UBC Theses and Dissertations

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UBC Theses and Dissertations

Children’s beliefs about forces in equilibrium Aguirre, Jose M. 1978

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CHILDREN'S BELIEFS ABOUT FORCES IN EQUILIBRIUM by JOSE M. AGUIRRE Teacher of Physics, U n i v e r s i t y of Chi l e , 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES Department of Science Education We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1978 Jose M. Aguirre, 1978 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 Co lumb ia , I ag ree that the 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 tudy . 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 purposes 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 . It i s u n d e r s t o o d that 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 thout my w r i t t e n p e r m i s s i o n . Jose M. Aguirre Department o f Science Education The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date June 27, 1978, A B S T R A C T C l i n i c a l i n t e r v i e w s to ex p l o r e c h i l d r e n ' s b e l i e f s about the concept of f o r c e were c a r r i e d out w i t h 32 c h i l d r e n (18 boys, 14 g i r l s ) , whose ages ranged from 6 to 14 y e a r s . Three tasks were used to i n v e s t i g a t e t h e i r b e l i e f s about the a c t i o n of a f o r c e , a c t i o n and r e a c t i o n , e q u i l i b r i u m of f o r c e s , and composition of f o r c e s . A conceptual p r o f i l e was c o n s t r u c t e d on the aspects of f o r c e covered i n the t a s k s . T h i s conceptual p r o f i l e was then used to c a t e g o r i z e the c h i l d r e n ' s b e l i e f s which were uncovered i n the i n t e r v i e w s . I t was found t h a t the i n t e r v i e w methodology was a f e a s i b l e approach f o r an e x p l o r a t o r y and d e s c r i p t i v e study of s t udents' b e l i e f s about a p a r t i c u l a r concept and t h a t the c h i l d r e n i n the sample had a s e t of t y p i c a l a p r i o r i b e l i e f s about f o r c e which they used to account f o r the d i f f e r e n t experimental s i t u a t i o n s . T h i s s e t of b e l i e f s was subsequently c a t e g o r i z e d i n three l e v e l s o f a b s t r a c t i o n to b r i n g to l i g h t the p o s s i b l e p a t t e r n s o f these b e l i e f s . The c h i l d r e n ' s ideas found i n the study and the c a t e g o r i z a t i o n o f these i n t o l e v e l s o f a b s t r a c t i o n c o u l d be u s e f u l f o r the c u r r i c u l u m developer and p a r t i c u l a r l y f o r the teacher i n p l a n n i n g t e a c h i n g s t r a t e g i e s . - i i i -TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES .... v i i ACKNOWLEDGMENTS v i i i CHAPTER ONE 1.00 INTRODUCTION 1 1.10 The General Problem 3 1.11 S p e c i f i c Problems 4 1.20 Methods o f Study 5 1.21 Data C o l l e c t i o n . ' 5 1.22 Tasks of the Study 6 1.23 The Subjec t s 6 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 o f the Study ... 7 1.40 L i m i t a t i o n s o f the Study 8 CHAPTER TWO 2.00 PSYCHOLOGICAL CONTEXT OF THE STUDY ... 10 2.01 P i a g e t ' s Theory o f De-velopment o f knowledge ... 10 2.02 O p e r a t i o n a l Knowledge ... 10 2.03 P h y s i c a l Knowledge 12 2.10 E d u c a t i o n a l Context of the Study 17 2.11 I n t r o d u c t i o n 17 2.12 The S u b j e c t Centered Approach 17 2.13 The C h i l d Centered Approach ... 2 2 Notes 26 - i v -Page CHAPTER THREE 3.00 INTRODUCTION ... 28 3.10 The C l i n i c a l Method 2 8 3.20 The Sample 30 3.21 C h a r a c t e r i s t i c s of the Sample 31 3.30 Description of the Tasks 33 3.40 The Format of the Interviews 4 2 CHAPTER FOUR 4.00 ANALYSIS OF DATA 45 4.10 Summarizing Interview Data 45 N 4.20 Format of the Conceptual P r o f i l e . . . 46 4.30 A Conceptual P r o f i l e f o r the Concept of Force 4 6 4.40 Results Following the Conceptual P r o f i l e .. ... 47 4.41 Format of the Results 4 7 4.42 Results of Interview Data ... 48 4.50 Broad Patterns of B e l i e f s 39 4.6 0 The Three Levels of Abstraction of Children's B e l i e f s about the Concept of Force 91 4.61 F i r s t Level of Abstraction... 91 4.62 Second Level of Abstraction.. 93 4.63 Third Level of Abstraction... 9 4 CHAPTER FIVE 5.00 CONCLUSIONS, EDUCATIONAL IMPLICATIONS, AND RECOMMENDATIONS 96 5.10 Summary of the Study 96 5.20 Conclusions of the Study 96 -v-page 5.30 E d u c a t i o n a l I m p l i c a t i o n s 101 5.40 Recommendations f o r F u r t h e r Research 104 BIBLIOGRAPHY .... 108 APPENDIX 112 - V I -LIST OF TABLES Page 3.1 The Age, Grade, and Sex of Subjects 32 - v i i -LIST OF FIGURES Page FIGURE 3.1 M a t e r i a l s f o r Task 1 and I n t e r -viewer's and Subject's P o s i t i o n ... 34 3.2 M a t e r i a l s f o r Task 2 and I n t e r -viewer's and Sub j e c t ' s P o s i t i o n ... 37 3.3 M a t e r i a l s f o r Task 3 and I n t e r -viewer's and Subject's P o s i t i o n ... 4 0 - v i i i -ACKNOWLEDGMENT I wish to express my deep a p p r e c i a t i o n to P r o f e s s o r s G. E r i c k s o n , T. Hobbs, G.H. Cannon, and P. Mathews f o r agreeing to a c t as members o f the t h e s i s committee. To P r o f e s s o r G. E r i c k s o n , my t h e s i s a d v i s e r , I owe a s p e c i a l debt of g r a t i t u d e f o r h i s advice and guidance. H i s r e a d i n e s s to d i s c u s s any s m a l l d e t a i l o f my work whenever I needed was encouraging. I am a l s o p l e a s e d to acknowledge the h e l p f u l and necessary d i s c u s s i o n s w i t h P r o f e s s o r s G.H. Cannon and T. Hobbs, which helped to c l a r i f y some of the important problems encountered d u r i n g my study. I must a l s o mention here the important c o o p e r a t i o n o f the c h i l d r e n i n t e r v i e w e d and t h e i r t e a c h e r s , e s -p e c i a l l y ... Mr. N. Negrin, p h y s i c s teacher a t Gladstone Secondary S c h o o l . The p a t i e n c e of my daughters Carmen and A l e j a n d r a , and my companera B e t t y was a l s o important to my work s i n c e d u r i n g t h i s study I c o u l d n ' t d e d i c a t e enough time to them. F i n a l l y , I wish to thank Mrs. Carmen de S i l v a who has d i s p l a y e d g r e a t p a t i e n c e i n t y p i n g t h i s t h e s i s . -1-CHAPTER ONE 1.00 INTRODUCTION Theory has long been r e c o g n i z e d as a guide to a d d r e s s i n g problems of e d u c a t i o n a l p r a c t i c e . Broudy (1965) has attempted t o c l a r i f y the r e l a t i o n s h i p be-tween theory and p r a c t i c e i n a p r o f e s s i o n a l f i e l d such as e d u c a t i o n . He o u t l i n e s f o u r problemsareas which he claims to be unique to e d u c a t i o n . One of these areas i s the development and j u s t i f i c a t i o n of s t r a t e g i e s of t e a c h i n g and l e a r n i n g . B r i e f l y s t a t e d , Broudy c l a i m s t h a t t h e o r e t i c a l knowledge can be used, i n s e v e r a l d i f f e r e n t ways, to address problems of p r a c t i c e . One way i s t o t r y and apply the theory d i r e c t l y (e.g. deducing hypotheses from the theory, to t r y and s o l v e the problem). But, Broudy p o i n t s out t h a t knowledge can a l s o be used i n an i n t e r p r e t a t i v e manner. In t h i s way knowledge p r o v i d e s us w i t h broad conceptual maps t h a t permit us to b e t t e r understand the phenomena. I t has been i n t h i s l a t t e r sense t h a t t h e o r e t i c a l knowledge has had the most impact on e d u c a t i o n a l problems. One a r e a of knowledge t h a t has been d i s c u s s e d e x t e n s i v e l y f o r i t s p o t e n t i a l use i n e d u c a t i o n i s t h a t o f c o g n i t i v e theory. In p a r t i c u l a r , the t h e o r e t i c a l p e r s p e c t i v e s of Ausubel, Bruner and P i a g e t have been used to j u s t i f y p a r t i c u l a r t e a c h i n g s t r a t e g i e s o r even - 2 -programs. The t h e o r e t i c a l p e r s p e c t i v e of i n t e r e s t i n t h i s study i s P i a g e t ' s theory o f i n t e l l e c t u a l development. Some educators have d e r i v e d p r e s c r i p t i o n s from t h i s theory which suggest t h a t c u r r i c u l u m content ought to be c o o r d i n a t e d with the stage of i n t e l l e c t u a l development of the l e a r n e r . Those r e s e a r c h e r s u s i n g t h i s approach tend to p l a c e most of the emphasis upon d e f i n i n g those developmental stages i n terms o f o p e r a t i o n a l s t r u c t u r e s (e.g. see Lawson and Renner (1975), Lawson and Wollman (1976). However, the p r e s e n t study s u b s c r i b e s to the view t h a t l e a r n e r knowledge of con-t e n t , the c h i l d r e n ' s knowledge t h a t they b r i n g to the l e a r n i n g s i t u a t i o n , i s a l s o an important component i n d e v e l o p i n g any s e t of i n s t r u c t i o n a l procedures. In t h i s study, the broad concepts examined w i l l be those of f o r c e and the composition of f o r c e s . There are s e v e r a l reasons f o r s e l e c t i n g these concepts: (a) they are prominent t o p i c s i n secondary school c u r r i c u l a , (b) c h i l d r e n encounter s i t u a t i o n s i n v o l v i n g f o r c e s throughout t h e i r c h i l d h o o d y e a r s , (c) they p r e s e n t an o p p o r t u n i t y to i n v e s t i g a t e how c h i l d r e n understand a v e c t o r i a l q u a n t i t y . Knowledge o f c h i l d r e n ' s i d e a s about s c i e n t i f i c concepts i s as important to c u r r i c u l u m makers as i t i s to s c i e n c e t e a c h e r s . To the c u r r i c u l u m developer f o r example, i t c o u l d h e l p to develop i n s t r u c t i o n a l m a t e r i a l s -3-t h a t are s u i t a b l e to a broad spectrum of students; to decide at what p a r t i c u l a r grade or age l e v e l s c e r t a i n concepts might be presented; to a s s i s t students w i t h c e r t a i n types of misconceptions by developing a range of i n s t r u c t i o n a l m a t e r i a l s and a c t i v i t i e s . For the science teacher, t h i s type of knowledge could help by enab l i n g them to b e t t e r understand t y p i c a l d i f f i c u l t i e s experienced by students and so a l t e r t h e i r teaching s t r a t e g i e s i n an e f f o r t to r e s o l v e these d i f f i c u l t i e s . While a wide v a r i e t y of approaches have been used to study the p a t t e r n of b e l i e f s h e ld by a c h i l d about a concept (e.g. see Preece (1976), Shavelson (1974), D r i v e r (1973) , A l b e r t (1974) and Pines (1977)),, the author has decided to use an adaptation of Pia g e t ' s (1969) c l i n i c a l method. I t was f e l t t h a t t h i s technique would generate the type of r i c h data source r e q u i r e d f o r c a t e g o r i z i n g and o r g a n i z i n g c h i l d r e n ' s b e l i e f s i n t o a coherent p a t t e r n . Furthermore, t h i s data would a l s o be u s e f u l f o r i n t e r -p r e t i n g the r e s u l t s from any p e n c i l and paper q u e s t i o n n a i r e t h a t might be constructed to f o l l o w up on the present study. Since there are no w e l l defined hypotheses to t e s t , t h i s study must be considered as d e s c r i p t i v e and ex-p l o r a t o r y i n nature. Instead, i t w i l l attempt to generate hypotheses f o r f u r t h e r research i n a more c o n t r o l l e d s i t u a t i o n . 1.10 THE GENERAL PROBLEM This study has two main o b j e c t i v e s . The f i r s t one i s to f i n d out what ideas c h i l d r e n have about the concept - 4 -of force; that i s , how they resolve concrete problem situations involving judgments and explanations about t h i s v e c t o r i a l quantity. The second i s to look for trends or patterns i n the development of the concept of force i n children from the ages of six to fourteen. The author i s making an assumption that there exists i d e n t i f i a b l e patterns of ideas common to a number of children. One of the major issues i n the study then i s how to i d e n t i f y these patterns and inte r p r e t them so that they might have some application to classroom i n s t r u c t i o n a l practices. Since the study i s descriptive and exploratory i n nature, i t i s not possible to express the problem state-ment i n the form of a s p e c i f i c hypothesis. I t i s d i f f i c u l t and not r e a l l y useful to t ry to predict i n advance what kind of b e l i e f s children have about the concept of force,' However, the broad problem area can be broken down into more s p e c i f i c aspects i n the next section. 1.11 S p e c i f i c Problems The children's b e l i e f s about the following s p e c i f i c aspects of the concept of force were investigated. These aspects are expressed i n form of a l i s t of research questions. The s p e c i f i c research questions focus on children's b e l i e f s about: a) the action of forces as i l l u s t r a t e d by the tasks i n the study, b) the action and reaction p r i n c i p l e , - 5 -c) the i d e a of e q u i l i b r i u m i n a system i n v o l v i n g two or more f o r c e s , d) the e f f e c t o f changing the c o n f i g u r a t i o n o f weights and the r e s u l t a n t f o r c e they e x e r t , e) the composition o f f o r c e s . These r e s e a r c h q u e s t i o n s are f u r t h e r d i v i d e d i n t o more s p e c i f i c q u e s t i o n s ( i n t e r v i e w q u e s t i o n s i n the t a s k s ) . These s p e c i f i c q u e s t i o n s are f u l l y p r esented i n chapter t h r e e . The i n t e r v i e w q u e s t i o n s cover the s p e c i f i c a a r e a s o f the concept o f f o r c e which were probed i n the i n t e r v i e w s to o b t a i n data on c h i l d r e n ' s b e l i e f s r e l a t e d t o the r e s e a r c h q u e s t i o n s . 1.20 METHODS OF STUDY 1.21 Data C o l l e c t i o n The method chosen t o c o l l e c t the d a t a f o r t h i s study can be d e s c r i b e d as a m o d i f i e d c l i n i c a l method. The c l i n i c a l method, which r e q u i r e s p e r s o n a l c o n t a c t w i t h each s u b j e c t , was thought t o be most s u i t a b l e because i t produces a r i c h supply o f i n f o r m a t i o n about c h i l d r e n ' s conceptions o f p h y s i c a l phenomena. The m o d i f i c a t i o n o f the method, as d e s c r i b e d by P i a g e t (1969), comes from the use of a s t a n d a r d i z e d p r o t o c o l . S t a n d a r d i z e d q u e s t i o n s (asking the same ques t i o n s and i n the same order to a l l s u b j e c t s ) are used i n t h i s study f o r two reasons. F i r s t l y , s i n c e the search i s f o r c h i l d r e n ' s b e l i e f s o f s p e c i f i c aspects o f f o r c e , i t i s important t h a t every c h i l d i n the study have a s i m i l a r experimental s e t t i n g i n c l u d i n g the common tasks and q u e s t i o n s . Secondly, i t was f e l t t h a t - 6 -a more s t a n d a r d i z e d p r o t o c o l c o u l d be more r e a d i l y m o d i f i e d f o r use w i t h a group o f s t u d e n t s . (For example, a c l a s s o f s t u d e n t s ) . Even though, a more s t a n d a r d i z e d p r o t o c o l was used, the s t r e n g t h s o f the c l i n i c a l i n t e r v i e w were maintained where p o s s i b l e by u s i n g some open-ended p r o b i n g q u e s t i o n s and a d j u s t i n g some o f the q u e s t i o n s to take i n t o account p r e v i o u s responses made by the s u b j e c t . The i n t e r v i e w s were video-taped so t h a t a c c u r a t e t r a n s c r i p t s c o u l d be prepared to a s s i s t i n the a n a l y s i s o f the data. 1.22 Tasks, of the Study The experiments o r tasks used i n t h i s study were developed and implemented by P i a g e t e t a l (1973). Three o f the nine t a s k s t h a t they used were i n c l u d e d i n t h i s study, w i t h some s m a l l m o d i f i c a t i o n s . These t a s k s w i l l be d e s c r i b e d i n f u l l i n chapter t h r e e . 1.2 3 The Subjects The primary focus of the study was hot to determine the p r e c i s e age a c h i l d i s capable of g r a s p i n g a concept but to determine what t y p i c a l b e l i e f s are expressed by c h i l d r e n when they attempt to p r e d i c t and e x p l a i n s i t u -a t i o n s o r experiments d e a l i n g w i t h the concept o f f o r c e . S i n c e i t i s an e x p l o r a t o r y study, the r e p r e s e n t a t i v e n e s s and the s i z e o f the group o f s u b j e c t s i s not c r u c i a l to the r e s u l t s . I t i s important, however, to work w i t h normal c h i l d r e n , from a wide v a r i e t y o f backgrounds. The sample c o n s i s t e d of 32 c h i l d r e n (18 boys and 14 g i r l s ) , - 7 -ranging from 6 to 14 years o f age. E f f o r t s were made to determine some background i n f o r m a t i o n about the c h i l d (parent o c c u p a t i o n , economic s t a t u s , etc.) so as to t r y and a v o i d the i n t r o d u c t i o n o f any sy s t e m a t i c b i a s e s , such as u s i n g s u b j e c t s who were a l l i n the same socio-economic group. 1.30 EDUCATIONAL SIGNIFICANCE OF THE STUDY The n o t i o n o f f o r c e along w i t h the n o t i o n o f movement are some of the f i r s t p h y s i c a l experiences t h a t c h i l d r e n encounter i n t h e i r f i r s t years o f l i f e . They begin p u l l i n g and pushing o b j e c t s fromaa very e a r l y age and through the years g r a d u a l l y c o n s t r u c t t h e i r own hypotheses about p u l l i n g , pushing, e x e r t i n g p r e s s u r e , o r l i f t i n g o b j e c t s . That i s , those ideas are formed i n the absence o f any formal i n s t r u c t i o n by the school system. C h i l d r e n formulate t h e i r b e l i e f s by a c t i n g upon o b j e c t s and o c c a s i o n a l l y t r y i n g to express t h e i r ideas to o t h e r c h i l d r e n or a d u l t s . S i n c e , these b e l i e f s are o f t e n very d i f f e r e n t from those taught f o r m a l l y i n the s c i e n c e c u r r i c u l u m , i t would be u s e f u l f o r educators to be aware o f these p r i m i t i v e b e l i e f s h e l d by c h i l d r e n . The r e s u l t s o f the study about the c h i l d r e n ' s b e l i e f s can be a p p l i e d t o problems o f e d u c a t i o n a l p r a c t i c e by c r e a t i n g i n s t r u c t i o n a l s t r a t e g i e s based on knowledge o b t a i n e d from the study o r by p r o v i d i h g t b t h e s c i e n c e t e a c h e r w i t h the ideas t h a t c h i l d r e n used to t r y and account f o r s i t u a t i o n s i n v o l v i n g f o r c e s . I f teach e r s are aware of - 8 -c h i l d r e n ' s b e l i e f s , they can respond to given s i t u a t i o n s i n such a way to m a i n t a i n the b a s i c i n t e g r i t y o f the c h i l d ' s i d e a s . However, they may t r y to i n t r o d u c e t h e i r students to s i t u a t i o n s or experiments which may i l l u s t r a t e c e r t a i n anomalies or phenomena they have not c o n s i d e r e d b e f o r e . The purpose of such t e a c h i n g s t r a t e g i e s would be to encourage the students to modify o r change (perhaps g r a d u a l l y ) t h e i r e x i s t i n g b e l i e f s i n favour o f a more encompassing viewpoint. 1.4 0 LIMITATIONS OF THE STUDY Since , t h i s i s a d e s c r i p t i v e study, there i s no s p e c i f i c h y p o thesis being t e s t e d ; r a t h e r , the knowledge c l a i m t h a t i s b e i n g made ce n t e r s around: (a) the use o f the c l i n i c a l i n t e r v i e w as a v a l i d technique f o r g a t h e r i n g data about c h i l d r e n ' s b e l i e f s and (b) the a n a l y s i s of the i n t e r v i e w data. With r e s p e c t to the f i r s t i s s u e , the author r e a l i z e s the l i m i t a t i o n s o f u s i n g a r a t h e r s m a l l number o f s u b j e c t s . , I t i s not p o s s i b l e to g e n e r a l i z e to the whole p o p u l a t i o n o f s c h o o l c h i l d r e n from the r e s u l t s o f t h i s study; however, i t p r o v i d e s a s t a r t i n g p o i n t f o r f u r t h e r , more systematic i n v e s t i g a t i o n s i n t h i s a r e a . The second i s s u e , t h a t of r e d u c i n g the i n t e r v i e w data to a s e r i e s o f statements, i n a c o n c e p t u a l p r o f i l e , i s b a s i c a l l y a problem o f making i n f e r e n t i a l c l a i m s to account f o r some observed behaviour. There are no e x t e r n a l c r i t e r i a t o judge the accuracy o r v a l i d i t y o f t h i s procedure o t h e r than s u b m i t t i n g i t to o t h e r s to see i f they agree with the claims being made or encouraginggother researchers to try and reproduce our r e s u l t s . One further v a l i d i t y check would be to design a paper and pencil questionnaire, based upon the interview data, to see i f these statements make any sense to other students. - 1 0 -CHAPTER TWO 2.00 PSYCHOLOGICAL CONTEXT OF THE STUDY 2.01 P i a g e t ' s Theory of Development of Knowledge To Pi a g e t , the development of knowledge i n an i n d i v i d u a l , i s a spontaneous process which occurs as a r e s u l t of c o n t i n u a l encounters between the i n - ' d i v i d u a l and t h e i r immediate environment. T h i s de-velopment i s something a c t i v e and dynamic; i t i s a process t h a t becomes more complex as one grows from c h i l d h o o d to adulthood. As soon as one s t a r t s modi-f y i n g or t r a n s f o r m i n g o b j e c t s i n the environment f o r our own purpose, and understanding the nature of these t r a n s f o r m a t i o n s , P i a g e t c l a i m s t h a t t h i s i n v o l v e s two types of knowledge — o p e r a t i o n a l knowledge and p h y s i c or experimental knowledge. 2.02 O p e r a t i o n a l Knowledge The understanding of the t r a n s f o r m a t i o n s he r e f e r s t o as o p e r a t i o n a l knowledge. From P i a g e t ' s p e r s p e c t i v e knowledge of o p e r a t i o n s i s very b a s i c and fundamental to the process of i n d i v i d u a l s coming to know something about the world. P i a g e t d e f i n e s o p e r a t i o n s as i n t e r i o r i s e d a c t i o n s which modify the o b j e c t under study; they are ;r ever s i b le"'" and are always r e l a t e d to other o p e r a t i o n s - t h a t i s , a p a r t of a t o t a l o p e r a t i o n a l s t r u c t u r e . To P i a g e t , these • - 1 1 -o p e r a t i o n a l s t r u c t u r e s c o n s t i t u t e the n a t u r a l p s y c h o l o g i c a l r e a l i t y , i n terms o f which the de-velopment of knowledge must be understood. P i a g e t has a s c r i b e d the process o f development of knowledge i n an i n d i v i d u a l i n g e n e r a l i n terms of f o u r c o n t r i b u t i n g f a c t o r s : maturation ( i n the sense of p s y c h o l o g i c a l growth), experience, s o c i a l t r a n s -m i s s i o n , and e q u i l i b r a t i o n . None of them, s e p a r a t e l y , i s s u f f i c i e n t to e x p l a i n the dynamic process o f de-velopment of knowledge. R e f e r r i n g to the f a c t o r of e x p e r i e n c e , P i a g e t d e f i n e s two k i n d s of experience which are psycho-l o g i c a l l y very d i f f e r e n t -- p h y s i c a l experience and the l o g i c a l - m a t h e m a t i c a l e x p e r i e n c e . These types of experiences are r e s p o n s i b l e f o r g e n e r a t i n g the two k i n d s of knowledge r e f e r r e d to e a r l i e r . The l o g i c a l -mathematical experience i s r e l a t e d to the a c t i o n s e f f e c t e d upon the o b j e c t s ; knowledge i s not drawn from the o b j e c t s but from the s e t of a c t i o n s which modify the o b j e c t s . These are the experiences t h a t o p e r a t i o n s are made of and they are the b e g i n n i n g of l o g i c a l d e ductions. The subsequent steps w i l l c o n s i s t of i n t e r i o r i z i n g these a c t i o n s and then of combining wi t h other a c t i o n s to form o p e r a t i o n a l s t r u c t u r e s . -12-But, these l o g i c a l experiences must a l s o be supported by concrete m a t e r i a l . That i s , the p h y s i c a l e x p e r i e n c e s . 2.03 P h y s i c a l Knowledge: P h y s i c a l experience occurs when one a c t upon o b j e c t s and draw some knowledge about the o b j e c t s by a b s t r a c t i o n s from the o b j e c t s . For example, to d i s c o v e r t h a t one o b j e c t i s h o t t e r than another, a c h i l d touches both and f i n d s which one i s h o t t e r . T h i s i s the c u r r e n t use o f the word experi e n c e , t h a t i s , as i t i s used by the e m p i r i c i s t s . The f a c t o r r e l e v a n t to t h i s study i s t h a t o f p h y s i c a l experiences o r p h y s i c a l knowledge. C h i l d r e n ' s b e l i e f s about a s p e c i f i c concept have been formed by t h e i r ex-p e r i e n c e s with concrete m a t e r i a l s t h a t they have en-countered through t h e i r l i v e s . I t i s from these s o r t s of experience:• t h a t c h i l d r e n have n a t u r a l l y developed t h e i r ideas about some s p e c i f i c s c i e n t i f i c concepts. I t i s p h y s i c a l knowledge r e l a t e d to s p e c i f i c concepts t h a t c u r r i c u l u m makers and teachers should c o n s i d e r when p l a n n i n g programs to teach these concepts. No- formal c l a i m w i l l be made i n t h i s study t h a t the b e l i e f s i d e n t i f i e d can be construed as proper cog-n i t i v e s t r u c t u r e , i n the sense o f P i a g e t ' s o p e r a t i o n a l s t r u c t u r e s . T h i s i s a d e s c r i p t i v e and e x p l o r a t o r y study. The aim i s i n t r y i n g to d e s c r i b e the c h i l d r e n ' s b e l i e f s i n terms of t h e i r p h y s i c a l knowledge; t h a t i s , how - 1 3 -c h i l d r e n have been c o n s t r u c t i n g t h e i r i d e a s based on the experiences t h a t they have encountered. T h i s study assumes t h a t P i a g e t ' s c o n s t r u c t i o n i s t p e r s p e c t i v e i s h e l p f u l i n p r o v i d i n g a broad t h e o r e t i c a l framework f o r i n t e r p r e t i n g the i n t e r v i e w data. At the end, i t i s expected to o b t a i n a s e t of p a t t e r n s o f c h i l d r e n ' s b e l i e f s which can be thought o f as one type o f r e -p r e s e n t a t i o n o f the p h y s i c a l knowledge developed by c h i l d r e n through t h e i r encounters with t h e i r e n v i r o n -ment . Bohm (1965)also takes a c o n s t r u c t i o n i s t p e r s -p e c t i v e when a n a l y z i n g how s c i e n t i s t s come to p e r c e i v e the p h y s i c a l world. In an appendix to h i s book on The S p e c i a l Theory of R e l a t i v i t y , e n t i t l e d 'Physics and P e r c e p t i o n ' , Bohm claims t h a t our p e r c e p t i o n o f the p h y s i c a l world i s determined by "a c o n s t r u c t i o n o f an i n n e r show" ( i . e . , our mind) t h a t i s based upon constant a b s t r a c t i o n from our ex p e r i e n c e s . These a b s t r a c t i o n s occur a t d i f f e r e n t l e v e l s , a c c o r d i n g t o Bohm, ran g i n g from very p r i m i t i v e "immediate p e r c e p t i o n s " to h i g h e r l e v e l s of a b s t r a c t i o n which he claims to be the founda-t i o n o f s c i e n t i f i c knowledge. The p r o g r e s s i o n through these l e v e l s of a b s t r a c t i o n i s i l l u s t r a t e d by means of a h i s t o r i c a l example i n the f o l l o w i n g q u o t a t i o n : -14-"Consider, f o r example the experience of l o o k i n g out a t the n i g h t sky. A n c i e n t man a b s t r a c t e d from the s t a r s the p a t t e r n s of animals, men, and gods, and t h e r e a f t e r was unable to look a t the sky without s e e i n g such e n t i t i e s i n i t . Modern man knows t h a t what i s r e a l l y behind t h i s view is. an immeasurable u n i v e r s e of s t a r s , g a l a x i e s , g a l a x i e s o f g a l a x i e s , e t c . , and t h a t each person, having a p a r t i c u l a r p l a c e i n t h i s u n i v e r s e , o b t a i n s a c e r t a i n p e r s p e c t i v e on i t , which i s what i s seen i n the n i g h t sky. Such a man does not see animals, gods, e t c . , i n the sky, but he sees an immense u n i v e r s e t h e r e . But even the view of modern s c i e n c e i s probably t r u e o n l y i n a c e r t a i n domain. So f u t u r e man may form a very d i f f e r e n t n o t i o n o f the i n v a r i a n t t o t a l i t y t h a t i s behind our view o f the n i g h t sky, i n which prese n t n o t i o n s w i l l perhaps be seen as a s i m p l i f i c a t i o n , approximation, and l i m i t i n g case, but a c t u a l l y very f a r from being com-p l e t e l y t r u e . Can we not say then t h a t a t every stage man was extending h i s p e r c e p t i o n of the n i g h t sky, going from one l e v e l o f a b s t r a c t i o n to another, and i n each stage thus being l e d to hypotheses on what i s i n -v a r i a n t , which are able to stand up b e t t e r to f u r t h e r t e s t s , p r o b i n g s , e t c . ? But i f t h i s i s the case, then the most a b s t r a c t and g e n e r a l s c i e n t i f i c i n v e s t i g a t i o n s are n a t u r a l e x t e n s i o n s of the very same process by which the young c h i l d l e a r n s to come i n t o p e r c e p t u a l c o n t a c t w i t h h i s environment". The f i r s t l e v e l of a b s t r a c t i o n can be thought o f as corresponding to p e r c e p t i o n s based merely on sense -15-impressions or putting i n words what i s d i r e c t l y observed without adding any explanation nor acting with the purpose of making modifications upon the objects. Later, the subject perceives and embodies certai n s t r u c t u r a l features based not only on ab-stractions from immediate sensations/ but also on a series of abstractions over a more extended set of e a r l i e r perceptions. Because they now have a broader range of experience, which has been incorporated into the "inner show", i t i s possible for a higher l e v e l of abstraction to occur. At each l e v e l of abstraction a person views the world through a certain structure of ideas, with which one reacts immediately to each new experience (assimi-l a t i o n and accommodation i n Piaget's theory). Thus Bohm concludes: "In t h i s way we come to believe that cer t a i n ways of conceiving and perceiving the world cannot be otherwise, although i n f a c t they were d i s -covered and b u i l t up by us when we were children, and have since then become habits that may well be appro-priate only i n c e r t a i n domains of experience". A given l e v e l of abstraction then summarizes the invariant features of a certain domain of experience which has become habitual or obvious. The children's b e l i e f s obtained i n this study might be thought of. i n terms of these domains of experience. The encountering -16-of new and various experiences i s a continual process of " t r i a l and error" i n which what i s shown to be fal s e i s continually being set aside, while new struc-tures are continually being put forth for c r i t i c i s m . An example would c l a r i f y the ideas presented so f a r . In a Piagetian experiment, the subjects are given a piece of modelling clay. The experimenter pushes with a metal rod f i t t e d at i t s end with a disc , while the c h i l d does the same from his side. The question i s : W i l l one of us drive his rod i n farther that the other, and, i f so, which one? Children up to the age of 11 or 12 naturally answer that the adult i s stronger and w i l l drive h i s rod i n farther (low l e v e l of abstraction). But children 12 years of age and older give more complex explanations such as: "when you push strongly, I r e s i s t strongly, and when I push gently you r e s i s t gently, so we get compensation" (higher l e v e l of abstraction). Both children's answers contain the r e f l e c t i o n s and perceptions of past experiences and i l l u s t r a t e how knowledge develops. The underlying assumptions of the present study are based upon a type of constructionist viewpoint which holds knowledge to be a dynamic and active process. The ideas spelled out i n . t h i s process of "development of knowledge, explained by Piaget and Bohm, can be used to a s s i s t i n the inter p r e t a t i o n of the b e l i e f s expressed by the subjects interviewed. -17-2.10 EDUCATIONAL CONTEXT OF THE STUDY 2.11 I n t r o d u c t i o n The process of s c i e n c e c u r r i c u l u m development, p a r t i c u l a r l y the p h y s i c s s c h o o l c u r r i c u l u m , c o u l d be d i -vided' i n two main p e r i o d s i n North-America. The p r e -c i s e d i v i s i o n l i n e i s not c l e a r but i t can be s a i d t h a t the r e d i s c o v e r y o f P i a g e t , a t the be g i n n i n g o f the 6 0's, was one of the s t a r t i n g p o i n t s f o r the t r a n s i -t i o n . What i s the main d i f f e r e n c e between these two p e r i o d s ? The f i r s t one can be c a l l e d the s u b j e c t matter ce n t e r e d o r simply the s u b j e c t c e n t e r e d c u r r i c u l u m p e r i o d , and the second one the c h i l d c e n t e r e d c u r r i c u l u m p e r i o d . U n t i l the new i n t e r e s t i n P i a g e t the d i s -c i p l i n a r y experts and s c h o l a r s made many of the c u r r i -culum d e c i s i o n s by c o n s i d e r i n g o n l y the nature of the s u b j e c t area they were t e a c h i n g . Very l i t t l e a t t e n t i o n was giv e n t o the c h i l d ' s p s y c h o l o g i c a l development and the ideas they brought to the l e a r n i n g s i t u a t i o n . A f t e r r e a l i z i n g the s i g n i f i c a n c e o f P i a g e t ' s f i n d i n g s some c u r r i c u l u m makers and teachers c o n s i d e r e d the c h i l d as a more prominent p a r t o f the c u r r i c u l a r process and t h i s was the s t a r t f o r the c h i l d - c e n t e r e d c u r r i c u l u m e r a . 2.12 The Subject Centered Approach During the f i r s t p e r i o d ( s u b j e c t - c e n t e r e d o r non-c h i l d - c e n t e r e d ) two k i n d s of approaches were used to de-c i d e about c u r r i c u l u m content. They were the h i s t o r i c a l o r c h r o n o l o g i c a l approach and the l o g i c a l ( l o g i c a l from the p e r s p e c t i v e of the d i s c i p l i n e ) approach. - 1 8 -When u s i n g the h i s t o r i c a l approach, the c u r r i ^ culum makers would suggest t h a t the c u r r i c u l u m content should be based on the c h r o n o l o g i c a l o r d e r i n which the concepts were developed. I t was assumed t h a t students c o u l d b e s t l e a r n these concepts f o l l o w i n g the same h i s t o r i c a l o r d e r without any f u r t h e r p e d a g o g i c a l a n a l y s i s . For example, i n p h y s i c s , the c l a s s i c a l o r t r a d i t i o n a l o r d e r o f content i s : measurement (time, d i s t a n c e , mass), mechanics, heat, l i g h t , sound, e l e c t r i c i t y , magnetism, s t r u c t u r e o f matter and s t r u c t u r e of the atom. Some c u r r i c u l u m makers and teachers thought t h a t t h i s was the " n a t u r a l and l o g i c a l " o r d e r f o r t e a c h -i n g them a t s c h o o l . From here, i t i s c l e a r t h a t there was no c o n s i d e r a t i o n o f the c h i l d . The f u n c t i o n o f the c h i l d was to l e a r n what i t was supposed to l e a r n , u s u a l l y by memory, s i n c e the c h i l d ' s p s y c h o l o g i c a l development 2 was not c o n s i d e r e d a t a l l . The l o g i c a l approaches d i f f e r e d from the h i s t o r i c a l i n t h a t o t h e r aspects were c o n s i d e r e d i n " r e s p e c t to con-t e n t and i t s o r d e r . One l o g i c a l approach was to put the emphasis on the s c i e n t i f i c method. T h i s method, the same as was- used by s c i e n t i s t s , was imposed a t s c h o o l . I t was assumed t h a t i f students had the ch o i c e t o "use" i t , they would understand what s c i e n c e was about and they had a . " t o o l " t o understand the p h y s i c a l world. T h i s assumption c o u l d be c o r r e c t but the implementation o f i t was incomplete due to the f o l l o w i n g reasons: -19-l i t t l e d i r e c t i o n was given, students' ideas were not considered, teachers were i l l - p r e p a r e d to teach science, laboratory space was i n s u f f i c i e n t , and equipment was scarce and sophisticated (only teachers were allowed to use i t ) ; thus, l i t t l e of.value was achieved. In 19 30 the National Society for the study of Education Yearbook, e n t i t l e d "A Program for Teaching Science", had a profound e f f e c t upon the f i e l d of science education. This program was thought to i n -fluence the d i r e c t i o n of science education and research for two decades. The Program Committee took the stand that objectives and curriculum content should be formulated i n terms of major ideas, concepts and p r i n c i -ples that control the understanding of s c i e n t i f i c facts and t h e i r application i n the world. In developing new courses of physics i t was suggested that a few large concepts be used as organizing themes, then, d i f f e r e n t l o g i c a l approaches could be developed following these themes. Examples of large concepts were: "the inde-s t r u c t i b i l i t y of matter and energy", and " a l l physical phenomena are based upon energy transformations". The object of using these themes was to avoid the t r a d i t i o n a l compartmentalization of physics ( h i s t o r i c a l approach) into short, separate, unrelated topics. Unfortunately the Second World War stopped the implementation of t h i s program. - 2 0 -The main s h i f t sought w i t h the new program was to change the r a t i o n a l e o f s c i e n c e t e a c h i n g , moving from a p h i l o s o p h i c a l o r t h e o r e t i c a l approach, l a c k i n g student involvement i n experimentation, to a more l a b o r a t o r y - o r i e n t e d approach i l l u s t r a t i n g Newtonian p h y s i c s . While t h e r e was the d e s i r e to c o n s i d e r the c h i l d i n the development of the c u r r i c u l u m t h e r e was not s u f f i c i e n t knowledge of how to do i t . Dewey s t a t e d t h a t we must teach to the "whole c h i l d " and t h a t i n -d i v i d u a l d i f f e r e n c e s should be c o n s i d e r e d i n the t e a c h -i n g p r o c e s s . T h i s d e s i r e to improve the t e a c h i n g of s c i e n c e was continued d u r i n g the 50's w i t h the so-c a l l e d c u r r i c u l u m r e v o l u t i o n . One o f the purposes of the c u r r i c u l u m r e v o l u t i o n was to b r i n g e d u c a t i o n i n t o the 20th century by con-s i d e r i n g the l a t e s t advances i n the f i e l d s o f knowledge t h a t a f f e c t the process of e d u c a t i o n . P a r t i c u l a r l y most r e c e n t advances i n n a t u r a l sciences"^ were con-s i d e r e d when p l a n n i n g the new s c h o o l c u r r i c u l a . Even c o n s i d e r i n g these important changes, the c h i l d was s t i l l not a t the c e n t r e of the t e a c h i n g - l e a r n i n g p r o -c e s s . C u r r i c u l u m makers, educators, and s c i e n t i s t s were t h i n k i n g o n l y i n terms of the l a s t advances i n t h e i r r e s p e c t i v e f i e l d s and new ways how to p r e s e n t them to the c h i l d r e n . But n e i t h e r the c h i l d ' s p s y c h o l o g i c a l development nor t h e i r i d e a s about s c i e n t i f i c - 2 1 -concepts were being s e r i o u s l y c o n s i d e r e d y e t . I t i s t r u e t h a t the Disc o v e r y Methodology was h i g h l y recommended, where c h i l d r e n had the o p p o r t u n i t y t o show t h e i r i n t e r e s t s and a b i l i t i e s but there was no i n t e r e s t t o f i n d out the a l t e r n a t i v e ideas t h a t c h i l d r e n have i n some content areas. I t was a s o r t o f " d i r e c t e d d i s c o v e r y " , t h a t i s , c h i l d r e n should d i s c o v e r what the teacher leads (sometime i n d i r e c t l y ) them to d i s c o v e r . Another l o g i c a l approach t o develop a new c u r r i c u l u m was o f t e n based upon an a n a l y s i s of the s t r u c t u r e o f the d i s c i p l i n e (Bruner, 1960) . One p a r t i c u l a r l o g i c was to t r y and e s t a b l i s h a h i e r a r c h i c a l o r d e r o f concepts, going from the s i m p l e s t concept t o the most complex ones. Again, the d i s c i p l i n a r y experts decided about t h i s h i e r a r c h i c a l o r d e r . There are many c u r r e n t s c h o o l p h y s i c s textbooks w r i t t e n u s i n g t h i s approach. To mention o n l y some of them: Barton and Raymer(1966), Krauskopf and B e i s e r (The P h y s i c a l World, 1960), MacLachlan, M c N e i l l and B e l l (Matter and Energy, 1963) , B.stwden and F r e d e r i c k s (1966) . U n f o r t u n a t e l y some s c i e n c e t e a c h e r s took the textbooks as the o n l y guide and f o l l o w e d the book page by page. In these cases, the textbook, which u s u a l l y r e p r e s e n t s one or two persons' p o i n t o f view, was the whole c u r r i c u l u m . Another example but d e v e l o p i n g another 4 l o g i c a l o r d e r o f content was the PSSC P h y s i c s Course . -22-The s t a f f d e v e l o p i n g t h i s course d e f i n e d f o u r l a r g e concepts: The Universe, the wave nature o f matter, the p a r t i c u l a t e nature of matter, and the e l e c t r o m a g n e t i c nature of matter. Using these themes they s t r u c t u r e d the PSSC course. The e v a l u a t i o n s made on t h i s course have demonstrated t h a t i t can be c o n s i d e r e d a w e l l -designed course f o r students who are very i n t e r e s t e d i n the f i e l d of p h y s i c s but not f o r the m a j o r i t y of h i g h school students. A f t e r r e a l i z i n g some of the d e f e c t s of the PSSC course some s c i e n t i s t s and teachers met a t Harvard U n i v e r s i t y to d i s c u s s the c r e a t i o n of a completely new type o f p h y s i c s course. 5 T h i s new course, c a l l e d The P r o j e c t P h y s i c s Course , would take a more humanitarian p o i n t o f view. The con-t e n t of the course was a l s o s t r u c t u r e d around l a r g e concepts. But even when i t was planned i n such a way t h a t c h i l d r e n c o u l d advance a t t h e i r own pace, the p s y c h o l o g i c a l development o f students was not c o n s i d e r e d . The P r o j e c t P h y s i c s Course i s c o n s i d e r e d by some to be the b e s t e f f o r t t o improve the p h y s i c s t e a c h i n g , and i t has been s u b j e c t to a number o f e v a l u a t i o n s t u d i e s . (Welch and Walberg 1968; Welch, Walberg and Watson, 19 71; Welch, 1968; Walberg, 1967, Welch and Rathman, 1968; Welch, 1967) . 2.13 The C h i l d - C e n t e r e d Approach The c h i l d - c e n t e r e d c u r r i c u l u m might be c h a r a c t e r -i z e d by the importance p l a c e d upon the p s y c h o l o g i c a l and mental development o f c h i l d r e n as b a s i c i n p u t s - 2 3 -when p l a n n i n g the school c u r r i c u l u m . Then, t h i s p e r i o d i s c h a r a c t e r i z e d f o r u s i n g a p s y c h o l o g i c a l approach. T h i s does not mean t h a t everywhere t h i s approach was being used, but a t l e a s t , t h e r e were n a t i o n a l e f f o r t s to c o n s i d e r i t s e r i o u s l y and some s c i e n c e c u r r i c u l u m supported by N a t i o n a l Foundations were c r e a t e d . Some elementary s c i e n c e programs have attempted to i n c o r p o r a t e some o f the P i a g e t " s conceptions i n t h e i r programs, ( f o r example, Science C u r r i c u l u m Improvement Study (SCIS), the N u f f i e l d Primary S c i e n c e , S/13.) . T h i s c h i l d - c e n t e r e d p e r i o d i s s t i l l i n ; i t s -i n f a n c y . The i n v e s t i g a t i o n o f ideas t h a t c h i l d r e n h o l d 6 labout s c i e n t i f i c concepts i s s t i l l going on . The c h i l d - c e n t e r e d approach has been f o l l o w i n g two d i f f e r e n t d i r e c t i o n s i n the l a s t y e a r s . One suggests t h a t c u r r i c u l u m content ought to be matched to the stage o f development of the l e a r n e r ( P i a g e t i s stages o f development). To i l l u s t r a t e , R e n n e r and Lawson (1975) have proposed as a necessary c o n d i t i o n f o r s e l e c t i o n o f c u r r i c u l u m content a t the secondary o r p o s t secondary l e v e l s t h a t the content be " u s e f u l f o r h e l p i n g s t u d e n t s " i n u s i n g formal r e a s o n i n g a b i l i t i e s . There are two problems a s s o c i a t e d w i t h t h i s type o f a p p l i c a t i o n o f P i a g e t ' s theory t o c u r r i c u l u m problems. The f i r s t i s r e l a t e d to the low l e v e l o f c o r r e l a t i o n -24-commonly found among piagetian tasks which are supposed to depend on the same structures (the decalage , problem or regression to a lower stage of development). The second problem i s related to the d i f f i c u l t y of c l a s s i -fying given subjects according to developmental stage (the c r i t e r i o n problem)'(Hobbs (1977)* Chiappetta (1975) , Howe (1974)). The second d i r e c t i o n or approach i s based on de-velopmental studies of p a r t i c u l a r concepts or content. One of the concerns here i s to i d e n t i f y consistent patterns of development (children's beliefs) of the p a r t i c u l a r concepts i n question. What are the children's key ideas i n the process of attainment of the concepts? I f t h i s information i s obtained then what are the appro-priate strategies to teach the concepts? What sequences are appropriate? In t h i s kind of research, stages of development with t y p i c a l age ranges could be determined but t h i s i s not e s s e n t i a l . However, the use of Piaget's more general theory of i n t e l l e c t u a l development might help i n interpreting some of the children's b e l i e f s , since, i t i s a very powerful tool for analysis of i n -terview data ( c l i n i c a l method). The present study i s of the l a t t e r type since the major i n t e r e s t i s i n t r y i n g to i d e n t i f y consistent patterns of student b e l i e f s about the concept of force. These patterns should contain information of how children - 2 5 -p e r c e i v e some aspects o f th.e concept of f o r c e a t d i f f e r e n t ages. Through the yea r s , the c h i l d r e n would be expected t o develop a more complete under-sta n d i n g o f the concept, and t h e i r e x p l a n a t i o n s and p r e d i c t i o n s should r e f l e c t t h i s change. T h i s p e r i o d of c h i l d - c e n t e r e d c u r r i c u l a has j u s t s t a r t e d w i t h the c o n s i d e r a t i o n o f the p s y c h o l o g i -c a l development o f the c h i l d i n the p l a n n i n g o f new school c u r r i c u l a . I f the ideas t h a t c h i l d r e n have about p h y s i c a l concepts are i n c l u d e d i n the sch o o l c u r r i c u l u m then children can be thought o f as genuine . . . 7 p a r t i c i p a n t s i n the t e a c h i n g - l e a r n i n g process . To reach t h i s stage, i t i s necessary t o do much r e s e a r c h i n the d i r e c t i o n of e x p l o r i n g c h i l d r e n ' s b e l i e f s on concepts i n c l u d e d i n the sch o o l c u r r i c u l u m . The p r e -sent study i s f o c u s i n g " upon t h a t p a r t i c u l a r problem. NOTES ' R e v e r s i b l e a c t i o n : a c t i o n t h a t can take p l a c e i n both d i r e c t i o n s . For example: adding or s u b s t r a c t i n g , j o i n i n g or s e p a r a t i n g . The t e a c h i n g of p h y s i c s as a secondary school s u b j e c t was g i v e n g r e a t e r s t a t u s when, i n 1 8 7 2 , Harvard U n i v e r s i t y made p h y s i c s an a c c e p t a b l e s u b j e c t f o r entrance requirement. The g e n e r a l agreement then was to teach the concepts i n a h i s t o r i c a l o r d e r of development. P h y s i c s by 1900 was taught as a means of d i s c i p l i n i n g the mind w i t h more and more emphasis being p l a c e upon mathematical and q u a n t i t a t i v e treatment of the expense of i n f o r m a t i o n a l and experimental treatment. M i l l i k a n thought t h a t the s o l e purpose of h i g h s c h o o l p h y s i c s should be to i n t e r e s t and t r a i n the p u p i l i n o b s e r v a t i o n of a g r e a t number of p h y s i c a l phenomena. The Report of the Commission on the R e o r g a n i z a t i o n of Science i n Secondary Schools p u b l i s h e d i n 1920 s h i f t e d the emphasis i n p h y s i c s t e a c h i n g away from s u b j e c t matter as such towards the s o c i a l u t i l i t y concept. One of the reasons f o r the s h i f t was t h a t content had too l a r g e l y been handed down by t r a d i t i o n through textbooks. I t had been l a r g e l y based on l o g i c a l o r g a n i z a t i o n , n e g l e c t i n g i n t e r e s t s of p u p i l s and laws of l e a r n i n g . As knowledge i n p h y s i c s grew, teachers thought i t necessary to i n c l u d e more and more m a t e r i a l i n the p h y s i c s courses. P h i l o s o p h y , p o l i t i c a l and economical s c i e n c e s , s o c i o l o g y , psychology were a l s o c o n s i d e r e d . An e x c e r p t from the Appendix 3, PSSC book, 1960: "During the f a l l o f 1956 and the w i n t e r of 1957, under the l e a d e r s h i p of the PSSC S t e e r i n g Committee, r e s e a r c h physicists,and p h y s i c s teachers (author's remarks: "experts i n the f i e l d " ) - o f t e n they are the same.people - o u t l i n e d d r a f t e d , and d i s c u s s e d many of the i d e a s t h a t now appear i n t h i s book". A f t e r r e a d i n g the whole appendix, there i s no mention of c o n s i d e r i n g knowledge t h a t c h i l d r e n b r i n g t o the l e a r n i n g s i t u a t i o n . cont' d - 2 7 -NOTF.S - continued.";. 5. The P r o j e c t P h y s i c s Course i s based on the i d e a s and r e s e a r c h o f a n a t i o n a l c u r r i c u l u m development p r o j e c t t h a t worked i n three phases. F i r s t , the authors - a h i g h school p h y s i c s teacher, a u n i v e r s i t y p h y s i c i s t , and a p r o f e s s o r of s c i e n c e e d u c a t i o n - c o l l a b o r a t e d to l a y out the main goals and t o p i c s of a new i n -t r o d u c t o r y p h y s i c s course. They worked from 1962 to 1964, and the f i r s t v e r s i o n of the t e x t was t r i e d out i n two schools w i t h encouraging r e s u l t s . In the second phase, a l a r g e number of c o l l a b o r a t o r s (high school p h y s i c s t e a c h e r s , astronomers, chemists, h i s t o r i a n s , p h i l o s o p h e r s of s c i e n c e , s c i e n c e educators p s y c h o l o g i s t s , e v a l u a t i o n s p e c i a l i s t s , e n gineers, f i l m makers, a r t i s t s and g r a p h i c designers) were brought together from a l l p a r t s of the n a t i o n s , and the group worked t o g e t h e r f o r over f o u r years under the t i t l e Harvard P r o j e c t P h y s i c s . In the l a s t phase, the t h r e e o r i g i n a l c o l l a b o r a t o r s s e t out to develop the v e r s i o n s u i t a b l e f o r l a r g e s c a l e p u b l i c a t i o n by t a k i n g i n t o account the e v a l u a t i o n r e s u l t s from the t r y o u t c a r r i e d out from 1964 to 196 8. 6. A study conducted by Raven (1967) about the concept of momentum showed t h a t c h i l d r e n between 5 and 8 years o l d go through the f o l l o w i n g concept sequence: momentum, c o n s e r v a t i o n of matter, p r o p o r t i o n a l use of mass and speed w i t h momentum h e l d constant, and speed. Whereas one l o g i c a l - h i e r a r c h i c a l sequence f o r t e a c h i n g the concept o f momentum might be: c o n s e r v a t i o n of matter, speed, p r o p o r t i o n a l use of mass and speed w i t h momentum h e l d constant and f i n a l l y momentum. P i a g e t , a f t e r many experiments w i t h c h i l d r e n , has found t h a t the sequence of some p h y s i c a l and mathematical i d e a s developed by c h i l d r e n does not correspond to the c h r o n o l o g i c a l o r h i s t o r i c a l o r d e r (from the Greeks to the present) but, conforms to an o r d e r t h a t l i n k s the more fundamental ideas to the d e r i v e d ones. 7. There has been very l i t t l e research to look for these strategies to produce a desired s h i f t when a c h i l d has "misconceptions". - 2 8 -CHAPTER T H R E E 3.00 INTRODUCTION T h i s chapter d e a l s w i t h the method o f c o l l e c t i n g the data. Since a m o d i f i e d P i a g e t i a n c l i n i c a l technique was used, some background about t h i s method i s presented. The s e l e c t i o n o f the s u b j e c t s i s e x p l a i n e d , and the tasks and t h e i r r e s p e c t i v e p r o t o c o l s are developed i n f u l l . 3.10 THE CLINICAL METHOD In the l a s t decades, t h e r e have been two schools o f thought o f how one should proceed w i t h the study o f c o g n i t i v e behaviour : one based on a m u l t i v a r i a t e model, i n which the most " r e l e v a n t " v a r i a b l e s are c o n s i d e r e d and others are c o n t r o l l e d . The ' r e l e v a n t behaviours' are o f t e n s t u d i e d i n c o n t r i v e d experimental s i t u a t i o n s , o r a s e t o f a p r i o r i c a t e g o r i e s are used t o c l a s s i f y behaviour o c c u r r i n g i n ;.a n a t u r a l s e t t i n g . Once, t h i s measurement procedure has occ u r r e d , the r e s u l t i n g numbers are manipulated a c c o r d i n g to some s t a t i s t i c a l model A second approach can be c h a r a c t e r i z e d as b e i n g more e x p l o r a t o r y o r d e s c r i p t i v e i n nature. The focus o f t h i s approach i s to i d e n t i f y r e l e v a n t v a r i a b l e s and p o t e n t i a l hypotheses f o r subsequent studies. One u s e f u l technique which i s i n c r e a s i n g i n p o p u l a r i t y , i s the c l i n i c a l i n t e r v i e w method. Th i s technique r e q u i r e s the i n t e r v i e w e r to a c t i v e l y e x p l o r e the thoughts and b e l i e f s expressed by the s u b j e c t about the - 2 9 -topic of i n t e r e s t (Piaget, 1969). In a c l a s s i c a l Piagetian c l i n i c a l interview, the interviewer and subject engage i n conversation about what the interviewer thinks i s relevant to his inv e s t i g a t i o n . In the present study, the interviewer has a fixed set of questions (standardized protocol), and so might be con-sidered a modified c l i n i c a l method. However, the strengths of the c l i n i c a l interview • were maintained by asking probing questions i n an attempt to insure the r e l i a b i l i t y and v a l i d i t y of the students' responses. This non-standardized probing also 'served-; to uncover deeper ' insights which often are not apparent from the l i t e r a l i n -terpretation of the dialogue. In using t h i s method, the interviewer attempts to form judgments, or hypotheses i n his own mind about the interviewee's thinking and then systematically sets out to check them out. Consequently, the interview generates much more data than an experimental study, however, the analysis of these data i s often d i f f i c u l t and time consuming. The most serious objections to the c l i n i c a l method are 'that i t i s unstructured, subjective, and prone to experimental bias. However, i f the protocol for the i n t e r -view i s planned i n advance and s i m i l a r lead questions are given to a l l the subjects, then, some degree of control i s obtained. Less subjective, i n s i g h t f u l , and interpretive judgments about children's responses are obtained -30-i f (1) experienced i n t e r v i e w e r s proceed w i t h the i n t e r -view, and (2) videotape i s used, to r e p l a y and check a l l behaviour o c c u r r i n g d u r i n g the i n t e r v i e w . The p r e s e n t study r e l i e d upon the use o f a videotape r e c o r d e r to r e c o r d the o v e r t behaviour o f the i n t e r v i e w e r and the s u b j e c t . T h i s o b j e c t i v e r e c o r d allows o t h e r s access to the raw data f o r the purpose o f d i s p u t i n g or de-v e l o p i n g a l t e r n a t e c l a i m s to those made by the i n v e s t i -g a t or to account f o r the observed behaviour. In summary, a l l the data necessary f o r t h i s study was o b t a i n e d from the videotapes f i l m e d d u r i n g the i n t e r v i e w s . 3.20 THE SAMPLE Two important aspects were c o n s i d e r e d i n s e l e c t i n g s u b j e c t s f o r the sample: 1) the s u b j e c t s were a l l h e a l t h y and w e l l - a d j u s t e d c h i l d r e n , and 2) they had not been taught f o r m a l l y the concept o f f o r c e , i n c l u d i n g the s u b s i d i a r y concepts such as: a c t i o n and r e a c t i o n , e q u i l i b r i u m , and composition o f f o r c e s . These c r i t e r i a were checked by a s k i n g the teacher about the p h y s i c a l and emotional s t a t e o f the c h i l d and whether they had s t u d i e d f o r c e s t h a t year. The c h i l d was a l s o asked i n the course of the i n t e r v i e w i f he had been asked "questions l i k e t h i s " a t s c h o o l . As i n d i c a t e d i n Chapter One, the o b j e c t i v e o f the study - 3 1 -is: not to determine a t what p r e c i s e age a c h i l d grasps a p a r t i c u l a r concept, but to determine t y p i c a l b e l i e f s ex-pressed by c h i l d r e n when they attempt t o p r e d i c t and e x p l a i n expected r e s u l t s of experiments d e a l i n g w i t h the concept o f f o r c e . The sample was not randomly s e l e c t e d from a w e l l d e f i n e d p o p u l a t i o n ; t h e r e f o r e , " s t a t i s t i c a l l y speaking", the r e s u l t s o b t a i n e d are v a l i d o n l y f o r the s u b j e c t s i n -cluded i n the sample. I t was decided to proceed i n t h i s way, s i n c e , t h i s i s an e x p l o r a t o r y study. However, e f f o r t s were made to a v o i d any s y s t e m a t i c b i a s by not s e l e c t i n g a l l s u b j e c t s from the same s c h o o l , o r u s i n g schools l o c a t e d i n one p a r t i c u l a r area of- the c i t y . 3.21 C h a r a c t e r i s t i c s o f the Sample The Ss f o r the sample were taken from the f o l l o w i n g areas i n g r e a t e r Vancouver: P o r t Coquitlam, Burnaby, Ea s t Vancouver and P o i n t Grey ( u n i v e r s i t y d i s t r i c t ) . The sample i s shown i n Table 3.1, i n c l u d i n g age and sex d i s t r i -b u t i o n s . To f a c i l i t a t e the p r e s e n t a t i o n o f ages, i t was d e c i d e d to c o n s i d e r the years completed o n l y ; f o r example, a s u b j e c t 8 years and 11 months, was c o n s i d e r e d 8 years o l d . Due to t h i s procedure the balance o f boys to g i r l s v a r i e s s l i g h t l y from one age to the next. Since sex was not con-s i d e r e d to be a major independent v a r i a b l e no d e l i b e r a t e attempt was made to match the groups. The major concern - 3 2 -TABLE 3.1 The Age, Grade,and Sex of S u b j e c t s Age (years) School grade Sex boys g i r l s T o t a l 6 2 1 1 2 7 2 2 2 4 8 3 2 1 3 9 4 1 5 4&5 10 1 4 5 11 6 2 1 3 12 7 2 2 4 13 8 2 2 4 14 9 2 2 T o t a l 18 14 T o t a l : 3 2 -33-was to t r y and e s t a b l i s h a t y p i c a l sample of s u b j e c t s . There was a considerable amount of d i v e r s i t y among the subjects w i t h respect to the socio-economic back-ground and l e v e l s of achievement i n school. The s o c i o -economic data was i n f e r r e d 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 s , i n p a r t i c u l a r focusing upon t h e i r p a r e n t s 1 o c c u p a t i o n a l s t a t u s . The teachers were asked to s e l e c t c h i l d r e n from a wide range of i n t e l l e c t u a l a b i l i t y . This was c l e a r l y demonstrated during the i n t e r v i e w s , when some 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 while others were concent to respond to many questions posed by the i n v e s t i g a t o r w i t h a simple r e s -ponse and made no attempt at an e x p l a n a t i o n f o r t h e i r p r e d i c t i o n . 3.30 DESCRIPTION OF THE TASKS The tasks t h a t were used i n t h i s study were modi-f i c a t i o n s of those described by J . P i a g e t e t aJL (1973) . TASK ONE Apparatus: A r e c t a n g u l a r wooden board w i t h a p u l l e y a t one end was used (see Figure 3.1). A blue p l a s t i c r e -ference p l a t e i s attached a t one end to an e l a s t i c band which i s h e l d by a thumb tack. The other end of the p l a t e i s attached to a s t r i n g , which goes over the p u l l e y and hangs down below the board. Three metal hooks spaced 10 cm apart are attached to the end of the s t r i n g . Three or more washers (each weighing approximately 50 g) are used to hand upon the hooks. - 3 4 -This task was s p e c i f i c a l l y chosen to explore the children's b e l i e f s about the concept of the action of a force, the action and reaction p r i n c i p l e , and con-servation of weight. B: board P: plate E: e l a s t i c band S : s t r i n g T: thumb tack Pu: pulley W: • washers ( 50 H: hooks <^ 60 cm<' : > Interviewer s i t s on t h i s side H J J Figure 3.1 Materials for Task 1 and Interviewer's and Subject's Position Interview Protocol for Task One As an introduction to each of the tasks the interviewer f a m i l i a r i z e d the subject with the task materials. - 3 5 -Research Question: Concept o f the A c t i o n o f a Force I: I n t e r v i e w e r , S: Subject 1^: Could you d e s c r i b e to me what i s going to happen i f you put t h i s washer i n the upper hook? I 2 : Could you show me how the blue p l a t e i s going to move?- How f a r ? I ^ : ( a f t e r S p l a c e d the washer) What i s the washer doing a t t h i s moment? (The i n t e r v i e w e r then probes f u r t h e r t o e s t a b l i s h as p r e c i s e l y as p o s s i b l e the nature o f the c h i l d ' s b e l i e f s , u s i n g the child's words when p o s s i b l e . The c h i l d ' s words are a l s o used i n subsequent d i s c u s s i o n s when i t i s c o n s i d e r e d a p p r o p r i a t e to do s o ) . 1^: You t o l d me t h a t the p l a t e moved a l i t t l e b i t , can you e x p l a i n me why i t d i d not continue moving? (Or why d i d the p l a t e stop where i t did?) A l t e r n a t i v e I : I f S mentions t h a t the washer and the e l a s t i c are p u l l i n g the p l a t e i n o p p o s i t e d i r e c t i o n . , 1^ Q : What do you mean by that " ? (I can probe here : number o f f o r c e s a c t i n g upon the p l a t e , magnitude of f o r c e s , and d i r e c t i o n o f force s ) Then I ask q u e s t i o n 1^ ^ A l t e r n a t i v e I I : I f S does not mention the a c t i o n o f the e l a s t i c band upon the p l a t e . I'_ ,: The p l a t e i s s t a t i o n a r y now. I s the washer s t i l l p u l l i n g ? - 3 6 -I g : : I f you put one more washer i n the same hook, what do you t h i n k i s going to happen? How f a r w i l l the p l a t e move t h i s time? (I h o l d the p l a t e w h i l e the S puts on the washer and then l e t s i t go t o permit the p l a t e to move). 1^: And i f you put one more washer i n the same hook? (I again h o l d the p l a t e u n t i l p r e d i c t i o n i s made). Ig: I f you remove one washer, what w i l l happen i n t h i s case? Research Question: The A c t i o n and Reaction P r i n c i p l e . 1^: You s a i d b e f o r e t h a t the washers are p u l l i n g the p l a t e , what e l s e i s p u l l i n g ? (or : Is an y t h i n g e l s e p u l l i n g ? ) A l t e r n a t i v e I : I f S r e a l i z e s t h a t a l l o b j e c t s i n the task are p u l l i n g each o t h e r : I ^ Q QZ What o b j e c t s are p u l l i n g the p l a t e (the e l a s t i c band, the s t r i n g ) ? I^ Q ^: In what d i r e c t i o n are they p u l l i n g ? 1^0 2 : Y o u s a i d t h a t the s t r i n g i s p u l l i n g the p l a t e and t h a t the p l a t e i s p u l l i n g the s t r i n g : Are they p u l l i n g i t the same way or d i f f e r e n t ? A l t e r n a t i v e I I : I f S does not r e a l i z e t h a t a l l o b j e c t s are p u l l i n g each o t h e r , go to q u e s t i o n I - ^ i ' P r o b i n g C o n s e r v a t i o n o f Weight: ! I ^ ^ : What do you expect i s going to happen to the p l a t e i f you put the same three washers i n the lowest Hook? Why do you t h i n k so? (I h o l d the p l a t e - 3 7 -w h i l e S moves the washers). 1^2 : What do you expect i s going t o happen i f you put one washer i n each hook? (I h o l d the p l a t e while the S attaches the washers). Why do you t h i n k so? Why are they going t o p u l l the same TASK TWO Apparatus: A r e c t a n g u l a r wooden board; 2 p u l l e y s , one i n each end; blu e p l a t e a t the centre has a s t r i n g a t t a c h e d to each end l e a d i n g over the two p u l l e y s ; each s t r i n g has 2 hooks about 10 cms J spaced; s i x washers are needed (see F i g . 3.2). T h i s task was s p e c i f i c a l l y chosen t o e x p l o r e the c h i l d r e n ' s b e l i e f s about the concept o f e q u i l i b r i u m when f o r c e s i n o p p o s i t e d i r e c t i o n are a c t i n g upon an o b j e c t . Concept o f a c t i o n o f f o r c e s and composition o f f o r c e s are a l s o probed w i t h t h i s t a s k . B : board Pu : p u l l e y P : blue p l a t e H : hook S : s t r i n g W : washer (or more, or l e s s ) ? Subject s i t s on t h i s , s i d e p 6 0 cm . S B ")40 cm In t e r v i e w e r s i t s on t h i s s i d e F i g u r e 3.2 M a t e r i a l s f o r Task 2 and In t e r v i e w e r ' s and Sub j e c t ' s P o s i t i o n Interview P r o t o c o l f o r Task Two Research Question: Concept of e q u i l i b r i u m Could you d e s c r i b e to me what i s going to happen i f you put t h i s washer i n the upper hook on your s i d e ? A l t e r n a t i v e I: I f S p r e d i c t s t h a t the blue p l a t e w i l l move/all the way towards him or her: Why? what c o u l d you do to keep the p l a t e s t a t i o n a r y about here ( c l o s e r to the c e n t r e o f the board)? A l t e r n a t i v e I I : I f S p r e d i c t s t h a t the b l u e p l a t e w i l l move towards him or her but not a l l the way; Why i s i t going to stop t h e r e and not f a r t h e r on? Then go to q u e s t i o n I2.0 ( A f t e r S has p l a c e d one washer on each s i d e ) . I f you put one more washer i n the upper hook i n your s i d e , what do you expect i s going to happen? Why ? What c o u l d you do to keep the p l a t e s t a t i o n a r y here ( c l o s e r to the c e n t r e ) ? Why do you suggest th a t ? You have 2 washers and 2 hooks i n your s i d e , the same i n my s i d e , what do you expect i s going to happen i f you put one washer i n each hook? Why do you t h i n k so? (I move the p l a t e about 5 cm; a l o n g the s t r i n g towards the s u b j e c t and holds the p l a t e a t the new p o s i t i o n ) : What w i l l happen i f I l e t i t go? Why? - 3 9 -A l t e r n a t i v e I: I f S p r e d i c t s t h a t the p l a t e w i l l move i n e i t h e r d i r e c t i o n or go back to the c e n t r e : 1^ Q : Why do you t h i n k so? , Is anything e l s e p u l l i n g the p l a t e ? How f a r i s i t going t o move? A l t e r n a t i v e I I : I f S p r e d i c t s t h a t the p l a t e w i l l s t ay on the new p o s i t i o n : I7 : Could you t e l l me why i t won't move? Ig : (I move the p l a t e about 5 cm> i n a d i r e c t i o n p er-p e n d i c u l a r t o the s t r i n g s and h o l d i t t h e r e ) : What do you expect i s going to happen i f I l e t i t go i n t h i s case? Why do you th i n k so? TASK THREE Apparatus: A c i r c u l a r board (40 cm,; diameter) w i t h a h o l e r i g h t a t the centre' 3 p u l l e y s , which can be p l a c e d at v a r i o u s p o s i t i o n s around the board; a metal r i n g i s att a c h e d to 3 s t r i n g s and i s h e l d at the c e n t r e by a wooden peg; each o f the s t r i n g s go over the p u l l e y s and have a hook a t the-end; f i f t e e n washers are needed. (See F i g . 3.3). Th i s task was chosen s p e c i f i c a l l y to expl o r e the c h i l d r e n ' s b e l i e f s about the concept of composition o f f o r c e s . T h e i r concept o f e q u i l i b r i u m can a l s o be probed w i t h t h i s t a s k . Interview P r o t o c o l f o r Task -Three Note: S was t o l d t h a t no changes would be p e r m i t t e d on I's s i d e o f the board when t r y i n g to keep the r i n g a t the c e n t r e without b e i n g h e l d by the peg. - 3 9 -A l t e r n a t i v e I: I f S p r e d i c t s t h a t the p l a t e w i l l move i n e i t h e r d i r e c t i o n or go back to the c e n t r e : Tj g : Why do you t h i n k so? , Is anything e l s e p u l l i n g the p l a t e ? How f a r i s i t going to move? A l t e r n a t i v e I I : I f S p r e d i c t s t h a t the p l a t e w i l l s t a y on the new p o s i t i o n : I ^ 1 : Could you t e l l me why i t won't move? Ig : (I move the p l a t e about 5 cm :. i n a d i r e c t i o n p er-p e n d i c u l a r t o the s t r i n g s and h o l d i t t h e r e ) : What do you expect i s going to happen i f I l e t i t go i n t h i s case? Why do you t h i n k so? TASK THREE Apparatus: A c i r c u l a r board (40 cm, ; diameter) w i t h a h o l e r i g h t a t the centre'.'3 p u l l e y s , which can be p l a c e d at v a r i o u s p o s i t i o n s around the board; a metal r i n g i s att a c h e d to 3 s t r i n g s and i s h e l d at the c e n t r e by a wooden peg; each o f the s t r i n g s go over the p u l l e y s and have a hook a t the-end; f i f t e e n washers are needed. (See F i g . 3.3). Th i s task was chosen s p e c i f i c a l l y to explore the c h i l d r e n ' s b e l i e f s about the concept of composition o f f o r c e s . T h e i r concept o f e q u i l i b r i u m can a l s o be probed wi t h t h i s t a s k . I nterview P r o t o c o l f o r Task - T h r e e Note: S was t o l d t h a t no changes would be p e r m i t t e d on I's s i d e o f the board when t r y i n g to keep the r i n g a t the c e n t r e without b e i n g h e l d by the peg. -40-B S Pu H c i r c u l a r board s t r i n g pulley hook r : r i n g P : wooden peg W : washers R stands for the set of washers'iatSS * s side F 1 and F 2: stands for the set of washers i n each hook at I's side Pu Subject s i t s on t h i s side Interviewer s i t s on t h i s side Figure 3.3 Materials for Task 3 and Interviewer's  and Subject's Position Research Question; The concept of equilibrium with 3 forces acting i n opposite d i r e c t i o n . 1^ : ( I n i t i a l l y the two pulleys at I's side are together side by side i n such a way that the strings at I's side are p a r a l l e l or forming an angle of 0 ° , the other pulley i s just i n the opposite side at S's side. The I puts 3 washers i n one of the hooks i n his side): Could you describe to me what i s going to happen i f I p u l l out t h i s peg? Why? (The peg must be always holding the ring i n the middle. A f t e r each experimental s i t u a t i o n , the peg must be put back to hold the r i n g i n the centre). What c o u l d you do to keep the r i n g i n the middle? Why do you t h i n k so? ( I f S has succeeded: R = 3 Ws, = 3 WS. Then, I put 3 washers i n the o t h e r hook i n h i s s i d e ) : What w i l l happen i n t h i s case i f I p u l l out the peg? What c o u l d you do to keep the r i n g i n the middle? Research Question : The concept o f composition o f f o r c e s ( I f S has succeeded : R = 6 Ws, = 3 Ws, and F 2 = 3 Ws. Then the I moves the p u l l e y s oh h i s s i d e u n t i l each s t r i n g forms an angle o f 4 5° w i t h the i n i t i a l p o s i t i o n , the angle formed by the two s t r i n g s i s 9 0 ° ) : I f I p u l l out the peg, what do you expect i s going t o happen? What c o u l d you do to keep the r i n g i n 2 the middle without b e i n g h e l d by the peg? ( I f S has succeeded: R = 4 Ws, F^ = 3 Ws, and F 2 = 3 Ws. Then, I moves the p u l l e y on h i s s i d e u n t i l the angle formed by the s t r i n g s i s 120°): I f I p u l l out the peg, what do you expect i s going to happen? Why? ( I f S has succeeded: R = 3 Ws, F,^ = 3 Ws, and F 2 = 3 Ws. Then, the I moves the p u l l e y s on h i s s i d e u n t i l the angle formed by the s t r i n g s i s 180°). I f I p u l l out the peg, what do you expect i s goin to happen? Why? What c o u l d you do to keep the r i n g i n the middle? Why do you suggest t h a t ? ( I f S has succeeded: R has no washer, F^ = 3 Ws, and F~ = 3 Ws. Then, the I moves the p u l l e y s on h i s .side - 4 2 -u n t i l the angle formed by the s t r i n g s i s 2 4 0 ° . I t i s a s i m i l a r s i t u a t i o n to q u e s t i o n I g i n Task Two): I f I p u l l out the peg, what do you expect i s going t o happen? Why? How f a r w i l l the r i n g move? Why? 1^: (The I moves back the p u l l e y s to h i s s i d e , l e a v i n g the s t r i n g s on h i s s i d e forming an angle o f 9 0 ° , and p u t t i n g 3 Ws.in and F^r and 4 Ws. i n R. He reminds S t h a t i n t h i s p o s i t i o n , b e f o r e the r i n g would stay i n the middle. Then, the I moves the p u l l e y s on h i s s i d e - . -. u n t i l the s t r i n g s form an angle o f 7 5 ° ) : I f I p u l l out the peg, what do you expect i s going to happen? Why? What c o u l d you do to keep the r i n g i n the middle? Why do you suggest t h a t ? I ^ Q : ( I f S has succeeded: R = 5 Ws. F.^  = 3 Ws. and = 3 Ws. Then, the I puts one more washer i n F ^ ) : I f I p u l l out the peg, what i s going to happen? Why? What c o u l d you do t o keep the r i n g i n the middle? Why do you suggest t h a t ? (In t h i s case, S must add one washer on h i s s i d e (R = 6 Ws) and moves the p u l l e y on h i s s i d e about 3 cm. to b r i n g the r i n g to the middle p o s i t i o n . 3 . 4 0 : THE FORMAT OF THE INTERVIEW Most o f the i n t e r v i e w s were c a r r i e d out on U.B.C. Campus ( F a c u l t y o f E d u c a t i o n ) . Only s i x of the i n t e r v i e w s were made i n a High School, l o c a t e d i n E a s t Vancouver. The experimenter and the s u b j e c t were the o n l y ones pr e s e n t d u r i n g the i n t e r v i e w and the s u b j e c t agreed t o allow the i n t e r v i e w to be recorded by vide o t a p e . The - 4 3 -average i n t e r v i e w r e q u i r e d approximately 30 minutes., to complete. ..In each i n t e r v i e w the i n v e s t i g a t o r t a l k e d i n f o r m a l l y w i t h the c h i l d f o r ten o r more minutes be f o r e f o r m a l l y i n i t i a t i n g the interview.. In t h i s i n f o r m a l t a l k i t was e x p l a i n e d to the c h i l d t h a t the i n t e r v i e w was not a t e s t ; t h a t he or she must f e e l f r e e to answer the q u e s t i o n s ; and t h a t t h e i r responses would not be marked i n any way. Some simple b i o g r a p h i c a l data was a l s o c o l l e c t e d i n t h i s i n f o r m a l c h a t . The c h i l d was t o l d by the i n v e s t i g a t o r t h a t he was i n t e r e s t e d i n h i s or her i d e a s about the r e s u l t s of some "games o r experiments t h a t we would be doing". They were a l s o t o l d t h a t the purpose of the i n t e r v i e w was to c r e a t e new i d e a s and methods f o r t e a c h i n g s c i e n c e . - 4 4 -NOTES l i Power (1976) i n an a r t i c l e c o n t r a s t i n g d i f f e r e n t paradigms i n e d u c a t i o n a l r e s e a r c h c h a r a c t e r i z e s the a g r i c u l t u r a l - s c i e n t i f i c model ( m u l t i v a r i a t e model) i n f o l l o w i n g q u o t a t i o n : "The id e a t h a t one can u t i l i z e the powerful i n t e l l e c t u a l and s t a t i s -t i c a l t o o l s o f s c i e n c e s i n st u d y i n g e d u c a t i o n a l as w e l l as n a t u r a l phenomena i s a l o g i c a l outcome of the success s t o r y o f s c i e n c e The f a c t t h a t we possess powerful s t a t i s t i c a l t o o l s which permit us to i n t r o d u c e many v a r i a b l e s i n complicated designs does not mean t h a t we should add new v a r i a b l e s without c a r e f u l thought". 2, In t h i s case, i f S f e e l s l o s t and the task seems d i f f i c u l t f o r him or her, the i n t e r v i e w must be concluded. When I takes t h i s ^ d e c i s i o n , he must be smooth and p o l i t e w i t h S, i n such a way t h a t S does not f e e l t h a t he o r she f a i l e d . But be f o r e t a k i n g the d e c i s i o n to end the i n t e r v i e w , I must.give enough time to S, s i n c e , i t i s s e c u r e l y the f i r s t time t h a t these Ss encounter t h i s k i n d o f experiment. I t i s adivisable t h a t Ss have the chance o f t r y i n g 2 or 3 times to b r i n g the r i n g t o the middle be f o r e ending the i n t e r v i e w . CHAPTER FOUR 4.00 ANALYSIS OF DATA 4.10 Summarizing Interview Data To analyze the i n t e r v i e w data, an attempt was made to i d e n t i f y common or t y p i c a l responses t o the i n t e r v i e w q u e s t i o n s to see i f groups of c h i l d r e n seem t o h o l d a s i m i l a r view o f f o r c e . To do t h i s , i t was necessary to c o n s i d e r the s e v e r a l d i f f e r e n t a spects o f the concept of f o r c e which were covered by the three t a s k s i n t h i s study. That i s , the broad concept of f o r c e has a s t r u c t u r e , which c o n t a i n s other major concepts. For i n s t a n c e , a c t i o n and r e a c t i o n , e q u i l i b r i u m , can be thought o f as major concepts. Each major concept c o n t a i n s other s u b s i d i a r y concepts ( v a r i a b l e s r e l e v a n t to the major c o n c e p t s ) . I t i s c l e a r t h a t the three tasks used i n t h i s study d i d not begin t o cover a l l the aspects of the concept of f o r c e . The aspects o f the concept of f o r c e covered by the 3 tasks were o r g a n i z e d i n a s t r u c t u r e which was c a l l e d a Conceptual P r o f i l e of the concept of f o r c e , which i s a c a t e g o r i z a t i o n of a l l the c h i l d r e n ' s b e l i e f s a c c o r d i n g to c o n t e n t - o r i e n t e d c a t e g o r i e s . A Conceptual P r o f i l e , then, i s one way of r e p r e s e n t i n g the p a t t e r n of b e l i e f s of a group of c h i l d r e n w i t h r e s p e c t to s e l e c t e d aspects of the concept o f f o r c e . -46-4.20 Format of the Conceptual P r o f i l e A c o n c e p t u a l p r o f i l e was c r e a t e d by s t a r t i n g out w i t h the major concepts of concern. These major concepts were then broken down i n t o concepts which are s u b s i d i a r y or s u b - t o p i c s r e l a t e d t o the major concepts and were des-c r i b e d i n terms of the tasks performed by the s u b j e c t s . . 4.30 A Conceptual P r o f i l e f o r the Concept of Force 1.0. CONCEPT OF THE ACTION OF A FORCE 1.1 The e f f e c t of hanging one washer upon the system i n task one. 1.2 R e l a t i o n s h i p between the f o r c e s e x e r t e d and the number o f washers added i n task 1. 1.3 The e f f e c t of hanging one washer on sub-j e c t ' s s i d e i n task 2. 2.0. CONCEPT OF ACTION AND REACTION 2.1 R e c i p r o c i t y o f f o r c e s by p a i r s of o b j e c t s . 3.0.• .CONCEPT OF EQUILIBRIUM 3.1 The e f f e c t of the weight of the washer once the p l a t e has stopped moving i n task 1. 3.2 I d e n t i f i c a t i o n of a l l f o r c e s a c t i n g upon the p l a t e i n an e q u i l i b r i u m p o s i t i o n i n task 1. 3.3 The e f f e c t of f o r c e s w i t h equal magnitude a c t i n g i n o p p o s i t e d i r e c t i o n s i n task 2 and task 3. 3.4 What f o r c e s are a c t i n g i n an e q u i l i b r i u m s i t u a t i o n i n task 2. 4.0. CONCEPT OF THE EFFECT OF CHANGING THE CONFIGURATION OF WEIGHTS. 4.1 The e f f e c t of moving the s e t o f 3 washers (Ws) from the upper hook to the lowest one i n task 1. 4.2 The e f f e c t of p u t t i n g one washer i n each o f the hooks i n task 1 and task 2. -47-5.0 CONCEPT OF COMPOSITION OF TWO FORCES. 5.1 The e f f e c t o f d i s p l a c i n g the p l a t e i n a p e r p e n d i c u l a r d i r e c t i o n r e s p e c t to the o r i g i n a l l i n e o f f o r c e s i n task 2. 5.2 The composition o f two f o r c e s w i t h equal magnitude (the r e s u l t a n t f o r c e w i l l be balanced by a t h i r d force) and forming the f o l l o w i n g a n g l e s : 90°, 120°, 180°, 240°, and 75° i n task 3. 5.3 The composition o f two f o r c e s w i t h d i f f e r e n t magnitude (the r e s u l t a n t f o r c e w i l l be balanced by a t h i r d force) and forming an angle of 75° i n task 3 A c t u a l l y , a l l the major concepts c o u l d be covered by each o f the three t a s k s , but each task was prepared e s p e c i a l l y to t r y some s p e c i f i c a spects o f the concept o f f o r c e . However, when i t corresponds, a c h i l d ' s b e l i e f shown i n one of the tasks c o u l d be proven i n the o t h e r t a s k s . T h i s i s recommendable, p a r t i c u l a r l y , when the experimenter has some doubts about the s t r e n g t h o f the c h i l d ' s b e l i e f . 4.40 R e s u l t s F o l l o w i n g the Conceptual P r o f i l e The r e s u l t s are presented as responses to q u e s t i o n s about the major concepts and the s u b s i d i a r y concepts of the conceptual p r o f i l e . 4.41 Format of the R e s u l t s 1. Major concept 2. S u b s i d i a r y concepts 3. Interview q u e s t i o n s r e l a t e d to the s p e c i f i c s u b s i d i a r y concepts 4. T o t a l number o f s u b j e c t s ( a b b r e v i a t e d as T) answering the i n t e r v i e w q u e s t i o n . - 4 8 -5. T y p i c a l c h i l d r e n ' s b e l i e f s * ( c h i l d r e n had, d i f f e r e n t b e l i e f s about one s p e c i f i c s u b s i d i a r y concept. Here, these d i f f e r e n t b e l i e f s are ~ presented as b e l i e f A, b e l i e f B, e t c ) . 6. Number o f s u b j e c t s s u b s c r i b i n g each p a r t i c u l a r b e l i e f . A b b r e v i a t e d as Ss. 7. E x c e r p t s from the i n t e r v i e w s . Passages from two or three i n t e r v i e w s b e l o n g i n g to s u b j e c t s i n Ss were chosen 8. Comments about the s u b s i d i a r y concepts and the major concept. 4.42 R e s u l t s o f I n t e r v i e w Data 1.0 CONCEPT OF THE ACTION OF A FORCE. 1.1 The e f f e c t o f hanging one washer upon the system i n task 1. Interview q u e s t i o n : Could you d e s c r i b e to me what i s going to happen i f you put t h i s washer i n the upper hook? T = 31 * The c h i l d r e n ' s b e l i e f s were mainly o b t a i n e d from the p r e d i c t i o n s , t h a t i s , t h e i r f i r s t r e a c t i o n s ' t o the q u e s t i o n s ; the i n t e r v i e w e r asked sometimes o t h e r questions to c h a l l e n g e the s u b j e c t ' s b e l i e f s to see how s t r o n g they were. Sometimes, the s u b j e c t changed h i s or her i d e a due to the "other q u e s t i o n s " . Where i t was p o s s i b l e , an attempt was made to look f o r the same idea s i n o t h e r s i t u a t i o n s . Caution was e x e r c i s e d i n p h r a s i n g the p r o v i n g q u e s t i o n s to a v o i d g i v i n g " c l u e s " to Ss. - 4 9 -T y p i c a l C h i l d r e n ' s B e l i e f s * 1.1.A. "The washer w i l l go down, the p l a t e i s going to move a l i t t l e and the e l a s t i c band w i l l s t r e t c h " Ss = 31, (2-6y; 4-7y; 4-8.y; 5-9y; 4-10y; 3 - l l y ; 4-2y; 3-13y; 2-14y) Note: - (2-6y) means 2 s u b j e c t s 6 years o l d , and so on. - -About the ages: Completed years were on l y c o n s i d e r e d . A s u b j e c t was not c o n s i d e r e d a year o l d e r u n t i l h i s or her b i r t h d a y ; example: a s u b j e c t 10 years and 11 months o l d was c o n s i d e r e d 10 years o l d . E x c e r p t s : Doug (8,0): "The washer w i l l go down and w i l l take the blue p l a t e and dragging alone and the e l a s t i c i s going to s t r e t c h " . Comments: A l l s u b j e c t s p r e d i c t e d what i t a c t u a l l y happened, the d i f f e r e n c e among them was the p r e d i c t i o n o f the p l a t e ' s d i s p l a c e -ment. Some o f them f o r e t o l d 10 cm ', oth e r s 0.5 cmr, and the ot h e r s i n between. For a l l s u b j e c t s itwas clear that a force . a p p l i e d upon the system would cause movement. * The t y p i c a l c h i l d r e n ' s b e l i e f s were phrased by the experimenter, who t r i e d t o i n c l u d e i n one statement s i m i l a r b e l i e f s o f a group o f c h i l d r e n h o l d i n g t h a t i d e a and to u s e ; c h i l d r e n ' s words where p o s s i b l e . -50-1.2 R e l a t i o n s h i p between the f o r c e s e x e r t e d and the number of washers added i n task 1. I n t e r v i e w Question: Could you d e s c r i b e to me what i s going t o happen i f you put one more washer i n the same hook? and i f you put one more washer? T = 31 T y p i c a l C h i l d r e n ' s B e l i e f s 1.2.A. "The p l a t e w i l l move t h a t d i s t a n c e because f o r each washer we put before i t moved t h a t d i s t a n c e (the same d i s t a n c e ) " Ss = 29 (2-6y; 3-7y; 4-8y; 5-9y; 2-10y; 4 - l l y ; 4-12y; 3-13y; 2-14y). Excerpts: C h a n t a l l e (6,6): "... w i t h one W the p l a t e moved to here (about 2 cm ) w i t h 2 Ws., i t moved to her (2 cm ), then, w i t h one more, i t has to move the same d i s t a n c e . . . . " C h r i s (8,4): "... p l a t e moves always the same di s t a n c e w i t h each W added..." I.2.B. " P l a t e w i l l move more by adding more washers but not the same d i s t a n c e " . Ss = 2, ( l - 7 y ; l-10y) Ex c e r p t s : Frank (10.4): o n l y t h a t much ( p l a t e ' s displacement about 2 cm ) because t h i s washer i s not too heavy... (he agreed t h a t a l l Ws. were equal but he chose a l l the p l a t e ' s displacements t o t a l l y d i f f e r e n t ) . - 5 1 -Comments: In 1.2. A, the p l a t e ' s displacements are p r o p o r t i o n a l to the number of Ws. added, then, the f o r c e s e x e r t e d are p r o p o r t i o n a l to the amount of Ws. added. In 1.2.B, the p l a t e ' s displacements chosen by the two Ss. showed t h a t they don't see the p r o p o r t i o n a l i t y between the two v a r i a b l e s 29 our of 31 Ss. saw the p r o p o r t i o n a l i t y between the f o r c e s and the numbers o f washers. 1.3. - The e f f e c t s of hanging one washer on S's s i d e i n task 2. Interview Question: What do you expect i s going to happen i f you put one W on the upper hook i n your s i d e ? T = 31 T y p i c a l C h i l d r e n ' s B e l i e f : .1.3.A. "The p l a t e w i l l move t h i s way (toward the S) about t h a t much ( C h i l d r e n ' s p r e d i c t i o n s v a r i e d between 1 cm to 10 cm; , ) because t h i s W i s not heavy enough". Ss:18, ( l - 6 y ; 3-7y; 1.8y; 5-9y; 4-10y; 1 - l l y ; l-12y; 2-13y). E x c e r p t s : N a t a l i e (7,10): "the p l a t e w i l l move t h a t much (2 cm;.) because t h e r e i t moved bef o r e w i t h one washer (she was r e f e r r i n g to task 1) " Doug (8,0): " P l a t e w i l l go to here (1 cm ) because t h i s washer i s h e a v i e r than those 2 hooks (at E's s i d e ) " . B e t t y (12,11): " P l a t e w i l l move toward me t h a t f a r (half-way) because there i s no weight i n your s i d e " . I.3.B. "The p l a t e w i l l stay there because there i s o n l y one W". Ss = 3, (2-6y; l - 7 y ) . - 5 2 -E x c e r p t s : Heather (7,0): " P l a t e won't move because there i s o n l y one W". 1.3. C. " P l a t e w i l l move toward me a l l the way because now there i s weight o n l y on my s i d e " . Ss. = 9, ( l - 8 y ; l-10y; 1 - l l y ; 3-12y; l-13y; 2-14y). E x c e r p t s : Jenny (8,7): " P l a t e w i l l move a l l the way because now there i s the o t h e r s t r i n g , b e f o r e i t was the e l a s t i c " . V i c k y (10,4): " P l a t e w i l l f l y toward me because there i s weight o n l y i n my s i d e " . Rick (12,10): " P l a t e w i l l move a l l the way because one W weighs more than those hooks". Comments: Some s u b j e c t s answered as i f the e l a s t i c band were s t i l l on, r e f e r r i n g to task 1, even when, the I reminded them about the change, some o f them s t i l l kept t h e i r answers. Subjec t s answering 1.3.A and 1.3.B do not have yet the concept o f net f o r c e , which produces the net movement. Perhaps, f o r the 18 Ss. answering t h a t the p l a t e would move not a l l the way, the presence of the s t r i n g and the hooks on the o p p o s i t e s i d e was a d i s t r a c t o r . They thought these ( s t r i n g & hooks) were p u l l i n g , not much l i k e the washer, but enough to stop the p l a t e moving a l l the way. A suggested change here, f o r f u r t h e r r e s e a r c h , might be: p r e s e n t a s i m i l a r s i t u a t i o n to them but without the s t r i n g and hooks a t I's s i d e , and l a t e r , add the s t r i n g s w i t h the hooks and ask the same q u e s t i o n . 9 out of 31 Ss. s a i d " "there i s weight a c t i n g o n l y i n my s i d e , then, the p l a t e would toward me a l l the way". These Ss. saw the a c t i o n o f one f o r c e o n l y a c t i n g upon the o b j e c t . -53-O v e r a l l Comments f o r the Major Concept A c t i o n o f a Force There i s the p o s s i b i l i t y t h a t the s e t t i n g of Task 1 which i n c l u d e d the thumb tack and the e l a s t i c band produced a " f i x e d " i d e a about the a c t i o n o f f o r c e s e x i s t i n g a t I's s i d e i n some s u b j e c t s . T h i s was shown i n the answers g i v e n to q u e s t i o n 1.3 i n task 2. Even when some Ss. were reminded about the d i f f e r e n c e s between the two t a s k s , some Ss. s t i l l kept t h e i r i d e a s . The r e s u l t s o b t a i n e d about the 3 s u b s i d i a r y concepts can be summarized now: When a p p l y i n g 2 f o r c e s i n o p p o s i t e d i r e c t i o n s upon an o b j e c t , the p l a t e w i l l move i n the d i r e c t i o n o f the g r e a t e r magnitude, the net f o r c e a c t s o n l y u n t i l c e r t a i n p o i n t and then, i t stops a c t i n g ; ( i t i s not c l e a r as to reasons why); the weight of a s e t of s i m i l a r o b j e c t s i s p r o p o r t i o n a l to the number o f o b j e c t s . C h i l d r e n do not t a l k about d i r e c t i o n of movement, i n s t e a d they say: way of movement, f o r example: "the p l a t e i s going to move t h a t way". 2.0 CONCEPT OF ACTION AND REACTION 2.1 R e c i p r o c i t y o f f o r c e s by p a i r s o f o b j e c t s . T h i s s u b s i d i a r y concept has two i n t e r v i e w q u e s t i o n s . -54-a) I nterview Questions: You t o l d me t h a t the washer was p u l l i n g (see comments) the p l a t e , what e l s e i s p u l l i n g a t t h i s moment? T = 28. T y p i c a l C h i l d r e n ' s B e l i e f : 2.1.A. "The s t r i n g i s p u l l i n g the p l a t e , the p l a t e i s not p u l l i n g the s t r i n g " . Ss. = 19, ( l - 6 y ; 3-7y; 3-8y; 5-9y; 4-10y;2-lly) E x c e r p t s : C h r i s (8,4): "... the Ws. are p u l l i n g the s t r i n g , the s t r i n g i s p u l l i n g the p l a t e , the p l a t e i s not p u l l i n g the s t r i n g , i t i s j u s t s t a y i n g t h e r e , the e l a s t i c i s not p u l l i n g the p l a t e . . . . " Greg (9,4): The s t r i n g p u l l s the p l a t e , the p l a t e p u l l s the s t r i n g o n l y i f we take o f f the washers, the p l a t e i s not p u l l i n g the s t r i n g r i g h t now..." Jenny (8,5): "The p l a t e i s not p u l l i n g the washers because i t i s not heavy enough as those washers..." Kevin (11,6):".... the p l a t e i s s o r t o f p u l l i n g the s t r i n g , but not, the e l a s t i c i s p u l l i n g the p l a t e , so the s t r i n g i s g e t t i n g p u l l e d but i t i s not g e t t i n g p u l l e d as much as the washers p u l l the s t r i n g . . . " 2.I.B. "The p l a t e i s t r y i n g to p u l l back but i t doesn't have enough s t r e n g t h " . Ss. = 9, (4-12y; 3-13y; 2-14y) E x c e r p t s : Rick (12,10): "....Both s i d e s (the washers and the e l a s t i c ) are p u l l i n g but the washers are a l i t t l e b i t s t r o n g e r than the e l a s t i c . . . " S t a n l e y (14,7): There are two t h i n g s p u l l i n g the p l a t e , the weight o f the washers and the e l a s t i c , the p l a t e i s not r e a l l y p u l l i n g the s t r i n g , but the p l a t e i s p u l l i n g the e l a s t i c . . . " -55-Comments: I f S d i d not understand the q u e s t i o n , S was reminded about s a y i n g the washer was p u l l i n g , and was asked i f anything e l s e was p u l l i n g . Most of Ss. answered: the Ws. are p u l l i n g the s t r i n g , the s t r i n g i s p u l l i n g the p l a t e , the p l a t e i s s t r e t c h i n g the e l a s t i c , the thumb tack i s h o l d i n g e v e r y t h i n g . They were asked d i r e c t l y : Is the p l a t e p u l l i n g the s t r i n g o r the washers?, they s a i d : "no". - The Ss. who s u b s c r i b e to 2..1.A range from 6 to 11 years o f age, and the ones who s u b s c r i b e to 2.l.B. range from 12 to 14, w i t h r e s p e c t to t h i s a spect of the task ( a c t i o n and r e a c t i o n ) ; the Ss. are c l e a r l y d i v i d e d i n two groups. One group, i n which c h i l d r e n see the f o r c e s a c t i n g o n l y i n one d i r e c t i o n , u n i d i r e c t i o n a l approach, or they don't see the r e c i p r o c i t y of f o r c e s ; and the o t h e r group, i n which c h i l d r e n see the f o r c e s a c t i n g i n both d i r e c t i o n s but not w i t h the same magnitude. Most of the Ss. understand t h a t a f o r c e i s t r a n s m i t t e d from one o b j e c t to another i f they are j o i n e d by a s t r i n g or something e l s e , f o r example: The weight o f the washers puUJs the p l a t e by means o f the s t r i n g . b) Interview Question: What i s the thumb tack doing? T: 30 T y p i c a l C h i l d r e n ' s B e l i e f : 2.I.C. "The thumb tack i s h o l d i n g the e l a s t i c band, i t i s not p u l l i n g " . Ss. 25, (2-6y; 4-7y; 3-8y; 4-9y; 4-10y; 3 - l l y ; 2-12y; l-13y; 2-14y) E x c e r p t s : Ryan (7,6): "The tack i s h o l d i n g the e l a s t i c from moving, otherwise the p l a t e and the s t r i n g would f a l l " . Jenny (98, 7): "The thumb tack i s not p u l l i n g the e l a s t i c , the Ws. are p u l l i n g the e l a s t i c " - 5 6 -Lauch (11,3): "The thumb tack i s p r e v e n t i n g the e l a s t i c to s p r i n g back, i f i t weren't th e r e , e v e r y t h i n g would be on the ground. 2.I.D. "The thumb tack i s probably p u l l i n g the e l a s t i c " . Ss. : 4, (2-12y; 2-13y) E x c e r p t s : Rick (12,10): the tack i s h o l d i n g the e l a s t i c i t i s a l s o p u l l i n g . The tack i s s t r o n g e r than the e l a s t i c because i t i s d r i v e n i n t o the wood". Teresa (13,10): "the tack i s p r o b a b l y p u l l i n g the e l a s t i c " . Comments: - A f t e r a n a l y z i n g the c h i l d r e n ' s ideas f o r t h i s a s p e c t o f the task, i t seems to the experimenter t h a t c h i l d r e n t h i n k t h a t o b j e c t s have a s o r t o f " c a p a c i t y " f o r e x e r t i n g f o r c e s . Then, i n a p a i r o f o b j e c t s i n t e r a c t i n g w i t h each o t h e r , the one w i t h g r e a t e r " c a p a c i t y " f o r e x e r t i n g f o r c e s p u l l s more. For example, the thumb tack, due to the f a c t t h a t i t i s d r i v e n i n t o the wood, i s e x e r t i n g a g r e a t e r f o r c e upon the e l a s t i c than the e l a s t i c upon the tack. - Language problem: what i s the d i f f e r e n c e between h o l d i n g and p u l l i n g ? A problem f o r f u r t h e r r e s e a r c h . - S u b j e c t s , a f t e r s a y i n g the tack i s h o l d i n g the e l a s t i c , were asked d i r e c t l y : Is the tack p u l l i n g the e l a s t i c ? Most o f the Ss. s a i d : "No". - Two o b j e c t s can p u l l one another o n l y i f both o b j e c t s can move. I f one o f the o b j e c t s cannot move, t h a t i s , i t i s f i x e d , i t can o n l y h o l d the o t h e r but cannot p u l l i t . O v e r a l l Comments About the Major Concept: A c t i o n and R e a c t i o n - A f t e r a n a l y z i n g the answers f o r q u e s t i o n s (a) and (b), i t i s c l e a r t h a t nobody i n t h i s sample has grasped the a c t i o n and r e a c t i o n p r i n c i p l e y e t . The Ss. having the b e l i e f 2.1.A. are f a r from understanding i t , s i n c e they s t i l l have the u n i d i r e c t i o n a l approach o f f o r c e s . - 5 7 -The Ss. having the b e l i e f 2.I.B. are c l o s e r to the p r i n c i p l e , b u t they have an incomplete understanding when they say: "the p l a t e i s t r y i n g to p u l l back but i t doesn't have enough s t r e n g t h " , f o r t h i s they c o u l d mean: the p l a t e can't p u l l the washers because i t can't l i f t i t . In any case, t h e i r b e l i e f s were not emphatic i n a s s u r i n g the a c t i o n of the p l a t e upon the washers as i t was when they s a i d the washers are p u l l i - g the p l a t e . - More evidence f o r the c o n c l u s i o n presented above i s shown when a n a l y z i n g the answer f o r q u e s t i o n (b), i n which 24 out o f 30 Ss. assured t h a t the thumb tack was o n l y " h o l d i n g " the e l a s t i c band, i t was not " p u l l i n g " . On the ot h e r hand, most o f these Ss. s a i d t h a t the e l a s t i c band was " p u l l i n g " the thumb tack. 3.0 CONCEPT OF EQUILIBRIUM 3.1 The e f f e c t o f the weight of the washer once the p l a t e has stopped moving i n task 1. There are two i n t e r v i e w q u e s t i o n s r e s p e c t to t h i s a s p e c t of the task : a) Interview Question: What i s the washer doing i n t h i s moment? ' T = 31 T y p i c a l C h i l d r e n ' s B e l i e f s : 3.1.A "The weight o f the washer p u l l s the s t r i n g , which i s p u l l i n g (or p u t t i n g - 5 8 -pressure, or weighing down) the p l a t e " . Ss.: 31, "(2-6y; 4-7y; 3-8y; 5-9y; 4-10y 3 - l l y ; 4-12y; 3-13y; 2-14y) Excerpts: Rashida (6,7): "... the washer i s heavy and i t i s p u l l i n g the s t r i n g down and s t r e t c h i n g the e l a s t i c and the p l a t e can move..." Ch r i s (8,4) : /"the washer i s p u t t i n g pressure and t h i s s t r i n g gets t i g h t , the washer made the p l a t e move.." Lauch (11,9) : "the washer i s weighing down t h i s (the s t r i n g ) . . . . i t i s making the e l a s t i c longer and moved down the p l a t e " . Comments: Language problem: f o r c h i l d r e n , words as p u l l i n g p u t t i n g pressure, p r e s s i n g down, weighing down, could mean the same t h i n g . I t i s an i n t e r e s t i n g problem f o r f u r t h e r research This question i s asked immediately a f t e r p l a t e stopped moving (see p r o t o c o l of Task. 1), then, f o r a l l the' Ss. was s t i l l obvious t h a t the washer was p u l l i n g . b) ' Interview Questions: I s the washer s t i l l p u l l i n g ? T: 26 T y p i c a l C h i l d r e n ' s b e l i e f s : 3.1.A "The washer i s not p u l l i n g ( p u t t i n g pressure, etc.) because the p l a t e i s not moving, the washer i s h o l d i n g the p l a t e " . Ss.: 10, (3-7y; 2-9y; 2 - l l y ; 2-12y; l-13y) Excerpts: Ryan (7,6) : "...the washer i s not p u l l i n g because i t only p u l l s when i t moves down, a f t e r the p l a t e stopped b a l a n c i n g , i t i s not p u l l i n g , the washer only p u l l s when we put i t on...." - 5 9 -Dianne (8,11): "... washer p u l l e d o n l y when I j u s t put i t t h e r e , now i t i s a l r e a d y on t h e r e , i t i s j u s t s t a y i n g and not p u l l i n g . . . . " Joseph (12,8): "....the washer i s tugging the s t r i n g , i t i s not p u l l i n g " 3.I.C. "The washer i s p u l l i n g r i g h t now and the p l a t e i s not moving". Ss.:: 16, (3-8y; 3-9yy; 3-10y; 1 - l l y ; 2-12y; 2-13y; 2-14y). E x c e r p t s : Tobby (9,3): the washer i s s t i l l p u t t i n g pressure because the washer i s s t i l l on...." Jeremy (9,8): "....the washer i s p u l l i n g , the p l a t e doesn't move because i t i s a l l what the e l a s t i c can s t r e t c h . . . . " Comments: This i s a c h a l l e n g i n g q u e s t i o n t o f i n d out what i s the d i f f e r e n c e between p u l l i n g and h o l d i n g f o r the c h i l d r e n . 10..§ s• answered- t h a t washer was p u l l i n g ( p u t t i n g p r e s s u r e , p r e s s i n g down, etc.) i n q u e s t i o n (a), changed t h e i r minds when they were asked d i r e c t l y about i n q u e s t i o n (b). I t i s c l e a r t h a t f o r these s u b j e c t s , p u l l i n g i m p l i e s movement. L e t ' s see one case: Ryan (7,6) i n q u e s t i o n (a) answered: "the washer i s p u l l i n g the s t r i n g , the p l a t e and the e l a s t i c . . . . " : and the answer f o r q u e s t i o n (b) was: the washer i s not p u l l i n g because i t onl y p u l l s when i t moved down...." 16 Ss. out o f 2 6 agreed t h a t the washer was p u l l i n g when the p l a t e was s t a t i o n a r y . There i s not a c l e a r d i v i s i o n to group the Ss. i n stages with r e s p e c t t o t h i s aspect of the task . 3.2. I d e n t i f i c a t i o n of a l l f o r c e s a c t i n g upon the p l a t e i n e q u i l i b r i u m - s i t u a t i o n i n Task 1. Interview Question: Why d i d the p l a t e stop where i t d i d ? Note: T h i s aspect o f the task was not asked t o a l l the s u b j e c t s f o r not having a long i n t e r v i e w w i t h a l l the c h i l d r e n . T: 13 -60-Typical Children's Beliefs:. 3.2.A. "The plate stopped there because the washer i s not heavy enough, another washer i s necessary to move farther. (There was no mention of the action of the e l a s t i c band upon the plate) '!. Ss. 6, (l-6y; l-8y; l-9y; l-10y; 1 - l l y ; l-14y). Excerpts: Jenny (8,5) : "The plate stopped there because t h i s washer i s not heavy enough.." Heather (11,7): " because the washer doesn't have enough weight to make move farther..." 3.2.B. "The plate stopped there because the e l a s t i c band i s p u l l i n g back" (2 Ss. said: the e l a s t i c i s holding back the p l a t e ) . Ss. 6, (l-8y; 2 - l l y ; 2-12y; l-13y) Excerpts: Dough (8,0): "The plate stopped there because the washer i s not heavy enough and also because the e l a s t i c band, when you put pressure here (on the hook), the e l a s t i c band stretches, i f you put more pressure the plate can go farther". Lauch (11,10): "....because the e l a s t i c band i s stretching and preventing the plate to move farther, the washer stretches the e l a s t i c . . . " Rick (12,10): the plate i s going to move that way (in the d i r e c t i o n of the action of the weight) u n t i l c e r t a i n point and the e l a s t i c i s going to stop i t " . 3.2.C. "I don't know why the plate stopped moving..." Ss. 1, (l-13y) Comments: After analyzing t h i s aspect of the task, i t was r e a l i z e d that the concept of amount of forces acting upon the plate i s an im-portant one, since, h a l f of the interviewees saw only the action of the washer. This aspect should have been investigated i n a l l subjects. -61-7 out of 13 Ss. saw only the a c t i o n of the weight of the washers upon the p l a t e , they di d n ' t mention at a l l the a c t i o n of the e l a s t i c band upon the p l a t e . In other p a r t s of the task, some of the Ss. s a i d the p l a t e was p u l l i n g the e l a s t i c band, but here, i t i s c l e a r t h a t the e l a s t i c band was not p u l l i n g the p l a t e . I t was not c l e a r how they thought th a t the p l a t e was i n e q u i l i b r i u m without the a c t i o n of another equal f o r c e . 6 out of 13 Ss. a f f i r m e d t h a t the p l a t e stopped where i t was, because the e l a s t i c band was p u l l i n g back, i t was c l e a r from t h e i r answers t h a t both the e l a s t i c band and the washer were p u l l i n g w i t h the same fo r c e . These b e l i e f s can't be assigned to d e f i n i t e span of ages or stages. 3.3. The e f f e c t of forces w i t h equal magnitude a c t i n g i n opposite d i r e c t i o n . There are 3 i n t e r v i e w questions respect to t h i s s u b s i d i a r y concept. a) Interview Question: (Having already put 1 W at S's side i n task 2): What could you do to keep the p l a t e s t i l l r i g h t there ( i n the middle of the board)? T : 31 T y p i c a l C h i l d r e n ' s B e l i e f s : 3.3.A. "Remove the washer i n my si d e TI: We should keep i t ) . . . . t a p e the p l a t e . . . . I don't know how..." Ss. 3, (2-7y; l-10y) Excerpts: Jenny (10.4): "To keep the p l a t e i n the middle, you can tape or ho l d the s t r i n g w i t h your hand (.1 suggested to use washers) .... put 1 W i n your side".. 3.3.B. "Put one washer i n your s i d e , then, we have one weight i n each s i d e " . - 6 2 -Ss. 28, (2-6y; 2-7y; 3-8y; 5-9y; 4-10y; 3 - l l y ; 4-12y 3-13y; 2-14y) E x c e r p t s : C h a n t a l l e (6,6): "Put one washer there (I's side) because I have one here" Corey (7,10): "Put one washer i n your s i d e . . . they are b a l a n c i n g a c r o s s t h i s (along the s t r i n g ) " . Dianne (8,11): "Keep i t balanced, put another washer i n your s i d e " . Comments - For 2 8 out of 31 Ss. i t was; clear t h a t the p l a t e would be s t a t i o n a r y i n the middle of the board i f the same amount of washers were put i n both s i d e s . T h i s shows t h a t most of the Ss. have the concept of e q u i l i b r i u m i n the case when f o r c e s i n o p p o s i t e d i r e c t i o n can be a p p l i e d and the o b j e c t upon which the f o r c e s are being a p p l i e d s t a y s i n the middle of the board. T h i s b e l i e f was found i n c h i l d r e n r anging from 6 to 14 years of age. b) Interview Que s t i on: (Having a l r e a d y put 2 Ws. a t S's s i d e and 1 W. a t I's s i d e ) : What c o u i d you do t o keep the p l a t e s t i l l i n the middle? The 31 Ss. answered: "Put one more washer i n your s i d e " . Comments: The 31 Ss. a f f i r m e d the n e c e s s i t y of having equal amount of washers on each s i d e to keep the p l a t e s t a t i o n a r y i n the middle of the board. Three Ss. who c o u l d n ' t s o l v e the task i n the p r e v i o u s s i t u a t i o n l e a r n e d from the p r e v i o u s experimental r e s u l t t h e i r answers. c) I n t e r v i e w Question: (3 f o r c e s a c t i n g upon the system, 2 of them a c t i n g i n the same d i r e c t i o n and o p p o s i t e to the t h i r d one i n task 3. Having a l r e a d y put 3 washers i n each hook: 3 i n each of the hooks, the two p u l l e y s are touching each other and i n o p p o s i t e p o s i t i o n to the t h i r d one, a t I's s i d e and 3 i n the hook at S's s i d e ) : What i s i t going to happen i f I p u l l out the peg? -63-What c o u l d you do to keep the r i n g s t i l l a t the c e n t r e ? T: 31 T y p i c a l C h i l d r e n ' s B e l i e f s : 3.3.D. - "To keep the r i n g a t the c e n t r e I have t o put 3 more washers i n my s i d e , so I have 6 washers i n each s i d e " . Ss.: 25, (3-7y; 2-8y; 4-9y; 5-10y; 2 - l l y ; 4-12y; 3-13y; 2-14y) E x c e r p t s : N a t a l i e (97,10): "To keep the r i n g i n the middle, I put 3 more Ws. i n my s i d e " . Tobby (9,3) • "I can put 3 more Ws, i n my hook, then, you have 6 a l t o g e t h e r and. I have 3 here". 3.3.E. - "the r i n g i s going t o stay a t the c e n t r e because there are 3 washers i n each hook". Ss,: 3, ( l - 8 y ; l - 9 y ? 1 - l l y ) E x cerpts Dough (8,0): "The p l a t e won't move a t a l l because we have the same amount of weight i n each hook". Heather (11,4): "To keep the r i n g i n the middle, put 3 Ws. i n your hooks, and I put 3 more washers i n my hook, now, i t ' s going t o stay because there are the same number of washers i n each hook. 3.3.F. - "I don't know how, maybe by p u t t i n g 3 washers on the r i n g " . Ss: 3, (2-6y; l - 7 y ) . E x c e r p t s : Rashida (6,7): "To keep the r i n g i n the middle, keep o n l y one washer i n each hook because i t w i l l be l i g h t e r , i f i t i s h e a v i e r i t w i l l move". C h a n t a l l e (6,6): "Put 3 more washers on the top of the r i n g o r upon the s t r i n g i f you want to keep the r i n g i n the middle". -64-Comments This could be considered as a cross-check . - . .. question of Question 3.3.A. i n task 2. - This aspect of the task reinforces.even more the idea that the object (ring) has to be i n the centre to be i n equilibrium. Other planned questions would be necessary to ask to f i n d out i f the Ss. who answered c o r r e c t l y , have the idea that the ring i s only i n equilibrium when i t i s at the centre. - 25 out of 31 Ss. affirmed that the ring would stay at the centre i f the same amount of washers were put i n both sides, 3 and 3 at I's side, and 6 at S's side. When a force i s divided i n 2 components, both acting i n the same d i r e c t i o n , most of the Ss. were able to see that the resultant was simply the arithmetical addition of both, as a condition to keep the r i n g stationary at the centre. 3.4. - What forces are acting i n on equilibrium s i t u a t i o n i n task 2. There are two interview questions i n t h i s subsidiary concept. a) Interview Question: (Having already put 2 washers i n each side i n task 2): What are these washers doing i n t h i s moment? T: 20 Typical Children's B e l i e f s 3.4.A. - "The washers are holding the plate i n the middle" (I: asked: What do you mean by that. Ss answered: Well, the washers keep the plate from going down". Ss: 8, (l-7y: 2-8y: l-9y; 3-10y; 1 - l l y ) . Excerpts; Lauch (11,10): "The washers keep the plate from going down". Greg (9,8): "These washers the plate, and these washers the plate even, that i s , the 3.4.B. - "Each p a i r of wahs way (d i r e c t i o n ) " . (at S's side) are holding (at I's side) are holding same" . rs i s p u l l i n g i n opposite -65-Ss. 20, (1-6Y; 2-7y; l - 8 y ; 3-9y; 2-10y 2 - l l y ; 4r-12y; 3-13y; 2-14y). E x c e r p t s : N a t a l i e (7,10): "These washers (S's side) are p u l l i n g t h i s way (towards the S) and these washers (I's side) are p u l l i n g t h a t way (towards the I ) , they are p u l l i n g together ( s i m u l t a n e o u s l y ) , then, the p l a t e s t a y s " . Rick (12,10): "Both ( p a i r o f washers) want to reach the ground, but because both have the same amount o f weight, they are p u l l i n g the same, then, the p l a t e s t a y s t h e r e " . Joseph (12, 10) : "They are both tugging, but when they aire tugging, they h o l d the p l a t e " . Comments: 20 out of 28 Ss. a f f i r m e d t h a t each p a i r o f washers i n each s i d e were p u l l i n g the p l a t e i n o p p o s i t e way ( d i r e c t i o n ) . T h i s shows c l e a r l y t h a t the Ss. saw two equal f o r c e s a c t i n g upon the p l a t e i n o p p o s i t e d i r e c t i o n , the e f f e c t o f t h i s was t h a t the p l a t e was s t a t i o n a r y i n the middle of the board. The o t h e r 8 Ss., which s a i d t h a t the washers were h o l d i n g the p l a t e i n the middle, might a l s o be i n c l u d e d i n the f i r s t category, but they were not so s p e c i f i c i n t h e i r answers as the f i r s t group. The key word f o r t h i s group remains i n what they mean by h o l d i n g . b) I n t e r v i e w Q u e s t i o n: (I d i s p l a c e d the p l a t e towards the S i n about 6 cms. and h o l d i t t h e r e ) : What w i l l happen i f I remove my f i n g e r from the p l a t e ? T: 30 T y p i c a l C h i l d r e n ' s B e l i e f s : 3.4.C. - " P l a t e w i l l s t ay s t i l l where i t i s now because there are s t i l l 2 washers i n each s i d e " . Ss: 14, (2-7y; l - 6 y ; l - 8 y ; l - 9 y ; 2-10y; 3 - l l y ; 2-12y; 2-14y). -66-E x c e r p t s : Corey (7,10): " P l a t e w i l l stay where i t i s because both s i d e s b alance, both s i d e s have the same weight". V i c k y (10,4): " P l a t e w i l l s t a y there because i t i s s t i l l the same weight i n both s i d e s " . 3.4.D. - " P l a t e w i l l go back to the middle because o n l y over t h e r e , i t i s i n e q u i l i b r i u m " . Ss: 12, (l-16y; l - 7 y ; l - 8 y ; 3-9y; 2-10y; 2-12y; 2-13y) E x c e r p t s : Doug (8,0): " P l a t e w i l l go back because you are p u l l i n g the p l a t e and there i s the same weight i n both s i d e s , the p l a t e has to be r i g h t a t the c e n t r e " . Tobby (9,3): "The p l a t e i s going to go back to where i t was b e f o r e because the washers have to be a t the same l e v e l (same h e i g h t ) : Now, t h e r e i s more p r e s s u r e i n your s i d e (washers are h i g h e r a t I's s i d e ) " . Frank (10,4): " P l a t e i s going to go back to the middle because the washers have to be even (same h e i g h t ? ) , your s i d e w i l l move down u n t i l both have the same h e i g h t " . 3.4.E. - "The p l a t e w i l l move towards me (towards the S.) because these Washers are c l o s e r to the ground". Ss: 3, ( l - 8 y ; l - 9 y ; l - 1 3 y ) . E x c e r p t s : Dianne (8,11): "The p l a t e w i l l move towards me a l l the way because these washers (at S's side) are lower than your washers, my washers p u l l more because they are lower". B e t t y (12,11) : "The p l a t e i s going to move a l l the way because these washers (at S's side) are more down and they p u l l more". Comments: - 12 Ss. out of a t o t a l of 30 have the b e l i e f t h a t the system i s i n e q u i l i b r i u m o n l y when the p l a t e i s i n the middle. Some o f them i n t h i s group claimed t h a t the washers i n both s i d e s have to be a t the same l e v e l o r h e i g h t as c o n d i t i o n o f e q u i l i b r i u m . -67-- 14 out of 30 Ss. s a i d t h a t the p l a t e w i l l s t a y where i t was h e l d because there were s t i l l the same amount of washers i n each s i d e . For these Ss., the only c o n d i t i o n to have the p l a t e i n e q u i l i b r i u m i s to have the same amount of washers i n each s i d e no matter i f the p l a t e i s i n the middle or somewhere i n between the two p u l l e y s . - 3 out of 30 Ss. i n s i s t e d i n t h a t the p l a t e would move towards them because the washers i n t h e i r s i d e were c l o s e r t o the ground, then they were p u l l i n g more. - These b e l i e f s can't be a s s i g n e d to a d e f i n i t e span of ages. O v e r a l l Comments About the Major Concept o f E q u i l i b r i u m - For these Ss., p u l l i n g and h o l d i n g meant d i f f e r e n t t h i n g s . I t i s important to mention here t h a t i n Task 1, one end of the p l a t e was a t t a c h e d to a f i x e d o b j e c t (the t a c k ) , w h i l e the other end was a t t a c h e d to the washers which were f r e e to move. For some Ss. the f r e e end c o u l d " p u l l " , whereas the f i x e d end c o u l d " h o l d " . But i n Task 2, both ends are f r e e and the p l a t e can be " p u l l e d " from both s i d e s . The i n t e r v i e w q u e s t i o n s r e l a t e d t o the concept of e q u i l i b r i u m i n t h i s task were c l e a r l y answered. For almost a l l the Ss. there was a c l e a r n e c e s s i t y to-, have the same f o r c e s a c t i n g i n o p p o s i t e d i r e c t i o n to have the p l a t e i n e q u i l i b r i u m , however, some Ss. saw as another c o n d i t i o n of e q u i l i b r i u m t h a t the p l a t e be'' a t the c e n t r e of the board or the washers be -a t the same h e i g h t on each s i d e . -68-4.0. CONCEPT OF THE EFFECT OF CHANGING THE CONFIGURATION OF WEIGHTS. 4.1. The e f f e c t o f moving the s e t o f 3 washers from the upper hook to the lowest hook i n task 1. Inte r v i e w Question: (The 3 Ws. were p l a c e d on the upper hook, there are 3 hooks t i e d t o the s t r i n g ) : What do you t h i n k i s going t o happen w i t h the p l a t e i f you move a l l the washers from the upper hook to the lowest hook? T: 30 T y p i c a l C h i l d r e n ' s B e l i e f s : 4.1.A. "The p l a t e w i l l move more because the washers are f a r t h e r down or washers p u l l more when they are c l o s e r to the ground". Ss: 15, ( l - 6 y ; 3-7y; l - 8 y ; 2-9y; 2-10y; 2 - l l y ; l-12y; l-13y; 2-14y) E x c e r p t s : Heather (7,0): the p l a t e w i l l move more toward me because these washers are h e a v i e r when they are at the bottom...." L o r e l i e (10,6): p l a t e w i l l move more toward me because these washers are h e a v i e r down t h e r e . . . . " S t a n l e y (14,7):".... p l a t e w i l l move f a r t h e r because the washers are c l o s e r t o the ground, then, they have more weight...." 4.I.B. " P l a t e w i l l move backward because the washers are down more and there i s not much weight p u l l i n g (washers c l o s e r to the ground weigh l e s s ) " . Ss: 5, ( l - 6 y ; l - 7 y ; l - 9 y ; l-10y; 1 - l l y ; E x c e r p t s : C h a n t a l l e (.6,7) the p l a t e i s going to go backward because the washers used to be up on the top, they were h i g h e r ; now, they are down t h e r e , then, i t w i l l move backward...." -69-Sandra (10,0): the plate w i l l move less because when washers are down there, they p u l l l e s s . . . " 4.I.C. - "Plate w i l l stay there because there are s t i l l the same amount of washers or weight". Ss: 8, (l-8y; l-9y; l-10y; 1 - l l y ; 2-12y; 2-13y) Excerpts: Chris (8,4) : "the plate w i l l move the same, the washers are going to be down there, but they have the same pressure". Jenny (10,4) : plate w i l l stay there because there i s s t i l l the same amount of weight p u l l i n g i t " . Two Special Cases: Jenny (8,0): "It i s going to p u l l more because these hooks are a l i t t l e heavy i f you put a l l the washers on the lowest hook, those two hooks (the hooks upon the lowest one) are going to p u l l now; because before when they were underneath of the washers, they were not p u l l i n g " . Frank (10,0) : "Probably, the plate w i l l move back a l i t t l e because those washers do not have enough room to f a l l down". Comments 15 out of 30 Ss. affirmed that the plate would move farther because when washers were closer to the ground, they weigh more, therefore, they p u l l more. These Ss. had_ more information about gravity and maybe they have heard that gravity increases when one i s closer to the ground. Then, they could be applying t h i s law, but what they don't know yet i s that t h i s change of gravity i s noticeable only for much greater changes of height. 5 Ss. affirmed that the plate would move backward because when washers were closer to the ground, they weigh le s s , therefore, they p u l l l e s s . 8 Ss. affirmed that the plate would stay at the same place because there was the same weight acting. These Ss. didn't see any change i n the force exerted when the washers were removed. - 7 0 -These b e l i e f s can't be assigned t o a s p e c i f i c span o f ages. 4.2. The e f f e c t o f p u t t i n g one washer i n each hook i n task 1. Interview Question: What do you t h i n k i s going to happen w i t h the p l a t e i f you put one washer i n each hook? (there are 3. washers and 3 hooks). T:-. 30 T y p i c a l C h i l d r e n ' s B e l i e f s : 4.2 .A. - "The p l a t e w i l l move more because the washers p u l l more when they are separated". Ss: 6,; (l-6y; 2-7y; l - 9 y ; 2-13y) Ex c e r p t s Rashida (6,7) : "The p l a t e w i l l move a l i t t l e b i t more because each hook has a washer t h a t makes i t more h e a v i e r than when a l l the washers are i n o n l y one hook and a l s o there i s one more down". Greg (9,8) : "The p l a t e w i l l move a l i t t l e more forward because t h e r e i s a l i t t l e more weight now, when they are separated, each one p u l l s a l i t t l e more". B e t t y (13,11): "The p l a t e i s going to move f a r t h e r because there i s one washer i n each hook". 4.2.B. - "The p l a t e w i l l move l e s s j b e c a u s e the washers are spread out and they p u l l l e s s (as a whole they p u l l l e s s ) " . Ss: 3, (2-7y; l-9y) Ryan (7,6) : "The p l a t e w i l l move backwards because th e r e i s l e s s weight now, because the washers are separated now, i t makes them l i g h t e r " . Dianne (8,11). "The p l a t e w i l l move a l i t t l e l e s s because washers are not t o g e t h e r now". 4.2.C. T- "The p l a t e w i l l s t ay where i t i s because there i s s t i l l the same weight". Ss: 15, (I-6y; 3 -8y; l-9y; 3-10y; 2 - l l y ; l-13y; 2-14y). -71-Excerots: Doug (8,0): "The plate i s going to stay there because i t i s s t i l l the same weight". Vicky (10,4): "The plate w i l l stay there because there i s the same weight, you didn't add or take o f f any" . 4.2.D. - "The plate w i l l stay there because before i t didn't move when washers were moved from the top to the bottom". Ss:: 6, (l-9y; 2-10y; 1 - l l y ; 2-12y) Excerpts: Jeremy (9,4) : "The plate i s not going to move more because i t didn't move when the washers were down there, I thought i t ' d be stronger, so i t won't move more". Sandra (10,0): "The plate w i l l stay there because i t stayed when washers were on the top and on the bottom". Rick (12,10): "The plate i s going to stay the same on^vthe basis that when the washers were together i t stayed the same, when I moved them from the top to bottom, i t didn't move". Comments: 21 out of 30 Ss. had the b e l i e f that the plate would stay i f the Ws. were spread out, even when 6 of them claimed that i t ' d stay because when Ws. were moved before i t stayed. There i s a strong p o s s i b i l i t y that children learned the answer for question 4.2 from the experimental r e s u l t of question 4.1. Then, t h e i r "primitive" answers could have been d i f f e r e n t i f question 4.1 were eliminated. 4.3. Cross-check Question: The e f f e c t of putting one washer i n each of the two hooks at S's side when the system i s i n equilibrium in task 2. Interview Question: If you put one washer i n each hook i n you side, what do you think i s going to happen with the whole thing? T: 25. -72-T y p i c a l C h i l d r e n ' s B e l i e f s : 4.3.A. - "The p l a t e w i l l s t ay where i t i s because there are s t i l l 2 washers i n each hook". Ss: 22, ( l - 6 y ; l - 7 v ; 3-8y; 4-9y; 3-10y; 3 - l l y ; 3-12y; 2-13y; 2-14y) E x c e r p t s : Rashida (6,7): "The p l a t e w i l l s t ay because there are s t i l l two washers i n each s i d e " . Tobby (9,3): "The p l a t e i s going to s t a y because i t i s s t i l l the same weight". 4.3.B. - "The p l a t e w i l l move towards me (towards the S) almost a l l the way because one washer i s c l o s e r to the ground". Ss: 3, ( l - 6 y ; l - 9 y ; l - 1 0 y ) . E x c e r p t s : Jeremy (9,4): "The p l a t e w i l l move towards me a b i t because t h i s washer i s c l o s e r to the ground". Comments: Sin c e , t h i s q u e s t i o n i s a cross-check q u e s t i o n , i f the answers f o r q u e s t i o n 4.2 are r e c a l l e d , where o n l y 15 Ss. s a i d t h a t the p l a t e would stay i f the c o n f i g u r a t i o n were changed, now, i n t h i s q u e s t i o n , 22 Ss. answered r e a f f i r m i n g t h a t the p l a t e would stay i f the con-f i g u r a t i o n were changed. C l e a r l y , some Ss. have l e a r n e d from task 1, the c o r r e c t answers. O v e r a l l Comments about the Major Concept: The E f f e c t of Changing the C o n f i g u r a t i o n of Weights: This aspect of the task, p a r t i c u l a r l y 4.2 and 4.3, would have been more r e l e v a n t to check the c o n s e r v a t i o n of weight. S i n c e , b e s i d e the f o r c e a p p l i e d by the e l a s t i c band i n task 1, a l l other f o r c e s i n the 3 tasks were the weight of the washers.. The e f f e c t o f the change of the washers (weights) c o n f i g u r a t i o n upon the displacement , . of- the p l a t e was looked f o r . But these - 7 3 -displacements were the o b j e c t i v e measurement of the f o r c e e x e r t e d , then, the change of c o n f i g u r a t i o n a f f e c t s o n l y the f o r c e e x e r t e d , which was the weight of the Ws. Acc o r d i n g to the above statement, 22 out of 26 Ss. are conservers o f weight. 5.0. CONCEPT OF COMPOSITION OF TWO FORCES: 5.1 The e f f e c t of d i s p l a c i n g the p l a t e i n a p e r p e n d i c u l a r d i r e c t i o n to the o r i g i n a l l i n e of f o r c e s i n task 2. Interview Question: (.1. d i s p l a c e s the p l a t e i n a p e r p e n d i c u l a r d i r e c t i o n i n about 8 cm... and holds i t there) : What w i l l happen i f the p l a t e i s r e l e a s e d ? T: 30 T y p i c a l C h i l d r e n ' s B e l i e f s : 5.1. A. "The p l a t e w i l l go back to the middle (with no c l e a r e xplanation) because i t has to be there ( A r i s t o t e l i a n i d e a ) " . Ss: 27, (2-6y; 3-7y; 2-8y; 5-9y; 4-10y; 2 - l l y ; 4-12y 3-13y; 2-14y) E x c e r p t s : Ryan (7,6) "The p l a t e w i l l move to the middle because these s t r i n g s are p u l l i n g on the way down to the middle, i t i s l i k e a s l i n g - s h o t " . Jenny (8,7): "The p l a t e i s going to move back because the s t r i n g s have to be s t r a i g h t here i n the middle". Jenny (10,4): "The p l a t e i s going to go back because the s t r i n g s are n a t u r a l y s t r a i g h t i n the middle, you are f o r c i n g the p l a t e to be t h e r e " . 5. I.B - "The p l a t e w i l l stay up t h e r e " . Ss: 3, ( l - 8 y ; l-10y; 1 - l l y ) . E x c e r p t s : Heather (7,0): "The p l a t e i s going to stay--tap there because i t stayed when you put i t there (when i t was d i s p l a c e d towards the S, see 3.4.B). Commeh t s : I t was c l e a r f o r 27 out of 30 Ss. t h a t the system would r e t u r n to the e q u i l i b r i u m p o s i t i o n , to the middle of the board, i f i t were r e l e a s e d . The p r e d i c t i o n was t h a t the o b j e c t would move i n the d i r e c t i o n of the r e s u l t a n t f o r c e , which means t h a t they Were able .to. compose two f o r c e s . Some of them made an analogy w i t h the s l i n g - s h o t . The e x p l a n a t i o n s f o r composing the two f o r c e s were a k i n d of A r i s t o t e l i a n e x p l a n a t i o n s , such as the s t r i n g s have to be s t r a i g h t i n the middle, t h a t i s t h e i r n a t u r a l p o s i t i o n . No i n t e n t s to i n c l u d e the components i n t h e i r e x p l a n a t i o n s was seen. 5.2. The composition of two f o r c e s (the r e s u l t a n t f o r c e w i l l be balanced by a t h i r d f o r c e ) w i t h equal magnitude and forming the f o l l o w i n g angles: 90 , 120°, 180°, 240°, and 75°. ( I n i t i a l l y the angle between F i and F 2 i s 9 0°, F, and F 2 have 3 washers, and R has 6 washers(Ws). The r i n g i s h e l d a t the c e n t r e by the peg i n t h i s and i n the f o l l o w i n g s i t u a t i o n s ) : I f I p u l l out the peg, what do you t h i n k i s going to happen wi t h the r i n g ? What c o u l d you do to keep the r i n g s t i l l a t the c e n t r e (without moving the pulleys),? T: 29. (Note; T, the t o t a l number of Ss. answering the r e s p e c t i v e q u e s t i o n , i s going to vary i n task 3, s e v e r a l Ss. c o u l d n ' t continue the task,, i t being d i f f i c u l t f o r them). T y p i c a l C h i l d r e n ' s B e l i e f s : (Note: A l l the c h i l d r e n ' s b e l i e f s w i t h r e s p e c t to a l l the q u e s t i o n s i n 5.2 and 5.3 are d i v i d e d i n . t h r e e p a r t s : (1) answer to the q u e s t i o n : what happen with the r i n g ( r ) i f the peg i s removed, (2) how to keep the r i n g ( r ) a t the c e n t r e , and (3) second i n t e n t to keep the r a t the c e n t r e , i f i t ' s the case) . 5.2.A. "The r i n g w i l l stay a t the centre because there i s the same weight i n both s i d e s . . . ( r i n g moved). I don't know how to keep the r i n g a t the c e n t r e . Ss: 1, ( l - 6 y ) . E x c e r p t s : C h a n t a l l e (6,6): " I f you want the r i n g a t the c e n t r e , I have to remove a l l the washers i n my s i d e . . . 5.2.B. - "The r i n g w i l l s t ay a t the centr e because there i s the same weight i n both s i d e s (r moved),.:.... I don't know what e l s e to do " Ss: 4, (2-7y; l - 8 y ; l - 1 3 y ) . E x c e r p t s : N a t a l i e (7,10): to keep the r i n g a t the c e n t r e I have to take 3 Ws. o f f from my s i d e , then, we have the same amount i n each hook...." Tommy (13,14): " to keep the r a t the c e n t r e I take o f f 3 Ws. from here, t h a t way, we have 3 Ws. i n each s i d e (hook) " 5.2.C. -"' The:'ring w i l l s t ay a t the c e n t r e because there i s the same weight on both s i d e s . . . . (r moved).;, to keep the r i n g , put the same amount of washer i n each hook...(r moved) I put 4 Ws. i n my s i d e . , (r s t a y e d ) " . Ss: 8, ( l - 6 y ; l - 8y; 2-9y; 3-12y; l-14y) E x c e r p t s : C h r i s (8,4) : " by p u t t i n g 3 Ws. i n each hook, r i n g moved toward you, then. I put 5 or 4 i n mv s i d e " Sue (12,7): " I put one more W i n my s i d e because wi t h 3 here i t moved toward you...." 5.2.D. - "Ring w i l l move toward me because those 6 (3 and 3 a t I's side) are a p a r t , they p u l l l e s s when they are a p a r t (r moved) to keep the r i n g a t the c e n t r e , I have to put the same amount of washers i n each hook (r moved) I don't know what e l s e t o do..." - 7 6 -Ss: 3, (2-9y; l-10y) E x c e r p t s : Frank (10,4): " To keep r i n g a t the c e n t r e , leave 3 i n those hooks (F^ and F 2) and 5 Ws. here.... (r moved) I don't know what e l s e t o do ...." 5.2.E. - "Ring w i l l move toward me because those 6 Ws. (3 and 3 a t I's side) are f a r a p a r t , they p u l l l e s s now... (r moved).... to keep the r i n g a t the c e n t r e , I have to put the same amount of Ws. i n each hook (r moved) because t h e * r i n g moved towards you and I w i l l put one more W i n here v . ...... (R=4, r stayed)....."^." Ss: 13, ( l - 8 y ; l -9y; 4-10y; 3 - l l y ; l-12y; 2-13y; l-14y) E x c e r p t s : L o r e l i e (10,7): " w i t h 3 Ws. i n here, the r i n g moved toward you, i f I put 5 or 4 here, i t c o u l d s t a y . . . . " Lauch (11,10): " i f I put 4 Ws. i n here (R:4), the r i n g w i l l s t a y , because b e f o r e w i t h 3, i t moved toward you..." Comments: F i n a l l y , 21 Ss. out of 29 were able to compose c o r r e c t l y the two f o r c e s when forming an angle of 9 0°. 13 Ss. p r e d i c t e d t h a t the r i n g would s t a y p r o v i d i n g t h a t there was the same weight i n both s i d e s . 16 Ss. gave as e x p l a n a t i o n f o r the r i n g moving toward them because when F i and F2 are a p a r t they p u l l l e s s . The f i r s t s t r a t e g y of these Ss. to b r i n g the system i n e q u i l i b r i u m w i t h the r i n g a t the c e n t r e was the n e c e s s i t y of having the same number of washers i n each hook. Even when these Ss. p r e d i c t e d the r i n g moving toward them, t h a t i s , they knew t h a t R (6 Ws.) was p u l l i n g more than F i and F2 (3 Ws. each), r e g a r d l e s s of the angle formed by F i and F 2 , they looked f o r the e a s i e s t answer, which was having same amount of Ws. i n each hook, to b r i n g the r i n g t o the c e n t r e . - 7 7 -Comments: Only 13 Ss. from the 16 mentioned above (11 ranging from 10 to 14 years of age) were able to suggest a second s t r a t e g y to b r i n g the r i n g t o the c e n t r e , by n o t i c i n g t h a t w i t h R=6, the r i n g moved to the S, and by i n c r e a s i n g F i and F2 the r i n g moved toward the I , then, the a l t e r n a t i v e way : c o u l d be by d e c r e a s i n g the number of washers i n R (with R : 4 Ws. r i n g stayed a t the c e n t r e ) . Nobody used as f i r s t s t r a t e g y the decrease of number of washers i n R. T h i s means t h a t a l l the Ss. l e a r n e d the c o r r e c t answer from the t a s k . I t a l s o means t h a t none of the Ss. had, as p r i m i t i v e i d e a , the n o t i o n of composition of f o r c e s . b) ( I n i t i a l l y , angle ( F i , F2) = 120°, F x = F 2 — 3 Ws.. , R = 4 Ws,) I f I p u l l out the peg, what do you t h i n k i s going to happen w i t h the r i n g ? What c o u l d you do to keep the r i n g s t i l l a t the c e n t r e ? T: 21 T y p i c a l C h i l d r e n ' s B e l i e f s : 5.2.b.A. - "The r i n g w i l l s t ay a t the c e n t r e because there i s no change i n the amount of washers (r moved).... To keep the r i n g a t the c e n t r e I take o f f 1 W i n my s i d e , then, there are 3 Ws. i n each hook (no mention o f the equal s e p a r a t i o n among the s t r i n g s ) " . Ss: 2, ( l - 8 y ; 1 - l l y ) E x c e r p t s : C h r i s (8,4) : " i f I take one washer o f f from my s i d e the r i n g i s going to s t a y because there i s the same amount of Ws. i n each end...." 5.2.b.B. - "The r i n g w i l l move toward me because there i s more weight i n my s i d e (r moved) To keep the r i n g a t the c e n t r e , I take o f f one W from my s i d e , so there are 3 Ws. i n each hook (no mention of equal s e p a r a t i o n among the washers)". Ss: 8, (2-9y; 2-10y; 1 - l l y ; 2-12y; l - 1 4 y ) . - 7 8 -E x c e r p t s : Greg (9,8) : " every time you separate more then (F^ and F 2 ) , i t seems there i s l e s s weight i n your s i d e . . . . i f I take 1 W o f f from here, the r i n g i s going to stay " Rick (12,10): " There are 4 Ws. here and 3 and 3 over t h e r e , then, the r i n g w i l l move toward me.... i f I take o f f 1 W from here, the r i n g w i l l s t a y . . . . " 5.2.b.C. - "The r i n g w i l l move toward me because F i and F 2 are f a r t h e r a p a r t and R has more weight (than F i and F 2 i n d i v i d u a l l y ? ) t o keep the r i n g a t the c e n t r e , I take 1 W o f f from my s i d e , then, there are 3 Ws. i n each hook (no mention of equal s e p a r a t i o n among the washers)". Ss: 5, ( l - 8 y ; 1^9y; l-10y; 1 - l l y ; l - 1 3 y ) . E x c e r p t s : Doug (8,0): " Ring w i l l move toward me because there are 4 Ws. here and those s t r i n g s are a p a r t . . . . to keep the r i n g a t the c e n t r e , I take o f f 1 W from here because we need the same weight i n each hook " Sandra (10,0): "The r i n g w i l l move toward me because those washers (F^ and F 2 ) are more separated now and my s i d e has more t h i n g s (washers); i f those washers were i n the middle, they would p u l l more but they are separated, then, I have to take 1 W o f f from my s i d e to keep the r i n g a t the c e n t r e " . 5.2.b.D. - "Ring w i l l move toward me because those ( F j and F 2 ) are f a r t h e r a p a r t and t h i s (R) has more weight than each one o f those to keep the r i n g a t the c e n t r e I have to take 1 W o f f from my s i d e , we need the same number o f Ws. i n each hook because those (the s t r i n g s ) are the same d i s t a n c e a p a r t " . Ss. 6, ( l - 9 y ; 2-12y; 2-13y; l-14y) E x c e r p t s : Jeremy (9,4): "This (R) has more weight than those ( F i and F 2 ) , when those are a p a r t , they can't j o i n t h e i r weight e a s i l y to keep the r i n g a t the middle I remove 1 W from my hook, because a l l the s t r i n g s are almost the same l e n g t h a p a r t " . E x c e r p t s : Sue (12,7): " I t ' s going to p u l l t h i s way (toward the S) because now, a l l - s i d e s are equal and my s i d e has more weight to keep the r i n g a t the c e n t r e , I take 1 W o f f " . Comments: 19 Ss. p r e d i c t e d the r i n g moving toward the S's s i d e , o f f e r i n g as p r o o f t h a t F^ and F 2 were f a r t h e r a p a r t and t h a t R had more weight than F-j_ and F 2 i n d i v i d u a l l y . These Ss. have l e a r n e d from ;;the p r e v i o u s experimental r e s u l t t h a t when F^ and F 2 are a p a r t they p u l l l e s s . 15 Ss., as f i r s t s t r a t e g y to keep the r i n g a t the c e n t r e , suggested having the same amount of Ws. i n each hook but without s a y i n g a n y t h i n g w i t h r e s p e c t to the e q u a l i t y of s e p a r a t i o n between the strings-. S i n c e , f o r t h i s aspect of the task, the c i r c u l a r board i s d i v i d e d i n 3 equal p a r t s , this f a c t i s not d i f f i c u l t to v i s u a l i z e . o n l y 6 Ss. suggested ."having same amount of washers i n each hook because the s t r i n g s were same d i s t a n c e a p a r t . I n t e r v i e w Question: ( I n i t i a l l y , angle (F]_ and F 2) = 180°, F l = F 2 R = 3 Ws.) . I f I p u l l out the peg, what do you t h i n k i s going to happen w i t h the r i n g ? What co u l d you do t o keep the r i n g a t the centre? T: 21 T y p i c a l C h i l d r e n ' s B e l i e f s : 5.2.C.A. - "The r i n g w i l l s t a y where i t i s because a l l hooks have the same weight (no mention o f the a n g l e s ) , ( r moved) to keep the r i n g at the* 'centre, I take o f f 1 W here (r moved) I don't know what e l s e t o do...." Ss: 1,(1,6) 5.2.C.B. ~ "The r i n g w i l l s t a y because there i s the same weight i n each hook (no mention of the a n g l e s ) , (r moved).... to keep r i n g a t the c e n t r e ( f i r s t s t r a t e g y ) : I add washers i n those (In F\ and F?), (r moved).... (second s t r a t e g y ) i t lias t o be equal weight i n each hook...." - 8 0 -Ss: 2,(l-9y; 1 - l l y ) E xcerpts: David (9,8): "The r i n g i s going to stay (r moved).... to keep i t at the c e n t r e , add 1 W i n each of those ( i n F-, and F2) . . . (r moved) . . . .take 1 W o f f from here t r moved) .... oh, leave 2 Ws. i n each hook, then a l l are at the same l e v e l . . . " 5.2.C.C. - "The r i n g w i l l stay because the same weight i n each hook and same distance between F]_ and R, and F2 and R (r moved).... to keep the r i n g at the centre, I take 1 W o f f from here (r moved) take one more o f f take a l l Ws. o f f (R:0)...'(r stayed)". Ss: 8,(l-9y; 4-10y; 2 - l l y ; l-13y) Excerpts: L o r e l i e (10,7): "The r i n g w i l l stay because there i s the same weight i n each side (each hook), (r moved).... take 1 W o f f from here .... take one more .... take the l a s t one..." Kevin (11, 7): " The p l a t e i s going to stay because a l l the washers are p u l l i n g i n d i f f e r e n t angles and a l l are p u l l i n g w i t h the same weight (r moved)... to keep the r i n g at the c e n t r e , I can take 1 W o f f from here ( r moved) Oh, .... I can take a l l Ws. o f f from here...." 5.2.C.D. - "The r i n g w i l l move toward me because there i s more weight i n my side and those ( F i and F2) are f a r t h e r apart to keep the r i n g a t the c e n t r e , I take 1 W o f f from here I take 1: more o f f Take a l l Ws o f f . . . . " Ss: 6, ( l - 8 y ; 2-9y; 3-12y) Excerpts: Greg (9,8): "The r i n g w i l l move down here because t h i s (R) has more weight than each one of those and you moved them apart more, then they don't have much weight to keep the r i n g a t the c e n t r e , I take 1 W o f f from here.... I take one more.... I take the l a s t one...." -81-ExcerDts: . ., fi . —^. (12,10): "The r i n g w i l l move to here because e v e r y t h i n g i s on t h i s s i d e now....To keep the r i n g a t the middle, I take 1 W o f f from here Oh, I remove a l l the Ws. from here...." 5.2.c.E. - "The r i n g w i l l move toward me because there i s no weight p u l l i n g t h i s (R).... t o keep the r i n g a t the c e n t r e , I have t o take a l l the Ws. o f f from t h i s (R)." Ss: 3, (l-12y; 2-14y) E x c e r p t s : Sue (12,7): " I t ' s going to p u l l down t h i s way because there i s no weight p u l l i n g from over there ( f a c i n g R), then, t o keep the r i n g a t the c e n t r e , I have t o take a l l the washers o f f from here (R)". St a n l e y (14,7) : " I t ' s going to p u l l t h i s way because t h a t s t r i n g (the ones j o i n i n g F i and F 2 ) i s almost s t r a i g h t , then, t h i s one (R) i s p u l l i n g toi.here, the r i n g i s b e i n g p u l l e d by t h i s s i d e . . . . to keep the r i n g i n the middle, I have to take a l l the Ws. o f f from here...." 5.2.C.F. ^ "Ring w i l l move toward me t o keep the r i n g a t the ce n t r e I have to add more Ws. i n those F i and F 2) ". Ss; 1, ( l - 1 3 y ) . Comments: Th i s aspect o f the task should have been f a m i l a r f o r the Ss. due to the s i m i l a r i t y w i t h task 2. 10 Ss. p r e d i c t e d t h a t the r i n g would stay a t the c e n t r e . T h i s i s an amazing r e s u l t a f t e r having found i n the p r e v i o u s aspect t h a t 19 Ss. from the same group of 21 i n d i c a t e d t h a t .when F^ and F 2 are ' -: separated they p u l l l e s s . 10 Ss. p r e d i c t e d t h a t the r i n g would move toward the S because F i and F 2 were f a r t h e r a p a r t and th e r e was more weight at S's s i d e . Only 3 Ss. suggested to i n c r e a s e the number o f Ws. i n F i and F 2 to keep the r i n g a t the c e n t r e as f i r s t s t r a t e g y . - 8 2 -Comments: 14 Ss, suggested t a k i n g some washers from R to keep the r i n g a t the c e n t r e . Most o f them were able to keep the r i n g a t the c e n t r e by removing the washers from R one by one. Only 3 Ss. suggested immediately the n e c e s s i t y of t a k i n g a l l the washers from R to keep the r i n g a t the c e n t r e . d) Interview Question:' ( I n i t i a l l y : angle (Flf F2) = 240°, F;L = F 2 = 3 Ws. R = 0): I f I p u l l out the peg, what do you t h i n k i s going to happen to the r i n g ? T: 20 T y p i c a l C h i l d r e n ' s B e l i e f s : 5.2.d.A. - "The r i n g w i l l s t a y because there i s the same amount of washers i n each hook". Ss: 4, ( l - 8 y ; 2-10y; l-13y) E x c e r p t s : C h r i s (8,4): " I t i s going to stay because there i s the same amount of Ws. i n each hook". Jenny (10,4): "The r i n g w i l l s t ay where i t i s because there i s n o t h i n g here (R:0) and o n l y these two ( F i and F2) are p u l l i n g and are e q u a l " . 5.2.d.B..- "The r i n g w i l l move u n t i l the s t r i n g s are s t r a i g h t o r i t i s going to move half-way". Ss: 11, (3-9y; 1 - l l y ; 4-12y; 2-14y) E x c e r p t s : Jeremy (9,4): "The r i n g w i l l move toward me j u s t to the middle". A l l i s o n (12,2): "The r i n g w i l l move toward me, about h a l f way because the s t r i n g s have to be s t r a i g h t i n here (half'-way p o s i t i o n ) " . 5.2.d.C. - "The r i n g w i l l move a l l the way because a l l the washers are i n my s i d e and they are p u l l i n g " . -83-Ss. 2, (l-10y; 1 - l l y ) E x c e r p t s : Lauch (11,10): " I t i s going to p u l l a l l the way because a l l these t h i n g s (washers) are i n t h i s s i d e o f the board (S's side) and they are p u l l i n g t h i s way (toward the S) "'. Comments: T h i s aspect o f task 3 i s i d e n t i c a l t o one of the a s p e c t i n task 2, showed i n 5.1., i n t h a t aspect 27 out of 30 Ss. p r e d i c t e d c o r r e c t l y . - 11 out o f 17 Ss. p r e d i c t e d the r i n g would move u n t i l s t r i n g s were s t r a i g h t and 2 Ss. s a i d t h a t the r i n g would move u n t i l s t r i n g s were s t r a i g h t and 2 Ss. s a i d t h a t the r i n g would move a l l the way. <- 4 Ss. p r e d i c t e d the r i n g would s t a y a t the c e n t r e because there was the same number of washers i n each hook without c o n s i d e r i n g the r e l a t i v e p o s i t i o n o f the washers. 5.2.e. - Interview Question ( I n i t i a l l y : angle (FT and F 2 ) = 75°, F X = F 2 = 3 washers, R = 4 Ws:. I f I p u l l out the peg, what do you t h i n k i s going to happen w i t h the r i n g ? What c o u l d you do t o keep the r i n g a t the c e n t r e ? T = 8 T y p i c a l C h i l d r e n ' s B e l i e f s 5.2.e.A. - "The r i n g w i l l move toward me because my s i d e has more weight (R:4) than those (F-^ and F 2 ) . . . ( r moved toward I) to keep the r i n g at the c e n t r e , I add 1 W i n R..(r s t a y e d ) " Ss: 2, (l-10y; 1 - l l y ) E x c e r p t s : Kevin (11,7): "The r i n g w i l l move toward me because t h i s s i d e i s overpowered there are 4 Ws here and o n l y 3 and 3 t h e r e ( r moved toward I ) . . . . t o keep the r i n g a t the c e n t r e , I have to put 2 more Ws. here (R:6)... (r moved toward S)....Oh, I need o n l y 5 Ws. here (R:5)" 5.2.e.B. - "The r i n g w i l l move toward you because those - 8 4 -(F-i and F2) a : t" e c l o s e r , they have more weight a l t o g e t h e r now,.,, to keep the r i n g a t the c e n t r e , I put 1 W. here (R:5)" Ss: 6, ( 1 - l l y ; 3-12y; 2-14y). E x c e r p t s : Lauch (11,10): " I t i s going to move toward you now because you moved those (F^ and F 2 ) c l o s e r , then, now they have more weight a l t o g e t h e r I put one more W here to keep the r i n g a t the c e n t r e " . Joseph (12,10): " I t i s going to move toward you because they (F^ and F 2 ) are c l o s e r t o g e t h e r and they are more as a team now, w h i l e more separated they are they work l e s s as a tern. Work as a team, I mean, they combine t h e i r weight; they don't combine t h e i r weight when they are more separated". S t a n l e y (14,7): " I t ' s going to p u l l t h a t way (toward the I) because those p u l l e y s are c l o s e r now, the washers work together now, they ( F i and F 2 ) both p u l l t o g e t h e r now because they are c l o s e r , b e f o r e when they were more separated, they were not working t o g e t h e r to keep the r i n g a t the c e n t r e , I put 1 W here (R:5)". Comments: Only 8 Ss. from the i n i t i a l sample of 31 remained f o r the l a s t 2 aspects o f task.3. I t was the e x p e r i -menter's d e c i s i o n t o end the i n t e r v i e w w i t h a l l the other s u b j e c t s i n the p r e v i o u s p a r t o f interview./-due to two main f a c t o r s : Ss. were t i r e d , which made them s t a r t guessing answers to p l e a s e the ex-perimenter, and Ss. were a c t u a l l y l o s t w i t h the t a s k s and were g i v i n g answers not r e l a t e d w i t h the experiments a t a l l (romancing answers, P i a g e t ) . A f t e r i n c r e a s i n g the angle from 0° to 24 0°, the angle i s decreased again to 75°. S i x of the 8 Ss. p r e d i c t e d t h a t the r i n g would move toward the experimenter because F\ and F 2 were c l o s e r what makes them p u l l more. These Ss. might have been u s i n g knowledge a c q u i r e d d u r i n g the i n t e r v i e w . The ages o f the 8 Ss. ranged from 10 to 14 y e a r s . -85-O v e r a l l Comments about the Concept o f Composition o f  Two Forces w i t h Equal Magnitude As i t was s a i d i n the comments f o r 5.2.a., the b e l i e f s t h a t the c h i l d r e n showed i n the answer when the angle formed by F^ and F 2 was changed f o r f i r s t time, were t h e i r p r i m i t i v e b e l i e f s ; s i n c e , a f t e r s e e i n g the experimental r e s u l t i n 5.2.a., they have l e a r n e d from the experiment and they are going to use t h i s r e s u l t i n the f o l l o w i n g cases o f v a r y i n g more the ang l e . Even when, each S had the chance to use the experimental r e s u l t s when F^ and F 2 formed ah angle o f 90° and to r e a l i z e what happens when the v a r i a b l e angle was changed. The p r e d i c t i o n s f o r the othe r angles (120°, 180°, 240°, 75°) showed t h a t most of Ss. d i d not make use of the f i r s t e xperimental r e s u l t (90°) when t r y i n g to p r e d i c t . T h i s shows t h a t some Ss. have not had y e t the necessary experiences to c o n s i d e r the d e c i s i v e f a c t o r s when s o l v i n g these k i n d s o f problems. Some of the Ss. d i d n ' t have a common s t r a t e g y to solv e the d i f f e r e n t problems of the task, they were changing t h e i r i d e a s i n each a s p e c t . For most of them'the v a r i a b l e angle: was hot important and they kept c o n s i d e r i n g o n l y the v a r i a b l e amount o f washers, when t r y i n g to s o l v e the problems. 5.3. The composition of two f o r c e s (the r e s u l t a n t w i l l be balanced by a t h i r d f o r c e ) w i t h d i f f e r e n t magnitude and forming an angle o f 75°. - 8 6 -I n t e r v i e w Question; ( I n i t i a l l y : angle (Fx and F2) = 75°, F i = 4 Ws.,F2 = 3 Ws. and R = 5 Ws): I f I p u l l out the peg, what do you t h i n k i s going to happen to the r i n g ? What c o u l d you do to keep the r i n g a t the c e n t r e ? T: 8 T y p i c a l C h i l d r e n ' s B e l i e f s : 5.3.A. - "The r i n g w i l l move toward you i n t h a t d i r e c t i o n (along F i 's s t r i n g ) . . . ( r moved i n between FT 's s t r i n g and the c e n t r a l l i n e drawn on the b o a r d ) . . . . t o keep the r i n g a t the c e n t r e , I add 1 W. here (R: 6 ) . . . . ( r moved c l o s e r to the c e n t r e ) . . . . I don't know what e l s e to do...." Ss: 1, ( l - 1 0 y ) . E x c e r p t s : Sandra (10,0): "The r i n g w i l l move toward you (I ask: In what d i r e c t i o n ? ) . . . . along t h a t s t r i n g (F^ s t r i n g ) .... to keep the r i n g a t the c e n t r e , I have t o add 1 W here ( R : 6 ) . . . . ( r moved) .... I don't know what e l s e to do " 5.3.B. - "Ring w i l l move towards you (TJ_: what d i r e c t i o n ? ) i n t h a t d i r e c t i o n ( i n between the F]_' s s t r i n g and the c e n t r a l l i n e drawn on the b o a r d ) . . . . t o keep the r i n g a t the c e n t r e , I add 1 W. i n here (R:6) (r stayed c l o s e r to the c e n t r e ) . S s : l , ( l - 1 2 y ) E x c e r p t s : Sue (12,7): "The r i n g w i l l move t h a t way (towards the I ) , not along the F^'s s t r i n g , more to the l e f t ( i n between F i ' s and the c e n t r a l l i n e ) , not a l l the way, about t h a t much (1/3 o f t o t a l way) to keep the r i n g a t the c e n t r e . I can't do anything, maybe, I can put 1 W i n t h i s s i d e (R:6) (r stayed c l o s e r t o the centre) I don't know what e l s e t o do " 5.3.C.: "The r i n g w i l l move towards you i n t h a t d i r e c t i o n (along F^'s s t r i n g ) .... to keep the r i n g a t the c e n t r e . I add 1 W i n here (R:6) (r moved c l o s e r to the centre) I move t h i s p u l l e y to the r i g h t or to the l e f t . . . ( r was very c l o s e to the c e n t r e ) " - 8 7 -Ss: 4, C2^11y; l-12y; l-14y) E x c e r p t s : Lauch (11,10): "The r i n g w i l l move towards you along the s t r i n g about t h a t f a r (1/3 of t o t a l way) to keep i t a t the c e n t r e , I can put lr.W :here ( R : 6 ) . . . ( r stayed c l o s e r t o the centre) you cut 1 W. i n h a l f . . . . Oh, I can move t h i s p u l l e y t o here (to the r i g h t , r was f a r t h e r from the cen t r e now) o r to here (to the l e f t , r was c l o s e r t o the c e n t r e ) " . W i l l i o n (14,11): "The r i n g w i l l move t h a t way (towards the I) alo n g t h a t l i n e ( F j ' s s t r i n g ) to keep i t at the c e n t r e I can move t h i s t h i n g (the p u l l e y ) I can a l s o i n c r e a s e the weight here ( R : 6 ) . . . . ( r stayed very c l o s e t o the centre'). 5.2.D. - "The r i n g w i l l move toward you i n t h a t d i r e c t i o n ( i n between F^'s s t r i n g and the c e n t r a l l i n e ) to keep the r i n g a t the c e n t r e I add 1 W. i n here (R = 6) I move the p u l l e y to the r i g h t or to the l e f t " Ss: 2, (l-12y; l-14y) E x c e r p t s : Joseph (12,10): "The r i n g w i l l move t h a t way (towards the I, i n between F\ s t r i n g and the c e n t r a l l i n e ) to keep the r i n g a t the middle, I can add one more weight here (R=6) .... I c o u l d add h weight more Oh, I can move t h i s ( p u l l e y ) to the l e f t a b i t (r stayed a t the c e n t r e ) " . S t a n l e y (14,7): " I t ' s going to p u l l towards t h e j l ) , . i n t h a t d i r e c t i o n ( i n between the F i s t r i n g and the c e n t r a l l i n e ) to keep the r i n g a t the c e n t r e , I can put 1 W. here (R = 6, r stayed c l o s e r t o the centre) I can change the angle, I can move the p u l l e y towards there (to the S's l e f t ) . . . . ( r stayed at the centre) " Comments: 5 out of 8 Ss. p r e d i c t e d t h a t the r i n g would move toward the I i n the d i r e c t i o n g i v e n by the s t r i n g t i e d to F;L (.4 Ws.) s i n c e F^ was g r e a t e r than F 2 . - 8 8 -Comments: The o t h e r 3 Ss. p r e d i c t e d t h a t the r i n g would move towards the I i n a d i r e c t i o n i n between the s t r i n g a t t a c h e d to F l and the c e n t r a l l i n e drawn on the board, which shows t h a t these Ss. understand b e t t e r the a c t i o n of two f o r c e s working t o g e t h e r . The o t h e r 5 Ss. mentioned above, c o n s i d e r e d o n l y the e f f e c t o f the g r e a t e r f o r c e and they d i d n ' t c o n s i d e r at a l l the e f f e c t of F 2 . The 8 Ss. suggested the a d d i t i o n : o f 1 W on R to keep the r i n g a t the c e n t r e , showing c l e a r l y the they understand the concept o f E q u i l i b r i u m . 6 of the 8 Ss., be s i d e s the a d d i t i o n o f 1 W. on R suggested the n e c e s s i t y o f moving the p u l l e y a t S's s i d e to b r i n g the r i n g t o the c e n t r e , a f t e r d i s p l a c i n g t h i s p u l l e y a b i t to the r i g h t and to the l e f t , they had success i n keeping the r i n g very c l o s e to the c e n t r e . Only these 6 Ss. out of 31 demonstrated an a b i l i t y t o work w i t h two v a r i a b l e s s i m u l t a n e o u s l y (weight and a n g l e ) , which would mean t h a t they would be ready to be taught the composition o f f o r c e s . - 8 9 -4.50 BROAD PATTERNS OF BELIEFS There appears to be c o n s i d e r a b l e consensus t h a t c h i l d r e n a c q u i r e many of t h e i r b e l i e f s by means o f a s e r i e s o f a b s t r a c t i o n s from experience w i t h p h y s i c a l phenomena. (For example see the w r i t i n g s o f P i a g e t , Bruner and Bohm). Given t h i s p e r s p e c t i v e , one way of l o o k i n g a t d i f f e r e n t b e l i e f s expressed by c h i l d r e n i n an i n t e r v i e w s e t t i n g i s to examine them i n terms o f t h e i r degree o f a b s t r a c t i o n from the a c t u a l concrete s i t u a t i o n . These a b s t r a c t i o n s occur a t d i f f e r e n t l e v e l s , a c c o r d i n g to Bohm, ranging from very p r i m i t i v e "immediate p e r c e p t i o n " to h i g h e r l e v e l s of a b s t r a c t i o n . S u b j e c t s o p e r a t i n g a t the lower l e v e l tend to e x p l a i n a problem s i t u a t i o n i n terms o f one or more i s o l a t e d v a r i a b l e s . These e x p l a n a t i o n s are g e n e r a l l y based upon d i r e c t sense impressions. In h i g h e r l e v e l s they account f o r the s i t u a t i o n i n terms o f i n t e r a c t i n g v a r i a b l e s due to a b s t r a c t i o n s formed from p r e v i o u s e x p e r i e n c e s . The f i n a l stage of a n a l y s i s then c o n s i s t s o f c a t e g o r i z i n g the c h i l d r e n ' s b e l i e f s i n t o three 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 . The f i r s t l e v e l of a b s t r a c t i o n c o n t a i n s those b e l i e f s t h a t are c l o s e s t to a d i r e c t r e p o r t i n g of the c h i l d ' s o b s e r v a t i o n . B e l i e f s t h a t are immediate p e r c e p t i o n s of the experimental s i t u a t i o n s . At t h i s l e v e l the c h i l d simply d e s c r i b e s the observed - 9 0 -r e s u l t i n t h e i r own words; there i s no attempt to look f o r r e l a t i o n s h i p s among the v a r i a b l e s i n the s i t u a t i o n . The second l e v e l o f a b s t r a c t i o n c o n t a i n s more s o p h i s t i c a t e d b e l i e f s . The c h i l d now begins to f o r -mulate some ideas about p o s s i b l e r e l a t i o n s h i p s to account f o r the o b s e r v a t i o n s made i n the experimental s e t t i n g . More f a c t o r s i n v o l v e i n t h e i r e x p l a n a t i o n s are now pr e s e n t but some important v a r i a b l e s which are r e l e v a n t f o r a complete comprehension o f the s i t u a t i o n are s t i l l l e f t o ut. The t h i r d l e v e l o f a b s t r a c t i o n c o n t a i n s those b e l i e f s t h a t account f o r the i n v a r i a n t f e a t u r e s i n the experiments. The i n d i v i d u a l b r i n g s to l i g h t the b a s i c o p e r a t i o n s , movements and changes, w i t h i n which c e r t a i n c h a r a c t e r i s t i c s have been found to be i n v a r i a n t , r e -s u l t i n g i n a " t o t a l p i c t u r e " o f the s i t u a t i o n * . A t t h i s l e v e l , the s u b j e c t s are ab l e to account f o r the s i t u a t i o n by c o n s i d e r i n g the r e l a t i o n s h i p s among the v a r i a b l e s . * a c l e a r example o f i n v a r i a n t c h a r a c t e r i s t i c i s t h a t of Newtonian mechanics which c o n s i s t e d o f the d i s c o v e r y o f the i n v a r i a n c e o f c e r t a i n r e l a t i o n s h i p s (Newton's law of motion), i n wide v a r i e t y o f systems, movements, changes of frames of r e f e r e n c e , e t c . -91-While a n a l y z i n g the c h i l d r e n ' s b e l i e f s and l a t e r when c a t e g o r i z i n g these b e l i e f s i n the l e v e l o f a b s t r a c t i o n , i t was r e a l i z e d t h a t i t i s not p o s s i b l e to match e x p l i c i t l y these b e l i e f s o r the l e v e l s w i t h a given s e t o f ages. That i s , i t i s not p o s s i b l e to e s t a b l i s h t h a t the f i r s t l e v e l corresponds to a determined i n t e r v a l o f ages; the same i s tru e f o r the oth e r two l e v e l s o f a b s t r a c t i o n . Subjects w i t h d i f f e r e n t ages (from 6 t o 14 years old) were found having b e l i e f s i n each o f the three l e v e l s . From the data c o l l e c t e d , i t might be s a i d , but onl y i n g eneral terms, t h a t the h i g h e r l e v e l s correspond t o the o l d e r c h i l d r e n i n the sample but not to a s p e c i f i c range o f ages. 4.60 THE THREE LEVELS OF ABSTRACTION OF CHILDREN'S  BELIEFS ABOUT THE CONCEPT OF FORCE The b e l i e f s c o n tained i n each l e v e l o f a b s t r a c t i o n are ordered a c c o r d i n g to the order o f the major concepts e s-t a b l i s h e d i n the conceptual p r o f i l e (see : page 46" o f t h i s Chapter 4 ) . 4.61 F i r s t L e v e l o f A b s t r a c t i o n A. A c t i o n o f a Fo r c e : A f o r c e i s a c t i n g upon an o b j e c t o n l y i f the o b j e c t i s moving, once the o b j e c t stops moving, the f o r c e has ceased a c t i n g . [See r e s u l t s o f Conceptual P r o f i l e , p a r t 3.1, q u e s t i o n b ( h e r e a f t e r a b b r e v i a t e d as: C P : 3.1;b). B e l i e f h e l d by s u b j e c t s from 6 to 13 years ( h e r e a f t e r a b b r e v i a t e d as: Ss: (6-13)y]. -92-B. A f i x e d body (a n a i l d r i v e n i n t o the wood, a w a l l , a t r e e ) cannot p u l l . _ ' . I t can o n l y h o l d o t h e r o b j e c t s . ( C P . : 2.1;b, Ss: (6-14)y) C. The a c t i o n of a f o r c e i m p l i e s p u l l i n g , t h e r e f o r e , motion. H o l d i n g does not imply the a c t i o n o f any f o r c e . ( C P . : 2.1;b, Ss: (6-14)y) A c t i o n and R e a c t i o n : When two o b j e c t s are i n t e r a c t i n g by means o f a s t r i n g , o n l y one o b j e c t i s e x e r t i n g a f o r c e on the o t h e r , without r e c i p r o c i t y of a c t i o n . ( C P . : 2.1;a. Ss: ( 6 - l l ) y ) Concept of E q u i l i b r i u m : An o b j e c t i s i n e q u i l i b r i u m i f i t i s being p u l l e d by another o b j e c t and h e l d by a t h i r d o b j e c t . ( C P . : 2.1;b C P . : 3.1;b . Ss: (6-14)y) C o n f i g u r a t i o n of Weights (Conservation of Weight): A. Objects c l o s e r to the ground p u l l l e s s because they have l e s s weight. ( C P . : 4.1 . Ss: ( 6 - l l ) y ) B. Weight of a s e t o f o b j e c t s p u l l s l e s s or more when they are separated than when they are t o -gether . ( C P . : 4.2 . Ss: (6-13)y) Composition o f F o r c e s : The r e s u l t a n t of two f o r c e s w i t h equal magnitude and forming an angle d i f f e r e n t from zero degree i s -93-obtained by addina t h e i r magnitudes a r i t h m e t i c a l l y . The angle formed by the two components i s not con-s i d e r e d . ( C P . : 5.2;a. Ss: (6-14)y) 4.62 Second l e v e l of A b s t r a c t i o n  A c t i o n o f F o r c e s : When two f o r c e s are a c t i n g upon an o b j e c t , i t moves i n the d i r e c t i o n o f the net f o r c e u n t i l the motion com-pensates f o r the net f o r c e , b r i n g i n g the o b j e c t to r e s t . ( C P . : 1.3 . Ss: (6-13)y) A c t i o n and Rea c t i o n : When two o b j e c t s are i n t e r a c t i n g by means of a s t r i n g w i t h the f i r s t o b j e c t p u l l i n g a second o b j e c t , t h i s second object i s t r y i n g to p u l l the f i r s t but i t does not have enough s t r e n g t h -- b i d i r e c t i o n a l approach wi t h f o r c e s a c t i n g r e c i p r o c a l l y but w i t h d i f f e r e n t mag-nitude . ( C P . : 2.1; (2.IB) . Ss: (12-14)y) Concept o f E q u i l i b r i u m : Two equal f o r c e s keep an o b j e c t i n s t a t i c e q u i l i b r i u m o n l y i f the o b j e c t i s j u s t i n the middle p o s i t i o n i n between the bodies which apply the f o r c e s . ( C P . : 3.4;b . Ss: (6-13)y) C o n f i g u r a t i o n of Weights: A. Objects c l o s e r to the ground can p u l l the same as o b j e c t s i n h i g h e r p o s i t i o n because weight o f an o b j e c t i s independent of i t s h e i g h t . ( C P . : 4.1 . Ss. (8-13)y) . -94-B. A s e t o f o b j e c t s p u l l s the same when they are separated o r t o g e t h e r . ( C P . : 4.2; (4.2c) . Ss: (6-14)y) Composition o f For c e s : The r e s u l t a n t o f two f o r c e s w i t h equal magnitude and forming angles g r e a t e r than zero degree i s o b t a i n e d by c o n s i d e r i n g magnitude and s e p a r a t i o n o f the com-ponents . When the s e p a r a t i o n o f the components i s gr e a t e r , the combination of them p u l l l e s s and l e s s . ( C P . : 5.2; a,b,c. Ss: (8-14)y) 4.63 T h i r d L e v e l o f A b s t r a c t i o n  A c t i o n of Fo r c e s : When two f o r c e s are a c t i n g upon an o b j e c t , i t moves w h i l e there i s a net f o r c e a c t i n g . ( C P . : 1.3C) . Ss: (8-14)y) A c t i o n and Rea c t i o n : Whenever one body e x e r c i s e s a f o r c e upon a second body, the second body always e x e r t s upon the f i r s t a f o r c e o p p o s i t e i n d i r e c t i o n and equal i n magnitude. (Nobody i n the sample h e l d t h i s concept. I t can be claimed t h a t t h i s concept i s not grasped n a t u r a l l y but i t has to be t a u g h t ) . Concept Of E q u i l i b r i u m : Two equal f o r c e s keep an o b j e c t i n s t a t i c e q u i l i b r i u m r e g a r d l e s s o f the p o s i t i o n o f the o b j e c t -95-i n between the bodies e x e r t i n g the f o r c e s . ( C P . : 3.4;b . Ss: (6-14)y) Composition o f F o r c e s : The r e s u l t a n t of two f o r c e s w i t h d i f f e r e n t magnitude and forming an angle d i f f e r e n t from zero degrees i s c l o s e r to the component w i t h g r e a t e r magnitude. ( C P . : 5.3 Ss: (14)y) . - 9 6 -C H A P T E R F I V E 5.00 CONCLUSIONS/ EDUCATIONAL IMPLICATIONS AND  RECOMMENDATIONS 5.10 Summary of the Study The two main o b j e c t i v e s of t h i s study were: (a) to explore what ideas or b e l i e f s c h i l d r e n have about the concept of f o r c e , and (b) to look f o r trends or . ; ; : patterns i n the development of the concept of forc e i n c h i l d r e n ranging from 6 to 14 years of age. The pro-cedures used to explore the c h i l d r e n ' s b e l i e f s c o n s i s t e d of i n d i v i d u a l i n t e r v i e w s w i t h 32 c h i l d r e n . The a n a l y s i s of the i n t e r v i e w data was done i n two steps. F i r s t , a conceptual p r o f i l e was constructed which contained several aspects of the concept of force as ex e m p l i f i e d by the three i n t e r v i e w t a s k s . The c h i l d r e n ' s b e l i e f s presented as answers to the questions asked during the i n t e r v i e w s were keyed to the major .sub-s i d i a r y concepts i n the conceptual p r o f i l e . A second step c o n s i s t e d of examining the c h i l d r e n ' s b e l i e f s i n terms of three l e v e l s of a b s t r a c t i o n . I t was suggested th a t these three l e v e l s might represent a set of broad developmental patterns i n c h i l d r e n ' s understanding of the concept of f o r c e . 5.20 Conclusions of the Study Although the problems addressed i n t h i s study were not presented i n form of hypotheses, t e n t a t i v e conclusions -97-can be o f f e r e d about the methods used i n the study and the i d e a s t h a t c h i l d r e n h e l d about the' p a r t i c u l a t e concepts of f o r c e presented i n the i n t e r v i e w s e t t i n g . F i r s t / the c o n c l u s i o n s about the t a s k s , method o f c o l l e c t i n g data, and the method o f a n a l y s i s are presented. 1) The i n t e r v i e w methodology (a m o d i f i c a t i o n o f the P i a g e t i a n c l i n i c a l i n t e r v i e w ) was a u s e f u l technique f o r c o l l e c t i n g . d a t a about c h i l d r e n ' s b e l i e f s . Through an i n t e r v i e w approach a r i c h supply o f c h i l d r e n ' s b e l i e f s was o b t a i n e d . T h i s same type o f data was not p o s s i b l e to o b t a i n from more s t a n d a r d i z e d paper and p e n c i l techniques. 2) The three tasks of the study can be c o n s i d e r e d v a l i d f o r the purpose of c o l l e c t i n g r e l i a b l e data concerning c h i l d r e n ' s i d e a s about f o r c e . T h i s c o n c l u s i o n seems j u s t i f i e d s i n c e the c h i l d r e n seemed to be genuinely i n v o l v e d w i t h the problems a r i s i n g from each of the t a s k s . The idea s presented by the c h i l d r e n were reasonable and c o n s i s t e n t throughout the three t a s k s . None o f the c h i l d r e n ever appeared t o be bored or t o t a l l y confused when proposing' some i d e a o r ex-p l a n a t i o n to account f o r t h e i r o b s e r v a t i o n s . 3) A con c e p t u a l p r o f i l e , which i n c l u d e s aspects o f the concept of f o r c e i l l u s t r a t e d by the th r e e t a s k s , proved to be an a c c e p t a b l e method to analyze the i n t e r v i e w data. - 9 8 -The c a t e g o r i z a t i o n of c h i l d r e n ' s ideas i n t o a s e r i e s o f major and s u b s i d i a r y concepts allowed the data to be analyzed i n a very o r d e r l y way. I t proved to be an e f f i c i e n t and f r u i t f u l method f o r convert-i n g the l a r g e amount o f data i n t o a form which has p o t e n t i a l uses f o r teachers and c u r r i c u l u m d e v e l o p e r s . A number o f c o n c l u s i o n s can a l s o be reached r e -gard i n g the s u b s t a n t i v e b e l i e f s i d e n t i f i e d from the i n t e r v i e w data. 4) A l l c h i l d r e n i n the sample, from 6 t o 14 years of age, possessed some a p r i o r i i d e a s about the concept of f o r c e . T h i s assumption was made by the author b e f o r e proceeding with the r e s e a r c h . I t appeared to be v e r i -f i e d d u r i n g the i n t e r v i e w s s i n c e a l l s u b j e c t s p r o v i d e d some i d e a s t o account f o r t h e i r observations'; although t h e i r i d e a s v a r i e d g r e a t l y from s u b j e c t to s u b j e c t . 5) From the data c o l l e c t e d , i t was concluded t h a t c e r t a i n ideas about f o r c e were found i n c h i l d r e n o f a l l ages i n c l u d e d i n the study. A few ot h e r ideas seemed to be more age de-pendent. I t was found out t h a t s i m i l a r b e l i e f s on the same major concepts were h e l d by c h i l d r e n r anging from 6 to 14 years of age. I t was common to f i n d the same b e l i e f - 9 9 -throughout the sample. For example, the b e l i e f t h a t a f o r c e i s a c t i n g upon an o b j e c t o n l y i f the o b j e c t i s moving was h e l d by s u b j e c t s from 6 to 13 years o f age. On the o t h e r hand, the concept of a c t i o n and r e a c t i o n seems t o be age dependent (see task 1, qu e s t i o n 9 ) s i n c e younger c h i l d r e n (6 to 11 years o f age) f e l t t h a t o n l y one o b j e c t was p u l l i n g i n t h e i r o b s e r v a t i o n s when two o b j e c t s were i n t e r a c t i n g . And o l d e r c h i l d r e n (12 to 14) a f f i r m e d t h a t the two o b j e c t s were p u l l i n g , even when one of the o b j e c t s was p u l l i n g s t r o n g e r than the ot h e r . The f o l l o w i n g c o n c l u s i o n i s r e l a t e d to o b j e c t i v e (b) o f the study. 6)' Three d i f f e r e n t p a t t e r n s o f b e l i e f s were hypothesized from the i n t e r v i e w d a t a . These p a t t e r n s were i n t e r p r e t e d i n terms o f d i f f e r e n t l e v e l s o f a b s t r a c t i o n . T h i s stage o f a n a l y s i s was done by t a k i n g the i n -ter v i e w data as a whole and c a t e g o r i z i n g the p a r t s o f i t (the s e t o f b e l i e f s ) , i n such a way t h a t each c a t e -gory c o n t a i n s s i m i l a r kinds o f e x p l a n a t i o n s about the major concepts. Three c a t e g o r i e s o r l e v e l s were de-f i n e d f o r each major concept o f the conceptual p r o f i l e . In examining the kin d s o f ideas i n each of these l e v e l s i t may be p o s s i b l e to o b t a i n some i n s i g h t i n t o -100-the way c h i l d r e n develop an understanding about the concept o f f o r c e . However, i t i s not b e i n g c l a i m e d i n the p r e s e n t study t h a t a l l c h i l d r e n f o l l o w the same o r d e r o f development; t h i s type o f c l a i m would r e q u i r e a much more c a r e f u l and c o n t r o l l e d study. These l e v e l s may i n d i c a t e one p o s s i b l e mode o f de-velopment. F i n a l l y , the author c o n s i d e r s i t important to i n c l u d e i n the c o n c l u s i o n s e c t i o n some of the more prominent i d e a s about the concept of f o r c e h e l d by c h i l d r e n throughout the sample. 7) F o l l o w i n g are a s e r i e s o f s u b s t a n t i v e i d e a s expressed by the s u b j e c t s about the concept o f f o r c e . - S u b j e c t s from 6 to 11 years o f age h e l d the b e l i e f t h a t o n l y one body e x e r t s a f o r c e i n a s i t u a t i o n where t h e r e are two b o d i e s i n t e r -a c t i n g . S u b j e c t s from 12 t o 14 y e a r s t y p i c a l l y f e l t t h a t when two bodies a r e i n t e r -a c t i n g , one was e x e r t i n g a f o r c e w h i l e the o t h e r was t r y i n g t o e x e r t a f o r c e but d i d not have enough s t r e n g t h . No s u b j e c t s i n the sample used the word f o r c e i n d e s c r i b i n g any o f the o b s e r v a t i o n s they made. A l l s u b j e c t s were aware t h a t the weight o f the washers were r e s p o n s i b l e f o r e x e r t i n g the p u l l i n the t h r e e t a s k s . Most o f the s u b j e c t s f e l t t h a t f i x e d b o d i e s cannot e x e r t a p u l l . They can o n l y h o l d o t h e r b o d i e s . A l l s u b j e c t s i n the study seemed to have an i n t u i t i v e grasp of the concept o f e q u i l i b r i u m i n a s i t u a t i o n where two equal f o r c e s were a c t i n g i n o p p o s i t e d i r e c t i o n s . Although, many s u b j e c t s expressed the n o t i o n t h a t an o b j e c t i s i n e q u i l i b r i u m o n l y when i t i s i n the middle p o s i t i o n between the bodies t h a t e x e r t the two o p p o s i t e equal f o r c e s . -101-Approximately h a l f o f the s u b j e c t s were aware t h a t two equal f o r c e s forming an angle g r e a t e r than zero degrees do not add a r i t h m e t i c a l l y . There was l i t t l e i n d i c a t i o n t h a t the s u b j e c t s had any f i r m n o t i o n o f the v e c t o r i a l nature of f o r c e when attempting t o account f o r the observed r e s u l t s . 5.30 E d u c a t i o n a l I m p l i c a t i o n s In the s e c t i o n on "The E d u c a t i o n a l Context of the Study" i h Chapter Two, i t was emphasized t h a t c h i l d r e n ' s i d e a s should be c o n s i d e r e d by those de-v e l o p i n g s c i e n c e c u r r i c u l u m and a l s o by s c i e n c e t e a c h e r s i n t h e i r d a i l y task o f t e a c h i n g s c i e n c e concepts to students. T h i s study has found t h a t the understanding t h a t c h i l d r e n develop about the concept of f o r c e c o n s i s t s of a number o f d i f f e r e n t i d e a s and e x p l a n a t i o n s (some r e s e a r c h e r s have r e f e r r e d t o them as m i s c o n c e p t i o n s ) . The broad aim o f most o f the s c i e n c e c u r r i c u l u m pro-j e c t s developed i n the l a s t decades, seems to be d i r e c t e d toward h e l p i n g the c h i l d to p e r c e i v e n a t u r a l phenomena i n a more meaningful manner. However, r e s u l t s from t h i s study might suggest t h a t some of the concepts i n the c u r r i c u l u m are not r e l a t e d t o or b u i l t upon the a b s t r a c t i o n s t h a t the c h i l d has made i n t h e i r many i n -formal encounters w i t h n a t u r a l phenomena. That i s , presen t c u r r i c u l a are not b u i l t upon nor do they con-s i d e r c h i l d r e n ' s c o n c e p t i o n s . Instead, the c h i l d r e n are - 1 0 2 -expected t o spend most of t h e i r time accommodating to the concepts'*" t h a t have no meaning i n terms o f t h e i r e x p e r i e n c e . I t may be u n r e a l i s t i c to expect t h a t a c h i l d can grasp r a t h e r a b s t r a c t s c i e n t i f i c concepts a f t e r a b r i e f exposure to them i n one or two e x p e r i -ments, p l u s some e x p l a n a t i o n i n a textbook. The author f e e l s t h a t the f i r s t step t o h e l p the c h i l d r e n to improve t h e i r understanding o f c e r t a i n s c i e n c e concepts i s to expl o r e how they t h i n k about s i t u a t i o n s i n v o l v i n g those concepts. T h i s study was focussed i n t h a t d i r e c t i o n and the c l a i m b e i n g made i s t h a t the c h i l d r e n ' s conceptions o f f o r c e r e v e a l e d c o u l d be very u s e f u l t o c o n s i d e r i n the development of new c u r r i c u l u m m a t e r i a l . F o r example, i n task three F^ and F^ formed an angle o f 90°, the c o n c e p t i o n o f most c h i l d r e n was t h a t the r i n g would stay; a t the c e n t r e . T h i s c o n c e p t i o n was based on the b e l i e f t h a t the s e p a r a t i o n o f and F^ would not a f f e c t the p r e v i o u s s i t u a t i o n o f e q u i l i b r i u m when F^ and F^ were t o g e t h e r . C u r r i c u l u m developers and teachers must c o n s i d e r these "misconceptions"and use them to p l a n t e a c h i n g s t r a t e g i e s d i r e c t e d a t a more comprehensive view of f o r c e s . I f t h i s i s not done, t h e r e e x i s t s the r i s k t h a t c h i l d r e n w i l l be always l o o k i n g to- the a u t h o r i t y o f the teac h e r t o p r o v i d e " c o r r e c t " e x p l a n a t i o n s even though they make a l i t t l e i n t u i t i v e sense t o the student. They - 1 0 3 -w i l l learn that s c i e n t i f i c questions are to be answered only by the r i g h t answers that appear i n the books,.or . advanced, by the teacher and not by th e i r own thinking. In short, they w i l l be discouraged from attempting to think about problems on t h e i r own. Based on the ideas developed above, the suggestion i s that c u r r i c u l a should not be b u i l t exclusively upon preconceived objectives, which are based on t r a d i t i o n a l s c i e n t i f i c paradigms. Rather, the curriculum should also include considerations of those ideas and ways o f thinking which children develop as a r e s u l t of considerable informal experience as they are growing up. However, i t should be mentioned that there are some p r a c t i c a l problems that can ari s e >\ with the im-plementation of t h i s child-centered approach. In p a r t i -cular, the teacher becomes a very important factor to consider. Relevant questions are: How can the teacher be helped to become sensitive to the children's ideas and natural thought processes and thus respond to them in an appropriate manner? Do the teachers have to de-termine the children's b e l i e f s for each class? Do the teachers have to create teaching strategies for each situation? F i r s t of a l l , teachers would not have to be ex-perts i n exploring children's b e l i e f s . They should, however, be aware that t h i s knowledge exists and they must f e e l comfortable with using the information i n -104-t h e i r c l a s s e s . Rather, i t i s the c u r r i c u l u m developers who would c o n s i d e r c h i l d r e n ' s b e l i e f s when p l a n n i n g new c u r r i c u l a and they c o u l d p r o v i d e examples of p o t e n t i a l i n s t r u c t i o n a l sequences based upon t h i s i n f o r m a t i o n . Thus, by making the t e a c h e r s s e n s i t i v e t o c h i l d -ren's thought processes and by e n a b l i n g them to r e -cognize i d e a s which c h i l d r e n h o l d which may be i n t e r -f e r i n g - w i t h the formal l e s s o n s they are p r e s e n t i n g , i t i s b e i n g claimed t h a t the t e a c h i n g and l e a r n i n g o f some s c i e n c e concepts can be g r e a t l y improved. 5.40 Recommendations f o r F u r t h e r Research The o v e r a l l i m p l i c a t i o n s of t h i s study c o u l d be g r e a t l y enhanced by a number of follow-up s t u d i e s . These recommended s t u d i e s a r e : 1) Expand the t a s k s used i n the study to cover o t h e r a s p e c t s o f the concept o f f o r c e . S i n c e the p r e s e n t study was l i m i t e d t o those aspects o f the concept of f o r c e ( a c t i o n o f a f o r c e , a c t i o n and r e a c t i o n , concept of e q u i -l i b r i u m , c o n f i g u r a t i o n of weights, and com-p o s i t i o n o f f o r c e s ) d e p i c t e d by the three t a s k s , i t would be worthwhile to study o t h e r c h a r a c t e r -i s t i c s o f f o r c e s , such as the d i r e c t i o n a l aspect o f a f o r c e , the concept o f net f o r c e , and the f o r c e f u n c t i o n a p p l i e d by an e l a s t i c band. - 1 0 5 -P l a n more c o n t r o l l e d experimental in<-v e s t i g a t i o n s by t a k i n g as hypotheses some f i n d i n g s of the study. Other v a r i a b l e s t h a t c o u l d a f f e c t the development o f concepts might be a l s o i n c l u d e d i n these f u r t h e r i n v e s t i g a t i o n s . V a r i a b l e s such as sex, socio-economic and c u l t u r a l background o f the s u b j e c t s , which have been r e p o r t e d by o t h e r authors (Kamara, 1.971',) to .influence the development o f c h i l d r e n ' s b e l i e f s . These experimental s t u d i e s would r e q u i r e t h a t the s i z e and c h a r a c t e r i s t i c s of the sample must be c a r e f u l l y planned u s i n g p r e c i s e s t a t i s t i c a l t e c hniques. Develop a method o f a n a l y s i s which would match i n d i v i d u a l s u b j e c t s w i t h p a r t i c u l a r l e v e l s o f a b s t r a c t i o n . S i n c e , the l e v e l s of a b s t r a c t i o n were c a t e g o r i z e d c o n s i d e r i n g the composite be-l i e f s expressed by a l l s u b j e c t s i t would be worthwhile to see i f i t i s p o s s i b l e to c a t e -g o r i z e i n d i v i d u a l s a c c o r d i n g to a p a r t i c u l a r l e v e l . I f t h i s were p o s s i b l e then s p e c i a l t e a c h i n g s t r a t e g i e s c o u l d be prepared f o r i n -d i v i d u a l s a t a g i v e n l e v e l . -106-41 Study the language used by the s u b j e c t s when e x p l a i n i n g t h e i r b e l i e f s about the concept of f o r c e . I t would be i n t e r e s t i n g and u s e f u l t o f i n d out what they a c t u a l l y meant by p u l l i n g , h o l d i n g , p u t t i n g p r e s s u r e , and o t h e r terms. Furthermore i t may h e l p to understand b e t t e r how these b e l i e f s have developed from t h e i r p r e v i o u s e x p e r i e n c e s . 5) Develop group instruments ( f o r example, paper and p e n c i l q u e s t i o n n a i r e ) based on the be-l i e f s o b t a i n e d i n t h i s study to i n v e s t i g a t e the p r e v a l e n c e o f these b e l i e f s i n a c l a s s s e t t i n g . 6) Develop a s e r i e s of t e a c h i n g s t r a t e g i e s based on the r e s u l t s o f t h i s study. These s t r a t e g i e s c o u l d be c r o s s - r e f e r e n c e d t o the paper and p e n c i l instrument suggested i n recommendation (5) . 7) :', Carry out r e s e a r c h s t u d i e s to e x p l o r e c h i l d r e n ' s b e l i e f s about o t h e r s c i e n t i f i c concepts, such as momentum and energy. These s t u d i e s c o u l d f o l l o w the same methodology used i n t h i s study. -107-N O T E S 1. 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Totowa, N.JT1 L i t t l e f i e l d , Adams and Co., 1969. Pia g e t , J . Pia g e t ' s Theory. In P. Mussen (Ed.). Carmichael's Manual of C h i l d Development. New York: John Wiley and Sons, 1970. P i a g e t , J . , " P h y s i c a l World of the C h i l d " . Physics Today: June 1972. Pi a g e t , J . La Composition Pes Forces e t l e problem des  vecteurs . Etudes d* epistemologie gene'tique. (Vol .XXX) P a r i s : Presses U n i v e r s i t a i r e s de France, 1973. Pi a g e t , J . La formation de l a n o t i o n de f o r c e . Etudes d' epistemologie genetique. (Vol.XXX) P a r i s : Presses U n i v e r s i t a i r e s de France, 1973. Pine s , A.L. S c i e n t i f i c Concept Learning i n C h i l d r e n : The E f f e c t of P r i o r Knowledge on R e s u l t i n g C o g n i t i v e S t r u c t u r e Subsequent to A-T I n s t r u c t i o n . Unpublished Ph.D. t h e s i s , C o r n e l l U n i v e r s i t y , N.Y. Power, C.N., "Competing Paradigms i n Science Education Research". Journal of Research i n Science Teaching. 1976, 13, 579-587. Preece, P.F.W. "Mapping c o g n i t i v e s t r u c t u r e : a com-parison . of methods" . .. J ournal of Educational Psychology, 19 76 , 68 (1) , 1-8 . - - " - 1 1 1 -PSSC P h y s i c s Course. Toronto; The Copp C l a r k P u b l i s h i n g Co. L t d . , 1960. Raven, Ronald. "The Development of the Concept o f Momentum i n Primary School C h i l d r e n " . J o u r n a l o f  Research i n Science Teaching. 1967, 5_, 216-223. "Report of the Commission on the R e o r g a n i z a t i o n o f Science i n Secondary Schools". V.S. Bureau of Ed u c a t i o n B u l l e t i n s . 1920, 26_, 16. Sayre, S., and B a l l , D.W.'"Piagetian C o g n i t i v e Develop-ment and Achievement i n Sc i e n c e s " , J o u r n a l o f Research  i n Science Teaching, 1975, 12_, 165-174. "Science", The E n c y c l o p e d i a o f E d u c a t i o n a l Research, 1960, p. 1217. Shave1son, R.J. "Methods f o r examining r e p r e s e n t a t i o n s of a s u b j e c f matter s t r u c t u r e i n a student's memory". J o u r n a l of Research i n Science Teaching, 1974 , . 11 .;(3) , 231-249 . The P r o j e c t P h y s i c s Course - Handbook, New York: H o l t , R i n e h a r t , and Winston, Inc., 1970. Welch, W.W.;. "High School P h y s i c s E n r o l l m e n t s " , P h y s i c s Today. 1967, 20_, 9-13. Welch, W.W. "Some C h a r a c t e r i s t i c s o f High School P h y s i c s Students: C i r c a 1968". J o u r n a l o f Research i n Science  Teaching. 1969, 6_, 242-247. Welch, W.W. ,and) Rothman, A.I. "The Success o f R e c r u i t e d Students i n a New P h y s i c s Course", S c i e n c e E d u c a t i o n , 1968, 52, 270-273. Welch, W.W., Walberg, Ik J., and Watson',"F.G. "A Case Study i n C u r r i c u l u m E v a l u a t i o n : Harvard P r o j e c t P h y s i c s " . Unpublished mimeograph, U n i v e r s i t y o f Minnesota, M i n n e a p o l i s , 1971. APPENDIX TRANSCRIPT OF AN INTERVIEW Kevin's In t e r v i e w (11, 7) (The f i r s t few minutes were spent making him comfortable, c h a t t i n g about h i s s c i e n c e c l a s s and parents, answering q u e s t i o n s about the videotape camera, and s e t t i n g the m a t e r i a l s f o r task one). I: I n t e r v i e w e r , S: Subject, W: Washer(s) I: T h i s i s a k i n d of game or experiment i f you want. We have a s t r i n g with 3 hooks, a p u l l e y , a p l a s t i c p l a t e , an e l a s t i c band and the thumb tack. Could you d e s c r i b e to me what i s going to happen i f you put one washer(W) here i n t h i s hook (the top hook). S: It [the. waihe.fi) ti, gotng to pull the plate tn about 3 cm., juit onty bccauie. theJiz ti, only one. wctght. I: You are t a l k i n g about weight. What i s the d i f f e r e n c e between a weight and a washer? S: Well, the. waihe.fi ti, a iofit ol wetght because tt hai we.tght. 1^ you put a we.tght on the. itittng tt pulli the. btntng and tfi you put a waihe.fi tt i>ttll pulli, the. itfitng .. I : O.K. What e l s e i s going to happen? I mean w i t h the s t r i n g , the e l a s t i c band. S: We.ll, tht i>tntng ti, comtng he.ne, thz plate, ti gotng to come. he.h,e. and the elaittc ti gotng to itn.e.tdh. I: O.K. Do i t , p l e a s e . (The I n t e r v i e w e r h e l d the p l a t e w h ile the S u b j e c t put °» the washer,-, and t h e n he r e l e a s e d i t ) . I t moved, not:too much b u t . i t moved.; I am going to make a mark where the p l a t e i s now. Kevin, c o u l d you t e l l me what i s t h i s washer doing here a t t h i s moment? S: We.ll, you told me putttng tt on -I: Yes, but what i s i t doing now wi t h the whole t h i n g ? S: I t ' i holdtng the e.laittc ^K.om putttng the. plate, back . . . . I t ' i holdtng the. plate, back &n.om pulltng the. e.laittc. . . . i>tom maktng the. e.laittc come, back agatn. -.113-I: Yeh I t ' s h o l d i n g the p l a t e here and what i s the e l a s t i c band doing? S: It'A th.yi.viQ to puZZ back -I: Why d i d not the p l a t e move f a r t h e r ? Why d i d i t move o n l y to here? (I showed the mark). S: Be.cau.Ae. the. we.Xght pu.ZZi> the. btntna down on. the. wa^hcn. pu.ZZi> the. Attitng down and he.n.e. the.n.e. X.& the. puZZe,y whtch goe.4 an.ou.nd  I : The q u e s t i o n i s why the p l a t e d i d n ' t move f a r t h e r . S: Oh, X.t dtdn't move lon.wan.d mon.c be.cau.6e. the. cZa&ttc X.& hoZdtng It. I: I s the washer p u l l i n g r i g h t now? S: ye.h, X.t'& puZZXng -I: What do you t h i n k i s going to happen i f you put one more washer there (on the same hook)? S: I thtnk -it'& go-ing lan.the.n. -I : How f a r do you t h i n k i s i t going to go? Could you make a mark here (on the board)? (The S made a mark, about 2 cm:., the I h e l d the p l a t e w h i l e the S put the W). I t moved a l i t t l e more. Now, what w i l l happen i f you put one more? Make a mark, p l e a s e . (S made a mark, about 2 cm,, I h e l d the p l a t e while S put the W). I t moved a l i t t l e more again You were t e l l i n g me before t h a t these washers are p u l l i n g the p l a t e , what e l s e i s i t p u l l i n g ? t here are d i f f e r e n t t h i n g s here, what e l s e i s ' p u l l i n g ? S: The. 6tn.tng I : What i s p u l l i n g the s t r i n g ? S: The. wat>he.n.& I: And what e l s e i s p u l l i n g ? S: The gh.avX.ty. I: What do you mean by g r a v i t y ? S: The gn.avi.ty th pu.ZZX.ng the. wai>he.n.i> down -_ 1-14-I : Now, what about these t h i n g s ( e l a s t i c , p l a t e ) ? S: ThlA [the plate) 1A trying to pall back, but theAe [the waAherA) have got more Atrenglh than the elastic, AO the plate moveA forward and 11 doeAn't go back. I: Why do you say t h a t the washers have more stre n g t h ? S: The elaAtlc 1A Alrelched and It -LA trying to come back, and thlA [the waAherA) afie really com-ing down realty hard and thtA [the elaAtlc) 1A not pulling aA hard. I : You say t h a t the s t r i n g i s p u l l i n g the p l a t e , i s the p l a t e p u l l i n g the s t r i n g ? S: YeA, Aure It 1A, bat not like the elaAtlc 1A palling the plate AO the Airing 1A getting palled bat It 1A not getting aA palled aA mach aA the weight or waAherA. I : Yeh, you say t h a t the p l a t e i s p u l l i n g the e l a s t i c . I s the e l a s t i c p u l l i n g the p l a t e ? S: Yeh, the elaAtlc 1A pulling the plate.... the Airing 1A pulling the plate AO the plate 1A pulling two AldeA.... the Atrlng and the elaAtlc. I : Now, what i s the thumb tack doing here? S: It1A holding the elaAtlc farom going forward -I : I s the thumb tack p u l l i n g ? S: Hot -I: Ah, i t ' s not p u l l i n g , i t ' s h o l d i n g -S: Yeh, It1 A j'uAl Alaylng there and It'A holding the elaAtlc -I: Now, Kevin, what do you t h i n k i s going t o happen i f you put the three washers down there (on the lowest hook)? S: I think that the plate 1A going to come farther even more I: Why do you t h i n k so? S: Well becauAe ah 11 1A near the ground and It1 A getting: forced down more. I: What happens when those washers are nearer to the ground? S: The gravity 1A pulling them more and more. I: O.K. Do i t p l e a s e -(I h e l d the p l a t e while the S moved the 3 Ws to the lowest hook). S: OH -I : I t d i d n ' t move, how c o u l d you e x p l a i n i t ? S: Maybe, the. etaittc ti putttng too hand. now. I: What do you mean by too hard? S: I guza . . . maybe. the. ttttte. waihefii have. the. iame. wzt'giht and tt dtdn't fieatty matte.fi how the. gfiavtty wai putttng. I: Another change you would l i k e to do i s c o u l d you put pl e a s e one washer i n each hook What do you t h i n k i s going to happen i n t h i s case? S: I thtnk that tt [the. ptate.) ti gotng to itay -I : Why do you t h i n k so? S: Be.cauie. tt ti the. iame. witght . . . . att the. waihzfii have. the. iame. wztght ai whe.n the.y wzfie tn one. hook at the. {tfiit one and we. put tt on the. bottom one. . . . . . . tt dtdn't move. bzcauiz the.y had the. iame witght . . . . and now.... I thtnk tt won't move, bzcauie. tt ti i t t t t the. iame wztght -I: O.K. (I r e l e a s e d the p l a t e ) . . . . t h a t i s t r u e O.K. Kevin, now we w i l l move to the game number two (The S and the I prepared the s e t t i n g o f Task 2 ) . TASK TWO I: I f you put one W i n t h a t hook (top hook a t s u b j e c t ' s s i d e ) . What i s going to happen? S: Thti [the. ptate.) ti gotng to come, ^ofiwafid [towafid the. S) -I: How f a r ? S: Unttt that itn.it hook [at I ' i itde.) fieaahe.i the. putte.y -I: Why? S: Becauie thti we.tght ti gotng to putt tt [the. ptate.) att the. way -_ 1.16-(S put the W, the p l a t e moved a l l the way). I: That i s t r u e . . . . i f you want t o keep the p l a t e i n the middle what c o u l d you do? S: You can put anothzn. one. on that i>lde. [1'i, Aide.) -(I put one W on h i s side) I : That i s t r u e . O.K. I f you put one more W i n your s i d e i n the same hook, what do you t h i n k i s going to happen? S: The. plate. I i going to come u n t i l the. vie.tghthX.ti, the. ground. I : O.K i f you want to keep the p l a t e i n the middle what c o u l d you do? S: Put a second waihen, on the iln.it hook [at I'i iX.de) I: O.K now, c o u l d you t e l l me what are these washers doing here? What are these Ws (at I's side) and those washers (at S's side) doing? S: Welt, thae waihe.Ki on. thcXn. weight l i putting down and thoie. waihe.n.6 they an.e. p u l l i n g down and io the. plate. i l a y i In the, middle.. I: Now, what w i l l happen i f you put one washer i n each hook i n your s i d e ? S: I think I t ' i going to i t a y the iame. because. when we did the. experiment with the. e l a s t i c It didn't malten,.... the. I think 11'A going lo be the iame and It won't matlen, now (S put one W i n each hook) -I: That i s t r u e . . . . one o t h e r t h i n g I would l i k e to do i s the f o l l o w i n g : I am going t o move t h i s p l a t e towards you .... to here (about 5 cms) and h o l d i t w i t h my f i n g e r s What w i l l happen i f I l e t i t go? S: Because theie two waihen,i have, lo pull thoie two wa&he.n.& but they weigh the. &ame &o lhe.t>e wai>he.n.& an.e. not able, lo pull thoi>e. up be.cauAe. lhe.y we.lghl the. &amz ai, lhe.i,e. two -(I r e l e a s e d the p l a t e ) . I: That i s t r u e . . . . Now, I am going to move the p l a t e i n t h i s d i r e c t i o n . (I d i s p l a c e d the p l a t e i n a p e r p e n d i c u l a r d i r e c t i o n i n r e s p e c t t o the d i r e c t i o n o f the s t r i n g s and h e l d i t t h e r e ) . What i s going to happen i n t h i s case? S: 11'i going to go back lo the. middle. --,117-I: Why? S: Thz&z waihzm anz putttng itnatght down .... and be.cau.6e. thzy anz putttng itnatght down t h t i [thz ptate.) hai to go to the. mtddte -I: But there i s no s t r i n g here (pulling towards the middle) S: ye.fi, but t h z i z a/te. putttng hand hznz and thoiz anz putttng hand.... thznz, t t hai to go to the mtddte. -I: O.K. .... now, we can move to the experiment number three. (S and I prepared the se t t i n g for Task Three). T A S K T H R E E I: Well Kevin, I am going to s t a r t putting 3 Ws i n one of these hooks ( l e f t hook at I's s i d e ) . What i s going to happen i f I p u l l out the peg? S: Thti [hook, at S'i i t d z ) t i gotng to move, up and t h t i i t n t n g wtll move {onwand [towandi the. I) -I: O.K., i f you want to keep the ring i n the middle, what could you do? S: I have to put 3Wi hene. -I: Now, I w i l l put 3 more Ws i n the other hook (at I's s i d e ) . What i s going to happen i n t h i s case i f I p u l l out the peg? S: Thoie two hooki wttt go down and t h t i onz wttt go up unttt t t h t t i the. puttzy. I: And the ring? S: It wttt go towandi you ai ^an ai t h t i hook gozi -(I pulled out the peg) I: That i s true.... then, what could you do i f you want to keep the ring i n the middle? S: I havz to comptztz i t x Wi hznz -I: But these washers on my side are separated, there are three i n each hook? S: That dozin't mattzn bzcauiz thzy anz att jotnzd to thz iamz.... I: Now Kevin, I am going to move these pulleys t h i s one here and the other one here (pulleys at I's side formed an angle of 90 ). _ 118-What i s going to happen i f I p u l l out the s t i c k i n t h i s case? -Thli one [hook al S'i ilde) will go down. : What happens when they are separated? They don't equal the iame weight ai they were when they weKe together .... then the King li going to come thli way [towandi the S) -How f a r ? Until the ring comei to the pulley. That's t r u e even when the r i n g d i d n ' t move a l l the way.., ... I f you want to keep the r i n g i n the middle, what c o u l d you do? I can lake 3 o{,{, {,Kom hefie on. you can put 3 moKe Wi. In youh, hooki -O.K. What i s going to happen i f you take 3 o f f ? The King will itay In the middle -: I don't see very c l e a r why? : Becauie each hook hai 3 Wi, and the IhKee weigh the iame : O.K. (S removed 3 Ws from h i s side) -Oh, i t moved towards here (toward the I ) . What c o u l d you do i n t h i s case i f you want to keep the r i n g i n the middle? : 7 ihould put iome moKe Wi In heKe 1 don't know how many -: Why do you need to put more Ws there? : Becauie I need more weight to make thli [hook at S'i ilde) come down. : O.K. Try i t -(S put one) Oh, now, i t s t a y s . Now, I want to move these p u l l e y s a l i t t l e more, t h i s one here and the o t h e r one here ( s t r i n g s at I's s i d e formed an angle o f 120°). And i n t h i s case what i s going to happen i f I p u l l out the s t i c k ? -119-I t ' i gotng to come, towandi hznz' [towandi thz S) Why do you t h i n k so? Thti itntng [at S'i itdz) izzmi to be ian away ^nom thoiz two. Maybe i f you stand up you can see b e t t e r . Mat/be not but tt wttt come cloizn to hznz [towandi thz S) Why? Because thznz anz 4 Wi hznz and only 3 Wi on thoiz -Yeh. O.K., we can t r y (I p u l l e d out the peg). That's t r u e . W e l l , what c o u l d you do to keep the r i n g i n the middle? Takz onz o££ ^nom hznz [at S'i itdz) on zliz put onz W tn zazh ofi thoiz -Do i t p l e a s e .... t h a t ' s t r u e . Why does i t stay now? y.zh, bzzauiz thzy anz tn dt^znznt anglzi thzy anz putttng tn dt^znznt anglzi. . . . now thoiz anz faanthzn apant and thzy anz not putttng ai much ai whzn thzy wznz togzthzn. Now Kevin, I ' l l move these p u l l e y s a l i t t l e more (180°). What w i l l happen now? I thtnk. tVi gotng to itay tn thz mtddlz bzzauiz all ofa thzm anz putttng tn dt^znznt anglzi and thzy anz putttng wtth thz iamz wztght... and thzy wttt dnop wtth thz iamz ipzzd... io zazh onz ti gotng to pull towandi zazh othzn. thzy r.anz all, putttng thz iamz io tVi gotng to itay tn thz mtddlz. Oh, i t moved towards you Why d i d i t move towards you? I don't know -W e l l , what c o u l d you do to keep the r i n g i n the middle? Takz away onz W ^nom hznz -(S took one W) Oh, i t s t i l l moves. What e l s e c o u l d you do? _ 12 0-S: Take all the Wi o^. * I : Why? S: Because thoie two are. pulling the iame way - and there l i nothing pulling that way [^rom the. opposite. o{ S'i Aide.) -I : I see, O.K. Do i t please That's t r u e . O.K. Kevin.... now I am going to move these p u l l e y s a l i t t l e more (24 0O) , what w i l l happen now i f I p u l l out the peg? S: IV i going to come towardi here [toward* the. 5 ) . I : O.K. th a t ' s t r u e . Now, we are going to come back to the beginning. Remember, we had 3 i n each of these hooks (forming an angle of 90°) and 4 Ws i n tha t hook -But now, I ' l l move these p u l l e y s a l i t t l e c l o s e r (75°) , What w i l l happen i f I p u l l out the s t i c k ? S: IV i going to come, thli way [toward* the. S) -I : Why? S: Because, thli, one. hai 4 Wi, and thoie. only 3 Wi,, thli one. ove.rpowe.red thoie (I removed the peg) I: Oh, i t moved towards me, how could you e x p l a i n i t ? S: I guea becauie there were 6 Wi there and only 4 Wi here, the ilx overpowered the ^our. I : Why? S: Yeh, becauie 6 Wi weigh more than 4 Wi io they pull towardi that way -I : O.K. what could you do to keep the r i n g i n the middle? S: I have to put 6 Wi here -(S put 2 Ws) I: Oh not, i t moved towards you now. What e l s e c ould you do? S: Take one o.fifi firom here -I : O.K. Kevin, I am going to put- one' more W i n t h i s hook ( l e f t hook at I's s i d e ) . What i s going to happen i n t h i s case? S: IVi going lo itay In the middle -_ 121-T: Why do you think so? You have 3, 4, and 5 Ws now? S: .... Oh not . . . . tt'6 gotng to pull towandi that way [towandi the. hook, wtth 4 Wi) . I: Why? S: Bzcauiz bzionz wtth 3 and 3 tn thoiz hooki, tt moved thnough the. mtddlz but now wtth that zxtna onz tt wtll movz towandi thznz. [S ihowzd wtth hti fitngzn thz dtnzztton along thz itntng wtth 4 Wi). I: How f a r i s i t going to move? S: About halfi way -(I removed the peg) . I: Do you think i t moved along the string? S : Mot. I: Then, what could you do to keep the rin g i n the middle? S : Takz onz 0 & & hznz and put onz W tn thz othzn hook -I: I don't want to make changes i n my side, you can make changes i n your side. S : I ' l l put onz W hznz -I: Do i t please (The ring stayed else to the middle) What else could you do? S: Maybz I can movz thti pullzy a btt. I: O.K., do i t please, i n what direction? S : That way [towand thz ntght itdz o{ S) (The r i n g and everything dropped to ground). I: What else could you do? S: Maybz movz tt to thz othzmtdz. I: O.K., t r y i t please (S moved i t to his l e f t a b i t . The r i n g stayed very close to the centre t h i s time). Now, I t i s almost i n the middle. -12 2 -S: Vzh., tV & not z.<xt>y. I: Well Kevin, we can f i n i s h the experiments here. Thank you very much. I'/hope you enjoyed doing these experiments. 

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