t that there were many other Ideas expressed by the c h i l d r e n which could not be accommodated to the c a l o r i c theory proper. The decision was made to c o n s t r u c t a unique C h i l - dren's P e r s p e c t i v e ; a l b e i t one which was s i m i l a r i n some re s p e c t s to 4 t h i s e a r l i e r m a t e r i a l conception of heat. Sev e r a l of the statements used to develop the C h i l d r e n ' s Perspec- t i v e are discussed below as they r e l a t e to Ron's Conceptual Inventory. The remaining statements are o u t l i n e d i n Chapter Four. Since the s t a - tements are d i r e c t l y r e l a t e d to some of the experiments performed during the i n t e r v i e w they c o n s i s t of two p a r t s : the o b s e r v a t i o n a l p a r t des- c r i b i n g what happened i n the experiment and an explanatory p a r t , i n 51 BOLD PRINT, which i s the Idea to account f o r the o b s e r v a t i o n . (1) The whole rod gets hot because: THE HEAT BUILDS UP IN ONE PART UNTIL IT CAN'T HOLD ANYMORE AND THEN IT MOVES ALONG THE ROD. This Idea, which i s found i n a rudimentary form i n S e c t i o n 2.3 of Ron's Conceptual Inventory, i l l u s t r a t e s the m a t e r i a l aspect of heat as i t p o r t r a y s heat accumulating i n one spot and then, l i k e a f l u i d , overflows to another p a r t of the metal rod. (2) The temperature of the water decreases when an i c e cube was added because: SOME OF THE COLD LEFT THE ICE CUBE AND WENT INTO THE WATER. I t was i n t e r e s t i n g t h a t many of the c h i l d r e n i n t e r v i e w e d men- tioned the e x i s t e n c e of c o l d as an opposite to heat. Note that i t i s a l s o endowed w i t h a m a t e r i a l property as i t i s t r a n s f e r r e d from the i c e cube to the water. The b a s i s f o r t h i s Idea i s i n S e c t i o n 1.3 of Ron's Conceptual Inventory. (3) The red l i q u i d went up the tube because: THE HEAT MAKES THE RED LIQUID LIGHTER AND SO IT RISES. This statement does not focus upon the m a t e r i a l property of heat but r a t h e r the i n t u i t i v e n o t i o n t h a t heat makes things r i s e . While some of the c h i l d r e n were content to leave the e x p l a n a t i o n at t h i s p o i n t , many others l i k e Ron attempted to search f o r some i n t e r m e d i a t e , cau s a l agent. In Ron's case he q u a l i f i e s the statement he makes about hot water r i s i n g (Idea 3.1) w i t h Idea 3.11, which suggests that i t i s the bubbles, added during h e a t i n g , that take up space and so f o r c e the l i q u i d up the tube. 52 NOTES FOR CHAPTER THREE 1. These c h i l d r e n were p a r t i c i p a t i n g i n a program i n which one or two c l a s s e s of elementary school c h i l d r e n are brought out to the U n i v e r s i t y of B r i t i s h Columbia campus f o r a week to work w i t h pros- p e c t i v e teachers i n the F a c u l t y of Education. 2. Diagrams of any non-obvious pieces of equipment used i n the tasks are given i n Appendix B. 3. Barton and L a z a r s f e l d (1955) have w r i t t e n a comprehensive a r t i c l e e n t i t l e d "Some Functions of Q u a l i t a t i v e A n a l y s i s i n S o c i a l Research" which i s devoted to an examination of the d i f f e r e n t types of a n a l y s i s i n s t u d i e s i n v o l v i n g q u a l i t a t i v e data. 4. I t may be p o s s i b l e to f a s h i o n an argument s i m i l a r to that used by E l k i n d i n h i s i n t r o d u c t i o n to P i a g e t ' s (1968) S i x P s y c h o l o g i c a l S t u d i e s . He suggests that P i a g e t o f t e n seeks p a r a l l e l s between the thought of c h i l d r e n and e a r l i e r systems of thought, not to demonstrate r e c a p i t u l a - t i o n , r a t h e r , to i l l u s t r a t e the " . . . p a r t i a l constancy of c o g n i t i v e s t r u c t u r i n g across long time p e r i o d s . " ( P i a g e t , 1968, p. v i i ) The major d i f f e r e n c e i s t h a t the c h i l d r e n ' s i n t u i t i v e conceptions have not yet been f o r m a l i z e d i n t o a comprehensive, a b s t r a c t system such as A r i s t o t l e ' s N a t u r a l Philosophy or the c a l o r i c theory. And so one sees glimpses of the somewhat s o p h i s t i c a t e d c a l o r i c theory, but the c h i l - dren o b v i o u s l y have not attempted to f o r m a l i z e t h e i r t h i n k i n g i n any way. 53 CHAPTER FOUR METHOD OF OBTAINING CONCEPTUAL PROFILES 4.00 I n t r o d u c t i o n I n Chapter Two i t i s s t a t e d t h a t the type of s t r u c t u r a l a n a l y s i s adopted f o r the present study was based upon a m u l t i d i m e n s i o n a l a n a l y s i s model. Using judgmental data produced by a s e m a n t i c - d i f f e r e n t i a l type of instrument, the model was employed to generate s t r u c t u r e s r e f e r r e d to as "Conceptual P r o f i l e s " of heat. The c o n s t r u c t i o n of these Con- c e p t u a l P r o f i l e s , which c o n s t i t u t e d Phase Two of the study, posed three major problems: (1) the choice of an a p p r o p r i a t e model to guide the a n a l y s i s ; (2) the development of an instrument that would meet the c o n s t r a i n t s imposed by the model on one hand, and the r e a l i t i e s of the classroom s e t t i n g on the other; and (3) the adoption of a set of a n a l y t i c a l techniques t h a t would y i e l d the d e s i r e d Conceptual P r o f i l e s . This chapter i s devoted to a d e s c r i p t i o n of the methods used to r e s o l v e these three b a s i c problems. 4.10 A Model f o r S t r u c t u r a l A n a l y s i s The problem of s t r u c t u r a l a n a l y s i s i n the present context i s to t r y and r e c o n s t r u c t i n a systematic way a s t r u c t u r e or o r g a n i z a t i o n of c h i l d r e n ' s b e l i e f s about heat, r e f e r r e d to i n t h i s study as a Conceptual P r o f i l e . A number of d i f f e r e n t models seemed a p p r o p r i a t e f o r t h i s r e - c o n s t r u c t i o n process. Two models were elaborated i n Chapter Two — the d e s c r i p t i v e analyses o f f e r e d by P i a g e t and Witz and E a s l e y i n con- t r a s t to the c l a s s of models i n v o l v i n g a m u l t i d i m e n s i o n a l a n a l y s i s . In view of the declared aims of the study, however, i t was argued i n Chap- t e r Two that a m u l t i d i m e n s i o n a l a n a l y s i s model held more p o t e n t i a l i n 54 terms of a c h i e v i n g those aims. While there are a number of a n a l y t i c a l methods which could be i n c l u d e d under the general c l a s s of m u l t i d i m e n s i o n a l a n a l y s i s , the s p e c i f i c model used f o r generating the d e s i r e d s t r u c t u r e s i n the present study i s a f a c t o r - a n a l y t i c model."'' Viewed i n simple terms, i t i s an a n a l y t i c a l procedure f o r reducing the M-dimensional space d e f i n e d by the M o r i g i n a l v a r i a b l e s to a space d e f i n e d by a minimum number of i n - dependent dimensions necessary f o r r e p r e s e n t i n g the e s s e n t i a l r e l a t i o n - ship between the o r i g i n a l v a r i a b l e s . T his reduced space can be thought of as a s t r u c t u r e i n which the r e l a t i o n s h i p between the o r i g i n a l v a r i a b l e s and the dimensions which d e f i n e the s t r u c t u r e i s expressed mathematically. I f the o r i g i n a l v a r i a b l e s are p s y c h o l o g i c a l i n nature, such as concepts or persons, then the dimensions of the reduced space can be i n t e r p r e t e d as important p s y c h o l o g i c a l dimensions of the v a r i a b l e s . B a s i c a l l y a f a c t o r - a n a l y t i c model f u n c t i o n s " . . . e i t h e r to t e s t hypotheses about the e x i s t e n c e of c o n s t r u c t s , or i f no c r e d i b l e hypo- theses are a t i s s u e , to search f o r c o n s t r u c t s i n a group of i n t e r e s t i n g v a r i a b l e s . " (Nunnally, 1967, p. 289) In us i n g the f a c t o r - a n a l y t i c model f o r the a n a l y s i s of the data i n Phase Two, both of these f u n c t i o n s were r e a l i z e d to some extent. One aspect of the a n a l y s i s e n t a i l e d a t e s t f o r the e x i s t e n c e of the h y p o t h e t i c a l c o n s t r u c t , 'the C h i l d r e n ' s Per- s p e c t i v e of heat', described i n Chapter Three. While at the same time a search was made to determine whether other c o n s t r u c t s , d e r i v e d from d i f f e r e n t P e r s p e c t i v e s of heat, could be d i f f e r e n t i a t e d by the s u b j e c t s . I 55 I n the study a type of s e m a n t i c - d i f f e r e n t i a l instrument, c a l l e d a Conceptual P r o f i l e Instrument ( h e r e a f t e r c a l l e d a C.P.I.)» was dev- eloped to assess the c h i l d r e n ' s conceptions of heat phenomena. The f a c t o r - a n a l y t i c model was f i r s t used to reduce the s i x - d i m e n s i o n a l space of the r a t i n g s c a l e s used i n the C.P.I, to a s t r u c t u r e d e f i n e d by two independent dimensions or sets of s c a l e s . One set of s c a l e s was termed " b e l i e f - s c a l e s " and the other s e t , " f a m i l i a r i t y - s c a l e s " . Responding to one s c a l e a t a time, the s u b j e c t s were r e q u i r e d to r a t e the d i f f e r e n t statements about heat i n terms of the s t r e n g t h of t h e i r b e l i e f s about the statements and i n terms of the degree to which they were f a m i l i a r w i t h the ideas contained i n the statements. By f a c t o r - a n a l y z i n g the responses to these statements i t i s p o s s i b l e to reduce the complexity of the dimensions used to d e f i n e the responses. The dimensions d e f i n i n g t h i s reduced space can p r o p e r l y be c a l l e d "Viewpoints of Heat" h e l d by the s u b j e c t s and they c o n s t i t u t e one method of s t r u c t u r i n g the set of statements contained i n the C.P.I. The view- p o i n t a n a l y s i s thus provides f o r a t e s t of whether the C h i l d r e n ' s P e r s p e c t i v e could i n f a c t be d i f f e r e n t i a t e d from the two other Perspec- t i v e s , the K i n e t i c P e r s p e c t i v e and the C a l o r i c P e r s p e c t i v e , and whether or not the l a t t e r two P e r s p e c t i v e s could be s i n g l e d out. The b a s i c r e l a t i o n s h i p being assessed by the s t r u c t u r a l a n a l y s i s of viewpoints i s the degree of p s y c h o l o g i c a l a s s o c i a t i o n between the v a r i o u s statements as perceived by the s u b j e c t s . This method of s t r u c t u r a l a n a l y s i s d i f f e r s from the d e s c r i p t i v e analyses of s t r u c t u r e o f f e r e d by Piaget and Witz and Easley i n at l e a s t two important ways: 56 (1) the r u l e s f o r c r e a t i n g the a n a l y t i c a l c a t e g o r i e s and the a s s i g n - ment of behaviors to those c a t e g o r i e s are e x p l i c i t i n the f a c t o r - a n a - l y t i c model but are mainly i n t u i t i v e i n the l a t t e r ; (2) the former model does not a l l o w f o r any s e r i o u s generation or a l t e r a t i o n of ex- i s t i n g t h e o r e t i c a l c o n s t r u c t s because i t i s r e s t r i c t e d to manipulating the i n p u t data. While the l a t t e r type of model has the p o t e n t i a l to develop a r i c h e r and more adaptable t h e o r e t i c a l framework due to i t s dependence upon the i n g e n u i t y and i n s i g h t of the t h e o r e t i c i a n . In con- t r a s t i n g these two a n a l y t i c approaches i t would appear as though they might w e l l be complementary — the more dive r g e n t t h e o r i z i n g approach being r e s p o n s i b l e f o r generating tenable hypotheses which could then be checked out ag a i n s t r e a l i t y by u s i n g a l a r g e number of s u b j e c t s i n a f a c t o r - a n a l y t i c study. Phases One and Two of the study correspond roughly to these complementary approaches. With the s t r u c t u r a l a n a l y s i s of the data c u l m i n a t i n g i n d i s c r e t e c l u s t e r s of concepts, or Viewpoints, some evidence has been accumulated to suggest that the su b j e c t s were indeed a b l e to d i f f e r e n t i a t e and d i s - c r i m i n a t e between the conceptual statements r e p r e s e n t i n g the d i f f e r e n t P e r s p e c t i v e s of heat. However, i t i s not p o s s i b l e to say whether or not there are groups of s u b j e c t s who hold to these Viewpoints d i f f e r e n - t i a l l y . To r e s o l v e t h i s problem, which i s very important f o r the ed u c a t i o n a l a p p l i c a t i o n of the a n a l y s i s , the model was a p p l i e d to a matrix of s u b j e c t s versus concept r a t i n g s . (That i s , a m a t r i x of i n - d i v i d u a l p r o f i l e s . ) The p r o f i l e space was reduced by the f a c t o r - a n a l y t i c model, using a transposed p r o f i l e m a t r i x , to a three-dimensional 57 s t r u c t u r e . These dimensions were defined by s e t s of p r o f i l e s of s i m i l a r shape. To determine whether these dimensions could be f u r t h e r r e f i n e d on the b a s i s of l e v e l and d i s p e r s i o n , those p r o f i l e s most r e p r e s e n t a t i v e of each dimension were f a c t o r - a n a l y z e d . The c l u s t e r s of p r o f i l e s ob- tained i n t h i s l a s t a n a l y s i s were used to c o n s t r u c t Model Conceptual P r o f i l e s — each Model P r o f i l e being an i d e a l i z a t i o n of a 'type of person' who responded to the C.P.I, i n a s i m i l a r f a s h i o n . These Model Conceptual P r o f i l e s , then, are the sought a f t e r r e c o n s t r u c t i o n of c h i l - dren's b e l i e f s about heat. 4.20 Development of the Conceptual P r o f i l e Instrument 4.21 O p e r a t i o n a l l z i n g the A t t r i b u t e Before d e s i g n i n g an instrument to measure the a t t r i b u t e of i n t e r e s t i n t h i s study — c h i l d r e n ' s conceptions of heat phenomena — s e v e r a l p r e l i m i n a r y problems had to be r e s o l v e d . The most important problem was o p e r a t i o n a l l y d e f i n i n g the a t t r i b u t e to be measured. U n l i k e the measu- rement of many p h y s i c a l a t t r i b u t e s (such as l e n g t h , weight, f o r c e , e t c . ) which u s u a l l y can be d e f i n e d i n such a way t h a t they can be measured d i r e c t l y , only i n d i c a n t s of p s y c h o l o g i c a l a t t r i b u t e s can be assessed. Consequently these a t t r i b u t e s are much more dependent upon theory. In measuring p s y c h o l o g i c a l a t t r i b u t e s , theory f u n c t i o n s f i r s t , to guide the d i f f i c u l t task of o p e r a t i o n a l l y d e f i n i n g the a t t r i b u t e ( t h a t i s , o b t a i n i n g some measurable i n d i c a n t of i t ) and second, to provide an i n t e r p r e t a t i o n of the measurements made on the i n d i c a n t s . Much of the input f o r g u i d i n g the i d e n t i f i c a t i o n of measurable i n - d i c a n t s of c h i l d r e n ' s conceptions of heat phenomena and the i n t e r p r e t a t i o n 58 of the measurements came from the i n t e r v i e w data. The set of Ideas which c o n s t i t u t e d the C h i l d r e n ' s P e r s p e c t i v e formed much of the theo- r e t i c a l b a s i s f o r developing the C.P.I. Statements r e p r e s e n t i n g t h i s P e r s p e c t i v e , along w i t h those from two other a l t e r n a t i v e P e r s p e c t i v e s , made up a p o o l of items from which the C.P.I, was developed. 4.22 Method of Assessing P s y c h o l o g i c a l R e l a t i o n s h i p A second problem,- that had to be considered p r i o r to the c o n s t r u c - t i o n of the C.P.I., was the choice among a v a i l a b l e techniques f o r ob- t a i n i n g an estimate of p s y c h o l o g i c a l r e l a t i o n s h i p . Most of the common techniques a v a i l a b l e f o r measuring p s y c h o l o g i c a l a t t r i b u t e s r e q u i r e the s u b j e c t s to make some type of judgment about a s e l e c t e d set of s t i m u l i . For example, the comparison procedures, such as p a i r e d comparison or successive i n t e r v a l s , r e q u i r e the s u b j e c t to rank a l l of the s t i m u l u s - p a i r s according to t h e i r s i m i l a r i t y . U n f o r t u n a t e l y a l l of the comparison methods r e q u i r e a l a r g e number of judgments to be made even f o r a modest number of s t i m u l i . I n t h i s study the a b s o l u t e minimum number of items considered f o r the C.P.I, was f i f t e e n ( f i v e items per P e r s p e c t i v e ) . Using the method of p a i r e d comparisons, f o r example, would have r e q u i r e d a t o t a l of 105 ( n ( n - l ) / 2 ) judgments. Obviously t h i s method would be i n a p p r o p r i a t e f o r general classroom use. Another technique f o r gathering data on the r e l a t i o n s h i p of p s y c h o l o g i c a l a t t r i b u t e s r e q u i r e s the s u b j e c t s to do a comparative s o r t i n g of a l l the s t i m u l i . In the most common of these techniques, the Q-sort, the s u b j e c t s must s o r t a l l of the s t i m u l i i n t o a number of ordered c a t e g o r i e s . The i n v e s t i g a t o r has the freedom to determine the number of 59 c a t e g o r i e s and the membership of each category. By usi n g a f i x e d d i s t r i b u t i o n t h i s f o r c e s a l l of the su b j e c t s to have the same mean r a t i n g and same standard d e v i a t i o n of r a t i n g s , whereas i n a ' f r e e - s o r t ' the subject i s allowed to determine both of these parameters w i t h the subsequent l o s s i n s t a n d a r d i z a t i o n of the su b j e c t ' s r a t i n g s which i s c h a r a c t e r i s t i c of the Q-sort. These s o r t i n g techniques, then, have the advantage of being able to accommodate a l a r g e number of s t i m u l i without r e q u i r i n g an i n o r d i n a t e number of judgments. But whether a s o r t i n g task could be t r a n s l a t e d i n t o a procedure s u i t a b l e f o r the t a r g e t age (11 to 15 years) and could be e a s i l y administered i n a classroom s e t t i n g c o u l d not be predetermined. A number of t r i a l s e s s ions were i n i t i a t e d i n order to determine the f e a s i b i l i t y of u s i n g some type of s o r t i n g procedure. Each of these sessions c o n s i s t e d of s m a l l groups (from two to four c h i l d r e n ) who were given up to 35 statements about heat to s o r t i n t o p i l e s t h a t were a l i k e i n some way. (That i s , a f r e e - s o r t method was used.) These statements were drawn from the three P e r s p e c t i v e s of heat as discussed i n S e c t i o n 4.24. The c h i l d r e n were g r a d u a l l y introduced to the task through two t r a i n i n g s e s s i o n s . F i r s t , a deck of p l a y i n g cards was used to i l l u s - t r a t e the number of d i f f e r e n t ways i n which the cards could be s o r t e d i n t o p i l e s . Then a set of statements about s i c k n e s s and h e a l t h , designed to approximate the form of the heat statements, were i n t r o - duced. The c h i l d r e n and the i n v e s t i g a t o r discussed d i f f e r e n t ways i n which these cards could be s o r t e d . F i n a l l y the statements about heat were int r o d u c e d . 6Q While the c h i l d r e n were able to s o r t the p l a y i n g cards i n t o numer- ous p i l e s , they experienced more d i f f i c u l t y w i t h the statements about "health and s i c k n e s s ' . T h e i r f i r s t s o r t i n g of the 'health and s i c k n e s s ' statements was g e n e r a l l y i n t o p i l e s of r i g h t and wrong, o r , agree and dis a g r e e . However, when the i n v e s t i g a t o r pointed out other ways of s o r t i n g these statements ( f o r example, " p i l e s of k i d ' s ideas and a d u l t ideas") they r e a d i l y agreed t h a t t h i s was a l s o a good way to separate the cards. When they began to s o r t the statements about heat i t was soon apparent that the p r e f e r r e d method was again to use two p i l e s . In the words of the c h i l d r e n "the cards i n that p i l e are ideas that I s o r t of l i k e or agree w i t h , but the cards i n t h i s p i l e are ideas that I don't l i k e much." Most of the c h i l d r e n thus appeared to employ a type of preference c r i t e r i o n i n making the s o r t w i t h the heat statements. Although a preference c r i t e r i o n would be q u i t e acceptable f o r an assessment of p s y c h o l o g i c a l r e l a t i o n s h i p , more than two c a t e g o r i e s would be d e s i r a b l e to gain s u f f i c i e n t d i s c r i m i n a t i o n amon g the statements. An attempt was made i n a subsequent t r i a l s e s s i o n to c r e a t e at l e a s t four c a t e g o r i e s by i n s t r u c t i n g the c h i l d r e n to d i v i d e each of the two p i l e s one more time. Again they seemed to understand the task but had great d i f f i c u l t y i n d i s c r i m i n a t i n g between those ideas they " l i k e d a l o t " and those they "only l i k e d a l i t t l e " . Given the amount of p r e l i m i - nary i n s t r u c t i o n s necessary and the amount of i n d i v i d u a l a t t e n t i o n r e q u i r e d i t was decided that a s o r t i n g procedure would not be a s u i t a b l e procedure f o r use i n c o l l e c t i n g data i n a classroom s e t t i n g . . Another method that has been used to generate data f o r m u l t i - 61 dimensional a n a l y s i s i s that of the semantic d i f f e r e n t i a l , as des- c r i b e d by Osgood et a l . (1957). The subject i s r e q u i r e d to respond to a s t i m u l u s i n terms of a number of s c a l e s anchored by b i - p o l a r a d j e c t i v e s . In s e l e c t i n g the s e t of a d j e c t i v e s the i n v e s t i g a t o r i s , i n e f f e c t , p r o v i d i n g the sub j e c t w i t h a set of c r i t e r i a to be used i n making h i s judgment about the s t i m u l i . Contrary to the previous techniques of comparative judgment, the semantic d i f f e r e n t i a l r e - qu i r e s the sub j e c t to make a number of independent judgments along predetermined s c a l e s , u s u a l l y c o n s i s t i n g of seven steps each. In order to e s t a b l i s h the degree of r e l a t i o n s h i p a m ong the s t i m u l i , or the statements (which c o n t a i n ideas about heat from the three P e r s p e c t i v e s ) , the f a c t o r - a n a l y t i c model i s a p p l i e d to an i n t e r - statement c o r r e l a t i o n m a t r i x . The r e s u l t a n t dimensions of the reduced 'viewpoint space' can be i n t e r p r e t e d as a measure of p s y c h o l o g i c a l r elatedness of the heat statements f o r the given sample of s u b j e c t s . 4.23 A l t e r a t i o n s i n the Standard Semantic D i f f e r e n t i a l Format Most of the previous s t u d i e s u s i n g the semantic d i f f e r e n t i a l have adhered to the standard format as set out by Osgood et a l . (1957) i n The Measurement of Meaning. This i s p a r t i c u l a r l y t r u e of those s t u d i e s d i r e c t e d toward an e l u c i d a t i o n of the semantic space of c h i l - dren. (For example, see DiVesta, 1966; Long et a l . , 1968; and W i l l i a m s , 1972) But i n the development of the present instrument two b a s i c a l t e r a t i o n s were made i n the standard format. The semantic d i f f e r e n t i a l i s d escribed by Osgood et a l . as " . . . e s s e n t i a l l y a combination of con- t r o l l e d a s s o c i a t i o n and s c a l i n g procedures " (Osgood et a l . , 1957, 62 p. 20). As they are seeking a type of a s s o c i a t i o n response t h e i r i n s t r u c t i o n s to the subj e c t suggest that they should "...work at a f a i r l y h i g h speed...[as] i t i s your f i r s t impressions, the immediate ' f e e l i n g s ' about the items, that we want." (p. 84). In c o n t r a s t to t h i s procedure the i n v e s t i g a t o r was seeking a slower, more t h o u g h t f u l 2 response, or judgment, of the statements. This d i f f e r e n c e i n response o r i e n t a t i o n was due to an assumption by the i n v e s t i g a t o r that the instrument would be tapping some form of genuine c o g n i t i v e s t r u c t u r e and not simply sentiments h e l d toward the statements. The second a l t e r a t i o n i s a d e v i a t i o n i n the form of p r e s e n t a t i o n of the s t i m u l i . G e n e r a l l y the s t i m u l i c o n s i s t of one or two words which permits the su b j e c t to read i t q u i c k l y and respond immediately. I t was decided that the s t i m u l i f o r the C.P.I, ought to be s i m i l a r to the Ideas i d e n t i f i e d i n the i n t e r v i e w s , and so the l e n g t h would c e r - t a i n l y exceed two or three words. The inherent problems i n v o l v e d i n a s i t u a t i o n where there are a number of words i n the s t i m u l i have been discussed i n the l i t e r a t u r e under the t o p i c of concept-scale i n t e r - a c t i o n s . Simply s t a t e d , i t i s d i f f i c u l t to know i f the su b j e c t i s responding to the whole statement or p a r t s of i t . (Bashook and F o s t e r , 1973.) Or i t i s p o s s i b l e t h a t a s u b j e c t i s u s i n g some of the s c a l e s i n judging one p a r t of the statement and other s c a l e s i n judging another p a r t . For the purposes of i n t e r p r e t a t i o n the i n v e s t i g a t o r must be a l e r t to t h i s type of i n t e r a c t i o n e f f e c t when a complex stimulus i s being judged. In an e f f o r t to assess the impact of these d e v i a t i o n s and a l s o to 63 t r y to e s t a b l i s h a number of a p p r o p r i a t e s c a l e s , two somewhat i n f o r m a l t r i a l s e s s ions were held w i t h two and three c h i l d r e n r e s p e c t i v e l y . Before c o n s t r u c t i n g the f i n a l v e r s i o n of the C.P.I, a f u r t h e r t r i a l run was made i n a grade f i v e classroom under a c t u a l t e s t c o n d i t i o n s . On the b a s i s of the f i r s t i n f o r m a l s e s s i o n i t was apparent that the s t a - tements were too a b s t r a c t and that they would have to be accompanied by some concrete demonstration of the heat phenomena being r e f e r r e d to i n the statement. The second s e s s i o n i n c l u d e d s e v e r a l of the demonstrations used i n the i n t e r v i e w tasks and proved to be much more s u c c e s s f u l . These demonstrations are described i n d e t a i l i n S e c t i o n 4.33. Feedback from the c h i l d r e n provided the i n v e s t i g a t o r w i t h u s e f u l i n f o r m a t i o n regarding t h e i r perceptions of the type of judgments they were being requested to make and r e s u l t e d i n s e v e r a l changes being made on the a d j e c t i v a l s c a l e s . As a r e s u l t of the classroom t r i a l s e s s i o n the i n v e s t i g a t o r discovered a prime example of a 'concept-scale' i n t e r - a c t i o n . A number of c h i l d r e n responded to one of the statements by i n d i c a t i n g that they f e l t i t was 'very t r u e ' and yet on another s c a l e f u r t h e r down the page they i n d i c a t e d t h a t i t was 'very much u n l i k e t h e i r i d e a s ' . A f t e r q u e s t i o n i n g s e v e r a l c h i l d r e n about t h i s apparent anomaly i t became c l e a r that they were responding to the o b s e r v a t i o n a l p a r t of the statement w i t h the ' t r u e - f a l s e ' s c a l e (of course i t was t r u e because t h i s p a r t of the statement was simply a summary of a demonstra- t i o n they had j u s t observed) and to the explanatory p a r t of the statement w i t h the ' l i k e my i d e a s - u n l i k e my i d e a s ' s c a l e . This confusion was r e s o l v e d by p l a c i n g the o b s e r v a t i o n a l p a r t of the statement i n s m a l l 64 p r i n t at the top of the page and p u t t i n g the more important explanatory part i n b o l d p r i n t and e n c l o s i n g i t i n a box. The f i n a l v e r s i o n of the C.P.I, i s presented i n Appendix C. According to the feedback from these sessions i t seemed that the c h i l d r e n were enjoying both the demonstrations and the challenges pro- vided by the C.P.I. F u r t h e r , they appeared to experience no a p p r e c i a b l e d i f f i c u l t y i n making the r e q u i r e d judgments i n order to complete each of the items on the C.P.I. 4.24 C o n s t r u c t i o n of the Conceptual P r o f i l e Instrument An u n d e r l y i n g assumption of Phase Two of the study was t h a t the Ideas i d e n t i f i e d from the i n t e r v i e w data are a l s o c h a r a c t e r i s t i c of the t h i n k i n g of other c h i l d r e n . These Ideas, then, o u t l i n e d e a r l i e r as a C h i l d r e n ' s P e r s p e c t i v e , formed the primary b a s i s of item c o n s t r u c t i o n f o r the C.P.I. The remainder of the items were c o n s t r u c t e d from two other a l t e r n a t e P e r s p e c t i v e s of heat ~ the c u r r e n t kinetic theory of heat and i t s predecessor, the c a l o r i c theory of heat. P a r a l l e l items from these three P e r s p e c t i v e s provided the c h i l d r e n w i t h an o p p o r t u n i t y to d i s c r i m i n a t e among the statements; they a l s o enabled the i n v e s t i g a t o r to determine the extent to which the o l d e r c h i l d r e n may have embraced the more s o p h i s t i c a t e d k i n e t i c theory. Statements r e p r e s e n t i n g the C h i l d r e n ' s P e r s p e c t i v e were taken, where p o s s i b l e , d i r e c t l y from the most p r e v a l e n t and t y p i c a l Ideas i d e n t i f i e d i n the i n t e r v i e w t r a n s c r i p t s . Since the procedure was f u l l y o u t l i n e d i n Chapter Three i t w i l l not be repeated here. Once a number of p o t e n t i a l statements from the C h i l d r e n ' s P e r s p e c t i v e were adapted 65 to correspond w i t h the demonstrations being used to accompany the C.P.I., p a r a l l e l statements from each of the other two P e r s p e c t i v e s were cons t r u c t e d . Two c r i t e r i a were used i n the c o n s t r u c t i o n of a l l the statements: , (1) the language and phrasing of the statements must be such that a t y p i c a l grade f i v e student could comprehend i t ; (2) the statement must maintain the b a s i c i n t e g r i t y of the P e r s p e c t i v e from which i t was d e r i v e d . An o p p o r t u n i t y to determine the degree to which the s t a t e - ments s a t i s f i e d the f i r s t c r i t e r i o n was provided by the numerous t r i a l s e s s i ons during which the i n v e s t i g a t o r was c o n s t a n t l y seeking fe e d - back on the c h i l d r e n ' s a b i l i t y to understand the statements. A check on the second c r i t e r i o n was made by s u b m i t t i n g the statements to three people who were knowledgeable about the k i n e t i c and c a l o r i c t h e o r i e s 3 of heat. Changes suggested by these judges were i n c o r p o r a t e d i n t o the f i n a l v e r s i o n of the C.P.I. 4.30 A d m i n i s t r a t i o n of the Conceptual P r o f i l e Instrument 4.31 D e s c r i p t i o n of the Subjects The f i n a l v e r s i o n of the C.P.I, was administered i n 12 classrooms s i t u a t e d i n three d i f f e r e n t schools i n the c i t y of Vancouver. These schools were s e l e c t e d by the research s t a f f of the Vancouver School Board and were described as ' t y p i c a l ' schools i n the Vancouver system. A t o t a l of 322 students p a r t i c i p a t e d : 100 from grade f i v e , 125 from grade seven and 87 from grade ni n e . However, those students who e i t h e r d i d not complete the C.P.I, or e l s e marked i t i n an obvious p a t t e r n ( f o r example, usi n g one column down a page f o r s e v e r a l pages, or marking 66 each page w i t h an i d e n t i c a l p a ttern) were e l i m i n a t e d from the a n a l y s i s . The f i n a l sample c o n s i s t e d of 276 students: 76 from grade f i v e , 117 from grade seven and 83 from grade n i n e . 4.32 D e s c r i p t i o n of A d m i n i s t r a t i o n Procedures The i n v e s t i g a t o r was present and r e s p o n s i b l e f o r i n t r o d u c i n g the C.P.I, and performing the demonstrations f o r a l l twelve s e s s i o n s . T y p i c a l l y the procedures c o n s i s t e d of a short i n t r o d u c t i o n by the i n - v e s t i g a t o r i n d i c a t i n g that he was from the U n i v e r s i t y of B r i t i s h Columbia and that he was i n t e r e s t e d i n t h e i r ideas about heat and temperature. They were t o l d that the C.P.I, was not a t e s t but was more l i k e a game where they would be asked to i n d i c a t e how they f e l t about some ideas — obtained from t a l k i n g to other students of t h e i r age about heat. The r u l e s f o r the game were explained by f i r s t reading together the f i r s t two pages of the booklet and then c a r e f u l l y working through two sample items. During t h i s s h o r t t r a i n i n g program i n d i v i d u a l students were asked to i n d i c a t e how they responded on the v a r i o u s s c a l e s and why they d i d so. Using t h i s approach the i n v e s t i g a t o r f e l t t hat most of the students were able to understand: (1) the two-part form of the s t a t e - ment — the o b s e r v a t i o n a l p a r t i n s m a l l p r i n t and the explanatory p a r t i n b o l d p r i n t — and (2) the meaning of the s c a l e s . Once the i n v e s t i g a - t o r was s a t i s f i e d t h a t a l l of the students were ready to proceed he introduced the f i r s t demonstration. 4.33 D e s c r i p t i o n of the Demonstrations and Statements The f i r s t demonstration and accompanying set of items centered around the h e a t i n g of two aluminium rods of d i f f e r e n t t h i c k n e s s . A 67 single candle was placed under each rod and, in effect, a race was initiated to see which rod would get hot enough to melt some attached wax in which was embedded a large drawing pin. While awaiting the out- come of the experiment, the students were asked which one they thought would get hot f i r s t so as to get them involved in the experiment. When the pin dropped from the large rod f i r s t many children were v i s i b l y surprised. The investigator returned their attention to the booklet on their desk and said something l i k e : "Now, here are some different ideas that try to explain what we have just observed. Remember i t i s the idea in bold print in the box that i s important not the smaller print which simply t e l l s us what we observed. I ' l l read the idea out to you and then you can mark the blanks to indicate how you feel about that idea. I am interested in the ways that you think about the idea in the box, not what your friend or even your teacher thinks." The f i r s t set of three items were then presented individually to the class. A l l three statements began with the same small-print intro- duction, each statement being on a separate page. Figure 4-1 i s a reproduction of one page from the C.P.I. The large rod heated up faster than the small rod because: (1) THE LARGE ROD ATTRACTS MORE HEAT PARTICLES THAN THE SMALL ROD. (2) THE LARGE ROD HAS MORE METAL PARTICLES TO MOVE AROUND. (3) THE LARGE ROD HAS MORE AIR SPACES INSIDE FOR THE HEAT TO TRAVEL THROUGH. The second set of items also refer to the above demonstrations. They were introduced by the investigator in the following way: "We observed that the pin f e l l off at the opposite end of the rod from The large rod heated up faster than the small rod because THE LARGE ROD ATTRACTS MORE HEAT PARTICLES THAN THE SMALL ROD Very Much Somewhat S l ight lv N P I t h p r — i n-^+i,, "o r—r- 1 A^ree A r r r B O oxxgatxy weixner Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Clear ^ l e a r ^ S ^ h t l y Neither Sl ight ly Somewhat ' Very Olear clear Clear Clear nor Confusing Confusing Confusing Confusing 6 Easy S ° E a s v a t  S1i£tly w N e i t h e r ' S l i ^ l y Somewhat ' Very y E a S y E a s y Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t Tvll  S ° S f S 1 j ^ t l y Neither Sl ight ly HSol^whalT ' — v i r 7 T r u e T r u e T ™ e nor False False False False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas 69 where i t was being heated. The next ideas we are going to look at attempt to e x p l a i n why the whole rod gets hot when we only heated i t at one end w i t h the candle." The next three statements were: The whole rod gets hot because: (4) THE HEAT BUILDS UP IN ONE PART UNTIL IT CAN'T HOLD ANYMORE AND THEN THE HEAT MOVES ALONG THE ROD. (5) THE FASTER MOVING METAL PARTICLES BUMP INTO EACH OTHER ALL THE WAY THROUGH THE ROD. (6) THE HEAT PARTICLES FROM THE FLAME ARE ATTRACTED TO ALL PARTS OF THE ROD. A second demonstration was begun a t t h i s p o i n t . S i x cubes o f d i f f e r e n t m a t e r i a l s — copper, steel,aluminium, wood, sugar, and wax — were heated i n a t r a y by two candles w h i l e the c l a s s observed. Most of students immediately i n d i c a t e d that the wax would melt but o p i n i o n s were d i v i d e d over the other o b j e c t s . As soon as the wax melted the i n v e s t i g a - t o r drew the a t t e n t i o n of the c l a s s to the statements concerned w i t h why the wax melted. The wax melted because: (7) IT WAS A SOFT SUBSTANCE. (8) THE HEAT PARTICLES WENT INSIDE AND FORCED THE WAX PARTICLES APART. (9) THE WAX PARTICLES WERE MOVING ABOUT SO FAST THAT THEY COULD NOT HOLD ON TO EACH OTHER SO WELL. Once the c l a s s had f i n i s h e d w i t h these items the i n v e s t i g a t o r placed the f i v e remaining cubes, which were s t i l l being heated by the candles, on a bl o c k of wax and allowed the c l a s s to see how f a r each of the cubes sank i n t o the wax. From t h i s they r e a d i l y i n f e r r e d that the wood and suger cubes d i d not get very hot at a l l w h i l e the metal 70 cubes got very hot. The c l a s s went on to do the next s e t of items. The metal cubes were h o t t e r than the wood or sugar because: (10) THE METAL CUBES DREW IN MORE HEAT PARTICLES THAN THE OTHER CUBES. (11) IT WAS MORE DIFFICULT FOR THE AIR TO GET INSIDE THE HARD METAL CUBES TO COOL THEM. (12) THE METAL PARTICLES ARE EASIER TO MOVE. At t h i s p o i n t a s i n g l e item t h a t was r e l a t e d t o the demonstration was introduced to the c l a s s . T his was an e x t r a item from the C h i l d r e n ' s P e r s p e c t i v e that was q u i t e p r e v a l e n t among the Ideas expressed by the l e s s s o p h i s t i c a t e d c h i l d r e n i n the i n t e r v i e w s . The metal cubes d i d not melt because: (13) THEY WERE NOT HEATED LONG ENOUGH. The next four items were introduced to the c l a s s without the b e n e f i t of a demonstration. T h i s was done because the i n v e s t i g a t o r assumed th a t a l l of the c h i l d r e n had experienced the e f f e c t of lowering the temperature of some water, or a s o f t d r i n k , by adding an i c e cube. The student's s t r o n g p o s i t i v e r e a c t i o n to the i n v e s t i g a t o r ' s query about t h i s assumption i n d i c a t e d that they experienced no d i f f i c u l t y under- standing the o b s e r v a t i o n a l p a r t of the statement. The temperature of the water decreased when an i c e cube was added because: (14) THE ICE CUBE ATTRACTED SOME OF THE HEAT PARTICLES AWAY FROM THE WATER. (15) SOME OF THE COLD LEFT THE ICE CUBE AND WENT INTO THE WATER. 16) THE WATER PARTICLES LOSE SOME OF THEIR SPEED BY BUMPING INTO THE ICE PARTICLES. 71 Once again a popular C h i l d r e n ' s Idea, which was r e l a t e d to the above statements was i n c l u d e d . A l a r g e i c e cube takes longer to melt than a s m a l l i c e cube because: (17) THE LARGE ICE CUBE HAS A COLDER TEMPERATURE THAN THE SMALL ICE CUBE. The l a s t demonstration c o n s i s t e d of t a k i n g the l i q u i d expansion apparatus used i n the i n t e r v i e w task (described i n Appendix B) and immersing i t i n hot water. The next three statements were concerned w i t h e x p l a i n i n g the observed r e s u l t s . The red l i q u i d i n the tube went up because: (18) THE HEAT MAKES THE RED LIQUID LIGHTER AND SO IT RISES. (19) THE LIQUID'S PARTICLES MOVED MORE QUICKLY AND SO TOOK UP MORE SPACE. (20) THE HEAT PARTICLES TAKE UP SPACE INSIDE THE LIQUID AND FORCE- THE LIQUID OUT THE TUBE. When these items were completed the i n v e s t i g a t o r i n d i c a t e d t h a t there were nine more ideas about heat and temperature and that he would l i k e them to complete these items on t h e i r own. He f u r t h e r i n d i c a t e d that w h i l e the f i r s t two items were of the same type as the previous ones ( t h a t i s , they had an o b s e r v a t i o n a l p a r t and an explanatory p a r t ) the remaining seven items were j u s t general ideas about heat and temperature and so d i d not have any sm a l l p r i n t a t the top of the page. The remaining statements a r e : Objects rubbed together get hot because: (21) THE PARTICLES INSIDE THE OBJECTS MOVE FASTER. (22) THE HEAT PARTICLES INSIDE THE OBJECT ARE FORCED OUT. 72 The next seven statements, then, d i d not have any s m a l l p r i n t preceding the id e a i n the box. (23) HEAT IS THE MOTION OF AN OBJECT'S PARTICLES. (24) TEMPERATURE IS A MEASURE OF THE MIXTURE OF HEAT AND COLD INSIDE AN OBJECT. (25) HEAT IS A SUBSTANCE SOMETHING LIKE AIR OR STEAM. (26) ALL OBJECTS CONTAIN A MIXTURE OF HEAT AND COLD. (27) TEMPERATURE IS A MEASURE OF THE NUMBER OF HEAT PARTICLES IN AN OBJECT. (28) HEAT IS MADE UP OF TINY PARTICLES THAT CAN MOVE. (29) TEMPERATURE IS A MEASURE OF THE SPEED OF PARTICLES IN AN OBJECT. 4.40 A n a l y s i s of the Instrument Data The a n a l y t i c a l methods employed to transform and compress the raw data from the C.P.I, proceeded through two separate stages. F i r s t , the number of independent dimensions or s c a l e - c l u s t e r s used by the s u b j e c t s were determined through a component a n a l y s i s . Once the s c a l e dimen- s i o n a l i t y was i d e n t i f i e d , then the second stage c o n s i s t e d of generating statement-clusters by performing a component a n a l y s i s on a persons by statements m a t r i x f o r the averaged scores on a p a r t i c u l a r s c a l e dimension. These s t a t e m e n t - c l u s t e r s , or Viewpoints, were then used as the primary input data f o r the p r o f i l e a n a l y s i s discussed i n S e c t i o n 4.50. Since these two stages are standard a n a l y t i c procedures and furthermore have been o u t l i n e d i n some d e t a i l .by McKie and Foster (1972), only the s u b s t a n t i v e aspects of these procedures, as they r e l a t e to the present study, w i l l be rep o r t e d . 73 4.41 A n a l y s i s of the Scale D i m e n s i o n a l i t y I n developing the s c a l e s f o r the C.P.I, the i n v e s t i g a t o r attempted to ' b u i l d i n ' two separate c r i t e r i a or dimensions f o r judgment. Since the a t t r i b u t e to be assessed by the C.P.I, was " c h i l d r e n ' s conceptions of heat phenomena" one c r i t e r i o n f o r judgment c l e a r l y ought to be some type of " b e l i e f dimension". A f t e r t r y i n g out a number of p o t e n t i a l s c a l e s d uring the t r i a l s e s s ions i t appeared that a second set of s c a l e s , t e n t a t i v e l y l a b e l l e d a " f a m i l i a r i t y dimension", would be u s e f u l f o r i n - t e r p r e t i n g the s u b j e c t ' s perceptions of the v a r i o u s heat concepts being presented i n the items. A common p r a c t i c e when u s i n g a semantic d i f f e r e n t i a l i s to i n - clude a f a i r l y l a r g e number of s c a l e s ( i n most s t u d i e s the number of s c a l e s range from 15 to 30) so as to b e t t e r sample a l l p o s s i b l e bases of judgment which an i n d i v i d u a l might n a t u r a l l y use. The most promi- nent s c a l e - c l u s t e r s (dimensions of judgment) used by the s u b j e c t s are determined by some a p p r o p r i a t e a n a l y t i c a l method. I t i s the i n v e s t i g a - t o r ' s o p i n i o n that the use of a l a r g e number of s c a l e s not only induces boredom i n the s u b j e c t s , hence i n c r e a s i n g c a r e l e s s n e s s and u n r e l i a b i l i t y i n t h e i r responses, but, a l s o i s unnecessary when the d e s i r e d dimensions f o r judgment are known i n advance. Since the i n v e s t i g a t o r was able to determine whether a p p r o p r i a t e s c a l e s were chosen to represent the d e s i r e d dimension through component a n a l y s i s , i t was decided to t r y and minimize the monotony of the task by choosing a minimal number of s c a l e s f o r each d e s i r e d dimension. Thus s i x s c a l e s were used i n the present study w i t h the e x p e c t a t i o n that two independent scale-dimensions would emerge from the s u b j e c t ' s responses. I 74 Although F i s h b e i n and Raven (1967) have used a number of s c a l e s to assess a b e l i e f dimension, s e v e r a l of t h e i r s c a l e s ( f o r example, probable-improbable, l i k e l y - u n l i k e l y , and p o s s i b l e - i m p o s s i b l e ) d i d not seem to be meaningful to the s u b j e c t s i n the t r i a l s e s s i o n s . Only one of t h e i r s c a l e s , the t r u e - f a l s e s c a l e , was r e t a i n e d f o r use. The other two s c a l e s used were the agree-disagree s c a l e and the l i k e my i d e a s - u n l i k e my ideas s c a l e . P o t e n t i a l s c a l e s which were explored i n the t r i a l s e s s ions to e s t a b l i s h a second dimension were suggested by Nunnally's (1967) " u n d e r s t a n d a b i l i t y " dimension and T a y l o r ' s (1966) " d i f f i c u l t y " dimension. The s c a l e s which were e v e n t u a l l y used i n the C.P.I, were: c l e a r - c o n - f u s i n g , e a s y - d i f f i c u l t , and f a m i l i a r - u n f a m i l i a r . This l a s t set of s c a l e s was termed a " f a m i l i a r i t y dimension" w h i l e the other three s c a l e s ( t r u e - f a l s e , agree-disagree, and l i k e my i d e a s - u n l i k e my ideas) were l a b e l l e d as a " b e l i e f dimension." To a s c e r t a i n the degree of correspondence between the b u i l t - i n dimensions and the a c t u a l responses of the s u b j e c t s , the data cube was f i r s t c o l l a p s e d over persons to produce a statements by s c a l e s m a t r i x . The columns of t h i s - m a t r i x were then i n t e r c o r r e l a t e d and the r e s u l t a n t s c a l e s by s c a l e s c o r r e l a t i o n m a t r i x subjected to a component 4 a n a l y s i s , f o l l o w e d by varimax r o t a t i o n . The eigenvalues of the com- ponent m a t r i x , along w i t h the l o a d i n g s of the r o t a t e d components appear i n Table 4-1. As i s evident from Table 4-1 the f i r s t two components are by f a r the most dominant accounting f o r 96% of the t o t a l v a r i a n c e . Thus only TABLE 4-1 Rotated P r i n c i p a l Component-Loadings f o r I n t e r - S c a l e C o r r e l a t i o n M a t r i x V a r i a b l e s Components (Scales) I I I Agree Disagree .9758 -.1836 Cl e a r - Confusing .1578 -.9639 Easy - D i f f i c u l t .2184 -.9683 True - F a l s e .9700 -.1807 F a m i l i a r - U n f a m i l i a r .5493 -.7758 L i k e my ideas - U n l i k e my ideas .8332 -.5160 Variance 4.457 1.305 Per cent 74.29 21.76 76 two components were r o t a t e d to y i e l d the s c a l e dimensions used by the subjects i n making t h e i r responses. ~* An examination of the s c a l e s that load h i g h l y on the f i r s t component r e v e a l s the " b e l i e f dimension" that was b u i l t i n t o the s c a l e s . L i k e w i s e , the second component gives evidence f o r the " f a m i l i a r i t y dimension". These r e s u l t s were used to o b t a i n a b e l i e f - s c o r e on a statement f o r a p a r t i c u l a r s u b j e c t by averaging t h e i r scores on s c a l e s 1, 4 and 6. A f a m i l i a r i t y - s c o r e was obtained by averaging scores over s c a l e s 2, 3 and 5. 4.42 A n a l y s i s of Statement D i m e n s i o n a l i t y Having obtained a composite b e l i e f - s c o r e and f a m i l i a r i t y - s c o r e , the second stage of the a n a l y s i s was to examine the data f o r evidence of meaningful c l u s t e r s of statements. These c l u s t e r s can be l i k e n e d to a p a r t i c u l a r v i e w p o i n t of heat. I n e f f e c t , t h i s procedure c o n s i s t s of a type of e m p i r i c a l check upon the three P e r s p e c t i v e s that were b u i l t i n t o the items. The question being addressed by t h i s stage i s : Did the c h i l d r e n p e r c e i v e any b a s i c d i f f e r e n c e s between the statements? In other words,did some statements c l u s t e r together i n the 'Viewpoint Space' i n such a manner as to suggest a c o n s i s t e n t way of l o o k i n g a t and t h i n k i n g about heat phenomena? A second q u e s t i o n n a t u r a l l y f o l l o w s : What i s the p o t e n t i a l d i a g n o s t i c v a l u e of these c l u s t e r s of Viewpoints once they are i d e n t i f i e d ? The a n a l y s i s s t a r t e d w i t h a persons by statements m a t r i x of b e l i e f or f a m i l i a r i t y - s c o r e s produced by the previous stage. On the b a s i s of the l a r g e number of c h i l d r e n who were e i t h e r not able to complete the e n t i r e C.P.I, or began to p a t t e r n t h e i r responses a f t e r the f i r s t twenty 77 items, a d e c i s i o n was made to i n c l u d e only those statements which were r e l a t e d to the demonstrations. As there was a t o t a l of 276 s u b j e c t s who completed t h i s p a r t of the C.P.I, the r e s u l t a n t data m a t r i x con- s i s t e d of a 276 by 20 (persons by statements) matr i x of b e l i e f - s c o r e s . A s i m i l a r m a t r i x of f a m i l i a r i t y - s c o r e s was a l s o analyzed. As b e f o r e , the columns of the m a t r i x were c o r r e l a t e d to y i e l d an i n t e r - s t a t e m e n t c o r r e l a t i o n m a t r i x which was the input data f o r a component a n a l y s i s . R e s u l t s of the varimax r o t a t e d component loadi n g s f o r the b e l i e f - scores are reproduced i n Table 4-2. Since the component s t r u c t u r e f o r the s t a t e m e n t - c l u s t e r s was somewhat more complex than that of the s c a l e - c l u s t e r s , the d e c i s i o n r e g a r d i n g the number of components to r o t a t e was not so s t r a i g h t f o r w a r d . The s i x components reported i n Table 4-2 are a r e s u l t of r o t a t i n g o n l y those components w i t h an eigenvalue greater than one. However, an examination of these components r e v e a l only one c l e a r l y d e f i n e d dimension, the f i r s t component. This component contains f i v e statements w i t h h i g h l o a d i n g s (greater than .40). A l l f i v e statements belong to the K i n e t i c P e r s p e c t i v e . Statements belonging to the other two P e r s p e c t i v e s , the C h i l d r e n ' s and the C a l o r i c , appear to be s p l i t among the other f i v e components. For example, the C h i l d r e n ' s statements were s p l i t between the second and the f i f t h component. To determine whether t h i s type of ' f i s s i o n ' was due to the number of com- ponents r o t a t e d , i t was decided to r o t a t e fewer components i n search of a more i n t e r p r e t a b l e s o l u t i o n . Three a d d i t i o n a l computer runs were made r o t a t i n g 5, 4 and 3 com- ponents r e s p e c t i v e l y . The s o l u t i o n given i n Table 4-3, w i t h four 78 TABLE 4-2 Rotated Principal Component-Loadings for Inter-Statement Correlation Matrix of Belief-Scores (Six Components Rotated) Variables Components (Statements) .1 II III IV V VI 1 (Caloric)* -.1078 .2013 .6352 .1780 -.0490 .1835 2 (Kinetic) -.3145 .1480 - .6282 -.0266 -.1853 -.0057 3 (Childrens) -.2900 .0692 .2288 -.0857 -.2966 .5516 4 (Childrens) .0196 .1829 -.0459 .1887 -.6587 -.2486 5 (Kinetic) -.6534 -.1686 .3465 -.1433 -.0553 .0521 6 (Caloric) -.0246 .3422 .0686 .3314 .1166 .6151 7 (Childrens) .0762 .2356 .1027 -.0511 -.6303 .1170 8 (Caloric) -.3555 .0819 -.0141 .4393 -.0529 -.0623 9 (Kinetic) -.6874 .0987 .0814 .1958 -.0895 -.1096 10 (Caloric) .0523 .0989 .1498 .7507 .0344 .0565 11 (Childrens) -.1932 .0851 .0808 .0761 -.6105 .1565 12 (Kinetic) -.4592 .3105 .2223 -.0279 .0372 -.5185 13 (Childrens) -.2694 .4623 -.5368 -.1389 -.1068 .1317 14 (Caloric). -.2417 .6581 -.0437 .2693 -.0282 -.0585 15 (Childrens) -.0814 -.2381 -.3255 .5302 -.4082 .0013 16 (Kinetic) -.7712 .1102 -.0211 .0863 .0166 .1257 17 (Childrens) .0625 .6370 .2033 -.0345 -.2809 .1393 18 (Childrens) ;.0223 .5438 .1276 .0283 -.2826 .0487 19 (Kinetic) -.6773 .0141 .0073 .0734 -.0124 .0743 20 (Caloric) -.1747 .0707 .1418 .3923 -.1916 .2101 Variance 3.719 1.988 1.443 1.302 1.137 1.0155 Per cent 18.60 9.94 7.21 6.51 5.69 5.08 *The heat Perspective from which the statement i s taken i s in brackets. For a f u l l description of the statement see Section 4.33. TABLE 4-3 Rotated P r i n c i p a l Component-Loadings f o r Inter-Statement C o r r e l a t i o n M a t r i x of B e l i e f - S c o r e s (Four Components Rotated) V a r i a b l e s Components (Statements) I I I I I I IV 1 ( C a l o r i c ) — .1033 .1079 .6722 .1362 2 ( K i n e t i c ) -.3304 .1601 .5887 -.0748 3 (C h i l d r e n s ) -.1829 .2188 .4698 .1116 4 (C h i l d r e n s ) -.0287 .5732 -.1367 .1785 5 ( K i n e t i c ) - .6251 -.1374 .3441 -.0999 6 ( C a l o r i c ) .0591 .1575 .3742 .4342 7 (C h i l d r e n s ) .0936 .5861 .1652 .0381 8 ( C a l o r i c ) -.3739 .0747 -.0191 .4055 9 ( K i n e t i c ) -.7048 .0995 .0686 .1738 10 ( C a l o r i c ) .0334 .0147 .1543 .6765 11 (C h i l d r e n s ) -.1570 .4529 .1553 .1970 12 ( K i n e t i c ) -.5715 .1703 .0339 -.2274 13 (C h i l d r e n s ) -.2467 .4640 -.3398 -.0463 14 ( C a l o r i c ) -.2913 .4949 .0304 .1812 15 ( C h i l d r e n s ) -.0614 .1115 -.3284 .6186 16 ( K i n e t i c ) -.7402 .0485 .0907 .1440 17 (C h i l d r e n s ) .0507 .6391 .3210 -.0449 18 (C h i l d r e n s ) .0004 .5763 .2024 .0068 19 ( K i n e t i c ) -.6521 -.0031 .0755 .1230 20 ( C a l o r i c ) -.1453 .1488 .2280 .4393 Variance 3 .719 1.988 1.443 1.302 Per cent 18 .60 9.94 7.21 6.51 80 components rotated, provided the c l e a r e s t and simplest s t r u c t u r e . Three out of the four components are i n t e r p r e t a b l e ( i n terms of the o r i g i n a l Perspectives) and no statements load highly on more than one component. A further encouraging observation i s that the f i r s t component (which might be c a l l e d a K i n e t i c Viewpoint) remains undisturbed by the fewer rotations thus providing some evidence that the manifest structure i s not simply an a r t i f a c t of the r o t a t i o n procedures. The statements loading high on the second component i n Table 4-3 can be interpreted as a Children's Viewpoint — formed by the f u s i o n of the second and f i f t h components of Table 4-2. This dimension or Viewpoint, contains s i x Children's statements and one C a l o r i c statement. Component four also has a very c l e a r conceptual s t r u c t u r e . I t contains four C a l o r i c statements with high loadings and one Children's statement. The only component that remains uninterpreted i s number three which has only three statements that load highly on i t — the f i r s t three on the C.P.I. One p o s s i b l e explanation f o r t h i s component i s that i t i s simply an a r t i f a c t of the C.P.I., based upon the uncertainty experienced by many of the subjects regarding the nature of the judgmental task. Hence i t i s possible that they may have responded to t h i s f i r s t set of three statements i n a s i m i l a r way as they attempted to get a better un- derstanding of what was required by the C.P.I. Another tenable hypo- thesis i s that the c h i l d r e n were not able to discriminate between the three statements and so made a s i m i l a r response to each. Results from a s i m i l a r treatment of the f a m i l i a r i t y - s c o r e s are presented i n Table 4-4. I n i t i a l l y the f i v e components with eigenvalues .TABLE 4-4 .Rotated P r i n c i p a l Component-Loadings f o r Inter-Statement C o r r e l a t i o n M a t r i x of F a m i l i a r i t y - S c o r e s (Four Components Rotated) .Variables Components (Statements) -I .11 •III IV 1 ( C a l o r i c ) .1891 .1255 _ .0030 .7650 2 ( K i n e t i c ) .2001 .1703 -.1279 .7366 3 (Ch i l d r e n s ) .3638 .1862 -.2057 .4302 4 (Ch i l d r e n s ) .1630 .7132 -.0167 .1069 5 ( K i n e t i c ) -.7218 .0652 .0061 .2667 6 ( C a l o r i c ) -.3305 .3180 -.1873 .3213 7 (C h i l d r e n s ) -.1042 .6210 -.0022 .1137 8 ( C a l o r i c ) -.5240 .3778 -.0212 .0740 9 ( K i n e t i c ) - .7109 .2484 -.1390 .1240 10 ( C a l o r i c ) .0470 .6012 -.1599 .3248 11 (Chi l d r e n s ) -.2383 .4291 -.2179 .1363 12 ( K i n e t i c ) -.5753 .1270 -.2256 .2035 13 (Ch i l d r e n s ) -.2317 .1899 -.4150 -.1855 14 ( C a l o r i c ) - .0973 .1111 -.6882 .2177 15 ( C h i l d r e n s ) -.0988 .6174 — .2394 -.0505 16 ( K i n e t i c ) -.7143 -.0205 -.3583 -.0148 17 (Chi l d r e n s ) -.1810 .0353 -.7360 .0172 18 (Chi l d r e n s ) -.1305 .1642 -.6106 .1503 19 ( K i n e t i c ) -.5596 .0742 -.3556 .2266 20 ( C a l o r i c ) -.1470 .3228 -.3138 .2698 Variance 5 .702 1.534 1.307 1.022 Per cent 28 .51 7.67 6 .53 5.12 82 greater than one were r o t a t e d , but again some co m p o n e n t - s p l i t t i n g was suspected. I t was decided that the s o l u t i o n obtained by r o t a t i n g four f a c t o r s was the most i n t e r p r e t a b l e . However, the inherent s t r u c t u r e of the components i s not as c l e a r as that obtained f o r the b e l i e f - scores. Once again the f i r s t component i s a very c l e a r K i n e t i c View- po i n t w i t h a very s i m i l a r s t r u c t u r e to the b e l i e f data — the o n l y ex- c e p t i o n i s the higher l o a d i n g on a C a l o r i c statement (item number 8). This r e s u l t might be explained by the resemblance of the statement to the emphasis on p a r t i c l e motion i n the K i n e t i c P e r s p e c t i v e . Unfor- t u n a t e l y , the s t r u c t u r e of the other components are not q u i t e as c l e a r . Instead of o b t a i n i n g a c l e a r s e p a r a t i o n of the C h i l d r e n ' s and the C a l o r i c Viewpoints, as was the case w i t h the b e l i e f - s c o r e s , components two and three predominantly c o n t a i n h i g h l o a d i n g C h i l d r e n ' s statements w i t h one C a l o r i c statement i n each. Since two of the C a l o r i c statements, items 6 and 20, f a i l e d to loa d h i g h l y on any of the r o t a t e d components, i t would seem that no d i s t i n c t C a l o r i c Viewpoint was perc e i v e d by the sub- j e c t s . As befo r e , the f i r s t three statements are c l u s t e r e d together i n a s i n g l e component. The f a m i l i a r i t y - s c o r e s , then, produced a c l e a r K i n e t i c Viewpoint and two somewhat ambiguous C h i l d r e n ' s Viewpoints. To r e t u r n to the questions posed e a r l i e r i t can now be s t a t e d w i t h some confidence that the c h i l d r e n were able to d i s c r i m i n a t e between the v a r i o u s statements r e p r e s e n t i n g the three d i f f e r e n t P e r s p e c t i v e s . In terms of the student's b e l i e f s about the statements, three r e l a t i v e l y c l e a r Viewpoints were i d e n t i f i e d which correspond r a t h e r c l o s e l y to the ' b u i l t - i n ' P e r s p e c t i v e s . While these Viewpoints are not as c l e a r l y 83 defined f o r the f a m i l i a r i t y - s c o r e s , there i s /i d e f i n i t e s p l i t between a K i n e t i c Viewpoint of heat and what appears to be a substance n o t i o n of heat. The second q u e s t i o n concerning the p o t e n t i a l u s e f u l n e s s of these Viewpoints i s somewhat more d i f f i c u l t to address. One p o t e n t i a l approach suggested by McKie and Foster (1972) in v o l v e t i the c r e a t i o n of p r o f i l e s of i n d i v i d u a l s based upon the person's set of f a c t o r s cores. Such a p r o ' f i l e c ontains much more i n f o r m a t i o n than the type of composite score that i s the product of many science achievement t e s t s or a t t i t u d e s c a l e s . Furthermore, a p r o f i l e can be used i n a d i a g n o s t i c c a p a c i t y by matching an i n d i v i d u a l ' s p r o f i l e w i t h an a p p r o p r i a t e Met of teaching s t r a t e g i e s . This type of matching procedure r e s t s on the assumption made by the i n v e s t i g a t o r that the C.P.I, i s tapping some aspect of c o g n i t i v e s t r u c t u r e (perhaps a t y p e of p h y s i c a l deep s t r u c t u r e ) and hence the l i t e r a t u r e on s t r u c t u r a l change and development could serve to guide the development of teaching s t r a t e g i e s . However, before an i n d i v i d u a l ' s Conceptual P r o f i l e can be of d i a - g n o s t i c v a l u e to the teacher, i t must be accompanied by a set of Model Conceptual P r o f i l e s that w i l l permit the teacher to i d e n t i f y an i n d i v i d u a l ' s Conceptual P r o f i l e as a member of a given c l a s s or f a m i l y of Model Con- c e p t u a l P r o f i l e s . Once an i n d i v i d u a l ' s Conceptual P r o f i l e i s so catego- r i z e d i t i s then p o s s i b l e to match i t w i t h a p a r t i c u l a r type of teaching s t r a t e g y designed f o r that c l a s s of P r o f i l e s . 4.50 The A n a l y s i s of Model Conceptual P r o f i l e s By a Model Conceptual P r o f i l e i s meant a h y p o t h e t i c a l p r o f i l e of 84 scores that i s t y p i c a l of a group of s u b j e c t s who have responded i n a s i m i l a r way on the C.P.I. To o b t a i n a c l u s t e r of p r o f i l e s one must f a c t o r analyze over s u b j e c t s ( g e n e r a l l y r e f e r r e d to as Q-analysis) i n s t e a d of the u s u a l f a c t o r i n g of responses as found i n S e c t i o n 4.41 and 4.42 (which i s c a l l e d R - a n a l y s i s ) . G u e r t i n and B a i l e y (1970) have mapped out a s e t of procedures, accompanied by a computer program, that w i l l analyze a l a r g e s e t of p r o f i l e s i n t o d i s c r e t e c l u s t e r s of s i m i l a r p r o f i l e s . Once a t i g h t c l u s t e r i s obtained then the Model Conceptual P r o f i l e , which G u e r t i n c a l l s a "modal p a t t e r n " , can be obtained simply by c a l c u l a t i n g the average p r o f i l e f o r a l l of the members of t h i s c l u s t e r . As such i t i s not a group s t a t i s t i c , but a s t a t i s t i c based upon the average score obtained by a group of s u b j e c t s whose p r o f i l e s are very s i m i l a r . To d i s g r e s s from Guertin's program b r i e f l y , m u c h of the c o n t r o - v e r s y over p r o f i l e a n a l y s i s has centered around the i s s u e of p r o f i l e s i m i l a r i t y . For example, see Cronbach. and Gleser (1953), Nunnally (1962) and G u e r t i n (1970). I t i s recognized by most that a simple product-moment c o r r e l a t i o n between p r o f i l e s only d i f f e r e n t i a t e s be- tween the shape of the p r o f i l e s and does not account f o r d i f f e r e n c e s i n l e v e l and d i s p e r s i o n . To i l l u s t r a t e t h i s p o i n t , consider the f o l - lowing example used by G u e r t i n (1970). I f the raw scores on f o u r items f o r persons A and B were: ITEMS 1 2 3 4 Mean D i s p e r s i o n A 10 20 10 20 10 15 B 100 200 100 200 100 150 85 The product-moment, r , f o r t h i s a r r a y of scores i s 1.00 which i n d i c a t e s a p e r f e c t c o r r e l a t i o n — a r e s u l t due to the s t a n d a r d i z a t i o n procedures i n v o l v e d i n c a l c u l a t i n g the c o r r e l a t i o n c o e f f i c i e n t . I t i s obvious, then, that the product-moment c o e f f i c i e n t c o nsiders only the r e l a t i v e shapes of the p r o f i l e s and ignores d i f f e r e n c e s i n the l e v e l (mean scores) and the d i s p e r s i o n of scores. Thus, the use of an i n t e r - p o i n t d i s t a n c e measure i n E u c l i d e a n space has become the accepted procedure f o r a n a l y z i n g f o r d i f f e r e n c e s i n l e v e l and d i s p e r s i o n of p r o f i l e data. While there i s s t i l l some disagreement r e g a r d i n g the best d i s t a n c e measure to use, the author accepts Guertin's p o s i t i o n that the best measure of t h i s d i s t a n c e (d) i s obtained by f i r s t squaring the i n t e r - p r o f i l e d i s t a n c e s to remove any negative terms and then t a k i n g the square root of t h i s e x p r e s s i o n . Thus d can be expressed as: where j and k are p r o f i l e s of persons being compared and i i s the i t h To r e t u r n to Guertin's program, then, the f i r s t step c o n s i s t e d of performing a Q-analysis on the p r o f i l e s (persons) by concepts m a t r i x using e i t h e r the b e l i e f or f a m i l i a r i t y - s c o r e s . As t h i s procedure i n - volved the formation of an i n t e r - p r o f i l e c o r r e l a t i o n m a t r i x p r i o r to the f a c t o r a n a l y s i s , the r e s u l t a n t f a c t o r s , or c l u s t e r s of p r o f i l e s , were based upon shape s i m i l a r i t y o n l y . In order to determine whether p r o f i l e s of the same shape could be i t e m o f an instrument c o n s i s t i n g of n items. 86 f u r t h e r separated on the b a s i s of l e v e l and d i s p e r s i o n the next step c o n s i s t e d of computing a s i m i l a r i t y m a t r i x ( i n t e r - p r o f i l e d i s t a n c e m a t r i x , or D-matrix) f o r those p r o f i l e s that c l u s t e r e d together on the ba s i s of shape alone. D e t a i l s of the computational procedures used i n forming t h i s D-matrix can be found i n G u e r t i n (1970). By f a c t o r i n g t h i s m a t r i x i t was p o s s i b l e to determine i f f u r t h e r s u b - c l u s t e r s of p r o f i l e s appeared w i t h i n the same shape f a m i l y as a r e s u l t of d i f f e r - ences i n l e v e l or d i s p e r s i o n . Once a l l of the p r o f i l e c l u s t e r s were i d e n t i f i e d f o r a given shape f a m i l y , then a "modal p a t t e r n " was com- puted f o r each c l u s t e r . This was accomplished by c a l c u l a t i n g a weighted mean score (using only the p r o f i l e s c h a r a c t e r i z i n g t h a t c l u s t e r ) f o r each of the statements. The weigh t i n g used was the p r o f i l e f a c t o r l o a d i n g from the a n a l y s i s of the s i m i l a r i t y m a t r i x . These "modal p a t t e r n s " are the d e s i r e d Model Conceptual P r o f i l e s and can be used i n a d i a g n o s t i c c a p a c i t y by some matching procedure between i n d i v i d u a l Conceptual P r o f i l e s and one of these Model Conceptual P r o f i l e s f o r the purposes of i n s t r u c t i o n . The r e s u l t s obtained f o r the p r o f i l e a n a l y s i s are presented i n Chapter F i v e . Chapter S i x i n c l u d e s a d i s c u s s i o n of how these Model Conceptual P r o f i l e s might be u t i l i z e d i n an i n s t r u c t i o n a l s e t t i n g . 87 NOTES FOR CHAPTER FOUR 1. Wish (1972) o u t l i n e s a v a r i e t y of techniques f o r generating data that can be subjected to some type of m u l t i d i m e n s i o n a l a n a l y s i s . 2. In the l i t e r a t u r e on the semantic d i f f e r e n t i a l the word,"concept", has been used i n a generic sense to stand f o r the stimulus being r a t e d by the s u b j e c t s . Since these s t i m u l i were most o f t e n one or two word nouns, or noun phrases, the term was q u i t e a p p r o p r i a t e . In the present i n s t a n c e the s t i m u l i c o n s i s t of r a t h e r lengthy two-part statements. Although the explanatory p a r t of the statement attempts to represent a p a r t i c u l a r conception of heat, i t was decided to d e v i a t e from the s t a n - dard s e m a n t i c - d i f f e r e n t i a l usage and r e f e r to the stimulus as a " s t a - tement" about heat. A p a r t i c u l a r item on the C.P.I., then, c o n s i s t s of a statement to be r a t e d and the s i x r a t i n g s c a l e s . 3. Some background i n f o r m a t i o n about the c a l o r i c and k i n e t i c t h e o r i e s may a s s i s t the reader i n a s s e s s i n g the v a l i d i t y and e f f e c t i v e n e s s of the items. The b a s i c p o s t u l a t e of the c a l o r i c theory was that heat e x i s t e d as some s u b t l e , i n d e s t r u c t i b l e f l u i d t h a t was capable of p e n e t r a t i n g a l l m a t e r i a l bodies. The elemental c o n s t i t u e n t s of t h i s f l u i d , i n keeping w i t h the Newtonian conception of the w o r l d , were thought to be p a r t i c l e s or corpuscules of c a l o r i c which occupied the space around the p a r t i c l e s of matter. There was an i n h e r e n t a f f i n i t y of a t t r a c t i o n be- tween p a r t i c l e s of c a l o r i c and p a r t i c l e s of matter — the degree of a t - t r a c t i o n depending upon the type of matter. This a t t r a c t i o n was ex- pressed as a number and c a l l e d the s p e c i f i c heat of the substance. I t was f u r t h e r hypothesized that the c a l o r i c p a r t i c l e s were mutually r e p u l s i v e and so the c a l o r i c would n a t u r a l l y move from an area of h i g h d e n s i t y to one of low d e n s i t y . That i s , from an o b j e c t , or p a r t of an o b j e c t , that was hot to one that was c o o l e r . With these three p o s t u l a t e s the c a l o r i c theory was able to account f o r most of the experimental observations of the day. Those observa- t i o n s which o f f e r e d momentary r e s i s t a n c e — such as (1) the weight of . an o b j e c t d i d not change when c a l o r i c was added to i t ; and (2) d u r i n g a phase change no change i n temperature occurs even though c a l o r i c i s being added — were i n c o r p o r a t e d i n t o the network of the t h e o r e t i c a l s t r u c t u r e by means of ad hoc a d d i t i o n s to the theory. In answer to the f i r s t problem i t was claimed that the f l u i d of p a r t i c l e s was so s u b t l e that e i t h e r i t possessed no measurable weight or e l s e the balances being used i n the experiments were not s u f f i c i e n t l y s e n s i t i v e . The second problem area r e q u i r e d a l i t t l e more im a g i n a t i v e s o l u t i o n . The t h e o r i s t s hypothesized that during a phase change the added c a l o r i c p a r t i c l e s d i d not i n c r e a s e the d e n s i t y of c a l o r i c around the atoms of matter (as temperature was d i r e c t l y r e l a t e d to the d e n s i t y of the c a l o r i c ) but, that these c a l o r i c p a r t i c l e s reacted c h e m i c a l l y w i t h the atoms to produce a type of ' l a t e n t c a l o r i c ' . When the phase change was reversed the bound-up ' l a t e n t ' c a l o r i c was again r e l e a s e d as ' f r e e ' 88 c a l o r i c thus accounting f o r the great amount of heat r e l e a s e d during a phase change. While there were some notable d i s s e n t e r s , such as the much p u b l i c i z e d Count Rumford, the c a l o r i c theory was by f a r the most favored theory of heat from the mid-18th Century u n t i l the mid-19th Century (Fox, 1971). While most readers w i l l be somewhat f a m i l i a r w i t h the p r e v a i l i n g k i n e t i c theory of heat,a b r i e f summary of i t s b a s i c tenets may be h e l p - f u l . Heat i s conceived not to be a separate type of matter, as was the case w i t h the c a l o r i c theory, but a p r o p e r t y a s s o c i a t e d w i t h the motion of m a t t e r i Heat i s thus defined as the t o t a l amount of energy possessed by the p a r t i c l e s of a body ( i n c l u d i n g a l l three p o s s i b l e types of motion: t r a n s l a t i o n , r o t a t i o n and v i b r a t i o n . ) Temperature i s considered to be a measure of the average k i n e t i c energy of the p a r t i c l e s of the o b j e c t . The temperature of an o b j e c t i s a l t e r e d by an exchange of energy between a hot and a c o l d body, as opposed to an exchange of a substance envisaged by the c a l o r i c theory. 4. The computer program used to c a r r y out t h i s a n a l y s i s was obtained from the U.B.C. computing center under the code name of *FAN. 5. Although the u s u a l problem of d e c i d i n g how many components or f a c t o r s to r o t a t e was e a s i l y r e s o l v e d i n t h i s f i r s t stage of the a n a l y s i s , t h i s was not so i n other stages. Because the d e l i b e r a t i o n s surrounding t h i s problem are somewhat s i m i l a r f o r a l l the cases a b r i e f d i s c u s s i o n of the i s s u e s i n v o l v e d seems warranted. F a c t o r s , or components i n the present c o n t e x t , are r o t a t e d f o r one b a s i c reason: " . . . t o o b t a i n a more i n t e r p r e t a b l e p a t t e r n of f a c t o r l o a d i n g s and to f a c i l i t a t e e s t i m a t i o n s of the scores of people on the f a c t o r s . " (Nunnally, 1967, p. 321) With t h i s b a s i c purpose i n mind the f i n a l d e c i s i o n r e g a r d i n g the number of f a c t o r s to r o t a t e was p r i m a r i l y based upon the judgment as to whether the components or f a c t o r s were rendered more i n t e r p r e t a b l e by the r o t a t i o n procedures. As t h i s j udg- ment i s o f t e n very d i f f i c u l t , a number of c r i t e r i a have been developed to p r ovide a n a l y s t s w i t h some b a s i c g u i d e l i n e s . For example, see C a t t e l l (1966). The most common c r i t e r i o n i s that of r o t a t i n g only those f a c t o r s w i t h eigenvalues g r e a t e r than one. In some i n s t a n c e s t h i s c r i t e r i o n i s i n a p p r o p r i a t e — as i s the case w i t h the a n a l y s i s of the p r o f i l e data i n S e c t i o n 5.10 due to the s i z e of the c o r r e l a t i o n m a t r i x and the r e s u l t a n t l a r g e eigenvalues. A second popular c r i t e r i o n i s the 'slope' c r i t e r i o n . This guide- l i n e i n v o l v e d graphing the magnitude of the eigenvalues versus the o r d i n a l value of the eigenvalue. Only those f a c t o r s which precede the p o i n t at which the slope becomes constant should be r o t a t e d . One, or sometimes both, of these c r i t e r i a were used i n order to narrow down the range of p o t e n t i a l f a c t o r s . I n t e r p r e t a b i l i t y of the f a c t o r s t r u c t u r e was the f i n a l c r i t e r i o n f o r d e c i d i n g which f a c t o r s to r e t a i n . 89 CHAPTER FIVE RESULTS OF THE CONCEPTUAL PROFILE ANALYSIS The s t r u c t u r a l a n a l y s i s of Phase Two of the study culminated w i t h the c o n s t r u c t i o n of a number of Model Conceptual P r o f i l e s . This chapter contains a d i s c u s s i o n and i n t e r p r e t a t i o n of the Model Conceptual P r o f i l e s r e s u l t i n g from the procedures described i n Chapter Four. 5.00 Model Conceptual P r o f i l e s f o r the B e l i e f - S c o r e s In order to o b t a i n the Model Conceptual P r o f i l e s based upon the s u b j e c t s ' b e l i e f s about concepts of heat s t a t e d i n items on the Con- ce p t u a l P r o f i l e Instrument (C.P.I.) , only those statements which were r e p r e s e n t a t i v e of the three Viewpoints (as o u t l i n e d i n S e c t i o n 4.42) were used f o r input to the G u e r t i n P r o f i l e A n a l y s i s Program. Hence statements 1, 2, and 3 i n the C P . I . , which comprised a n o n - i n t e r p r e t a b l e (by the experimentor) p r i n c i p a l component, were not i n c l u d e d i n the a n a l y s i s . The b a s i c data m a t r i x f o r the a n a l y s i s c o n s i s t e d of a 276 x 17 p r o f i l e s (persons) by statements m a t r i x of b e l i e f - s c o r e s . By t r a n s p o s i n g t h i s m a t r i x and i n t e r - c o r r e l a t i n g the columns, a 276 x 276 i n t e r - p r o f i l e c o r r e l a t i o n m a t r i x was produced. A p r i n c i p a l f a c t o r a n a l y s i s of the c o r - r e l a t i o n matrix was produced. A p r i n c i p a l f a c t o r a n a l y s i s of the c o r - r e l a t i o n m a t r i x was performed."'' Table 5-1 l i s t s the s i x t e e n eigenvalues obtained from the a n a l y s i s . Since a l l 16 of the eigenvalues were g r e a t e r than one, the i n i t i a l b a s i s f o r s e l e c t i n g the number of f a c t o r s to r o t a t e was based upon the "slope c r i t e r i o n . " A p l o t of the magnitude of the eigenvalues versus t h e i r o r d i n a l numbers i n d i c a t e d an i n f l e c t i o n p o i n t at the t h i r d 9Q TABLE 5-1 The 16 Eigenvalues from the P r i n c i p a l F a c t o r A n a l y s i s of the I n t e r - P r o f i l e C o r r e l a t i o n M a t r i x of B e l i e f - S c o r e s 1. 49.32 9. 12.99 2. 33.61 10. 11.81 3. 27.25 11. 11.58 4. 19.89 12. 10.31 5. 18.48 13. 9.42 6. 16.03 14. 8.32 7. 14.10 15. 8.10 8. 13.74 16. 6.71 eigenvalue and a gradual l e v e l l i n g o f f of the slope a f t e r t h i s e i g e n - v a l u e . Thus, i n i t i a l l y three f a c t o r s were r o t a t e d . Subsequent computer runs, r o t a t i n g four and s i x f a c t o r s were a l s o made on a t r i a l b a s i s . A comparison of the r e s u l t a n t f a c t o r s t r u c t u r e s i n d i c a t e d t h a t the i n i t i a l s o l u t i o n , w i t h three f a c t o r s r o t a t e d , was the most s a t i s f a c t o r y c o n s i d e r - i n g the f o l l o w i n g two c r i t e r i a : (1) the i n c i d e n c e of u n d e s i r a b l e f a c t o r s p l i t t i n g whereby a p r o f i l e loads h i g h l y (.50 or g r e a t e r ) on more than 2 one f a c t o r ; and (2) o p t i m a l p r o f i l e membership i n each f a c t o r . The three r e t a i n e d f a c t o r s , r e f e r r e d to by G u e r t i n as Shape Family F a c t o r s , d e f i n e unique f a m i l i e s of p r o f i l e s . Representative members of a Shape Family are p r o f i l e s having the same shape. As o u t l i n e d i n S e c t i o n 4.50 a f u r t h e r f a c t o r a n a l y s i s was performed on a s i m i l a r i t y , or D-matrix, obtained from each of the three Shape Family F a c t o r s . This step determined i f s u b - c l u s t e r s of p r o f i l e s could be i d e n - t i f i e d i n each Shape Family as a r e s u l t of d i f f e r e n c e s i n the l e v e l and d i s p e r s i o n . The r e s u l t s o f the D-matrix f a c t o r a n a l y s i s i n d i c a t e d t h a t the p r o f i l e s i n each Shape Family d i d not d i f f e r i n terms of l e v e l and d i s p e r s i o n i n any c l e a r l y i n t e r p r e t a b l e way. This can be seen i n pa r t . 91 i n Table 5-2 which gives the l a r g e s t s i x eigenvalues f o r each of the three i n t e r p r e t a b l e Shape F a m i l i e s . TABLE 5-2 The Largest S i x Eigenvalues Obtained by F a c t o r i n g the D-Matrices f o r Each of the Three Shape F a m i l i e s of B e l i e f - S c o r e s Eigenvalues 1 2 3 4 5 6 37.60 3.99 2.27 1.93 1.64 1.36 27.86 3.30 1.82 1.17 1.15 1.02 25.96 4.56 2.17 1.58 1.37 1.22 A p p l i c a t i o n of the "slope c r i t e r i o n " would suggest two p o s s i b l e c l u s t e r s of p r o f i l e s i n each Shape Family. In each case, however, the second p r o f i l e a s s o c i a t e d w i t h the second h i g h e s t eigenvalue could not be c l e a r l y d i s t i n g u i s h e d from the f i r s t . For t h i s reason only one set of p r o f i l e s was r e t a i n e d i n each Shape Family. The p r o f i l e s r e t a i n e d i n each Shape Family were subsequently r o t a t e d to y i e l d a set of p r o f i l e s i n each Shape Family which were c l e a r l y s i m i l a r i n terms of l e v e l and d i s p e r s i o n as w e l l as shape. These p r o f i l e s c o n s t i t u t e d the Model Con- c e p t u a l P r o f i l e s sought a f t e r i n the study. The three Model Conceptual P r o f i l e s are given i n Figures 5-1 through 5-3. These f i g u r e s are f o l - lowed by a l i s t of the statements i n Table 5-3, c l a s s i f i e d a ccording to each heat Viewpoint, as they appear i n the three Model Conceptual P r o f i l e s . 5.10 Model Conceptual P r o f i l e s f o r the F a m i l i a r i t y - S c o r e s In a s i m i l a r manner Model Conceptual P r o f i l e s were constructed f o r Figure 5-1 Model Conceptual Profile 1 (Belief-Scores; N = 58 Subjects) Figure 5-2 Model Conceptual Profile 2 (Belief-Scores; N = 43 Subjects) Kinetic Viewpoint Children's Viewpoint Caloric Viewpoint i i i i i i i 4 7 11 13 14 17 18 Statements on Conceptual Profile Inventory 5 9 12 16 19- 6 8 10 15 20 Figure 5-3 Model Conceptual Profile 3 (Belief-Scores; N = 46 Subjects) Kinetic Viewpoint Children's Viewpoint Caloric Viewpoint 4 7 i l 13 14 17 18 Statements on Conceptual Profile Inventory 5 9 12 i6 19- 18 6 8 10 15 20 95 the f a m i l i a r i t y - s c o r e s obtained f rom the C.P.I. As bef o r e , s e v e r a l items on the C.P.I, were excluded from the a n a l y s i s because they f a i l e d to load h i g h l y on the three heat Viewpoints f o r the f a m i l i a r i t y - s c o r e s described i n S e c t i o n 4.42. These items were 1, 2, 3, 6, and 20. TABLE 5-3 A L i s t of the Statements i n Each Viewpoint Used i n the P r o f i l e A n a l y s i s of the B e l i e f - S c o r e s KINETIC VIEWPOINT 5. The whole rod gets hot because: THE FASTER MOVING METAL PARTICLES BUMP INTO EACH OTHER ALL THE WAY THROUGH THE ROD. 9. The wax melted because: THE WAX PARTICLES WERE MOVING ABOUT SO FAST THAT THEY COULD NOT HOLD ON TO EACH OTHER SO WELL. 12. The metal cubes were h o t t e r than the wood or sugar because: THE METAL PARTICLES ARE EASIER TO MOVE. 16. The temperature of the water decreased when an i c e cube was added because: THE WATER PARTICLES LOSE SOME OF THEIR SPEED BY BUMPING INTO THE ICE PARTICLES. 19. The red l i q u i d i n the tube went up because: THE LIQUID'S PARTICLES MOVED MORE QUICKLY AND SO TOOK UP MORE SPACE. CHILDREN'S VIEWPOINT 4. The whole rod gets hot because: THE HEAT BUILDS UP IN ONE PART UNTIL IT CAN'T HOLD ANYMORE AND THEN THE HEAT MOVES ALONG THE ROD. 7. The wax melted because: IT WAS A SOFT SUBSTANCE. 11. The metal cubes were h o t t e r than the wood or sugar because: IT WAS MORE DIFFICULT FOR THE AIR TO GET INSIDE THE HARD METAL CUBES TO COOL THEM. 13. The metal cubes d i d not melt because: THEY WERE NOT HEATED LONG ENOUGH. 14. The temperature of the water decreased when an i c e cube was added because: THE ICE CUBE ATTRACTED SOME OF THE HEAT PARTICLES AWAY FROM THE WATER. 96 17. A l a r g e i c e cube takes longer to melt than a small i c e cube because: THE LARGE ICE CUBE HAS A COLDER TEMPERATURE THAN THE SMALL ICE CUBE. 18. The red l i q u i d i n the tube went up because: THE HEAT MAKES THE RED LIQUID LIGHTER AND SO IT RISES. CALORIC VIEWPOINT 6. The whole rod gets hot because: THE HEAT PARTICLES FROM THE FLAME ARE ATTRACTED TO ALL PARTS OF THE ROD. 8. The wax melted because: THE HEAT PARTICLES WENT INSIDE AND FORCED THE WAX PARTICLES APART. 10. The metal cubes were h o t t e r than the wood or sugar because: THE METAL CUBES DREW IN MORE HEAT PARTICLES THAN THE OTHER CUBES. 15. The temperature of the water decreased when an i c e cube was added because: SOME OF THE COLD LEFT THE ICE CUBE AND WENT INTO THE WATER. 20. The red l i q u i d i n the tube went up because: THE HEAT PARTICLES TAKE UP SPACE INSIDE THE LIQUID AND FORCES THE LIQUID OUT THE TUBE. The eigenvalues from a p r i n c i p a l f a c t o r a n a l y s i s of the i n t e r - p r o f i l e m a t r i x of f a m i l i a r i t y - s c o r e s are given i n Table 5-4. A l - though the f i r s t f a c t o r i s by f a r the most predominant i t was decided TABLE 5-4 The Eigenvalues from the P r i n c i p a l F a c t o r A n a l y s i s of the I n t e r - P r o f i l e C o r r e l a t i o n M a t r i x of F a m i l i a r i t y - S c o r e s 1. 61 .92 7. 16.67 2. 27 .25 8. 14.76 3. 22 .56 9. 13.85 4. 21 .46 10. 13.28 5. 19 .73 11. 11.81 6. 17 .73 12. 11.03 on the b a s i s of the "sl o p i of the D-matrix f o r both i Factors of the f a m i l i a r i t y - s c o r e s again i n d i c a t e d that ho f u r t h e r Figure 5-4 Model Conceptual Profile 4 (Familiarity-Scores; N = 94 Subjects) Figure 5-5 Model -Conceptual Profile 5 (Familiarity-Scores; N = 44 Subjects) 00 Kinetic Viewpoint Substance Viewpoint 1 Substance Viewpoint 2 ' 1 ' < • 1 ' l < I V I , , P 8 9 12 16 1-9 4 7 10 11 15 13 14 17 18 Statements on Conceptual Profile Inventory 99 s e p a r a t i o n could be obtained i n the p r o f i l e c l u s t e r s . Thus two Model Conceptual P r o f i l e s r e p r e s e n t i n g the s u b j e c t ' s f a m i l i a r i t y w i t h the statements are given i n Figures 5-4 and 5-5. 5.20 I n t e r p r e t a t i o n of the Model Conceptual P r o f i l e s I n Chapter Four the f u n c t i o n of the p r o f i l e a n a l y s i s was to d e t e r - mine a set of general p a t t e r n s , or models, t h a t d e s c r i b e c h i l d r e n ' s con- ceptions of heat phenomena. On the b a s i s of these p r o f i l e - c l u s t e r s i t was reasoned that i t would be p o s s i b l e to speculate about p o t e n t i a l teaching s t r a t e g i e s t h a t might be a p p r o p r i a t e f o r the groups of i n d i v i d u a l s portrayed by each of these Model Conceptual P r o f i l e s . A set of general d e s c r i p t i o n s of Model Conceptual P r o f i l e s , which are l i n k e d to i n s t r u c - t i o n a l a c t i v i t i e s , spares the teacher the i m p o s s i b l e task of t r y i n g to diagnose and design an i n s t r u c t i o n a l program f o r each i n d i v i d u a l i n the c l a s s . This s e c t i o n , then, w i l l p r o v i de a general d e s c r i p t i o n and an i n t e r p r e t a t i o n of each of the Model Conceptual P r o f i l e s obtained from the a n a l y s i s . 5.21 The B e l i e f P r o f i l e s Model P r o f i l e 1 The f i r s t three Model Conceptual P r o f i l e s i n F i g u r e s 5-1 to 5-3 were d e r i v e d from the s u b j e c t s ' b e l i e f - s c o r e s on the C.P.I. In examining the general shape of a l l three i t . i s apparent that the f i r s t P r o f i l e d i f - f e r s markedly from the other two. The most obvious d i f f e r e n c e i s the p o s i t i v e response towards the K i n e t i c V i e w p o i n t . i n c o n t r a s t to the other two P r o f i l e s . A second f e a t u r e of P r o f i l e 1 i s the g e n e r a l l y negative r e a c t i o n towards the statements which d e f i n e the C h i l d r e n ' s . V i e w p o i n t . More s p e c i f i c a l l y , the 58 s u b j e c t s who are portrayed i n P r o f i l e 1 100 appear to be embracing a n o t i o n of matter that i s p a r t i c u l a t e i n nature as i n d i c a t e d by a l l those statements i n the K i n e t i c Viewpoint that were r a t e d h i g her than +1 on the b e l i e f - s c a l e s . However, the very high r a t i n g s given to statements 10, 15, and 20 ( a l l of which represent a C a l o r i c Viewpoint) would suggest t h a t l i t t l e d i f f e r e n t i a t i o n i s being made between the nature of these p a r t i c l e s . That i s , the s u b j e c t s r e - presented by t h i s P r o f i l e appear to s u b s c r i b e to the n o t i o n t h a t heat c o n s i s t s of p a r t i c l e s s i m i l a r i n some resp e c t s to p a r t i c l e s which make up matter. Another prominent f e a t u r e of t h i s Conceptual P r o f i l e i s the s t r o n g r e j e c t i o n of those statements (namely 13, 17, and 18) which r e f l e c t what might be c a l l e d common-sense ideas about heat. These i d e a s , which may be based i n p a r t upon a set of p h y s i c a l i n t u i t i o n s evolved from e a r l y childhood encounters w i t h heat phenomena, were p r e v a l e n t i n many of the i n t e r v i e w s conducted. For example, ideas r e l a t i n g the s i z e and weight of an o b j e c t to i t s temperature were f r e q u e n t l y expressed. The more n e u t r a l responses to the other statements i n the C h i l - dren's Viewpoint might be i n t e r p r e t e d i n terms of the tendency of the s u b j e c t s to adopt a substance view of h e a t , even though heat i s des- c r i b e d i n these statements i n broad q u a l i t a t i v e terms r a t h e r than as a p a r t i c l e as i s the case i n the C a l o r i c Viewpoint. In summary, Model Conceptual P r o f i l e 1 suggests that the s u b j e c t s who f i t i n t o t h i s type of p a t t e r n tend t o b e l i e v e ideas about heat t h a t are l e s s dependent on common-sense or everyday experience. Thus, a combination of personal experience along w i t h some more a b s t r a c t n o t i o n s 101 about the nature of heat might w e l l account f o r t h i s group of s u b j e c t s who s t r o n g l y r e j e c t e d such b e l i e f s about heat as: (1) a s t e e l or copper cube w i l l melt i f i t i s l e f t under a candle long enough; or (2) the l a r g e r the i c e cube the c o l d e r i s i t s temperature. Furthermore, they c o n s i s t e n t l y responded i n a p o s i t i v e way to those statements that p o r t r a y heat to be the motion of p a r t i c l e s of matter. Although, as i n d i c a t e d e a r l i e r , they a l s o responded f a v o r a b l y to those statements i n which heat was d e p i c t e d as unique p a r t i c l e s capable of i n t e r a c t i n g w i t h matter. One p o s s i b l e e x p l a n a t i o n f o r t h i s d u a l - p a r t i c l e view i s that they d i d not d i f f e r e n t i a t e between the two types of p a r t i c l e s mentioned i n the statements (that i s , heat p a r t i c l e s and p a r t i c l e s of m a t t e r ) . Or, a l - t e r n a t i v e l y , they may have indeed perceived the d i f f e r e n c e and chose to t h i n k of heat as a type of s u b t l e p a r t i c l e , l i k e a i r , that could a l s o a f f e c t the motion of the p a r t i c l e s of matter. With the a v a i l a b l e data i t i s not p o s s i b l e to check out e i t h e r of these hypotheses. Model P r o f i l e 2 The second Model Conceptual P r o f i l e d i f f e r e d s i g n i f i c a n t l y from the f i r s t . Most evident i s the s h i f t of the statements from the K i n e t i c Viewpoint townwards to a p o i n t below the n e u t r a l p o s i t i o n . A second s i g n i f i c a n t s h i f t occurred w i t h four out of the s i x statements from the C h i l d r e n ' s Viewpoint moving upwards. Three of these statements (7, 17, and 18) moved over two s c a l e d i v i s i o n s i n the d i r e c t i o n of a stronger b e l i e f r a t i n g . Although there was a s m a l l trend downwards w i t h most of the C a l o r i c statements, none of the s h i f t s were much l a r g e r than one- h a l f of a s c a l e d i v i s i o n . Hence, f o r the purposes of i n t e r p r e t a t i o n the focus i s on the 1Q2 downward s h i f t of the K i n e t i c statements and the upward s h i f t of the three C h i l d r e n ' s statements. I t i s i n t e r e s t i n g to note that i n the l a t t e r , the three statements are a l l i n the general c l a s s d e s c r i b e d e a r l i e r as c h i l d r e n ' s "common-sense" ideas about heat. As they tend to appear at a r a t h e r e a r l y age i t would seem as though they are the products of a r a t h e r i n t u i t i v e p e r c e p t i o n of heat phenomena based l a r g e l y upon immediate sense data. For example, a s i x - y e a r i n t e r v i e w e d by the i n v e s t i g a t o r i n d i c a t e d t h a t l a r g e i c e cubes are at a lower temperature than s m a l l i c e cubes because they have more c o l d . These "common-sense" b e l i e f s about heat are l i k e l y formulated at a r a t h e r e a r l y age and then are never brought i n t o doubt at a l a t e r age when the c h i l d would be capable of s y s t e m a t i c a l l y checking out t h e i r i n t u i t i v e f e e l i n g s about the phenomena. To explore t h i s l i n e of thought f u r t h e r , c onsider the previous example whereby the c r i t e r i o n f o r coldness (temperature) was the s i z e of the i c e cube. I f a c h i l d ever had occasion to h o l d a l a r g e p i e c e of i c e i n one hand and a s m a l l p i e c e of i c e i n the o t h e r , then the sen- s a t i o n would l i k e l y be one l e a d i n g the c h i l d to assume that the l a r g e r one was c o l d e r . This same s e n s a t i o n would have l i k e l y had a g r e a t e r op p o r t u n i t y to occur when e s t i m a t i n g the temperature of d i f f e r e n t amounts of water ( f o r example, a c u p f u l versus a s i n k - f u l l versus a b a t h t u b - f u l l ) . In f a c t , i t was i n a s i t u a t i o n where c h i l d r e n were j u d g i n g the temperature of d i f f e r e n t amounts of water that the i n v e s t i g a t o r was 3 f i r s t a l e r t e d to t h i s 'amount c r i t e r i o n ' f o r j u d g i n g temperature. The other two C h i l d r e n ' s statements are a l s o amenable to an 103 i n t e r p r e t a t i o n suggesting a somewhat p r i m i t i v e n o t i o n of heat emanating from e a r l y encounters w i t h a v a r i e t y of p h y s i c a l phenomena. Thus, s t a - tement number seven, which suggests that s o f t substances are e a s i e r to melt, can be f r e q u e n t l y v e r i f i e d around the home — b u t t e r , s hortening and wax being prime examples. Because the c h i l d r a r e l y has an o p p o r t u n i t y to observe the m e l t i n g behavior of substances, i t i s u n l i k e l y that t h i s b e l i e f would ever be questioned by the c h i l d . I t might be questioned, f o r example, i f the c h i l d set up a m e l t i n g race between a hard substance such as i c e and a somewhat s o f t substance such as s y n t h e t i c rubber, or even a s o f t metal.such as l e a d . The other C h i l d r e n ' s statement of note, number 18, was based upon the n o t i o n that heat makes things r i s e . While i t i s not immediately obvious as to what d i r e c t contact a young c h i l d would have w i t h t h i s type of phenomenon, the phrase, 'heat always r i s e s ' , was heard on a number of occasions w h i l e i n t e r v i e w i n g the younger c h i l d r e n i n the p i l o t s e s s i o n s . The o n l y obvious examples t h a t were mentioned by the twelve- year o l d s were the heat rays r i s i n g above a t o a s t e r , o r over a hot road. Neve r t h e l e s s , i n the C.P.I, t h i s n o t i o n represents a genuine explana- t i o n acceptable to some of the c h i l d r e n to account f o r the r i s e of the l i q u i d i n the tube. The s i g n i f i c a n t downward displacement of the f i v e statements from the K i n e t i c Viewpoint suggests that the s u b j e c t s tend to r e j e c t these more complex ideas p o r t r a y i n g heat as the motion of p a r t i c l e s of matter i n f a v o r of the more "common-sense" view d e s c r i b e d above. A c c o r d i n g l y , i t might be argued that the ideas i n the C h i l d r e n ' s Viewpoint and the 104 C a l o r i c Viewpoint represent a p o s i t i o n somewhat c l o s e r to the concrete world t h a t the c h i l d a c t u a l l y experiences, whereas those ideas contained i n the K i n e t i c Viewpoint represents a l e v e l of a b s t r a c t i o n somewhat removed from t h i s e x p e r i e n t i a l world. In summary, i t has been suggested that the subjects who c o n t r i b u t e d to t h i s second Model P r o f i l e h e l d a somewhat more i n t u i t i v e or p r i m i t i v e view of heat than those s u b s c r i b i n g to the f i r s t Model P r o f i l e . The evidence f o r t h i s i n t e r p r e t a t i o n was based l a r g e l y upon the d e c l i n e of a l l the K i n e t i c concepts and the l a r g e i n c r e a s e towards a p o s i t i v e r a t i n g s on three of the C h i l d r e n ' s concepts. I t must be emphasized that these i n t e r p r e t a t i o n s are s p e c u l a t i v e i n nature, the only s u p p o r t i n g evidence being the experience obtained from the in-depth i n t e r v i e w s c a r - r i e d out e a r l i e r by the i n v e s t i g a t o r . Model P r o f i l e 3 The t h i r d f a m i l y of p r o f i l e s bears a s t r i k i n g resemblance to Model Conceptual P r o f i l e 2 (both having s i m i l a r response p a t t e r n s f o r the K i n e t i c and C a l o r i c Viewpoints) and a l s o bears some s i m i l a r i t y to Model Conceptual P r o f i l e 1. As most of the s i g n i f i c a n t d i f f e r e n c e s between the two p r o f i l e s occur i n the C h i l d r e n ' s Viewpoint, these w i l l be used to focus the d e s c r i p t i o n of Model Conceptual P r o f i l e 3. In comparing Model Conceptual P r o f i l e 3 w i t h Model Conceptual P r o f i l e 2 the most obvious d i f f e r e n c e i s the upward s h i f t of statement 13 and the downward s h i f t s of statements 17 and 18. Statement 13 sug- gests that i f you heat t h i n g s ( i n t h i s i n stance the metal cubes) long enough they w i l l melt. The u n d e r l y i n g view of heat that seems to be i 105 i m p l i e d ( s i m i l a r to that i n statement 4) i s t h a t the heat w i l l accumulate i n the ob j e c t u n t i l there i s a s u f f i c i e n t q u a n t i t y of heat to melt the o b j e c t . While t h i s attempt to r e c o n s t r u c t the s u b j e c t ' s i n t e r p r e t a t i o n of statement 13'has some i n t u i t i v e appeal, i t does not account f o r one very prominent o b s e r v a t i o n . Why does statement 13 have a reasonably p o s i t i v e r a t i n g i n Model P r o f i l e 3 and yet very negative r a t i n g s i n the other two Model P r o f i l e s ? One p o s s i b l e e x p l a n a t i o n of t h i s anomaly i s based upon a c o n v e r s a t i o n h e l d w i t h two grade nine students a f t e r they had f i n i s h e d responding to the C.P.I. They i n d i c a t e d that they responded f a v o r a b l y to statement 13 because they thought t h a t the cubes had indeed been heated long enough, but they would not melt s i n c e the candle flame simply could not supply enough heat. In other words, they were responding more to the o b s e r v a t i o n a l p a r t of the statement than the explanatory p a r t — an i n s t a n c e of the problem discussed e a r l i e r i n Chapter Four under the general t o p i c of concept-scale i n t e r a c t i o n s . Thus the d i s c r e p a n t response p a t t e r n s to statement 13 may simply be an a r t i f a c t of the ambiguity of the wording i n the statement. 5 Two other statements i n the C h i l d r e n ' s Viewpoint, statements 17 and 18, have s h i f t e d markedly downward from t h e i r p o s i t i o n i n P r o f i l e 2. Both of these statements have been e a r l i e r d i s c u s s e d under the l a b e l of "common-sense" ideas about heat. Thus, on the b a s i s of the tr e n d emerging i n the C h i l d r e n ' s Viewpoint (with the exception of the anomalous concept 13) i t would seem th a t there i s a tendency away from "common- sense" ideas towards the somewhat more a b s t r a c t view of heat e x e m p l i f i e d i n Model P r o f i l e 1. Although t h i s has not yet been manifest i n the 106 K i n e t i c Viewpoint, the general decrease i n the d i s p e r s i o n of scores i n the C h i l d r e n ' s Viewpoint a l s o suggests t h a t Model P r o f i l e 3 might be a k i n d of t r a n s i t i o n s t a t e to a more a b s t r a c t l e v e l of understanding of heat phenomena. To pursue the matter of s h i f t s i n understanding a b i t f u r t h e r , one would expect, on the b a s i s of both i n school and out of school experience, that the grade f i v e students should have a higher membership i n the Model P r o f i l e which has the most p o s i t i v e set of b e l i e f - s c o r e s on the "common-sense" statements (that i s , P r o f i l e 2). And c o n v e r s e l y , more grade nine students ought to be a t t r a c t e d to the more a b s t r a c t p a r t i c l e n o t i o n of heat ( P r o f i l e 1 ) . I f P r o f i l e 3 represents those students i n a type of t r a n s i t i o n stage, then i t ought to c o n t a i n a mixture of s t u - dents from a l l the grades. Table 5-5 provides i n f o r m a t i o n of grade membership i n each P r o f i l e . Since there were an unequal number of s u b j e c t s from each grade l e v e l com- p l e t i n g the C.P.I., the percentages i n brackets are the most a p p r o p r i a t e index. These percentages are c a l c u l a t e d by t a k i n g the number of s u b j e c t s i n a p a r t i c u l a r grade who subscribed to a given P r o f i l e , m u l t i p l y i n g by 100 and d i v i d i n g by the t o t a l number of s u b j e c t s i n t h a t grade who com^ p l e t e d the C.P.I. For example, there were e i g h t s u b j e c t s i n grade 5 i n Model Conceptual P r o f i l e 1. As there were a t o t a l of 76 s u b j e c t s i n grade 5 who completed the C.P.I, only 10% of these s u b j e c t s s u b s c r i b e to a view of heat c h a r a c t e r i z e d by Model P r o f i l e 1. Thus n e i t h e r of the t o t a l s i n the row nor the columns sum to equal 100% as only.53% of a l l the s u b j e c t s are accounted f o r by the three p r o f i l e s . 107 TABLE 5-5 Model Conceptual P r o f i l e Membership by Grade L e v e l (Percentage of Students i n t h a t Grade Representative of each Model Conceptual P r o f i l e i s Given i n Brackets) Model Conceptual P r o f i l e mo, 1 ( B e l i e f - Scores) No. 2 ( B e l i e f - Scores) No. 3 ( B e l i e f - Scores) No. 4 ( F a m i l i a r i t y Scores) No. 5 ( F a m i l i a r i t y Scores) As p r e d i c t e d above, the grade nine s u b j e c t s have the highest per- centage f o r P r o f i l e 1 and the grade f i v e s u b j e c t s have the hi g h e s t per- centage f o r P r o f i l e 2 . While P r o f i l e 3 does indeed have a mixture, i t i s somewhat s u r p r i s i n g t o note the r a t h e r h i g h number (21%) of grade nine s u b j e c t s i n t h i s P r o f i l e . 6 Thus these f i g u r e s do provide some prima f a c i e evidence f o r the l e v e l s p o s i t e d above. Although i t i s tempting to spe c u l a t e about the e x i s t e n c e of develop- mental stages or l e v e l s of understanding, i t must be r e a l i z e d t h a t the Grade 5 Grade 7 Grade 9 T o t a l s 8 26 24 58 (10%) (22%) (29%) 21 16 6. 43 (28%) (14%) (7%) 7 22 17 46 (9%) (19%) (21%) 33 31 30 94 (43%) (27%) (36%) 7 26 11 44 (9%) (22%) (13%) 108 evidence presented has been c i r c u m s t a n t i a l at b e s t . Much more in-depth e x p l o r a t i o n i n t o the nature and g e n e r a l i t y of these Model Conceptual P r o f i l e s would be r e q u i r e d to support any s e r i o u s c l a i m of a genuine developmental trend. 5.22 The F a m i l i a r i t y P r o f i l e s When the C.P.I, was b e i n g c o n s t r u c t e d i t was f e l t t h a t a judgmental dimension a s c e r t a i n i n g the s u b j e c t s ' f a m i l i a r i t y w i t h the concepts would be u s e f u l when i n t e r p r e t i n g the f i n a l r e s u l t s . And l i k e the b e l i e f - s c o r e s i t was thought that a number of d i f f e r e n t shape f a m i l i e s could be i d e n - t i f i e d through the p r o f i l e a n a l y s i s procedures. However, a cursory ex- amination of F i g u r e s 5-4 and 5-5, which i l l u s t r a t e Model Conceptual P r o f i l e s 4 and 5 r e s p e c t i v e l y , i n d i c a t e s that there i s only a very s l i g h t d i f f e r e n c e between these two shape f a m i l e s . T h i s would seem to i n d i c a t e that o n l y one f a c t o r should have been r o t a t e d . This apparent u n i f o r m i t y i n the responses to the f a m i l i a r i t y - s c a l e s across a l l three grade l e v e l s i s an i n t e r e s t i n g o b s e r v a t i o n i n i t s e l f . I t i n d i c a t e s the l a c k of evidence f o r a developmental trend as had been hypothesized f o r the s u b j e c t s ' b e l i e f - s c o r e s . Furthermore, a glance at Table 5-5 i n d i c a t e s a f a i r l y even d i s t r i b u t i o n across a l l the grades f o r both of the p r o f i l e s based upon the f a m i l i a r i t y - s c o r e s . Thus the i n f o r m a t i o n t h a t w i l l be of i n t e r p r e t i v e value i s the r e l a t i v e r a t i n g s f o r each of the Viewpoints. Although the r a t i n g s of the statements i n the Model Conceptual P r o f i l e s which are based upon the f a m i l i a r i t y - s c o r e s d i f f e r from those obtained by an a n a l y s i s of the b e l i e f - s c o r e s , some comparisons can be drawn between the two judgmental dimensions. The f i r s t obvious d i f f e r e n c e 109 is the small dispersion of ratings on the statements for a particular Viewpoint. In other words, there was l i t t l e differentiation between the statements in a given Viewpoint on the basis of familiarity. But the feature of real interest i n Model Profiles 4 and 5 is the relative familiarity rating on each of the Viewpoints. In both of these profiles the Kinetic statements are very close to the neutral mark while those statements constituting the two substance Viewpoints are significantly higher. In Model Profile 4 they are around the +2 mark. It is therefore clear from these data that the statements in the Kinetic Viewpoint were perceived by many of the subjects to be less familiar than those concepts which depicted heat as a type of substance or particle. This finding lends some support to the argument advanced earlier regarding the developmental trend in Viewpoints of heat. As the "common-sense" ideas l i k e l y derive from early, concrete experiences with heat phenomena, one would expect the statements re- presenting the Children's Viewpoint to be more familiar than the abstract notions of the Kinetic Viewpoint. 7 NOTES FOR CHAPTER FIVE 110 1. The p r i n c i p a l f a c t o r a n a l y s i s was c a r r i e d out u s i n g a computer program i n G u e r t i n (1970) which was l a b e l l e d , "ED 777 — P r o f i l e A n a l y s i s Package." This program was subsequently a l t e r e d by Page (1974) to i n c r e a s e the i n v e s t i g a t o r ' s f l e x i b i l i t y i n manipulating each of the v a r i o u s sub-routines and to i n c r e a s e the number of p r o f i l e s t h a t c o u l d be computed. I t was t h i s r e v i s e d version t h a t was used i n the study. 2. "Optimal p r o f i l e membership" i s taken to mean a s u f f i c i e n t number of p r o f i l e s to e s t a b l i s h a s i g n i f i c a n t and h o p e f u l l y g e n e r a l i z a h l e p a t t e r n of scores. However, the number of p r o f i l e s should not be so l a r g e as t o e l i m i n a t e genuine d i f f e r e n c e s between the p r o f i l e s when they are averaged i n the l a s t a n a l y t i c a l step. 3. When the 12 y e a r - o l d s i n the f i n a l i n t e r v i e w were faced w i t h the s i t u a t i o n r e q u i r i n g them to judge the temperature of two d i f f e r e n t amounts of water from the same source, four out of ten employed t h i s 'amount c r i t e r i o n ' . S e v e r a l of those who d i d not use t h i s c r i t e r i o n r e p l i e d that the c o n t a i n e r w i t h the l a r g e r amount of hot water would take longer to c o o l down. Hence, they were beginning to make the d i s t i n c t i o n between the temperature of an o b j e c t and the amount of heat possessed by that o b j e c t . 4. The i n v e s t i g a t o r attempted to d i s c u s s the responses of s e v e r a l sub- j e c t s at each grade l e v e l a f t e r they had completed the C.P.I. This was done w i t h a group of f o u r grade f i v e students and two grade ni n e students. U n f o r t u n a t e l y the meeting that was arranged w i t h the grade seven students d i d not take p l a c e due to circumstances beyond the c o n t r o l of the i n - v e s t i g a t o r . 5. A f u r t h e r reason f o r s u s p e c t i n g the v a l i d i t y of statement 13 i s that i t was one of the e x t r a statements from the C h i l d r e n ' s P e r s p e c t i v e t h a t was i n c l u d e d i n the C.P.I, and no p a r a l l e l statements from the other two P e r s p e c t i v e s were c o n s t r u c t e d . I t i s f e a s i b l e to suggest that the sub- j e c t s d i d not p e r c e i v e the connection between t h i s statement and the demonstration that was performed. 6. Although there i s c o n s i d e r a b l e amount of d i v e r s i t y among the t o p i c s taught i n Science 8 and 9 i n B r i t i s h Columbia s c h o o l s , the recommended course of study does i n c l u d e a s e c t i o n on the k i n e t i c molecular theory of heat. Hence one would expect a more s i g n i f i c a n t grade 9 membership i n P r o f i l e 1 than was i n f a c t observed. An attempt was made to d e t e r - mine the s u b j e c t s ' previous s c h o o l experience w i t h heat phenomena by asking them to i n d i c a t e i f they had s t u d i e d heat before i n s c h o o l . Many of the grade 5 and 7 s u b j e c t s i n d i c a t e d that they could not remember and so no formal f i g u r e s were kept. However, i n grade 9 over one-half of the s u b j e c t s i n d i c a t e d that they had p r e v i o u s l y done a u n i t on heat and temperature. 7. The assumption here i s that the s u b j e c t s were indeed u s i n g two d i f - f e r e n t judgmental dimensions i n responding to a statement. That i s , a subject was capable of d i s t i n g u i s h i n g between being f a m i l i a r w i t h the idea being presented i n a statement and b e l i e v i n g the i d e a . The f a c t s I l l t h a t two d i s t i n c t dimensions emerged from the a n a l y s i s of the s c a l e s and that the Model P r o f i l e s d i f f e r e d s i g n i f i c a n t l y between the b e l i e f - scores and the f a m i l i a r i t y - s c o r e s would appear to support t h i s assumption. 112 CHAPTER SIX ILLUSTRATIVE APPLICATIONS OF THE STUDY This chapter i s devoted to an examination of some of the i s s u e s and problems a s s o c i a t e d w i t h the t h i r d phase of the study — the ap- p l i c a t i o n of the r e s u l t s to an e d u c a t i o n a l s e t t i n g . Two d i s t i n c t ways i n which knowledge of t h i s k i n d can be a p p l i e d are i d e n t i f i e d and discussed i n separate s e c t i o n s , u s i n g i l l u s t r a t i v e examples of each type of a p p l i c a t i o n . 6.00 Two Ways of A p p l y i n g the Study Broudy et a l . (1964) have d e l i n e a t e d four d i f f e r e n t ways i n which knowledge can be used. These are f o r the purpose of r e p l i c a t i o n , a s s o c i a t i o n , i n t e r p r e t a t i o n and a p p l i c a t i o n . Since the l a s t two are of concern to t h i s study, they are the s u b j e c t of d i s c u s s i o n i n t h i s sec- t i o n . In u s i n g knowledge i n an i n t e r p r e t a t i v e manner, one i s attempting to g ain a b e t t e r understanding of a problem by c a t e g o r i z i n g i t according to some e x i s t i n g t h e o r e t i c a l framework or at l e a s t according to a hypo- t h e s i z e d set of r e l a t i o n s h i p s . To put i t another way, the i n t e r p r e t i v e use of knowledge can be thought of as an endeavor to l o c a t e a problem on some ap p r o p r i a t e c o g n i t i v e map and so make the phenomenon more i n - t e l l i g i b l e by c l a r i f y i n g and o r g a n i z i n g i t i n terms of f a m i l i a r set of c a t e g o r i e s . On the other hand, an a p p l i c a t i v e usage of knowledge goes beyond merely r e n d e r i n g the problem i n t e l l i g i b l e ; i t e n t a i l s the combination of theory along w i t h a set of s p e c i f i c techniques to a c t u a l l y s o l v e the problem. Thus, a body of t h e o r e t i c a l p r o p o s i t i o n s , or "systems of 113 meanings" as Broudy c a l l s them, i s e s s e n t i a l to both usages. However, i f these t h e o r e t i c a l e n t i t i e s are to be used a p p l i c a t i v e l y to s o l v e meaningful problems of p r a c t i c e then a set of supporting techniques must be developed. An i l l u s t r a t i o n of how the r e s u l t s of the study might be used i n both an i n t e r p r e t i v e and an a p p l i c a t i v e manner i s presented i n the s e c t i o n to f o l l o w . 6.10 I l l u s t r a t i o n of an I n t e r p r e t i v e Use of the Study One of the r e c u r r i n g themes of t h i s d i s s e r t a t i o n has been the emphasis upon c a r r y i n g out a type of s t r u c t u r a l a n a l y s i s of c h i l d r e n ' s b e l i e f s . I t has been argued t h a t the r e a l v a l u e of a s t r u c t u r a l p e r s p e c t i v e l i e s i n i t s p o t e n t i a l to embed i n s t r u c t i o n a l problems i n a broader t h e o r e t i c a l context. The t h e o r e t i c a l s t r u c t u r e , or "system of meanings" being used i n the present d i s c u s s i o n i s t h a t obtained from Chapters Three and Five."'' These chapters o u t l i n e d an hypothesized set of b e l i e f s t y p i c a l l y h e l d by c h i l d r e n and a set of proposed r e l a - t i o n s h i p s among those b e l i e f s . To b r i e f l y review these r e s u l t s , i t was reported that many c h i l - dren subscribe to a set of b e l i e f s t h a t view "heat", and sometimes " c o l d " , as a type of s u b t l e , m a t e r i a l substance w i t h some p r o p e r t i e s s i m i l a r to that of a i r . Heat, or c o l d , was conjectured to be capable of movement from one o b j e c t to another w i t h a consequent change i n tempe- r a t u r e of the o b j e c t s i n q u e s t i o n . Some types of o b j e c t s , l i k e metals, were thought to be i n h e r e n t l y able to a t t r a c t heat and so they n a t u r a l l y would get hot more r a p i d l y than other substances such as wood, g l a s s , or s y n t h e t i c s when plac e d on a hot p l a t e . When these b e l i e f s are considered 114 along w i t h the r e s u l t s from the p r o f i l e a n a l y s i s i n Chapter F i v e , then, the teacher has a v a i l a b l e a p o t e n t i a l s t r u c t u r e f o r i n t e r p r e t i n g . the behaviors and ideas expressed by a group of c h i l d r e n engaged i n i n v e s t i g a t i o n s of heat phenomena. For example, one of the most d i f f i c u l t problems encountered by most c h i l d r e n , and many a d u l t s , i s d i s t i n g u i s h i n g between the concepts of heat and temperature. In c o n s i d e r i n g heat to be a type of substance that can accumulate i n an obje c t (and thus r a i s e i t s temperature) one can r e a d i l y understand why a great d e a l of conceptual confusion e x i s t s i n t h i s area. According to t h i s view, which seems to be p r e v a l e n t i n many-."children, temperature i s simply a measure of the amount of heat h e l d by an o b j e c t . In other words, no d i s t i n c t i o n i s made between the 2 i n t e n s i t y of heat and the amount of heat possessed by a body. Now i f teachers are aware of t h i s substance viewpoint of heat h e l d by many c h i l d r e n , they ought to b e t t e r understand the b a s i c nature of the d i f f i c u l t y . Possessing t h i s understanding, the teacher i s i n a much b e t t e r p o s i t i o n to make d e c i s i o n s r e g a r d i n g the most f r u i t f u l approach to pursue. The teacher may a l l o w the c h i l d r e n to continue to work w i t h t h e i r present ideas w i t h the e x p e c t a t i o n that they w i l l r e s o l v e the d i f - f i culty through guided d i s c o v e r y . Or, the teacher may attempt to p o i n t out the d i f f e r e n c e s between heat and temperature u s i n g concrete examples 3 designed to do so. Another a l t e r n a t e pathway, recommended by one e l e - mentary science program, i s to have the teacher " i n v e n t " , a f t e r s u i t a b l e preparatory experiences w i t h heat and temperature, the concepts of "heat" and "temperature." 4 While the s t r a t e g y to be employed depends i n part upon such f a c t o r s i 115 as the c h i l d r e n ' s previous experience w i t h heat and temperature and whether they are p r e s e n t l y aware of conceptual d i f f i c u l t i e s , a know- ledge of c h i l d r e n ' s perceptions of heat i s u s e f u l f o r d e c i d i n g upon a p a r t i c u l a r approach and then developing i t i n t o a v i a b l e teaching s t r a t e g y . Given t h i s very b r i e f i l l u s t r a t i o n of how knowledge of c h i l d r e n ' s conceptual commitments can be used to understand a s e r i o u s problem of p r a c t i c e f r e q u e n t l y encountered when c h i l d r e n are stud y i n g the t o p i c of heat, the next step e n t a i l s the development of techniques to r e s o l v e such problems. 6.20 I l l u s t r a t i o n of an A p p l i c a t i v e Use of the Study To use knowledge i n an a p p l i c a t i v e manner the teacher must f i r s t understand the b a s i c nature of the problem. Second, he should possess a s e t of techniques t h a t w i l l enable him to s e r i o u s l y address the problem. Perhaps one of the most u s e f u l techniques from the teacher's p o i n t of view i s a set of teaching s t r a t e g i e s . Thus, the f o l l o w i n g two se c t i o n s d i s c u s s the i m p l i c i t problems that must be r e s o l v e d p r i o r to desi g n i n g a s e r i e s of teaching s t r a t e g i e s , and a b r i e f i l l u s t r a t i o n of one such s t r a t e g y . 6.21 Problems of Designing Teaching S t r a t e g i e s Before any s e r i o u s p l a n n i n g can commence i n desi g n i n g a teaching s t r a t e g y a c l e a r v i s i o n of the d e s i r e d i n s t r u c t i o n a l goals i s a n e c e s s i t y . T h i s i s i m p l i e d i n the very conception of a s t r a t e g y — a p r e s c r i b e d s et of moves or maneuvers i n order to a t t a i n some s p e c i f i e d goal or end s t a t e . There i s disagreement among science educators w i t h regard to g o a l s , 116 and i n p a r t i c u l a r the means to be employed f o r a t t a i n i n g a set of p r e s c r i b e d g o a l s . Most, however, would agree that one d e s i r a b l e out- come of science education i s students who have i n q u i r i n g and i n q u i - s i t i v e minds. That i s , students who have both the s k i l l s and the d e s i r e to t r y and seek out more encompassing and powerful ways of l o o k i n g at the world. Thus, the teaching f u n c t i o n s employed i n e v o l v i n g a set of teaching s t r a t e g i e s must be s u p p o r t i v e of the above g o a l . I n c o n s i d e r i n g the t o p i c of heat, one can speculate about a number of p o t e n t i a l l y e f f e c t i v e teaching f u n c t i o n s , or maneuvers as they w i l l be c a l l e d , which comprise an o v e r a l l teaching s t r a t e g y . To begin w i t h , the teacher must encourage the students to become f a m i l i a r w i t h a wide range of phenomena a s s o c i a t e d w i t h heat and temperature and i n so doing, develop a set of i n t u i t i v e ideas or b e l i e f s about heat. These encounters should be of s u f f i c i e n t depth t o a l l o w the students t o c l a r i f y t h e i r ideas such t h a t they have the confidence to begin making p r e d i c t i o n s about the outcomes of subsequent i n v e s t i g a t i o n s . Given that students have a t t a i n e d a somewhat s t a b l e set of b e l i e f s , another teaching maneuver might i n v o l v e the c r e a t i o n of a s i t u a t i o n that leads to an unexpected outcome f o r the students. This anomalous event i s designed to i n t r o d u c e an element of u n c e r t a i n t y i n t o the student's b e l i e f s , w i t h the e x p e c t a t i o n t h a t the u n c e r t a i n t y w i l l e v e n t u a l l y be r e s o l v e d w i t h a type of r e o r g a n i z a t i o n or r e s t r u c t u r i n g of the c h i l d ' s i n t u i t i o n s and b e l i e f s which c o n t r i b u t e s to the attainment of i n s t r u c t i o n a l g o a l s . I f a c h i l d i s now able to understand a wider range of phenomena, then t h i s s h i f t could be considered as proceeding towards a more powerful and encompassing conception of heat. 117 The teaching maneuvers j u s t sketched out above can be f o r m a l i z e d i n t o a teaching s t r a t e g y wherein each maneuver i s described i n terms of the teaching f u n c t i o n s that i t performs. Hence, the f i r s t teaching f u n c t i o n may be i n t r o d u c i n g the students to a v a r i e t y of s i t u a t i o n s i n v o l v i n g experiences w i t h the e f f e c t s of heat and temperature — th a t i s , a set of e x p e r i e n t i a l maneuvers. These might be f o l l o w e d by c l a r i f i c a t i o n maneuvers, the purpose of which would be to have the students c a r e f u l l y t h i n k about t h e i r i d e a s . The w i l l i n g n e s s and a b i l i t y to make p r e d i c t i o n s about the outcomes of nove l i n v e s t i g a t i o n s would be an i n d i c a t i o n of the success of the c l a r i f y i n g maneuvers. Another s e r i e s of maneuvers co u l d be d i r e c t e d toward c r e a t i n g s i t u a t i o n s which would l e a d to r e s u l t s t h a t are unexpected or perhaps even c o n t r a d i c t o r y to those b e l i e f s p r e s e n t l y h e l d by the c l a s s or a p a r t i c u l a r group of students. The impact of an anomaly maneuver i s d i r e c t e d towards g e t t i n g the students to r e c o n s i d e r t h e i r previous p o s i t i o n . This may e n t a i l students adopting.an e n t i r e new set of ideas about heat. The r e s t r u c t u r i n g i n v o l v e d may take c o n s i d e r a b l e time and l i k e l y some guidance from the teacher. Another p o s s i b l e outcome of an anomaly maneuver i s the m o d i f i c a t i o n by the students of some p a r t of t h e i r e x i s t i n g framework. In e i t h e r case, i t i s apparent that these maneuvers have to be s e l e c t e d to f i t the p a r t i c u l a r p a t t e r n of b e l i e f s expressed by the students. F i n a l l y , one l a s t set of maneuvers might be employed to a s s i s t the students i n accommodating to the unexpected outcomes. As w i t h each of the above, these r e s t r u c t u r i n g maneuvers could be accomplished i n many d i f f e r e n t ways ranging from c l a s s d i s c u s s i o n and other peer group 118 i n t e r a c t i o n s to more d i r e c t i n t e r v e n t i o n procedures by the teacher. R e t u r n i n g now to the c e n t r a l i s s u e of u s i n g the r e s u l t s of t h i s study i n an a p p l i c a t i v e manner, i t should be evident that the C.P.I., i n c o n j u n c t i o n w i t h the Model Conceptual P r o f i l e s , could p l a y a very prominent r o l e i n terms of the design and s e l e c t i o n of a p p r o p r i a t e teaching s t r a t e g i e s . With the a s s i s t a n c e of the C.P.I, and the Model Conceptual P r o f i l e s , the teacher i s a s s i s t e d i n the d i f f i c u l t task of diagnosing the e x i s t i n g conceptions of heat h e l d by i n d i v i d u a l members of the c l a s s . Since teaching s t r a t e g i e s can be designed f o r each Model Conceptual P r o f i l e , the teacher can a d m i n i s t e r the C.P.I, and' then match or catego- r i z e i n d i v i d u a l s , or groups of i n d i v i d u a l s , a ccording to one of the Model P r o f i l e s . The remaining step i n v o l v e s a d e c i s i o n t o choose an a p p r o p r i a t e maneuver, or set of maneuvers, from among those l i s t e d f o r a p a r t i c u l a r Model P r o f i l e , say, i n a guidebook accompanying the C.P.I. 6.22 An Example of an A p p l i c a t i v e Use I n an endeavor to f u r t h e r c l a r i f y the types of teaching maneuvers and the matching of an i n d i v i d u a l student to one of the Model Conceptual P r o f i l e s , t h i s s e c t i o n w i l l , i l l u s t r a t e these procedures by t a k i n g the scores obtained by one i n d i v i d u a l on the C.P.I, and map out p o t e n t i a l i n s t r u c t i o n a l a c t i v i t i e s . In F i g u r e 6-1 the scores f o r a grade seven subject are graphed i n a s i m i l a r f a s h i o n to the Model Conceptual P r o f i l e s i n Chapter F i v e . To b e t t e r v i s u a l i z e the match between the i n d i v i d u a l p r o f i l e and the Model Conceptual P r o f i l e judged to be most s i m i l a r , F i g ure 6-2 i s immediately 119 below and i s simply a r e p r o d u c t i o n of Model Conceptual P r o f i l e 2. The l i s t of statements used i s a l s o reproduced i n Table 6-1 f o r ready r e f e r e n c e . TABLE 6-1 A L i s t of the Statements i n Each Viewpoint Used i n the P r o f i l e A n a l y s i s of the B e l i e f Scores KINETIC VIEWPOINT 5. The whole rod gets hot because: THE FASTER MOVING METAL PARTICLES BUMP INTO EACH OTHER ALL THE WAY THROUGH THE ROD. 9. The wax melted because: THE WAX PARTICLES WERE MOVING ABOUT SO FAST THAT THEY COULD NOT HOLD ON TO EACH OTHER SO WELL. 12. The metal cubes were h o t t e r than the wood or sugar because: THE METAL PARTICLES ARE EASIER TO MOVE. 16. The temperature of the water decreased when an i c e cube was added because: THE WATER PARTICLES LOSE SOME OF THEIR SPEED BY BUMPING INTO THE ICE PARTICLES. 19. The red l i q u i d i n the tube went up because: THE LIQUID'S PARTICLES MOVED MORE QUICKLY AND SO TOOK UP MORE SPACE. CHILDREN'S VIEWPOINT 4. The whole rod gets hot because: THE HEAT BUILDS UP IN ONE PART UNTIL IT CAN'T HOLD ANYMORE AND THEN THE HEAT MOVES ALONG THE ROD. 7. The wax melted because: IT WAS A SOFT SUBSTANCE. 11. The metal cubes were h o t t e r than the wood or sugar because: IT WAS MORE DIFFICULT FOR THE AIR TO GET INSIDE THE HARD METAL CUBES TO COOL THEM. 13. The metal cubes d i d not melt because: THEY WERE NOT HEATED LONG ENOUGH. 14. The temperature of the water decreased when an i c e cube was added because: THE ICE CUBE ATTRACTED SOME OF THE HEAT PARTICLES AWAY FROM THE WATER. 17. A l a r g e i c e cube takes longer to melt than a s m a l l i c e cube because: THE LARGE ICE CUBE HAS A COLDER TEMPERATURE THAN THE SMALL ICE CUBE. 120 F i g u r e 6-1 An I n d i v i d u a l P r o f i l e of B e l i e f - S c o r e s For a Grade 7 Subject i i i i i » • » • • » • » i » i i i 5 9 12 16 1 9 4 7 11 13 14 17 18 6 8 10 15 20 Statements on Conceptual P r o f i l e Inventory F i g u r e 6-2 Model Conceptual P r o f i l e 2 (N= 43 Subjects) i i i I i l i i i J i l I l 1 I i 5 9 12 16 19 4 7 11 13 14 1 7 B 6 8 10 15 2 0 Statements on Conceptual P r o f i l e Inventory 121 18. The red l i q u i d i n the tube went up because: THE HEAT MAKES THE RED LIQUID LIGHTER AND SO IT RISES. CALORIC VIEWPOINT 6. The whole rod gets hot because: THE HEAT PARTICLES FROM THE FLAME ARE ATTRACTED TO ALL PARTS OF THE ROD. 8. The wax melted because: THE HEAT PARTICLES WENT INSIDE AND FORCED THE WAX PARTICLES APART. 10. The metal cubes were h o t t e r than the wood or sugar because: THE METAL CUBES DREW IN MORE HEAT PARTICLES THAN THE OTHER CUBES. 15. The temperature of the water decreased when an i c e cube was added because: SOME OF THE COLD LEFT THE ICE CUBE AND WENT INTO THE WATER. 20. The red l i q u i d i n the tube went up because: THE HEAT PARTICLES TAKE UP SPACE INSIDE THE LIQUID AND FORCES THE LIQUID OUT THE TUBE. Having c a t e g o r i z e d the i n d i v i d u a l p r o f i l e according to one of the a v a i l a b l e Model Conceptual P r o f i l e s , i n t h i s i n s t a n c e Model Conceptual P r o f i l e 2, the teacher could then c o n s u l t a guidebook which could be prepared c o n t a i n i n g a l i s t of suggested teaching maneuvers c r o s s - r e f - erenced according to the Model Conceptual P r o f i l e s . An i l l u s t r a t i o n of some t y p i c a l a c t i v i t i e s under each teaching maneuver i s given f o r Model Conceptual P r o f i l e 2 i n Table 6-2. These are but a few of the p o s s i b l e a c t i v i t i e s and they are based i n p a r t upon the i n t e r p r e t a t i o n s given to Model Conceptual P r o f i l e 2 i n Chapter F i v e . I t would be d e s i r a b l e to have a l a r g e d i v e r s i t y of a c t i v i t i e s so as to i n s u r e that the teacher could f i n d some that would be compatible w i t h the past experiences and present i n t e r e s t s of the students i n h i s c l a s s . The v a r i o u s teaching maneuvers o u t l i n e d i n Table 6-2 are very general i n nature and are meant to o r i e n t the reader to p o t e n t i a l 122 Table 6-2 L i s t of P o s s i b l e Teaching Maneuvers to Accompany Model Conceptual P r o f i l e Two 1. E x p e r i e n t i a l Maneuvers (a) B a s i c thermometry a c t i v i t i e s ( i ) measure the temperature o f common classroom o b j e c t s ( i i ) measure the temperature of o b j e c t s i n a l l three s t a t e s — gas, l i q u i d , and s o l i d ( i i i ) c r e a t e a c t i v i t i e s f o r hard-to-measure o b j e c t s such as the i n s i d e of an ice-cube. (b) Change of s t a t e a c t i v i t i e s ( i ) observe d i f f e r e n t substances m e l t i n g on a t r a y — l i k e b u t t e r , sugar, wax, l e a d , e t c . ( i i ) h o l d ice-cube races to see who can melt an ice-cube the f a s t e s t and who can keep an ice-cube from m e l t i n g the l o n g e s t . I I . C l a r i f i c a t i o n Maneuvers (a) C l a s s d i s c u s s i o n of r e s u l t s ( i ) A f t e r doing s e v e r a l a c t i v i t i e s c a l l the c l a s s or group together to d i s c u s s the r e s u l t s . Those r e s u l t s which are i n doubt could be repeated as a group a c t i v i t y . ( i i ) Ask group members to t h i n k about the r e s u l t s and to express t h e i r ideas to account f o r them. (b) Competing viewpoints of heat ( i ) I f d i f f e r e n t students or groups have d i f f e r e n t ideas to account f o r the r e s u l t s , encourage them to d i s - cuss and debate these ideas among each other. I I I . Anomaly Maneuvers (a) Temperature change a c t i v i t i e s ( i ) Engage students i n water mixing experiments; a l t e r i n g f i r s t the temperature between the two o r i g i n a l con- t a i n e r s and then the amounts of water i n each c o n t a i n e r . ( i i ) Observe the temperature e f f e c t s of adding d i f f e r e n t objects at the same temperature (say 100•* C.) to given q u a n t i t i e s of l i q u i d . (b) Heat versus temperature a c t i v i t i e s ( i ) Have an ice-cube m e l t i n g race between a i r at 25° C. (or higher i f there i s access to an oven) and water at a lower temperature. 123 ( i i ) Observe the temperature of 50 ml. of water heated by a standard candle and 100 ml. of water heated by a s i m i l a r candle. (c) S p e c i f i c heat a c t i v i t i e s ( i ) P l a c e s i m i l a r s i z e d o b j e c t s made of d i f f e r e n t substances (wood, metals, sugar, g l a s s , etc.) i n a t r a y over a hot p l a t e f o r a short w h i l e and then observe the r e s u l t s when they are placed on a b l o c k of wax. IV. R e s t r u c t u r i n g Maneuvers (a) Group D i s c u s s i o n s ( i ) Discuss unexpected r e s u l t s from the anomaly maneuvers and encourage them to t h i n k of p o s s i b l e explanations. ( i i ) Encourage i n d i v i d u a l s o r groups w i t h d i f f e r e n t b e l i e f s to explore them more f u l l y e i t h e r i n d i s c u s s i o n or f u r t h e r i n v e s t i g a t i o n s . (b) Teacher I n t e r v e n t i o n ( i ) The teacher i n t r o d u c e s a competing viewpoint ( p r o v i d i n g i t i s c l e a r that the students are under no o b l i g a t i o n to accept i t on the b a s i s of a u t h o r i t y ) . ( i i ) The teacher attempts to p o i n t out i n c o n s i s t e n c i e s between student;s ideas and the a c t u a l o b s e r v a t i o n s . 124 a c t i v i t i e s and d i s c u s s i o n s . However, the i n d i v i d u a l p r o f i l e c ould a l s o be used by the teacher i n a d i a g n o s t i c c a p a c i t y . For example, the p r o f i l e i n F i g u r e 6-1 i n d i c a t e s some very strong b e l i e f s i n those statements which were e a r l i e r r e f e r r e d to as "common-sense" ideas about heat (notably numbers 4, 7, 11, 15, and 18). S e v e r a l of these might be used as the b a s i s f o r a s e r i e s of i n v e s t i g a t i o n s to be undertaken by t h i s student and others who responded i n a s i m i l a r manner. Taking statement 7 as an example, the expressed b e l i e f i s that s o f t t h i n g s melt more r e a d i l y than hard t h i n g s . On the b a s i s of t h i s b e l i e f , a student could then examine the m e l t i n g behavior of a number of hard and s o f t o b j e c t s (an e x p e r i e n t i a l maneuver). The teacher might a l s o encourage the students to t h i n k about why s o f t t h i n g s appear to melt more r e a d i l y — the f i r s t steps toward the p o s s i b l e f o r m u l a t i o n of a p o s i t i o n r e g a r d i n g the r e l a t i o n s h i p between heat and matter. An anomaly maneuver might be int r o d u c e d by the teacher by exposing the student to some s o f t m a t e r i a l s that do not melt e a s i l y ( f o r example, substances l i k e styrofoam, p u t t y , play-dough, etc.) and some hard substamces that do melt e a s i l y ( l i k e i c e , some p l a s t i c s , e t c . ) . Thus i t can be seen that the i n d i v i d u a l statements on the C.P.I, can a l s o be used i n a d i a g n o s t i c c a p a c i t y . P r o v i d i n g that the teacher has s u f f i c i e n t time, those students who i n d i c a t e d s t r o n g b e l i e f s about some of the common-sense ideas could be engaged i n i n v e s t i g a t i o n u s i n g those ideas expressed about heat as a s t a r t i n g p o i n t . Im summary, then, u s i n g e i t h e r the s p e c i f i c statements from the C.P.I, as the p o i n t of departure, or the maneuvers contained i n a teacher's guidebook, the teacher's r o l e i s that of g e t t i n g the students 125 to t h i n k more c r i t i c a l l y about the b e l i e f s that they h o l d . And i n so doing, the students should a t t a i n a more powerful way of l o o k i n g at heat and temperature phenomena. 126 NOTES FOR CHAPTER SIX 1. While the d i s c u s s i o n i n t h i s s e c t i o n i s r e s t r i c t e d to the r e s u l t s obtained from t h i s study, one could a l s o consider the i m p l i c a t i o n s of using the body of l i t e r a t u r e on s t r u c t u r a l growth i n an i n t e r p r e t i v e sense. That i s , the se t s of b e l i e f s i d e n t i f i e d i n the study can be con- strued as one type of s t r u c t u r e and so ought to be subject to the same types of c o n d i t i o n s employed by others i n seeking to promote s t r u c t u r a l change. See, f o r example, Kuhn (1963); Palmer (1964); S i e g e l (1969); and F u r t h and Wachs (1974). 2. That t h i s d i s t i n c t i o n i s most d i f f i c u l t to i n t u i t d i r e c t l y from the phenomena can be seen from i t s r a t h e r l a t e h i s t o r i c a l appearance. Black i s g e n e r a l l y given c r e d i t f o r being the f i r s t to c l e a r l y draw the d i s - t i n c t i o n between the i n t e n s i t y of the c a l o r i c f l u i d surrounding the p a r t i c l e s of matter (a measure of i t s temperature) and the t o t a l amount of c a l o r i c possessed by a body (a measure of i t s h e a t ) . This conception was f i r s t p u b lished as p a r t of a s e r i e s of l e c t u r e s by Black i n 1803 which i n d i c a t e s that the d i s t i n c t i o n had eluded many who were very f a m i l i a r w i t h heat and temperature phenomena d u r i n g a p e r i o d of over one hundred years. 3. This procedure might w e l l resemble the "teaching moves" des c r i b e d by Smith et a l . (1961) f o r teaching a p a r t i c u l a r concept. 4. The Science Curriculum Improvement Study f i r s t i n t roduces the c h i l - dren to the t o p i c by engaging them i n s e v e r a l a c t i v i t i e s w i t h heat phenomena. However, the teacher then " i n v e n t s " the terms "temperature" and "thermal energy" (heat) i n order to a s s i s t the c h i l d r e n to under- stand and i n t e r p r e t these phenomena. 5. The a c t u a l matching procedure i s probably accomplished most e a s i l y by p l o t t i n g the i n d i v i d u a l ' s scores on a transparent sheet and then l a y i n g t h i s over the Model Conceptual P r o f i l e s f o r a d i r e c t comparison. 127 CHAPTER SEVEN CONCLUSIONS AND RECOMMENDATIONS 7.00 Overview of the Study The three s p e c i f i c problems addressed i n t h i s study were di s c u s s e d i n Chapter One. I n v e s t i g a t i o n s of these problems corresponded to three d i s t i n c t phases of the study. Phase One sought to i d e n t i f y and document the range of s u b s t a n t i v e b e l i e f s about heat and temperature h e l d by c h i l d r e n . The procedures used to i n v e s t i g a t e t h i s problem c o n s i s t e d of i n t e r v i e w s w i t h c h i l d r e n ranging i n age from 6 to 13 years. Only the set of ten formal i n t e r v i e w s , conducted w i t h 12 y e a r - o l d s , were reported i n Chapter Three. The i n f o r m a t i o n obtained from the i n t e r v i e w data formed the b a s i s f o r the i n v e s t i g a t i o n s of the next two phases. Phase Two attempted to e s t a b l i s h some evidence f o r the e x i s t e n c e of a s e t of r e l a t i o n s h i p s among the b e l i e f s about heat and temperature he l d by c h i l d r e n . To t h i s end a measuring instrument was constructed r e f l e c t i n g b e l i e f s about heat obtained from: (1) the i n t e r v i e w d a t a , (2) a cur r e n t s c i e n t i f i c theory of heat (the k i n e t i c t h e o r y ) , and (3) an e a r l i e r s c i e n t i f i c theory (the c a l o r i c t h e o r y ) . The instrument was administered to twelve c l a s s e s of students: f o u r c l a s s e s i n grades 5, 7, and 9 r e s p e c t i v e l y . An a n a l y s i s of the data c o l l e c t e d w i t h the instrument r e s u l t e d i n the i d e n t i f i c a t i o n of s e v e r a l t y p i c a l b e l i e f p a t t e r n s , which were l a b e l l e d Model Conceptual P r o f i l e s . These P r o f i l e s , d i s c ussed i n Chapter Four and F i v e , served as one component of the e m p i r i c a l foun- d a t i o n used i n the l a s t phase of the study. 128 Chapter S i x addressed the t h i r d s p e c i f i c problem — the a p p l i c a - t i o n of the study to an e d u c a t i o n a l s e t t i n g . Two ways i n which the r e s u l t s could be used to i n c r e a s e the e f f e c t i v e n e s s of the classroom teacher were discussed and i l l u s t r a t e d . The chapter concluded w i t h the p r e s e n t a t i o n of a b r i e f o u t l i n e of a p o s s i b l e s e t of t e a c h i n g maneuvers th a t were keyed to the Model Conceptual P r o f i l e s . Thus the techniques developed i n Phase Two of the study were shown to be of po- t e n t i a l d i a g n o s t i c value to the classroom teacher. 7.10 Conclusions of the Study A number of t e n t a t i v e c o n c l u s i o n s can be o f f e r e d i n response to the three problems that have provided d i r e c t i o n f o r the study. These c o n c l u s i o n s , however, can best be i n t e r p r e t e d as t e n t a t i v e hypotheses suggesting f u r t h e r e m p i r i c a l work, r a t h e r than f i r m answers to the questions posed i n Chapter One. The i n t e n t of Phase One was to i d e n t i f y the s u b s t a n t i v e b e l i e f s about heat and temperature h e l d by c h i l d r e n . I t was argued t h a t the methodology most ap p r o p r i a t e f o r t h i s task was a s e r i e s of open-ended i n t e r v i e w s . From the a n a l y s i s of the i n t e r v i e w data s e v e r a l c o n c l u - sions appear to be j u s t i f i e d . (1) Most young c h i l d r e n between the ages of s i x and twelve possess a body of b e l i e f s about heat and temperature that can be i d e n t i f i e d i n an i n t e r - view s i t u a t i o n . T h i s was, of course, an assumption t h a t was made by the author p r i o r to the i n v e s t i g a t i o n . And w h i l e the s u b j e c t s i n t e r v i e w e d v a r i e d g r e a t l y i n terms of knowledge and t h e i r a b i l i t y to express that know- ledge, i t can be s a i d that the u n s t r u c t u r e d i n t e r v i e w technique i s a 129 f r u i t f u l method f o r i d e n t i f y i n g c h i l d r e n ' s i n t u i t i o n s about p h y s i c a l phenomena. The remaining two co n c l u s i o n s f o r Phase One represent an attempt to d i s t i l l from the i n t e r v i e w data c l u s t e r s of b e l i e f s about heat and temperature t h a t appeared to be shared by most of those c h i l d r e n i n - terviewed. (2) Heat was thought to be a type of substance which possessed i t s own unique p r o p e r t i e s . T h i s substance view could be i d e n t i f i e d i n many of the i n t e r v i e w s . Many of the c h i l d r e n sought to d e s c r i b e heat i n terms of fumes, r a y s , waves, or used an analogy — something l i k e a i r . In most in s t a n c e s heat was considered to be a mobile or a c t i v e agent capable of independent movement through space and a l s o able to penetrate most o b j e c t s . A l - though the mechanism f o r p e n e t r a t i o n i s not at a l l c l e a r , i t may be that a i r spaces i n o b j e c t s (which were f r e q u e n t l y mentioned) provided a type of passageway. B e l i e f s about the potency of heat were r e v e a l e d when some c h i l d r e n described i t s a b i l i t y to "break apart c e l l s " of c e r t a i n o b j e c t s and so cause them to melt. The next prominent set of b e l i e f s centered around t h e i r conception of temperature. The c o n c l u s i o n might be expressed as: (3) Temperature i s a measure of the hotness of an o b j e c t and i s a r e s u l t of the amount of heat that i s added to i t . A l l o f the c h i l d r e n i n t e r v i e w e d were f a m i l i a r w i t h the term, "temperature", and were aware of the r e l a t i o n s h i p between the hotness of an o b j e c t and i t s temperature. However, t h i s p h y s i c a l i n t u i t i o n may a l s o be r e s p o n s i b l e f o r the set of b e l i e f s surrounding the change of 130 temperature i n o b j e c t s . For example, s e v e r a l of the c h i l d r e n claimed that the temperature of water was lowered when some of the water was poured out. A l s o when hot and c o l d water were mixed the f i n a l tempera- ture of the mixture was determined by many c h i l d r e n u s i n g a simple a d d i t i o n or s u b t r a c t i o n o p e r a t i o n of the two i n i t i a l temperatures. Both of the above can be understood i n terms of a view that suggests the temperature of an o b j e c t i s determined by the amount of heat pos- sessed by the o b j e c t . As was i l l u s t r a t e d i n Chapter S i x , the i n t u i t i o n s and b e l i e f s that c o n s t i t u t e d these two broad areas may be l a r g e l y r e s p o n s i b l e f o r the d i f f i c u l t i e s encountered by many c h i l d r e n when they are introduced to the k i n e t i c theory of heat i n a scho o l s e t t i n g . In Phase Two the emphasis s h i f t e d towards i d e n t i f y i n g , a p a t t e r n of r e l a t i o n s h i p s or a s t r u c t u r e i n c h i l d r e n ' s b e l i e f s . To accomplish t h i s end, an instrument was cons t r u c t e d and data were c o l l e c t e d and analyzed f o r 276 s u b j e c t s . The f i r s t important r e s u l t of t h i s a n a l y s i s i n d i c a t e d t h a t : (4) The s u b j e c t s were able to d i s t i n g u i s h between the statements r e p r e s e n t i n g each of the three d i f f e r e n t p e r s p e c t i v e s of heat. This r e s u l t was obtained by performing a p r i n c i p a l component analys on the b e l i e f r a t i n g s of statements i n the C.P.I. The three i n t e r - p r e t a b l e components obtained from the a n a l y s i s indeed corresponded to the heat P e r s p e c t i v e s t h a t were o r i g i n a l l y used to design the statements, g i v i n g some support to the c o n s t r u c t v a l i d i t y of the instrument. A second a n a l y t i c a l procedure was employed to determine i f there were any s i m i l a r i t y i n the response p a t t e r n s among the s u b j e c t s . This 131 p r o f i l e a n a l y s i s y i e l d e d the f o l l o w i n g r e s u l t : (5) Three d i s t i n c t p a t t e r n s of b e l i e f - s c o r e s were obtained f o r the s u b j e c t s . These p a t t e r n s were i n t e r p r e t e d i n terms of d i f f e r e n t l e v e l s of understanding of heat phenomena. On the b a s i s of the r e s u l t s summarized i n c o n c l u s i o n s (4) and (5) i t was i n f e r r e d that a unique set of s t r u c t u r a l r e l a t i o n s h i p s among c h i l d r e n ' s b e l i e f s c ould be determined u s i n g the a n a l y t i c a l procedures o u t l i n e d e a r l i e r . F u r t h e r , i t was reasoned that these r e l a t i o n s h i p s should form the nucleus of an e f f o r t to develop c u r r i c u l a r m a t e r i a l s or teaching s t r a t e g i e s i n the area of heat and temperature. The l a s t phase of the study was s p e c u l a t i v e i n nature and was d i r e c t e d towards o u t l i n i n g the p o t e n t i a l a p p l i c a t i o n s to an e d u c a t i o n a l s e t t i n g . Two d i f f e r e n t ways of u s i n g the r e s u l t s were i l l u s t r a t e d . A l - though no e m p i r i c a l work was done i n t h i s phase, i t was concluded t h a t : (6) The knowledge obtained from the study c o u l d be used to develop a set of teaching s t r a t e g i e s t h a t c o u l d have a p p l i c a t i o n i n the classroom. These s i x c o n c l u s i o n s , then, represent condensed statements of the c o n t r i b u t i o n s made by the present study. Although most of these r e f e r to s u b s t a n t i v e r e s u l t s , the u n d e r l y i n g methodological procedures are a l s o noteworthy. That i s , the open-ended i n t e r v i e w procedures, the develop- ment of the s e m a n t i c - d i f f e r e n t i a l classroom instrument and the a n a l y t i c techniques used to generate the Model Conceptual P r o f i l e s a l l appear to be u s e f u l ways of c o l l e c t i n g and p r o c e s s i n g i n f o r m a t i o n on c h i l d r e n ' s b e l i e f s and i n t u i t i o n s about n a t u r a l phenomena. 7.20 Recommendations f o r F u r t h e r Research Given the e x p l o r a t o r y nature of the study s e v e r a l p o t e n t i a l f o l l o w - 132 up studies might be suggested. This section includes an outline of the broad problems to be addressed and contains brief comments on some of the issues accompanying each of these problem areas. The recommended studies can be thought of as f a l l i n g along a type of continuum defined at one end by a type of study which i s directed towards elucidating the theoretical issues raised by this study and at the other end by a study which i s aimed at evaluating the effects of the study upon class- room practice. 1 Some questions worthy of further investigation are l i s t e d below, beginning at the elucidation end of the continuum and proceeding toward the evaluation end. (1) Can the genesis and subsequent development of the underlying conceptual structures be more clearly identified and mapped out? (2) How valid i s the hypothesized Children's View- point of heat? Is the substance notion of heat as pervasive as suggested by the present study? (3) Can more evidence be obtained regarding the hypothesized developmental trend from a common- sense level of understanding heat phenomena to one which i s more abstract in nature? (4) Are there any significant differences i n heat viewpoints that can be attributed to specific variables such as: age, sex, geographical location, etc.? (5) How might the existing methodology be applied to an investigation of children's ideas about other relevant topics? (6) Can a set of appropriate teaching strategies be created to match the Model Conceptual Profiles? (7) Are these teaching strategies effective in bringing about the desired aims of the program? 133 Having set out t h i s abbreviated l i s t , i t remains to provide a l i t t l e more substance f o r at l e a s t some of these p r o s p e c t i v e s t u d i e s . Because the procedures employed i n t h i s study ( s p e c i f i c a l l y the open- ended i n t e r v i e w technique along w i t h the development of the C.P.I, and methods of a n a l y s i s ) were judged to be s a t i s f a c t o r y by the author, i t i s recommended that some combination of these procedures be s e r i o u s l y considered i n any follow-up s t u d i e s . The f i r s t two questions i n the above l i s t are mainly concerned w i t h g e n e r a l i z i n g the r e s u l t s of the present study to a l a r g e r sample of s u b j e c t s . Hence, i t i s suggested that a type of open-ended i n t e r - view technique be used w i t h a much l a r g e r sample of s u b j e c t s , ranging from 6 years to 16 years of age. Some of the tasks used i n the present study could be u t i l i z e d , however, w i t h the suggested age range some work would be r e q u i r e d to modify the i n t e r v i e w so that i t would be ap- p r o p r i a t e f o r both the younger and o l d e r s u b j e c t s . Since the research hypotheses are a l r e a d y d e f i n e d to some e x t e n t , there would be no need to engage i n the e x t e n s i v e p i l o t work de s c r i b e d i n t h i s study. Question (4) could a l s o be approached i n a s i m i l a r manner i f c a r e f u l a t t e n t i o n were p a i d to the sampling procedures used to a s c e r t a i n the causes of any observed d i f f e r e n c e s i n response p a t t e r n s . That i s , i f i t were being hypothesized that boys have a more a b s t r a c t view of heat than g i r l s , then one would have to be c a r e f u l to match the samples on other v a r i a b l e s that might a f f e c t the r e s u l t s ( f o r example, age, school achievement, i n t e l l i g e n c e , i n t e r e s t , e t c . ) . On the other hand, these two questions could a l s o be addressed 134 using the C.P.I., or some a l t e r a t i o n of i t . E x t ensive use of t h i s type of classroom instrument would a l s o a l l o w a s e t of norms to be e s t a b l i s h e d and so produce a more r e l i a b l e and v a l i d instrument. As bef o r e , the sampling problem would be very important i f one were a t - tempting to t e s t c e r t a i n hypothesized r e l a t i o n s . The l a s t two problems are d i r e c t e d at an implementation of the e x i s t i n g r e s u l t s i n t o a classroom s i t u a t i o n , and follow-up s t u d i e s eva- l u a t i n g the e f f e c t s of such a program. The r e s u l t s reported i n t h i s d i s s e r t a t i o n are b e l i e v e d by the author to be of s u f f i c i e n t v a l i d i t y and i n t e r e s t to warrant the i n i t i a t i o n of an i n s t r u c t i o n a l program designed to t r a n s l a t e the procedures o u t l i n e d i n Chapter S i x i n t o a form s u i t a b l e f o r use by the classroom teacher. While i t would ob- v i o u s l y be d e s i r a b l e to base the program upon a w e l l - e s t a b l i s h e d t h e o r e t i c a l b a s i s , i t i s argued here that work on both ends ~ the t h e o r e t i c a l and the p r a c t i c a l — could take p l a c e u s i n g the present r e s u l t s as a s t a r t i n g p o i n t . I f and when a l t e r a t i o n s are made i n the t h e o r e t i c a l p e r s p e c t i v e , these could be i n c o r p o r a t e d i n t o the p r a c t i c a l program. The work i n developing a s u i t a b l e i n s t r u c t i o n a l program would e n t a i l the c r e a t i o n of a set of teaching maneuvers that i s c r o s s - referenced to p a r t i c u l a r l e v e l s of understanding, or Model Conceptual P r o f i l e s . Suggestions were made i n S e c t i o n 6.32 as to i s s u e s that might be i n v o l v e d i n a task of t h i s nature. Furthermore, these teaching maneuvers must conform to the u s u a l c o n s t r a i n t s upon the classroom t e a - cher, such as time and equipment. Once the development and implementation of an a p p r o p r i a t e 135 i n s t r u c t i o n a l program i s accomplished, the l a s t question becomes more important. How does one determine the valu e or e f f e c t i v e n e s s of the program? Very l i t t l e of t h i s type of e v a l u a t i v e research i s a c t u a l l y c a r r i e d out i n e d u c a t i o n a l research because i t i s so d i f f i c u l t to d e f i n e and c o n t r o l the r e l e v a n t v a r i a b l e s . The author's o p i n i o n i s t h a t i t i s e x a c t l y t h i s k i n d of research that has the g r e a t e s t p o t e n t i a l f o r making a s i g n i f i c a n t c o n t r i b u t i o n to classroom p r a c t i c e and to our understanding of how the c h i l d a c q u i r e s i n c r e a s i n g l y complex knowledge of h i s p h y s i c a l environment. On a concluding note, i t would seem q u i t e obvious t h a t i f the recommended program o u t l i n e d i n t h i s d i s s e r t a t i o n , matching i n s t r u c t i o n a l maneuvers to the d i a g n o s i s of the c h i l d ' s understanding of heat phenomena, proves to be s u c c e s s f u l then the b a s i c methodological techniques should a l s o be a p p l i e d to other areas of i n t e r e s t i n the c u r r i c u l u m (question 5 above). I n t h i s way a catalogue c o u l d be assembled which would serve as a type of i n s t r u c t i o n a l resource f o r the teacher. This catalogue might c o n t a i n i n f o r m a t i o n on t y p i c a l b e l i e f s h e l d by c h i l d r e n a t d i f - f e r e n t ages (or l e v e l s ) along w i t h l i s t s of suggested a c t i v i t i e s . The a c t i v i t i e s might take the form of some predetermined or e m p i r i c a l l y e s t a b l i s h e d teaching s t r a t e g y designed to achieve a p a r t i c u l a r aim. A l t e r n a t i v e l y , these a c t i v i t i e s c ould a l s o be simply c a t e g o r i z e d ac- cording to the i n t e r e s t s and ideas h e l d by c h i l d r e n thus a l l o w i n g the teacher, or the student, to make the d e c i s i o n regarding the usage and the sequence of the a c t i v i t i e s . 136 NOTE FOR CHAPTER SEVEN 1. For a f u r t h e r d e s c r i p t i o n of the d i s t i n c t i o n between e l u c i d a t o r y and e v a l u a t i v e types of research s t u d i e s , see Glass (1971). i 137 BIBLIOGRAPHY Anderson, R. C h i l d r e n ' s A b i l i t y to Formulate Mental Models to E x p l a i n N a t u r a l Phenomena. Paper presented at the annual meeting of the N a t i o n a l A s s o c i a t i o n ' f o r Research i n Science Teaching, 1965. 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A n a l y s i s of Frameworks i n Young C h i l d r e n . Unpublished paper, U n i v e r s i t y of I l l i n o i s , 1970. Witz, K. and E a s l e y , J . C o g n i t i v e Deep S t r u c t u r e and Science Teaching. Paper presented at a conference on "Operations and D i d a c t i c s " , at Centre de recherche, U n i v e r s i t y of Quebec, Mo n t r e a l , 1971. 142 APPENDIX A A T r a n s c r i p t of Ron's I n t e r v i e w Age: 12 years 8 months Notes: (1) E = experimentor S = subj e c t (2) ( ) = an e x p l a n a t i o n of some non-verbal a c t i o n judged to be important to the i n v e r v i e w . (3) For a d e s c r i p t i o n and/or p i c t u r e of the m a t e r i a l s used i n each of the tasks see Appendix B. 143 Ron's In t e r v i e w (S was brought i n t o the i n t e r v i e w room and the f i r s t few minutes were spent making him comfortable and answering any questions that he posed about the room and the microphones. He was then shown the l i q u i d expansion apparatus used i n the f i r s t task.) Task Number One S: What's t h i s ? E: I don't know. What do you suppose that i s ? S: A co l o r e d wire? ( R e f e r r i n g to the red l i q u i d i n the stem) E: Okay, i t might be a c o l o r e d w i r e . What do you suppose i t looks l i k e ? S: This i s the temperature here i n s ' t i t ? No. (S p o i n t s to the top of the red l i q u i d i n the stem) E: What do you mean i t ' s a temperature? S: Well what's that there? That pink l i n e can you see i t ? Is that the water i n there? E: Do you suppose there's anyway th a t we could f i n d out? S: Take i t o f f . E: That's one way, yes. I was going to ask you a qu e s t i o n about t h a t . Have you ever seen anything t h a t looks l i k e that before? S: This? No, w e l l a thermometer. E: You t h i n k i t looks l i k e a thermometer? What does a thermometer do? S: Measures temperature. E: How? S: Well the temperature o u t s i d e and i n s i d e a room. E: Can i t t e l l you the temperature of anything? S: I t h i n k so, yes. E: What I was going to ask you, do you t h i n k you could maybe get that l i q u i d to go down, only by touching t h i s bottom p a r t here. J u s t the g l a s s . S: Can you heat i t or anything? E: Sure, do you t h i n k that might make i t go down? S: I thought that would make i t go up. When you heat something does i t expand or what? E: L i k e what d i d you have i n mind? 144 L i k e an i c e cube. I f you melt i t w i l l i t expand or go smaller? L i k e say I have a handfu l of i c e and you l e t i t melt. W i l l the water be bigger than the i c e was? I don't know. I've never t r i e d t h a t . How do you suppose we c o u l d f i n d out? Get a pyrex, put i n a t h i n g f u l l of i c e and melt i t . So we have i c e i n a g l a s s l i k e t h a t and then what? And then melt i t . And then what would happen? And see i f , I know, i t goes e i t h e r up or down. I can't remember though. Say I have that much i c e (S p o i n t s to a spot h a l f way up on a beaker s i t t i n g on the t a b l e ) and when i t m e l t s , whether i t w i l l l o s e or whatever. Or t h i s might be at a c e r t a i n tem- perature i t might go up that h i g h , l i k e i f i t was put i n the f r i d g e or anything, not long enough to f r e e z e , i t might go f a r - ther down. I don't r e a l l y know what th a t i s . We have some water here. Should we t r y p u t t i n g i t i n some water and see what happens? Can you t e l l me anything about t h a t water? What about the temperature? Co o l , not hot. Do you t h i n k that the l i q u i d would go up or do you t h i n k i t would (S i n t e r r u p t s ) This i s warmer. (the apparatus) Is th a t water, t h a t ' s l i q u i d i n there i s n ' t i t ? I'm not r e a l l y sure what i t i s . We can c a l l i t red l i q u i d . This is warmer, i t i s n ' t hot and i t i s n ' t t h i s temperature (S p o i n t s to the beaker of water) This i s q u i t e c o o l . So what do you suppose w i l l happen i f we put that (apparatus) i n there? (beaker of water) Th i s (S p o i n t s to red l i q u i d ) might go down? You t h i n k i t might go down? I t i s . I t ' s going down. How f a r down do you t h i n k i t w i l l go? 145 S: I t ' s stopped now. I t h i n k . No i t hasn't stopped. I t h i n k i t w i l l go about that f a r . E: That f a r ? S: Yes, h a l f an i n c h or quarter of an i n c h . The water i s g e t t i n g warmer. E: Do you want to mark where you t h i n k i t w i l l go? S: Oh no, i t ' s going down a long way. E: Do you want to r e v i s e your estimate? S: Maybe i t w i l l go as f a r as that i s to there . (S p o i n t s to the b o t - tom of the stem) E:. To where? S: There, where the water i s to there, but I don't t h i n k so. E: What do you suppose i s happening to the water? You mentioned some- t h i n g about the water e a r l i e r . S: I t ' s g e t t i n g warmer. E: Why i s i t g e t t i n g warmer? S: Because of the heat of the, not the heat but, j u s t because of the other water around i t i n t h i s g l a s s here. E: What about the g l a s s , u n f o r t u n a t e l y we've got two g l a s s e s and two s e t s of l i q u i d here so w e ' l l have to t r y s o r t i n g that out. S h a l l we take i t out f o r a second? And t h i s way you can p o i n t to the one that you are r e f e r r i n g t o . You thought that t h i s water ( i n the beaker) was g e t t i n g warmer? S: Yes. E: And why was i t g e t t i n g warmer again now? S: Because of t h i s water. (S p o i n t s to apparatus) E: Because of the water i n the g l a s s t h e r e . S: Hey, now t h i s ( l i q u i d i n the stem) w i l l go up, r i g h t ? E: You t h i n k that w i l l go up? Why? S: Because i t w i l l get warm. I mean t h i s , i t doesn't f e e l any c o l d e r than i t already was. I t would be ( i n a u d i b l e ) so I f i g u r e d i t would go up and maybe. You have hot water there don't you? E: Yes. S: We can put t h i s (the apparatus) i n hot water and see i f i t goes up. 146 You want to t r y p u t t i n g i t i n hot water. I'm very i n t e r e s t e d i n why you thought t h i s water was g e t t i n g warmer. And you were about to t e l l me. Cause when t h i s (apparatus) was i n that (beaker of water) the tem- perature of t h i s g l a s s would he a l i t t l e warmer than t h i s water, and so a l l t h i s water i n here would warm t h i s g l a s s and the warmth i n t h i s g l a s s would warm t h i s water. The warmth from the gl a s s ? L i k e i f you've got a b o i l i n g hot spoon and you put i n i n the water i t would go warm. J u s t l i k e on the beach you know when the t i d e goes out and the sun heats the sand and then the t i d e comes i n and the water's warmer because of the hot sun. Let's see, t h i s (a metal p l a t e ) i s n ' t q u i t e the same, but i t ' s something l i k e a spoon. And i f I put i t , do you know what t h i s i s ? Yes, i t ' s a hot p l a t e . Now i f I l e f t i t on there f o r a long time and i t got r e a l l y hot. We haven't got time to do that but l e t ' s j u s t say i t i s , then I take i t and I put i t i n here (a beaker of wat e r ) . I s that what you said? Then what's going to happen? This water w i l l get warmer. And how would i t get warmer? From the heat of t h a t . (the p l a t e ) From the heat of t h a t . Where does t h i s heat come from? The hot p l a t e And i t goes i n t o here i s that i t ? Yes. I t warms up and now when i t ' s warm i t goes i n t o there (the p l a t e ) and i t warms the water. How does the heat go from the hot p l a t e i n t o here? (the p l a t e ) W e l l , i t ' s attached. Yes, i t ' s touching i t . Yes i t ' s touching i t and I guess metal a t t r a c t s heat. Well what about when we put i n i n here, what happens? When we put i t i n the water? 147 S: The water a t t r a c t s the heat from t h a t . That cools down. Because the water i s a c o l d e r temperature. E: So the heat i s l e a v i n g t h i s ( p l a t e ) i s i t ? And going i n t o the water. What do you suppose heat looks l i k e ? S: You can see i t on some very hot days r i s i n g from the road s o r t of you know i n waves? I f you're d r i v i n g on the road. I t j u s t s o r t of looks l i k e fumes. E: So you t h i n k t h a t i s what goes on when you put t h i s (the p l a t e ) on the hot p l a t e . The heat goes from the hot p l a t e to there? S: I don't know how t h a t machine works but probably there's something warming the metal up, and then the metal. E: The top of the hot p l a t e you mean? S: Yes, the top warms t h a t . (the metal p l a t e ) E: Now you wanted to t r y the experiment d i d n ' t you? Do you t h i n k t h a t ' s (a beaker of hot water) f a i r l y hot or i s i t not very hot? S: I t ' s hot enough. E: Now what do you t h i n k i s going to happen? S: This (the apparatus) here s o r t o f , could I put my f i n g e r on t h e r e , put my hand around there w i t h my body heat to see i f i t r a i s e s . Hey i t ' s r a i s i n g . O.K. now I ' l l put i t i n here, (the c o l d water beaker) I t r a i s e d f o r a second, but now i t ' s going down g r a d u a l l y . E: Now what do you t h i n k ' s going to happen when you put i t i n here? (hot water) S: I t ' l l r a i s e . E: Do you t h i n k i t w i l l go very f a s t ? S: Yes. E: Why? S: Because of the heat i n the water. Cause i t went up f a i r l y f a s t j u s t w i t h the heat of my hand. I t h i n k i t would go a l l the way up to the top. E: You t h i n k i t would go a l l the way to the top? S: Yes. Unless t h i s doesn't, t h i s temperature here doesn't c o o l down tha t water. See i t could happen. 148 E: I'm not sure what you mean. S: The temperature of t h i s g l a s s (the apparatus) i s c o l d e r than the temperature of t h i s water here and so the temperature of t h i s g l a s s might c o o l down the water. E: How does i t do that? S: Well i t might w e ' l l see. E: When something c o o l s something e l s e down, what do you suppose happens? When we say that t h i s water cooled down t h i s (the apparatus) you s a i d . How does that happen? S: • I don't know. E: You were t a l k i n g something about the heat or when you put t h i s i n th e r e , i t cooled down. S: I know how i t warms up. E: How does i t warm up? S: I t o l d you. How i t c o o l s down, guess i t does the op p o s i t e . E: O.K. Let' s t r y t h i s experiment here and see what happens. S: I t dropped and then i t rose q u i t e f a s t . E: Boy, i s i t ever going f a s t . (5 second pause) Yes. Yes i t looks l i k e you're r i g h t . What's going to happen? S: I t ' s going to r a i s e to the top q u i t e f a s t and then i t w i l l come out. When that c o o l s down now, i t w i l l s t o p, maybe. That's what I think.. E: How long do you t h i n k i t w i l l take to c o o l down? S: I s that dyed water? No i t couldn't be dyed water could i t ? E: Why? S: Cause i t ' s got some chemical i n i t cause dyed water doesn't r i s e I don't t h i n k . Can I t a s t e i t ? E: W e l l j u s t a l i t t l e b i t . S h a l l we take i t out now. What do you t h i n k would happen i f we j u s t used o r d i n a r y water i n there? S: I don't t h i n k i t would do anything. I f i t got hot enough i t would s t a r t b ubbling and the water would r i s e . I f i t got hot enough i t would s t a r t b o i l i n g , then the water would r i s e up here. No i t wouldn't. You'd have t o , the hot a i r , or the steam would go up here and then you put a r e a l l y c o l d c l o t h or have t h i s tube bent 149 i n t o c o l d water and then when the steam h i t the c o l d water i t would go through the tube. I t would t u r n back i n t o water, and then we'd have i t i n t o the top of the j a r and there would be water going i n t o the j a r . Have you done that before? Yes we d i d i t i n a sc i e n c e r e p o r t , a sc i e n c e experiment. But i f we j u s t had o r d i n a r y water and put i n i n t h i s j a r of hot water, what do you t h i n k i t would do then? I don't t h i n k i t would do anything. What about i f we used m i l k ? I don't t h i n k i t would do anything I'm j u s t t r y i n g to t h i n k of some other l i q u i d that we might put i n there. What l i q u i d do you t h i n k would work? I f I knew what that was, I'd t e l l you. Why do you t h i n k t h a t works? Why do you suppose t h a t happens? What do you t h i n k i s happening there? I know! That could be j u s t p l a i n water. But the water i s g e t t i n g h o t t e r so i t r i s e s r i g h t . The more i t r i s e s , the more i t goes up. Now why does the water r i s e ? I know. I know th a t t h i n g t h a t I was t h i n k i n g of now. I f you had a g l a s s of water say that h i g h and f r o z e t h a t . The water would go down a b i t and when you melted i t , i t would go up to the same t h i n g . Remember I was t a l k i n g about that? So I know now. That's what I t h i n k . Would you l i k e to t r y e x p l a i n i n g that to me again. When i t gets h o t t e r , the water r i s e s and as i t r i s e s i t goes up the tube. Why does the water r i s e when i t gets hot? (5 second pause) What do you suppose water i s l i k e ? What i s i t made out of? Ice? I don't know, water. You t h i n k i c e i s made out of water? Yes, w e l l water i s made out of water. L i k e the clouds are made out of water going across the ocean. 150 : W e l l I was wondering, why when i t gets hot does i t r i s e ? : Why does i t r i s e when i t gets hot. I don't know. I t h i n k you t o l d me why i t gets hot. I'm s t i l l i n t e r e s t e d to know how the heat goes from t h i s water ( i n the beaker) i n t o that water, ( i n the l i q u i d expansion apparatus) : Through the g l a s s . I t j u s t warms the g l a s s and then the g l a s s warms t h a t . : Does i t go r i g h t through the g l a s s ? : No. Well i t warms the whole g l a s s up and then the g l a s s warms the water j u s t l i k e t h i s (a p a i r of tong s ) , i f you had t h i s hot i t would warm the water. : Now you s a i d the heat, there's heat i n here (E p i c k s up the tongs) and then when you put i t i n t h e r e , the heat leaves t h i s and goes i n t o the water. Does that mean th a t there's heat i n t h i s water? : Yes. That's d e f i n i t e l y c o o l e r than i t was, but maybe t h a t ' s j u s t because i t was s i t t i n g . : I f we use t h i s water i t ' s f a i r l y h o t . I s there heat i n t h a t water? : Yes. : And i f we put th a t (the apparatus) i n t o there (the w a t e r ) , what would happen to the heat? : I t would c o o l down. I f i t was o f f the hot p l a t e . : You put t h i s i n t o here and you say i t would c o o l down eh? What would the heat do? What would happen to the heat? : W e l l t h i s (the apparatus) would take some of the heat up. : So where would the heat go? : Into t h i s . (the apparatus) : How would i t do that? : By warming the g l a s s and the g l a s s warms the water, or whatever the substance i s i n there. : Is there heat down i n there? Would there be? : Yes. : Do you suppose the heat's got anything to do w i t h the water r i s i n g ? : The heat yes. Yes d e f i n i t e l y cause I hel d my hand there. 151 E: How do you suppose the heat makes i t r i s e ? S: I don't know. E: Yes tha t ' s a tough question cause I'm not r e a l l y s u r e . S: I couldn't even guess a t t h a t . E: You don't have any ideas . I'm i n t e r e s t e d i n any ideas that you may have at a l l . You can t h i n k about i t f o r awhile and we can go on and do some other th i n g s i f you want. Do you t h i n k you can t e l l me how hot t h i s water i s ? S: I t ' s q u i t e hot. I t h i n k we could use that as a thermometer. Because we could measure how f a s t i t would go up f o r a c e r t a i n heat. F i r s t we'd have to get a r e a l thermometer and t e s t the heat of t h i s water and then we put i n here and t e s t how f a s t i t would go up and then we'd get an i d e a . Then we'd have to have c o o l i n g water but i t would have to be warmer than t h i s f o r i t to go up and t e s t the heat of the water. Then put t h i s up and see how s l o w l y i t goes up and then we can j u s t get some d i f f e r e n t water t h a t has to be a l i t t l e h o t t e r than t h i s , put t h i s i n without no temperature or nothing and see how f a s t i t goes up and we could estimate i t and put the thermometer i n t o the water and see how c l o s e we are. Do you want to do that? E: U n f o r t u n a t e l y we probably need a stop watch wouldn't we? I ' l l t e l l you what, there's some other th i n g s t h a t I want to do, that I want to t a l k to you about and i f we have some time w e ' l l t r y t h a t . Now. That's (the metal p l a t e t h a t was r e s t i n g on the hot p l a t e ) f a i r l y hot now. Do you know what t h i s i s ? S: I t ' s s o r t of a hot p l a t e too. E: I t ' s asbestos a c t u a l l y . S: J u s t l i k e a t home, when you come i n w i t h the dinner on a hot p l a t e . E: Now what do you suppose i s going to happen i f I were to put t h i s on top of that p l a t e ? (E places hot metal p l a t e on asbestos pad and motions as i f to put the expansion apparatus on the hot metal p l a t e ) S: I t would r a i s e the l e v e l . F i r s t , l e t ' s c o o l t h i s down and get i t r i g h t down. ( R e f e r r i n g to the l e v e l of the l i q u i d i n the apparatus) E: I'm not going to a c t u a l l y put i t on cause I t h i n k i t might crack t h i s 152 i t ' s too hot. J u s t t e l l me what you t h i n k might happen. What about the temperature? S: This would go up q u i t e f a s t . E: And what about the temperature of t h i s water here? S: I t would heat. E: And what about t h a t , the temperature of the metal? S: I t would c o o l down because i t ' s g i v i n g some of i t ' s heat i n t o t h a t . E: So i t ' s the heat t h a t ' s doing i t , and i f we sat i t on there and l e f t i t on there f o r about 15 minutes what do you suppose would happen to the temperatures? S: They'd both c o o l down probably. This (the metal p l a t e ) would c o o l down anyway i f you j u s t l e f t i t there cause the heat i s going i n t o the a i r . E: J u s t disappears i n t o the a i r ? How do you suppose i t does.that? S: I t j u s t l e t s o f f the fumes I was t a l k i n g about l i k e heat was. Probably there's a l l s o r t s of fumes i n that metal that l e t s i t out g r a d u a l l y . E: Do you t h i n k that fumes go i n s i d e here (the apparatus) when i t heats up? S: Yes. How about j u s t l e a v i n g that f o r about 15 minutes and then w e ' l l see i f i t c o o l s down or not. Task Number Two E: Now I have t h i s hot water. You were going to t e l l me, you want to guess how hot that i s ? S: I don't know. About 180 degrees. Which i s b o i l i n g temperature again? E: For water I t h i n k i s 212 or something l i k e t h a t . S: Yes I t h i n k i t ' s about 180 or 160. E: Is there any way we could f i n d out? S: Get a thermometer. E: I j u s t happen to have one which i s very handy. Now you n o t i c e there's two s c a l e s on t h a t . S: Yes. T h i s i s the s c a l e we're l o o k i n g at r i g h t ? E: W e l l no you were t a l k i n g about the other s c a l e . Do you know what the name of that s c a l e i s ? S: No. E: That's c a l l e d a Fahrenheit s c a l e . 153 S: I t seems to be 145. E: W e l l you guessed 160 d i d n ' t you. That's p r e t t y c l o s e . Now what about t h i s one ( c o l d water) i n here? Do you want to guess f i r s t ? S: I'd say 50 to 70 degrees. E: You're g i v i n g y o u r s e l f a l i t t l e b i t of range t h i s time. S: I t ' s stopped now. I'm t a k i n g the temperatures from a p o o l . You know that a pool's heated to 80 degrees. I f e e l the water i n the pool and f e e l t h i s . E: Yes i t ' s about 60. O.K. and what was t h i s 145? S: I t ' s probably about 140 now. I t ' s c o o l i n g down (S measures the temperature of the hot water again) E: W e l l i t looks l i k e you're r i g h t . You must have s t u d i e d temperatures q u i t e a b i t b e f o r e . O.K. l e t ' s say i t ' s 140. Now I want you to t e l l me what the temperature of that w i l l be, t h i s water. (E pours a s m a l l amount of hot water out i n t o another s m a l l beaker) Without touching i t (as S s t a r t e d to put h i s hand i n t o the water) S: 100 to 120. E: And t h i s one? (S pours more hot water i n t o a second s m a l l beaker — about twice as much as i n the f i r s t s m a l l beaker) S: 130. E: Why do you t h i n k that one i s higher than that one? S: Cause there's more i n i t . E: And what about t h i s water? (the hot water i n the o r i g i n a l l a r g e c o n t a i n e r ) S: That's 140. There's more of t h a t . E: How d i d that water go from 140 to 120? (the water i n the f i r s t s m a l l beaker) S: Because the g l a s s i s c o o l e r . E: Have you ever seen anything l i k e that before? (E b r i n g s out the two chamber mixing box) S: No. E: Do you want to take a look at i t ? S: Does t h i s r i s e ? (S p o i n t s to the b a r r i e r i n the box) 154 E: I t ' s j u s t a l i t t l e t i g h t . What we're going to do, I'm going to pour some of t h i s water t h a t was 140 i n t o there and pour an equal amount i n t o that s i d e . And that was what — 60 was i t ? I t i s equal, about the same? Now what do you t h i n k the temperature of t h i s water would be r i g h t now? S: Did you pour i t from the b i g g l a s s ? O.K. 110. E: And t h i s water would be? S: That was 60 r i g h t ? 70. E: Why do you t h i n k 70? E: Cause t h i s g l a s s (the beaker) here would probably be the same tempe- r a t u r e and t h i s g l a s s (S p o i n t s to the mixing box) would be warmer. Therefore i t would warm the water a b i t . E: This g l a s s (the beaker) would be the same temperature as? S: The water, and t h i s (the mixing box) would probably be room tempe- r a t u r e or probably warmer than t h a t . E: How l e t ' s say th a t we l e t t h i s s i t f o r about ten minutes what do you t h i n k , would t h i s (E p o i n t s to the hot water si d e ) temperature be the same? S: No. E: What would i t be? S: Probably about 80 to 90 degrees. E: And t h i s temperature? (E p o i n t s to the c o l d s i d e ) S: Around 80 degrees, around there. E: About the same? Why do you suppose i t would be the same? S: Because they would go to. room temperature? E: You thought t h i s would be 80 or 90 and you.thought t h i s would be about 70 or 80. Would they go higher than room temperature? S: No. I don't t h i n k so. E: So you t h i n k i t would be 70 more than 80. S: Yes. E: Why d i d you t h i n k i t might be 80? S: Well i t might be a l i t t l e warmer because of the g l a s s . E: Do you t h i n k i t makes any d i f f e r e n c e having that b a r r i e r there? Do you t h i n k any heat w i l l go? 155 W e l l yes t h a t ' s why. I t h i n k t h e y ' l l be the same degrees. No I don't want to i n f l u e n c e you, but why do you t h i n k t h e y ' l l be about the same? Because they might j u s t , they're almost r i g h t together now. I t i s almost as i f you mixed them w i t h that b a r r i e r . What do you t h i n k t h a t b a r r i e r does? I t j u s t takes the hot water i n t o the c o l d water j u s t l i k e I was t a l k i n g about b e f o r e . I t takes the hot water i n t o the c o l d water? W e l l i t takes the heat, the c o l d heat i n t o the warm heat. So i s some heat c o l d and some heat warm? Urn, yes. How do you suppose i t would do that? Does i t go through that? (E p o i n t s to the b a r r i e r ) Yes, unless t h i s i s a s p e c i a l g l a s s . No I t h i n k i t ' s j u s t made out of green m a t e r i a l so i t would look d i f f e r e n t l y . L e t ' s j u s t pretend here f o r a minute that we have, have you ever seen a microscope before? Yes. L e t ' s say we had a r e a l powerful microscope and suppose that we could look a t the i n s i d e of that b a r r i e r . What might i t look l i k e i n s i d e ? Do you suppose t h a t you could draw f o r me on the blackboard how you t h i n k that the, when you say the c o l d heat would go t h i s way and the warm heat would go the other way. How might t h a t look? Do you t h i n k you might be able to do something l i k e t hat f o r me? Yes. I know e x a c t l y how i t would look. Here's the b a r r i e r and i n s i d e i s s o r t of bubbles l i k e t h a t , a i r bubbles, s m a l l s m a l l , s m a l l a i r bubbles. (S draws the f o l l o w i n g diagram on the blackboard) °D 0 j y tt ft. <• v vC ' > g*V>V>U t> & " t 6 C v pP *7>0 Hot s; <w 156 E: This i s i n s i d e the b a r r i e r ? Which i s the c o l d water and which i s the hot water? S: This i s the c o l d water. E: And t h i s i s the hot. So, i n s i d e the b a r r i e r there's t i n y a i r bubbles. You t h i n k you could see those? How do you suppose the, how does the c o l d heat and the warm heat go through there? S: W e l l t h i s heat (S p o i n t s to hot sid e ) heats the — I ' l l draw some bubbles down here too (at the bottom of the b a r r i e r ) . T h i s hot water heats t h i s (the b a r r i e r ) and i t t r a v e l s through here. And t h i s c o l d water c o o l s t h i s (the b a r r i e r ) and i t t r a v e l s through here and i t j u s t meets and then t h i s would be a l l the same tempera- t u r e , t h i s b a r r i e r . E: I s t h i s the c o l d water t h a t ' s t r a v e l l i n g through or i s i t the heat? S: I t ' s the heat. E: What do you suppose the, what happens to the a i r bubbles? S: I don't know. I guess nothing. Unless the heat, l i k e there might be hot a i r i n t h i s one and c o l d a i r i n t h i s one. (S p o i n t s to d i f f e r e n t bubbles i n the diagram) I know. Cold heat t r a v e l s f a s t e r than hot heat, r i g h t ? I t ' s more powerful, because when you t u r n on the tap a t the same speed, say you have two n o z z l e s , you t u r n on both taps and you put i n the plug i n the s i n k . Then you have them both going a t the same speed, c o l d and hot, and when you stop them, i t w i l l be more c o l d than hot, the water. E: So you t h i n k c o l d heat i s what? S: So t h i s w i l l o b v i o u s l y c o o l . This might grow a l i t t l e warmer. E: Do you t h i n k those bubbles have anything to do w i t h i t though? S: No I don't t h i n k so. , E: I f we had t h i s r e a l powerful microscope, do you suppose that we coul d see t h i s heat? Do you t h i n k we could see heat? Would the c o l d heat look any d i f f e r e n t from the warm heat? S: No I don't t h i n k so. Yes maybe i t would. Yes i t would, but I don't know what i t would look l i k e . E: So why d i d you put the a i r bubbles i n ? 157 Cause I know th a t ' s what i t looks l i k e i n the g l a s s . Does a l l g l a s s have a i r bubbles i n i t ? Yes, e v e r y t h i n g does. Everything? Yes I t h i n k so. Does water have a i r bubbles i n i t ? Yes. I t has t o , how do f i s h breathe? Unless i t ' s cut o f f . I f you keep a f i s h i n a c o n t a i n e r of water so i t can l i v e i n t h a t water you know, i t can't be f r e s h water unless i t ' s a f r e s h water f i s h , then cut o f f the a i r , you know, put a s e a l over t h i s , have a couple of f i s h i n there and i n a couple of days they'd use up a l l the a i r bubbles and they'd d i e cause there would be no a i r g e t t i n g i n t o the water. Have you ever t r i e d that or you j u s t t h i n k t h a t ' s what would happen. I know t h a t , I t h i n k I know. I'm i n t e r e s t e d i n what you t h i n k might happen i f we p u l l t h a t b a r r i e r up. O.K. l e t ' s p u l l that b a r r i e r up. Now what do you suppose i s going to happen? I t w i l l . m i x , the water. I t w i l l a l l be the same temperature. I t won't be the same temperature, i t w i l l be a d i f f e r e n t temperature but i t w i l l be a l i t t l e h o t t e r than the c o l d water was to s t a r t w i t h but the hot water w i l l be c o l d e r than i t was to s t a r t w i t h . So what do you t h i n k ? The temperature on t h i s s i d e was 140 d i d we say That was 140 and th a t was 60. And what do you t h i n k the f i n a l temperature of that mixture might be? Between 80 and 90. Probably 95. How d i d you a r r i v e a t that? Wait, I ' l l f i g u r e i t out another way. The hot water was 140 and the c o l d water was 60 so what's i n between that? So i n between that i s I guess 100. And then the c o l d water w i l l c o o l down the heat so I t h i n k i t w i l l be e x a c t l y what I s a i d between 90 and 95, t h a t ' s what I t h i n k now. You l o s t me i n that l a s t b i t , you s a i d f i r s t i t would be 100 and then you s a i d the c o l d water w i l l do what? 158 S: Cool down the heat a b i t . E: I don't understand what you mean by that. S: Well the cool water sort of rules the hot water, so i t would be a l i t t l e cooler than half way. E: Do you want to try i t ? S: Yes. Well I was wrong about that. It i s 82 degrees. E: Let's try a l i t t l e different mixture this time. Why do you suppose It was 82? S: The cold water would rule i t . I guess the cold water rules i t a l i t t l e more than I expected. Do you want me to put this (the bar- rier) back in? E: Yes. Now let's try a l i t t l e different one this time. That's cold water yes. Put that much cold water in there. Is there an ex- periment you'd like to try? Do you see what I'm trying to do? One of them has twice as much. (the hot side has twice as much water) Now let's ask the same sort of questions. What do you think w i l l happen after 10 minutes or so? What do you think the temperature of this (hot) water w i l l be? S: After 10 minutes? Do you take this out? (S points to the barrier) E: No with i t i n . S: It w i l l be around 100 degrees. E: And i t was originally about 140. And what do you think that water (cold) w i l l be? S: About 80 degrees. No 70. E: And why do you think i t w i l l be 70? S: Because the hot water w i l l warm this. (S points to the cold side) And the other water w i l l cool the hot. E: And i t wouldn't get any hotter than the 70? O.K. let ' s , do you want to pul l i t again. What do you think the temperature of that water w i l l be now? S: 95 to 100 no 95 to 105. E: Now why do you think that? S: I know i t w i l l be a l i t t l e hotter than i t was before because there's more hot water, that's why. 159 E: O.K. do you want to try i t . It looks li k e you were right on that time. S: It's 102 or 103. Task Number Three E: O.K. What do you think some of those things are? (E brings out an aluminium tray containing a number of different objects) S: Cubes and sort of circles round you know. E: Can you t e l l me what those cubes and round things are made out of? S: Sugar. E: Which one i s sugar? S: This one. (S points to a mothball) E: Do you want to smell that sugar? Does i t smell li k e sugar? S: No, what i s it? E: Have you ever smelled that smell before? S: Yes, I can't remember what i t i s . E: Have you ever seen them in a trunk that your mother keeps closed? To protect them against moths. S: Oh yes, that's right. E: Now do you know what i t is? S: No, I uh mothballs? E: That's right. What about these other things? S: Metal, butter, wood, t i n , brass, sugar. E: Now I'm just going to move a few of these things here so that we can keep them separated. What do you suppose we're going to do with these? S: I don't know. I guess that's just the weight of i t , i t f e l t like a magnet a b i t . E: What do you suppose that is? (E places another object on the tray) S: I can't see i t . Ice cubes? E: Yes. Now do you know what I'm going to do with i t ? (the tray f u l l of objects) S: No. E: Do you know why I put this up here? (E places the tray on the hot plate) 16Q S: Are you going to melt it? E: I don't know, do you suppose that would S: You're going to put a l l these on there (the hot plate) right? E: Yes; S: You're going to see which melts f i r s t and see which heats f i r s t . Now I think the ice w i l l melt f i r s t , then the butter, and then the sugar and the wood w i l l , well i t w i l l heat f i r s t . E: What about the mothball? S: What is a mothball made out of? E: I don't know. What's i t feel like? S: Sort of salty. How are these made? E: I really don't know. S: What makes them? E: I think they're manufactured some place. S: Why to you put mothballs i n a trunk? E: To keep moths away. You know what moths do to clothes. S: Well I never knew that before. I always thought a mothball was some- thing that moths made. E: So you think, which i s going to melt f i r s t ? S: The ice. E: The ice cube and then? S: The butter, the sugar and then the mothball i f i t does melt at a l l . E: Do you think i t might not melt at a l l ? S: Yes, I don't know, does salt melt? Do you want to try i t ? E: I haven't got any. Maybe you could try i t some other time. What about brass? S: O.K. Now i t won't melt. E: You don't think i t w i l l melt? S: It w i l l i f i t gets to a certain extent. You know, how do you think they moulded this? It w i l l but I don't think i t would melt a l o t . And the wood w i l l get hot I suppose, I don't think i t w i l l burn. E: What about the wire? (solder rolled up into a ball) S: Well i t w i l l get hot. I ' l l show you what get's hot f i r s t . The wire w i l l get hot f i r s t , no the t i n w i l l get hot f i r s t , the wire and the 161 brass l a s t . And then, no the wood l a s t , then the brass and then the wood. E: When you say get hot, what does that mean? S: Heat up. E: And how w i l l we know? S: F e e l i t . E: J u s t by f e e l i n g i t , and we wouldn't see i t melt? S: No. E: Why don't these other t h i n g s melt? S: You mean these things? They are s o l i d substances. E: This (sugar) i s s o l i d . So i s t h i s ( i c e cube) S: They have got a i r bubbles. I don't know. E: Have you any id e a why some things melt and others don't? S: Because they have, uh I don't know. E: Do you want to put i t cn? (S puts t r a y on the hot p l a t e ) Now what's happening? S: The i c e i s m e l t i n g and the mothball i s m e l t i n g . The sugar i s n ' t . E: W e l l i t looks l i k e you were r i g h t . I d i d n ' t n o t i c e which melted f i r s t d i d you? S: W e l l you can't r e a l l y t e l l w i t h the water and the b u t t e r . E: Now how about those other t h i n g s , do you suppose they are g e t t i n g hot? I wonder how we'd f i n d out. (S attempts to take the temperature of the wood w i t h a thermometer) Can you see the temperature? S: I t ' s 95 degrees r i g h t now. E: What about some of the other things? A c t u a l l y I t h i n k we'd b e t t e r take i t o f f . What i s going to happen when I take i t o f f ? S: I t w i l l c o o l down. E: What about (S i n t e r r u p t s ) S: The b u t t e r i s h o t t e r (S proceeds to touch some of the 32 o b j e c t s ) Now i t i s n ' t so hot. That (brass) i s the h o t t e s t , t h a t ' s ( s t e e l ) the second h o t t e s t , t h a t ' s (wood) the c o o l e s t . This doesn't even melt. The sugar. E: Why do you suppose i t doesn't melt? Why d i d you t h i n k i t would melt? 162 S: I know. I always thought i t was the heat in the coffee that would melt the thing (the sugar) but I guess i t ' s just the liq u i d . E: Melt the? S: Melt the sugar in the coffee. E: I suppose there's a way we could find out that couldn't we? S: Yes. E: How would we do that? S: Get the water back again. E: That's something you could try at home. Why do you suppose the sugar cube didn't melt? No, let's try i t the other way around. Why did you think i t would melt? S: Because of the heat. Like I always thought i t was the heat in the coffee, that would make i t melt. But now I know i t ' s the li q u i d . E: You think i t ' s the heat that makes the butter melt and the ice cube? S: Yes. E: How does i t do that, do you suppose? S: I know that from making fresh buttered popcorn you melt the butter. And ice cubes melt in the sun. E: How do you suppose the heat does that? (10 second pause) Could you use our powerful microscope again and t e l l me how you think, say some- " thing like a piece of ice melts, take a look at a piece of ice here. S: It w i l l melt because of the room temperature. E: And what's making i t melt? S: The room temperature or the temperature of that. (the paper towel on which the ice cube was resting) E: How does i t do that? S: Because this (ice cube) i s on the surface. E: How does the room temperature make i t melt? S: Just from the heat waves. E: And what do the heat waves do? S: They transfer into that (ice cube) and make i t water, cycle i t back to water, I guess that's what you c a l l i t . Just lik e when you take the steam into water, f i r s t you.have water, then make i t into steam, then 163 you have water again. What do you c a l l that again? It's not important. Do you suppose we could measure the temperature of that ice cube? Yes. What do you think the temperature of that might be? What i s freezing temperature? Oh yes 32 degrees. I think that w i l l be 32 degrees. No. I think i t w i l l be 15 degrees. Why do you think i t w i l l be colder? I just think i t i s . What do you think the temperature of that would be? (E brings out a much larger ice cube) Around 15 degrees. Same temperature. Same temperature even though i t ' s bigger? Yes. Now i f we put that, i f I take this and I put this ice cube into here (a beaker of water) what do you suppose w i l l happen? It will' melt. Why w i l l i t melt? Because of the,that water. It's hotter than 15 degrees cause i t i s 60 degrees. So i t i s warmer than the ice cube and the heat rays in the water w i l l transfer into the ice cube and melt i t back to water. And that water w i l l raise. That water w i l l what? Raise what i t was. Which water? The water in there, because of the ice cube melting. Oh I see, you mean the level. I thought you meant raise the temperature. What w i l l happen to the temperature of the water? This (the water) w i l l get colder. The water. What about the temperature of the ice cube, what w i l l happen to i t ? It w i l l get warmer. That's why i t w i l l melt. How hot do you think we can get that ice cube? 164 S: Without melting it? E: Well i f we leave that ice cube s i t t i n g in warm water for 10 minutes, how hot do you think the ice cube w i l l get? S: Well before melting you mean or just before i t disintegrates? E: Just how hot do you think the ice cube i s now? S: The same temperature. No i t ' s 32 degrees or more, you know 33, 34, something like that. E: Now could we get the temperature of ice to go up even higher, let's say i f we put this (the ice cube) on the heat. S: Yes I guess so. Before i t disintegrates, i t would get hot. E: How hot do you think i t would get? S: What is the body temperature? E: I think i t ' s 90 something. S: I think i t would get up to 100 degrees, i t would probably get up to boiling. E: And then what would happen? S: Then i t couldn't get any higher. Until i t disintegrates and then i t would b o i l . E: And what would happen to the temperature of the water? S: It would get hotter too. It's the water that i s getting hot and transferring into the ice cube. If i t i s in the water but i f you put the ice cube on the hot plate alone, then i t would be the ice cube i t s e l f that was getting hot. E: Now i f I put this onto the hot plate by i t s e l f , what's getting hotter now? S: The ice cube. E: And how hot do you think we can get it? If we put a thermometer in the middle of the ice cube say to measure i t . S: What's boiling temperature? E: 212. S: O.K. i t would get up to 212 degrees. E: What about, now you were saying something about the water? Is that the water that's coming off the ice cube? 165 S: No i t ' s the water i n there. (the beaker) E: So the water i n here, what w i l l happen to i t ? S: I t got hot and then the i c e cube gets hot a t the same time because the water has fumes of heat and i t goes i n t o the i c e cube. E: That's what I wanted to know. Let me j u s t draw t h i s here so I can see i f I understand. There's the j a r and here's the water and here's the i c e cube. Now can you show me what you mean when you say what's g e t t i n g hot. S: S h a l l I draw a hot p l a t e too. E: No l e t ' s not put i t on a hot p l a t e so i t ' s not on a hot p l a t e . S: The water i s 70 degrees. E: Let ' s say the water i s 70 degrees. Before we put the i c e cube i n . S: Now the fumes from here (the water) go i n t o t h a t (the i c e cube). While the fumes i n here (the i c e cube) are about 70 degrees. E: So the i c e cube then becomes 70 degrees. And then what happens to the water? S: I t gets c o o l e r . E: Oh the water gets c o o l e r . I thought you s a i d i t got h o t t e r . S: I f i t ' s on a hot p l a t e i t would. E: I see what you were meaning, i t was on the hot p l a t e . No I meant i f i t was j u s t standing out. So what would the temperature of the water get to? S: I t would be lower. E: Why i s that? S: Because of the i c e cube.. E: L e t ' s say the i c e cube melts down to t h a t s i z e , so w e ' l l j u s t draw a s m a l l i c e cube i n here, now how hot do you t h i n k t h a t i c e cube i s , f i r s t of a l l , t h i s i s 10 minutes, how hot do you t h i n k that water would be now? S: 5 5 - 6 0 degrees. E: O.K. l e t ' s put that down. L e t ' s say 55 degrees O.K? Now how hot do you t h i n k the i c e cube i s ? S: The same temperature. E: You t h i n k i t would be the same temperature? 166 No i t would be around 45 degrees. Cause i t ' s getting hotter while this (the water) i s getting cooler. I thought that the ice cube was 70 degrees before. I was wrong. Say i t was 30 degrees before. No, i t was 35 degrees before. Task Number Four E: What do you suppose i s going to happen i f I heat that up? (E ini t i a t e s a new task by bringing out. rod with three pins attached using wax) S: The rod? The wax w i l l melt and the pins w i l l drop. E: Have you done this before have you? S: No. E: How did you know that would happen? S: Cause I knew that was wax on there and that i t would melt as the rod got hot. E: Why i s that? S: Because i f you transfer the heat into the wax, the wax melts. E: Now what transfers the heat into the wax? s; The rod. E: But I'm heating the rod way over here. S: I know but the whole rod w i l l get hot. E : Why i s that? S: Cause, i t ' s a l l joined together, the same thing. How about i f we heat i t over there. (S points to a place on the rod close to the pins) E: Where? S: Right there. You see i f those drop off, then we'll know. Right? Then we'll know i f the rod get's hot. E: Why do you think the whole rod gets hot? S: Cause i t ' s a l l one substance. It's a l l joined together. It keeps on transferring the heat to there and to there a ud there. E: How do you suppose i t does that? S: It just travels through the rod. Just from the heat rays,you know. I S: E: S: 167 E: Yes. Does i t t r a v e l through a l l things? S: No. E: Does i t t r a v e l through the a i r ? S: Yes. E: What things doesn't i t t r a v e l through? (10 second pause) S: I guess i t does t r a v e l through a l l t h i n g s . E: Can't t h i n k of anything that i t doesn't? S: No. (S s t a r t s to touch the rod near the f i r s t pin) E: I s i t hot there? I guess t h a t ' s a way of f i n d i n g out i s n ' t i t ? J u s t by f e e l i n g i t . Which p i n do you t h i n k w i l l f a l l ? ( p i n nearest the candle flame drops) S: I was j u s t about to say t h a t . E: Why? S: Cause i t t r a v e l s along and so i t goes to there and i t t r a v e l s to there and there. (S motions along the rod) E: I see. (E places a number of d i f f e r e n t s i z e s and types of rods. on the t a b l e i n f r o n t of S) Have you ever seen anything l i k e these before? S: This i s copper. This i s metal I suppose. (S p i c k s up an aluminium rod) E: Now I haven't put pins on a l l those rods but what do you suppose t h i s one here i s e x a c t l y the same as that one there (a copper rod s i m i l a r to the one used i n the demonstration) Which do you t h i n k w i l l t r a v e l f a s t e s t i n which rod? (E a l s o hands S a much t h i c k e r aluminium rod) S: This one (copper) Cause i t ' s s m a l l e r . I t doesn't have as much rod to get the heat t o . E: What about between these two? (E hands S a copper rod and an aluminium rod of the same s i z e ) S: This one. (copper) Cause we d i d th a t i n the other experiment to see which one got h o t t e r and the copper one d i d . Remember? E: With the cubes? S: Yes. So t h i s one (copper) d e f i n i t e l y . E: Did we use one, we d i d n ' t use t h i s type d i d we? 168 S: That's metal i s n ' t i t ? E: I t h i n k i t ' s a type of metal, yes. S: We used i t , we had a metal tube. E: Yes maybe we d i d . So, why do you t h i n k i t t r a v e l s f a s t e r i n the copper? S: Cause i t ' s j u s t a c e r t a i n k i n d of chemical. E: Do you know why i t might t r a v e l f a s t e r here (copper rod) than i n here?(aluminium rod) S: No. E: Do you want to f e e l i t ? S: W e l l t h i s (copper rod) i s d e f i n i t e l y h e a v i e r . I t might j u s t because i t i s b i g g e r . E: You s a i d i t would t r a v e l f a s t e r i n the sm a l l e r rod, when you had these two. S: That's because they were the same substance. E: O.K. l e t ' s take a look a t these two (E hands S a s o l i d copper and a hollow copper rod) S: Are they the same substance? S: Yes. S: Then i t w i l l t r a v e l f a s t e r i n t h i s one (hollow copper rod) E: Why? S: Because i t doesn't have to f i l l i n the h o l e . I t ' s hollow. Because j u s t the same as t h i s , o n l y t h i s i s s m a l l e r , i t doesn't have to f i l l as much and that one i s s m a l l e r than t h a t one I t h i n k . E: I t ' s s m a l l e r because? S: Because i t ' s hollow. E: What about these two? Do you t h i n k i t would t r a v e l i n these? (E hands S a s o l i d and a hollow g l a s s rod) S: Yes. E: Do you know what these are? S: G l a s s . E: Which do you t h i n k i t w i l l t r a v e l f a s t e r i n ? S: Are they both hollow? E: No, t h i s one's s o l i d . 169 S: The hollow one. E: You think i t w i l l t r a v e l f a s t e r i n the hollow one. S: No I don't. I've changed my whole thing around. Now, because the a i r can get i n there and cool i t down. Correct? E: I don't know. I should t r y that. What do you think? S: That's what I think. This ( s o l i d glass rod) w i l l t r a v e l f a s t e r and th i s ( s o l i d copper rod) w i l l t r a v e l f a s t e r . E: Let's t r y the glass ones f i r s t . You think i t w i l l t r a v e l f a s t e r i n the hollow one or the s o l i d one? S: The s o l i d one. E: And the reason why? S: Is because the a i r can get i n the hollow one and cool i t down. E: You think the a i r w i l l cool i t down? Why would i t do that? S: From the rays, j u s t l i k e i n the water, the room temperature water and the hot water. E: And so that would be also the case here too? S: Yes. Task Number Five E: O.K. we're j u s t going to take a real quick look at another thing here. I'm curious to see what you might think of t h i s . Do you want to j u s t take a look at that and see. S: What i s i t ? I t ' s a metal bar. With, I don't know what that i s . E: That's the d i a l . And can you see what's on the back of the d i a l ? S: A p i n . E: A p i n on i t . Now watch what happens when I, I'm going to r e s t the metal rod on the p i n O.K? Now watch what I'm going to do now. (E slowly moves the metal rod with h i s hand so that the d i a l turns) See I'm j u s t going to move the rod along there l i k e that. Can you see what happens to the d i a l ? And then I move i t back. So i f you move i t that way, the d i a l turns that way and i f you move i t t h i s way i t turns that way. Now I'm going to take and put that rod on the - needle. Is that j u s t about zero? (E l i n e s up d i a l to zero point) S: Yes. There, that's pretty good. 170 E: Now what do you t h i n k we're going to do? S: Heat the rod? E: Yes, then what's going to happen? S: I t w i l l heat the p i n . E: Why do you t h i n k i t w i l l heat the pin? S: Cause i t t r a n s f e r s heat. E: And then what do you suppose might happen? S: Heat the paper I guess. E: Is anything happening? S: -Yes, i t ' s g e t t i n g dark. E: Did you set the d i a l a t zero? S: Yes. I t moved. I t ' s moving. I t ' s at 10. I t ' s moving, i t ' s a t about 12 now. How does that do that? I can't understand i t . E: I gave you some c l u e s . S: Well i s the rod moving? I guess i t ' s m e l t i n g and s t r e t c h i n g . E: How do you t h i n k i t might do that? S: From the heat. I see i t m e l t i n g i n one p l a c e s o r t o f . I t ' s 20 now. I guess t h a t ' s the temperature, i t measures how hot t h a t bar i s eh? E: Well how do you t h i n k i t does t h a t though? Why does t h a t move? S: I guess i t melts t h a t and i t s t r e t c h e s and then i t turns the t h i n g . E: Is there something we could do to t h a t to f i n d out? S: No. (E blows out the two candles t h a t were h e a t i n g the rod) E: Is anything happening to the d i a l now? S: No. Hey i t ' s going back. I t ' s going back to zero. I guess because the rod i s c o o l i n g o f f . I t must s h r i n k . E: How do you suppose the heat makes i t do that? S: I don't know. E: Can you dream up any ideas? (E places i c e cube on rod) S: I t ' s going back to zero (15 second pause as E and S watch the e f f e c t of the i c e cube on the rod) I t ' s at zero. E: Are you w a i t i n g to see what happens when i t c o o l s down? S: Does that r a i s e and go down? E: What? 171 S: The rod. E: No. Why? S: I thought when you do t h a t , I thought I saw i t r a i s e . E: No I moved i t and i t moved back l i k e t h a t . Do you t h i n k a l l metals would do that? S: Yes. E: What happens when you heat l i q u i d s up? S: When you heat l i q u i d s ? I t r i s e s . E: How does i t do that? S: J u s t from the heat. I know! When you heat something l i k e hot water, i t gets bubbles i n i t r i g h t ? And when the bubbles come i n , i t takes up space and t h a t ' s why the water r i s e s . E: Where do the bubbles come from? S: I knew you were going to ask t h a t . I don't know. E: Could you apply t h a t i d e a to the rod here? S: Maybe the rod r a i s e s no. I can't understand i t . T his has stumped me. E: Well i t i s l a t e so we had b e t t e r be g e t t i n g you back to school now. 172 APPENDIX B Diagrams of the I n t e r v i e w Room and the Apparatus Used i n Some of the Tasks 173 Figure B-l Diagram of Room Used to Interview the Subjects —> Blackboard S's Chair 1 1 Tables < : — ) Microphone E's Chair Table for > storing apparatus One-way mirror ~> Camera 174 Figure B-2 Diagrams of the Apparatus Used i n Some of the Interview Tasks Task One 125 ml. Erlenmeyer t flask 30 cm. > capillary tube One-hole rubber ^ stopper Coloured -> Water The Liquid Expansion Apparatus" Task Three Removable barrier Water-Mixing Apparatus 175 Figure B-2 Continued Task Four & j M e t a l rod -> Candle P i n s embedded i n wax 7 Wooden base Tra n s f e r of Heat Apparatus Task F i v e N a i l f a s t e n i n g rod to frame Wooden frame Movable cardboard d i a l Reference po i n t on frame L i n e a r Expansion Apparatus 176 APPENDIX C A Copy of the Conceptual P r o f i l e Instrument Information Sheet Name of School Your Grade Your Age Have you ever studied about heat and temperature in school? If yea, how long did you study i t ? In what grade(s) did you study i t ? IDEAS ABOUT HEAT AND TEMPERATURE 178 Today we are going to do some experiments on heat and temperature and play a type of word game about these experiments. Before we do the experiments I want to explain how to play the game. ANIMAL CRACKERS ' LOOP AT "THAT STAR, ELWOOP?) WHU DO 4O0 SUPPOSE ^ THE, U6HT PULSATES ' U^EIT'S DOlM<S ? A I THINK IT'S THE RESULT ^ OF ATOMS AMD ELECTRON} S WlLDWSPINNING WtWlKTHE ATMOSPHERE OF NEUTRON „ STARS, THUS CAUSl/xl<S A fiLI^HTHOQSe-LllcE BEACON. ' I I" 8 I'M 50(2T OF G-LAD I DIDN'T <3H)& HIM MY "SPACEMAN W>TH A FLASHLIGHT" THEORY... Just as Elwood and Lyle had different ideas to explain a star in the cartoon, people often have different ideas to explain heat and temperature. In the word game after the experiments you w i l l be shown a number of different statements that some people have used to explain what happened. I want to know how YOU FEEL about the ideas in these statements. To pract ise, l e t ' s take a look at a statement about •sickness* and I ' l l show you how the game works. Suppose the statement wasi People get sick because THEY DO NOT GET ENOUGH VITAMINS. As you can see there are 2 parts to this statement. The f i r s t part in small print t e l l s us what the statement i s about. In this example i t i s about people getting s i c k . The second part is in the box and is in CAPITAL LETTERS• It i s an IDEA explaining why people get sicko I want you to t e l l me how you fee l about this idea. After reading and thinking about the idea in the box suppose that you decide that people always get sick when they do not get enough vitamins. Then you should put a mark in the blank above "Very Much Agree" as shown belowi X i i « « « « Very Much Somewhat S l ight ly Neither S l ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree 179 But suppose you fe l t that people often get sick when they do not get enough vitamins. Then you should put a mark in the blank above "Somewhat Agree" as shown belowi t X i t t t t Very Much Somewhat Sl ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Or, you might fee l that people only sometimes get sick when they do not have enough vitamins. Then you should mark the blank above "Slightly Agree" as shown belowi « i X i t i i Very Much Somewhat Sl ight ly Neither S l ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Suppose that you real ly cannot decide i f vitamins are related to sickness or not. What blank would you mark? REMEMBER that you should only mark one blank in each row. I am also interested in other ways you feel about the same idea. For example, in the second row on each page you are to decide i f the idea is clear or confusing. There are six rows which ask you how you feel about the idea in the box at the top of the page. You are to put ONE mark in each row. Let 's work through two other ideas on sickness to see i f you understand how this game works. We w i l l discuss any questions you may have after you have completed the next two pages• People get sick because GERMS ENTER THEIR BODIES AND CAUSE INFECTIONS. Very Much Somewhat S l ight ly Neither S l ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither S l ight ly Somewhat VeTy" Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing Very Somewhat S l ight ly Neither Sl ight ly Somewhat virT Easy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False S l ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar oo o Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Trfoao Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas People get sick because THEY GET TOO MUCH SLEEP, j Very Much Somewhat S l ight ly Agree Agree Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear Sl ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing Somewhat Confusing Very Confusing Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i cu l t D i f f i cu l t D i f f i c u l t D i f f i cu l t Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very True True True True nor False False False False i i i t i i Very Somewhat Sl ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Like My Like My Like My Like My Unlike My Unlike My Unlike My Ideas Ideas Ideas Ideas nor Ideas Ideas Ideas Unlike My Ideas The large rod heated up faster than the small rod because THE LARGE ROD ATTRACTS MORE HEAT PARTICLES THAN THE S^AUTRODF V e I L p p ° h S ° m e w h a t S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree clear S ^ h t l y Neither Sl ight ly Somewhat V e ^ oiear Clear Clear Clear nor « — ~ . „ . Confusing Confusing Confusing Confusing & Easv S ° S ! ^ h a t S 1 j g h t l y N e i t h e r ' Sl ight ly Somewhat VeTy" *asy Easy Easy Easy nor D i f f i cu l t D i f f i c u l t D i f f i c u l t D i f f i cu l t Trll S ° S a t s l J g W l y E i t h e r Sl ight ly Somewhat —VeTy" irue True True True nor False False False False Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar t i t i t t Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Like My Like My Like My Like My Unlike My Unlike My Unlike My Ideas Ideas Ideas Ideas nor Ideas Ideas Ideas Unlike My The large rod heated up faster than the small rod because THE LARGE ROD HAS MORE METAL PARTICLES TO MOVE AROUND. Very Much Somewhat S l ight ly Neither Sl ightly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing i i i t i i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i cu l t D i f f i cu l t D i f f i c u l t D i f f i cu l t » i i i i i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very True True True True nor False False False False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar Sl ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The large rod heated up faster than the small rod because THE LARGE ROD HAS MORE AIR SPACES INSIDE FOR THE HEAT TO TRAVEL THROUGH. Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very" E a s y Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t Very Somewhat S l ight ly Neither Sl ight ly Somewhat VerV True True True True nor False False False False i t Very Somewhat S l ight ly Neither Sl ight ly Somewhat viFy" Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar f"i M 7- v u : A 6 » " j ncxojici. axxgnxxy aomewnat Very Much Like My Like My Like My Like My Unlike My Unlike My Unlike My ideas Ideas Ideas Ideas nor Ideas Ideas Ideas H n H l f a Mir The whole rod gets hot because THE HEAT BUILDS UP IN ONE PART UNTIL IT CAN'T HOLD ANYMORE AND THEN THE HEAT MOVES ALONG THE ROD. Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t Sl ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False i i t i . i i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Somewhat S l ight ly Neither S l ight ly Somewhat Very Much Like My Like My Like My Like My Unlike My Unlike My Unlike My Ideas Ideas Ideas Ideas nor Ideas Ideas Ideas Unlike My Ideas The whole rod gets hot because | THE FASTER MOVING METAL PARTICLES BUMP INTO EACH OTHER ALL THE WAY THROUGH THE ROD. Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing; Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar Sl ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The whole rod gets hot because THE HEAT PARTICLES FROM THE FLAME ARE ATTRACTED TO ALL PARTS OF THE ROD. Very Much Somewhat S l ight ly Neither S l ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither S l ight ly Somewhat Very" Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The wax melted because | IT WAS A SOFT SUBSTANCE. V e J L l « C h S ° m e w h a t S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree p ? I L Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor n~~*..~t±- _ _  y . Confusing Confusing Confusing Confusing Very Somewhat S l ight ly Neither Sl ight ly Somewhat VeTy" *asy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t Trul  S°?r.at S l ight ly Neither S l ight ly Somewhat v i r 7 True True True True nor False False - False False F a l n L r * Somewhat S l ight ly Neither S l ight ly Somewhat v^Z Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar V L i k e M S ? h T S ? v r S a t S l ight ly Neither S l ight ly Somewhat Very Much is-j? ^ ^ ^ s M y Unlike My Ideas The wax melted because THE HEAT PARTICLES WENT INSIDE AND FORCED THE WAX PARTICLES APART• Very Much Somewhat S l ight ly Neither S l igh t ly" Somewhat' Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither S l ight ly" Somewhat VeTy" Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing Very Somewhat S l ight ly Neither Sl ight ly Somewhat ' Very fcasy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t ! S Somewhat S l ight ly Neither Sl ight ly Somewhat ~ T i r T T r u e T r u e True True nor False False False False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The wax melted because THE WAX PARTICLES WERE MOVING ABOUT SO FAST THAT THEY COULD NOT HOLD ON TO EACH OTHER SO WELL. Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Somewhat Very Much Disagree Disagree Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Somewhat Very Confusing Confusing Confusing Very Easy Somewhat Easy Sl ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly Somewhat Very D i f f i c u l t D i f f i c u l t D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar S omewhat Unfamiliar Very Unfamiliar o Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The metal cubes were hotter than the wood or sugar because | THE METAL CUBES DREW IN MORE HEAT PARTICLES THAN THE OTHER CUBES* V 6 S r P p C h Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Clear S ^ h t l v Neither S l ight ly Somewhat VeTy" uiear Clear Clear Clear nor n — ~- - s _ - y „ . . Confusing Confusing Confusing Confusing 5 Easv Somewhat S l ight ly Neither " S l ight ly ' Somewhat VeTy" *asy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar iJ3 Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The metal cubes were hotter than the wood or sugar because IT WAS MORE DIFFICULT FOR THE AIR TO GET INSIDE THE HARD METAL CUBES TO COOL THEM. Very Much Somewhat Agree Agree S l ight ly Agree Neither Agree nor Disagree S l ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing S l ight ly Confusing Somewhat Confusing Very Confusing i t i t i • i Very Somewhat S l ight ly Neither S l ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t t • i t i t i Very Somewhat S l ight ly Neither S l ight ly Somewhat Very True True True True nor False False False False » » t i « t Very Somewhat S l ight ly Neither S l ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Somewhat S l ight ly Neither S l ight ly Somewhat Very Much Like My Like My Like My Like My Unlike My Unlike My Unlike My Ideas Ideas Ideas Ideas nor Ideas Ideas Ideas Unlike My Ideas The metal cubes were hotter than the wood or sugar because | THE METAL PARTICLES ARE EASIER TO MOVE* t t ! i t i Very Much Agree i Somewhat Agree S l ight ly Agree i Neither Agree nor Disagree i t S l ight ly Disagree Somewhat Disagree i t Very Much Disagree Very Clear t S omewhat Clear S l ight ly Clear i Neither Clear nor Confusing i i S l ight ly Confusing Somewhat Confusing t t Very Confusing Very Easy t Somewhat Easy S l ight ly Easy i Neither Easy nor D i f f i c u l t t i S l ight ly D i f f i c u l t Somewhat D i f f i c u l t i i Very D i f f i c u l t Very True i Somewhat True S l ight ly True t Neither True nor False t t S l ight ly False Somewhat False t i Very False Very Familiar i Somewhat Familiar S l ight ly Familiar t Neither Familiar nor Unfamiliar i i S l ight ly Unfamiliar Somewhat Unfamiliar i i Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The metal cubes did not melt because THEY WERE NOT HEATED LONG ENOUGH. Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing i i t i t t Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t t t i i t i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very True True True True nor False False False False » « i i i i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The temperature of the water decreased when an ice cube was added because THE ICE CUBE ATTRACTED SOME OF THE HEAT PARTICLES AWAY FROM THE WATER. " Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t Sl ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar Sl ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas T h e t e m P e ^ t u r e of the water decreased when an ice cube was added because SOME OF THE COLD LEFT THE ICE CUBE AND WENT INTO THE WATTrp . Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing; Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Somewhat Verv Much Unlike My Unlike My Unlike Sy Ideas T j — J Ideas Ideas The temperature of the water decreased when an ice cube was added because I THE WATER PARTICLES LOSE SOME OF THEIR SPEED BY DUMPING INTO THE ICE PARTICLES. Very Much Somewhat S l ight ly Neither . S l ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing t » t i i ; » Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t t i i t t t Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very True True True True nor False False False False i i t i • i i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas A large ice cube takes longer to melt than a small ice cube because [ THE LARGS ISK CUBE HAS A COLDER TEMPERATURE THAN THE SMALL ICE CUBE,""] Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree S l ight ly Disagree Scmswhat Disagree- Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Co Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The red l iqu id in the tube went up because THE HEAT MAKES THE RED LIQUID LIGHTER AND SO IT RISES. Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing Very Somewhat S l ight ly Neither S l ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t Very Somewhat S l ight ly Neither S l ight ly Somewhat Very True True True True nor False False False False i i i i _____ i t Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas The red l iqu id in the tube went up because THE LIQUID'S PARTICLES MOVED MORE QUICKLY AND SO TOOK UP MORE SPACE. \ Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very E a s y Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t * « » i t t Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very T r u e True True True nor False False False False » » , i i t t Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Somewhat S l ight ly Neither S l ight ly Somewhat Very Much Like My Like My Like My Like My Unlike My Unlike My Unlike My Ideas Ideas Ideas Ideas nor Ideas Ideas Ideas Unlike My Ideas The red l iqu id in the tube went up because THE HEAT PARTICLES TAKE UP SPACE INSIDE THE LIQUID AND FORCES THE LIQUID OUT THE TUBE. Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing S l ight ly Confusing Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False S l ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar O Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas Objects rubbed together get hot because THE PARTICLES INSIDE THE OBJECTS MOVE FASTER, Very Much Somewhat Agree Agree S l ight ly Agree Neither Agree nor Disagree S l ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither S l ight ly Somewhat Very Clear nor Confusing Confusing Confusing Confusing & Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False S l ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar o N3 Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas S l ight ly Somewhat Very Much Unlike My Unlike My Unlike My Ideas Ideas Ideas Objects rubbed together get hot because [ THE HEAT PARTICLES INSIDE THE OBJECT ARE FORCED OUT. — I i i i i i i Very Much Somewhat S l ight ly Neither . S l ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree t i i r 'i t Very Somewhat S l ight ly Neither S l ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing t ; t t t t i Very Somewhat S l ight ly Neither S l ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t i i i i i t Very Somewhat S l ight ly Neither S l ight ly Somewhat Very True True True True nor False False False False * i i i • t i Very Somewhat S l ight ly Neither S l ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar _________________ « ______________ • __________________ * ______________ • ________________ > i Very Much Somewhat S l ight ly Neither S l ight ly Somewhat Very Much Like My Like My Like My Like My Unlike My Unlike My Unlike My Ideas Ideas Ideas Ideas nor Ideas Ideas Ideas Unlike My Ideas HEAT IS THE MOTION OF AN OBJECT'S PARTICLES. Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t Sl ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Familiar Very Much Like My Ideas Somewhat Familiar Somewhat Like My Ideas Sl ight ly Familiar S l ight ly Like My Ideas Neither Familiar nor Unfamiliar Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas O TEMPERATURE IS A MEASURE OF THE MIXTURE OF HEAT AND COLD INSIDE AN OBJECT. Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree S l ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing S l ight ly Confusing Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t S l ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False S l ight ly False Somewhat False Very False Very Familiar Somewhat Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar S l ight ly Unfamiliar Somewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor* Unlike My Ideas S l ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas HEAT IS A SUBSTANCE SOMETHING LIKE AIR OR STEAM. Very Much Somewhat S l ieht lv " w p U h ^ — o-. . . ^ — 1 — . » _ _ _ _ _ A g ~ e A g r e e Agist A|J3r S35£ ~ clear S c ° S a t S ^ ! " l y j Z i t t e t - - s i i i h t i F ' "sSSiv^t-Clear " „ , " " S " ^ aomewnat Verv . dear c w nor Confusing Confusing Conning ll?y S ° _ 2 " t S 1 ^ > / " t h e r Slightly ' Somewhat " V e r y Easy E a s y nor Difficult Difficult D i f l l L l t 52 t l" liŜ T '^Sr '-_f False raj.se False -~ K-BS S'S'S Unfamiliar Very Much Somewhat S l ight ly N e i t h e r q n ^ + i 1 -= • - _ Like My Like My L ik f My Like Mv Vnlfvtl Somewhat Very Much Ideas I a e a s I d e a s y Ideal n^r ^ i d e l s * U n „ ^ U n l i k e ^ Unlike My a I d e a s Ideas ALL OBJECTS CONTAIN A MIXTURE OF HEAT AND COLD. Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree Very Somewhat S l ight ly Neither Sl ight ly "Somewhat VeTy Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing Very Somewhat S l ight ly Neither Sl ight ly Somewhat " Very fcasy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t Tr»ne» Somewhat S l ight ly Neither Sl ight ly Somewhat VeTy" True True True True nor False False False False Somewhat S l ight ly Neither Sl ight ly Somewhat VeTy" Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Like My Ideas S omewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas TEMPERATURE IS A MEASURE OF THE NUMBER OF HEAT PARTICLES IN AN OBJECT. t i t i i i Very Much Somewhat S l ight ly Neither Sl ight ly Somewhat Very Much Agree Agree Agree Agree nor Disagree Disagree Disagree Disagree t t t t t i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Clear Clear Clear Clear nor Confusing Confusing Confusing Confusing t t s t i i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Easy Easy Easy Easy nor D i f f i c u l t D i f f i c u l t D i f f i c u l t D i f f i c u l t » i i i t i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very True True True True nor False False False False » • » » i » i Very Somewhat S l ight ly Neither Sl ight ly Somewhat Very Familiar Familiar Familiar Familiar Unfamiliar Unfamiliar Unfamiliar nor Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas HEAT IS MADE UP OF TINY PARTICLES THAT CAN MOVE. Very Much Agree Somewhat Agree S l ight ly Agree Neither Agree nor Disagree Sl ight ly Disagree Somewhat Disagree Very Much Disagree Very Clear Somewhat Clear S l ight ly Clear Neither Clear nor Confusing Sl ight ly Confusing Somewhat Confusing Very Confusing Very Easy Somewhat Easy S l ight ly Easy Neither Easy nor D i f f i c u l t Sl ight ly D i f f i c u l t Somewhat D i f f i c u l t Very D i f f i c u l t Very True Somewhat True S l ight ly True Neither True nor False Sl ight ly False Somewhat False Very False Very Somewhat Familiar Familiar S l ight ly Familiar Neither Familiar nor Unfamiliar Sl ight ly Unfamiliar S omewhat Unfamiliar Very Unfamiliar Very Much Like My Ideas Somewhat Like My Ideas S l ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas Very Much Unlike My Ideas TEMPERATURE IS A MEASURE OF THE SPEED OF PARTICLES T M A H n B T g ™ * Verv Wunh t i t i Agree Verv Somewhat Agree S l ight ly Agree t Neither Agree nor Disagree t Sl ight ly Disagree t # Somewhat Disagree i t Very Much Disagree Clear Verv Somewhat Clear S l ight ly Clear i Neither Clear nor Confusing t S l ight ly Confusing t Somewhat Confusing t Very Confusing Easy * Verv oomewnat Easy S l ight ly Easy i Neither Easy nor D i f f i c u l t t S l ight ly D i f f i c u l t • Somewhat D i f f i c u l t • t Very D i f f i c u l t True i Very o omewnat True S l ight ly True i Neither True nor False t S l ight ly False i • Somewhat False i t Very False Familiar » Verv Much oumewnaX Familiar S l ight ly Familiar t Neither Familiar nor Unfamiliar t S l ight ly Unfamiliar i Somewhat Unfamiliar i i Very Unfamiliar Like My Ideas o oiaewnax Like My Ideas Sl ight ly Like My Ideas Neither Like My Ideas nor Unlike My Ideas Sl ight ly Unlike My Ideas Somewhat Unlike My Ideas t Very Much Unlike My Ideas O 211 APPENDIX D AN ITEM ANALYSIS" OF THE THREE HEAT PERSPECTIVES IN THE CONCEPTUAL PROFILE INSTRUMENT Legend f o r the Tables (1) C.P.I. Item: Refers to the number of the item on the Conceptual P r o f i l e Instrument. (2) B e l i e f Scale: 1 = agree-disagree b i p o l a r s c a l e 4 = t r u e - f a l s e b i p o l a r s c a l e 6 = l i k e i d e a s - u n l i k e my ideas b i p o l a r s c a l e (3) Mean Score: The average score obtained on that s c a l e f o r a l l a l l 276 s u b j e c t s . I t was a 7 p o i n t s c a l e . (4) Standard D e v i a t i o n : The average d e v i a t i o n of scores on that s c a l e f o r a l l of the s u b j e c t s . (5) ST C o r r e l a t i o n : The c o r r e l a t i o n c o e f f i c i e n t of the s c a l e score and the item score c o r r e c t e d f o r overlap. (6) TT C o r r e l a t i o n : The c o r r e l a t i o n c o e f f i e i e n t of the s c a l e score and the t o t a l score on a l l of the items f o r a p a r t i c u l a r heat p e r s p e c t i v e . (7) Hoyt's R e l i a b i l i t y : T his i s Hoyt's r e l i a b i l i t y c o e f f i c i e n t f o r a given item. (8) Standard E r r o r : T h i s i s the standard e r r o r of measurement f o r a given item. The computer program used to perform the a n a l y s i s i s e n t i t l e d LERTAP and i s a v a i l a b l e from the s t a t i s t i c s l a b o r a t o r y i n the F a c u l t y of Education, U n i v e r s i t y of B r i t i s h Columbia. TABLE D-l Analysis of the Statements Representing the Kinetic Perspecti C.P.I. Item Belief Scale Mean Score Standard Deviation ST Correlation TT Correlation Hoyt *s Re l i a b i l i t y Standard Error 2 1 4 6 3.21 3.04 4.06 1.75 1.47 1.79 .737 .698 .599 .478 .498 .447 .82 1.50 5 1 4 6 3.73 3.56 4.05 2.00 1.81 2.02 .811 .790 .705 .627 .617 .637 .88 1.49 9 1 4 6 3.80 3.63 4.13 1.95 1.80 1.88 .861 .846 .754 .659 .631 .645 .91 1.27 12 1 4 6 3.97 3.76 4.24 1.85 1.58 1.75 .780 .779 .718 .532 .508 .520 .87 1.35 16 1 4 6 4.06 3.90 4.35 1.90 1.77 1.92 .770 .803 .650 .652 .649 .606 .86 1.50 19 1 4 6 3.20 3.17 3.58 1.84 1.77 1.85 .842 .882 .742 .572 .623 .641 .91 1.23 Overall Statictics for Kinetic 67.43 19.24 .89 6.25 Perspective (n=276) N3 N3 TABLE D-2 An Item Analysis of Items Representing the Children's Perspective C.P.I. Belief Mean Standard ST TT Hoyt's Standard Item Scale Score Deviation Correlation Correlation R e l i a b i l i t y ' Error 1 3.86 2.09 .752 .408 3 4 3.69 1.83 .797 .435 .86 1.56 6 4.16 1.83 .661 .370 1 2.98 1.96 .799 .540 4 4 3.01 1.79 .795 .430 .88 1.45 6 3.28 1.88 .697 .444 1 3.19 2.12 .863 .515 7 4 3.09 2.01 .886 .546 .92 1.31 6 3.23 2.02 .778 .507 1 3.14 1.89 .821 .499 11 4 3.07 1.71 .812 .485 .89 1.32 6 3.50 1.82 .732 .450 1. 4.28 2.38 .846 .397 13 4 4.13 2.34 .888' " .459 .92 1.54 6 3.98 2.27 .757 .448 1 3.49 2.02 .821 .531 14 4 3.55 1.92 .852 .511 .90 1.39 6 3.75 1.95 .735 .471 1 3.72 2.21 .834 .542 18 4 3.62 2.11 .875 .555 .90 1.50 6 3.78 2.90 .716 .468 Overall Statistics for Children's 87.06 23.92 .86 8.73 Perspective (=276) TABLE D-3 An Item Analysis of Items Representing the Caloric Perspective C.P.I. Belief Mean Standard ST TT Hoyt's Standard Item Scale Score Deviation Correlation Correlation R e l i a b i l i t y Error 1 2.27 1.37 .616 .393 1 4 2.37 1.36 .594 .451 .70 1.59 6 3.60 1.76 .400 .293 1 3.43 1.96 .798 .540 6 4 3.42 1.75 .810 .520 .88 1.43 6 3.95 1.85 .683 .544 1 3.29 1.73 .754 .443 8 4 3.11 1.49 .736 .490 .85 1.39 6 3.64 1.71 .659 .505 1 1.87 1.10 .765 .510 10 4 2.09 1.21 .745 .491 .85 1.05 6 2.46 1.45 .683 .451 1 2.33 1.49 .782 .433 15 4 2.38 1.37 .796 .413 .88 1.11 6 2.53 1.55 .746 .384 1 2.57 1.62 .767 .501 20 4 2.59 1.48 .838 .499 .88 1.24 6 3.09 1.79 .725 .542 Overall Statistics for Caloric 50.98 Perspective (n=276) 13.14 .79 5.92 215 D i s c u s s i o n The data summarized i n the preceeding three t a b l e s s u b s t a n t i a t e s the r e s u l t s obtained from the f a c t o r - a n a l y t i c procedures. That i s , there i s a r e l a t i v e l y h i g h degree of i n t e r - c o r r e l a t i o n between the three b e l i e f s c a l e s f o r a p a r t i c u l a r item as i n d i c a t e d by the ST c o r r e l a t i o n . (See S e c t i o n 4.41 i n t e x t ) There i s a l s o a f a i r l y h i g h p o s i t i v e c o r r e l a t i o n between items f o r a p a r t i c u l a r heat p e r s p e c t i v e — the TT C o r r e l a t i o n . On the b a s i s of the Hoyt r e l i a b i l i t y c o e f f i c i e n t s a l l of the items would appear to be r e l i a b l e . However, perhaps the best i n d i c a t o r of how a p a r t i c u l a r item i s f u n c t i o n i n g ( i n terms of i t s c o n t r i b u t i o n to a p a r t i c u l a r heat p e r s p e c t i v e ) i s the TT c o r r e l a t i o n s between the s c a l e responses f o r an item and the t o t a l score on a l l of the items represent- i n g a p a r t i c u l a r heat p e r s p e c t i v e . Using t h i s c r i t e r i o n two items on the C a l o r i c P e r s p e c t i v e , items 1 and 15 are questionable s i n c e they c o n t a i n TT c o r r e l a t i o n s which are below .40. A l s o two items on the C h i l d r e n ' s P e r s p e c t i v e c o n t a i n low c o r r e l a t i o n s on one of the three s c a l e s , items 3 and 13. I t i s i n t e r e s t i n g to note t h a t two of the above items, numbers 1 and 3, were omitted from the p r o f i l e a n a l y s i s because they they f a i l e d to l o a d h i g h l y on those components i d e n t i f i e d as the three ' b u i l t i n ' heat p e r s p e c t i v e s . (See S e c t i o n 4.42 i n the t e x t ) While the c o r r e l a t i o n s f o r the other item omitted from the p r o f i l e a n a l y s i s , item 2, are not as low, they are s i g n i f i c a n t l y lower than those reported f o r the other items i n the K i n e t i c P e r s p e c t i v e . F u r t h e r , the r e s u l t s expressed by the standard e r r o r of measurement i n d i c a t e that the scores obtained from the b e l i e f s c a l e s of the C.P.I. 216 are accurate to within plus or minus three-quarters of a scale division (seven scale divisions were used). Hence some confidence can be ex- pressed in interpreting the belief scores from the C.P.I. In summary, the item analysis indicates that the care taken in the preparation and f i e l d testing has yielded a f a i r l y reliable instrument.

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