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Children’s beliefs about free-fall motion Kuhn, Kenneth C. 1979

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CHILDREN'S BELIEFS ABOUT FREE-FALL MOTION by KENNETH C. KUHN B . S c , U n i v e r s i t y of B r i t i s h Columbia, 1964 •T.B., Vancouver School of Theology (U.B.C.), 1967 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS THE FACULTY OF GRADUATE STUDIES Department of Science Education We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF B R I T I S H COLUMBIA J u l y , 1979 Kenneth. C. Kuhn, 19 79 In presenting th i s thesis in par t i a l fu l f i lment of the requirements for an advanced degree at the Univers ity of B r i t i s h Columbia, I agree that the Library shal l make i t f ree ly avai lable for reference and study. I further agree that permission for extensive copying of th i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publ icat ion of th i s thesis for f inanc ia l gain shal l not be allowed without my written permission. Department of E J(Jrru ~f~ ton  The Univers ity of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ABSTRACT Students' b e l i e f s about f r e e - f a l l motion were exp l o r e d u s i n g s t r u c t u r e d i n t e r v i e w s . The sample of 24 students was composed of 6 students (3 boys, 3 g i r l s ) s e l e c t e d from grades 6, 8, 10 and 11 r e s p e c t i v e l y . Three s e t s of tasks i n v o l v i n g one a c t u a l experiment and a number of simulated thought problems were used to i n -v e s t i g a t e (a) the student's b e l i e f s about the motion of a s i n g l e o b j e c t , (b) the r e l e v a n c e of the v a r i a b l e s of h e i g h t d i f f e r e n c e , i n i t i a l v e l o c i t y d i f f e r e n c e , frame of r e f e r e n c e d i f f e r e n c e and weight d i f f e r e n c e f o r two o b j e c t s and (c) the combined a c t i o n of these f a c t o r s when more than one was present. I t was found t h a t the i n t e r v i e w methodology and tasks used were e f f e c t i v e f o r c o l l e c t i n g the data r e q u i r e d i n an e x p l o r a t o r y study of t h i s type. I t was p o s s i b l e to c a t e g o r i z e the mode of a c t i o n of each v a r i a b l e i n terms o f : (a) not o p e r a t i n g , (b) as o p e r a t i n g i n a s h o r t impulse o n l y , (c) as o p e r a t i n g but slowly d i s s i p a t i n g , or (d) as o p e r a t i n g w i t h a continuous a c t i o n . Examples of most response c a t e -g o r i e s o c c u r r e d a t a l l l e v e l s but a number of p o s s i b l e de-velopmental trends by grade were e v i d e n t . A l s o there was a p o s s i b l e i n d i c a t i o n of the r e s i s t a n c e of c e r t a i n i n t u i t i v e b e l i e f s to standard kinematics i n s t r u c t i o n f o r the grade 11 p h y s i c s group. The r e s u l t s of t h i s study c o u l d be u s e f u l to the classroom teacher as w e l l as to the d e s i g n e r of a s c i e n c e c u r r i c u l u m . I t suggests t h a t students are able to e x p l o r e some problems of motion beginning a t the grade 6 l e v e l ; t h a t they should be allowed to e x p l o r e the r e l e v a n c e of r e l a t e d v a r i a b l e s ; and t h a t they should be encouraged to express and e x p l o r e t h e i r own b e l i e f s which they b r i n g to the classroom about motion. - i v -C O N T E N T S Page ABSTRACT i i i TABLE OF CONTENTS . ... ... V LIST OF TABLES i x LIST OF FIGURES ... x ACKNOWLEDGEMENTS . ... x i CHAPTER ONE 1.00 INTRODUCTION 1 1.10 SPECIFIC PROBLEMS 4 1.20 METHODS OF STUDY 4 1.21 Data C o l l e c t i o n 4 1.2 2 Tasks of the Study 5 1.23 The Subjects 5 1.30 EDUCATIONAL SIGNIFICANCE OF THE STUDY 6 1.40 LIMITATIONS OF THE STUDY 7 1.41 Developmental Aspect 7 1.42 I n s t r u c t i o n a l Aspect 9 CHAPTER TWO 2.00 INTRODUCTION 10 2.10 LITERATURE IN THE BROAD PROBLEM AREA ... 10 2.11 Two P e r s p e c t i v e s 10 2.20 LITERATURE IN THE SPECIFIC CONTENT AREA.. 14 2.30 LITERATURE SUGGESTING IMPLICATIONS FOR CURRICULUM AND INSTRUCTION 17 2.40 SUMMARY 20 - V -Page CHAPTER THREE 3.00 INTRODUCTION ... 22 3.10 INTERVIEW PROCEDURE 22 3.11 The Apparatus 23 3.12 T r a i n i n g S e s s i o n 3.20 TASKS 26 3.21 A S i n g l e Object In F r e e - F a l l 27 3.22 Average Speed Task 28 3.23A The F a c t o r of Height 29 3.24A The F a c t o r of I n i t i a l V e l o c i t y With I n i t i a l S e p a r a t i o n - E a r t h Frame.. 30 3.25A The F a c t o r of I n i t i a l V e l o c i t y -Shotputs I n i t i a l l y Even - E a r t h Frame.. 31 3.2 3B The F a c t o r of Height - I n t e r n a l Frame.. 31 3.24B The F a c t o r of I n i t i a l V e l o c i t y With I n i t i a l S e p a r a t i o n -I n t e r n a l Frame 31 3.2 5B The F a c t o r of I n i t i a l V e l o c i t y -Shotputs I n i t i a l l y Even -I n t e r n a l Frame 31 3.26A The F a c t o r of Weight Versus the F a c t o r of Height - Heavy Shotput Below 32 3.26B The F a c t o r of Height - Heavy Shotput Above 32 3.27 The F a c t o r of Weight Versus the F a c t o r of I n i t i a l V e l o c i t y w i t h I n i t i a l S e p a r a t i o n 32 3.28 The F a c t o r of Weight Versus the F a c t o r of I n i t i a l V e l o c i t y -Shotputs I n i t i a l l y Even ... 33 3.29 A d d i t i o n s 33 3.30 SUBJECTS 33 - v i -CHAPTER FOUR Page 4.00 INTRODUCTION 35 4.10 METHODS OF ANALYSIS 36 4.11 The C h a r a c t e r i s t i c s of Motion of A S i n g l e Shotput i n F r e e - F a i l 36 4.120 The Relevance of Other F a c t o r s 37 4.121 Height ... 37 4.122 I n i t i a l V e l o c i t y 37 4.123 Weight ... 39 4.130 The Combined E f f e c t of F a c t o r s 39 4.131 Height and Weight ... ... ... 4 0 4.132 I n i t i a l V e l o c i t y and Weight 41 4.133 Height and I n i t i a l V e l o c i t y ... 42 4.20 RESULTS 43 4; 210 A S i n g l e Shotput i n F r e e - F a l l 44 4.211 Data Table 4.1 44 4.212 T y p i c a l Responses ... 45 4.213 Trends i n the Data 4 8 4.220 Relevant V a r i a b l e ... 48 4.221 Height ... 48 4.2211 Data Table 4.2 49 4.2212 T y p i c a l Responses 48 4.2213 Trends i n the Data 52 4.222 I n i t i a l V e l o c i t y 52 4.2221 Data Table 4.3 53 4.2222 T y p i c a l Responses . . . . . . 52 4.2223 Trends i n the Data 55 4.223 Weight 56 4.2231 Data Table 4.4 ... ... ... 57 4.2232 T y p i c a l Responses . ... ... 56 4.22 3 3 Trends i n the Data 58 - v i i -Page 4.230 The Combined E f f e c t of the V a r i a b l e s of Height, I n i t i a l V e l o c i t y and Weight ... 58 4.2310 Height and Weight ... 58 •4.2311 Data Table 4.5 59 4.2312 T y p i c a l Responses 58 4.2 313 Trends i n the Data 61 4.2320 I n i t i a l V e l o c i t y and Weight 61 4.2321 Data Table 4.6 ... ... 62 4.2322 T y p i c a l Responses 61 4.2 3 23 Trends i n the Data 6 3 4.2330 Height and I n i t i a l V e l o c i t y ... 63 4.2331 Data Table 4.7 64 4.2332 T y p i c a l Responses 63 4.2333 Trends i n the Data ... 65 4.24 Trends i n the Data Taken as a Whole 65 4.250 E x p l a n a t i o n s Given f o r the Responses ... 66 4.351 Force and Height ... ... 66 4.352 Energy and Height 67 4.253 Force and V e l o c i t y 68 4.260 The Sources of B e l i e f 70 4.361 A u t h o r i t i e s C i t e d 70 4.362 Experiences C i t e d 71 4.263 A n a l o g i e s Drawn 71 4.270 R e v i s i o n s of Response ... 72 4.271 Quotations 73 CHAPTER FIVE 5.00 SUMMARY OF THE STUDY 76 5.10 CONCLUSIONS 77 5.11 Method 77 5.12 B e l i e f s - Developmental Trends 78 5.13 B e l i e f s - The E f f e c t s o f I n s t r u c t i o n 80 5.14 E x p l a n a t i o n s and Sources of B e l i e f ... ... 82 5.20 EDUCATIONAL IMPLICATIONS 82 5.30 RECOMMENDATIONS FOR FURTHER RESEARCH 85 - v i i i -LIST OF TABLES Page Table 4.1 The C h a r a c t e r i s t i c s of Motion of a S i n g l e Shotput i n F r e e - F a l l Motion ... 44 4.2 The Relevance of Height as an Independent V a r i a b l e A f f e c t i n g F r e e - F a l l Motion 49 4.3 The Relevance of I n i t i a l V e l o c i t y as an Independent V a r i a b l e A f f e c t i n g F r e e - F a l l Motion 53 4.4 The Relevance of Weight as an Independent V a r i a b l e A f f e c t i n g F r e e - F a i l Motion 57 4.5 The Combined E f f e c t of the In-dependent V a r i a b l e s Height and Weight 59 4.6 The Combined E f f e c t of the Independent V a r i a b l e s I n i t i a l V e l o c i t y and Weight 62 4.7 The Combined E f f e c t of the In-dependent V a r i a b l e s Height and I n i t i a l V e l o c i t y 64 - i x -L I S T OF FIGURES gure 3.1 The Apparatus ACKNOWLEDGEMENT I wish to express ray a p p r e c i a t i o n to P r o f e s s o r s G. Ex.-ic.k-!> on, T. Hobbi, and W. Botdt f o r a c t i n g as members of the t h e s i s committee. P r o f e s s o r 6 . EK.-Lc.k6 on has been p a r t i c u l a r l y h e l p -f u l as my t h e s i s a d v i s o r . He has p r o v i d e d encourage-ment when necessary and has shown g r e a t p a t i e n c e i n h e l p i n g me work through a l l of the d e t a i l s o f t h i s study. Mr. K. kn.mbth.oviQ, p h y s i c s teacher a t A r g y l e Secondary School and Mr. W. AndzMon p r i n c i p a l o f Fromme Elementary School were most c o o p e r a t i v e i n p r o v i d i n g the sample f o r the study. I c o u l d not have completed the study without my w i f e V^fivat, who always found a q u i e t p l a c e f o r me to work. My daughters Mdt-l-t>i>a. and Vzntj6e were w i l l i n g to cooperate even though they d i d n ' t always understand why I c o u l d not spend time with them. F i n a l l y , I wish to thank Mrs. Carmen de S i l v a f o r being p a t i e n t when t y p i n g t h i s t h e s i s . - x i -1 CHAPTER ONE 1.0 0 INTRODUCTION A number of p e r s p e c t i v e s f o r c u r r i c u l u m de-velopment and i n s t r u c t i o n stem from c o g n i t i v e theory. Two of these are a t the ce n t r e of P i a g e t * s theory of i n t e l l e c t u a l development. The f i r s t of these i s the r o l e of s k i l l s i n l o g i c and reasoning as p r e r e q u i s i t e s f o r l e a r n i n g concepts. T h i s p e r s p e c t i v e has been used e x t e n s i v e l y i n r e s e a r c h concerned with the a c q u i s i t i o n of a v a r i e t y of s c i e n c e concepts (Lawson and Wollman, 1976; Renner, 1976). Such r e s e a r c h has generated a number of i n s i g h t s u s e f u l f o r classroom i n s t r u c t i o n . The second p e r s p e c t i v e i s the r o l e played by the b e l i e f s and concepts about a phenomenon brought by the student to the classroom; t h a t i s the Aub&tancz of the a c t u a l b e l i e f s and concepts h e l d by c h i l d r e n . P i a g e t r e f e r s to t h i s d i s t i n c t i o n as p h y s i c a l or e x p e r i e n t i a l knowledge as c o n t r a s t e d w i t h o p e r a t i o n a l or l o g i c o -mathematical knowledge. ( E r i c k s o n , 1979, p.221) T h i s p e r s p e c t i v e has not been used as e x t e n s i v e l y i n r e s e a r c h . However i t has generated a number of r e -cent i n v e s t i g a t i o n s . ( D r i v e r and E a s l e y , 1978). 2 Some of them produce suggested strategies for teaching (Walters and Boldt, 1970; Barnes, 1970). Also some curriculum projects (Tiberghien and Delacote, 1976) have used th i s perspective. Certain l i m i t a t i o n s may be placed on the a b i l i t y of students to learn c e r t a i n science concepts by the l o g i c a l complexity of the concepts. However, a student requires more than l o g i c alone to understand a concept (Robertson and Richardson, 1975). If th i s i s the case, more than the students' a b i l i t y to apply the l o g i c a l steps involved i n a concept merits investigation. Whittaker (1975) among others has suggested that i t would be most valuable to determine the s t u d e n t w a y of thinking about a concept. On the related issue of the use of Piagetian tasks for assessing pupils' development i n science, i t would seem that more valuable information could be gained by both curriculum de-velopers and the pr a c t i s i n g teacher through interviewing pupils i n order to understand t h e i r ideas and ways of thinking about a topic i n question (Whittaker 19 75) rather than as a device for c l a s s i f y i n g pupils and prescribing programmes for them. (Driver and Easley, 1978, p.79). The present study i s an investigation of students' b e l i e f s about objects i n f r e e - f a l l motion. I t was, there-fore, conducted from the second perspective. Free f a l l 3 motion m e r i t s i n v e s t i g a t i o n f o r a number of important reasons: (a) Concepts of motion are c e n t r a l to the p h y s i c s c u r r i c u l u m ( k i n e m a t i c s ) ; (b) F r e e - f a l l i n v o l v e s very r a p i d a c c e l e r a t i o n . I t i s more d i f f i c u l t to apply "everyday" n o t i o n s s i n c e i t i s a more s u b t l e r e g u l a r i t y i n nature. T h i s makes i t more of a conceptual problem. In a d d i t i o n , a v a r i e t y of c o n d i t i o n s of p o s i t i o n , i n i t i a l v e l o c i t y and weight can e a s i l y be arranged; (c) Motion i s a c e n t r a l component of many experiences which do not i n v o l v e formal i n s t r u c t i o n and, t h e r e f o r e , students' concepts of motion are i n f l u e n c e d by these independent sources of b e l i e f ; (d) A number of r e l a t e d concepts such as those of f o r c e and energy are i n v o l v e d as w e l l . The i n t e r v i e w methodology (a m o d i f i c a t i o n of the P i a g e t i a n c l i n i c a l interview) was chosen to c o l l e c t the data. Based on p r e v i o u s experience (Kuhn, 1978) i t was a n t i c i p a t e d t h a t t h i s i n t e r v i e w methodology would generate a r i c h bank of v a l i d and r e l i a b l e d a ta. Hypotheses were not d e f i n e d as would be r e q u i r e d f o r an experimental study. As a r e s u l t , the study was c l e a r l y d e s c r i p t i v e and e x p l o r a t o r y . T h i s type of p r e l i m i n a r y i n -v e s t i g a t i o n can be extremely u s e f u l f o r l a t e r experimental s t u d i e s . I t should be p o s s i b l e to generate f a i r l y s p e c i f i c hypotheses f o r f u r t h e r r e s e a r c h from the r e s u l t s of t h i s study. 4 The study was e x p l o r a t o r y because students' b e l i e f s about motion have not y e t been addressed by r e s e a r c h to any s i g n i f i c a n t extent. Consequently, i t was not p o s s i b l e to p r e d i c t i n advance e x a c t l y which p a t t e r n s of b e l i e f would emerge. However, c e r t a i n s p e c i f i c b e l i e f s were examined i n the context of the tasks which were designed f o r the study. 1.10 SPECIFIC PROBLEMS Students' b e l i e f s were analysed i n three areas: (a) What are the c h a r a c t e r i s t i c s of motion of a s i n g l e o b j e c t i n f r e e - f a l l ? (b) How r e l e v a n t are the f a c t o r s o f h e i g h t , i n i t i a l v e l o c i t y and weight to the motion of two o b j e c t s i n f r e e - f a l l as seen from both an e x t e r n a l and an i n t e r n a l frame of r e f e r e n c e ? (c) What i s the combined e f f e c t o f these t h r e e v a r i a b l e s when more than one v a r i a b l e i s present? In a d d i t i o n t o the b e l i e f s themselves, the sources of the b e l i e f s were sought. E x p l a n a t i o n s f o r the b e l i e f s were s o l i c i t e d u s i n g a d d i t i o n a l probing q u e s t i o n s . More s p e c i f i c q u e s t i o n s are g i v e n i n Chapter Three where the tasks are d i s c u s s e d i n d e t a i l . 1.20 METHODS OF STUDY 1.21 Data C o l l e c t i o n The s t r u c t u r e d i n t e r v i e w methodology used t o c o l l e c t d ata was s i m i l a r t o t h a t employed by Nussbaum and Novak 5 (1976) i n t h e i r study on c h i l d r e n ' s concepts of the e a r t h . A standard p r o t o c o l was employed (the same ques t i o n s were asked i n the same order to a l l s u b j e c t s ) . In a d d i t i o n to t h i s standard p r o t o c o l , e x p l a n a t i o n s were sought by a d d i t i o n a l q u e s t i o n i n g . An audiotape c a s s e t t e r e c o r d e r was used to o b t a i n a c c u r a t e r e c o r d s of the i n t e r v i e w s . Verbatim t r a n s c r i p t s were prepared from s e c t i o n s o f the i n t e r v i e w s to be used i n the a n a l y s i s of the data. 1.22 Tasks of the Study The tasks which were used i n t h i s study were developed by the author. They were based on the r e s u l t s of an e a r l i e r i n v e s t i g a t i o n (Kuhn, 1978). A l s o they were p i l o t t e s t e d u s i n g two separate c l a s s groups of p h y s i c s 11 students. Responses to the tasks were i n a w r i t t e n form. In a d d i t i o n , s e v e r a l grade 10 and grade 11 students were i n d i v i d u a l l y i n t e r v i e w e d to determine the s u i t a b i l i t y of the tasks f o r an i n t e r v i e w format. The tasks employed taught experiments u s i n g an apparatus novel to the students ( F i g . 3.1). Indoor shotputs were used as f a l l i n g o b j e c t s , p h o t o c e l l s were used to d e t e c t the motion and a d i g i t a l d e v i c e was used to d i s -p l a y the times i n v o l v e d . Both the tasks and the apparatus are d e s c r i b e d i n d e t a i l i n Chapter Three. 1.23 The Su b j e c t s There were two c o n s i d e r a t i o n s which i n f l u e n c e d the s e l e c t i o n of s u b j e c t s . On the one hand, i t was a n t i c i p a t e d 6 t h a t some developmental trends might emerge from the data. Thus, s i x students (three boys and three g i r l s ) were s e l e c t e d r e s p e c t i v e l y from the grade 6, 8, 10, 11 l e v e l s r e s u l t i n g i n a t o t a l of 24 i n t e r v i e w s . A second c o n s i d e r a t i o n was to examine the e f f e c t of b e l i e f s about f r e e - f a l l motion h e l d by students who had j u s t f i n i s h e d an i n s t r u c t i o n a l u n i t on i i n e m a t i c s . A sample of s i x (three boys and three g i r l s ) students e n r o l l e d i n a P h y s i c s 11 course was used. One of the main i n t e n t i o n s was to see i f common-sense b e l i e f s which are not n e c e s s a r i l y c o n s i s t e n t w i t h the formal concepts which they had d e a l t w i t h i n t h e i r i n s t r u c t i o n a l u n i t on kinematics would tend to p e r s i s t i n s p i t e of such i n -s t r u c t i o n . A l l students were s e l e c t e d from an elementary and a secondary s c h o o l i n North Vancouver, which are a d j a c e n t to each o t h e r . 1.30 EDUCATIONAL SIGNIFICANCE OF THE STUDY Motion i n the common-sense world of experience i s s i g n i f i c a n t l y d i f f e r e n t from motion as d e s c r i b e d by kinematics formulas. Kinematics formulas apply i n an i d e a l world without c o m p l i c a t i o n s of f r i c t i o n , f o r example, and i n i s o l a t i o n from r e l a t e d n o t i o n s . In the common-sense world motion i s experienced with r e l a t e d f o r c e s and a p p l i c a t i o n s of energy. C h i l d r e n form concepts of 7 motion i n t h i s world of experience without any formal i n s t r u c t i o n . They c a r r y these b e l i e f s about motion with them to t h e i r formal experiences i n the classroom. These do not n e c e s s a r i l y match the formal d e s c r i p t i o n of the concepts i n the c u r r i c u l u m . These p r e v i o u s be-l i e f s may not simply be r e p l a c e d by the formal concepts. A v a r i e t y of other p o s s i b i l i t i e s e x i s t . For example, the student may keep both separate i n h i s mind, or he may simply become confused. In any case i t i s u s e f u l f o r the educator to be aware of the s p e c i f i c nature of these b e l i e f s . The r e s u l t s of t h i s study can r e l a t e d i r e c t l y to e d u c a t i o n a l p r a c t i c e . For example, changes i n the c u r r i c u l u m and i n i n s t r u c t i o n a l s t r a t e g y c o u l d be made to s p e c i f i c a l l y a llow f o r the accommodation of the b e l i e f s i d e n t i f i e d . Teacher behaviour toward the student would a l s o be aided i f they were aware o f the students' b e l i e f s . The teacher would be i n c l i n e d to c o n s i d e r the s i g n i f i c a n c e of the students' b e l i e f s . They would be i n c l i n e d to c r e a t e an atmosphere i n the classroom where the student f e l t a t ease i n e x p r e s s i n g and e x p l o r i n g these b e l i e f s . i 1.40 LIMITATIONS OF THE STUDY 1.41 Developmental Aspect In t h i s study i t was assumed t h a t an i n t e r v i e w methodology was e f f e c t i v e i n i d e n t i f y i n g genuine b e l i e f s 8 of students. However, there are l i m i t a t i o n s to the i n t e r v i e w methodology. F i r s t , i t l i m i t e d the s i z e of the sample. Consequently,the sample cannot be con-s i d e r e d r e p r e s e n t a t i v e of a wide p o p u l a t i o n . I n f e r e n c e s made must t h e r e f o r e be guarded. The number of responses i n each category may not r e p r e s e n t e x a c t l y the number of responses f o r a wide p o p u l a t i o n . That i s perhaps l e s s important than the f a c t t h a t the genuine p a t t e r n s of b e l i e f should be i d e n t i f i e d . These p a t t e r n s of b e l i e f c o u l d very w e l l be represented i n a wider p o p u l a t i o n . Second, the i n t e r v i e w s were time-consuming. Consequently, they had to be conducted over a two-month p e r i o d . The s p r i n g break a l s o o c c u r r e d i n the middle of the s e r i e s of i n t e r v i e w s which again p r o t r a c t e d the time. Students were requested not to d i s c u s s t h e i r i n t e r v i e w experience, and, as f a r as c o u l d be determined, they d i d not. During t h i s p e r i o d there was a l s o an e x t e n s i v e media coverage of the A l b e r t E i n s t e i n Centennial . c e l e b r a t i o n accompanied by d i s c u s s i o n of h i s ideas concerning motion and r e l a t i v i t y . There was not even an offhand r e f e r e n c e to t h i s i n the explanations, so i t was assumed t h a t i t had no s i g n i f i c a n t e f f e c t on the r e s u l t s . There are a l s o p o s s i b l e l i m i t a t i o n s to the e f f e c t i v e -ness of the tasks employed. They were p r e t e s t e d , b u t t h e i r r e l i a b i l i t y and v a l i d i t y were not e x t e n s i v e l y i n v e s t i g a t e d . 9 A l s o the tasks themselves may have been l i m i t i n g . Other important b e l i e f s about f r e e - f a l l motion not s p e c i f i c a l l y r e l a t e d to the tasks used may not have been i d e n t i f i e d . 1.42 I n s t r u c t i o n Aspect There were a number of a d d i t i o n a l l i m i t a t i o n s s p e c i f i c a l l y r e l a t e d to the problem of i n v e s t i g a t i n g the e f f e c t s of i n s t r u c t i o n on students' b e l i e f s . In a d d i t i o n to the f a c t t h a t o n l y a very s m a l l sample was used, i n t e r v i e w s were conducted a f t e r the i n -s t r u c t i o n o c c u r r e d . No data was c o l l e c t e d f o r b e l i e f s o c c u r r i n g b e f o r e i n s t r u c t i o n . A l s o , the nature of t h i s i n s t r u c t i o n was not c a r e f u l l y c o n t r o l l e d . I t must be noted, however, t h a t P h y s i c s 11 i s an e l e c t i v e academic course and tends to draw i t s enrolment from the more abl e segment of the student p o p u l a t i o n . These students tend to perform b e t t e r than the average a f t e r formal i n s t r u c t i o n . They should have a b e t t e r understanding of the formal concepts of kinematics a f t e r i n s t r u c t i o n than the average grade 11 student. T h e r e f o r e , i n -t u i t i v e b e l i e f s noted to p e r s i s t a f t e r i n s t r u c t i o n , even f o r such a s m a l l group, would be s i g n i f i c a n t . 10 CHAPTER TWO B A C K G R O U N D OF THE STUDY 2.00 INTRODUCTION In t h i s chapter the r e l a t e d l i t e r a t u r e w i l l be reviewed i n the f o l l o w i n g three areas: 1) The broad problem area of students' development of s c i e n c e concepts. 2) The more s p e c i f i c problem area of students' development of the concepts of speed and a c c e l e r a t i o n . 3) The i m p l i c a t i o n s of these r e s e a r c h f i n d i n g s concerning the development of s c i e n c e con-cepts f o r c u r r i c u l u m and i n s t r u c t i o n . 2.10 LITERATURE IN THE BROAD PROBLEM AREA 2.11 Two P e r s p e c t i v e s The problem of the development of s c i e n c e con-cepts i n students has been e x t e n s i v e l y i n v e s t i g a t e d and r e p o r t e d i n the l i t e r a t u r e . At l e a s t two d i f f e r e n t p e r s p e c t i v e s are e v i d e n t i n these i n v e s t i g a t i o n s . These are the nomothetic and i d e o g r a p h i c p e r s p e c t i v e s , ( D r i v e r and :• E a s l e y , 1978) . In nomothetic s t u d i e s .the students;'* a c q u i s i t i o n of the s t r u c t u r e of t h e o r e t i c a l concepts which r e f l e c t 11 contemporary s c i e n t i f i c knowledge i s paramount. ...there are s t u d i e s i n which the p u p i l s ' understanding i s assessed i n terms of the congruence of t h e i r responses w i t h accepted s c i e n t i f i c i d e a s . Having s p e c i f i e d such a standard the r e s e a r c h task i s then to assess the degree to which p u p i l s ' understanding conforms to t h a t standard, the age and order a t which c e r t a i n ideas develop and to i n d i c a t e common d e v i a t i o n s from such an accepted view. (Dri v e r and ..-.Easley, 1978 , p. 65) From the nomothetic p e r s p e c t i v e r e a d i n e s s f o r concept l e a r n i n g i s a l s o of major concern. A major i n h i b i t o r to concept formation appears to be maturation as a f u n c t i o n of age l e v e l . Younger c h i l d r e n do not possess the a b i l i t y to t h i n k a b s t r a c t l y and t h e i r concept c l a s s i f i c a t i o n s may not have pro-gressed much beyond grouping. (Voelker, 1975, p.12). Researchers working from t h i s p e r s p e c t i v e are i n t e r e s t e d i n e s t a b l i s h i n g age or grade norms and seeking a sequence of concepts which can be presented i n terms of t h e i r d i f f i c u l t y . They contend t h a t sequencing of s c i e n c e concepts i n the c u r r i c u l u m i s u s u a l l y not based on r e s e a r c h f i n d i n g s but on other f a c t o r s (Voelker, 1975, p.5). How-ever, the o r g a n i z a t i o n f o r l e a r n i n g of concept sequences and the p l a c i n g of students a t the proper p o i n t i n these sequences by grade has proven to be very d i f f i c u l t . 12 In ideographic studies the students' alternative frameworks are of central concern. These look "more fundamentally at the pupils own understanding and i t s development" (Driver and Easley, 1978, p.61). I t i s assumed here that the student develops science concepts from his concrete experiences i n a common-sense world and not only from formal science i n s t r u c t i o n . These concepts are not simply misconceptions, but constitute alternative frameworks: ... i t i s the problem of the alternative frameworks which aris e from students' personal experience of natural events and th e i r attempt to make sense of them for themselves p r i o r to in s t r u c t i o n , on which ideographic studies mainly attempt to throw some l i g h t . Here the focus i s on an individual's personal experience. (Driver and Easley, 1978, p.62) In addition, i t i s suggested by some researchers that preconceptions (Ausubel, 1962) are "amazingly tenacious and r e s i s t a n t to extinction" (Driver and Easley, 1978, p.61). There i s some evidence that students have great d i f f i c u l t y i n accommodating t h e i r thinking to new ex-periences presented by in s t r u c t i o n (Driver, 1973). Many commom-sense (Walters and Boldt, 1970) views of the world could, i n fact, be found among the adult population. 13 T h i s i n d i c a t i o n of the r e s i s t a n c e of common-sense ideas to i n s t r u c t i o n does not n e c e s s a r i l y mean t h a t i n s t r u c t i o n i s u s e l e s s or t h a t the o r d e r i n g of concepts i s not an important i s s u e . Rather, i t means t h a t the o r d e r i n g of concepts i s not o n l y a matter of l o g i c a l complexity. P s y c h o l o g i c a l o r d e r i n g ( D r i v e r and E a s l e y , 1978) of concepts by d i f f i c u l t y i n v o l v e s other f a c t o r s such as the degree to which the t h e o r e t i c a l concept i s e v i d e n t i n everyday experience. Two methods have been: used to determine concept o r d e r i n g . One method of determining t h i s o r d e r i n g i s by comparing mean scores on tasks by age. Another method i s by having each p u p i l perform a range of tasks and u s i n g the r e s u l t s to determine the sequence i n which they can be s u c c e s s f u l l y performed ( D r i v e r and E a s l e y , 1978, p.65). I t has been suggested by some t h a t the h i s t o r y of s c i e n t i f i c i d e a s , to •some extent, r e f l e c t s a type of p s y c h o l o g i c a l o r d e r i n g of students' e x p l a n a t i o n s of p h y s i c a l phenomena (D r i v e r and E a s l e y , 1978, p.70). However the A r i s t o t e l e a n , G a l i l e a n , Newtonian or E i n s t e i n i a n p o i n t of view serve more as a source of ideas than anything e l s e . The o r d e r i n g of students' concepts i s important i n o r g a n i z i n g m a t e r i a l s f o r i n s t r u c t i o n . In a d d i t i o n , i t i s important to develop t e a c h i n g s t r a t e g i e s which take concept development i n t o account. To t h i s end Walters and B o l d t (1970) have proposed the use of 'prescience t e a c h i n g s t r a t e g y ' (p.176) which i s designed to " f a c i l i t a t e t r a n s i t i o n s from a 14 c o n c r e t e - p e r c e p t u a l l e v e l of understanding to an a b s t r a c t -conceptual l e v e l " (Walters and B o l d t , 1970, p.176). De-velopment begins to take p l a c e when awareness of " c o n t r a d i c -t i o n between thought and experience" occurs (Walters and B o l d t , 1970, p.176). A ' t r a n s i t i o n a l t e a c h i n g s t r a t e g y ' c o u l d then be a p p l i e d a c c o r d i n g to the need of the student. " I t may be (1) t h a t the c h i l d needs new i n f o r m a t i o n about phenomena or (2) t h a t he needs to u t i l i z e i n f o r m a t i o n he a l r e a d y has but i s unable to a s s i m i l a t e " (Walters and B o l d t , 1970, p.177). In summary,nomothetic and i d e o g r a p h i c p e r s p e c t i v e s are both concerned w i t h the problem of c o o r d i n a t i n g i n -s t r u c t i o n a l m a t e r i a l s w i t h concept development. However, they both have d i f f e r e n t emphases. Researchers working from the nomothetic p e r s p e c t i v e have been p r i m a r i l y i n t e r e s t e d i n determining the ages at which students can handle the l o g i c i m p l i c i t i n s c i e n c e concepts. Researchers working from the i d e o g r a p h i c p e r s p e c t i v e have the a d d i t i o n a l i n t e r e s t of (a) i d e n t i f y i n g the a l t e r n a t i v e ways students i n t e r p r e t phenomena from t h e i r own everyday concr e t e experiences and (b) determining how these a l t e r n a t i v e frameworks are i n -v o l v e d i n the students' l e a r n i n g of s c i e n c e concepts. 2.20 LITERATURE IN THE SPECIFIC CONTENT AREA Students' a b i l i t y t o perform tasks i n v o l v i n g concepts of speed and a c c e l e r a t i o n has r e c e i v e d a t t e n t i o n from three d i f f e r e n t p e r s p e c t i v e s . 15 (1) E m p i r i c a l s t u d i e s documenting the a c q u i s i t i o n of these concepts. (2) S t u d i e s i d e n t i f y i n g a l t e r n a t i v e frameworks f o r r e l a t e d concepts. (3) S t u d i e s e v a l u a t i n g l o g i c a l requirements necessary to understand these concepts. The f i r s t p e r s p e c t i v e d e a l s with the a c q u i s i t i o n of these concepts. Few e m p i r i c a l s t u d i e s have been c a r r i e d out i n t h i s area. Raven's (1972) use of P i a g e t ' s i n c l i n e d plane experiment i s the most s i g n i f i c a n t and has shown t h a t , a t l e a s t f o r low r a t e s of a c c e l e r a t i o n and speeds, many twelve-year -olds i n t e r p r e t a c c e l e r a t i o n a t l e a s t as g r a d u a l l y i n -c r e a s i n g speed. However, i n t h i s study the tasks used are r e l a t i v e l y simple. For example, s i n c e two o b j e c t s are not used simultaneously, such independent v a r i a b l e s as r e l a t i v e p o s i t i o n or h e i g h t on the plane, time of r e l e a s e which determines i n i t i a l v e l o c i t y , and mass of the b a l l s are not t e s t e d f o r t h e i r e f f e c t on the students' i n t e r p r e t a t i o n of the motion. A l s o , i n t h i s study, low speeds are used throughout. T h i s makes the motion p e r c e p t u a l l y simple as compared to ra p i d l y - m o v i n g o b j e c t s which become b l u r r e d . In a d d i t i o n , t h e r e i s some evidence t h a t preceding and over-t a k i n g are not the o n l y c r i t e r i a f o r motion a n a l y s i s (Morei, Kojima and Deno, 19 76). These r e s e a r c h e r s contend t h a t instantaneous v e l o c i t y i s i n v o l v e d as w e l l i n making d i s t a n c e and time i n f e r e n c e s . 16 With r e s p e c t to the development of concepts of v e l o c i t y and a c c e l e r a t i o n , Grass (1972) concluedes t h a t a " r i b b o n s p i r a l " o f concept arrangement e x i s t s f o r motion. He suggests t h a t concepts of motion be i n t r o d u c e d r e p e a t e d l y over a p e r i o d of s e v e r a l y e a r s . In t h i s way a g r e a t e r degree of understanding of the same types of motion and of more complex forms can be a t t a i n e d i n subsequent y e a r s . Un-f o r t u n a t e l y , the d e t a i l s of t h i s suggested sequencing are not provided and have not been t e s t e d . The second p e r s p e c t i v e i s t h a t of the search f o r a l t e r n a t i v e frameworks. Here Nussbaum's and Novak's (1976) study i l l u s t r a t e s the method w e l l , although i t i s the o n l y one i n t h i s category. In t h i s study c h i l d r e n ' s concepts of the e a r t h were i n v e s t i g a t e d u s i n g imaginary f r e e - f a l l i n g o b j e c t s . These were l o c a t e d a t d i f f e r e n t p o i n t s on the e a r t h . The p r e d i c t i o n s a l s o had to be e x p l a i n e d . Audiotape r e c o r d i n g s of the inverviews and the drawings made by the p u p i l s were analysed i n terms of u n d e r l y i n g c o n c e p t u a l frameworks. F i v e such frameworks were i d e n t i f i e d v a r y i n g from the f l a t e a r t h and no concept of extended space to a s p h e r i c a l e a r t h i n extended space. Although the study was undertaken w i t h 7-8 year o l d s , i t was r e p o r t e d t h a t a l l f i v e frame-works had been i d e n t i f i e d with 12-14 year o l d p u p i l s . ( D r i v e r and E a s l e y , 1978, p.78) The t h i r d p e r s p e c t i v e , the l o g i c a l requirements i n -volved i n understanding accepted concepts, has been researched more e x t e n s i v e l y . Weinreb and B r a i n e r t (1975) conclude t h a t the groupement theory of P i a g e t seems i n a p p r o p r i a t e to 17 c o n s t r u c t the l e v e l s of c o g n i t i v e development necessary to analyze space and time concepts, w h i l e Boulanger (1976) has shown t h a t attempts to t r a i n c h i l d r e n f o r the schema of p r o p o r t i o n a l reasoning makes the student d i s t r u s t h i s own i n s i g h t s and o b s e r v a t i o n s . In f a c t , Body (1978) con-cludes t h a t the a n a l y s i s of l o g i c a l requirements f o r tasks as expressed by the requirements of 'formal o p e r a t i o n s ' has been much o v e r - s i m p l i f i e d , as t h i s i s so d i f f i c u l t to d e f i n e and the c o n t e x t u a l e f f e c t s are so s i g n i f i c a n t . 2.30 LITERATURE SUGGESTING IMPLICATIONS FOR CURRICULUM  AND INSTRUCTION A l t e r n a t i v e frameworks of students p r e s e n t a r e a l problem f o r the d e s i g n of c u r r i c u l a and t e a c h i n g s t r a t e g i e s . On the one hand,there i s c o n s i d e r a b l e evidence t h a t these frameworks e x i s t and p r e s e n t problems to the student,, i n -s p i t e of standard i n s t r u c t i o n . On the other hand,some d i r e c t i o n s have been suggested to d e a l w i t h the problems presented by a l t e r n a t i v e frameworks. Some c u r r i c u l u m pro-j e c t s have even been designed which d e a l s p e c i f i c a l l y w i t h a l t e r n a t i v e frameworks. The problem of these a l t e r n a t i v e frameworks does not simply evaporate i f ignored. They tend to r e s i s t standard i n s t r u c t i o n . M isconceptions i n the areas of dynamics have r e c e i v e d p a r t i c u l a r a t t e n t i o n . In a study of high s c h o o l and u n i v e r s i t y students, Lebouter (19 76) i d e n t i f i e d commonly h e l d 18 misconceptions related to ideas of force and motion which p e r s i s t despite i n -struction. These have been explored more thoroughly by Viennot (1974) who analysed attempts at solving dynamic problems by university physics students. The results indicate that ce r t a i n pre-Galilean ideas p e r s i s t and reappear i n sophisticated tasks. (Such as student's attempt to solve problems involving simple harmonic motion or p r o j e c t i l e motion). (Driver and Easley, 1978, p.67). In fact,Driver and Easleyy. (1978) suggest there may be some cases i n which formal i n s t r u c t i o n obstructs learning. (Piaget, 1973). Several solutions have been proposed and a few programs have been implemented to deal with the problem presented by the apparent i n a b i l i t y of standard i n s t r u c t i o n to deal adequately with alternative frameworks. I t i s necessary to s t a r t from the students' view-point i n i n s t r u c t i o n . Ausubel, for instance, contends that the chi l d ' s conceptions can be manipulated, providing the i n s t r u c t i o n allows the children to anchor new information on relevant s p e c i f i c ideas previously ex i s t i n g i n his cognitive structure. (Nussbaum and Novak, 1976, p.549) Informal communication i n small groups has been used to f a c i l i t a t e conceptual development (Ten Voorde, 1977). But,, the central issue which i s involved, i s a dramatic change "amounting at times to a paradigm s h i f t i n pupils' thinking and the conditions which f a c i l i t a t e i t " (Driver and Easley;,'. 1978, p. 80). 19 Walters and Boldt (1970, p.177) have outlined a s p e c i f i c teaching strategy appropriate for t h i s t r a n s i t i o n a l process. Its main thrust i s to tes t thought against ex-perience. Very often the main impetus for sustained e f f o r t of t h i s kind of a c t i v i t y comes from the challenge of matching expectations with nature. Usually t h i s poses a l l sorts of puzzles that have to be resolved. The solving of these puzzles i s often a highly creative undertaking. Through developmental a c t i v i t y of t h i s kind, the learner eventually en-counters puzzles which he cannot resolve no matter how hard he t r i e s . If the con-frontation becomes serious enough, the puzzle may acquire the force of an anomaly and i n i t i a t e a new conceptual change. (Walters and Boldt, 1970, p.177) Erickson (1979) has proposed the use of 'anomaly maneuvers' to a c t i v e l y promote uncertainty and change i n the students' framework. Once students have attained such a set of b e l i e f s another teaching maneuver might i n -volve the creation of a s i t u a t i o n that leads to unexpected outcome for the students. Such an anomaly mane.uve.K i s designed to introduce an element of uncertainty into the student's b e l i e f s , with the expectation that the un-certainty w i l l eventually be resolved with a type of reorganization otlrestructuring of the chi l d ' s i n t u i t i o n s and b e l i e f s . (Erickson, 1979, p.22) Following t h i s , a set of 'restructuring maneuvers'- were proposed to help i n the students' accommodation of outcomes that were unexpected. Some attempts are being made to actually implement curriculums which take alternative frameworks into account. 20 One such program i s t h a t of Delacote i n France. ( D r i v e r and E a s l e y , 1 9 7 8 , p . 7 7 ) . T h i s p r o j e c t i n v o l v e s students between the ages 9 - 1 5 y e a r s . I t i s attempting to develop and e v a l u a t e a s c i e n c e program which aims t o i d e n t i f y the a l t e r n a t i v e frameworks of students and h e l p them to a s s i -m i l a t e t h e o r e t i c a l frameworks. F i n a l l y , B r o w n and Desforges ( 1 9 7 7 ) c a u t i o n t h a t i t i s important a t t h i s stage i n the r e s e a r c h not to be too ambitious i n developing taxonomies which are too compre-hensive. A b u i l d i n g process i s r e q u i r e d . The i m p l i c a t i o n s f o r c u r r i c u l u m design are that, • i n i t i a l l y , we must abandon the search f o r g e n e r a l s t r u c t u r e s and s e t about producing taxonomies of behaviours f o r s p e c i f i c areas of the c u r r i c u l u m . In the long term, when s u f f i c i e n t taxonomies have been e s t a b l i s h e d , we may look again f o r g e n e r a l s t r u c t u r e s , but to s t a r t , as P i a g e t does, with a search f o r such g e n e r a l i t y has proved to be i n a p p r o p r i a t e ; , (Brown and Desforges, 1 9 7 7 , p . 1 6 ) 2.40 SUMMARY The l i t e r a t u r e i n the g e n e r a l problem area i n d i c a t e s t h a t two p e r s p e c t i v e s , the nomothetic and the i d e o g r a p h i c , have been used i n r e s e a r c h i n g the development of s c i e n c e concepts i n students. In the s p e c i f i c area, the problem of the development of students' concepts of motion, has not been researched e x t e n s i v e l y except from the P i a g e t i a n framework. A l s o s e r i o u s c h a l l e n g e s have been l e v e l l e d a g a i n s t a number of 21 i t s c l a ims ( p a r t i c u l a r l y the groupement t h e o r y ) . The p r e s e n t study i d e n t i f i e s students' b e l i e f s about motion i n the context of t h e i r i n t u i t i o n s and ex-p e r i e n c e . In t h i s sense i t i s an i d e o g r a p h i c r a t h e r than a nomothetic approach to the problem. The i n v e s t i g a t i o n of the students' b e l i e f s about f r e e - f a l l motion i s s i g n i f i c a n t s i n c e : (a) Problems of motion are c e n t r a l to p h y s i c s . (b) A v a r i e t y of a l t e r n a t i v e frameworks are p o s s i b l e . (c) Problems of motion show evidence of r e s i s t a n c e to standard i n s t r u c t i o n . (Lebouter, 1976; Viennot, 1974). I t has a l s o been suggested i n the l i t e r a t u r e t h a t a l t e r n a t i v e frameworks prese n t a r e a l c h a l l e n g e to i n -s t r u c t i o n and c u r r i c u l u m d e s i g n . 22 CHARTER THREE METHODS OF STUDY 3.00 INTRODUCTION T h i s chapter w i l l d e a l w i t h three aspects of the methods used. The s e c t i o n d e a l i n g w i t h the i n t e r v i e w procedure i n c l u d e s a d e s c r i p t i o n of the apparatus and of the t r a i n i n g s e s s i o n . The s e c t i o n which d e s c r i b e s the tasks g i v e s a d e t a i l e d account of tasks d e a l i n g with a s i n g l e o b j e c t i n f r e e - f a l l and tasks i n v o l v i n g two o b j e c t s i n f r e e - f a l l under v a r y i n g c o n d i t i o n s of he i g h t , i n i t i a l v e l o c i t y and weight. F i n a l l y , the s e c t i o n d e a l i n g w i t h the s u b j e c t s d e s c r i b e s t h e i r s e l e c t i o n and the composition of the sample. 3.10 INTERVIEW PROCEDURE Each i n t e r v i e w was conducted u s i n g a s i m i l a r s e t of procedures. F i r s t , a t r a i n i n g s e s s i o n was completed to ensure t h a t the s u b j e c t s understood the o p e r a t i o n of the equipment. Second, the same s e t of three tasks was admi n i s t e r e d to each s u b j e c t . These i n t e r v i e w s were conducted d u r i n g the months of March and A p r i l , 1979. They were conducted 23 immediately a f t e r s c h o o l i n a room wi t h o n l y the student and the i n t e r v i e w e r p r e s e n t . Each i n t e r v i e w was recorded using a c a s s e t t e tape r e c o r d e r . Normally,only one i n t e r -view was conducted on any day. A t r a n s c r i p t was made of each i n t e r v i e w on the same day i t was conducted. The i n t e r v i e w s were conducted i n the f o l l o w i n g o r d e r . F i r s t , t h e grade 10 students; then,the grade 11 students; then,the grade 8 students; a n d , f i n a l l y - t h e grade 6 students were i n t e r v i e w e d . These i n t e r v i e w s took an average of about t h i r t y minutes. The l a s t i n t e r v i e w s w i t h the grade 6 students tended t o be a l i t t l e s h o r t e r , having an average l e n g t h of about twenty minutes. A l l i n t e r v i e w s used the same tas k s , b u t fewer follow-up q u e s t i o n s tended to be r e -q u i r e d f o r the grade 6 stu d e n t s . 3.11 The Apparatus The apparatus shown i n F i g u r e 3.1 was s e t up and used i n the i n t e r v i e w s . I t was chosen f o r i t s n o v e l t y as w e l l as f o r i t s accuracy. Generally,few problems were encountered i n the i n t e r -views . The students d i d not appear to be i n t i m i d a t e d by the apparatus and,in f a c t , t h e use of p h o t o c e l l s and a d i g i t a l timer c r e a t e d i n t e r e s t because of t h e i r n o v e l t y . The hundredths and thousandths.decades of the d i g i t a l counter were covered w i t h opaque e l e c t r i c a l tape. As a r e s u l t , only the tens, u n i t s and tenths decades c o u l d be read. 24 'Photocells V e r t i c a l Support L i g h t Beams F i g u r e 3.1 The Apparatus THORNTON ASSOCIATE DECADE COUNTER TYPE DEC-101 DIGITAL COUNTER AND POWER SUPPLY Th i s degree of accuracy i n the timer was co n s i d e r e d to be p r e c i s e without being c o n f u s i n g . The counter was s t a r t e d when the l i g h t beam a t the top was i n t e r r u p t e d . I t was stopped when the beam a t the bottom was i n t e r r u p t e d . Thus , the time of t r a n s i t of an o b j e c t moving through the gap between the f i r s t and second p h o t o c e l l s was measured as i t s u c c e s s i v e l y i n t e r r u p t e d f i r s t the top and then the bottom beam on i t s way through the gap. The sources and p h o t o c e l l s were attached t o c o l o u r e d c l o t h e s p i n s . They,therefore, c o u l d be c l i p p e d onto any p o s i t i o n on the metre s t i c k s . As a r e s u l t , a gap of any s i z e a t any The p h o t o c e l l s were c l i p p e d on and moveable. The top one was atta c h e d to a blu e c l o t h e s p i n , and the bottom one to a red c l o t h e s p i n . 25 l o c a t i o n c o u l d e a s i l y be s e t up. The b l u e c l o t h e s p i n s were a t the top of the gap and the red c l o t h s p i n s were at the bottom. A d d i t i o n a l blue and red c l o t l f e s p i r i s were pr o v i d e d so t h a t p o s i t i o n s of a s e r i e s of gaps c o u l d be simulated and remain on the metre s t i c k s . Three shotputs were used. Two i d e n t i c a l r e d ones weighed 4 kgv One h e a v i e r yellow shotput weighed- 6 kg. 3.12 T r a i n i n g S e s s i o n The t r a i n i n g s e s s i o n both acquainted the student with the apparatus and enabled the i n v e s t i g a t o r to determine whether they understood i t s o p e r a t i o n . At f i r s t the i n -v e s t i g a t o r moved h i s hand through the gap to show the student how the d i g i t a l counter r e g i s t e r e d time. Then the student was i n s t r u c t e d t o s t a r t and stop the timer i n a s i m i l a r way w i t h t h e i r hand f o r a gap of ten centimetres d i s t a n c e between the l i g h t beams. The f o l l o w i n g procedure was used: I. - I n t e r v i e w e r ; S. - S u b j e c t I. - "Would you s t a r t and stop the timer the way I d i d . Move your hand f a i r l y s l owly." S. - The student performed t h i s a c t i o n . I. - "How long d i d t h a t take?" S. - The student read the d i g i t a l timer. I. - "Now would you do the same t h i n g but move your hand a l i t t l e f a s t e r . " S. - The student performed the a c t i o n . I. - "How long d i d t h a t take?" S. - The student read the timer. 26 I. - "Now,would you move your hand through even faster than that." S. - The student performed the action. I. - "How long did i t take t h i s time?" S. - The student read the timer. I. - "Now,would you explain how the speed of your hand i s related to the reading on the timer." The interview did not proceed u n t i l the student c l e a r l y indicated that for a fixed gap the time of t r a n s i t was de-creased as the speed of the hand was increased. I t was also to be indicated that for a gap twice the size the speed would have to be increased to re g i s t e r the same time of t r a n s i t as for the smaller gap. Follow-up questions were used i f necessary,but no s i g n i f i c a n t problems occurred. 3.20 THE TASKS The tasks were designed to tes t the following: (a) The student's b e l i e f s about the motion of a single object i n f r e e - f a l l (tasks 3.21, 3.22). (b) The student's b e l i e f s about the e f f e c t of height (task 3.23A), i n i t i a l v e l o c i t y (task 3.24A, 3.25A) frame of reference (tasks 3.23A, 3.24B, •3..25B-) and weight (tasks 3.26A, 3.26B) on the motion of an object i n f r e e - f a l l . (c) The student's b e l i e f s about the combined action of the variables of height and i n i t i a l v e l o c i t y (tasks 3.24A, 3.24B, 3.25A, 3.25B), height and weight (tasks 3.26A, 3.26B), and i n i t i a l v e l o c i t y and weight (3. H, 3.28). 27 3.21 A S i n g l e Object i n F r e e - F a i l A gap of 10 cm'< was s e t between the p h o t o c e l l s which were pinned r e s p e c t i v e l y a t the zero centimetre and ten centimetre p o s i t i o n s . One of the 4 Kg indoor shotputs was h e l d i n p o s i t i o n immediately above the f i r s t p h o t o c e l l and dropped through the gap. T h i s drop was timed and the student was f i r s t requested to read the time f o r the f a l l . In t h i s case the timer read one-tenth of a second on a l l o c c a s i o n s . (This was the o n l y experiment a c t u a l l y done. A l l the remaining tasks were done as thought problems). The f o l l o w i n g i n s t r u c t i o n s were then g i v e n . The shotput which was dropped from zero continued i t s f a l l p ast the 10 cm mark. Suppose t h a t we had p l a c e d the f i r s t p h o t o c e l l mounted on the b l u e c l o t h e s p i n at the 50 cm mark. T h i s one, you remember s t a r t s the timer. (This clothespin'was then pinned a t the 50 cm mark) . Now, the shotput which s t a r t e d a t zero cm would f a l l f o r 50 cm and then s t a r t the timer. The second photo-c e l l mounted on the r e d c l o t h e s p i n stops'jthe timer. Where would you p l a c e t h i s second p h o t o c e l l so t h a t the timer would read one-tenth of a second? A f t e r t h e i r p o s i t i o n i n g of the lower p h o t o c e l l , the student was asked to e x p l a i n t h e i r reasons f o r choosing t h a t p a r t i c u l a r l o c a t i o n . The student was asked to compare the speed of the shot-put i n the gap from zero cm to 10 cm and the speed i n the gap s t a r t i n g a t 50 cm. T h i s was done to check the meaning of the student's p r e d i c t i o n . I f the p r e d i c t e d gap was the same s i z e (10 cm), t h i s should have i n d i c a t e d t h a t the speed 28 was judged to be constant. I f the p r e d i c t e d gap .was l a r g e r than 10 cm,this should have i n d i c a t e d t h a t the speed was judged to i n c r e a s e or a c c e l e r a t e . T h i s procedure was repeated f o r d i f f e r e n t i n t e r v a l s i n the path of the f r e e - f a l l i n g shotput. The student was asked to c o n s t r u c t a p p r o p r i a t e gaps s t a r t i n g s u c c e s s i v e l y at the 100 cm, 150 cm, and 200 cm marks. A d d i t i o n a l b l u e and red c l o t h s p i n s were used by the students to mark s u c c e s s i v e gaps. In t h i s way p r e v i o u s l y marked gaps c o u l d remain on the s c a l e as a continuous r e c o r d . The student was asked, i n a d d i t i o n , what would happen to the speed of the shotput i f i t was a b l e t o f a l l f u r t h e r b e f o r e h i t t i n g the ground. Again,not o n l y a p r e d i c t i o n , but a l s o an e x p l a n a t i o n was requested. 3.22 Average Speed Task Only those students who i n d i c a t e d t h a t some form of a c c e l e r a t i o n was o c c u r r i n g proceeded to the next p a r t of the task. T h i s task i n d i c a t e d whether the student b e l i e v e d t h a t v e l o c i t y v a r i e s w i t h displacement or w i t h e l a p s e d time. The student's a t t e n t i o n was d i r e c t e d to the d e s i g n a t e d gap s t a r t i n g a t the 100 cm mark. For t h i s gap the f o l l o w i n g t h r e e l o c a t i o n s were to be i n d i c a t e d : a) "At what p o i n t i n t h i s gap was the shotput going the slowest speed?" A l l o f the students then p o i n t e d to the b l u e c l o t h e s p i n . b) "At what p o i n t i n t h i s gap was the shotput going the f a s t e s t speed?" A l l o f the students then, p o i n t e d to the 'red. c l o t h e s p 29 c) "At what p o i n t i n t h i s gap was the shotput going a t a speed which was one-half way between the slowest speed and the f a s t e s t speed?" 3.23A The F a c t o r of Height - E x t e r n a l E a r t h Frame The e f f e c t of a h e i g h t d i f f e r e n c e between two shot-puts was t e s t e d i n t h i s t a s k . One shotput was h e l d by the i n t e r v i e w e r a t the zero cm mark w h i l e the student h e l d the second i d e n t i c a l shotput a t the 25 cm mark. He was g i v e n the f o l l o w i n g problem. I - "How b i g i s the gap between the shotputs?" S - 25 cm. I - "Suppose I counted one, two, three,go,and on the word 'go' you dropped your shotput and I dropped my i d e n t i c a l shotput a t e x a c t l y the same time. Can you d e s c r i b e the gap between the two shot-puts as they f a l l down?" If they i n d i c a t e d t h a t the top one would b e g i n to over-take the bottom one,some a d d i t i o n a l q u e s t i o n s were used to make t h i s p r e c i s e . I - "Does the top one c a t c h the bottom one?" S - ( I f yes) I - "Does i t pass?" S - "What happens to the gap between them a f t e r t h a t ? " A d d i t i o n a l e x p l a n a t i o n s were sought w i t h the q u e s t i o n : I - " P l e a s e e x p l a i n why you t h i n k t h a t (the p r e d i c t i o n ) would happen?" 30 3.24A The F a c t o r of I n i t i a l V e l o c i t y - E x t e r n a l E a r t h  Frame wi t h I n i t i a l S e p a r a t i o n The e f f e c t of time s e p a r a t i o n or the advantage of an i n i t i a l v e l o c i t y was t e s t e d i n t h i s t a s k . Again,the same two i d e n t i c a l shotputs were used. One shotput was h e l d by the i n t e r v i e w e r a t the zero cm mark w h i l e the student h e l d the second shotput at the 100 cm mark. The f o l l o w i n g problem was given-'r I - "Suppose t h a t I counted one, two, t h r e e , go, and dropped my shotput, but you waited s; ydu d i d not drop yours a t the same time. Suppose you waited u n t i l mine had f a l l e n t i l l i t was a t the 4 0 cm mark. (The shotput was p o s i t i o n e d a t t h a t p o i n t ) . J u s t when i t reached t h a t 4 0 cm mark you dropped yours. A f t e r t h a t they both would be f a l l i n g . How f a r a p a r t are they j u s t as you drop your shotput?" S - "60 cm (between 40 cm and 100 cm)" I - "Would you d e s c r i b e the gap between the two as they f a l l f u r t h e r ? " S - ( I f i t i s d e s c r i b e d as g e t t i n g s m a l l e r due to the i n i t i a l v e l o c i t y of the top shotput,the next q u e s t i o n s are asked). I - "Does the top one c a t c h up to the bottom one?" S - ( I f the answer i s yes...) I - "Does i t pass?" S - (If the answer i s yes...) I - "Then what happens?" S -I - "Can you e x p l a i n your answer?" S - (Gives an e x p l a n a t i o n , i f p o s s i b l e ) . 31 3.25A The F a c t o r of I n i t i a l V e l o c i t y - E x t e r n a l E a r t h  Frame w i t h Shotputs I n i t i a l l y Even The e f f e c t of time s e p a r a t i o n or the advantage of an i n i t i a l v e l o c i t y was again t e s t e d i n t h i s case. I t was very much the same as i n 3.24A except w i t h the second shotput w a i t i n g a t the 100 cm mark while the f i r s t shotput was dropped from the zero cm mark. However, i n t h i s case, the e f f e c t of an i n i t i a l v e l o c i t y was more s h a r p l y accentuated. The top one was d e s c r i b e d as dropping u n t i l i t was even wi t h the bottom one a t the 100 cm mark bef o r e the l a t e r one was r e l e a s e d . T h i s was demonstrated by p o s i t i o n i n g the shotputs a c c o r d i n g to the d e s c r i p t i o n . The f o l l o w i n g q u e s t i o n s were asked. I - "Where i s the other shotput j u s t as you drop yours?" S - " J u s t b e s i d e mine." I - "Can you compare t h e i r p o s i t i o n s j u s t a f t e r you drop yours?" S — ( I f the top one i s d e s c r i b e d as p a s s i n g the bottom one? I - "Can you d e s c r i b e the gap between the two as they f a l l f u r t h e r ? " S w • • • • I - "Why does t h i s happen?" S - (Gives an e x p l a n a t i o n , i f p o s s i b l e ) 3.23B, 3.24B, 3.25B I n t e r n a l Frame At t h i s p o i n t i n the i n t e r v i e w tasks 3.23A, 3.24A, and 3.25A were repeated e x a c t l y , but w i t h a change i n the frame of r e f e r e n c e . In the 'A' form the frame was e x t e r n a l to the 32 shotputs. I t was an e a r t h frame, the frame of the student. To t e s t the student's a b i l i t y to s h i f t frames of r e f e r e n c e , a common problem i n k i n e m a t i c s , the *'-'B' form of the tasks used an i n t e r n a l frameattached to the lower shotput. The student was to imagine t a k i n g a s i t t i n g p o s i t i o n on the lower shotput, r i d i n g i t down as i t f e l l and o b s e r v i n g the b a l l above. T h i s presence would not change any a c t i o n . The student was o n l y an observer. The problem was to d e s c r i b e o b s e r v a t i o n s made from t h a t i n t e r n a l frame. The c o n s i s t e n c y of these d e s c r i p t i o n s w i t h those g i v e n from the e a r t h frame were noted. 3.26A and 3.26B The F a c t o r of Weight Versus the F a c t o r of Height These two tasks were a repeat of task3.23A w i t h one d i f f e r e n c e ~ the two shotputs were not i d e n t i c a l i n weight. The v a r i a b l e s of weight and h e i g h t were p i t t e d a g a i n s t each other i n the 'A' and 'B' forms of t h i s t a s k . One red 4 kg shotput was used with one y e l l o w 6 kg shotput. The student was r e q u i r e d to handle them to v e r i f y t h i s d i f f e r e n c e i n weight. In 3.26A the 4 kg shotput was on top and the 6 kg shotput was on the bottom. In 3.26B the 6 kg was on top and the 4 kg shotput was on the bottom. 3.27 The f a c t o r of Weight Versus The F a c t o r of I n i t i a l  V e l o c i t y - I n i t i a l S e p a r a t i o n T h i s task was a r e p e t i t i o n of task 3, .2 4A again with the same d i f f e r e n c e of weight i n the shotputs. Weight and 33 i n i t i a l v e l o c i t y were p i t t e d a g a i n s t each other u s i n g the 4 kg shotput on the top and the 6 kg shotput on the bottom. The h e i g h t c o u l d a l s o have been c o n s i d e r e d as a v a r i a b l e . 3.28 The F a c t o r of Weight Versus The F a c t o r of I n i t i a l  V e l o c i t y - Shotputs I n i t i a l l y Even T h i s task was a repeat of 3.25A again w i t h the same d i f f e r e n c e of weight i n the shotputs. Again, weight and i n i t i a l v e l o c i t y were p i t t e d a g a i n s t each other, but the i n i t i a l v e l o c i t y i s accentuated by a l l o w i n g the top shot-put to draw a l o n g s i d e the bottom one. 3.29 A d d i t i o n s A f t e r the i n t e r v i e w was completed, the student was i n v i t e d to add any f u r t h e r comments or i n f o r m a t i o n . In many cases the students wished to d i s c u s s the t a s k s . They wanted to know what the ' r i g h t ' answers were. 3.30 SUBJECTS Si x students were i n t e r v i e w e d a t f o u r d i f f e r e n t grade l e v e l s , making a t o t a l of twenty-four s u b j e c t s . These were s e l e c t e d from grade 6, grade 8, grade 10 and grade 11 students, r e s p e c t i v e l y . Each sample of s i x students from each grade was composed of three g i r l s and three boys. These s u b j e c t s were randomly s e l e c t e d from a g i v e n c l a s s of students by choosing names from subgroups of boys' and g i r l s ' names w r i t t e n on s l i p s of paper. 34 The grade 6 students were s e l e c t e d out of an average c l a s s of students from a North Vancouver e l e -mentary s c h o o l . The grade 8, grade 10 and grade 11 students were s e l e c t e d out of s c i e n c e c l a s s e s from a North Vancouver secondary s c h o o l . A l l of the grade 8 and grade 10 students were s e l e c t e d from g e n e r a l s c i e n c e c l a s s e s . General s c i e n c e i s a r e q u i r e d course f o r a l l grade 8 and 10 students. S i x grade 11 students were chosen from a P h y s i c s 11 c l a s s . T h i s i s an e l e c t i v e academic course. T h i s group had j u s t completed s e c t i o n f o u r (Motion i n One Dimension) i n A L a b o r a t o r y Course i n P h y s i c s . T h i s group, t h e r e f o r e , had completed i n s t r u c t i o n i n kinematics and were assumed to have competence i n a p p l y i n g the normal kinematics equation, graphs, and to understand the c o n s t a n t value of 'g', the a c c e l e r a t i o n due to g r a v i t y . T h i s grade 11 group was i n c l u d e d to determine i f there are any s i g n i -f i c a n t d i f f e r e n c e s i n the response p a t t e r n e d to those students who had not r e c e i v e d formal i n s t r u c t i o n i n k i n e m a t i c s . 35 CHAPTER FOUR R E S U L T S 4.00 INTRODUCTION Th i s chapter d e a l s with the methods of a n a l y s i s and r e s u l t s of the i n v e s t i g a t i o n . A Methods of A n a l y s i s s e c t i o n d e t a i l s the i n t e r p r e t a t i o n and c l a s s i f i c a t i o n of the responses task by task. Subtask responses are co n s i d e r e d w i t h i n the three major tasks d e a l i n g w i t h the c h a r a c t e r i s t i c s of f r e e - f a l l motion, the re l e v a n c e and behaviour of independent v a r i a b l e s a f f e c t i n g the motion, and the combined e f f e c t of the independent v a r i a b l e s . A R e s u l t s s e c t i o n f i r s t d e t a i l s the responses under the same th r e e major tasks mentioned above. A t a b l e of f r e q u e n c i e s of responses w i t h i n d e f i n e d c a t e g o r i e s i s giv e n f o r each of the three major t a s k s . T h i s t a b l e g i v e s f r e q u e n c i e s o f responses by grade, by grade and sex, and by sex. The grade 11 p h y s i c s group i s a l s o c o n s i d e r e d as a treatment by i n s t r u c t i o n group. T y p i c a l responses are quoted t o i l l u s t r a t e the c l a s s i f i c a t i o n system. Trends w i t h i n the data are then noted. 36 F o l l o w i n g t h i s , the R e s u l t s s e c t i o n d e t a i l s the g e n e r a l trends when a l l three major t a s k s are c o n s i d e r e d t o g e t h e r . Then, an e x p l a n a t i o n s e c t i o n uses q u o t a t i o n s to i l l u s t r a t e the sources c i t e d by the students f o r t h e i r b e l i e f s . F i n a l l y , there i s a d i s c u s s i o n of a few cases i n the grade 11 group i n which changes of mind o c c u r r e d . 4.10 METHODS OF ANALYSIS T h i s s e c t i o n d e t a i l s the methods used to c l a s s i f y the responses f o r the tasks d e s c r i b e d i n S e c t i o n s 3.21 through 3.28. The terms used f o r response c a t e g o r i e s are a l s o used i n the data t a b l e s which appear i n the R e s u l t s s e c t i o n which f o l l o w s . 4.11 The C h a r a c t e r i s t i c s of Motion of a S i n g l e Shotput  i n F r e e - F a l l (Table 4.1) The c h a r a c t e r i s t i c s of motion f o r a s i n g l e shotput i n f r e e - f a l l were s t u d i e d (tasks 3.21, 3.22). The f o l l o w i n g f o u r response c a t e g o r i e s were d e r i v e d from a n a l y s i n g the t r a n s c r i p t s (task 3.21): 1) Constant v e l o c i t y - The speed of the o b j e c t was constant from beginning to end. 2) A c c e l e r a t i o n as an impulse - The speed of the o b j e c t was i n c r e a s i n g i n a s h o r t impulse* o n l y i n the f i r s t 10 cm to a constant speed. 3) A c c e l e r a t i o n to a t e r m i n a l v e l o c i t y - The a c c e l e r a -t i o n decreased i n r a t e such t h a t a f i n a l c o n s t a n t or t e r m i n a l v e l o c i t y was achieved. 4) A c c e l e r a t i o n as a continuous a c t i o n - The a c c e l e r a -t i o n was uniform without being q u a l i f i e d . The word impulse w i l l be used to i n d i c a t e a c t i o n as a b u r s t over-a s h o r t time i n t e r v a l . 37 Only those students who i n d i c a t e d t h a t some form of a c c e l e r a t i o n was t a k i n g p l a c e proceeded to the next p a r t of task 3.22. In t h a t case two response c a t e g o r i e s were e v i d e n t : 1) A c c e l e r a t i o n as a continuous a c t i o n - Speed v a r i e d w i t h displacement. The p o i n t a t which the h a l f -way speed o c c u r r e d was the exact midpoint of the gap. 2) A c c e l e r a t i o n as a continuous a c t i o n - speed v a r i e s w i t h elapsed time - A l o c a t i o n other than the mid-p o i n t was chosen. An a p p r o p r i a t e e x p l a n a t i o n f o r t h i s c h o i c e was g i v e n . 4.12 The Relevance of Other F a c t o r s The r e l e v a n c e of the v a r i a b l e s of h e i g h t , i n i t i a l v e l o c i t y and weight were s t u d i e d (tasks 3.23 through 3.28). 4.121 The Relevance of Height as an Independent V a r i a b l e  A f f e c t i n g F r e e - F a i l Motion (Table 4.2) The f o l l o w i n g f o u r response c a t e g o r i e s were d e r i v e d from a n a l y s i n g the t r a n s c r i p t s f o r the f a c t o r of h e i g h t (tasks 3.23A, 3.23B). 1) Height i s not a f a c t o r - The gap between the two shotputs remained a c o n s t a n t v a l u e of 25 cm as they f e l l . 2) Height operates o n l y i n an impulse mode - The top shotput gained o n l y a s h o r t d i s t a n c e on the bottom one and no more a f t e r t h a t . 3) Height operates, but d i s s i p a t e s i n e f f e c t - The top shotput a t l e a s t overtook the bottom one or passed i t and then remained a f i x e d d i s t a n c e ahead. 4) Height operates as a continuous a c t i o n - The top shotput overtook the bottom one, passed i t and then continued to i n c r e a s e i t s s e p a r a t i o n . 4.122 The Relevance of I n i t i a l V e l o c i t y As An In-dependent V a r i a b l e A f f e c t i n g F r e e - F a i l Motion (Table 4.3) The f o l l o w i n g f o u r response c a t e g o r i e s were d e r i v e d from a n a l y s i n g the t r a n s c r i p t s f o r the f a c t o r of i n i t i a l v e l o c i t y (tasks 3.24A, 3.25A, 3.24B, 3.25B0). 38 1) I n i t i a l v e l o c i t y i s not a factor.-. - The i n i t i a l s e p a r a t i o n of 60 cm i n the delayed drop (task 3.24A, 3.24B) doesn't decrease as they f a l l . - They s t a r t even a t the 100 cm mark i n the second delayed drop. They remain even a l l the way down (task 3.25A, 3.25B). 2) I n i t i a l v e l o c i t y operates o n l y i n an impulse mode. - In the f i r s t delayed drop the i n i t i a l s e p a r a t i o n of 60 cm i s reduced o n l y a very l i t t l e and subsequently remains c o n s t a n t (tasks 3.24A, 3.24B). - In the second delayed drop they s t a r t even at the 100 cm mark. The one t h a t was dropped f i r s t gains o n l y a few cm then remains a f i x e d d i s t a n c e ahead or even l o s e s i t s advantage (tasks 3.25A, 3.25B). 3) I n i t i a l v e l o c i t y operates but d i s s i p a t e s i n i t s e f f e c t . - In the f i r s t delayed drop the i n i t i a l s e p a r a t i o n of 60 cm i s reduced. The one t h a t was dropped f i r s t a t l e a s t overtakes the bottom one, p o s s i b l y even passes i t • but subsequently remains a f i x e d d i s t a n c e ahead (tasks 3.24A, 3.24B). - In the second delayed drop they s t a r t even at the 100 cm mark. The one t h a t was dropped f i r s t passes the bottom one and then a t t a i n s a s u b s t a n t i a l s e p a r a t i o n which subsequently remains c o n s t a n t (tasks 3.25A, 3.25B). 4) I n i t i a l v e l o c i t y operates as a continuous a c t i o n . - In the f i r s t delayed drop the i n i t i a l s e p a r a t i o n of 6 0 cm i s reduced. The one t h a t was dropped f i r s t o v ertakes, passes and continues to i n c r e a s e i t s s e p a r a t i o n from the second one (tasks 3.24A, 3.24B). 39 In the second delayed drop they s t a r t even a t the 100 cm mark. The one t h a t was dropped f i r s t passes the second one and continues to i n c r e a s e i t s s e p a r a t i o n from the second one (tasks 3.25A, 3.25B). 4.123 The Relevance of Weight,as an Independent V a r i a b l e A f f e c t i n g F r e e - F a l l Motion (Table 4.4) The f o l l o w i n g four response c a t e g o r i e s were d e r i v e d Kfrom a n a l y s i n g - the t r a n s c r i p t s f o r the f a c t o r of weight (tasks 3.26A,3.26B) . 1) Weight i s not a f a c t o r . - I f two shotputs of unequal weight are separated by a d i f f e r e n c e i n h e i g h t and dropped s i m u l t a -neously, the r e s u l t i s the same whether the l i g h t e r one i s on top (task 3.26A) or the h e a v i e r one i s on the top (task 3.26B). 2) Weight operates o n l y i n a s h o r t impulse mode. - The h e a v i e r shotput gains a few centimetres and . no more on the l i g h t e r one (task 3.26A, 3.26B). 3) Weight operates,but d i s s i p a t e s i n i t s e f f e c t . - I f i t i s lower, the h e a v i e r one gains a s u b s t a n t i a l d i s t a n c e on the l i g h t e r one. T h i s d i s t a n c e of s e p a r a t i o n subsequently remains a constant value (task 3.26A). I f the heavier, one i s h i g h e r , i t at l e a s t catches the l i g h t e r one, passes i t and subsequently remains a f i x e d d i s t a n c e ahead (task 3.26B). 4) Weight operates as a continuous a c t i o n . - I f the h e a v i e r one i s on the bottom i t s s e p a r a t i o n from the l i g h t e r one continues to i n c r e a s e (task 3.26A). I f the h e a v i e r one i s higher, i t catches the l i g h t e r one, passes i t and "its s e p a r a t i o n from the l i g h t e r one continues to i n c r e a s e . 4.130 The Combined E f f e c t of V a r i a b l e s The study a l s o attempted to i s o l a t e the combined e f f e c t of the v a r i a b l e s of h e i g h t , weight and i n i t i a l v e l o c i t y . Each of the p o s s i b l e combinations of v a r i a b l e s had a-number l o g i c a l p o s s i b i l i t i e s . These were the f o l l o w i n g : 1) Neither; - of the v a r i a b l e s a c t . 2) Only the f i r s t v a r i a b l e i n a combination a c t s . 3) Only the second v a r i a b l e i n a combination a c t s . 4) Two v a r i a b l e s both a c t , b u t the f i r s t one was more important than the second one. I t s e f f e c t was st r o n g e r . 5) Two v a r i a b l e s both a c t w i t h equal s t r e n g t h or importance. 6) Two v a r i a b l e s both a c t , b u t the second one was more important or st r o n g e r than the f i r s t one. 4;131 The combined E f f e c t o f /the Independent V a r i a b l e s  H e i g ht and Weight (Table 4.5) The f o l l o w i n g s i x response c a t e g o r i e s were e v i d e n t : 1) N e i t h e r one i s a p p l i e d . - The i n i t i a l h e i g h t s e p a r a t i o n of 25 cm between shotputs of d i f f e r e n t weight remains . constant when dropped s i m u l t a n e o u s l y no matter which one i s h igher (task 3.26A, 3.26B). 2) Height o n l y i s a p p l i e d . The 25 cm h e i g h t d i f f e r e n c e decreases i n the same way f o r two.shotputs o f d i f f e r e n t weight no matter which one i s on top. (task 3.26A,.3.26B). 3) Weight o n l y i s a p p l i e d . - The 25 cm h e i g h t d i f f e r e n c e i n c r e a s e d immediately when the h e a v i e r one i s a t the bottom (task 3.26A) I t decreases immediately when the h e a v i e r one i s at the top (task 3.26B). 4) The e f f e c t s of h e i g h t and weight are of the same importance. - The 25 cm h e i g h t d i f f e r e n c e remains constant when the h e a v i e r one i s a t the bottom (task 3.26A) I t decreases r a p i d l y when the h e a v i e r one i s a t the top (task 3.26B). 41 5) The e f f e c t of h e i g h t i s more important than the e f f e c t of weight. - The 25 cm h e i g h t d i f f e r e n c e decreases when the he a v i e r one i s a t the bottom (task 3.26A). I t decreases much f a s t e r when the h e a v i e r one i s at the top (task 3.26B). 6) The e f f e c t o f weight i s more important than the e f f e c t of h e i g h t . - The 2 5 cm h e i g h t d i f f e r e n c e i n c r e a s e s when the he a v i e r one i s a t the bottom (task 3.26A). I t overtakes the bottom one a t a f a s t e r r a t e when the h e a v i e r one i s a t the top. 4.132 The Combined E f f e c t of the Independent V a r i a b l e s I n i t i a l V e l o c i t y and Weight (Table 4.6). The f o l l o w i n g s i x response c a t e g o r i e s were e v i d e n t . 1) N e i t h e r one i s a p p l i e d . - I f the i n i t i a l s e p a r a t i o n was 60 cm i n the f i r s t delayed drop wi t h shotputs of d i f f e r e n t weight (task 3.27) the s e p a r a t i o n remained a t t h a t v a l u e . - I f they were even a t the 100 cm mark i n the second delayed drop w i t h shotputs of d i f f e r e n t weight (task 3.28) they remained even the r e s t of the way down. 2) I n i t i a l v e l o c i t y o n l y i s a p p l i e d . - In the same f i r s t delayed drop the i n i t i a l s e p a r a t i o n o f 60 cm decreased with time (task 3.27) . - In the second delayed drop where they were even at the 100 cm mark (task 3.28) the one t h a t was dropped f i r s t passed the second h e a v i e r one. - The p r e d i c t i o n s i n both of the tasks above was the same as the p r e d i c t i o n s f o r the e q u i v a l e n t tasks i n which t h e r e was no weight d i f f e r e n c e (tasks 3.24, 3.25). 3) Weight o n l y i s a p p l i e d . - In the same f i r s t delayed drop i f the i n i t i a l s e p a r a t i o n of the shotputs was 60 cm (task 3.27) t h i s s e p a r a t i o n began to i n c r e a s e as soon as the lower h e a v i e r shotput was r e l e a s e d . 42 - In the same second delayed drop i f the two shotputs were even a t the 100 cm mark (task 3.28), the lower h e a v i e r one immediately began to g a i n d i s t a n c e on the one t h a t was dropped f i r s t . 4) I n i t i a l v e l o c i t y i s equal i n e f f e c t to weight. - In the same f i r s t delayed drop i f the i n i t i a l s e p a r a t i o n of the shotputs was 60 cm (task 3.27), the gap remained the same from the beginning or s h o r t l y t h e r e a f t e r . - In the same second delayed drop i f the two shotputs were even a t the 100 cm mark (task 3.28), the top l i g h t e r one passed the bottom one. The gap between the two e i t h e r remained c o n s t a n t or the h e a v i e r one-overtook the l i g h t e r one, and then they remained even f o r the r e s t of the f a l l . 5) Weight has a g r e a t e r e f f e c t than i n i t i a l v e l o c i t y . - In the same second delayed drop i f the two shotputs were even a t the 100 cm mark (task 3.28), the top l i g h t e r shotput f i r s t passed the bottom one. A f t e r t h i s , the h e a v i e r one overtook the l i g h t e r one, passed i t and continue to have the advantage of a f a s t e r speed or a c c e l e r a t i o n . 6) I n i t i a l v e l o c i t y has a g r e a t e r e f f e c t than weight. - In the same second delayed drop i f the two shotputs were even a t the 100 cm mark (task 3.28), the h e a v i e r shotput receded behind the l i g h t e r one which had the advantage of an i n i t i a l v e l o c i t y . 4.133 The Combined E f f e c t of the Independent V a r i a b l e s  Height and I n i t i a l V e l o c i t y The f o l l o w i n g four of the s i x p o s s i b l e response c a t e g o r i e s were e v i d e n t : 1) N e i t h e r one i s a p p l i e d . - In the f i r s t delayed drop w i t h shotputs of equal weight the i n i t i a l s e p a r a t i o n (between the top and bottom shot-puts) was 60 cm. T h i s s e p a r a t i o n remained the same s i z e as t h e y . f e l l . 43 2) Height o n l y i s a p p l i e d . - In the task i n v o l v i n g the simultaneous drop of two shotputs o f equal weight (task 3.23) there was an i n i t i a l s e p a r a t i o n o f 25 cm. A h e i g h t advantage i s a p p l i e d . No a d d i t i o n a l advantage i s gi v e n to the top shotput i f i t - i s dropped f i r s t (task 3.24, 3.25). 3) I n i t i a l v e l o c i t y o n l y i s a p p l i e d . - The top shotput has no advantage i n the simultaneous drop of two shotputs of equal weight with a 2 5 cm h e i g h t s e p a r a t i o n (task 3.23A, 3.23B). However, the top one does have an advantage i n the delayed drop (task 3.24A, 3.24B). 4) I n i t i a l v e l o c i t y and h e i g h t e f f e c t s add. -> Height i s an advantage f o r the top shotput i n the simultaneous drop w i t h an i n i t i a l h e i g h t d i f f e r e n c e (task 3.24A, 3.23B). Height and i n i t i a l v e l o c i t y are d e s c r i b e d as a double advantage f o r the top shotput. These add together f o r the top shotput when the bottom one i s delayed (task 3.24, 3.25). 4.20 RESULTS T h i s s e c t i o n has three s u b s e c t i o n which r e f e r back to the th r e e corresponding S e c t i o n s 4.11, 4.12 and 4.13, r e s p e c t i v e l y . In each case a t a b l e of r e s u l t s i s g i v e n , t y p i c a l responses are quoted to i l l u s t r a t e the c l a s s i f i c a -t i o n system c l e a r l y and trends within the data are de-l i n e a t e d . In a d d i t i o n , S e c t i o n 4.24 d e l i n e a t e s the o v e r a l l trends w i t h i n the data and S e c t i o n 4.25 d e t a i l s the o r i g i n s of the b e l i e f s d e t a i l e d . Table 4.1 The C h a r a c t e r i s t i c s of Motion of a Single Shotput i n Free-F a l l (From Tasks 3.21 and 3.22) Constant Acceleration Acceleration to a Acceleration as a Acceleration Group V e l o c i t y as an Impulse Terminal Velocity Continuous Action as a Continuous Speed Varies With Action Speed Displacement Varies with Elapsed Time TOTALS BY GRADE Grade 6 3 0 0 3 0 Grade 8 0 1 2 1 2 Grade 10 1 1 2 1 1 *Grade 11 0 0 0 4 2 Totals 4 2 4 9 5 TOTALS BY SEX G i r l s 2 0 0 6 4 Boys 2 2 4 3 1 Totals 4 2 4 9 5 TOTALS BY SEX AND GRADE GIRLS Grade 6 1 0 0 2 0 Grade 8 0 0 0 1 2 Grade 10 1 0 0 1 1 Grade 11 0 0 0 2 1 BOYS Grade 6 2 0 0 1 0 Grade 8 0 1 2 0 0 Grade 10 0 1 2 0 0 Grade 11 0 0 0 2 1 Totals 4 2 4 9 5 * Instruction Group 45 4.212 Typical Responses The quotations c i t e d are accompanied by the c l a s s i f i -cations assigned to them as well as other pertinent i n -formation. I. - Interviewer ; S. - Subject 1) CLASSIFICATION - Constant v e l o c i t y , no acceleration. Subject - L. a grade 6 g i r l . Gaps Marked by the Subject - (50-60); (100-110); (150-160) ; (200-210) . Quotation - For task 3.21: I. - "Why did you place the pegs that way?1' S. - "'Cause i f i t ' s 10 cm at the top i t would s t i l l f a l l the same coming down." I. - "How do the speeds i n the gaps compare?" S. - "They're the same." I. - " A l l the way down?" S. - "Yes." 2) CLASSIFICATION - Acceleration as a short impulse. Subject - P.G. a grade 8 boy. Gaps marked by the Subject - (50-60); (100-110); (150-160); (200-210). Quotations - (For 3.21>) "Why did you indicate the gaps i n that way?" "Because up at the top they were 10 cm apart so down below they should be the same." "Why do you think so?" "Objects move pretty much the same speed going down." I. -S. -I . -s . -46 In task 3.25 a s h o r t impulse of a c c e l e r a t i o n i s d e s c r i b e d . S. - "Voufti, would go a little, bit lutithth. b&cauAe. mine, would have, to i>tant up." I. - "Would i t pass?" S. - " I t would pass a couple of cen t i m e t r e s and then stay the same." 3) CLASSIFICATION - A c c e l e r a t i o n which d i s s i p a t e d to a t e r m i n a l v e l o c i t y . S u b j e c t - L.W. a grade 10 boy. Gaps Marked by the Subject - (50-65); (100-140); (150-200) ; (200-260) . Quotation — For task 3.21 I. - "What would happen i f the shotput c o u l d f a l l f u r t h e r ? " S. - "The b a l l would g a i n speed up to a c e r t a i n p o i n t and then, u l t i m a t e l y , because of the f o r c e of g r a v i t y , i t can't go any f a s t e r . I t i s o n l y so stro n g ... I t ( g r a v i t y ) w i l l a l l o w i t (the shotput) to go to a c e r t a i n speed and w i l l s t ay the same f o r the r e s t of i t s f a l l . " 4) CLASSIFICATION - A c c e l e r a t i o n i n a continuous manner. Subject - K.C. a grade l o g i r l . Gaps Marked by the Subject - (950-64); (100-120); (150-178); ( 2 0 0 - f u r t h e r ) . Quotations - For task 3.21 I. - "Why d i d you put the cloth e s p e g s f u r t h e r a p a r t ? " S. - "'Cause the b a l l i s going f a s t e r . Probably i t gained momentum as i t comes down." I. - "What would happen i f i t c o u l d f a l l f u r t h e r ? " S. - "The speed of the b a l l would be i n c r e a s i n g , and the d i s t a n c e would be i n c r e a s i n g . " 47 5) CLASSIFICATION - Speed v a r i e s d i r e c t l y w i t h displacement. Subject - D.C. a grade 11 boy. P o s i t i o n Marked i n Second Gap - In a gap running from 100 to 200 the 150 cm p o i n t was chosen f o r the occurrence o f the halfway speed. Quotations T For task 3.21 i n r e f e r e n c e t o the second gap. S. - " I t ' s going f i v e times as f a s t t here (points to 50) so t h a t means i t w i l l be f i v e times the d i s t a n c e . " For task 3.22. I. - "At what p o i n t i n the gap w i l l the speed occur which i s halfway between the f a s t speed and the slowest speed?" S. - "150 cm." I. - "Why?" S. - "H a l f the d i s t a n c e ; h a l f the speed." 6) CLASSIFICATION - Speed v a r i e s w i t h elapsed time. Subject - K.K. a grade 8 g i r l . P o s i t i o n Marked i n Second Gap - In a gap running from 100 to 112 cm a p o i n t i n the f i r s t h a l f of the gap was chosen. Quotation - For task 3.22 I. - "At which p o i n t i s i t going a t a speed halfway between the f a s t e s t and slowest speeds i n the gap?" S. - " J u s t before h a l f of the number. L i k e t h e r e ' s twelve centimetres here (points),;, so maybe i t would be f i v e . " I. - "Why i s t h a t ? " S. - "Because as i t ' s p i c k i n g up s p e e d , i t doesn't take as much time... 48 so i t would... I t ' s not going the same speed a l l the way down,so you c o u l d n ' t say i n the middle i t ' s j u s t halfway... I t ' s hard to e x p l a i n . " 4.213 Trends In the Data f o r the C h a r a c t e r i s t i c s o f A c c e l e r a t i o n The f o l l o w i n g trends are e v i d e n t i n the r e s u l t s : 1) Only three of the grade 6 students a p p l i e d a c c e l e r a t i o n . 2) A l l other students a p p l i e d a c c e l e r a t i o n with the e x c e p t i o n of the grade ten student. 3) The three grade 6 students who a p p l i e d a c c e l e r a t i o n d i d not q u a l i f y i t i n any way. I t was simply a continuous a c t i o n . 4) No g i r l s a t any l e v e l q u a l i f i e d a c c e l e r a t i o n as r e a c h i n g a t e r m i n a l v e l o c i t y or as o p e r a t i n g i n the form of a s h o r t impulse. 5) S i x boys i n grade 8 and 10 q u a l i f i e d a c c e l e r a t i o n as having a t e r m i n a l v e l o c i t y or as o p e r a t i n g i n the form of a s h o r t impulse. 6) In the grade 11 i n s t r u c t i o n group a c c e l e r a t i o n was t r e a t e d by a l l students as having a continuous form of a c t i o n . 7) No grade 6 students c o n s i d e r e d t h a t speed v a r i e d w i t h e l a p s e d time. Those who accepted a c c e l e r a t i o n c o n s i d e r e d t h a t speed v a r i e d with displacement. 8) The v e l o c i t y v a r i e s w i t h displacement i n t e r -p r e t a t i o n of a c c e l e r a t i o n o c c u r r e d a t a l l grade l e v e l s , even i n the grade e l e v e n treatment group. 4.2212 T y p i c a l Responses - The E f f e c t of Height 1) CLASSIFICATION - Height i s not a r e l e v a n t f a c t o r . S u b j e c t - S. a grade 6 boy. Quotation - For task 3.2 3A Table 4.2 The Relevance of Height as an Independent Variable Affecting F r e e - F a l l Motion (From Tasks 3.23A and 3.23B) Is not A Operates Only i n An Operates But Dissipates Operates As Group Factor Impulse In Its Ef f e c t A Continuous Action TOTALS BY GRADE Grade 6 5 1 0 0 Grade 8 3 0 1 2 Grade 10 2 0 3 1 *Grade 11 4 0 2 0 TOTALS 4 0 2 0 TOTALS BY SEX GIRLS 4 1 4 3 BOYS 10 0 2 0 TOTALS 14 1 6 3 TOTALS BY SEX AND GRADE GIRLS Grade 6 2 1 0 0 Grade 8 1 0 0 2 Grade 10 0 0 2 1 Grade 11 1 0 2' 0 BOYS Grade 6 3 0 0 0 Grade 8 2 0 1 0 Grade 10 2 0 1 0 Grade 11 3 0 0 0 TOTALS 14 1 6 3 Instruction Group 50 I. - " C o u l d you d e s c r i b e the gap between the two as they f a l l ? " S. - " L e t ' s see . I t ' s 25 a t the t o p , s o i t ' d keep 25 cm as i t f e l l . " I. - "Would i t s tay 25?" S. - "Yes" I . - "Why?" S. - "One was dropped lower than the o t h e r , a n d t h e y ' r e the same weight , and they get going a t the same t i m e " . 2) CLASSIFICATION - H e i g h t i s a f a c t o r which operates o n l y as an i m p u l s e . Sub jec t - S . G . a grade 6 g i r l . Quota t ions - For task 3 .23A: S. - " W e l l , they might come c l o s e r t o g e t h e r as they come to the ground. The space w i l l become s h o r t e r . " I . - " W i l l i t c a t c h up?" S. - "Not a l l the way?" For t a s k 3.2 3B: S. - "The b a l l w i l l p r o b a b l y come c l o s e r . . . t h e top one and s t a y the same." 3) . CLASSIFICATION - H e i g h t as a f a c t o r d i s s i p a t e s s l o w l y i n i t s e f f e c t . S u b j e c t - P . M . a grade 8 boy . Q u o t a t i o n - For task 3.2 3A S. - " I t h i n k t h a t one, the one on the t o p , would go f a s t e r because i t has more room. L i k e t h i s one ( p o i n t s to the bottom one) has l e s s . You s t a r t e d i t l o w e r . T h i s one ( p o i n t s to the top one) has more of a chance , because i t has more space between t h i s one and t h a t . . . and t h a t one. So i t h a s . . . T h i s one ( p o i n t s to the top one) uses up t h i s f a r ( i n d i c a t e s the 25 cm gap) to c a t c h up t h a t amount ( h e i g h t ) . So t h i s one (top) 51 a l r e a d y d i d t h i s , a n d i t a l r e a d y has f a s t e r speed by the time i t reaches t h i s p a r t ( p o i n t s to the 25 cm mark)., and t h i s one (bottom) s t i l l i s slower from when you r e l e a s e i t . " I. - "Would i t c a t c h the bottom one?" S. - "Itwould c a t c h i t j u s t a l i t t l e lower than where you r e l e a s e d t h i s one (bottom)." I. - "About where would t h i s happen?" S. - "40 cm." I. - "Would i t pass?" S. - "The top one would h i t the ground f i r s t . " I. - "What would the s e p a r a t i o n between them be?" S. - "There won't be much of a gap near the end. I t would stay the same. I t (lower one) might c a t c h up again. No. That one, the one t h a t was a t the top would win." I. - "What would happen t o the gap between them a f t e r the top one passed?" S. - " I t would stay the same or get l e s s again." 4) CLASSIFICATION - Height as a f a c t o r a c t s i n a continuous mode." Sub j e c t - S.S. a grade 8 g i r l . Quotations - For task 3.23A: S. - "I t h i n k t h a t i f they're dropped over a g r e a t e r d i s t a n c e , t h e one t h a t ' s got more h e i g h t would g a i n more speed and cat c h up." I. - " W i l l i t pass?" S. - " I t w i l l probably pass." I. - "Why?" S. - "Because it'.s (bottom) s t i l l g a i n i n g speed a l l the time,but not at the same r a t e ; " 52 For task 3.2 3B: I. - "What would you see as you looked up?" S. - "Th i s g r e a t b a l l speeding towards you and s l o w l y c a t c h i n g up with you... I t would leave you behind." 4.2213 Trends ,in the Data f o r ,fhe S i g n i f i c a n c e  pf Height The f o l l o w i n g trends are e v i d e n t i n the r e s u l t s : 1) In a l l cases a d d i t i o n a l h e i g h t was e i t h e r an advantage or was not a f a c t o r a t a l l . I t never was c o n s i d e r e d t o be a disadvantage. 2) F i v e of the s i x grade 6 students d i d not apply the v a r i a b l e . The one g i r l who d i d apply i t c o n s i d e r e d t h a t i t acted as a s h o r t impulse o n l y . 3) E i g h t of the twelve g i r l s a p p l i e d the f a c t o r of h e i g h t i n some form. 4) Ten of the twelve boys d i d not apply i t i n any form. The two who d i d apply i t c o n s i d e r e d t h a t i t d i s s i p a t e d i n e f f e c t . 5) Two of the three grade ele v e n p h y s i c s g i r l s s t i l l a p p l i e d the f a c t o r of h e i g h t i n a d i s s i p a t i n g form of a c t i o n . 6) No p h y s i c s 11 b o y s - a p p l i e d the f a c t o r i n V.. any form. 4.2222 T y p i c a l Response - The E f f e c t o f I n i t i a l V e l o c i t y 1) CLASSIFICATION - I n i t i a l v e l o c i t y i s not con-s i d e r e d . S u b j e c t - i . a grade 6 g i r l . Quotations - For task 3.24A: I. - "How f a r a p a r t are they at the beginning?" S. - " !:60 cm ap a r t . " Table 4.3 The Relevance of I n i t i a l V e l o city As An Independent Variable A f f e c t i n g F r e e - F a l l Motion (From Tasks 3.24A, 3.24B, 3.25A, and 3.25B) Group Is Not A Factor Operates Only In An Impulse Mode Operates But Dissipates i n Its Ef f e c t Operates As A Continuous Action TOTALS BY GRADE Grade 6 Grade 8 Grade 10 *Grade 11 3 0 1 0 2 1 1 0 0 2 3 3 1 3 1 3 TOTALS 4 4 8 8 TOTALS BY SEX GIRLS BOYS 2 2 2 • 2 3 5 5 3 TOTALS 4 4 8 8 TOTALS BY SEX AND GRADE GIRLS Grade 6 Grade 8 Grade 10 Grade 11 1 0 1 0 2 0 0 0 0 0 1 2 0 3 1 1 BOYS Grade 6 Grade 8 Grade 10 Grade 11 2 0 0 0 0 1 1 0 0 2 2 1 1 0 0 2 TOTALS 4 4 8 8 Instruction Group L n I. - "What happens t o t h i s gap as they both f a l l ? " S. - "They would be 60 cm ap a r t . " For task 3.24B: I. - "What would you see?" S. - "A red b a l l f a l l i n g 60 cm on top of me." For task 3.25A: S. - "They drop a t the same time and h i t the f l o o r t o gether." I. - "Do they stay together a l l the way?" S. - "Yes." For task 3.25B: S. - " I ' d see a b a l l b e s i d e me as I'm going down." 2) CLASSIFICATION - I n i t i a l v e l o c i t y operates as a s h o r t impulse o n l y . Subject - P.G. a grade 8 boy. Quotations - For task 3.24A: S. - "Yours would go l i t t l e b i t f u r t h e r , because mine would have to s t a r t up." I. - "Would i t pass?" S. - " I t would pass a couple of centimetres and then stay the same." 3) CLASSIFICATION - I n i t i a l v e l o c i t y operates but wi a s l o w l y d i s s i p a t i n g e f f e c t . S u b j e c t - P.M. a grade 8 boy. Quotations - For task 3.25A: S. - " I t passes, goes t o a c e r t a i n p o i n t ahead and stays t h a t f a r ahead." I. - "Why does t h a t happen?" 55 S. - "The f i r s t one's a l r e a d y going? so i t passes the second one. Then,the second one s t a r t s and the space i s a l r e a d y there where ... where i t ' s a l r e a d y going i n the f i r s t p l a c e (100 cm) ... and t h a t a f t e r the second one goes, the g r a v i t y i s the same on both of them and j u s t so they go down at the same r a t e . So,the space sta y s the same." For task 3.25B: S. - " I ' d see i t go p a s t me?and then i t ' d follow,and then I'd be f o l l o w i n g i t . Because the d i s t a n c e between us... I t would be going down a t the same v e l o c i t y a f t e r a w h i l e . " 4) CLASSIFICATION - I n i t i a l v e l o c i t y operates i n a continuous manner. Subject - K.C. a grade 10 g i r l . Q uotations - For task 3.24A S. - "The f i r s t one (top) would have a l i t t l e more of a chance to go f a s t e r , s o maybe (pause) t h i s one (top) would c a t c h up a l i t t l e b i t . I guess maybe i t ' l l ... Yeah! I guess i t should j u s t keep c a t c h -i n g up and pass the o t h e r one (lower) ... The d i s t a n c e between them would i n c r e a s e . " I. - "Why would t h i s happen?" S. - "Because i f t h i s one (top) i s going f a s t e r when i t ' s f a l l i n g and so ... because i t has t h a t d i s t a n c e (40 cm separation) a t f i r s t , the d i s t a n c e between 40 cm and 100 cm... I t ' s going to have t h a t e x t r a l i t t l e push i n the beginning,and i t w i l l keep going." 4.2223 Trends .In the Data f o r ,'the S i g n i f i c a n c e of  I n i t i a l V e l o c i t y The f o l l o w i n g trends are e v i d e n t i n the r e s u l t s : 1) T h i s f a c t o r was not a p p l i e d by 3 grade 6 students. Two a d d i t i o n a l students o n l y a p p l i e d the f a c t o r as a s h o r t impulse^while one boy a p p l i e d i t i n a continuous manner. 2) The f a c t o r was a p p l i e d to some extent by a l l the r e s t of the students except by one grade 10 g i r l . 56 3) Of the twenty students who a p p l i e d the f a c t o r , o n l y e i g h t c o n s i d e r e d i t to p r o v i d e a continuous advantage. Only one of these e i g h t was a grade 6 student. 4) Three of the grade 11 students s t i l l b e l i e v e d t h a t the advantage provided by an i n i t i a l v e l o c i t y s l o w l y d i s s i -pated . 4.2232 T y p i c a l Responses - The E f f e c t o f Weight 1) CLASSIFICATION - Weight i s not r e l e v a n t . S u b j e c t - L. a grade 6 g i r l . Quotations - For task 3.26A: S. - "They should stay the same." I. - "Why?" S. - "They stay the same because the p u l l of g r a v i t y i s the same as ... the same whether an o b j e c t ' s h e a v i e r or l i g h t e r . " For task 3.26B: S. - " I t would be 25 cm a p a r t (as they f e l l ) . " I. - " A l l the way down?" S. - "Yes, a l l the way down." 2) No cases o c c u r r e d i n which weight was d e s c r i b e d as o p e r a t i n g i n an impulse made of a c t i o n . 3) CLASSIFICATION - Weight d i s s i p a t e s as a f a c t o r . S u b j e c t - K.S. a grade 6 boy. Quotations - For task 3.26B: I. - "Would the top one c a t c h up?" S. - "Maybe ... i f i t c o u l d f a l l a long way ... I guess so." I. - "Would i t pass?" S. - "No." I. - "Why not?" S. - "I don't know. They would probably j u s t c a t c h up ... and stay even." Table 4.4 The Relevance of Weight As An Independent Variable Affecting Free-Fall Motion (From Tasks 3.26A and 3.26B) Is Not A Operates Only In An Operates But Operates As A Group Factor Impulse Mode Dissipates In Continuous Its E f f e c t Action TOTALS BY GRADE Grade 6 1 0 0 5 Grade 8 2 0 0 4 Grade 10 1 0 1 4 *Grade 11 1 0 0 5 TOTALS 5 0 1 18 TOTALS BY SEX GIRLS 2 0 1 9 BOYS 3 0 0 9 TOTALS 5 0 1 18 TOTALS BY SEX AND GRADE GIRLS Grade 6 1 0 0 2 Grade 8 1 0 0 2 Grade 10 0 0 1 2 Grade 11 0 0 0 3 BOYS Grade 6 0 0 0 3 Grade 8 1 0 0 2 Grade 10 1 0 0 2 Grade 11 1 0 0 2 TOTALS 5 0 1 18 * Instruction Group 58 4) CLASSIFICATION - Weight operates i n a continuous manner. Subject - L. a grade 11 g i r l . Quotations - For task 3.26A: I. - "What happens to the distance between them?" S. - " I t spreads apart. That one (top) goes slower and th i s one (bottom) goes faster than that one." I. - "Do they keep spreading apart?" S. - "I guess so." I. - "Why?" S. - "This one i s heavier so i t f a l l s faster than that one." 4.22 3 3 Trends In The Data For The Significance Of Weight The following trends are evident i n the r e s u l t s : 1) The factor of weight was applied by most of the students (19 of 24). 2) The factor was applied by a l l groups; for example, by 5 of 6 grade eleven students. 3) The factor was applied by 9 boys and by 10 g i r l s . 4) The factor was applied as a continuous i n -fluence i n a l l but one of the 19 cases. This exception was a grade ten g i r l who interpreted i t as a di s s i p a t i n g factor with time. 4.2312 Typical Responses - The Combined E f f e c t Of Height  and Weight 1) CLASSIFICATION - The Height and weight variables are roughly equal i n e f f e c t . Quotations - For task 3.26A: S. - "I think that they w i l l probably go the same speed Table 4.5 The Combined E f f e c t of The Independent Variables Height and Weight (From Tasks 3.26A and 3.26B) Neither One Height Only Weight Only The E f f e c t s Of The E f f e c t The E f f e c t Is Applied Is Applied Is Applied Height and Weight Of Height Of Weight roup Are Of The Same Is More Is More Importance Important Important Than The Than The Ef f e c t Of Ef f e c t Of Weight Height TOTALS BY GRADE Grade 6 1 0 5 0 0 0 Grade 8 1 1 2 1 0 1 Grade 10 1 0 1 1 0 3 *Grade 11 1 0 3 0 0 2 TOTALS 4 1 11 2 0 6 TOTALS BY SEX GIRLS 1 1 4 2 0 4 BOYS 3 0 7 0 0 2 TOTALS 4 1 11 2 0 6 TOTALS BY SEX AND GRADE GIRLS Grade 6 1 0 2 0 0 0 Grade 8 0 1 1 1 0 0 Grade 10 0 0 0 1 0 2 Grade 11 0 0 1 0 0 2 BOYS Grade 6 0 0 3 0 0 0 Grade 8 1 0 1 0 0 1 Grade 10 1 0 1 0 0 1 Grade 11 1 0 2 0 0 0 TOTALS 4 1 11 2 0 6 Instruction Group cn 60 down,because t h a t h e a v i e r one w i l l go down q u i t e f a s t because i t ' s heavy,and h e a v i e r t h i n g s f a l l quicker., and I t h i n k they w i l l probably f a l l t o g e t h e r . : ... I t h i n k t h a t a t f i r s t i t w i l l not be t w e n t y - f i v e centimetres any more ... be l e s s . The top b a l l catches up a l i t t l e b i t . T h e n , t h e y ' l l probably stay a c e r t a i n space d i f f e r e n t ... a couple o f m i l l i m e t r e s d i f f e r e n t . " For task 3.26B: S. - "The h e a v i e r one would c a t c h up and probably pass the l i g h t e r one." I. - "Why?" S. - "The h e a v i e r one has more speed (height) and more weight, so i t would probably pass the l i g h t e r one." I. - "Why?" S. - "The h e a v i e r one has more speed (height) and more weight so, i t would probably pass the s m a l l e r one'.' 2) CLASSIFICATION - No cases o c c u r r e d i n which h e i g h t was c o n s i d e r e d to overcome the f a c t o r of weight. 3) CLASSIFICATION - Weight'is a much more important f a c t o r than h e i g h t . " Quotations - For task 3.26A: S. - "The d i s t a n c e (between) i n c r e a s e s . " I. - "Why?" S. - "Because t h a t one (lower) i s h e a v i e r . I t has more p u l l . There's more weight to p u l l i t downwards, and the speed i n c r e a s e s . " For task 3.26B: S. - "Between them (distance) would decrease, then i n c r e a s e a g a i n . Increase as i t passes." 61 4.2313 Trends ,in ;the Data ,:for ;:the Combined E f f e c t  of Height and Weight. The following trends are evident i n the r e s u l t s : 1) 16 of the 24 students did not consider both variables at the same time. 2) 4 students ignoredboth variables. 3) 11 students applied weight only. 4) Only 1 student applied height while ignoring weight as a factor. 5) In no case was height considered to dominate weight. 6) 6 students considered that weight dominated height. 7) Only 2 students, both g i r l s , applied height and weight as having, equal s i g n i f i c a n c e . 8) Grade 6 students did not compare these two variables,although i t must be pointed out that only one had applied height previously. 4.2322 Typical Responses - The Combined E f f e c t between  I n i t i a l V e l o c i t y and Weight 1) CLASSIFICATION - I n i t i a l v e l o c i t y and weight have equal importance. Subject - E.A. a grade 8 g i r l . Quotation - For task 3.28: I. - "Would the top one pass?" S. - "Maybe just a l i t t l e bit, but not that much at a l l . " I. - "What i f i t f e l l further?" S. - " I t wouldn't change that much." I. - "Why not?" S. - "It'd probably stay about the same because i t (top) would have a chance to get faster and faster,but t h i s one (bottom) i s heavier." Table 4.6 Combined E f f e c t Of The Independent Variables I n i t i a l V e l o city And Weight (From Tasks 3.27 and 3.28) Neither One I n i t i a l V e l o c i t y Weight Only I n i t i a l V e l o city Weight Has I n i t i a l Group Is Applied Only Is Applied Is Applied Is Equal In E f f e c t A Greater V e l o c i t y To Weight E f f e c t Than Has A I n i t i a l Greater V e l o c i t y E f f e c t Than Weight TOTALS BY GRADE Grade 6 1 1 3 0 1 0 Grade 8 0 2 0 1 3 0 Grade 10 0 1 1 1 3 0 *Grade 11 0 1 0 1 4 0 TOTALS 1 5 4 3 11 0 TOTALS BY SEX GIRLS 1 2 1 2 6 0 BOYS 0 3 3 1 5 0 TOTALS 1 5 4 3 11 0 TOTALS BY SEX AND GRADE GIRLS Grade 6 1 1 0 0 1 0 Grade 8 0 1 0 1 1 0 Grade 10 0 0 1 1 1 0 Grade 11 0 0 0 3 0 0 BOYS Grade 6 0 0 3 0 0 0 Grade 8 0 1 0 0 2 0 Grade 10 0 1 0 0 2 0 Grade 11 0 1 0 1 1 0 TOTALS 1 5 4 3 11 0 * Instruction Group 63 2) CLASSIFICATION - Weight dominates the e f f e c t on i n i t i a l v e l o c i t y . S ubject - G.P. a grade 11 boy. Quotations - For task 3.27: S. - "The space (between) begins to i n c r e a s e almost r i g h t away." I. - "Why?" S. - "Because the heavy one w i l l go f a s t e r . The l i t t l e one w i l l i n c r e a s e i n speed except the b i g one w i l l i n c r e a s e f a s t e r . " For task 3.28: S. - "I guess the l i g h t one would pass i t and as soon as you dropped the h e a v i e r one* i t would c a t c h the l i g h t e r one and pass i t again a t some p o i n t . I t w i l l keep a c c e l e r a t i n g w i t h t h a t one ( l i g h t ) except the space (between) would keep on g e t t i n g g r e a t e r . " 3) No cases o c c u r r e d i n which i n i t i a l v e l o c i t y had a g r e a t e r e f f e c t than weight. 4.2323 Trends In /the Data f o r ;the Combined E f f e c t of  I n i t i a l V e l o c i t y and Weight. 1) There was onl y one case from the grade 6 students i n which these two v a r i a b l e s were compared. 2) No students c o n s i d e r e d t h a t the e f f e c t of i n i t i a l v e l o c i t y was g r e a t e r than the e f f e c t of weight. 3) 11 of the 24 students c o n s i d e r e d t h a t the e f f e c t of weight was more important than the e f f e c t of an i n i t i a l v e l o c i t y . 4.2332 T y p i c a l Responses - The Combined E f f e c t of Height  and I n i t i a l V e l o c i t y CLASSIFICATION - The e f f e c t s of i n i t i a l v e l o c i t y and h e i g h t add. Subject - S.S. a grade 6 g i r l . Q uotations - For Task 3.23A: Table 4.7 The Combined E f f e c t s Of The Independent Variables Height And I n i t i a l V e l o city (From Tasks 3.24A, 3.24B, 3.25A and 3.25B) Neither One Is Height Only Is I n i t i a l Velocity I n i t i a l Velocity Group Applied Applied Only Is Applied And Height E f f e c t s Add TOTALS BY GRADE Grade 6 3 0 3 0 Grade 8 0 0 3 3 Grade 10 0 1 5 0 *Grade 11 0 0 6 0 TOTALS 3 1 17 3 TOTALS BY SEX GIRLS 1 1 8 2 BOYS 2 0 9 1 TOTALS 3 1 17 3 TOTALS BY SEX AND GRADE GIRLS Grade 6 1 0 2 0 Grade 8 0 0 1 2 Grade 10 0 1 2 0 Grade 11 0 0 3 0 BOYS Grade 6 2 0 1 0 Grade 8 0 0 2 1 Grade 10 0 0 3 0 Grade 11 0 0 3 0 TOTALS 3 1 17 3 Instruction Group 65 S. - "I think that i f i t ' s ... they're dropped over a greater distance,the one that's got more height would gain more speed and catch up." For task 3.34A: S. - "Just l i k e i n the l a s t one,I think that the one that was dropped from the highest point would s t i l l catch up 'cause i t ' s had a head s t a r t . It's moving faster,and i t ' s higher." The comparisons between these two variables were much more d i f f i c u l t to make. Often the responses were not as e x p l i c i t with respect to t h i s comparison as i n the other cases. 4.2333 Trends ,jri the Data for the Combined E f f e c t df Height  and I n i t i a l V e l o c i t y 1) No grade six, ten or eleven students e x p l i c i t l y considered these variables at the same time. 2) Most students (17 out of 24) considered i n i t i a l v e l o c i t y only when both were present. 3) Only one student considered height alone while ignoring i n i t i a l v e l o c i t y . 4.24 Trends- i n the Data Taken as a. Whole 1) Grade 6 boys did not q u a l i f y t h e i r applications of variables. In seven cases they did not apply the factors, and i n f i v e cases they applied them in a continuous manner. 2) Grade 6 g i r l s did not apply the factors i n f i v e cases or applied them i n a continuous mode i n four cases. They q u a l i f i e d the action of the factors i n three cases and applied them as short impulses i n these three instances. 3) Grade 11 students had f i v e cases of q u a l i f i e d actions. These factors, however, were never q u a l i f i e d as short impulses, but as slowly d i s s i p a t i n g factors. They"did apply the factors continuously i n fourteen cases and did not apply them i n f i v e cases. 66 4) Almost a l l f a c t o r s were a p p l i e d by some students a t a l l grade l e v e l s . The e x c e p t i o n was t h a t there were no cases i n which grade 6 students had a c l e a r e x p r e s s i o n of a c c e l e r a t i o n as v a r y i n g w i t h elapsed time. 5) Very few problems occ u r r e d i n s h i f t i n g frames of r e f e r e n c e . Two grade 6 students showed s l i g h t h e s i t a t i o n , but they were ab l e to a d j u s t without a problem. 6) Among grade 6 students there was o n l y one c l e a r case i n which two v a r i a b l e s ( i n i t i a l v e l o c i t y and weight) were compared. 7) The r e l a t i v e e f f e c t s of i n i t i a l v e l o c i t y and weight were compared the most. There were f o u r t e e n of twenty-four such cases. 8) The r e l a t i v e e f f e c t s of h e i g h t and i n i t i a l v e l o c i t y were compared i n three cases. 9) The r e l a t i v e e f f e c t s of h e i g h t and weight were compared i n e i g h t cases. 4.250 E x p l a n a t i o n s Given f o r the Response E x p l a n a t i o n s were not e a s i l y evoked from the students. As a r e s u l t , the numbers of occurrences f o r each e x p l a n a t i o n cannot be c o n s i d e r e d s i g n i f i c a n t . T h e r e f o r e , the e x p l a n a t i o n s are r e p o r t e d and examples are g i v e n but not number of occ u r r e n c e s . These e x p l a n a t i o n s were c o n s i s t e n t w i t h s i m i l a r responses g i v e n by other students who o f f e r e d no e x p l a n a t i o n s . 4.251 Force and Height Height i s a r e l e v a n t f a c t o r , because the f o r c e p u l l i n g the shotput to e a r t h i n c r e a s e s w i t h h e i g h t as measured from the f l o o r . 67 1) EXPLANATION - The increased force i s caused by thinner a i r . Subject - S.G. a grade 6 g i r l . For task 3.21: I. - "Why did you make the gap bigger?" S. - "Well, the weight, as i t comes to the ground. I t would s t a r t going faster 'cause the a i r - f i t ' s not... It's easier to drop something down 'caTrg"e the a i r i s harder to push down up there than down here (points to the bottom), so i t should drop faster." I. - "Suppose these (shotputs) are heavy enough so the a i r doesn't matter. Would there by any difference?" S. - "Not r e a l l y . I t should not be much difference." 2) EXPLANATION - Gravity increases with height. Subject - T. a grade 6 boy. For task 3.23A: I. - "Why does the top one catch up?" S. -."'cause the top one i s heavier. 'cause i t would be higher up,and gravity p u l l s i t down more, and then the other one would have l i k e less gravity p u l l i n g down, 'cause i t ' s lower." 4.252 Energy .and Height Height i s a relevant factor,because energy i s a consideration of the size of the gap between the floor, and the shotput influences the speed of t r a n s i t . 1) EXPLANATION - The top b a l l h i t s the f l o o r harder. Therefore,it must move faster. Subject - S.S. a grade 8 g i r l . For task 3.23A: S. - "I think that i f they're dropped over a greater distance, _then the one that's got more height would gain more speed and catch up ... The b a l l that was dropped from the higher height would h i t the ground a l o t harder,, because i t ' s going faster ... with more force." 68 2) EXPLANATION - The gap between the shotputsis a factor. Subject - K.C. a grade 10 g i r l . For Task 3.23A: S. - "The distance (between) would continue to increase." I. - "Why?" S. - "Because the space (between the shotput and the f l o o r ) . That one (top) has so much more (points to space between the shotputs) space to speed up." 3) EXPLANATION - The size of the gap between the shotput and the f l o o r i s a factor. Subject - P.M. a grade 8 boy. For task 3.23A: S. - "I think that one, the one on the top,would go faster,because i t has more room. Like t h i s one (bottom) has l e s s . You started i t lower. This one (top) has more of a chance,because i t has more space (points from the shotput to the f l o o r ) . " 4.253 Force And Ve l o c i t y Force determines v e l o c i t y which means that a constant force produces a constant speed. An increasing force i s required to produce acceleration. 1) EXPLANATION - T. c l e a r l y indicates constant speed for task 3.31 Subject - T. a grade 6 boy. He also indicates that heavier objects f a l l faster i n task 3.36. For task 3.31: I. - "How do the speeds compare i n each gap?" 69 S. - " I t ' d go the same." For task 3.26A: S. - "The h e a v i e r one would h i t the f l o o r , o r would i t have more space between than the other b a l l ? Mmmm. I t (the space between) widens . ...gets wider." I. - "Does i t continue to get wider?" S. - "Yes." I. - "For how long?" S. - " T i l l i t h i t s the p l a c e where i t was headed." I. - "Why does t h a t happen?" S. - "'cause i t ' s the h e a v i e r b a l l . " I . - "What does t h a t cause?" S. - "The b a l l to drop f a s t e r . " I. - "What makes the b a l l f a l l down?" S. - " G r a v i t y . " I. - "What does t h a t mean?" S. - " L i k e i t ' s something i n the e a r t h t h a t sort, of p u l l s t h i n g s down and helps you stay on the ground.'cause, o t h e r w i s e , f i f there was no g r a v i t y , you'd be*" f l o a t i n g a l l o v e r 7 t h e p l a c e . " 2) EXPLANATION - Since a c c e l e r a t i o n occurs and v e l o c i t y v a r i e s with force, then f o r c e must vary. Subject - L. a grade 11 g i r l . For task 3.21: I. - "Why does the speed i n c r e a s e ? " S. - "...the p u l l from g r a v i t y becomes stronger, and so the b a l l i s going to move f a s t e r . " I. - "How does i t become s t r o n g e r ? " 70 S. - "Well, i f you're farther away here (points to the top of "the scale) I f you're farther away from the p u l l of gravity.... farther away from the bottom.... the ground.... the p u l l i s not as strong,, because you're getting farther away from the ground." I. - "Suppose the p u l l was the same?" S. - "The speed would stay the same." 4.260 The Sources ,6f B e l i e f Several sources of b e l i e f s were i d e n t i f i e d . Sometimes authorities were c i t e d . Sometimes experience was drawn on. Sometimes analogies were used,but these were few i n number. 4.261 Authorities Cited A great d i v e r s i t y of authorities were c i t e d from cartoons to G a l i l e o . 1) AUTHORITY CITED - cartoons. Subject - R.H. a grade 8 boy. For task 3.25A: S. - "Everytime you ask me something, I just picture i t i n my mind. 'cause I always see i t i n cartoons and stu f f when they drop one rock> and then they drop another rock and they always catch up to each other and then they go l e v e l . " 2) AUTHORITY CITED - Galileo was c i t e d several times. In th i s case he was c i t e d with some doubts. Subject - K.P. a grade 10 g i r l . For task 3.26A: S. - "Probably the larger one would....I don't know.... that's confusing, 'cause I remember Gal i l e o and the big b a l l and the l i t t l e b a l l . I mean he said that they f a l l at the same time,but that doesn't make sense." 71 4.262 Experiences C i t e d A v a r i e t y of experiences,., some p e r s o n a l and ot h e r s not, were c i t e d to support s t a t e d b e l i e f s . 1) AUTHORITY CITED - P e r s o n a l experience w i t h t e n n i s b a l l s . S u b j e c t - K.K. a grade 8 g i r l . For task 3.23A: S. - "When I drop two t e n n i s b a l l s a t the same time one g r a d u a l l y . . . the high e r one catches up." 2) AUTHORITY CITED - T e l e v i s i o n show of the A p o l l o moon l a n d i n g . Subject - D.C. a grade 11 boy. For tasks 3.26A and 3.26B: S. - "On T.V. I'd see the A p o l l o land on the moon, and the f e a t h e r and the hammer were dropped from about s i x feet, and they both landed upon the moon's s u r f a c e a t the same time. I was amazed a t t h a t when I saw i t , because I was sure ... I thought t h a t s u r e l y the hammer was going to drop way f a s t e r than the f e a t h e r . That's probably where I p i c k e d up the id e a t h a t the b i g b a l l and the small b a l l would f a l l i n the same time." 4.263 A n a l o g i e s Drawn Few a n a l o g i e s were drawn which were of s i g n i f i c a n c e . T herefore,an exhaustive l i s t i s very s h o r t . 1) ANALOGY DRAWN - A horse race i s used t o compare speeds. Subject - S.S. a grade 8 g i r l . For task 3.25B: S. - " J u s t the b a l l s hooting past you l i k e a f a s t horse out of a gate when you are on an o l d nag." 72 2) ANALOGY DRAWN - An example i s drawn u s i n g the hei g h t of the Empire,.State B u i l d i n g . Sub j e c t - L.F. a grade 10 boy. For task 3.24A: S. - " I t i s l i k e i f you drop a penny from a s t o o l , i t ' s not going to make much of a dent i n the ground. You drop i t from the Empire S t a t e B u i l d i n g ; i t ' s going to go through a c a r and a couple of l a y e r s of pavement." 3) ANALOGY DRAWN - The f a l l i n g o b j e c t i s compared to one r o l l i n g . S u b j e c t - K.C. a grade 10 g i r l . For task 3.21: S. - " I f you r o l l e d a b a l l without f r i c t i o n , i t would j u s t keep going. So, wouldn't the same t h i n g happen i f you j u s t dropped the b a l l ? " 4.270 R e v i s i o n of Response An a d d i t i o n a l process seemed to be o p e r a t i n g i n the grade eleven p h y s i c s group. In three of the s i x i n t e r -views the s u b j e c t s gave an i n t u i t i v e response, and committed themselves to t h i s p o i n t o f view. T h e n , l a t e r on i n the i n t e r v i e w they r e v i s e d t h e i r response to g i v e what, i n f a c t , was a more acc u r a t e response. I t i s these f i n a l responses which appear on the data t a b l e s 4.1 through 4.7 . T h i s r e v i s i o n of response i n v o l v e d some unknown aspect o f the dynamics of the i n t e r v i e w . How-ever, one i n t e r p r e t a t i o n of t h i s process i s t h a t i n t u i t i v e p o i n t s of view tended to p e r s i s t a f t e r i n -s t r u c t i o n . These may have been g i v e n f i r s t . Then,upon. 73 r e f l e c t i o n , a p o i n t of view more c o n s i s t e n t w i t h l e a r n e d e x p l a n a t i o n s from i n s t r u c t i o n i n ki n e m a t i c s was gi v e n . I t should be noted t h a t t h i s r e v i s i o n of response o c c u r r e d o n l y i n the grade e l e v e n p h y s i c s group,and, t h e r e f o r e , i n s t r u c t i o n i n kinematics c o u l d w e l l have been i n v o l v e d . 4.271 Quotations to I l l u s t r a t e R e v i s i o n of Responses Subject - K.B. a grade 11 g i r l . Task - 3.25A and 3.23B. In task 3.25A there i s i n d e c i s i o n about whether an i n i t i a l v e l o c i t y i s a continuous advantage: S. - "The one t h a t you dropped (top) w i l l be going f a s t e r . " I. - "Can you p r e d i c t what happens as they pass?" S. - " I t comes even. Then passes. Yours w i l l a l r e a d y have an i n i t i a l v e l o c i t y . Yours i s going to keep on going. So mine i s going to be slower than yours, because i t s t a r t e d l a t e r . I. - "What w i l l happen to the d i s t a n c e between them?" S. - "Should stay the same. I t h i n k ... I'm not sure ... I keep on changing my mind! No. I t should remain the same d i s t a n c e a p a r t . " ' For task 3.23B there i s an i n i t i a l acceptance of the re l e v a n c e o f height,and then i t i s r e j e c t e d : I. - "What do you see?" S.. - "The top b a l l coming towards me." 74 I. - "Andrthen?" S. - " I t would be be s i d e me and then below me." I. - "Why?" S. - "One's a t a h i g h e r l e v e l ... been dropped from a highe r l e v e l . No! No! the top b a l l , i t ' s j u s t t h e r e , s t a y i n g the same d i s t a n c e . " Subject - B.B. a grade 11 boy. Tasks - 3.21 and 3.23A compared to 3.23B. For task 3.21 there i s u n c e r t a i n t y about the c o n t i n u i t y of a c c e l e r a t i o n : I. - "What i f i t cou l d f a l l f u r t h e r ? " S. - " I t would keep a c c e l e r a t i n g . Oh no! No! No!. I t would keep a c c e l e r a t i n g . " For 3.23A and 3.23B the r e i s an i n i t i a l a p p l i c a t i o n of the h e i g h t v a r i a b l e and then a r e j e c t i o n of i t : Now, f o r task 3.2 3B: S. - "Now t h a t I t h i n k o f i t , I don't t h i n k i t would (catch up) ... * cause" they' re both a c c e l e r a t i n g from two d i f f e r e n t p o i n t s , one lower than the othe r , but they wouldn't g a i n i n speed 'cause they're both a c c e l e r a t i n g a t a con s t a n t speed. I'm c o n t r a d i c t i n g my l a s t statement b e f o r e . What I'm saying now i s t h a t you drop both b a l l s a t the same time,and they're a t the same weight. They would stay an equal d i s t a n c e a p a r t . " T h i s student expressed concern a f t e r the i n t e r v i e w about h i s change of mind. He s t a t e d t h a t t h i s had occ u r r e d a t s e v e r a l p o i n t s f o r him and t h a t he had t r i e d hard t o be c o n s i s t e n t . Tasks - 3.21 and 3.24B. Subject - L. a grade 11 g i r l . In task 3.21 a theory of a c c e l e r a t i o n as caused by i n c r e a s i n g f o r c e i s advanced. In 3.24A t h i s i s r e j e c t e d . For task 3.21: S. - "Because the b a l l . I t ' s l i k e r o l l i n g d o w n h i l l . The g r a v i t y s t a r t s p u l l i n g on the b a l l ; a n d i t s t a r t s going f a s t e r and f a s t e r . The p u l l gets harder. L i k e you drop something and the p u l l from g r a v i t y becomes stronger.and.so,the b a l l i s going to move f a s t e r . " For task 3.24B: S. - "My t h i n g about the g r a v i t y i s wrong. I'm s t a r t i n g to t h i n k t h a t i s wrong. I don't know why i t does h i t . I t ' s not because of the g r a v i t a t i o n a l p u l l . " 76 CHAPTER FIVE C O N C L U S I O N S , E D U C A T I O N A L I M P L I C A T I O N S AND R E C O M M E N D A T I O N S 5.00 SUMMARY OF THE STUDY The three main o b j e c t i v e s i n t h i s study were: a) to i d e n t i f y students' b e l i e f s concerning the motion of o b j e c t s i n f r e e - f a l l ; b) to i d e n t i f y trends i n the development of these b e l i e f s among students ranging from the grade 8 to grade 11 l e v e l ; c) to i d e n t i f y the p o s s i b l e e f f e c t s of standard i n s t r u c t i o n i n kinematics on these b e l i e f s f o r grade 11 p h y s i c s students. I n d i v i d u a l i n t e r v i e w s were used i n the procedure w i t h 24 students. The i n t e r v i e w s were analysed from two p e r s p e c t i v e s . a) Responses were c l a s s i f i e d task by task . T o t a l s were c a t e g o r i z e d by sex and by grade. W i t h i n each of these groupings the responses were f u r t h e r c l a s s i f i e d by mode of a c t i o n f o r each v a r i a b l e and mode of combined a c t i o n when more than one v a r i a b l e was i n v o l v e d . b) E x p l a n a t i o n s were analysed to determine the sources of the b e l i e f s about f r e e - f a l l motion and any u n d e r l y i n g b e l i e f s about the r e l a t e d concepts of f o r c e and energy. 77 5.10 CONCLUSIONS OF THE STUDY The problems addressed i n t h i s study were not presented as formal hypotheses. However, a number of t e n t a t i v e c o n c l u s i o n s r e g a r d i n g the methods used, the b e l i e f s about f r e e - f a l l motion h e l d by students, and the e f f e c t s of i n s t r u c t i o n on student b e l i e f s can be o f f e r e d . 5.11 Method Co n c l u s i o n s are presented concerning the method of c o l l e c t i n g data, the tasks and the method of a n a l y s i s . 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 e f f e c t i v e f o r o b t a i n i n g responses and ex-p l a n a t i o n s f o r students' b e l i e f s . T h i s one-on-one method allowed the i n t e r v i e w e r to check responses and to probe e x p l a n a t i o n s . The s t r u c t u r e pro-v i d e d by the p r o t o c o l s a l s o generated data which c o u l d be c l a s s i f i e d i n d i s t i n c t c a t e g o r i e s . 2) The e i g h t tasks used i n the study can be co n s i d e r e d v a l i d f o r o b t a i n i n g r e l i a b l e data r e g a r d i n g students' b e l i e f s about o b j e c t s i n f r e e - f a l l . T h i s c o n c l u s i o n seems reasonable s i n c e i t was apparent t h a t the students were not confused by the t a s k s . They understood the i n s t r u c t i o n s and were a b l e to respond without n o t i c e a b l e d i f f i c u l t y . The n o v e l t y of the apparatus and ta s k s caught t h e i r i n t e r e s t , and they seemed at ease and w i l l i n g to f r e e l y express t h e i r p o i n t s of view. Ideas presented by the students were c o n s i s t e n t 78 throughout a l l of the tasks, and t h e i r e x p l a n a t i o n s were not simply i d i o s y n c r a t i c . No sig n s of boredom were ev i d e n t , a s i n most cases the students o f f e r e d to st a y a f t e r the i n t e r v i e w was concluded to h e l p d i s m a n t l e the apparatus and were anxious t o d i s c u s s the g e n e r a l problem area a t t h a t time. 3) The method of a n a l y s i s i n which responses were c a t e g o r i z e d task by task was an e f f e c t i v e means to determine trends i n the data. The modes of a c t i o n and i n t e r a c t i o n designated i n the data t a b l e s were c l e a r l y e v i d e n t i n the responses. A l a r g e amount of data was o b t a i n e d . T h i s method of c a t e g o r i z a t i o n made the volume of data manageable,and trends by grade, by sex, and by sex and grade were e v i d e n t . These t r e n d s , as w e l l as the e x p l a n a t i o n s offered,have p o t e n t i a l uses f o r teachers and developers of c u r r i c u l a . 5.12 B e l i e f s - Developmental Trends A number of c o n c l u s i o n s can a l s o be drawn from the data r e g a r d i n g the development of s u b s t a n t i v e b e l i e f s i n the students. 1) Developmental trends were e v i d e n t i n the data c o l l e c t e d r e g a r d i n g a s i n g l e o b j e c t i n f r e e -f a l l . Although some ^notion of a c c e l e r a t i o n was e v i d e n t a t a l l l e v e l s , i t was c l e a r t h a t many grade 6 students tended t o view f r e e - f a l l motion i n terms of con s t a n t v e l o c i t y , w h i l e grades 8 and 10 students had q u a l i f i e d n o t i o n s of 7 9 a c c e l e r a t i o n as not being continuous. Grade 11 p h y s i c s students t r e a t e d a l l a c c e l e r a t i o n as continuous. However, even i n t h i s grade 11 p h y s i c s group the m a j o r i t y s t i l l b e l i e v e d t h a t v e l o c i t y i n c r e a s e s as a f u n c t i o n o f displacement and not as a f u n c t i o n of ela p s e d time. 2) Developmental trends were e v i d e n t i n the data c o l l e c t e d r e g a r d i n g judgements made by the students about the r e l e v a n c e o r e f f e c t on f r e e -f a l l motion of d i f f e r e n c e s i n h e i g h t , i n i t i a l v e l o c i t y and weight u s i n g two shotputs. Although these v a r i a b l e s were c o n s i d e r e d a t a l l l e v e l s , some trends were e v i d e n t . Weight was most important at a l l l e v e l s (18 of 24) i n c l u d i n g the grade 11 group where the m a j o r i t y c o n s i d e r e d i t as r e l e v a n t . Few q u a l i f i c a t i o n s f o r the mode of a c t i o n of t h i s v a r i a b l e were made. I t simply acted c o n t i n u o u s l y or not a t a l l . I n i t i a l v e l o c i t y was the second most important v a r i a b l e . Three of the s i x grade 6 students ignored t h i s v a r i a b l e , w h i l e two others a p p l i e d i t as a s h o r t impulse o n l y . I t was a p p l i e d by a l l of the grade 11 students,although h a l f of these q u a l i f i e d i t s a c t i o n as not being con-t i n u o u s . Height was the l e a s t important factor,, but i t was a p p l i e d by over o n e - t h i r d of the students. I t was used i n f r e q u e n t l y by the grade 6 students, by most grade 10 students and s t i l l continued to be a p p l i e d by one-t h i r d of the grade 11 p h y s i c s students. There were no cases i n which the frame of r e f e r e n c e v a r i a b l e caused any s i g n i f i c a n t problems a t a l l . 80 3) Developmental trends were evident i n the data col l e c t e d regarding the combined action of the variables. Although a combination of variables was considered at a l l grade levels,there was only one case of a com-bined action of two variables for the grade 6 group. Of the combined actions possible,the one involving weight and i n i t i a l v e l o c i t y was most pronounced. Over one-half of the students considered weight to be a more important factor i n determining acceleration than i n i t i a l v e l o c i t y when they were presented i n opposing sit u a t i o n s . There were a few cases i n which they were both con-sidered to be of equal e f f e c t . There were no cases i n which i n i t i a l v e l o c i t y was considered to be more im-portant than weight. In only one-quarter (5 of 24) of the cases was i n i t i a l v e l o c i t y considered while weight was ignored. Height and weight were considered to have a combined e f f e c t by one-third of the students. The greatest number of these were i n the grade 8 and grade 10 groups, although i t was considered i n the grade 11 group as well. There were no cases of height being considered more important than weight. The few case's of height and i n i t i a l v e l o c i t y having a combined e f f e c t were a l l at the grade 8 l e v e l . I n i t i a l v e l o c i t y dominated the e f f e c t of height. 5.13 B e l i e f s - The E f f e c t s of Instruction A number of tentative conclusions can be offered regarding the possible resistance of the b e l i e f s of students r e g a r d i n g f r e e - f a l l motion to standard i n s t r u c t i o n i n kinematics f o r the grade eleven p h y s i c s group. 1) Although a l l of the p h y s i c s 11 students d e s c r i b e d f r e e - f a l l motion i n terms of continuous a c c e l e r a t i o n , speed was b e l i e v e d to v ary w i t h d i s t a n c e f a l l e n r a t h e r than w i t h elapsed time. T h i s i s c o n t r a r y to textbook equations i n ki n e m a t i c s which c l e a r l y d e s c r i b e speed as v a r y i n g d i r e c t l y w i t h elapsed time not wi t h d i s t a n c e . 2) Weight was c o n s i d e r e d to be a r e l e v a n t f a c t o r by 5 out of 6 of the grade 11 students. The a c c e l e r a t i o n due to g r a v i t y , 'g', i s con-s i d e r e d independent of weight i n k i n e m a t i c s . T h i s f i n d i n g , then, i s a st r o n g i n d i c a t i o n t h a t the v a r i a b l e of weight should not be ignored i n kinematic i n s t r u c t i o n . In f a c t , the one student who ignored weight d i d scTwith r e s e r v a t i o n s and o n l y because he had seen an A p o l l o moon experiment on t e l e v i s i o n . 3) H a l f of the students f e l t t h a t i n i t i a l v e l o c i t y gave a f a l l i n g o b j e c t a d i s s i p a t i n g advantage, although i n kinematics i t i s t r e a t e d as g i v i n g a continuous advantage to an o b j e c t which has an i n i t i a l v e l o c i t y over one which does not. 4) Height was c o n s i d e r e d to be an advantage by 2 of the 6 students. In Physics 11 h e i g h t i s u s u a l l y i g n o r e d . I f i t were c o n s i d e r e d , i n f a c t , h e i g h t would be a very s l i g h t d i s -advantage, not advantage. 5) I n i t i a l v e l o c i t y and weight were c o n s i d e r e d to produce a combined e f f e c t by 5 . -students and the combination of h e i g h t and weight by 2 students. There was o n l y one case i n which i n i t i a l v e l o c i t y was c o n s i d e r e d as the o n l y r e l e v a n t f a c t o r . In f a c t , a c c o r d i n g to standard k i n e m a t i c s theory, i n i t i a l v e l o c i t y i s the o n l y f a c t o r . 82 5.14 E x p l a n a t i o n s and Sources of B e l i e f s A number of t e n t a t i v e c o n c l u s i o n s can be o f f e r e d r e g a r d i n g the e x p l a n a t i o n s g i v e n by the students. 1) C e r t a i n sources of the b e l i e f s and e x p l a n a t i o n s came to be e v i d e n t . In some cases experience was drawn on, but i n ot h e r s v a r i o u s a u t h o r i t i e s were simply c i t e d and accepted. Few true a n a l o g i e s were a c t u a l l y drawn. 2) C e r t a i n r e l a t e d concepts were c o n s i d e r e d to be f a c t o r s a f f e c t i n g f r e e - f a l l motion. Concepts of f o r c e as they a f f e c t motion were a f a c t o r . E i t h e r v e l o c i t y or a c c e l e r a t i o n c o u l d be c o n s i d e r e d to vary with f o r c e . For example, the students' c o n c e p t i o n of the nature o f the f o r c e of g r a v i t y (as con s t a n t or as varying) would a f f e c t t h e i r concept o f f r e e - f a l l motion. 3) A number of cases of r e v i s i o n of responses are e v i d e n t . Three cases i n v o l v i n g a r e v i s i o n of a student's o r i g i n a l response took p l a c e f o r the grade 11 group. The i n t e r v i e w data i n d i c a t e s t h a t e i t h e r there was a c o n f l i c t between common-sense b e l i e f s and ideas presented i n the kinematics i n s t r u c t i o n or there was a g r e a t e r a b i l i t y to l e a r n from the tasks themselves than f o r the other groups. 5.20 EDUCATIONAL IMPLICATIONS A number of i m p l i c a t i o n s f o r i n s t r u c t i o n and c u r r i c u l u m d e s i g n a r i s e from t h i s study. 1) The common-sense world of the student does not correspond e x a c t l y to the i d e a l i z e d world of k i n e m a t i c s . 83 In the common-sense world the mass of o b j e c t s i s a f a c t o r because of a i r f r i c t i o n and the occurrence of t e r m i n a l v e l o c i t i e s . Force i s r e q u i r e d to keep o b j e c t s and mechanisms,like an automobile»in motion a t a con s t a n t v e l o c i t y . Motion ceases u n l e s s f o r c e i s a p p l i e d to over-come f r i c t i o n i n v a r i o u s i n t e r n a l p a r t s . B e l i e f s about motion a r i s e from experiences i n t h i s common-sense world> and these b e l i e f s need to be addressed by i n s t r u c t i o n . The student should be allowed to t e s t the re l e v a n c e of such f a c t o r s as weight and h e i g h t i n a d d i t i o n t o t h a t of i n i t i a l v e l o c i t y . T h i s may suggest more g e n e r a l l y t h a t i n an i n s t r u t i o n a l s e t t i n g v a r i a b l e s are too q u i c k l y narrowed to those r e l e v a n t i n the i d e a l i z e d world without l e t t i n g the student t e s t o t hers t h a t he b e l i e v e s to be r e l e v a n t t o the phenomenon (Cole and Raven, 1969). 2) The n o t i o n of r e a d i n e s s i s not as c l e a r l y u s e f u l with r e s p e c t t o concepts of motion, as might be assumed. k l l of the grade 6 students were q u i t e a b l e and w i l l i n g to c o n s i d e r the problems i n the t a s k s . I t seems e v i d e n t t h a t motion need not onl y be c o n s i d e r e d as a s e t of complex problems f o r which i n v o l v e d a l g e b r a i s needed. Many of the ideas touched upon i n the tasks c o u l d e a s i l y be t r a n s l a t e d i n t o a c t i v i t i e s which would be a p p r o p r i a t e f o r a l l l e v e l s used i n the study. The grade 6 students d i d not g e n e r a l l y c o n s i d e r the combined e f f e c t of more than one v a r i a b l e and tended to have a l e s s developed view of 84 f r e e - f a l l motion. However, i t would appear t h a t students a t even the grade 6 l e v e l are able to d e a l w i t h the concept a t l e a s t on a q u a l i t i v e l e v e l . 3) I n s t r u c t i o n i n kinematics should be more than an e x p l i c a t i o n o f known i d e a l r e s u l t s . Students ought to be abl e to e x p l o r e t h e i r own b e l i e f s and e x p l a n a t i o n s . Understanding does not seem to develop o n l y from a n a l y s i n g the data obtained from r a t h e r c o n t r i v e d experiments i n standard i n s t r u c t i o n which do not n e c e s s a r i l y r e l a t e to t h e i r own experience of c h a r a c t e r i s t i c s of motion. Some suggestions are noted i n Chapter Two ( S e c t i o n 2.40) to provide f o r t h i s . E x p l o r i n g these ideas i n s m a l l groups was suggested. T e s t i n g the ideas u s i n g 'anomaly maneuvers' and r e c o n c i l i n g c o n t r a d i c t i o n s u s i n g ' r e c o n s t r u c t i o n maneuvers' was a l s o suggested ( E r i c k s o n , 19 79). T h i s would a l l o w the student to accommodate new i n f o r m a t i o n . 4) The way i n which v a r i a b l e s were c o n s i d e r e d by the students has i m p l i c a t i o n s f o r i n s t r u c t i o n . V a r i a b l e s were not thought simply to be r e l e v a n t or not r e l e v a n t . They were a l s o judged to a c t i n s h o r t impulses or with a d i s s i p a t i n g e f f e c t . T h i s aspect,then, namely, the mode of a c t i o n of a v a r i a b l e , needs to be addressed i n i n s t r u c t i o n as w e l l as the i s s u e of the r e l e v a n c e of the v a r i a b l e s . A c t i v i t i e s , then, need to c o n s i d e r t h i s aspect of the i n s t r u c t i o n a l problem with r e s p e c t to motion. 85 Thus, the study i n d i c a t e d t h a t the common-sense world of the student c o n t a i n s a r i c h source of b e l i e f s which need to be addressed i n i n s t r u c t i o n . Students need to be able to e x p l o r e the r e l e v a n c e and a c t i o n of v a r i a b l e s they b e l i e v e to be r e l a t e d to problems of motion. T h i s i m p l i e s t h a t they w i l l be i n v o l v e d i n the d e s i g n i n g of experiments to t e s t t h e i r i d e a s . A l t e r n a t i v e a c t i v i t i e s should a l s o be a v a i l a b l e , s i n c e not a l l students have the same b e l i e f s . In a d d i t i o n , i t i s e v i d e n t t h a t the teacher needs t o be s e n s i t i v e t o the b e l i e f s of the student. The teacher needs to c r e a t e an atmosphere i n which the student f e e l s f r e e to express and t e s t h i s b e l i e f s , without being i n -t i m i d a t e d by a f e e l i n g t h a t o n l y ' r i g h t 1 answers wili;be considered. 5.30 RECOMMENDATIONS FOR FURTHER RESEARCH A number of follow-up s t u d i e s would g r e a t l y c l a r i f y and strengthen 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. These recommended s t u d i e s are: 1) Develop a group instrument which uses many of the tasks of t h i s study. T h i s would a l l o w f o r a r e p l i c a t i o n of the r e s u l t s of t h i s study u s i n g a much l a r g e r , c a r e f u l l y - c o n t r o l l e d sample of s t u d e n t s . 2) Design a s e t of tasks which s p e c i f i c a l l y examines the r e l a t i o n s h i p between f o r c e and motion) i n p a r t i c u l a r . , the case where g r a v i t y s u p p l i e s the f o r c e . A developmental study of dynamics would c l a r i f y f u r t h e r t h i s aspect of motion. The student, i t seems, may c o n s i d e r 86 f o r c e and motion together and not motion i n i s o l a t i o n without c o n s i d e r i n g i t s cause. 3) Conduct a c o n t r o l l e d experiment t e s t i n g the e f f e c t s of standard kinematics i n s t r u c t i o n . T h i s a l s o c o u l d compare the e f f e c t s of other forms of i n s t r u c t i o n which s p e c i f i c a l l y addressed the b e l i e f s of the students as w e l l as t h e i r e f f e c t on the students' a b i l i t y to s o l v e q u a n t i t a t i v e problems of motion. 4) Determine i f the c o n s t r u c t s of ' v a r i a b l e r e -levance' and 'mode of a c t i o n f o r v a r i a b l e s ' apply to the study of d i f f e r e n t concepts i n p h y s i c s . 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" P u p i l s and Paradigms: A Review of L i t e r a t u r e R e l a t e d to Concept Development i n A d o l e s c e n t Science Students". S t u d i e s i n Science Education, 5,. 61-84, 1978. Driver, R. The Representation of Conceptual Frameworks i n Young Ad o l e s c e n t Science s t u d e n t s . Ph.D. t h e s i s , U n i v e r s i t y of I l l i n o i s , Urbana, I l l i n o i s , 1973. E r i c k s o n , Gaalen L. " C h i l d r e n ' s Conceptions of Heat and Temperature". Science Education, 63 (2),. 221-2 30, 1979. F u l l e r , Robert G.; K a r p l u s , Robert and Lawson, Antone. "Can P h y s i c s Develop Reasoning?" P h y s i c s Today, Feb. : 23-28, 1977. Grass, C a l v i n F r e d e r i c k . A Study R e l a t i n g L e v e l s of Understanding of S e l e c t e d Concepts of Motion to Chrono-l o g i c a l Age Using V e r b a l Response to V i s u a l S timulus. D o c t o r a l t h e s i s a b s t r a c t , 1972. Johnson, Paul E.; Cos, David L. and Curran Thomas E. " P s y c h o l o g i c a l R e a l i t y of P h y s i c a l Concepts". Psycho-nomic Scie n c e , 19;-, 245-247, 1970. K a r p l u s , Robert. O p p o r t u n i t i e s f o r Concrete and Formal  T h i n k i n g on Science Tasks. Ed. 132 054, 1973. 88 Kuhn, Ken. Unpublished paper f o r E d u c a t i o n 580, U.B.C, F a c u l t y of Education, 19 78: Kuhn, Thomas S. "A F u n c t i o n f o r Thought Experiments". In R. Taton and I. Cohen (Eds.) Melanges Alexandre  Koyre. P a r i s : Hermon, 196 3. Lawson, A. and Renner, J . R e l a t i o n s h i p s of Science Subject Matter and Development L e v e l s of L e a r n e r s , J o u r n a l of  Research i n Science Teaching, 12, 347-358, 1975. Lawson, A.E. and Wollman, W.T. Encouraging the T r a n s i t i o n from Concrete to Formal C o g n i t i v e F u n c t i o n i n g - an Experiment, J o u r n a l of Research i n Science Teaching, 13, 413-430, 1976. L e b o u t e r - B a r r e l l , L. Concepts of Mechanics i n Young People, P h y s i c s E d u c a t i o n , 11(7), 462-466. Mori, I c h i o ; Kohima, Maxao; Deno, Tsutomu. "A C h i l d ' s Forming the Concept of Speed". Science E d u c a t i o n , 60, 521-529, 1976. Nussbaum, J . and Novak, J . An Assessment of C h i l d r e n ' s Con-cepts of the E a r t h U t i l i s i n g S t r u c t u r e d I n t e r v i e w s , Science E d u c a t i o n , 60(4), 535-550, 1976. P i a g e t , Jean. " P h y s i c a l World of the C h i l d " . P h y s i c s Today, June; 23-27, 1972. Raven, Ronald J . "The Development of the Concepts of A c c e l e r a t i o n i n Elementary School C h i l d r e n " . J o u r n a l of  Research i n Science Education, 9, 201-206, 1972. Rowell, J.A. and Dawson, C.J. Teaching a b o u t . F l o a t i n g and S i n k i n g : an Attempt to L i n k C o g n i t i v e Psychology w i t h Classroom P r a c t i c e , Science E d u c a t i o n , 61(2), 245-253, 1977. Renner, J.W. S i g n i f i c a n t P h y s i c s Content and I n t e l l e c t u a l Development, P h y s i c s E d u c a t i o n 11(7), 458-462, 1976. Robertson, W.W. and Richardson, E. The Development of Some P h y s i c a l S c ience Concepts i n Secondary School Students, J o u r n a l . o f Research i n Science Teaching, 12^319-330, 1975. Schmerler, John F r e d e r i c k . The V i s u a l P e r c e p t i o n of A c c e l e r a t e d Motion. D o c t o r a l T h e s i s A b s t r a c t , 1969. 89 Shulman, Lee; Tamir, Pinchas "Research on Teaching i n the N a t u r a l Sciences", Second Handbook of Research on Teaching. Chicago, Rand McNally: 1098-1141, 1973. Ten Voorde, H.H. Verwoorden en V e r s t a a n ( T a l k i n g and Under-standing), S.V.O.(6) Gravenhage. Viennot, L. Sens^Physique e t Raisonnement Formel en Dynamique El e m e n t a i r e , E n c a r t Pedagogique, 2, 35-46, 1974. V o e l k e r , A.M. Elementary School C h i l d r e n ' s Attainment of the Concepts of P h y s i c a l and Chemical Change; a R e p l i c a t i o n , J o u r n a l of Research i n Science Teaching, 12, 5-15. Walters Lou, and B o l d t , Walter "A View of Science and Some Teaching S t r a t e g i e s " . S c ience Education, 54(2), 17a,;3-178, 1970. Weinreb, N e i l , and B r a i n e r d , C h a r l e s J . "A Developmental Study of P i a g e t ' s Groupement Model of the Emergency of Speed and Time Concepts". C h i l d Development, 46 » 176-185, 1975. Whittaker, D.E. A Foot i n Both C o u n t r i e s . Contemporary Edu c a t i o n , 47(1), 11-18, 1975. 90 APPENDIX T R A N S C R I P T OF AN I N T E R V I E W The f o l l o w i n g i n t e r v i e w was chosen because i t i l l u s t r a t e s some of the dynamics of the i n t e r v i e w p r o c e s s . K.B., the s u b j e c t , was a grade 11 g i r l who had r e c e i v e d i n s t r u c t i o n i n k i n e m a t i c s . T h i s i n t e r v i e w a l s o i l l u s t r a t e s the 'changing of mind' r e f e r r e d to i n s e c t i o n 4.270 which occu r r e d only with the grade 11 group. K.B.'s Interview A few minutes were spent i n making K f e e l a t ease b e f o r e the tasks were a c t u a l l y s t a r t e d . She was t o l d t h a t the i n t e r v i e w e r was i n t e r e s t e d i n what she r e a l l y thought about the problems. She should not be concerned a t a l l about whether her answers were r i g h t or wrong or whether they were what she thought the i n t e r v i e w wanted her to say. She was a l s o t o l d t h a t t h i s i n t e r v i e w was not a p a r t of the P h y s i c s 11 course. The i n t e r v i e w e r was attempting to i d e n t i f y students' b e l i e f s about f a l l i n g o b j e c t s so t h a t these ideas might be taught more e f f e c t i v e l y . 91 I: I n terviewer ; S: Subject r': "I've got a t i m i n g d e v i c e . Get a s t o o l . Get up on i t , and I ' l l show you how i t works." S: "Ahem"... (Gets the s t o o l and looks a t the d i g i t a l t i m e r ) . I: " T h i s i s an e l e c t r o n i c timer. I t reads i n tenths o f a second and seconds. Okay?" S: (With p o i n t i n g to the scale) " T h i s i s seconds?" I: "No. T h i s i s tenths of a second." S: "Aha." I: "We'll be s t i c k i n g mainly to t h i s column." S: "Oh. Okay." I: (With p o i n t i n g ) "Now t h i s i s a p h o t o c e l l which means t h a t the l i g h t goes i n t o t h a t (points) and c l o s e s a sw i t c h . When I bl o c k out the l i g h t i t s t a r t s the timer." S: "Ahem. Okay." I: "When I block out the second l i g h t i t stops the timer." S: "Okay." I: "So t h a t i f I put my hand through t h e r e , f o r example ... Would you watch the timer." S: " A l l r i g h t . " I: (Performs a c t i o n ) "Go through the f i r s t one ( s t a r t s timer) ... and the second one and i t stops." S: "• That means t h a t we've got ... I t took about f o u r -tenths of a second." I: " A l l r i g h t , - would you do t h a t , too, p l e a s e . : S: (Performs a c t i o n ) . I: "Keep your hand t o g e t h e r . Don't l e t your f i n g e r s separate." S: "Could I j u s t stop i n the middle?" 92 I: "Yes. Go through j u s t f a i r l y f a s t now." S: "What i f you onl y b l o c k the l i g h t o f f paittway^" I: "Well i t ... There's a c e r t a i n p o i n t where the switch turns on and o f f . " S: "Oh, I see t h a t . Okay." (Performs a c t i o n ) . I : "Now, how long d i d t h a t take?" S: "Ahem ... three p o i n t three seconds." I: " A l l r i g h t . Go through i t a b i t f a s t e r . " S: (Performs a c t i o n ) . I: "That took..." S: " P o i n t e i g h t seconds." I: "Again, f a s t e r . " S: "(Performs a c t i o n ) . I: "That took. S: " P o i n t two seconds." I: " A l l r i g h t . What happens t o the time i f you go through faster,?" ^ S: "The time i s l e s s . " I: " I f you go slower " S: "The time i n c r e a s e s . " I: "Now»suppose t h a t I i n c r e a s e t h i s d i s t a n c e ( s e p a r a t i o n between p h o t o c e l l s ) . Suppose I put the second timer down to here (20 cm gap) and I move through a t the same speed t h a t made two-tenths of a second b e f o r e . What would the timer read then?" S: " I f you moved a t the same speed?" I: "Yes." S: "Oh>it would depend on how f a r you moved i t down." I: "Suppose we moved i t twice as f a r ? " 93 S: "Oh, i t would be f o u r - t e n t h s of a second." I: " A l l r i g h t . Suppose t h a t I moved i t down to here and made the space b i g g e r . What would I have to do to make the timer read two-tenths of a second the same as b e f o r e ? " S: "You'd have to speed up." I: " A l l r i g h t . So, do you th i n k you understand the timer?" S: "Yes." I: "Now we're going to time an o b j e c t . Could you g i v e me t h a t indoor shotput t h e r e ? " S: " T h i s one?" I: "Yes, the red one; e i t h e r one of the red ones." S: "Okay." I: " I t ' s p r e t t y heavy." S" "Yes i t i s . R e a l l y ! " I: "Now, what I m going to do i s time t h i s f i r s t gap." S: "Ahem." I: (Performs a c t i o n of dropping the shotput through the t i m e r ) . "How long d i d i t take?" S: "One-tenth of a second." I: "Now you see, t h a t ' s about 10 cm." S: "Yes." I: "Now, suppose t h a t I dropped the b a l l from here (0 cm mark). I t f a l l s a l l the way down." S: "Right." I: "Now suppose I put the f i r s t o f these p h o t o c e l l s , say, a t f i f t y . " S: " A l l r i g h t . " I: "Now, i t s the same b a l l t h a t ' s dropping. S: "Yes." 94 I: " I t ' l l f a l l down past the f i r s t p h o t o c e l l . Where would you have to put the second p h o t o c e l l so t h a t i t would read one-tenth of a second again?" (Simulates a c t i o n ) . S: "T h i s was 10 cm/so you'd have to put i t f a r t h e r a p a r t . " (Puts i t a t the 90 cm mark). I: "Yes/put i t a t 90 so t h a t you made the gap about 40 cm. Could you j u s t t e l l me why you d i d t h a t ? " S: "Well, because i t a c c e l e r a t e s as you drop i t . In one-t e n t h of a second i t ' s going to drop 10 cm up t h e r e ( p o i n t s to the t o p ) . I t ' s going to go q u i c k e r . I t ' s going t o a c c e l e r a t e , which means t h a t i n a s h o r t e r time i t ' s going to go more d i s t a n c e as i t drops f a r t h e r and f a r t h e r . " I: "Now suppose t h a t we put the f i r s t timer a t 100. About where would you put the second p h o t o c e l l so t h a t i t would take one-tenth of a second between these two?" S: "Ahem...here." I: "About 17 0?" S: "Yes." I: "Suppose we put the f i r s t timer a t 150; where would you put the second timer?" S: "Quite c l o s e t o the bottom here. Maybe a b i t o f f . " I: "More than 250?" S: "Aaa... No I guess t h a t would be about r i g h t . About t h a t . " I: "About 250?" S: "Yes." I: "Now, suppose you put the f i r s t timer a t 200; where would you put the second?" S: "About 300 or so." I: "Could you j u s t t e l l me again why you're making ... what i s happening to the speed of the body a s , i t ' s dropping?" S: "The speed of the body i s a c c e l e r a t i n g , which means t h a t i n the same amount of time i t ' s going t o f a l l f u r t h e r . " 95 I: "Suppose that i t could f a l l for a long distance?" S: "Ahem." I: "You know, f a l l r i g h t through a hole i n the f l o o r and keep on going. Can you say anything about the speed i n that case?" S: " I t would accelerate." I: "Would i t accelerate i n d e f i n i t e l y ? " S: "Are you saying that i t ' s f a l l i n g i n d e f i n i t e l y ? " I: "Well suppose i t could f a l l for a long distance." S: "Wellj i t ' s going to be accelerating u n t i l i t h i t s the ground,,because you've got no upward force. Well none" to r e a l l y speak of." I: "Suppose that i t f e l l ' say, 100 metres or even a longer distance. Would i t make any difference?" S: "To the acceleration?" I: "Yes." S: "Are you saying, would i t s t i l l accelerate?" I: "Yes." S: "Yes i t would." I: "Let's go back and look at thi s gap here. Now>you had one at 100 and the other one at 170. In this'centre gap where i s i t going the fastest?" S: "Right down here (170 mark)." I: "At the bottom?" S: "Yes." I: "And where i s i t going the slowest?" S: "Right at the top (100 cm mark) where the gap s t a r t s . " I: "Where i s i t going exactly h a l f the speed between the two?" S: "Ahem... Considering what we know, i f we knew the two v e l o c i t i e s , we'd add them up and divide by two." 96 I: "Yes. So/about where would i t be going t h a t half-way speed?" S: "I t h i n k i t ' s about here or so." I: " S o , i n a gap of 60 you're p o i n t i n g about 20 down from the top. Why would i t be going the half-way speed there?" S: " I t ' s always a c c e l e r a t i n g . . . s o i f we...mmm...it j u s t seems l o g i c a l to me. I don't know why,but i t does. I don't t h i n k i t would be going half-way between the two i n the middle. I don't t h i n k lower. I t h i n k i t ' s about 20 down." I: "Now a couple of other problems. We have two shotputs here. They're j u s t the same." S: "Yes." I: "Could you get up on the s t o o l here?" S: "Okay." I: "In t h i s case we're going to use two t o g e t h e r . You h o l d t h a t one down a t 25." S: "Okay." (Does s o ) . I: "And I'm going to h o l d t h i s one up a t 0." (Does s o ) . S: "Ahem." I: "Now, suppose t h a t we count one, two, three*go, and we both l e t the shotputs go a t e x a c t l y the same 'time." S: "At e x a c t l y the same time?" I: "Yes. Can you t e l l me what w i l l happen... Can you d e s c r i b e the d i s t a n c e between the two as they f e l l ? " S: "The d i s t a n c e between them should stay the same/because ...we have the f o r c e of g r a v i t y i s the same, i n ' b o t h cases. They both weigh the same. The one t h a t i s h i g h e r j u s t gets t o a c c e l e r a t e l o n g e r . So, I t h i n k they w i l l s t a y the same." I: "Now, suppose t h a t we put the second one down at 100. You can get down o f f the s t o o l . " S: "Okay." 97 I : "Now,, ho l d t h a t one down at 100 (Does so) . I. put t h i s one up a t O (Does so) and I drop i t (Simulates a c t i o n ) . You wait u n t i l i t ' s a t 40. J u s t when i t ' s at 40 you drop yours. Now, what w i l l happen to the d i s t a n c e between the two"as they keep f a l l i n g ? " S: "The d i s t a n c e between the two w i l l decrease because t h i s one (top) has a l r e a d y a c c e l e r a t e d to t h i s p o i n t (40 cm). S o ^ i t ' s going to be going f a s t e r . And, t h i s one (bottom) which i s j u s t s t a r t i n g t o a c c e l e r a t e . . . T h i s one (top) w i l l always have more... I t s v e l o c i t y w i l l always be g r e a t e r because i t s t a r t e d f i r s t . " I: " W i l l i t c a t c h up?" S: "Yes. I t h i n k so." I: " W i l l i t pass?" S: "Yes." I: "What about the space between the two a f t e r t h a t ? " S: "I t h i n k i t would continue to i n c r e a s e . " I: "Now, another s i t u a t i o n . Suppose I put t h a t one a t the top (does so) and you h e l d yours a t the 100 cm mark (Poes s o ) . I dropped it,-and you waited u n t i l i t was j u s t even (Simulates a c t i o n ) . " S: "Okay." I: "In t h a t case j u s t when i t was even, you dropped yours. What would happen then?" S: "Well, t h i s one i s going to be going a l o t faster,; the one t h a t you dropped." I: "Okay." S: "And, you're going much f a s t e r . And, t h i s one... I t ' s gonna s t a r t out and... Oh! I t h i n k they w i l l j u s t s t a y the same d i s t a n c e between them." I: "Can you j u s t run by t h a t one again. I t comes even, and then i t passes. Then what happens?" S: "Okay, j u s t w a it... T h i s (top) one's gonna come even. I t ' s gonna pass. The one t h a t you dropped. And mine's gonna s t a r t out. Yours w i l l a l r e a d y have an i n i t i a l v e l o c i t y . Yours i s going to be always s t a r t e d , so... yours i s going to keep on going; so mine i s going to be slower than yours?because i t s t a r t e d l a t e r . " 98 I: "So, what i s going t o happen t o the d i s t a n c e between them a f t e r i t passes'?" S: "I t h i n k i t should stay the same." I: "How f a r w i l l , i t go past ? " S: "Ahem... I t h i n k . . . I'm not sure. You mean i n exact d i s t a n c e ? " I: "No, j u s t approximately." S: "I'm not sure, but i t should remain the same d i s t a n c e a p a r t . I s a i d the o p p o s i t e b e f o r e i n the l a s t problem. I t h i n k I was wrong. The top one has an i n i t i a l v e l o c i t y , b u t . . . t h e y ' r e o n l y advancing. They're the same bodies, so the d i s t a n c e ( a f t e r passing) should stay the same between them,I t h i n k . I don't know what i t w i l l be, but i t should sTTay the same." I: "I'm j u s t going t o ask you these three i n a s l i g h t l y d i f f e r e n t way." S: "Okay." I: "In the f i r s t case imagine t h a t you're s i t t i n g on the bottom shotput. And,you're r i d i n g on i t , but your presence there doesn't change anything."" S: "Okay." I: "So»we have one 25 cm on top of the other (Simulates a c t i o n ) . " S: "Yes." I: "And we l e t go both a t the same time. As you r i d e the bottom shotput down,you look up. What do you see?" S: "The top b a l l coming towards me." I: "And,then?" S: " I t would be b e s i d e me and then below me." I: "Why would t h a t happen?" S: "One's a t a h i g h e r l e v e l . . . b e e n dropped from a higher l e v e l . No! No! The top b a l l . I t ' s j u s t t here s t a y i n g the same d i s t a n c e . I t should always be above me i f they're dropped a t the same time. I t ' s f a l l i n g at the same speed I am." 99 I: "Now, suppose we repeat the second example. You r i d e the bottom one. I t waits a t the 100 cm mark. I drop the f i r s t one from the 0 mark. (Simulates a c t i o n ) . You w a i t u n t i l i t i s a t the 40 cm mark. Then,the one you are on i s dropped. Remember,you are j u s t an observer. Your presence doesn't change anything. You r i d e the bottom one down and look up. What do you see?" S: "The top b a l l coming towards me... Then,I see i t b e s i d e me and, then, below me. Then,I'd see the bottom b a l l . . . I think -" that" i t ' s j u s t going t o be below me. I t ' s not going t o be f a l l i n g q u i c k e r or anything. I t doesn't seem l o g i c a l t o me t h a t i t should be going f a s t e r . " I: "Now, the t h i r d problem. I drop the f i r s t one from O. You w a i t a t 100 t i l l the top one i s even ('Simulates a c t i o n ) : then, yours i s dropped. You r i d e i t down. What do you" see?" S: "I look up. Then,I see the one t h a t was dropped e a r l i e r f a l l i n g ...passes me,and,then,it's going to be going the same speed as I am."' I: "A couple of other combinations, okay?" S: " A l l r i g h t ; sure." I: "Now/you h o l d t h a t one (heavier shotput) . You see, i t ' s q u i t e a b i t h e a v i e r than t h i s one." S: "Yes, i t i s . " ( V e r i f i e s ) I: "Now/ suppose you put t h a t one a t 25 (.Goes) and I put the l i g h t e r one at 0 (Does). We count one, two, three,go, and drop both a t the same time. Can you desc r i b e ' the"' space between the two as they f a l l ? " S: " I t ' s going to grow...because t h i s one (bottom) i s h e a v i e r ; s o i t ' s going to f a l l q u i c k e r . The h e a v i e r you are,the q u i c k e r you f a l l . " I: "Suppose t h a t I d i d the same t h i n g again, but I have the h e a v i e r one a t the top (Does),and you have the l i g h t e r one a t the bottom (Does)." S: "The top one i s going to pass the bottom one. The d i s t a n c e between them i s going to i n c r e a s e . " I: "Now>. do you remember the second problem w i t h two shotputs?" S: "I t h i n k so." 100 I: " T h i s time you h o l d the h e a v i e r one a t the 100 cm mark." S: "Okay (Does s o ) . " I: "I h o l d the l i g h t e r one a t 0 ( S i m u l a t e s ) . I drop i t , and you wait u n t i l i t i s a t 40 ( S i m u l a t e s ) . Then, you drop yours. What i s going to happen now?" S: "The d i s t a n c e between the two...this one (top) i s going to have an i n i t i a l v e l o c i t y . . . ahem...the d i s t a n c e between the two i s 60 cm...the d i s t a n c e between the two w i l l i n c r e a s e . " I: "Right from the s t a r t ? " S: "Yes." I: "Now, the t h i r d problem with shotputs. Now, you h o l d your h e a v i e r one a t 100 (Does). I h o l d my l i g h t e r one a t 0 (Does). I drop mine, and you w a i t ( S i m u l a t e s ) . You w a i t u n t i l mine i s even with yours, and then you drop yours, too. What happens?" S: "The l i g h t e r one i s going to be g o i n g . . . i t ' s going to be f a r t h e r down than the h e a v i e r one, and then the heavy one i s going to speed up and pass the l i g h t one." I: "Thank you, K. Do you have anything to add to any of your e x p l a n a t i o n s ? " S: "The h e a v i e r t h a t an o b j e c t i s , the more p u l l there i s a c t i n g on i t to f a l l . . . W e l l , the f o r c e i s always the same, but, the h e a v i e r an o b j e c t i s , the more q u i c k l y i t f a l l s because of g r a v i t y . " I: "Thank you, K., f o r being so open about your thoughts. I hope you have enjoyed doing the problems." S: "Yes, I d i d . " I: " J u s t one request... Please do not speak- to anyone about the problems. I have other i n t e r v i e w s to do, and I r e a l l y would l i k e not to have t a l k e d about them ahead of time." S: "Sure, I see t h a t . Thank you." 

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