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The design of an instructional model to transform students' alternate framework of dynamics Brace, Garry Richard 1988

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THE DESIGN OF AN INSTRUCTIONAL MODEL TO TRANSFORM STUDENTS' ALTERNATE FRAMEWORK OF DYNAMICS  by  GARRY RICHARD BRACE B.Sc, The University of British Columbia, 1971  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS  in THE FACULTY OF GRADUATE STUDIES (Department of Mathematics and Science Education)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA August 1988 ©  Garry Richard Brace  In  presenting  degree  this  at the  thesis in  University of  partial  fulfilment  of  British Columbia, I agree  freely available for reference and study. I further copying  of  department publication  this or of  thesis for by  his  or  the  representatives.  It  an advanced  Library shall make  it  is  granted  by the  understood  that  head  of  copying  my or  this thesis for financial gain shall not be allowed without my written  permission.  Department of Mathematics & Science The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  Date  that the  for  agree that permission for extensive  scholarly purposes may be her  requirements  October 7, 1988  Education  Abstract  This study concerns the design and implementation of an instructional model that was intended to explicate students' alternate conceptions of dynamics and transform them into a conceptual set which more closely approximates Newtonian conceptions of dynamics.  The  design of this instructional model has employed Frame Theory as the basis for the development of an analytical clue structure that was used to describe students' alternate conceptions of dynamics and track any changes to these conceptions as the lesson sequence progressed.  In  addition, this instructional model has attempted to utilize discordant event demonstrations as the catalyst required to initiate transformations of the alternate conceptions of dynamics held by students. Data for this study have been collected within an operational science classroom by video taping a series of lessons that dealt with the dynamics of linear acceleration and deceleration, and uniform motion.  These data were subsequently reduced to lesson transcripts  which were then analyzed, using the clue structure, for student conceptual data.  These data were then reconstructed into conceptual  frames that represented individual and collective student interpretations of force/motion events both before and after the demonstration of the discordant events.  'Before and after' comparisons  were then made of these frames in order to determine i f any conceptual transformation had occurred. Results from this study have indicated that a majority of students that took an active role in these classes explained the motion of  ii  objects, both before and after instruction, using a 'motion implies a force' set of conceptions.  This study also found that the explication  and representation of student conceptions of dynamics could be successfully accomplished by using the analytical clue structure to reconstruct transcript data into student interpretational frames of motion.  Comparisons of the interpretational frames that students were  employing before the demonstration of specific, discordant events with those frames that were being employed after these events indicated that use of discordant events to initiate conceptual transformation was only minimally successful.  Table of Contents Page Abstract  ii  List of Figures  vii  Acknowledgements  ix  Chapter 1.  The Problem and It's Setting  1  The Statement of the Problem  1  The Specific Problems  1  Definitions  2  A Psychological Setting for the Problem  3  Characteristics of Students' Personally Constructed Beliefs  3  Frame Theory and Personally Constructed Knowledge Rationale for the Problem  4 7  Educational Significance of the Problem  7  Theoretical Considerations  8  Limitations 2.  9  A Review of the Related Literature  12  The Ideographic Approach  13  Results  14  The Nomothetic Approach  16  Results  18  A Comparison of Results  20  iv  Chapter 3.  page The Research Design  25  The Instructional Model  25  The Instructional Strategy  26  The Development of the Analytical Clue Structure  28  Implementation of the Instructional Model  29 Methods of Data Collection  4.  30  The Classroom Case Study  32  The Lessons  34  The Dynamics of Acceleration  34  The Dynamics of Deceleration  42  The Dynamics of Uniform Motion  59  A Clue Structure Analysis of the Effectiveness of the Instructional Strategy  75  Student Interpretational Frames of Motion  76  Acceleration  77  Deceleration  82  Uniform Motion  88  Instructional Strategy Effects on Student Interpretational Frames of Motion  96  Acceleration  96  Deceleration  97  Uniform Motion  99  A Summary Analysis of the Major, Student Interpretational Frameworks of Motion v  101  Chapter 5.  page Conclusions, Discussion of Results, and Recommendations  105  Conclusions  105  Conclusions Concerning the Ability of the Instructional Model to Explicate Students' Concepts of Dynamics  106  Conclusions Concerning the Ability of the Instructional Model to Transform Student Conceptions of Dynamics  107  Conclusions Concerning the Design of the Instructional Strategy  110  Conclusions Concerning the Development of the Analytical Clue Structure  Ill  Summary Conclusions Concerning the Efficacy of the Instructional Model A Discussion of the Results  112 113  The Alternate Framework of Dynamics  113  The Elements of the Instructional Model  117  Recommendations  121  References  124  Appendix Student Problem Sheets  127  vi  List of Figures Figure  Page  1.  A Map of Student Concepts of Acceleration  2.  Teacher-Constructed Map of Newtonian  37  Concepts of Acceleration  38  3.  Acceleration Demonstration #2  40  4.  Deceleration Demonstration #1  49  5.  Deceleration Demonstration #2  51  6.  The Final Deceleration Problem  52  7.  Kari's Force Analysis of the Final Deceleration Problem  8.  53  Redesigned Concept Map of Acceleration and Deceleration  60  9.  Symbols Used in Frame Constructions  75  10.  Kelly's Acceleration Frame for Stationary Objects  11.  78  Kelly's Acceleration Frame for Moving Objects  79  12.  Jim's Acceleration Frame  81  13.  Kelly's Deceleration Frame  83  14.  Jim's Deceleration Frame  84  15.  Composite Deceleration Frame Derived from Hallway Demonstration  16.  86  Composite Deceleration Frame Applied to the Baseball Problem  88  17.  Brad's Frame for Uniform Motion  18.  Kari's Frame for Uniform Motion  vii  89 90  Figure  page  19.  Melanie's Uniform Motion Frame  93  20.  Brad's Expanded Frame for Uniform Motion  94  21.  Heinzy's Frame for Uniform Motion  22.  An Interpretational Framework of Motion  95  Based Upon the 'Motion Implies a Force' Conception 23.  102  A Newtonian Interpretational Framework of Motion  104  viii  Acknowledgements I would like to thank Dr. Gaalen L. Erickson of the Department of Mathematics and Science Education, the University of British Columbia, for his academic direction and support throughout a l l phases of the evolution of this thesis. I would also like to acknowledge the support provided to me by School District #24 (Kamloops) in the form of an educational sabbatical. Without this sabbatical this research would never have been started. Finally I would like to thank my wife and children without whose support and forbearance this research would never have been completed.  ix  CHAPTER ONE  The Problem and Its Setting  The Statement of the Problem A synthesis of previous research in students' beliefs of dynamics has delineated three, common viewpoints of force and motion. These are f i r s t , motion implies an application of force; second, force i s associated only with motive objects; and third, external surface forces are the only types of forces available.  This study postulates that  these three common viewpoints, together, represent an alternate framework of dynamics.  This study further postulates that this  alternative framework i s both pervasive and robust within student populations, and acts as an impediment to understanding Newtonian concepts of dynamics as presented in the classroom. This study has undertaken, as i t s general problem, the design of an instructional model which can be used to explicate the alternate conceptions held by students and help students transform these to ones which more closely approximate a Newtonian framework of dynamics. In particular, this study has focussed upon that segment of the alternate framework that implies that a l l forms of motion require an application of force. The Specific Problems The general problem can be subdivided into three specific problems or objectives. 1.  These are:  to design an instructional strategy that will explicate the  students' alternate framework of dynamics, and help them to transform 1  this alternate framework to a closer approximation of a Newtonian framework of dynamics. 2.  to develop a theoretical perspective that will serve as the  basis for an analytical clue structure (Roberts & Russell, 1975). 3.  to collect qualitative date, within an operational classroom,  that will allow inferences to be made concerning the influence of the instructional strategy on students' classroom concepts of dynamics on the basis of a clue structure analysis. Each of these three issues, and their constituent problems,  will  be further amplified within Chapter Three - The Research Design. Definitions alternate Framework An alternate framework i s a network of beliefs and conceptions concerning a class of things, situations, or events that has been constructed by an individual as a result of his or her experiences with specific members of the class. The elements of this network can include both intuitive and propositional knowledge. Theoretical Perspective Theoretical perspectives are "conceptualizations which provide ways of viewing the complexity of educational phenomena i n orderly and meaningful patterns (Tyler, 1972)", as cited by Roberts & Russell (1975). Clue Structure A clue structure i s defined as an analytical device used to ensure that the identified "theoretical perspectives are applicable to the phenomena being studied (Roberts & Russell, 1975, p. 115)."  2  Instructional Strategy An instructional strategy consists of the design and implementation of the principal elements of instruction. These elements can include instructional objectives, content, mode of content  presenta-  tion, and evaluation. Instructional Model An instructional model i s an organization structure that relates the proportions and sequencing of the elements of the instructional strategy to those of the clue structure.  A Psychological Setting for the Problem Characteristics of Students' Personally Constructed Beliefs Almost without f a i l , a l l researchers who have investigated students' personal knowledge of dynamics attribute the presence of this knowledge to an attempt, by the individual involved, to construct meaning from their experiences with the motions of objects.  This  experiential base is assumed to be constructed from a combination of physical and linguistic experiences, and analogic reasoning. Initially, due to a limited range of experiences, these meaning constructions might be represented as incoherent, "local theories" (Claxton, n.d., p. 8).  However, as the experiential base broadens,  Driver and Erickson (1983) suggest that these local theories can evolve into a "system of expectations" (p. 41) with predictive capabilities. Such a system will have strong idiosyncratic overtones and probably be continually reinforced because ' i t works'. Additionally, elements of this personal expectation or belief system can be used as warrants or  3  backing for warrants during the interpretation of novel, or new situations and events. Although personally constructed beliefs are strongly idiosyncratic, many similarities among the expectations and beliefs of individuals have been recognized by researchers. arises from, at least, two possibilities.  This apparent anomaly  These are: f i r s t , that  individuals will process information and construct meaning in similar ways, and second, that individuals are faced with a reasonably common set of experiential events from which to construct meaning. Thus, elements of personal knowledge, within specific contextual domains such as dynamics, can appear as universals. How might such a system of idiosyncratically constructed beliefs and expectations of dynamics be represented?  Initially, i t i s neces-  sary to accept the previous assumption that individuals process information and construct meaning in similar ways. Once this assumption i s accepted, one needs to locate a representation of individual information processing systems that could be generalizable across individuals.  Such an information processing system is found in  Minsky's (1975) frame theory. Frame Theory and Personally Constructed Knowledge Frame theory was developed by Minsky as a response to perceived problems with existing theories and models of human information processing techniques.  For Minsky, these theories and models were "on  the whole too minute, local, and unstructured to account - either practically or phenomenologically sense thought" (p. 211).  - for the effectiveness of common  In addressing these issues Minsky theorizes  that:  4  When one encounters a new situation (or makes a substantial change in one's views of the present problem) one selects from memory a substantial structure called a frame. This i s a remembered framework to be adapted to f i t reality by changing as necessary ... A frame i s a data-structure for representing a stereotyped situation, like being in a certain kind of living room, or going to a child's birthday party (P. 212). Thus, a frame "represents our inductive knowledge of the world as previous experience with that domain of objects" (Kuipers, 1975, p. 159) and, for the purposes of this research, will represent the fundamental unit of the theoretical perspective required to design the clue structure. In the simplest sense, a frame represents a mental structure that contains either procedural data (derived from physical experience) or declarative data (derived from linguistic experience) associated with a unique event or situation.  At this level, the data are idiosyncratic  and the frame appears to closely approximate Claxton's concept of a local theory.  These two types of frames can be integrated to form a  more complex, but s t i l l idiosyncratic, frame i f the individual perceives that they have originated from the same event. Once established, an idiosyncratic frame provides a ready-made, heuristic strategy that can be applied to an analogous event. If the strategy i s successful in providing a solution or explanation the frame will evolve in complexity.  This complexity can be represented as an  increase in the various levels within the frame. The lower levels of the frame will contain the specific, idiosyncratic data from both events and are referred to as default values (Kuipers, 1975, p. 158).  The default values from both events may or  may not overlap in their entirety depending upon the degree of similarity between the events.  They do, however, act as a set of data 5  expectations or inferences that will appear the next time the heuristic strategy i s used.  In this regard, the default values appear to  parallel the "system of expectations" mentioned by Driver and Erickson (1983). The upper levels of the frame will contain stereotypical information about both events.  As a result, these levels are fixed and  probably represent a conceptualization of the events i n question. Further 'successful' applications of this dynamic structure to other contextually similar events result i n an increase to the complexity of the frame.  This increasing complexity can be represented as a  continued expansion of the frame to include increasingly more generalized stereotypical knowledge and concepts associated within the context, and specific data (procedural or declarative) related to this knowledge. Within this representation the most general concept can be conceived as a superframe which subsumes the more specific frames. These specific frames, i n turn, subsume even more specific frames. In this fashion a "generalization hierarchy" (Winograd, 1975, p. 196) of frames i s constructed. This conceptualization of personal, inductive, domain-related knowledge as a collection of mental frames arranged i n a generalization hierarchy provides a theoretical perspective for the representation of personally constructed knowledge. This representation will be more fully discussed i n Chapter Three.  6  R a t i o n a l e f o r t h e Problem E d u c a t i o n a l S i g n i f i c a n c e of the Problem Many t e a c h e r s and r e s e a r c h e r s have r e c o g n i z e d t h a t l a r g e numbers of s t u d e n t s h o l d views of f o r c e and m o t i o n t h a t can b e s t be d e s c r i b e d as p r e - O a l i l e a n .  I t has been assumed (and i s assumed f o r t h e purposes  of t h i s r e s e a r c h ) t h a t t h e s e views r e p r e s e n t an impediment t o t h e acquisition  of Newtonian concepts of dynamics.  s t r o n g l y s t a t e d by V i e n n o t  T h i s s t a n c e i s most  (1979):  The i n t u i t i v e scheme i s , t h u s , widespread and t e n a c i o u s . I t r e s i s t s t h e t e a c h i n g of concepts which c o n f l i c t w i t h i t , and i t reappears even i n t h e e x p e r t when he o r she l a c k s t i m e t o reflect. Such t e n a c i t y i s p r o b a b l y connected w i t h t h e s e l f c o n s i s t e n c y of t h e scheme ... a major t e a c h i n g e f f o r t i s needed w h i c h goes beyond t h e c o n v e n t i o n a l t e a c h i n g of the Newtonian scheme a l o n e ... s t u d e n t s s h o u l d be h e l p e d t o make e x p l i c i t t h e i r own i n t u i t i v e r e a s o n i n g w i t h a l l i t s consequences, and t o compare t h i s w i t h what they a r e taught (p. 213). T h i s r e s e a r c h has s e t i t s e l f scheme ( a l t e r n a t i v e  t h e t a s k of t r a n s f o r m i n g t h e i n t u i t i v e  framework) by d e v e l o p i n g an i n s t r u c t i o n a l  model  t h a t does go beyond t h e t e a c h i n g of t h e Newtonian scheme a l o n e . d o i n g s o , i t was  By  c o n j e c t u r e d t h a t a more complete u n d e r s t a n d i n g  Newtonian concepts of dynamics, by s t u d e n t s , might be  of  achieved.  The i n s t r u c t i o n a l s t r a t e g y , a l t h o u g h d e s i g n e d e x t e r n a l l y t o the c l a s s r o o m , has been developed classroom.  and a s s e s s e d w i t h i n an o p e r a t i o n a l  T h i s form of p r a c t i c a l e v o l u t i o n has attempted  t o ensure  t h a t t h e i n s t r u c t i o n a l s t r a t e g y i s r e s p o n s i v e t o t h e demands of room systems.  T h i s r e s p o n s i v e n e s s , combined w i t h the i n h e r e n t  classflexi-  b i l i t y of t h e model, s h o u l d ensure t h a t t h e i n s t r u c t i o n a l model can adapted by t e a c h e r s t o meet t h e i r own  unique s e t s of  requirements.  T h i s r e s e a r c h r e p r e s e n t s an i n i t i a l s t e p i n t h e movement of a well-documented body of r e s e a r c h d a t a from a n a l y s i s t o  7  full-fledged  be  implementation  i n the classroom.  This i n i t i a l  step i n c o r p o r a t e s both a  n a t u r a l i s t i c , open form of i n q u i r y and a t h e o r e t i c a l d e v i c e d e r i v e d from i n f o r m a t i o n p r o c e s s i n g t h e o r y .  As s u c h , t h i s r e s e a r c h p r o v i d e s a  double p e r s p e c t i v e f o r f u t u r e r e s e a r c h .  F i r s t , t h e form of t h e i n q u i r y  w i l l p r o v i d e t h e b a s i s f o r more s y s t e m a t i c i n v e s t i g a t i o n s of t h e i n s t r u c t i o n a l model's a b i l i t y t o r e s o l v e t h e apparent  c o n f l i c t between  a l t e r n a t e frameworks and d e s i r e d concepts taught i n t h e c l a s s r o o m . Second, t h e use of frame t h e o r y as an a n a l y t i c a l t o o l f o r d e c i p h e r i n g c l a s s r o o m i n t e r a c t i o n s s h o u l d p r o v i d e f u t u r e r e s e a r c h e r s w i t h an a d d i t i o n a l p e r s p e c t i v e f o r i n t e r p r e t i n g and a s s e s s i n g t h e e f f i c a c y of o t h e r i n s t r u c t i o n a l models. In summary, t h i s r e s e a r c h can make s i g n i f i c a n t c o n t r i b u t i o n s t o the improvement of b o t h e d u c a t i o n a l p r a c t i c e and r e s e a r c h .  This  r e s e a r c h p r o v i d e s an i n s t r u c t i o n a l model t h a t i s d e s i g n e d t o i n c r e a s e students' understanding  of Newtonian dynamics, and, a t t h e same t i m e ,  remain r e s p o n s i v e t o t h e demands of t h e c l a s s r o o m and t h e p r a c t i c i n g teacher.  A d d i t i o n a l l y , t h i s r e s e a r c h p r o v i d e s a base f o r f u t u r e  s y s t e m a t i c r e s e a r c h c o n c e r n i n g t h e e f f i c a c y of t h e i n s t r u c t i o n a l model, and t h e use of frame t h e o r y as an a n a l y t i c a l p e r s p e c t i v e f o r i n t e r p r e t ing  c l a s s r o o m i n t e r a c t i o n s and s t u d e n t knowledge s t r u c t u r e s .  Theoretical Considerations T h i s r e s e a r c h d e v i a t e s from t h e s t a n d a r d p r a c t i c e o f c o n s t r u c t i n g the i n s t r u c t i o n a l s t r a t e g y , i n t o t a l i t y , from p r e v i o u s l y d e f i n e d educational theory.  T h i s d e v i a t i o n a r i s e s from two c o n s i d e r a t i o n s .  F i r s t , t o t h i s p o i n t , t h e g e n e r a l a r e a of r e s e a r c h i n which t h i s s t u d y i s l o c a t e d has been h e a v i l y i n v o l v e d w i t h c a t a l o g u i n g t h e elements of s t u d e n t s ' p e r s o n a l l y c o n s t r u c t e d knowledge, w i t h i n p a r t i c u l a r phenomenological  c o n t e x t s , and n o t i n d e v e l o p i n g t h e o r y o r u t i l 8  i z i n g theory  to explain the r e s u l t s .  As West, P i n e s , and S u t t o n (1982)  have p o i n t e d o u t : We c a n n o t j u s t l i s t t h o s e r e s e a r c h e r s who c l a i m t o be A u s u b e l i a n s , f o r example, and by d o i n g s o , d i s c r i m i n a t e t h e i r r e s e a r c h from t h o s e who c l a i m t o be B r u n e r i a n s o r K e l l i a n s (P. I D Second, t h e a c t s o f l e a r n i n g and u n d e r s t a n d i n g by an i n d i v i d u a l , w i t h i n a c l a s s r o o m environment, a r e " a r t i f a c t u a l " (Gowin, 1982, p. 26) e v e n t s unique t o t h e i n d i v i d u a l .  As a r e s u l t , no s i n g l e t h e o r y can  a d e q u a t e l y account f o r t h e m u l t i p l i c i t y o f l e a r n i n g modes p r e s e n t i n the c l a s s r o o m .  H a n i c a s and Secord (1983) e x p l i c i t l y r e c o g n i z e  this  problem when they argue t h a t : The p o i n t here i s p r e c i s e l y t h a t s p e c i f i c b e h a v i o r s - l i k e most e v e n t s i n t h e w o r l d - cannot be e x p l a i n e d as t h e s i m p l e m a n i f e s t a t i o n o f some s i n g l e law o r p r i n c i p l e ... Indeed, t h e a c t s o f p e r s o n s a r e open-systemic e v e n t s i n w h i c h a v a r i e t y of systems and s t r u c t u r e s a r e i n v o l v e d , systems t h a t a r e p h y s i c a l , b i o l o g i c a l , p h y s i o l o g i c a l , and ... s o c i o l o g i c a l as w e l l (p. 405). Because o f t h e s e c o n s i d e r a t i o n s , t h e r e s u l t i n g i n s t r u c t i o n a l s t r a t e g y cannot be c o n s i d e r e d  t o be immutable.  Rather, the strategy i s  open t o m o d i f i c a t i o n by t h e demands o f t h e c l a s s r o o m environment. t h i s way t h e g u l f between e d u c a t i o n a l  In  t h e o r y and p r a c t i c e might be  bridged.  Limitations This research  i s l i m i t e d i n two ways.  F i r s t , i t does n o t conform  w i t h t h e c l a s s i c a l view o f g e n e r a l i z a b i l i t y i n w h i c h e x t e r n a l  validity  i s e s t a b l i s h e d t h r o u g h t h e random s e l e c t i o n o f a sample from a w e l l defined population.  R a t h e r , t h i s r e s e a r c h has opted f o r a " n a t u r a l  b a s i s f o r g e n e r a l i z a t i o n " ( S t a k e , 1978, p. 5 ) . Second, t h e problem o f attempting  t o e s t a b l i s h equivalence  between t h e c o n s t r u c t s o f a frame  9  as a mental knowledge s t r u c t u r e , and t h e a l t e r n a t e framework i s extremely d i f f i c u l t .  As a r e s u l t , the v a l i d i t y of u s i n g elements of  frame t h e o r y as an a n a l y t i c d e v i c e i s open t o q u e s t i o n .  N e i t h e r of  t h e s e l i m i t a t i o n s i s , however, c o n s i d e r e d t o be a c r i t i c a l  design flaw.  The i s s u e of g e n e r a l i z a b i l i t y a r i s e s from two c o n s i d e r a t i o n s . F i r s t , because t h i s r e s e a r c h has attempted  t o develop an  instructional  model based on s t u d e n t b e l i e f s and c o g n i t i v e p r o c e s s i n g t e c h n i q u e s , i t has been c r u c i a l t h a t t h e s e b e l i e f s and t e c h n i q u e s be e x p l i c i t l y q u a l i t a t i v e l y described.  As a r e s u l t t h i s r e s e a r c h  and  has been l i m i t e d  to a s i n g l e , o p e r a t i o n a l c l a s s i n o r d e r t o o b t a i n t h e h i g h q u a l i t y , r i c h d e s c r i p t i o n s t h a t have been n e c e s s a r y f o r t h e development and assessment of t h e i n s t r u c t i o n a l model.  S e c o n d l y , as has a l r e a d y been  mentioned, t h i s r e s e a r c h has been d i r e c t e d a t d e v e l o p i n g a p r a c t i c a l i n s t r u c t i o n a l model t h a t c o u l d be adapted by p r a c t i c i n g t e a c h e r s t o meet t h e i r own  s e t s of r e q u i r e m e n t s .  T h i s d i r e c t i o n , however, r e q u i r e s  t h a t t h i s r e s e a r c h be p l a c e d w i t h i n a c l a s s r o o m c o n t e x t t h a t i s b o t h r e c o g n i z a b l e and e m p a t h e t i c  t o them, f o r as L i n c o l n and Guba (1985)  have p o i n t e d out . . . i f you want people t o u n d e r s t a n d b e t t e r than they o t h e r w i s e m i g h t , p r o v i d e them i n f o r m a t i o n i n t h e form i n which t h e y u s u a l l y e x p e r i e n c e i t . They w i l l be a b l e , b o t h t a c i t l y and p r o p o s i t i o n a l l y , t o d e r i v e n a t u r a l i s t i c g e n e r a l i z a t i o n s t h a t w i l l prove t o be u s e f u l e x t e n s i o n s of t h e i r u n d e r s t a n d i n g s (p. 120). The developmental attempt  n a t u r e of t h i s r e s e a r c h i s a l s o apparent  i n the  t o d e v e l o p an a n a l y t i c a l d e v i c e , the c l u e s t r u c t u r e , from the  c o n s t r u c t s of frame t h e o r y and t h e s t u d e n t s ' a l t e r n a t e frameworks.  At  t h i s s t a g e , i t i s not c l e a r whether o r not a l t e r n a t e frameworks can  be  p r o d u c t i v e l y i n t e r p r e t e d i n terms of frames, as o u t l i n e d by M i n s k y (1975).  C e r t a i n l y , t h e r e i s a d i f f e r e n c e i n the l e v e l of a p p l i c a t i o n 10  of t h e s e c o n s t r u c t s ; t h a t i s , frames a r e c o n s i d e r e d t o be i d i o s y n c r a t i c , whereas a l t e r n a t e frameworks a r e g e n e r a l i z e d r e p r e s e n t a t i o n s of c o m m o n a l i t i e s between i d i o s y n c r a t i c b e l i e f s .  The s t r e n g t h and p r e v a -  l e n c e of t h e c o m m o n a l i t i e s t h a t have l e d t o t h e c o n s t r u c t i o n of t h e a l t e r n a t e framework, however, i n d i c a t e t h a t t h e i n d i v i d u a l s i n v o l v e d have c o n s t r u c t e d knowledge from e x p e r i e n c e  i n remarkably s i m i l a r ways.  T h i s s i m i l a r i t y of c o n s t r u c t i o n lends credence t o t h e use of frames as a h e u r i s t i c device f o r a n a l y t i c a l  purposes.  Because of i t s developmental c h a r a c t e r , t h i s r e s e a r c h can o n l y be c o n s i d e r e d t o be a t a h y p o t h e s i s  generating stage.  As a r e s u l t , the  i s s u e s of g e n e r a l i z a b i l i t y and v a l i d i t y w i l l have t o be a d d r e s s e d more s y s t e m a t i c a l l y i n subsequent s t u d i e s .  11  CHAPTER TWO  A Review of t h e R e l a t e d L i t e r a t u r e  Over t h e p a s t decade an i n c r e a s i n g amount of s c i e n c e e d u c a t i o n r e s e a r c h has been d i r e c t e d towards u n c o v e r i n g and c a t a l o g i n g s t u d e n t s ' b e l i e f s c o n c e r n i n g s p e c i f i c p h y s i c a l phenomena.  I t has been hoped t h a t  such r e s e a r c h would e v e n t u a l l y l e a d t o an improvement i n t h e q u a l i t y of u n d e r s t a n d i n g o f t h e s e phenomena by s t u d e n t s i n t h e s c i e n c e s and t e c h n o l o g i e s ( G i l b e r t and W a t t s , 1983).  To d a t e , t h e r e s e a r c h t o p i c s  have been e c l e c t i c w i t h probes b e i n g launched a t a r e a s such as f o r c e , u n i f o r m and a c c e l e r a t e d m o t i o n , energy, e l e c t r i c i t y , h e a t , l i g h t , and t h e p a r t i c u l a t e n a t u r e of m a t t e r .  W i t h i n these areas a s u b s t a n t i a l  number of s t u d i e s have t a r g e t e d t h e a s s o c i a t e d a r e a s of f o r c e and m o t i o n as b e i n g e s p e c i a l l y f r u i t f u l beliefs.  f o r t h e d e l i n e a t i o n of s t u d e n t s *  The r a t i o n a l e f o r t h i s c h o i c e has p r o b a b l y b e s t been s t a t e d  by Champagne, K l o p f e r , and Gunstone (1982, p. 3 9 9 ) : The development of p r a c t i c a l p r i n c i p l e s of motion i s necess a r y f o r c o p i n g w i t h t h e moving o b j e c t s t h a t a r e encountered in daily l i f e . Thus, a l l s t u d e n t s b e g i n t h e f o r m a l s t u d y of mechanics w i t h an e x p e r i e n t i a l l y v e r i f i e d s e t of p r i n c i p l e s t h a t a l l o w them t o p r e d i c t t h e r e a l w o r l d . In a d d i t i o n , the same words t h a t a r e used t o d e s c r i b e and e x p l a i n motion i n everyday language a l s o a r e used by p h y s i c i s t s . W i t h i n t h e s e t of r e s e a r c h s t u d i e s t h a t have i n v e s t i g a t e d s t u d e n t s ' b e l i e f s c o n c e r n i n g f o r c e and m o t i o n , i . e . dynamics, two s u b - s e t s of r e s e a r c h c a t e g o r i e s have been r e c o g n i z e d .  These a r e : f i r s t ,  those  s t u d i e s t h a t have c a t a l o g u e d s t u d e n t b e l i e f s of dynamics on t h e b a s i s of t h e i r own m e r i t s and " w i t h o u t assessment a g a i n s t any e x t e r n a l l y d e f i n e d system"  ( D r i v e r & E a s l e y , 1978, p. 6 3 ) , and second,  those  s t u d i e s t h a t have a s s e s s e d s t u d e n t b e l i e f s of dynamics r e l a t i v e t o 1 2  t h e i r congruence w i t h a c c e p t e d s c i e n t i f i c c o n c e p t s .  These two  categor-  i e s a r e r e f e r r e d t o , r e s p e c t i v e l y , as the i d e o g r a p h i c and the nomot h e t i c ( D r i v e r & E a s l e y , 1978).  I t i s t h e s e two c a t e g o r i e s t h a t s h a l l  be used as the b a s i s f o r d e l i n e a t i n g r e s e a r c h s t r a n d s w i t h i n the literature. The  Ideographic  Approach  A g u i r r e (1978), Kuhn (1979), T r o w b r i d g e , Lawson and McDermott (1980), Watts (1983, 1982), and Watts and Z y l b e r s z t a j n (1981) have a l l d i r e c t e d t h e i r research along ideographic strands.  T h e i r s t u d i e s have  i n v e s t i g a t e d s t u d e n t s ' b e l i e f s of f o r c e s i n e q u i l i b r i u m , f r e e - f a l l m o t i o n , dynamics, g r a v i t a t i o n a l f o r c e , and f o r c e i n g e n e r a l . The  t e r m i n o l o g i e s used by t h e s e r e s e a r c h e r s t o d e s c r i b e t h e i r  a n a l y t i c a l u n i t s r e f l e c t t h e i r i d e o g r a p h i c approach.  A g u i r r e (1978)  and Kuhn (1979) b o t h seek t o d e s c r i b e s t u d e n t b e l i e f s . t i o n i s t h a t t h e s e b e l i e f s a r e e x p e r i e n t i a l l y based and, degree, formed e x t e r n a l l y t o f o r m a l i n s t r u c t i o n .  Their proposito a great  T r o w b r i d g e , Lawson,  and McDermott (1980a, b) seek t o e l i c i t the s t u d e n t s ' " n a i v e  concept-  u a l i z a t i o n s " (p. 1) which they equate w i t h p r i m i t i v e b e l i e f s o r ceptions.  precon-  Watts and Z y l b e r s z t a j n c o n s i s t e n t l y attempt t o r e c o n s t r u c t a  s t u d e n t s ' a l t e r n a t i v e framework which they d e f i n e as a s e t of  "coherent  i d e a s of the w o r l d based on t h e i r own  Clearly,  e x p e r i e n c e s " (p. 360).  t h e s e r e s e a r c h e r s have p r e d i c a t e d t h e i r s t u d i e s on s t r i k i n g l y assumptions.  similar  F i r s t , s t u d e n t s a r e p r o p r i e t o r s of i d i o s y n c r a t i c know-  ledge c o n c e r n i n g s c i e n t i f i c c o n c e p t s .  Second, t h i s knowledge has been  c o n s t r u c t e d on an e x p e r i e n t i a l f o u n d a t i o n .  F i n a l l y , t h i s knowledge has  been a c q u i r e d p r i o r t o f o r m a l i n s t r u c t i o n i n the c o n c e p t ( s ) i n question.  13  These assumptions are r e f l e c t e d i n the methodology and u t i l i z e d by the m a j o r i t y of t h e s e r e s e a r c h e r s .  W i t h the e x c e p t i o n  the s t u d i e s by Watts (1983, 1982), and Watts and all  researchers  subjects  Z y l b e r s z t a j n (1981),  have employed some form of c l i n i c a l  interview  would r e f l e c t t h e i d i o s y n c r a t i c n a t u r e of the knowledge b e i n g tigated.  of  Watts and Z y l b e r s z t a j n (1981) were i n t e r e s t e d i n  that inves-  "assessing  the p o p u l a r i t y of some p a r t i c u l a r a l t e r n a t i v e frameworks" (p. 360) a l a r g e sample of s t u d e n t s and In a d d i t i o n , a l l researchers no exposure t o f o r m a l  from  thus opted f o r a paper and p e n c i l t e s t .  have used s u b j e c t s who  have had  little  or  p h y s i c s i n s t r u c t i o n i n o r d e r t o i n v e s t i g a t e the  e x p e r i e n t i a l n a t u r e of t h i s knowledge. Results A l t h o u g h a number of d i f f e r e n t c o n t e x t s a r e employed i n t h e s e i n v e s t i g a t i o n s s i m i l a r i t i e s i n r e s u l t s do o c c u r .  A l l researchers  found  t h a t the m a j o r i t y of t h e i r s u b j e c t s b e l i e v e d t h a t i f an o b j e c t i s moving a f o r c e must be a c t i n g upon t h a t o b j e c t . p o s i t i o n was recognized constant  a l s o h e l d t o be t r u e .  by Kuhn "(1979) who  c o n v e r s e of  this  V a r i a t i o n s of t h i s p o s i t i o n were  found a number of h i s s u b j e c t s f o r c e , and by A g u i r r e  equating  (1978), Watts  and  Z y l b e r s z t a j n (1981), and T r o w b r i d g e , Lawson and McDermott (1980)  who  all  speed w i t h c o n s t a n t  The  found t h a t a m a j o r i t y of t h e i r s u b j e c t s b e l i e v e d t h a t m o t i o n due  the i n t e r a c t i o n of two b o d i e s was force.  Aguirre's  y e a r s of age  due  greater  (1978) r e s u l t s i n d i c a t e t h a t s u b j e c t s below t w e l v e  s i m p l i f y t h i s b e l i e f even f u r t h e r and  f o r c e i n the system thus s u g g e s t i n g dependent.  t o the body w i t h the  to  recognize  t h a t t h i s b e l i e f may  Both s t u d i e s by Watts (1982, 1983)  and  be  only  one  age  t h a t by Watts  and  Z y l b e r s z t a j n (1981) i n d i c a t e t h a t some c h i l d r e n r e q u i r e t h a t t h e r e be medium, such as a i r , t h r o u g h which a f o r c e can a c t . 14  In the case of  a  the  l a t t e r s t u d y t h i s b e l i e f was  s p e c i f i c a l l y c i t e d t o s u p p o r t the sub-  j e c t s ' c o n t e n t i o n t h a t the moon l a c k e d a g r a v i t a t i o n a l f i e l d .  These  r e s e a r c h e r s a l s o i d e n t i f i e d a b e l i e f among t h e i r s u b j e c t s t h a t an a p p l i c a t i o n of f o r c e always r e s u l t e d i n some form of a c t i o n . g r e a t e r the a p p l i c a t i o n of f o r c e , the g r e a t e r was activity. was  The  the r e s u l t a n t  The b e l i e f t h a t g r a v i t a t i o n a l f o r c e i n c r e a s e s w i t h  height  common t o a s u b s t a n t i a l number of s u b j e c t s i n the s t u d i e s of  A g u i r r e (1978), Kuhn (1979), Watts ( 1 9 8 2 ) , and Watts and Z y l b e r s z t a j n (1981).  A g u i r r e , however, found t h i s p e r c e p t i o n most p r e v a l e n t i n  s u b j e c t s l e s s than e l e v e n y e a r s of age s u g g e s t i n g t h a t i t may  be  age  dependent. Other b e l i e f s were r e c o g n i z e d i n s i n g l e s t u d i e s .  Watts (1983)  r e p o r t e d the e x i s t e n c e of the f o l l o w i n g b e l i e f s : f o r c e i s an o b l i g a t i o n t o complete an a c t i o n a g a i n s t some form of r e s i s t a n c e , o b j e c t s t h a t a r e r e s t r a i n e d i n p o s i t i o n have an i n h e r e n t f o r c e , o b j e c t s t h a t can  or  might cause e v e n t s t o o c c u r have an i n h e r e n t f o r c e , and moving o b j e c t s have i n h e r e n t f o r c e .  A g u i r r e (1978) a l s o r e p o r t e d the e x i s t e n c e of a  b e l i e f i n the i n h e r e n t f o r c e of r e s t r a i n e d o b j e c t s . i n h e r e n t f o r c e c o u l d o n l y ' h o l d ' and not  'pull'.  I n t h i s c a s e , the  A g u i r r e (1978) a l s o  r e c o g n i z e d t h a t a l a r g e number of h i s s u b j e c t s c o u l d o n l y i d e n t i f y a force e q u i l i b r i u m condition using a p o s i t i o n c r i t e r i o n .  Watts (1982)  i d e n t i f i e d the b e l i e f t h a t g r a v i t a t i o n a l f o r c e o n l y o p e r a t e s when objects  fall.  Viewed i n t o t a l i t y t h e s e b e l i e f s and p e r c e p t i o n s appear t o r e p r e s e n t a m i x t u r e of A r i s t o t e l i a n - l i k e and dynamics.  The  Impetus t h e o r i e s of  r e p r e s e n t a t i v e sample of s u b j e c t s of t h e s e s t u d i e s views  f o r c e and m o t i o n from a pre-Newtonian p o s i t i o n b u t , as Watts Z y l b e r s z t a j n (1981) n o t e d a t the b e g i n n i n g of t h e i r paper: 15  and  I t i s no news t h a t c h i l d r e n have pronounced A r i s t o t e l i a n views about f o r c e and m o t i o n , and o f t e n r e j e c t , o r f a i l t o a p p r e c i a t e , t h e s u b s t a n c e of Newton's v e r s i o n of mechanics (p. 360). The Nomothetic Approach The m a j o r i t y of s t u d i e s i n v e s t i g a t i n g s t u d e n t s ' b e l i e f s of f o r c e and m o t i o n have o c c u r r e d a l o n g t h e n o m o t h e t i c s t r a n d .  Researchers  o p e r a t i n g from t h i s p e r s p e c t i v e a r e Champagne, R l o p f e r , and Anderson ( 1 9 7 9 ) , Clement  (1981, 1977), d i S e s s a ( 1 9 8 1 ) , F l e s h n e r ( 1 9 7 0 ) , Gunstone  and White ( 1 9 8 1 ) , Helm ( 1 9 7 8 ) , L e i t h ( 1 9 8 2 ) , McCloskey ( 1 9 8 3 ) , M c C l o s k e y , Carmozza, and Green ( 1 9 8 0 ) , M i n s t r e l 1 ( 1 9 8 1 ) , S a l t i e l  and  Malgrange ( 1 9 8 0 ) , S j o b e r g and L i e ( 1 9 8 1 ) , Trowbridge and McDermott (1980a, b ) , and V i e n n o t (1979).  These r e s e a r c h e r s have a t t e m p t e d t o  assess student b e l i e f s r e l a t i v e to accepted s c i e n t i f i c the  concepts w i t h i n  f o l l o w i n g c o n t e x t s : c l a s s i c a l mechanics (Champagne, K l o p f e r , and  Anderson, 1979, S j o b e r g and L i e , 1981), c o m p u t e r - s i m u l a t e d m o t i o n i n two d i m e n s i o n s ( d i S e s s a , 1981), f o r c e ( F l e s h n e r , 1970), g r a v i t a t i o n a l f o r c e (Gunstone and W h i t e , 1981), dynamics (Helm, 1978), c u r v i l i n e a r and p r o j e c t i l e m o t i o n (McCloskey, 1983 and M c C l o s k e y , Carmozza,  and  Green, 1980), the 'at r e s t ' c o n d i t i o n of an o b j e c t ( M i n s t r e l l , 1981), motion and v e l o c i t y i n v a r y i n g frames of r e f e r e n c e ( S a l t i e l  and  Malgrange, 1980), v e l o c i t y and a c c e l e r a t i o n (Trowbridge and McDermott, 1980a, b ) , and energy and m o t i o n ( V i e n n o t , 1970).  The t e r m i n o l o g y ,  methodology, and s u b j e c t s used i n t h e s e s t u d i e s a l l r e f l e c t t h e nomothetic p e r s p e c t i v e . The t e r m i n o l o g i e s used by t h e s e r e s e a r c h e r s t o d e s c r i b e t h e i r a n a l y t i c a l u n i t s have s i m i l a r c o n n o t a t i o n s . Anderson ( 1 9 7 9 ) , Clement  Champagne, K l o p f e r , and  ( 1 9 8 1 ) , Helm ( 1 9 7 8 ) , L e i t h ( 1 9 8 2 ) , McCloskey  ( 1 9 8 3 ) , S j o b e r g and L i e ( 1 9 8 1 ) , and Trowbridge and McDermott (1980a, b)  16  a l l attempt  t o i d e n t i f y s t u d e n t s ' concepts and/or m i s c o n c e p t s .  The  i m p l i c a t i o n i s t h a t t h e s e w i l l n o t , i n a l l p r o b a b i l i t y , match t h e a c c e p t e d s c i e n t i f i c concept.  D i S e s s a (1981) attempts  to define  s t u d e n t s ' " n a i v e knowledge" ( p . 1) t h a t has y e t t o reach t h e s o p h i s t i cated l e v e l of the expert.  S i m i l a r l y , McCloskey, Carmozza and Green  (1980) t r y t o d e s c r i b e s t u d e n t " n a i v e b e l i e f s " ( p . 1139).  Fleshner  (1970) speaks o f d e t e r m i n i n g how " f o r m e r l y a c q u i r e d knowledge" ( p . 201) i s r a t i o n a l i z e d w i t h newly a c q u i r e d s c h o o l knowledge.  Gunstone and  White (1981) w i s h t o a s s e s s s t u d e n t s ' p r e d i c t i v e and e x p l a n a t o r y c a p a b i l i t i e s when f a c e d w i t h f o r m a l p h y s i c s problems. attempts  M i n s t r e l 1 (1981)  t o e l i c i t student p r e - or a l t e r n a t e conceptions p r i o r t o  i n s t r u c t i o n i n t h e a c c e p t e d s c i e n t i f i c concept.  Viennot  t o r e c o n s t r u c t s t u d e n t r e a s o n i n g p a t t e r n s i n an attempt how they i n t e r a c t w i t h t e a c h i n g .  (1979) wishes t o determine  What seems t o be i m p l i c i t i n these  t e r m i n o l o g i e s i s t h a t s t u d e n t b e l i e f s a r e somehow a t odds w i t h a c c e p t e d scientific  thought.  In a s i m i l a r f a s h i o n , t h e methodologies nomothetic  approach.  s c i e n t i f i c concepts  In order t o c o n t r a s t student b e l i e f s w i t h t h e m a j o r i t y o f r e s e a r c h e r s have employed paper and  p e n c i l t e s t s w i t h d e f i n a b l e ' r i g h t ' answers. methodological  u t i l i z e d r e f l e c t the  Exceptions to t h i s  format a r e found i n t h e i n v e s t i g a t i o n s o f Clement  (1977), d i S e s s a (1981), F l e s h n e r (1970), McCloskey (1983), M i n s t r e l 1 (1981) , and Trowbridge and McDermott (1980a, b ) . A l l o f t h e s e r e s e a r c h e r s , w i t h t h e e x c e p t i o n of M i n s t r e l 1, have used some form of clinical  i n t e r v i e w i n o r d e r t o observe t h e i r s u b j e c t s i n p h y s i c a l  situations.  M i n s t r e l ! ' s research occurs w i t h a classroom  setting,  where t h e r e s e a r c h e r i s t h e t e a c h e r , and t h u s , he has opted f o r a whole c l a s s d i s c u s s i o n / i n t e r v i e w format. 17  The  s u b j e c t s i n v e s t i g a t e d , w i t h the e x c e p t i o n of one s t u d y , have  been exposed t o some type of formal p h y s i c s i n s t r u c t i o n .  The  t h e s e s u b j e c t s has a l l o w e d the e x p l i c i t j u x t a p o s i t i o n of the  use  of  students'  b e l i e f s of dynamics w i t h the Newtonian c o n c e p t s of dynamics.  The  e x c e p t i o n t o the use of the s u b j e c t group has o c c u r r e d i n t h e s t u d y L e i t h (1982).  In t h i s i n s t a n c e the r e s e a r c h e r was  attempting  by  to  v a l i d a t e a s e t of t a s k s d e r i v e d from a P i a g e t i a n s t u d y and used a group of s c h o o l c h i l d r e n , 7-12  years of  age.  In g e n e r a l , r e s e a r c h e r s i n v e s t i g a t i n g s t u d e n t s ' b e l i e f s of dynamics from a n o m o t h e t i c p e r s p e c t i v e w i l l use  ' r i g h t answer' o r i e n t e d  paper and p e n c i l t e s t s g i v e n t o s t u d e n t s t h a t have been exposed t o some l e v e l of f o r m a l  instructions.  Results The  r e s u l t s from t h o s e s t u d i e s employing the n o m o t h e t i c approach  have, f o r the most p a r t , been deduced from e r r o r a n a l y s e s of  student  responses t o q u e s t i o n s  Newtonian  mechanics.  ( e i t h e r w r i t t e n or v e r b a l ) c o n c e r n i n g  These r e s u l t s w i l l  be d i s c u s s e d under two  categories:  f i r s t , those t h a t d e a l w i t h c o n c e p t s of dynamics, and second,  those  that deal with kinematics. A b e l i e f t h a t appears t o be p e r v a s i v e among s u b j e c t s s t u d i e d by a l a r g e number of r e s e a r c h e r s  (Champagne, K l o p f e r and Anderson,  Gunstone and W h i t e , 1981, M i n s t r e l l , 1981,  1979,  S a l t i e l and Malgrange,  and V i e n n o t ,  1979)  forces.  c o n v e r s e of t h i s b e l i e f has a l s o appeared f r e q u e n t l y and  The  i s t h a t a body a t r e s t i s d e v o i d of any  1980,  i n a number of forms. Minstrell  applied  Champagne, K l o p f e r and Anderson (1979),  and  (1981) r e p o r t t h a t a number of t h e i r s u b j e c t s h e l d the b e l i e f  than any a p p l i c a t i o n of f o r c e w i l l produce m o t i o n and  that a  constant  a p p l i c a t i o n of f o r c e w i l l produce u n i f o r m m o t i o n (Champagne, K l o p f e r 18  and Anderson, 1979).  A l l i e d w i t h t h i s b e l i e f are the b e l i e f s  that  v e l o c i t y i s p r o p o r t i o n a l t o the a p p l i e d f o r c e (Champagne, K l o p f e r Anderson, 1979)  and  t h a t a change i n a p p l i e d f o r c e r e s u l t s i n a c c e l e r -  a t i o n (Champagne, K l o p f e r and Anderson, 1979, 1982).  Clement ( 1 9 8 1 ) , d i S e s s a  Green (1980), S j o b e r g f i e d s u b j e c t s who  and  Clement, 1981,  Leith,  ( 1 9 8 1 ) , McCloskey (1983), Carmozza  and L i e (1981), and V i e n n o t (1979) a l s o  b e l i e v e d t h a t when two  and  identi-  or more f o r c e s a r e p r e s e n t  r e s u l t a n t motion w i l l be i n the d i r e c t i o n of the l a r g e s t f o r c e .  any  A l l of  t h e s e b e l i e f s c o n t r i b u t e t o a s t r u c t u r e t h a t Clement (1981) c a l l s  the  "motion i m p l i e s a f o r c e m i s c o n c e p t i o n " (p. 67).  T h i s s t r u c t u r e , as  McCloskey (1983) has p o i n t e d o u t , i s r e m i n i s c e n t  of t h e  pre-Galilean  Impetus Theory. Related  t o t h i s s t r u c t u r e i s the l a c k of c o n s i d e r a t i o n g i v e n  some s u b j e c t s t o frames of r e f e r e n c e Malgrange, 1980) 1981,  (McCloskey, 1983,  Saltiel  by  and  and a c t i o n / r e a c t i o n c o m b i n a t i o n s ( S j o b e r g and L i e ,  V i e n n o t , 1979).  Further  removed, but s t i l l  r e l a t e d to t h i s  s t r u c t u r e , i s the b e l i e f t h a t a p p l i e d f o r c e o c c u r s as o n l y a push or pull  ( F l e s h n e r , 1970)  Minstrell  which might l e a d t o the b e l i e f , r e p o r t e d  by  (1981) t h a t o n l y animate o b j e c t s can a p p l y a f o r c e .  S p e c i f i c b e l i e f s c o n c e r n i n g m o t i o n due been i d e n t i f i e d .  t o g r a v i t a t i o n a l f o r c e have  Gunstone and White (1981) r e p o r t e d t h a t a m i n o r i t y  s u b j e c t s thought t h a t g r a v i t a t i o n a l a c c e l e r a t i o n was o b j e c t ' s weight and weight was a reference  surface.  Sjoberg  a f u n c t i o n of  a f u n c t i o n of the o b j e c t ' s h e i g h t and L i e (1981) r e p o r t e d  that  m a t e l y 15% of t h e i r s u b j e c t s thought t h a t a g r a v i t a t i o n a l r e q u i r e s some form of medium f o r i t t o be  an  above  approxifield  effective.  O b s e r v a t i o n s c o n c e r n i n g s u b j e c t s ' b e l i e f s of k i n e m a t i c s made by L e i t h (1982), and Trowbridge and McDermott (1980a). 19  of  have been A l l of  t h e s e r e s e a r c h e r s found t h a t t h e i r s u b j e c t s tended t o compare t h e s p e e d / v e l o c i t y of two o b j e c t s on t h e b a s i s of p o s i t i o n (when two o b j e c t s a r e s i d e - b y - s i d e they have t h e same speed) o r d i s t a n c e l e d (the g r e a t e r the d i s t a n c e , the greater the speed).  L e i t h (1982)  a l s o found t h a t a b s o l u t e speed of an o b j e c t was equated w i t h t r a v e l time w i t h o u t  regard t o distance t r a v e l l e d .  travel-  least  Trowbridge and  McDermott (1980a, b) observed t h a t a s u b s t a n t i a l m i n o r i t y (up t o 30%) of t h e i r s u b j e c t s judged r e l a t i v e a c c e l e r a t i o n on t h e b a s i s of p o s i t i o n , i . e . i f one o b j e c t p a s s e d a n o t h e r i t had g r e a t e r a c c e l e r a t i o n . The  r e s u l t s of t h e i n v e s t i g a t i o n s c o n c e r n i n g  students' b e l i e f s of  mechanics t h a t have taken t h e n o m o t h e t i c approach a r e p r o b a b l y summed up by McCloskey (1983), and S j o b e r g and L i e (1981).  best  First,  McCloskey: Indeed, t h e i d e a s about m o t i o n h e l d by most p e o p l e w i t h no formal t r a i n i n g i n p h y s i c s , and by many who have completed a t l e a s t one p h y s i c s c o u r s e , a r e much c l o s e r t o t h e account g i v e n by t h e I m p e t u s Theory t h a n they a r e t o Newtonian mechanics ( p . 125) ... The s t r i k i n g s i m i l a r i t y between t h e views o f t h e medieval p h i l o s o p h e r s and those of our s u b j e c t s s u g g e s t s t h a t t h e Impetus Theory i s a n a t u r a l outcome of e x p e r i e n c e w i t h t e r r e s t r i a l m o t i o n (p. 1 2 7 ) . F i n a l l y , S j o b e r g and L i e : T h i s r a t h e r d e p r e s s i n g p i c t u r e " f o r c e s " (!) on us an unders t a n d i n g t h a t t h e f o u n d a t i o n o f c l a s s i c a l mechanics i s f a r from s e l f - e v i d e n t , which many t e x t b o o k s more o r l e s s assume. On t h e c o n t r a r y , Newton's laws a r e c o n t r a r y t o common sense i d e a s d e v e l o p e d i n t u i t i v e l y and s p o n t a n e o u s l y by p u p i l s (and a d u l t s ) (p. 18).  A Comparison o f R e s u l t s A comparison of t h e r e s u l t s of each r e s e a r c h s t r a n d r e v e a l s a s u b s t a n t i a l l e v e l o f congruence between b o t h s t r a n d s . was  evident i n s u b j e c t s ' b e l i e f s concerning  p o s s i b l e sources  t h e e f f e c t s of f o r c e s ,  o f f o r c e , and t h e types of f o r c e s . 20  T h i s congruence  The most commonly e l i c i t e d b e l i e f from s u b j e c t s i n b o t h  research  s t r a n d s was t h a t motion i s t h e r e s u l t of a c o n t i n u o u s a p p l i c a t i o n of force.  T h i s b e l i e f , o r i t s c o n v e r s e , was r e c o g n i z e d  operating  along  the ideographic  by a l l r e s e a r c h e r s  s t r a n d and by Champagne, K l o p f e r and  Anderson (1979), Clement (1981), Gunstone and w h i t e ( 1 9 8 1 ) , McCloskey ( 1 9 8 3 ) , McCloskey, Carmozza, and Green (1980), M i n s t r e l l S a l t i e l and Malgrange ( 1 9 8 0 ) , S j o b e r g (1979) from t h e n o m o t h e t i c group.  (1981),  and L i e (1981), and V i e n n o t  This b e l i e f reappeared, t h i n l y  d i s g u i s e d , i n t h e b e l i e f t h a t an a p p l i c a t i o n o f c o n s t a n t  f o r c e produced  u n i f o r m m o t i o n (Kuhn, 1978, Champagne, K l o p f e r and Anderson, 1979), o r as t h e b e l i e f t h a t an a p p l i c a t i o n o f a v a r i a b l e f o r c e r e s u l t s i n a c c e l e r a t i o n (Watts and z y l b e r s z t a j n , 1981, Champagne, K l o p f e r , and Anderson, 1979, Clement, 1981, L e i t h , 1982).  Again, the strand  b o u n d a r i e s appear i n v i s i b l e t o t h e s e b e l i e f s . D e s c r i p t i v e s t a t i s t i c s r e p o r t e d i n s t u d i e s from b o t h suggest t h a t t h i s c l a s s o f b e l i e f s may be p r e v a l e n t levels.  strands  a t many  educational  Clement (1981) r e p o r t e d t h a t 88% o f t h e f i r s t y e a r and  a p p r o x i m a t e l y 70% of t h e second, t h i r d , and f o u r t h year  engineering  s t u d e n t s t e s t e d a t an American u n i v e r s i t y found i t d i f f i c u l t " t o t h i n k about an o b j e c t c o n t i n u i n g t o move i n one d i r e c t i o n w i t h t h e t o t a l n e t f o r c e a c t i n g i n a d i f f e r e n t d i r e c t i o n " ( p . 6 7 ) . McCloskey (1983) found t h a t more than 33% of t h e American h i g h s c h o o l  and c o l l e g e s t u d e n t s he  i n v e s t i g a t e d e x p l a i n e d m o t i o n i n terms o f an Impetus Theory. m a t e l y o n e - t h i r d o f t h e Norwegian h i g h s c h o o l u t i l i z e d by S j o b e r g  Approxi-  and c o l l e g e s t u d e n t s  and L i e (1981) c o n s i s t e n t l y drew f o r c e arrows i n  the d i r e c t i o n o f m o t i o n o f a pendulum bob. Watts and Z y l b e r s z t a j n (1981) r e p o r t e d t h a t 85% of t h e B r i t i s h , f o u r t e e n y e a r o l d s u b j e c t s they t e s t e d a s s o c i a t e d f o r c e w i t h m o t i o n . 21  R e s u l t s such as these tend  t o suggest t h a t t h e b e l i e f t h a t m o t i o n i m p l i e s a f o r c e i s n o t o n l y common but p e r v a s i v e . Subjects' b e l i e f s concerning the i n t e r a c t i v e e f f e c t s of s i m u l taneous f o r c e s were a l s o found t o c o r r e s p o n d c l o s e l y . ideographic  Using the  approach A g u i r r e ( 1 9 7 8 ) , T r o w b r i d g e , Lawson, and McDermott  ( 1 9 8 0 ) , Watts and Z y l b e r s z t a j n (1981) r e p o r t e d  that t h e i r  subjects  a t t r i b u t e d any r e s u l t a n t m o t i o n o n l y t o t h e l a r g e s t f o r c e . diSessa  Similarly,  (1981), McCloskey (1983), McCloskey, Carmozza, and Green  (1980), S j o b e r g  and L i e (1981), and V i e n n o t (1979), u s i n g t h e nomo-  t h e t i c approach, r e p o r t e d t h a t t h e i r s u b j e c t s b e l i e v e d than any r e s u l t a n t m o t i o n would be i n t h e d i r e c t i o n o f t h e l a r g e s t f o r c e . D i r e c t l y a s s o c i a t e d w i t h t h e s e b e l i e f s i s t h e f a i l u r e of s u b j e c t s t o c o n s i d e r a c t i o n / r e a c t i o n c o m b i n a t i o n s ( S j o b e r g and L i e , 1981, V i e n n o t , 1979). Subjects  from b o t h s t r a n d s a t t r i b u t e d f o r c e t o o n l y t h o s e o b j e c t s  t h a t had m o t i v e c h a r a c t e r i s t i c s . W i t h i n t h e i d e o g r a p h i c (1983) and A g u i r r e  s t r a n d Watts  (1978) found t h a t s u b j e c t s a t t r i b u t e d an i n h e r e n t  f o r c e t o t h o s e o b j e c t s t h a t can o r might cause e v e n t s t o o c c u r . Minstrell  (1981), operating  from a n o m o t h e t i c p o s i t i o n , found t h a t h i s  s t u d e n t s b e l i e v e d t h a t o n l y animate o b j e c t s can a p p l y a f o r c e . b e l i e f s strongly r e f l e c t the p r e v a i l i n g b e l i e f , discussed  These  previously,  t h a t motion i m p l i e s f o r c e . E x t e r n a l body f o r c e s , such as g r a v i t y , a r e n o t r e c o g n i z e d s u b j e c t s i n v e s t i g a t e d under e i t h e r r e s e a r c h approach.  by some  S t u d i e s by Watts  (1983, 1982), Watts and Z y l b e r s z t a j n (1981), and S j o b e r g  and L i e (1981)  found t h a t s u b j e c t s r e q u i r e d g r a v i t y t o a c t t h r o u g h some form o f connecting  medium.  As a r e s u l t g r a v i t y i s t r a n s f o r m e d i n t o an e x t e r n a l  s u r f a c e f o r c e which p u l l s .  S i m i l a r r e s u l t s were found i n a study by 22  Fleshner  (1970).  He r e p o r t e d t h a t h i s s u b j e c t s b e l i e v e d t h a t f o r c e  c o u l d o n l y be a p p l i e d by a i n d i r e c t push o r p u l l .  These r e p o r t e d  b e l i e f s suggest t h a t o n l y e x t e r n a l s u r f a c e f o r c e s (pushes o r p u l l s ) a r e recognized. These c o n g r u e n t , o r c l o s e l y a s s o c i a t e d r e s u l t s suggest t h a t t h e s u b j e c t s i n v o l v e d i n t h e s e s t u d i e s view t h e e f f e c t s , s o u r c e s , of f o r c e s from a r e a s o n a b l y that t h i s viewpoint  common p o s i t i o n .  and types  Clement (1981) s u g g e s t s  i s a r e s u l t of a common, e x p e r i e n t i a l  interpreta-  t i o n of f o r c e : I n t h e r e a l w o r l d , where f r i c t i o n i s p r e s e n t , one must push an o b j e c t t o keep i t moving. Since f r i c t i o n i s often not recognized a s a f o r c e by t h e b e g i n n e r , t h e s t u d e n t may b e l i e v e t h a t c o n t i n u i n g m o t i o n i m p l i e s t h e presence of a c o n t i n u i n g f o r c e i n t h e same d i r e c t i o n , as a n e c e s s a r y cause of t h e motion (p. 6 6 ) . I f t h i s common v i e w p o i n t  i s v a l i d , i t appears t o r e p r e s e n t  framework of dynamics c o n s t r u c t e d  from t h r e e b a s i c t e n e t s :  an a l t e r n a t e first,  m o t i o n i m p l i e s an a p p l i c a t i o n o f f o r c e , second, f o r c e i s a s s o c i a t e d o n l y w i t h m o t i v e o b j e c t s , and t h i r d , e x t e r n a l s u r f a c e f o r c e s a r e t h e only types of f o r c e s a v a i l a b l e .  In o r d e r t o e x p l i c a t e and t r a n s f o r m  (where d e s i r e a b l e and pos-  s i b l e ) t h e a l t e r n a t e framework of dynamics t h i s r e s e a r c h has adopted c h a r a c t e r i s t i c s from b o t h o f t h e p r e v i o u s  research strands.  It  assumes, as does t h e i d e o g r a p h i c s t r a n d , t h a t t h e p r e s e n c e o f an a l t e r n a t e framework o f dynamics i s t h e r e s u l t o f an a c t i v e c o n s t r u c t i o n , on t h e p a r t o f an i n d i v i d u a l , t o e x p l a i n p e r s o n a l movement and the motion o f o b j e c t s .  F u r t h e r , t h i s r e s e a r c h assumes, as does t h e  n o m o t h e t i c s t r a n d , t h a t t h i s a l t e r n a t e framework w i l l be, t o some degree, a t odds w i t h a c c e p t e d s c i e n t i f i c  23  explanations  of m o t i o n .  M e t h o d o l o g i c a l l y , however, t h i s r e s e a r c h has d i v e r g e d strands.  from t h e s e  two  In o r d e r t o e x p l i c a t e the a l t e r n a t e framework of dynamics  t h a t i n d i v i d u a l s have c o n s t r u c t e d t h i s r e s e a r c h has u t i l i z e d a c l u e s t r u c t u r e a n a l y s i s of c l a s s r o o m  d i s c u s s i o n s and debates ( c o n c e r n i n g  m o t i o n of o b j e c t s ) r a t h e r t h a n c l i n i c a l pencil' tests.  i n t e r v i e w s or 'paper  the  and  A d d i t i o n a l l y , t h i s c l u e s t r u c t u r e has been i n c o r p o r a t e d  i n t o an i n s t r u c t i o n a l model t h a t has attempted t o t r a n s f o r m a l t e r n a t e framework of dynamics t o one the Newtonian framework of dynamics.  the  t h a t more c l o s e l y approximates The  d e s i g n of t h i s  instructional  model and i t s i m p l e m e n t a t i o n w i t h i n an o p e r a t i o n a l c l a s s r o o m s u b j e c t of Chapter Three - The R e s e a r c h D e s i g n .  24  are  the  CHAPTER THREE  The Research  Design  The d e s i g n base f o r t h i s s t u d y i s d e r i v e d from a s e t o f p r o c e d u r e s d e s c r i b e d , i n i t i a l l y i n t h e R u s s i a n l i t e r a t u r e , as a t e a c h i n g e x p e r i ment (Kalmykova,  1966).  More s p e c i f i c a l l y , t h i s s t u d y has used  p e r s p e c t i v e s from one of t h e two forms of t h e t e a c h i n g experiment t e s t i n g ( o r s e a r c h i n g ) form.  - the  T h i s form o f t h e t e a c h i n g experiment i s  used ...at t h e b e g i n n i n g s t a g e o f r e s e a r c h , when t h e e x p e r i m e n t e r , h a v i n g o u t l i n e d a h y p o t h e s i s , does n o t y e t c o n c e i v e w i t h s u f f i c i e n t c l a r i t y t h e o r g a n i z a t i o n a l forms o f i t s v e r i f i c a t i o n and i s w o r k i n g them out i n t h e p r o c e s s o f t h e e x p e r i ment i t s e l f , o r when he i s o u t l i n i n g a s e r i e s of v a r i a n t s o f t h e method and wants t o determine t h e most e f f e c t i v e o f them (Kalmykova, 1966, p. 1 8 ) . I n h e r e n t w i t h i n t h i s d e s i g n a r e two major components. The f i r s t of t h e s e i s t h e i n s t r u c t i o n a l model t h a t a c t s as an e x p e r i m e n t a l for  nucleus  t h e r e s e a r c h . The second component i n v o l v e s t h e i m p l e m e n t a t i o n o f  the model, w i t h i n an o p e r a t i o n a l c l a s s r o o m , i n o r d e r t o a s s e s s i t s a b i l i t y t o provoke t h e d e s i r e d c o n c e p t u a l change w i t h i n t h e s t u d e n t s . The c h a r a c t e r i s t i c s o f b o t h of these d e s i g n components w i l l be d i s c u s sed i n t h i s c h a p t e r .  The  I n s t r u c t i o n a l Model  As s t a t e d i n Chapter One, t h e i n s t r u c t i o n a l model c o n s i s t s of two elements:  f i r s t , an i n s t r u c t i o n a l s t r a t e g y , and second, an a n a l y t i c a l  c l u e s t r u c t u r e . Each of t h e s e two elements ually.  25  will  be d e s c r i b e d i n d i v i d -  The  Instructional Strategy The i n s t r u c t i o n a l s t r a t e g y has f o u r o b j e c t i v e s . 1.  t o e x p l i c a t e t h e a l t e r n a t e framework t h a t s t u d e n t s use when  d e a l i n g w i t h f o r c e / m o t i o n (dynamics) 2.  These a r e :  events.  t o have s t u d e n t s compare t h e concepts c o m p r i s i n g t h e i r  a l t e r n a t e framework of dynamics w i t h t h e Newtonian concepts of dynamics and  3.  (a)  r e c o g n i z e c o n c e p t u a l d i f f e r e n c e s , and  (b)  c l a r i f y t h e p o t e n t i a l s o u r c e s of t h e s e d i f f e r e n c e s .  t o have s t u d e n t s r e c o g n i z e (a)  t h e l i m i t a t i o n s of t h e i r a l t e r n a t e framework of dynamics as a mode o f i n t e r p r e t i n g f o r c e / m o t i o n e v e n t s .  (b)  Newtonian c o n c e p t i o n s of dynamics as more p l a u s i b l e and p r o d u c t i v e i n t e r p r e t a t i o n s of f o r c e / m o t i o n events.  4.  t o have s t u d e n t s t r a n s f o r m t h e i r e x i s t i n g mental  structure to  one more c l o s e l y a p p r o x i m a t i n g t h e Newtonian framework of dynamics, and use t h i s framework f o r t h e i n t e r p r e t a t i o n o f f o r c e / m o t i o n e v e n t s . In o r d e r t o a c h i e v e t h e s e o b j e c t i v e s , t h r e e complementary t a c t i c s have been used. F i r s t , i n o r d e r t o a c h i e v e t h e e x p l i c a t i o n of t h e components of the a l t e r n a t e framework of dynamics t h e s t u d e n t s were asked t o a n a l y z e , and draw concept maps (Gowin, 1982) - e i t h e r i n d i v i d u a l l y o r c o l l e c t i v e l y - of a s e r i e s of l a b o r a t o r y f o r c e / m o t i o n events t h a t a r e r e l a t e d t o dynamics events t h a t occur w i t h i n t h e normal, c u l t u r a l c o n t e x t . These concept maps then s e r v e d as a f o c a l p o i n t f o r t h e comparison of s t u d e n t c o n c e p t i o n s of dynamics w i t h Newtonian c o n c e p t i o n s .  26  The second t a c t i c used was  the j u x t a p o s i t i o n of s t u d e n t  con-  s t r u c t e d concept maps w i t h a t e a c h e r c o n s t r u c t e d Newtonian concept of the same event.  T h i s j u x t a p o s i t i o n was  then used t o generate  map  class  d i s c u s s i o n s i n which s t u d e n t s were c h a l l e n g e d t o d e f i n e and/or e x p l a i n i n d i v i d u a l concepts  t h a t were i n c o n f l i c t w i t h Newtonian  and encouraged t o q u e s t i o n the Newtonian concepts w i t h i n the The  conceptions  and t h e i r p o s i t i o n s  map.  t h i r d t a c t i c used was  the i n t r o d u c t i o n of d i s c o r d a n t ( i n the  r e s e a r c h e r ' s o p i n i o n ) events t h a t c o u l d not l o g i c a l l y or e m p i r i c a l l y e x p l a i n e d u s i n g t h e i r a l t e r n a t e framework(s).  These d i s c o r d a n t  then s e r v e d as f o c a l p o i n t s f o r c l a s s d i s c u s s i o n s c o n c e r n i n g  be  events  the  a b i l i t y of b o t h c o n c e p t u a l schemes t o p r o v i d e an adequate e x p l a n a t i o n / s o l u t i o n of the event.  In t h i s manner, i t was  hoped t h a t the  Newtonian framework would appear t o the s t u d e n t s as a more p o w e r f u l base f o r the i n t e r p r e t a t i o n of f o r c e / m o t i o n T h i s f i n a l t a c t i c was  events.  i n t e n d e d t o i n i t i a t e the t r a n s f o r m a t i o n of  the mental s t r u c t u r e ( r e p r e s e n t e d by the a l t e r n a t e framework) by p r o v i d i n g the s t u d e n t s w i t h a c l a s s of exemplary phenomena t h a t c o u l d b e s t be i n t e r p r e t e d u s i n g the Newtonian framework. were a l l p r e s e n t e d  as d e m o n s t r a t i o n s  These phenomena  and i n v o l v e d the u n i f o r m ,  positive  or n e g a t i v e , l i n e a r a c c e l e r a t i o n of o b j e c t s as a r e s u l t of the a p p l i c a t i o n of a c o n s t a n t f o r c e , and o b j e c t s w h i c h t r a v e l l e d w i t h l i n e a r , u n i f o r m m o t i o n as a r e s u l t of b a l a n c e d  forces.  I n i t i a l l y , the pheno-  mena used were d i v o r c e d from the s t u d e n t s ' n o r m a l , c u l t u r a l and i n v o l v e d apparatus  experiences  associated with a school science laboratory.  However, as the s t u d e n t s became more f a m i l i a r w i t h the Newtonian conceptual  scheme, m o t i o n problems more c l o s e l y a l l i e d t o the s t u d e n t s '  n o r m a l , e x p e r i e n t i a l base were used (see Appendix I - Student Problem 27  Sheets).  I n t h i s way,  the t r a n s f o r m e d  mental s t r u c t u r e s h o u l d have  more g e n e r a l i z e d u t i l i t y and p l a u s i b i l i t y r e l a t i v e t o the  original  a l t e r n a t e framework of dynamics. The  Development of the A n a l y t i c a l C l u e S t r u c t u r e The  development of the a n a l y t i c a l c l u e s t r u c t u r e (Roberts  R u s s e l l , 1975)  i n v o l v e s the r e p r e s e n t a t i o n of a s t u d e n t ' s  &  inductive  knowledge of a s p e c i f i c event or c l a s s of events i n terms of a s e t of frames (Minsky,1975) a r r a n g e d i n a g e n e r a l i z a t i o n h i e r a r c h y . The  s k e l e t o n of the g e n e r a l i z a t i o n h i e r a r c h y i s c o n s t r u c t e d  connecting  by  each of t h e s e frames ( r e p r e s e n t i n g a s p e c i f i c c o n c e p t ) t o  the n e x t , more g e n e r a l  frame, by an  ' i s a' l i n k which r e p r e s e n t s  class/super-ordinate c l a s s r e l a t i o n s h i p . Attached c e p t u a l frames, t h e n , w i l l  be s u b - c l a s s e s  a  sub-  t o each of the con-  of c o n c e p t s ,  or events which  a r e s p e c i a l i z a t i o n s of t h a t p a r t i c u l a r frame. To i l l u s t r a t e t h i s form of h i e r a r c h i a l s t r u c t u r e , the reader i s asked t o c o n s i d e r the g e n e r a l  concept ' p a r t ( s ) of a house'.  Attached  t o t h i s c o n c e p t , v i a ' i s a ' l i n k s , would be frames f o r each of  the  i n d i v i d u a l room t y p e s i n the house, i . e . bedroom, l i v i n g room, k i t c h e n , bathroom, and so on.  W i t h i n each frame would be the s p e c i a l i z e d d a t a  t h a t would a l l o w an o b s e r v e r  t o r e c o g n i z e each room t y p e .  these data could i n c l u d e s p e c i f i c , subordinate t o the immediate, s u p e r - o r d i n a t e a l l o w the o b s e r v e r rooms and  Further,  frames ( a g a i n  attached  frame by an ' i s a ' l i n k ) t h a t would  t o d i f f e r e n t i a t e , f o r example, between formal  living  f a m i l y rooms, and the master bedroom and c h i l d r e n ' s bedrooms.  As a r e s u l t of t h i s t y p e of a n a l y s i s a s t r u c t u r e e v o l v e s t h a t  repre-  s e n t s a t e m p l a t e t h a t c o u l d be used t o d e t e r m i n e whether or not s t r u c t u r e c o u l d be c o n s i d e r e d  t o be a house.  Conversely,  when t h i s  t y p e of s t r u c t u r e i s d e r i v e d from an a n a l y s i s of an i n d i v i d u a l ' s 28  a  i n d u c t i v e knowledge of houses a c l u e s t r u c t u r e d e v e l o p s t h a t  provides  an i n t e r p r e t a t i v e window i n t o what t h a t i n d i v i d u a l p e r c e i v e s a house t o be. The  p r o c e s s of a d d i n g s u b s t a n c e t o and r e f i n i n g the s k e l e t a l  s t r u c t u r e , w i t h i n the c o n t e x t of t h i s r e s e a r c h , i n v o l v e s a p p l i c a t i o n s of the e v o l v i n g c l u e s t r u c t u r e t o student v a r i e t y of f o r c e / m o t i o n  events.  are q u a l i t a t i v e l y analyzed  The  student  responses t o t h e s e e v e n t s  f o r a d d i t i o n a l conceptual  information that This addi-  i n f o r m a t i o n i s then i n c o r p o r a t e d i n t o the  c l u e s t r u c t u r e as e i t h e r s u b - c l a s s e s frames.  successive  responses t o a  i s r e l a t e d t o the p r e v i o u s l y c o n s t r u c t e d c l u e s t r u c t u r e . t i o n a l conceptual  clue  previous  of e x i s t i n g frames or as  In t h i s f a s h i o n , the c l u e s t r u c t u r e undergoes an  new  evolutionary  p r o c e s s t h a t r e s u l t s i n i n c r e a s i n g s o p h i s t i c a t i o n and a n a l y t i c a l power. For the purposes of t h i s r e s e a r c h , the development of the a n a l y t i c a l c l u e s t r u c t u r e has o c c u r r e d student.  at the l e v e l of the  individual  However, where t h e r e has been s u b s t a n t i a l congruence between  c l u e s t r u c t u r e s d e r i v e d from a group of s t u d e n t s , or where a group of students  has been i n agreement c o n c e r n i n g  the s p e c i f i c frames  and  s e q u e n c i n g of the frames w i t h i n a c l u e s t r u c t u r e , t h a t c l u e s t r u c t u r e has been i n t e r p r e t e d as b e i n g g e n e r a l l y r e p r e s e n t a t i v e of t h a t  student  group.  Implementation of the I n s t r u c t i o n a l Model Implementation of the i n s t r u c t i o n a l model o c c u r r e d w i t h i n the researcher's  own  t e n t h grade s c i e n c e c l a s s .  Within t h i s c l a s s , there  were 12 males and 19 females aged 14 and 15 y e a r s . c l a s s was  Membership i n t h i s  by computer assignment based p r i m a r i l y upon the  t e n t h grade c o u r s e s e l e c t i o n s .  These s t u d e n t s 29  students'  had not had any  prior,  f o r m a l i n s t r u c t i o n i n Newtonian dynamics. environmental  As a r e s u l t of t h e s e  c h a r a c t e r i s t i c s , t h i s component of t h e r e s e a r c h d e s i g n  r e p r e s e n t s a case s t u d y of t h e e f f i c a c y of t h e p r o t o t y p a l i n s t r u c t i o n a l model.  W i t h i n t h i s case s t u d y environment,  t h e r e s e a r c h e r assumed t h e  r o l e of an a c t i v e p a r t i c i p a n t o b s e r v e r . The assessment of t h e e f f i c a c y of t h e i n s t r u c t i o n a l model was based upon c o n s i d e r a t i o n s of i t s c a p a c i t y t o e x p l i c a t e t h e s t u d e n t s ' a l t e r n a t e framework of dynamics and, i f n e c e s s a r y , produce t h e d e s i r e d c o n c e p t u a l changes w i t h i n t h e s t u d e n t s .  The d e t e r m i n a t i o n of whether  or n o t t h e s e c o n c e p t u a l changes o c c u r r e d was based upon t h e r e s e a r c h e r ' s judgement and c l u e s t r u c t u r e a n a l y s i s of c l a s s r o o m t r a n s c r i p t i o n s and s t u d e n t concept maps.  These forms of a n a l y s e s s e r v e d as a t r a c k i n g  mechanism f o r c o n c e p t u a l change w i t h i n t h e s t u d e n t s and, i n t h i s r e g a r d , p r o v i d e d a q u a l i t a t i v e measure of t h e e f f e c t i v e n e s s of t h e instructional strategy. Methods of Data C o l l e c t i o n and A n a l y s i s V i d e o t a p i n g of a l l c l a s s r o o m s e s s i o n s p r o v i d e d t h e p r i m a r y d a t a . These d a t a were s u b s e q u e n t l y reduced t o a s e r i e s of t r a n s c r i p t i o n s d e a l i n g w i t h p a r t i c u l a r events w i t h i n t h e r e s e a r c h sequence.  The  t r a n s c r i p t i o n s were then a n a l y z e d f o r t h e major c o n c e p t u a l c o n t e n t and p a t t e r n s employed by i n d i v i d u a l s w i t h i n t h e c l a s s , and a h i e r a r c h y of t h e s e c o n c e p t u a l d a t a was c o n s t r u c t e d .  These d a t a forms then became  the b a s i s f o r t h e c l u e s t r u c t u r e a n a l y s i s . As t h e c l u e s t r u c t u r e a n a l y s i s was a p p l i e d t o t h e c o n c e p t u a l d a t a frame s t r u c t u r e s were g e n e r a t e d t h a t were i n t e n d e d t o r e p r e s e n t t h e major c o n c e p t u a l knowledge p a t t e r n ( s ) t h a t i n d i v i d u a l s t u d e n t s were using t o i n t e r p r e t the force/motion events.  Where t h e r e was s u b s t a n -  t i a l s u p p o r t by members of t h e c l a s s f o r a p a r t i c u l a r s e t of c o n c e p t u a l  30  d a t a , t h e r e s u l t i n g frame was assumed t o r e p r e s e n t a composite t u r e t h a t was a g r e e a b l e t o a m a j o r i t y of t h e c l a s s .  struc-  These frame s t r u c -  t u r e s were t h e n used t o t r a c k t h e e f f e c t t h a t t h e i n s t r u c t i o n a l s t r a t e g y was h a v i n g on t h e c o n c e p t u a l knowledge p a t t e r n s of t h e students. Secondary d a t a were o b t a i n e d i n t h e form o f s t u d e n t concept maps and worksheet answers.  generated  These d a t a forms were used as a  c r o s s - c h e c k on t h e v a l i d i t y of t h e e v o l v i n g frame s t r u c t u r e ( s ) by comparing t h e i r c o n c e p t u a l s t r u c t u r e s w i t h those c o n t a i n e d i n t h e frame structure.  I n summary, t h i s r e s e a r c h r e p r e s e n t s a case s t u d y o f t h e e f f e c t s t h a t an e x t e r n a l l y d e s i g n e d i n s t r u c t i o n a l s t r a t e g y has had on t h e c o n c e p t u a l knowledge p a t t e r n s t h a t s t u d e n t s use t o make sense o f f o r c e and motion e v e n t s .  These e f f e c t s have been t r a c k e d u s i n g a c l u e  s t r u c t u r e a n a l y s i s o f t h e concepts and c o n c e p t u a l p a t t e r n s , d e r i v e d p r i m a r i l y from t h e a n a l y s i s of c l a s s r o o m v i d e o t a p e s , t h a t s t u d e n t s have e x h i b i t e d when a t t e m p t i n g t o e x p l a i n a v a r i e t y o f f o r c e and motion events.  31  CHAPTER FOUR  The C l a s s r o o m Case Study  The case s t u d y c o v e r s e i g h t c l a s s p e r i o d s t i m e p e r i o d of t h i r t e e n s c h o o l  days.  Within  l e s s o n s were p r e s e n t e d t o t h e s t u d e n t s .  t h a t spanned a t o t a l  this period, f i v e  specific  These were:  LESSON 1 - An I n t r o d u c t i o n t o Dynamics and Dynamics Terminology. LESSON 2 - F o r c e A n a l y s i s T e c h n i q u e s . LESSON 3 - The Dynamics of A c c e l e r a t i o n . LESSON 4 - The Dynamics of D e c e l e r a t i o n . LESSON 5 - The Dynamics of U n i f o r m M o t i o n . Because t h i s case s t u d y i s p r i m a r i l y concerned w i t h t h e a n a l y s i s of t h e initial  c o n c e p t u a l s t r u c t u r e s t h a t t h e s t u d e n t s were u s i n g t o i n t e r p r e t  dynamics e v e n t s and any subsequent a l t e r a t i o n r e s u l t of t h e i n s t r u c t i o n a l  t o t h e s e s t r u c t u r e s as a  strategy, only the l a s t three  lessons  will  be p r e s e n t e d i n t h i s c h a p t e r . I t s h o u l d a l s o be n o t e d a t t h i s p o i n t t h a t , i n a p h y s i c a l sense, t h e r e i s no v e r b a l d i s t i n c t i o n between a c c e l e r a t i o n and d e c e l e r a t i o n . There i s , however, a v e c t o r i a l as a n e g a t i v e a c c e l e r a t i o n .  d i s t i n c t i o n with deceleration  appearing  Due t o t h e age of t h e s e s t u d e n t s and t h e i r  l a c k of s c i e n t i f i c / m a t h e m a t i c a l  s o p h i s t i c a t i o n , a verbal  distinction  has been s u b s t i t u t e d f o r t h e v e c t o r i a l . A l t h o u g h most p h y s i c s  t e x t s p r e s e n t Newton's Laws of M o t i o n i n  sequential  order,  reversed.  T h i s d e c i s i o n was based upon p r e v i o u s c l a s s r o o m s t u d i e s by  Minstrell  f o r t h e purposes of t h i s s t u d y , t h e o r d e r was  ( n . d . , p. 6 1 ) , who found 32  i n every c l a s s , on every t e s t , t h e p r o p o r t i o n o f t h e c l a s s g i v i n g Newtonian answers f o r t h e a c c e l e r a t i n g cases was g r e a t e r than t h a t f o r t h e c o n s t a n t v e l o c i t y c a s e s . Why were t h e a c c e l e r a t i n g cases e a s i e r f o r t h e s t u d e n t s t o handle? P i a g e t ' s t h e o r y ( 1 9 5 8 ) suggests t h a t r e a s o n i n g from t h e c o n c r e t e t o t h e a b s t r a c t i s e a s i e r than from t h e a b s t r a c t t o the c o n c r e t e . The c o n c r e t e f i r s t h a n d e x p e r i e n c e i n t h e i n s t r u c t i o n dealt with situations involving acceleration, Newton's Second Law. I t seemed l o g i c a l t h a t t h e c o n s t a n t v e l o c i t y c a s e , i n v o l v i n g Newton's F i r s t Law, s h o u l d be taught as a l o g i c a l consequence o f t h e a c c e l e r a t i o n case. Because t h e f o c u s o f t h i s r e s e a r c h i s t h e e l i c i t a t i o n and a l t e r a t i o n ( i f n e c e s s a r y and p o s s i b l e ) o f s t u d e n t s ' c o n c e p t i o n s o f m o t i o n , the case s t u d y was c o n c e n t r a t e d on d a t a c o l l e c t e d from t h e l a s t t h r e e lessons.  The d a t a from t h e s e l e s s o n s w i l l  be i n t r o d u c e d i n two  formats. The f i r s t d a t a form i s t r a n s c r i p t i o n s of c l a s s d i s c u s s i o n s c o n c e r n i n g motion events t h a t a r e p r e s e n t e d t o p r o v i d e a f l a v o u r o f t h e c l a s s r o o m environment,  and a m a c r o s c o p i c  view of i n i t i a l  student  c o n c e p t i o n s and any subsequent a l t e r a t i o n s t o t h e s e c o n c e p t i o n s . I n c l u d e d w i t h i n t h e s e t r a n s c r i p t i o n s a r e concept maps c o n s t r u c t e d by the c l a s s as a r e s u l t o f t h e i r d i s c u s s i o n s of f o r c e and motion  events.  These concept maps a r e p r e s e n t e d t o a l l o w a v i s u a l e x a m i n a t i o n o f t h e major concepts b e i n g employed by t h e s e s t u d e n t s t o i n t e r p r e t  these  events. The second  form of d a t a t o be p r e s e n t e d i s i n t e r p r e t a t i o n a l ,  c o n c e p t u a l frames c o n s t r u c t e d by t h e r e s e a r c h e r t o account  f o r attempts  by i n d i v i d u a l s t u d e n t s and/or t h e c l a s s t o i n t e r p r e t s p e c i f i c t y p e s of motion.  The use of t h e s e i n t e r p r e t a t i o n a l frames a l l o w s a more i n -  depth e x a m i n a t i o n o f t h e elements  of t h e a l t e r n a t e framework and  p r o v i d e s a means of i d e n t i f y i n g any subsequent a l t e r a t i o n t o t h i s framework as a r e s u l t o f t h e i n s t r u c t i o n a l s t r a t e g y .  33  The method o f  c o n s t r u c t i n g t h e s e i n t e r p r e t a t i o n a l frames w i l l be more f u l l y later i n this  chapter. The  The  Lessons  Dynamics of A c c e l e r a t i o n The  l e s s o n was begun by a s k i n g t h e s t u d e n t s why an o b j e c t , such as  a dynamics c a r t , would b e g i n t o a c c e l e r a t e and c o n t i n u e  5  10  15  20  discussed  to accelerate?  Kelly: Because t h e r e i s more f o r c e p u s h i n g i t t h a n t h e r e i s f r i c t i o n g o i n g a g a i n s t i t . The reason i s (pause) f r i c t i o n i s t r y i n g to stop i t . . . ( i n a u d i b l e ) . Teacher: Is t h a t f o r c e always t h e r e ? Kelly: No (pause) Y e s , i t would have t o be, depending on how l o n g , how f a r you wanted t o a c c e l e r a t e i t f o r . Teacher: We're g o i n g t o keep t h e t h i n g a c c e l e r a t i n g f o r as l o n g as we want. Kelly: Then t h e f o r c e always has t o be t h e r e . Teacher: So t h e r e has t o be a c o n t i n u o u s f o r c e a p p l i e d t o t h e o b j e c t , and t h e f o r c e has t o be l a r g e r than (pause)? Kelly: than t h e f r i c t i o n . Teacher: What do t h e r e s t of you t h i n k about t h a t ? I s t h a t t h e cause of a c c e l e r a t i o n ? (pause) Any o t h e r i d e a s about a c c e l e r a t i o n ? I s i t caused by a c o n t i n u o u s f o r c e ? Cory: It increases. Teacher: So, t h e f o r c e i s g e t t i n g l a r g e r ? Cory: Yeah. Teacher: A l l t h e t i m e (pause) so t h e f o r c e i s always g e t t i n g l a r g e r , and l a r g e r , and l a r g e r ? Another s t u d e n t : Yeah. Cory: Yes. At t h i s p o i n t , s t u d e n t i d e a g e n e r a t i o n  to refocus  tended t o a b a t e .  In order  them, b o t h K e l l y ' s ( a c c e l e r a t i o n i s a r e s u l t of t h e c o n t i n -  34  uous a p p l i c a t i o n of a c o n s t a n t f o r c e ) and Cory's ( a c c e l e r a t i o n i s a r e s u l t o f t h e a p p l i c a t i o n of an i n c r e a s i n g f o r c e ) concepts of t h e cause of a c c e l e r a t i o n , were w r i t t e n on t h e b l a c k b o a r d .  K e l l y was asked f o r  f u r t h e r c l a r i f i c a t i o n of h e r concept.  25  Teacher: K e l l y , c o r r e c t me i f I'm wrong, t h a t f o r c e i s always t h e same s i z e i s that r i g h t ? Kelly: Yeah.  T h i s c l a r i f i c a t i o n caused many o f t h e s t u d e n t s t o become a g i t a t e d and  v o c a l l y d i s a g r e e w i t h K e l l y ' s concept of a c o n s t a n t , c o n t i n u o u s  force causing a c c e l e r a t i o n .  I n t h e face of t h i s u n s u b s t a n t i a t e d  disagreement, K e l l y volunteered a f u r t h e r  30  clarification.  Kelly: It's s t i l l continuous force. I f you keep t h e f r i c t i o n on a t the same l e v e l , then i t ' s s t i l l c o n t i n u o u s f o r c e b u t , ah, t h e c o n t i n u o u s f o r c e i s g e t t i n g h a r d e r . I t ' s p u s h i n g more. Teacher: I s t h a t what you mean by t h i s statement ( r e f e r r i n g t o K e l l y ' s o r i g i n a l concept o f t h e cause o f a c c e l e r a t i o n t h a t had been w r i t t e n on t h e b l a c k b o a r d ) . Kelly: Yeah. Teacher: So your c o n t i n u o u s f o r c e i s a c o n t i n u o u s , i n c r e a s i n g f o r c e . K e l l y , however, was n o t c o m p l e t e l y w i l l i n g t o c a s t a s i d e h e r  o r i g i n a l i d e a t h a t a c c e l e r a t i o n might be caused by a applied, constant force.  continuously  She f i n i s h e d t h e debate w i t h a f u r t h e r  qualification.  35  Kelly: ...or you can have a c o n t i n u o u s f o r c e w i t h a d e c r e a s e i n t h e f r i c t i o n force.  35  At t h i s p o i n t i n t h e l e s s o n , t h e r e was o v e r a l l c l a s s agreement w i t h t h e i d e a t h a t an o b j e c t  ( i n t h i s case a dynamics c a r t ) would  a c c e l e r a t e i f an i n c r e a s i n g , c o n t i n u o u s f o r c e was a p p l i e d t o an o b j e c t as long as t h e f r i c t i o n a l applied force.  f o r c e remained c o n s t a n t  This s p i r i t  and s m a l l e r than t h e  o f c l a s s r o o m consensus was c a r r i e d over t o  the c o n s t r u c t i o n of an embryonic concept map t h a t attempted t o r e l a t e a c c e l e r a t e d motion t o f o r c e (see Figure 1 ) . The  next c l a s s began w i t h a r e v i e w of t h e a c c e l e r a t i o n concept map  t h a t t h e s t u d e n t s had g e n e r a t e d a t t h e end of t h e p r e v i o u s map was then j u x t a p o s e d  with a teacher-constructed  class.  This  map of Newtonian  c o n c e p t s o f a c c e l e r a t i o n ( s e e F i g u r e 2) and t h e s t u d e n t s were asked t o compare and comment upon t h e two maps.  5  10  15  Teacher: The r e a l d i f f e r e n c e (between t h e two maps) i s , i f you a p p l y a c o n s t a n t f o r c e w i l l you get a c c e l e r a t i o n ? I f you a p p l y an i n c r e a s i n g f o r c e , w i l l you g e t a c c e l e r a t i o n ? Jim: Yeah. Teacher: Yes? I n b o t h c a s e s ? Jim: Yeah. Teacher: Why? Jim: Because you're s t i l l a p p l y i n g a f o r c e . Teacher: So even i f t h e f o r c e I'm a p p l y i n g i s c o n s t a n t , i t i s s t i l l going t o accelerate? Jim: Yeah, i t ' s l a r g e r . Teacher: I n t e r e s t i n g ! K e l l y , you came up w i t h t h i s y e s t e r d a y ( s e e l i n e s 23 t o 25, p. 35) what do you t h i n k about t h a t ? Kelly: Yeah, e s p e c i a l l y on t h e s t a t i o n a r y one. Teacher: So you're g o i n g t o agree w i t h t h i s t o o . Even i f t h e f o r c e i s constant? Kelly: W e l l , ah ( p a u s e ) , what I don't t h i n k i s (pause) i t ' s t h e moving o b j e c t , r i g h t , (pause) You s a i d they were d o i n g t h i s 36  F i g u r e 1. A Map  of S t u d e n t s ' Concepts of A c c e l e r a t i o n  forces  are  balanced  applied in same d i r e c t i o n  as motion  causes  acceleration  37  F i g u r e 2. T e a c h e r - c o n s t r u c t e d Map Acceleration  of Newtonian Concepts of  forces  are  balanced  unbalanced  -i.e.  net f o r c e > 0 and  the  l a r g e r , constant  applied  force  to  stationary objects  moving objects in  same d i r e c t i o n as m o t i o n  causing  acceleration  38  20  25  30  35  f o r as l o n g as they wanted t o go f o r , r i g h t ? ( o b t a i n s c o n f i r m a t i o n from t h e t e a c h e r ) , (pause) I f you pushed 50 N on something f o r ah (pause) l i k e a l e n g t h o f time, i t s f i r s t b i t i s g o i n g t o a c c e l e r a t e and then s t o p . Melanie ( i n t e r j e c t i n g ) : If i t ' s a constant f o r c e , i t w i l l stay constant! Teacher ( a d d r e s s i n g K e l l y ) : So you f e e l t h a t t h e r e i s g o i n g t o be a p o i n t where, even though t h a t f o r c e i s c o n s t a n t , you're g o i n g t o back o f f t o a constant v e l o c i t y a f t e r awhile. Kelly: Yeah. Teacher: M e l a n i e , you had something t o s a y . Melanie: I f you have a c o n s t a n t f o r c e , then y o u ' l l have a c o n s t a n t velocity. Teacher: So you're g o i n g back t o t h i s t h e o r y t h a t we came up w i t h y e s t e r d a y , t h a t c o n s t a n t f o r c e ends up w i t h c o n s t a n t v e l o c i t y . You must have an i n c r e a s i n g f o r c e t o come up w i t h acceleration. Melanie: Yeah. I t appeared, a t t h i s p o i n t , t h a t t h e s t u d e n t s were wedded t o t h e  concept t h a t , i f an o b j e c t was t o a c c e l e r a t e c o n t i n u o u s l y ,  a constantly  i n c r e a s i n g f o r c e would have t o be a p p l i e d t o t h a t o b j e c t .  The u n i o n ,  however, was not w i t h o u t i t s f l a w s f o r b o t h J i m and K e l l y had suggested t h a t a c c e l e r a t i o n would o c c u r i f a c o n s t a n t object.  f o r c e was a p p l i e d t o an  A l t h o u g h , i n K e l l y ' s c a s e , q u a l i f i c a t i o n s had been a p p l i e d t o  the concept.  Two d e m o n s t r a t i o n s were p r e s e n t e d t o t h e c l a s s i n o r d e r  to provide  them w i t h p h y s i c a l s i t u a t i o n s t h a t would emulate b o t h  conceptual  schemes.  The  f i r s t d e m o n s t r a t i o n c o n s i s t e d o f an equipment t r o l l e y t h a t was  b e i n g p u l l e d by a s t u d e n t . estimated  The f r i c t i o n on t h e t r o l l e y had been  by measuring t h e amount of f o r c e r e q u i r e d t o j u s t b e g i n t h e  t r o l l e y moving.  The f o r c e t h a t t h e s t u d e n t was a p p l y i n g t o t h e t r o l l e y  was measured w i t h a s p r i n g s c a l e g r a d u a t e d i n newtons. asked t o c l o s e l y observe t h e m o t i o n of t h e t r o l l e y . 39  The c l a s s was  Three t r i a l s were made w i t h t h i s equipment. The f i r s t i n v o l v e d s t a r t i n g t h e t r o l l e y from a m o t i o n l e s s p u l l i n g i t with  (a) a c o n t i n u o u s l y  p o s i t i o n and then  i n c r e a s i n g f o r c e , and (b) a  constant  f o r c e of 20 N.  constant  f o r c e of 20 N once t h e t r o l l e y was moving.  The t h i r d t r i a l  i n v o l v e d t h e a p p l i c a t i o n of a  s t u d e n t s unanimously agreed t h a t t h e t r o l l e y The  two t r i a l s  In a l l cases, the  accelerated.  second d e m o n s t r a t i o n i n v o l v e d a p p l y i n g a c o n s t a n t  f o r c e of  a p p r o x i m a t e l y 5 N t o a dynamics c a r t u s i n g a system of p u l l e y s t h a t allowed 3).  a 500 g mass t o f a l l under t h e i n f l u e n c e of g r a v i t y ( s e e F i g u r e  A g a i n , t h e c l a s s unanimously agreed t h a t t h e a p p l i c a t i o n of t h i s  constant  f o r c e caused t h e c a r t t o a c c e l e r a t e .  Figure 3. Acceleration Denonstration #2 nass •  1  gravity i  At f i r s t  pass t h e i n s t r u c t i o n a l s t r a t e g y appeared t o have t h e  desired effects.  The i n i t i a l d e m o n s t r a t i o n ( o f an a c c e l e r a t i n g  dynamics c a r t ) and t h e subsequent d i s c u s s i o n of t h e c a u s e ( s ) of t h i s a c c e l e r a t i o n had exposed t h e s t u d e n t s ' tion. ing  general  conception  of a c c e l e r a -  T h i s was t h a t a c c e l e r a t i o n was caused by a c o n t i n u o u s l y  f o r c e a p p l i e d i n t h e same d i r e c t i o n as t h e i n i t i a l motion. 40  increasAddi-  t i o n a l l y , t h i s conception suggested that the m a j o r i t y a l s o adhere t o t h e g e n e r a l i z e d  of s t u d e n t s would  b e l i e f t h a t any form of m o t i o n must  i m p l y some a p p l i c a t i o n o f f o r c e f o r , i f a c c e l e r a t i o n was caused by a c o n t i n u o u s a p p l i c a t i o n of i n c r e a s i n g f o r c e , then u n i f o r m motion s h o u l d l o g i c a l l y be caused by an a p p l i c a t i o n o f c o n s t a n t f o r c e .  Whether t h i s ,  i n f a c t , would be t h e case would have t o w a i t f o r t h e l e s s o n s  dealing  w i t h uniform motion. That p a r t o f t h e i n s t r u c t i o n a l s t r a t e g y t h a t was i n t e n d e d t o a l t e r the s t u d e n t ' s g e n e r a l i z e d  c o n c e p t i o n o f t h e dynamics o f a c c e l e r a t i o n  appeared t o proceed f l a w l e s s l y .  When f a c e d w i t h e m p i r i c a l  from t h e d e m o n s t r a t i o n s t h e r e was unanimous agreement t h a t  evidence acceleration  would be caused t h e a p p l i c a t i o n o f a c o n s t a n t f o r c e a p p l i e d i n t h e same d i r e c t i o n as t h e i n i t i a l m o t i o n . was t h a t t h e c o n v e r s i o n  What was d i s t u r b i n g about t h i s event  from t h e f i r s t b e l i e f s t r u c t u r e t o t h e second  appeared t o o c c u r w i t h o u t any form of mental d i s s o n a n c e on t h e p a r t of the s t u d e n t s .  Considering  t h e v o c i f e r o u s disagreement t h a t had  r e s u l t e d from K e l l y ' s o r i g i n a l s u g g e s t i o n t h a t a c c e l e r a t i o n was a r e s u l t of t h e a p p l i c a t i o n o f a c o n s t a n t f o r c e ( s e e l i n e s 23 t h r o u g h 25, p. 3 5 ) , i t was d i f f i c u l t t o b e l i e v e t h a t t h e s t u d e n t s would r e l i n q u i s h t h e i r h o l d on t h e i r o r i g i n a l c o n c e p t u a l s t r u c t u r e so e a s i l y .  Was i t  p o s s i b l e t h a t t h e d e m o n s t r a t i o n s had c o n v i n c e d t h e s t u d e n t s t h a t t h e minimum c o n d i t i o n n e c e s s a r y f o r a c c e l e r a t i o n t o o c c u r was an a p p l i c a t i o n of a c o n s t a n t f o r c e and t h a t t h e i r o r i g i n a l c o n c e p t i o n was a s u b s e t o f t h i s , o r were t h e s e two c o n c e p t u a l s t r u c t u r e s now i n t h e minds of t h e s t u d e n t s and c o n t e x t s e n s i t i v e ? acceleration requires a continuously  coexistent  One s t r u c t u r e ,  i n c r e a s i n g f o r c e , t o be used f o r  e x p e r i e n t i a l / r e a l w o r l d c i r c u m s t a n c e s , and t h e o t h e r , a c c e l e r a t i o n r e q u i r e s a c o n s t a n t a p p l i c a t i o n o f f o r c e , t o be used f o r t h e i r 41  only  science  class.  The r e s o l u t i o n of t h e p o s s i b l e i n t e r p r e t a t i o n s had t o w a i t  u n t i l t h e c l u e s t r u c t u r e a n a l y s i s of t h e c l a s s d i s c u s s i o n s . The  Dynamics of D e c e l e r a t i o n The  d i s c u s s i o n of d e c e l e r a t i o n was i n i t i a t e d as a n a t u r a l c o r o l -  l a r y to the students'  previous  d i s c u s s i o n of a c c e l e r a t i o n .  While  d i s c u s s i n g what would happen t o t h e motion of a c a r i f t h e f o r c e s u p p l i e d t o t h e d r i v e wheels was reduced by h a l f w h i l e k e e p i n g t h e f r i c t i o n a l forces constant  ( b u t l e s s than t h e f o r c e s u p p l i e d by t h e  d r i v e w h e e l s ) , t h e q u e s t i o n was posed - how c o u l d you g e t t h i s c a r t o b e g i n t o slow down.  I n o t h e r words, under what c o n d i t i o n s would t h e  car  decelerate?  5  Teacher: I f t h i s i s a c c e l e r a t i o n ( r e f e r r i n g t o a d i a g r a m of a c a r , on the b o a r d , w i t h t h e f o r c e from t h e d r i v i n g wheels b e i n g l a r g e r t h a n t h e f r i c t i o n a l f o r c e ) , how do you g e t d e c e l e r a t i o n ? How do you g e t t h e c a r t o slow down? Kelly: Make t h e f r i c t i o n l a r g e r t h a n t h e f o r c e .  (Teacher draws a n o t h e r diagram of a c a r on t h e b l a c k b o a r d  and r e i t e r -  ates the question.)  10  15  Teacher: How do you g e t d e c e l e r a t i o n ? You want t o s l o w t h i s guy down. Jim: Decrease your push f o r c e . Teacher: How much a r e you g o i n g t o d e c r e a s e i t ? I f I was g o i n g t o draw a push f o r c e up here ( r e f e r r i n g t o t h e diagram) would i t be s m a l l e r t h a n t h i s ( r e f e r r i n g t o t h e f r i c t i o n a l f o r c e ) , l a r g e r t h a n t h i s , o r t h e same s i z e ? Jim: I t ' s g o i n g t o be l a r g e r . Teacher: I t ' s g o i n g t o be l a r g e r . Any o t h e r i d e a s ? Dina: ( i n a u d i b l e ) . . . i t ' l l be s m a l l e r so t h a t f r i c t i o n w i l l slow i t down. Teacher: Why does i t have t o be s m a l l e r ?  42  Dina:  20  25  So t h a t t h e f r i c t i o n overpowers t h e push f o r c e . Teacher: J i m , what do you t h i n k about t h a t ? Jim: ( i n a u d i b l e ) . . . i t w i l l stop i t . Teacher: I f I draw t h i s arrow up here ( r e f e r r i n g t o t h e push f o r c e ) t o be l a r g e r than t h e f r i c t i o n a l f o r c e , am I g o i n g t o end up w i t h t h i s s i t u a t i o n over here ( p o i n t i n g t o t h e a c c e l e r a t i o n diagram)? Jim: Yeah. Teacher: Am I s t i l l g o i n g t o be a c c e l e r a t i n g ? Jim: Yeah. I t ' l l be d e c e l e r a t i o n from your c o n s t a n t speed ...(inaudible)...you're not going t o stop . . . ( i n a u d i b l e ) . Two, d i a m e t r i c a l l y opposed c o n c e p t s o f t h e causes of d e c e l e r a t i o n  have emerged from t h i s d i s c u s s i o n .  K e l l y and Dina f e e l t h a t  deceler-  r  a t i o n o c c u r s when t h e f r i c t i o n a l  ( o r opposing) f o r c e s on an o b j e c t  become l a r g e r than t h e m o t i v e f o r c e , whereas J i m f e e l s t h a t  deceler-  a t i o n o c c u r s when t h e m o t i v e f o r c e d e c r e a s e s i n magnitude, but s t i l l remains l a r g e r than t h e f r i c t i o n a l  forces.  K e l l y ' s and Dina's i d e a  t h a t t h e n e t f o r c e on t h e o b j e c t must be i n t h e o p p o s i t e d i r e c t i o n r e l a t i v e t o an o b j e c t ' s m o t i o n i s a l o g i c a l e x t e n s i o n of t h e c o n c l u s i o n s , p r e v i o u s l y a r r i v e d a t by t h e s t u d e n t s , c o n c e r n i n g t h e cause o f acceleration.  Jim's i d e a , on t h e o t h e r hand, i s i n d i r e c t c o n t r a d i c -  t i o n with these conclusions  b u t i n k e e p i n g w i t h t h e 'motion i m p l i e s a  f o r c e ' s t r u c t u r e recognized i n the a c c e l e r a t i o n lesson.  Indeed, J i m  a p p a r e n t l y doesn't see any c o n t r a d i c t i o n between t h e p o s i t i o n he has t a k e n on d e c e l e r a t i o n and h i s p r e v i o u s s t a t e m e n t s on a c c e l e r a t i o n ( s e e l i n e s 1 t h r o u g h 11, p. 3 6 ) . J i m i s r e s o l u t e i n h i s b e l i e f and s u g g e s t s t h a t K e l l y ' s and Dina's concept w i l l  cause t h e o b j e c t t o s t o p .  When  asked t o r e c o n c i l e h i s concept w i t h t h e agreed upon f o r c e diagram of a c c e l e r a t i o n J i m f u r t h e r suggests that a r e d u c t i o n of the motive f o r c e .43  ( a l b e i t , k e e p i n g t h e n e t f o r c e i n t h e same d i r e c t i o n as t h e i n i t i a l motion) w i l l  r e s u l t i n d e c e l e r a t i o n but w i l l n o t s t o p t h e o b j e c t .  Jim's b e l i e f appears t o be a c o n s i s t e n t  subset of t h e concept t h a t  a c c e l e r a t i o n i s caused by an ever i n c r e a s i n g f o r c e . increasing force i s replaced  I f an ever  by a d e c r e a s i n g f o r c e s u r e l y  deceleration  must r e s u l t . The  robustness of t h i s b e l i e f suggests that J i m i s basing h i s  concept on p e r s o n a l ,  e x p e r i e n t i a l evidence.  c o u l d be c o l l e c t e d w h i l e d r i v i n g a c a r . and  T h i s type o f e v i d e n c e  I f t h e c a r was a c c e l e r a t i n g  t h e gas pedal was then s l i g h t l y r e l e a s e d  ( t h e m o t i v e f o r c e was  reduced) t h e r a t e of a c c e l e r a t i o n would d e c r e a s e .  T h i s d e c r e a s e might  then be i n t e r p r e t e d as d e c e l e r a t i o n w i t h t h e m o t i v e f o r c e s t i l l  being  a p p l i e d i n t h e d i r e c t i o n of m o t i o n . The  r e s t of t h e c l a s s had, so f a r , not e n t e r e d i n t o t h e debate on  the p o s s i b l e causes o f d e c e l e r a t i o n .  I n o r d e r t o e l i c i t any f u r t h e r  i d e a s o r arguments, b o t h c o n c e p t s , r e g a r d i n g r e s t a t e d and t h e s t u d e n t s ' o p i n i o n s  a c c e l e r a t i o n , were  were s o l i c i t e d .  Jody: The push f o r c e i s g o i n g t o be l a r g e r ( t h a n t h e f r i c t i o n a l f o r c e ) but s m a l l e r t h a n i t was b e f o r e . (Teacher draws a d i a g r a m of a c a r on t h e b l a c k b o a r d , next t o t h e diagram t h a t t h e c l a s s has agreed r e p r e s e n t s a c c e l e r a t i o n , w i t h t h e m o t i v e f o r c e reduced i n magnitude b u t s t i l l  l a r g e r than the f r i c t i o n a l  force.)  30  Teacher: There's t h e push f o r c e . I s i t l a r g e r than t h e f r i c t i o n a l force? I s t h e n e t f o r c e s t i l l i n t h e same d i r e c t i o n of t h e motion? The q u e s t i o n i s - i s t h a t ( p o i n t i n g t o t h e new diagram) g o i n g t o have t h e same e f f e c t as t h i s ( p o i n t i n g t o the a c c e l e r a t i o n diagram)? T h i s r e s u l t s i n a c c e l e r a t i o n  44  35  ( p o i n t i n g t o t h e a c c e l e r a t i o n d i a g r a m ) . What does t h i s ( p o i n t i n g t o t h e new diagram) r e s u l t i n ? Jim:  40  45  D e c e l e r a t i o n and t h e n a c c e l e r a t i o n . Teacher: Any o t h e r i d e a s ? Jim: W e l l , t h i s i s j u s t an example. When you push your pen l i k e t h i s and s l o w l y slow i t down ( J i m demonstrates w i t h h i s pen on t h e l a b bench) and you're s t i l l moving; s o , you took o f f some of t h e push f o r c e but you don't s t o p i t . Teacher: Suppose I took t h i s push f o r c e and I s h o r t e n e d i t up (makes the m o d i f i c a t i o n t o t h e d i a g r a m ) . I made i t s m a l l e r than t h e f r i c t i o n a l force.  (At t h i s p o i n t , a number o f u n i d e n t i f i e d s t u d e n t s v o l u n t e e r e d to the question  t h a t hadn't y e t been asked.  answers  They s u g g e s t e d t h a t t h e  c a r would ( a ) s t o p , o r ( b ) d e c e l e r a t e . )  50  55  60  65  Kelly: Its going t o decelerate. The f r i c t i o n f o r c e becomes s t r o n g e r than t h e push f o r c e and t h e n , sooner o r l a t e r , i t s g o i n g t o s t o p i f you keep i t a t t h a t , and i t s g o i n g t o s t o p and i t w i l l be a b a l a n c e d f o r c e . . . ( i n a u d i b l e ) . . . a f t e r i t s t o p s . Teacher: I n t e r e s t i n g ! Why do you t h i n k t h a t i s g o i n g t o o c c u r ? Kelly: Because t h e push f o r c e i s l e s s than t h e f r i c t i o n f o r c e and (pause) u n l e s s (pause) i f i t ' s g o i n g a l o n g a l e v e l road i t can't keep i t s m o t i o n up. Jim: Urn, I t h i n k t h a t i f you weren't moving t h e r e wouldn't be any f r i c t i o n . . . ( i n a u d i b l e ) . . . t h e f r i c t i o n would go down t o zero. Teacher: So, t h e s l o w e r you a r e moving, t h e l e s s w i l l be t h e f r i c t i o n force. Jim: Yeah. Teacher: I j u s t want t o g e t back t o something t h a t K e l l y s a i d a minute ago. Ah (pause) she s a i d t h a t t h i s ( p o i n t i n g t o diagram i n w h i c h t h e m o t i v e f o r c e i s l e s s than t h e f r i c t i o n a l f o r c e ) i s g o i n g t o r e s u l t i n d e c e l e r a t i o n and, u l t i m a t e l y i f i t keeps g o i n g on, t h i s i s g o i n g t o s t o p and r e v e r s e i t s d i r e c t i o n . Is that correct? Kelly: Reverse i t s d i r e c t i o n ? No! I t w i l l j u s t s t o p !  45  70  75  80  85  90  95  100  Teacher: I n t h i s s i t u a t i o n ( r e f e r r i n g t o t h e p r e v i o u s d i a g r a m ) , what i s t h e d i r e c t i o n of t h e n e t f o r c e g o i n g t o be? Jim: What do I t h i n k ? Teacher: No, what i s i t g o i n g t o be? The way i t ' s drawn r i g h t now. Tawnia: I t ' l l be one way f o r a w h i l e t h e n , when i t s t a r t s d e c e l e r a t i n g (pauses). Teacher: L e t ' s p u t some numbers on t h i s . T h i s might h e l p you. L e t ' s say t h a t t h e f r i c t i o n , i n t h i s c a s e , i s 100 N. The push f o r c e from t h e wheels i s 50 N. What i s t h e a c t u a l s i z e o f the n e t f o r c e g o i n g t o be? Kelly: 50 N. Teacher: OK. 50 N. Which d i r e c t i o n i s i t g o i n g t o be i n ? Many s t u d e n t s : Left to right! Teacher: Going t h a t way ( i n d i c a t i n g a d i r e c t i o n o p p o s i t e t o t h e m o t i o n direction). Many s t u d e n t s : Yeah! Another s t u d e n t : Opposite t o the d i r e c t i o n . Teacher: So t h e n e t f o r c e i s 50 N, and i t i s i n t h a t d i r e c t i o n (makes adjustment t o diagram on t h e b l a c k b o a r d ) . Now, you've got two competing p o s s i b i l i t i e s h e r e . E i t h e r t h i s ( p o i n t i n g t o the diagram w i t h t h e n e t f o r c e a p p l i e d i n t h e o p p o s i t e d i r e c t i o n t o t h e m o t i o n d i r e c t i o n ) causes d e c e l e r a t i o n o r , the o t h e r s i t u a t i o n , which had t h e push f o r c e b e i n g l a r g e r ( t h a n t h e f r i c t i o n a l f o r c e ) causes d e c e l e r a t i o n . Tawnia: How c o u l d t h a t ( r e f e r r i n g t o t h e l a t t e r c a s e ) cause deceleration? Teacher: W e l l , t h a t ' s what we're g o i n g t o t e s t o u t . Jim: W e l l , f r i c t i o n can't be s t r o n g e r than t h e push f o r c e because everything...(inaudible). Teacher: B r a d , you're d i s a g r e e i n g . Brad: F r i c t i o n can be l a r g e r than t h e push f o r c e because, when you put your f o o t on t h e brake i t s t o p s because of f r i c t i o n . Teacher: OK. Tawnia, then C a r l a . Tawnia: When you're t a l k i n g about d e c e l e r a t i o n and have t h e push f o r c e b e i n g l a r g e r ( t h a n t h e f r i c t i o n a l f o r c e s ) . Does t h a t work by when (pause) t h e f o r c e i s a p p l i e d but  46  105  110  115  120  125  i t i s not constant. I mean, you have t o have a c o n s t a n t f o r c e t o keep i t a c c e l e r a t i n g b u t , i f you j u s t have a push f o r c e l a r g e r t h a t ' s n o t c o n s t a n t t h e n you're g o i n g to d e c e l e r a t e . . . ( i n a u d i b l e ) Teacher: Do you mean i t ' s f l u c t u a t i n g ? I t ' s g e t t i n g l a r g e r then s m a l l e r and then l a r g e r and s m a l l e r ? Tawnia: I f i t ' s constant i t ' s going t o stay (pause), i t ' s going t o a c c e l e r a t e b u t , i f i t ' s not c o n s t a n t i t ' s g o i n g t o eventua l l y decelerate. Teacher: What I'm i n t e r e s t e d i n i s what you mean by 'not c o n s t a n t ' ? Tawnia: Um, OK. When you j u s t push something and you j u s t l e t i t go. Is t h a t what you mean by t h e push f o r c e b e i n g l a r g e r because i t ' s not a constant f o r c e but i t i s going t o d e c e l e r a t e . Teacher: See, i n t h a t c a s e , when you l e t i t go, I would s a y t h a t t h e r e i s no push f o r c e on i t a t a l l . Tawnia: Then how can i t d e c e l e r a t e i f a c o n s t a n t f o r c e i s a p p l i e d t o i t , w i t h t h e push f o r c e b e i n g l a r g e r ? Teacher: The push f o r c e b e i n g l a r g e r Tawnia ( i n t e r j e c t i n g ) : and a c o n s t a n t f o r c e , how can i t d e c e l e r a t e ? Teacher: That's my q u e s t i o n ! Tawnia: You s a i d t h a t we were g o i n g t o t e s t t h a t o u t . Teacher: That's r i g h t . Tawnia: But t h a t can't happen! J i m i s not w i t h o u t s u p p o r t e r s  i n the c l a s s .  appears t o agree w i t h Jim's c o n c e p t i o n  Jody, f o r one,  that deceleration requires a  reduction i n the motive force while s t i l l  k e e p i n g i t l a r g e r than any  o p p o s i n g f o r c e s ( s e e l i n e s 28 and 29, p. 4 4 ) . I n a d d i t i o n , some o t h e r s t u d e n t s agree w i t h Jim's i d e a t h a t , i f t h e m o t i v e f o r c e becomes l e s s than t h e opposing f o r c e s , an o b j e c t w i l l s t o p moving. K e l l y and D i n a a l s o f i n d s u p p o r t w i t h i n t h e c l a s s .  Tawnia, i n an  attempt t o r a t i o n a l i z e h e r a c c e p t a n c e of t h e i d e a t h a t a c c e l e r a t i o n i s a c h i e v e d t h r o u g h an a p p l i c a t i o n of c o n s t a n t  47  force,  p o i n t s out t h e  l o g i c a l i n c o n s i s t e n c y of Jim's argument ( s e e l i n e s 100 through 125, pp. 46 and 47).  She f i n i s h e s w i t h a most d e f i n i t e p r e d i c t i o n f o r those who  b e l i e v e t h a t a c c e l e r a t i o n can o c c u r d u r i n g those times when t h e n e t f o r c e i s o p p o s i t e t o t h e d i r e c t i o n o f motion - "But t h a t can't happen!". What i s n ' t c l e a r a t t h i s s t a g e i s , which o f t h e s e two views represents a majority p o s i t i o n w i t h i n the c l a s s .  In order t o c r y s t a l -  l i z e t h e debate, t h e s t u d e n t s were p r e s e n t e d w i t h another h a l l w a y demonstration.  As w i t h t h e a c c e l e r a t i o n d e m o n s t r a t i o n , an equipment  t r o l l e y was used as t h e moving o b j e c t w i t h t h e f o r c e s b e i n g s u p p l i e d by the s t u d e n t s .  T h i s d e m o n s t r a t i o n began w i t h a r e c r e a t i o n of t h e  a c c e l e r a t i o n demonstration.  The t r o l l e y was then r e p o s i t i o n e d and a  s t u d e n t began p u l l i n g i t w i t h a c o n s t a n t f o r c e of a p p r o x i m a t e l y 20 N. When i t was c l e a r t h a t t h e t r o l l e y was a c c e l e r a t i n g , a second  student  began p u l l i n g , i n t h e o p p o s i t e d i r e c t i o n , w i t h f o r c e o f a p p r o x i m a t e l y 20 N.  T h i s r e t r o g r a d e f o r c e , when combined w i t h t h e f r i c t i o n a l f o r c e  of a p p r o x i m a t e l y 8 N, p r o v i d e d a n e t f o r c e of 8 N a p p l i e d i n t h e o p p o s i t e d i r e c t i o n t o t h e i n i t i a l motion  (see Figure 4).  When asked t o  d e s c r i b e t h e type of motion t h a t r e s u l t e d from t h i s s i t u a t i o n , a m a j o r i t y o f s t u d e n t s agreed t h a t t h e t r o l l e y d e c e l e r a t e d . The c l a s s ended w i t h t h i s d e m o n s t r a t i o n and any f u r t h e r d i s c u s s i o n was d e f e r r e d t o t h e next  class.  The next c l a s s began w i t h a diagram of t h e p r e v i o u s d e m o n s t r a t i o n (see F i g u r e 4 ) .  The s t u d e n t s were then asked t o comment on t h e t y p e of  motion t h a t r e s u l t e d from t h e r e s o l u t i o n of f o r c e s . Teacher: What k i n d of motion d i d t h a t t r o l l e y e x h i b i t a t t h a t p o i n t ? Cindy: Deceleration. 48  Figure 4. Deceleration Denonstration #1 < pull force (28 N)  initial direction  of notion ^^^^  p u l l f o r c e (20 H)  —•friction  5  10  15  (8 N)  Teacher: Now, b e f o r e we go any f u r t h e r , i s t h e r e any disagreement on t h e o b s e r v a t i o n ? D i d everyone see t h a t ( r e f e r r i n g t o the t r o l l e y ) d e c e l e r a t i n g o r , d i d anyone e l s e see one of t h e o t h e r of t h e two o t h e r t y p e s of m o t i o n - as t r a v e l l i n g w i t h a constant v e l o c i t y or t r a v e l l i n g w i t h a c c e l e r a t i o n ? Jim: W e l l , a h , (pause) i t was d e c e l e r a t i n g b u t , a f t e r i t was f i n i s h e d d e c e l e r a t i n g i t was a t a c o n s t a n t v e l o c i t y . Teacher: OK. So you saw i t d e c e l e r a t i n g and, t h e n you saw i t t r a v e l l i n g w i t h a constant v e l o c i t y ? Jim: Yeah. W e l l , they d i d n ' t go l o n g enough. I t was s t a r t i n g a t the end. Teacher: So, i f we had a l l o w e d i t t o go l o n g e r , you t h i n k i t would have s t a r t e d t o t r a v e l w i t h a c o n s t a n t v e l o c i t y . So do you agree w i t h C i n d y , w i t h t h e f i r s t p a r t , t h a t t h e r e was d e c e l e r a t i o n there? Jim: W e l l , i t slowed down. Teacher: OK. Any o t h e r o b s e r v a t i o n s ? In t h e f a c e of d w i n d l i n g  the c o n t r a r y ,  peer s u p p o r t and e m p i r i c a l e v i d e n c e t o  J i m has made s i g n i f i c a n t m o d i f i c a t i o n s t o h i s t h e o r y of  d e c e l e r a t i n g motion.  P r e v i o u s l y he had argued t h a t d e c e l e r a t e d 49  motion  was a f u n c t i o n of a reduced m o t i v e f o r c e , however, t h e n e t f o r c e remained i n t h e same d i r e c t i o n as m o t i o n .  Additionally, this  still  force  s i t u a t i o n would n o t , u l t i m a t e l y , r e s u l t i n a c e s s a t i o n o f m o t i o n b u t , r a t h e r , some form of f o r w a r d motion would s t i l l t h i s d e m o n s t r a t i o n , he has now g r u d g i n g l y  be i n e f f e c t .  After  adopted t h e p o s i t i o n t h a t  d e c e l e r a t i o n i s a r e s u l t o f t h e n e t f o r c e opposing t h e o r i g i n a l d i r e c t i o n of m o t i o n . his  previous  However, he i s n o t w i l l i n g t o c o m p l e t e l y  i n t e r p r e t a t i o n a l frame.  d e c e l e r a t i o n by s u g g e s t i n g  abandon  He f i n i s h e s t h i s d i s c u s s i o n of  t h a t , under t h e s e new s e t o f c o n d i t i o n s ,  u n i f o r m m o t i o n w i l l be t h e r e s u l t when t h e d e c e l e r a t i o n i s completed and,  t h a t , i n f a c t , was what he saw. When p r e s s e d on t h i s  he e q u i v o c a t e s , allowed The  but s t r o n g l y s u g g e s t s t h a t t h e d e m o n s t r a t i o n wasn't  t o continue  t o i t s l o g i c a l end.  c l a s s consensus appeared t o f a v o u r  a t i o n occurred  observation  t h e concept t h a t  deceler-  when t h e n e t f o r c e was i n t h e o p p o s i t e d i r e c t i o n t o t h e  motion o f an o b j e c t .  T h i s consensus appeared r a t h e r v i g o r o u s l y  during  the next d e m o n s t r a t i o n . T h i s d e m o n s t r a t i o n was a v a r i a t i o n on t h e second a c c e l e r a t i o n demonstration (see Figure 3).  I n t h i s c a s e , however, a mass had been  added i n such a way t h a t a n e t f o r c e was a p p l i e d i n t h e o p p o s i t e d i r e c t i o n t o the c a r t ' s motion (see Figure 5).  When asked t o p r e d i c t  what type o f m o t i o n would be d i s p l a y e d by t h e c a r t under t h e s e c o n d i t i o n s , a number of s t u d e n t s r e p l i e d , w i t h some i n d i g n a t i o n , t h a t t h e c a r t must d e c e l e r a t e .  A f t e r t h e d e m o n s t r a t i o n c o n c l u d e d , t h e s e same  s t u d e n t s suggested ( w i t h an ' I t o l d you s o ' a i r ) t h a t d e c e l e r a t i o n was s e l f - e v i d e n t under t h e s e c o n d i t i o n s and t h a t f u r t h e r d e m o n s t r a t i o n s were p o i n t l e s s .  50  Figure 5. Deceleration Dertonstration #2 roof nass gravity  nass 2  mi r  friction  4  gravity  i n i t i a l d i r e c t i o n of notion-  Note: nass 1 < nass 2  An e p i s o d e o c c u r r e d i l l u s t r a t e d how  towards the end of t h i s c l a s s , however, t h a t  f r a g i l e and  c o n t e x t - s e n s i t i v e the s t u d e n t s u n d e r s t a n d -  i n g of d e c e l e r a t i o n dynamics r e a l l y was the concept  of 'motion i m p l i e s a f o r c e  and how 1  c l o s e t o the  surface  existed.  At the end of the f i r s t c l a s s on d e c e l e r a t i o n the s t u d e n t s been a s s i g n e d class.  The  a d e c e l e r a t i o n worksheet which was  questions  t o be due  on t h i s worksheet were d i s c u s s e d  d e c e l e r a t i o n d e m o n s t r a t i o n and,  w i t h the e x c e p t i o n  for this  a f t e r the  of the  5  a d i f f e r e n t matter.  Teacher: What a r e the f o r c e s a c t i n g on t h a t b a l l K a r i ? Kari: Gravity. Teacher: I s t h a t the o n l y f o r c e ? Kari: No. Teacher: Is there another force? Kari: Friction. Teacher: The d i r e c t i o n t h a t g r a v i t y i s o p e r a t i n g i n K a r i ? 51  final  final  problem, appeared t o p r e s e n t few d i f f i c u l t i e s t o the s t u d e n t s . f i n a l problem (shown below as F i g u r e 6) was  had  The  Figure 6. The F i n a l Deceleration Problen A baseball player has Just h i t a f o u l b a l l . The b a l l i s t r a v e l l i n g v e r t i c a l l y upwards. On the diagram below, draw the Force (or Forces) that are acting on the b a l l and which are p a r a l l e l to the d i r e c t i o n of notion. In addition, describe how the b a l l i s Rowing i.e. i s i t accelerating, decelerating, or t r a v e l l i n g with a constant speed?  1  Kari:  10  15  Um, down. Teacher: The d i r e c t i o n t h a t f r i c t i o n i s o p e r a t i n g i n ? Kari: I n t h e o p p o s i t e (pause) as g r a v i t y . Teacher: G r a v i t y i s o p e r a t i n g down, t h e b a l l i s g o i n g up. Which d i r e c t i o n i s the f r i c t i o n operating i n ? Kari: Oh, t h e b a l l i s g o i n g up. Down. Teacher: OK. F r i c t i o n i s o p e r a t i n g i n t h a t d i r e c t i o n . Can I s i m p l i f y t h i s diagram any r i g h t now? Kari: Yes, you can i n c l u d e f r i c t i o n and g r a v i t y as one. K a r i has p r o v i d e d  a c o r r e c t f o r c e a n a l y s i s of t h e problem.  Indeed, she has d i s p l a y e d a f a i r l e v e l of s o p h i s t i c a t i o n f o r t h i s grade l e v e l by r e c o g n i z i n g t h a t m u l t i p l e f o r c e s o p e r a t i n g  i n t h e same  d i r e c t i o n can be c o l l a p s e d i n t o a s i n g l e f o r c e ( s e e F i g u r e 7 ) .  This  a n a l y t i c a l s o p h i s t i c a t i o n , however, i s a d i d a c t i c veneer t h a t K a r i (and o t h e r s t u d e n t s ) s u b s e q u e n t l y s t r i p p e d o f f t o r e v e a l an e x p e r i e n t i a l c o r e based upon Impetus Theory.  52  Figure 7. Kari's Force  Analysis  f r i c t i o n  4  friction  20  25  30  +  gravity  Teacher: Ok, so we have a n e t f o r c e downward? Kari: Yeah. Teacher: Does everybody see what I'm d o i n g w i t h t h a t . J u s t combining t h e two because t h e y ' r e i n t h e same d i r e c t i o n . Another s t u d e n t : What about t h e push f o r c e ? Teacher: OK. J u s t hang on. (The t e a c h e r makes t h e n e c e s s a r y a d j u s t ments t o t h e diagram on t h e b l a c k b o a r d . ) OK, K a r i , any o t h e r f o r c e s on t h e r e ? Kari: Yeah. The push f o r c e g o i n g up. Teacher: What push f o r c e ? Kari: Urn, urn, from t h e b a l l . Teacher: Is t h e r e a n y t h i n g p u s h i n g t h e b a l l ? Another s t u d e n t : The b a t ! Teacher: The b a t i s down here ( i n d i c a t i n g a r e g i o n below t h e b l a c k board). At t h i s p o i n t , t h e c l a s s became v e r y a g i t a t e d and many s t u d e n t s  attempted t o p r o v i d e an answer t o t h i s problem. 53  35  40  45  50  55  60  Teacher: H o l d i t ! Now w a i t a m i n u t e ! Wait a m i n u t e ! I ' l l g e t t o o each of you, one a t a t i m e . Melody: Mr. B r a c e ! L i s t e n t o t h i s ! (Melody b e g i n s t o read out t h e problem, but s l o w l y t r a i l s o f f and s t o p s b e f o r e f i n i s h i n g it.) Teacher: Has t h e b a l l l e f t t h e bat? Many s t u d e n t s ( i n c l u d i n g M e l o d y ) : Yeah. Teacher: A r e t h e r e any o t h e r f o r c e s on t h e b a l l ? Melody: No, t h e r e a r e no o t h e r f o r c e s . J u s t t h e f o r c e s g o i n g downward. Teacher: Michelle. Michelle: A push f o r c e . Teacher: Where i s t h e push f o r c e coming from? Melody ( i n t e r j e c t i n g ) : W e l l what a r e you g o i n g t o c a l l t h e f o r c e ( d i r e c t e d a t Michelle)? Teacher: H o l d i t . Wait a minute. I s t h e r e a c o n t a c t f o r c e i n v o l v e d here? Another s t u d e n t : Yeah, t h e r e was. Teacher: You're s a y i n g t h e r e i s a c o n t a c t f o r c e ? Another s t u d e n t : Was! There was! Teacher: P a s t tense? I s that contact force s t i l l there? Many s t u d e n t s : No! Michelle: The push f o r c e i s s t i l l t h e r e , but t h e c o n t a c t i s n ' t . Teacher: Now w a i t a minute. How can you have a push f o r c e w i t h o u t a contact? Brad: As t h e soon as t h e b a l l l e f t t h e b a t , t h e f o r c e , urn, t h e r e was no more f o r c e and t h e b a l l i m m e d i a t e l y s t a r t e d t o decelerate. Teacher: So you're s a y i n g a t t h i s p o i n t t h e r e a r e no o t h e r f o r c e s on here ( r e f e r r i n g t o F i g u r e 6)? We have a m o t i o n g o i n g upwards, and t h e o n l y f o r c e s a r e g r a v i t y and f r i c t i o n o p e r a t i n g downward. Another s t u d e n t : Then how can i t be g o i n g upwards? 54  65  Another s t u d e n t : That's i m p o s s i b l e ! B a l l s b e i n g b a t t e d o r thrown i n t o t h e a i r have been common,  childhood experiences  f o r t h e m a j o r i t y , i f n o t a l l , of these  students.  I t i s c l e a r from t h e debate t h a t has taken p l a c e t h a t almost a l l of t h e s e s t u d e n t s have c o n s t r u c t e d an e x p l a n a t i o n f o r t h e upwards movement of o b j e c t s (under these c o n d i t i o n s ) t h a t i s c o n s i s t e n t w i t h Impetus Theory.  The s t r e n g t h w i t h which they put f o r t h t h e i r arguments  s u g g e s t s t h a t i t i s almost i n c o n c e i v a b l e t o them t h a t some o b j e c t c o u l d move upwards a g a i n s t t h e combined f o r c e s of g r a v i t y and f l u i d without  some k i n d of f o r c e t o p u s h . i t .  This e x p e r i e n t i a l l y  e x p l a n a t i o n i s so c o n c r e t e t o t h e s e s t u d e n t s have heard and/or a c c e p t e d  constructed  t h a t they appear t o n o t  t h e f o r c e and motion a n a l y s i s of t h i s system  b u t , i n s t e a d , have i m m e d i a t e l y of t h e dynamics of t h e system. initial  friction  opted f o r t h e i r own i n t e r n a l  presumption  Only Brad appears t o have heard t h e  f o r c e a n a l y s i s w i t h an open mind and has c o r r e c t l y r e l a t e d t h i s  to previous d e c e l e r a t i o n demonstrations.  A s i d e from t h i s one comment,  however, he d i d n o t e n t e r i n t o t h e debate t h a t c o n t i n u e d  t o rage around  him.  70  75  Teacher: H o l d i t ! W a i t ! W a i t ! C a r l a you were n e x t . We're g o i n g t o go C a r l a , K e l l y , and then back t o you guys. Carla: ( i n a u d i b l e ) when you s l o w l y p r e s s on t h e b r a k e s i t ' l l s l o w l y go t o a s t o p . When t h e b a t h i t s t h e b a l l , t h e b a l l w i l l go up and s l o w l y ( p a u s e ) , e v e n t u a l l y ( i n a u d i b l e ) . Teacher: So you agree t h a t t h e r e i s d e c e l e r a t i o n . Carla: Yeah. Teacher: Do you agree w i t h t h i s type of diagram, t h a t t h e o n l y f o r c e s o p e r a t i n g on here a r e g r a v i t y and f r i c t i o n and they o p e r a t e as a n e t f o r c e v e r t i c a l l y downward?  55  80  85  90  95  100  i05  110  115  Carla: ( i n a u d i b l e ) Yeah. Teacher: OK. K e l l y . Kelly: The b a l l moving i s t h e end r e s u l t of t h e c o n t a c t f o r c e . I don't know what you c a l l t h a t though. What do you ( p a u s e ) . You t e l l u s . I s t h e r e a name f o r a f o r c e a f t e r t h e c o n t a c t f o r c e ? The b a l l ' s s t i l l moving. The b a l l ' s g o i n g i s t h e end r e s u l t of t h e c o n t a c t f o r c e . But t h e c o n t a c t f o r c e i s over w i t h but i t s n o t g o i n g ( i n a u d i b l e ) . Teacher: What has been t h e r e s u l t o f t h e c o n t a c t f o r c e ? L e t ' s t r y and (pause). Kelly: The m o t i o n of t h e b a l l upwards. Teacher: OK. So t h a t ' s t a k e n c a r e of r i g h t here ( r e f e r r i n g t o t h e d i a g r a m ) , and your p o s i t i o n r i g h t now i s t h a t t h e r e i s no l o n g e r any c o n t a c t f o r c e . That has been t r a n s l a t e d i n t o a motion. Do you agree w i t h t h i s s i t u a t i o n (that the b a l l i s d e c e l e r a t i n g as a r e s u l t of t h e n e t f o r c e opposing t h e d i r e c t i o n of motion) i n so f a r as t h e o t h e r f o r c e s ? Kelly: Yeah. Teacher: OK. A c o u p l e o f more p o i n t s . Tawnia. Tawnia: When t h e b a l l l e a v e s t h e b a t t h e r e ' s a c o n t a c t f o r c e . I t s j u s t l i k e p u s h i n g and p u l l i n g down t h e h a l l w a y ( r e f e r r i n g t o the hallway demonstrations). You l e t i t go and i t j u s t keeps g o i n g and t h e f r i c t i o n a c t s on i t and i t d e c e l e r a t e s . I t s g o i n g t o happen w i t h t h e b a l l . There was a c o n t a c t f o r c e . I t ' l l move because of t h e c o n t a c t f o r c e and i t w i l l slow down because o f f r i c t i o n . So t h e o n l y f o r c e s t h a t were a c t i n g on i t was t h e c o n t a c t f o r c e , a t t h e b e g i n n i n g , then t h e f r i c t i o n a c t s on i t r i g h t away. And a f t e r t h e c o n t a c t f o r c e t h e r e i s o n l y a f r i c t i o n f o r c e . ,. Teacher: I s g r a v i t y o p e r a t i n g on t h e r e o r not? Tawnia: Yeah. Teacher: OK. So you want t o i n c l u d e g r a v i t y . OK, you guys. Kari: I don't u n d e r s t a n d . I f t h e r e ' s no f o r c e now how come i t s s t i l l g o i n g upwards? I t w i l l e v e n t u a l l y go down but t h e r e s t i l l has t o be some s o r t o f f o r c e on i t t o make i t c o n t i n u e to go upwards. Teacher: Can you come up w i t h some p l a c e where t h e r e i s an upwards f o r c e on t h e b a l l ? A r e t h e r e any f i e l d f o r c e s o r c o n t a c t f o r c e s p u s h i n g upwards? Kari: Not a t t h e moment. 56  120  125  130  135  140  Melody: What a r e you g o i n g t o c a l l i t ? There has t o be some f o r c e p u s h i n g i t up. Teacher: Why does t h e r e have t o be a f o r c e ? Melody: I t wouldn't move anywhere! Kari: Don't f o r c e s cause motion? Teacher: Definitely! K a r i , Melody, and T a n n i s ( t o g e t h e r ) : W e l l , i t s moving! Kelly (interjecting): W e l l , t h e r e was a f o r c e . There was a c o n t a c t f o r c e t h a t caused t h e motion ( i n a u d i b l e ) . Kari: I know t h a t ! Teacher: K e l l y I want you t o e x p l a i n t h a t p o s i t i o n t o t h o s e guys. K a r i and T a n n i s : We know t h a t ! Melody: What a r e you g o i n g t o c a l l i t ? Kari: Say t h a t you were t o l d t h a t t h e r e was f r i c t i o n f o r c e and g r a v i t y f o r c e a c t i n g on t h i s b a l l , you would t h i n k t h a t i t was g o i n g down. But no i t s n o t , i t s s t i l l g o i n g up! Teacher: Remember what you s a i d b e f o r e about t h e i n i t i a l m o t i o n . Now once you s t a r t t h e i n i t i a l motion and then a p p l y a f o r c e i n the o p p o s i t e d i r e c t i o n what t y p e of motion do you come up with? A student: Deceleration. Teacher: OK, l e t ' s f o l l o w t h i s r i g h t t h r o u g h t o t h e end. Melody: I t s d e c e l e r a t i n g when i t s g o i n g up. Kari: I understand i t S i r . I'm j u s t s a y i n g what do you c a l l i t . Teacher: I know. I'm t r y i n g t o s t a y away from t h e l a b e l f o r a minute. I want t o go r i g h t t h r o u g h t h i s p r o c e s s . Melody: Then we u n d e r s t a n d i t . In so f a r as t h i s c o n t e x t i s concerned, t h e 'motion i m p l i e s a  f o r c e ' s t r u c t u r e and i t s c o r o l l a r y , Impetus Theory, a r e f i r m l y entrenched i n these students.  Only Tawnia  ( s e e l i n e s 95 t h r o u g h 106, p.  56) and Brad ( s e e l i n e s 57 t o 59, p. 54) appear t o have a n a l y z e d t h e 57  situation  i n t h e l i g h t of t h e p r e v i o u s d e m o n s t r a t i o n s and l e s s o n s , and  can accept  t h a t t h e r e can be motion w i t h o u t a c o n t i n u o u s  motive f o r c e .  F o r t h e remainder of t h e s t u d e n t s who took p a r t i n t h i s debate however, i f a b a l l i s moving upwards t h e r e must be some f o r c e pushing i t upwards. These s t u d e n t s do, however, appear t o be w r e s t l i n g w i t h an interesting  dichotomy.  On t h e one hand t h e r e i s t h e i r almost unshak-  a b l e b e l i e f t h a t motion i s d i r e c t l y t i e d t o a c o n t i n u o u s W h i l e on t h e o t h e r hand  motive f o r c e .  they have been p r o v i d e d w i t h e m p i r i c a l  e v i d e n c e t h a t a p p l i e d , n e t f o r c e s can be o p e r a t i n g i n t h e o p p o s i t e direction  t o t h e motion of an o b j e c t .  situation  i s t h e r e a l i z a t i o n (among some of t h e s t u d e n t s ) t h a t  have stumbled i n t o a l o g i c a l t r a p .  Compounding t h i s p a r a d o x i c a l they  They have agreed w i t h t h e a n a l y s i s  of t h e f o r c e s a c t i n g on t h e b a l l but now must f i n d some o t h e r phantom f o r c e t o b u t t r e s s t h e i r c o n t e n t i o n t h a t , i n t h i s case, t h e b a l l can o n l y move upwards i f t h e r e i s a f o r c e pushing  i t upwards.  Their  cries  f o r h e l p i n r e s o l v i n g t h i s c o n f l i c t a r e c l e a r throughout t h e l a t t e r s t a g e s of t h i s debate.  Kelly  ( l i n e s 78 t h r o u g h 83, p. 5 6 ) , Melody  ( l i n e s 116 and 128, p. 5 7 ) , and K a r i ( l i n e 139, p. 57) a l l ask f o r a name f o r t h e f o r c e t h a t they assume i s c a u s i n g t h e m o t i o n of t h e b a l l . I t s as i f a name, p r o v i d e d by t h e t e a c h e r , would p r o v i d e them w i t h a w a r r a n t t h a t would v a l i d a t e t h e i r e x p e r i e n t i a l t h e o r y c o n c e r n i n g t h e upward motion of t h e b a l l .  When t h a t name i s not f o r t h c o m i n g ,  closure  t o t h e debate i s p r o v i d e d by Melody ( s e e l i n e 142, p. 57) who appears t o be g i v i n g n o t i c e t h a t she i s now p r e p a r e d  t o p l a y t h e s c h o o l game.  The game, i n t h i s c a s e , i s t h a t t h e r e a r e ' r i g h t ' answers t o s c h o o l q u e s t i o n s , but t h e r e a l answers a r e t o be found e l s e w h e r e .  58  The  Dynamics of U n i f o r m M o t i o n The  emergence of the  predominant c o n c e p t u a l a t i o n d i d not p r o v i d e motion.  The  'motion i m p l i e s a f o r c e ' b e l i e f as  s t r u c t u r e i n the f i n a l d i s c u s s i o n of an a u s p i c i o u s  the deceler-  e n t r a n c e t o a s t u d y of u n i f o r m  a n t i c i p a t e d s t r a t e g y f o r t h i s s e c t i o n of the s t u d y  been t o u t i l i z e the s t u d e n t s '  had  a p p r e c i a t i o n of Newtonian c o n c e p t s of  a c c e l e r a t i o n and d e c e l e r a t i o n as a l o g i c a l f o i l a g a i n s t the emergence of the  'motion i m p l i e s a f o r c e ' b e l i e f d u r i n g the d i s c u s s i o n s  ing uniform motion.  The  premature (from an i n s t r u c t i o n a l  concern-  point  of  view) appearance of t h i s s t r u c t u r e however, tended t o throw t h i s strategy into disarray.  A f t e r a number of a t t e m p t s t o r e d e s i g n  s t r a t e g y t o f i t t h i s new  environment, i t was  o r i g i n a l s t r a t e g y w i t h one m o d i f i c a t i o n .  d e c i d e d t o r e t a i n the  This m o d i f i c a t i o n involved  attempt t o r e i n f o r c e the Newtonian concepts of t i o n (and by d o i n g so, deemphasize the by engaging the c l a s s i n an e x t e n s i o n concept map  the  acceleration/decelera-  'motion i m p l i e s a f o r c e ' frame) of t h e i r e x i s t i n g  acceleration  t o i n c l u d e the d e c e l e r a t i o n c o n c e p t s .  Student d i s c u s s i o n l e a d i n g up t o and d u r i n g the r e d e s i g n of a c c e l e r a t i o n concept map  was  perfunctory.  as i f the debate i n  i t was  an i n s u l t t o  c l a s s had never o c c u r r e d ,  intelligence  t o be d i s c u s s i n g , a g a i n , a s e t of concepts t h a t was  self-evident.  The  and  the  I t was  the p r e v i o u s  8) was  an  r e d e s i g n of the a c c e l e r a t i o n concept map  their  (see  so Figure  a c h i e v e d r a p i d l y w i t h no debate or d i s s e n t .  The  d i s c u s s i o n of u n i f o r m m o t i o n began w i t h a d e f i n i t i o n - u n i f o r m  motion i s t r a v e l l i n g w i t h a constant component of t h i s concept was  speed.  i g n o r e d due  i c a l s o p h i s t i c a t i o n of t h e s e s t u d e n t s .  The  59  A g a i n the  t o age  and  vectorial  l a c k of mathemat-  s t u d e n t s were then asked f o r  Figure 8. Redesigned Concept Map of Acceleration and Deceleration  forces are  balanced  unbalanced  -i.e. net force > 0  and the larger, constant force is  applied to  stationary objects  moving objects in  opposite direction as motion  same direction as motion  causing  causing  deceleration  acceleration  60  t h e i r i d e a s c o n c e r n i n g what s e t of c o n d i t i o n s c o u l d r e s u l t i n an o b j e c t t r a v e l l i n g with a constant  speed.  Dina: When a c o n s t a n t I t was map  force i s applied.  p o i n t e d out t h a t t h i s s i t u a t i o n , a c c o r d i n g t o the concept  t h a t the s t u d e n t s had  j u s t generated,  could only r e s u l t i n a c c e l e r -  a t i o n or d e c e l e r a t i o n depending upon the d i r e c t i o n t h a t the f o r c e  was  being a p p l i e d i n . A g a i n the q u e s t i o n was  posed.  Kari:  5  10  15  20  A decelerating force. Teacher: You mean i t s g e t t i n g s m a l l e r and s m a l l e r and s m a l l e r ? ( K a r i nods her head i n agreement). W e l l , i f one f o r c e ( t h e l a r g e r f o r c e i n a f o r c e p a i r ) i s g e t t i n g s m a l l e r and s m a l l e r what happens t o the net f o r c e ? Brad: I t becomes e q u a l . Teacher: U l t i m a t e l y i t w i l l become e q u a l . Equal t o what? Brad: ( i n a u d i b l e ) a c a r won't d e c e l e r a t e or a c c e l e r a t e . I t w i l l j u s t s t a y a t one speed. Teacher: OK, but i f you have one f o r c e here and one f o r c e t h e r e , and t h e y ' r e a r e b o t h the same what's the net f o r c e ? Many s t u d e n t s : Zero. Teacher: Is t h a t g o i n g t o cause u n i f o r m motion? Brad: Yes. Teacher: So you f e e l t h a t i f the net f o r c e i s equal t o z e r o then y o u ' l l end up w i t h u n i f o r m m o t i o n . (Brad nods h i s head i n agreement.) So what your s a y i n g t h e n i s t h a t i f t h e r e i s no f o r c e , no net f o r c e o p e r a t i n g on an o b j e c t (pause). Brad: W e l l , t h e r e was. Now t h e r e i s n ' t , so i t s t a y s at t h e same speed. Teacher: So i f i t t r a v e l s at a c o n s t a n t speed net f o r c e i s z e r o .  61  Brad has e x h i b i t e d a h i g h l e v e l of a n a l y t i c a l s o p h i s t i c a t i o n  and  a n a l o g i c r e a s o n i n g t o a r r i v e at h i s c o n c l u s i o n c o n c e r n i n g the dynamics of  uniform motion.  Whether h i s s o l u t i o n i s p e r v a s i v e among o r a c c e p t -  a b l e t o the r e s t of the c l a s s remains t o be  seen.  Kari:  25  30  35  40  45  50  I don't b e l i e v e t h a t . I f you have b a l a n c e d f o r c e s then i t won't be moving. Teacher: OK. Why do you t h i n k i t won't be moving? Kari: Because i t has an equal amount of f o r c e p u s h i n g a g a i n s t each other. I f t h e y ' r e the same s t r e n g t h t h e y ' r e not g o i n g t o push each o t h e r . Teacher: B r a d , you were p r e t t y d e f i n i t e t h a t they were not g o i n g t o move ( s i c ) . Why not? Brad: I s a i d i t was gonna - i t won't d e c e l e r a t e or a c c e l e r a t e . I t has t o a c c e l e r a t e b e f o r e u n i f o r m motion and then the f o r c e s w i l l b a l a n c e out and s t a y a t u n i f o r m speed. Teacher: Are you two t a l k i n g about t h e same s e t of c o n d i t i o n s ? When you're t a k i n g about t r a v e l l i n g w i t h u n i f o r m motion, t h a t o b j e c t t h a t ' s g o i n g t o be t r a v e l l i n g w i t h u n i f o r m m o t i o n , was i t moving t o b e g i n w i t h or was i t stopped t o b e g i n w i t h ? Brad: I t would be moving t o b e g i n w i t h . Teacher: Then your p o s i t i o n i s then t h a t i f you t a k e a moving o b j e c t and you a p p l y b a l a n c e d f o r c e s t o i t then you end up w i t h u n i f o r m motion. Brad: Yes. Teacher: K a r i was your o b j e c t Kari (interjecting): Still. Teacher: I t was s t i l l t o b e g i n w i t h . So we have a d i f f e r e n t s e t of conditions. Kari: But I t h i n k i f we have b a l a n c e d f o r c e s i t ' l l d e c e l e r a t e . Teacher: Why w i l l i t d e c e l e r a t e ? Kari: Because t h e f o r c e s a r e equal and t h e y ' r e , I don't know, t h e y ' r e g o i n g t o want t o s t o p . Brad: They're not g o i n g t o s t o p . 62  55  60  Tawnia: That's r i g h t ( a p p a r e n t l y a g r e e i n g w i t h K a r i ) . Teacher: So, i n essence, what you're s a y i n g i s t h a t t h e r e i s a requirement f o r a c o n s t a n t f o r c e t o keep something moving. Is t h e r e a problem w i t h t h i s t h e n ( r e f e r r i n g t o t h e concept map)? I n t h i s case i t appears t h a t a c o n s t a n t f o r c e r e s u l t s i n acceleration or deceleration. Kari: Maybe I don't b e l i e v e i n u n i f o r m motion t h e n . Teacher: Brad d i d you want t o s a y something. Brad: W e l l , when an o b j e c t moves w i t h u n i f o r m motion i t can't speed up o r i t can't slow down so t h e r e a r e no f o r c e s ( i n a u d i b l e ) to speed i t up o r slow i t down. Brad i s a p p a r e n t l y  far  i n a m i n o r i t y p o s i t i o n w i t h i n t h e c l a s s i n so  as h i s e x p l a n a t i o n o f t h e causes o f u n i f o r m motion.  K a r i , Dina,  and Tawnia r e p r e s e n t t h e (supposed) m a j o r i t y view t h a t a n u l l n e t f o r c e c o n d i t i o n does n o t c o n t r i b u t e t o u n i f o r m motion and, by i n f e r e n c e , i f t h e r e i s motion  ( u n i f o r m o r o t h e r w i s e ) t h e r e must be a dominant f o r c e  present. In an attempt t o break t h e h o l d t h a t t h e 'motion i m p l i e s a f o r c e ' b e l i e f had over t h e c l a s s a d e m o n s t r a t i o n was p r e s e n t e d .  T h i s demon-  s t r a t i o n was g i v e n i n two p a r t s . The f i r s t p a r t of t h e d e m o n s t r a t i o n was d e s i g n e d t o demonstrate t h e e f f e c t o f b a l a n c e d f o r c e s on a s t a t i o n a r y o b j e c t - i n t h i s case an equipment t r o l l e y .  Not s u r p r i s i n g l y t h e s t u d e n t s were a b l e t o c o r -  r e c t l y p r e d i c t and a c c e p t t h e outcome of t h i s e v e n t . The second p a r t of t h e d e m o n s t r a t i o n was d e s i g n e d t o demonstrate t h e e f f e c t o f b a l a n c e d f o r c e s on a moving o b j e c t , a g a i n an equipment trolley.  I n t h i s case t h e t r o l l e y was i n i t i a l l y  a c c e l e r a t e d by a  s t u d e n t and t h e n a second s t u d e n t s u p p l i e d an equal f o r c e i n t h e opposite d i r e c t i o n .  B e f o r e t h e d e m o n s t r a t i o n began t h e s t u d e n t s were  asked t o p r e d i c t t h e motion o f t h e t r o l l e y when o n l y one s t u d e n t was 63  pulling i t .  A l l of t h o s e s t u d e n t s t h a t r e p l i e d i n d i c a t e d t h a t t h e  t r o l l e y should accelerate.  A f t e r a number of p r a c t i c e attempts t o  f a m i l i a r i z e t h e s t u d e n t s who were s u p p l y i n g t h e f o r c e s w i t h what was e x p e c t e d of them, and t o ensure t h a t t h e t r o l l e y would f o l l o w a s t r a i g h t p a t h , t h e c l a s s was asked t o c l o s e l y observe t h e motion of t h e t r o l l e y a f t e r t h e second, equal but opposing f o r c e had been a p p l i e d .  65  70  75  80  Teacher: H e i n z y , what t y p e o f motion d i d you t h i n k i t was t r a v e l l i n g w i t h once i t passed t h i s p o i n t where Cory s t a r t e d a p p l y i n g the f o r c e i n t h e o p p o s i t e d i r e c t i o n . Heinzy: I t slowed down. Teacher: As i t moved t h a t way towards t h e camera d i d i t c o n t i n u e t o get s l o w e r and s l o w e r ? Heinzy: I t stopped a t one p o i n t and s t a y e d a t t h a t p o i n t . Teacher: I'm s o r r y ? Heinzy: Or, i t kept a t a c o n s t a n t speed. Teacher: So t h e r e was a p e r i o d where i t appeared t o slow down and then i t t r a v e l l e d w i t h a c o n s t a n t speed. Heinzy: Yeah. Teacher: S t e v e , what do you t h i n k ? You f e l t i t slowed down f i r s t and then (pause) Steve: kept g o i n g a t t h e same speed. Teacher: Kari? Kari: Yup. U n i f o r m m o t i o n . The c l a s s was almost a t an end.  I t had been a c l a s s t h a t had  s i n g u l a r l y l a c k e d t h e energy and v i t a l i t y t h a t had been so e v i d e n t i n the f i n a l d i s c u s s i o n s of d e c e l e r a t i o n .  I t was as i f t h e m a j o r i t y of  t h e c l a s s was p l a y i n g Melody's ' s c h o o l game'. A l t h o u g h t h e d e m o n s t r a t i o n appeared  t o have c o n v i n c e d t h e s t u d e n t s  t h a t b a l a n c e d f o r c e s a p p l i e d t o a moving o b j e c t r e s u l t e d i n u n i f o r m 64  motion t h e r e was  a sense of unease i n t h e c l a s s .  This uneasiness  was  perhaps t y p i f i e d by the comments t h a t Tawnia and her l a b p a r t n e r K i r s t e n made as they were p r e p a r i n g t o l e a v e the c l a s s . Tawnia: I s t h a t r i g h t Mr. Brace? Teacher: How do you mean - i s i t r i g h t ? Tawnia: When you're moving and you a p p l y b a l a n c e d f o r c e s t h e n you t r a v e l a t a c o n s t a n t speed? Teacher: What d i d you see happening? Tawnia: W e l l I don't know? I don't even know i f they ( t h e s t u d e n t s who were a p p l y i n g the f o r c e s t o the t r o l l e y ) were a p p l y i n g balanced f o r c e s . Teacher: W e l l t h e y were b e i n g p r e t t y c a r e f u l . I t h i n k you can assume t h a t they were a p p l y i n g b a l a n c e d f o r c e s . Tawnia: So t h a t ' s r i g h t t h e n . Kirsten: Then why wouldn't i t s t o p ? Tawnia: Yeah.  85  90  The  'motion i m p l i e s a f o r c e ' b e l i e f was  s u r f a c e and Tawnia was  l u r k i n g j u s t below t h e  on the verge of succumbing t o i t ' s s e d u c t i v e  a t t r a c t i o n (as were, p r o b a b l y , many o t h e r s t u d e n t s ) .  Her attempt  to  o b t a i n a warrant from the t e a c h e r c o n c e r n i n g the ' T i g h t n e s s ' of the concept  t h a t b a l a n c e d f o r c e s would produce u n i f o r m motion was  an  attempt t o reduce the t e n s i o n and u n e a s i n e s s t h a t must have been b u i l d i n g w i t h i n her and throughout  the c l a s s .  A t e n s i o n and  t h a t stemmed from t h e c o n f l i c t between what her e x p e r i e n c e was  uneasiness  suggested  t r u e and the c o n c e p t u a l p a t h t h a t her t e a c h e r wanted t o l e a d her  down. she was  When t h a t warrant was not e x p l i c i t l y f o r t h c o m i n g and, i n s t e a d asked t o reexamine her own  o b s e r v a t i o n s , she has r e p l i e d ( w i t h  65  K i r s t e n ' s s u p p o r t ) w i t h an apparent a c c e p t a n c e o f t h e 'motion i m p l i e s a force  1  belief.  The l a s t c l a s s i n t h e dynamics u n i t was devoted t o t a c k l i n g , on, t h i s u n d e r l y i n g  head-  sense among t h e s t u d e n t s t h a t a l l m o t i o n , and  s p e c i f i c a l l y u n i f o r m m o t i o n , must be caused by some form o f a p p l i e d o r indigenous force.  The c l a s s was begun by r e v i e w i n g t h e d e m o n s t r a t i o n  from t h e p r e v i o u s day and randomly s e l e c t i n g s t u d e n t s t o e x p l a i n what they thought caused u n i f o r m m o t i o n .  Consistently  the students res-  ponded t h a t u n i f o r m m o t i o n r e s u l t e d when t h e n e t f o r c e on an o b j e c t became z e r o . t h i s concept.  A c l a s s s t r a w v o t e r e s u l t e d i n unanimous agreement w i t h The sense o f unease, p r e v a l e n t i n t h e p r e v i o u s c l a s s  however, remained.  I t was as i f t h e s t u d e n t s were p a r r o t i n g back what  they thought was e x p e c t e d of them.  I n an attempt t o draw out and  c o n f r o n t what was assumed t o be an almost s u b l i m i n a l , i n t u i t i v e  belief  i n t h e 'motion i m p l i e s a f o r c e ' concept t h e s t u d e n t s were p r e s e n t e d w i t h one f i n a l s e r i e s of d e m o n s t r a t i o n s . The f i r s t d e m o n s t r a t i o n c o n s i s t e d  s i m p l y o f p u s h i n g a dynamics  c a r t a c r o s s t h e f l o o r and then removing t h e push  5  10  force.  Teacher: I f I push t h i s c a r t a l o n g t h e f l o o r and I l e t i t go, t h e q u e s t i o n i s what would t h e f o r c e o r f o r c e s be a c t i n g on t h e c a r t ? B e f o r e we g e t t o t h e f o r c e o r f o r c e s one t h i n g I'd l i k e t o know i s what k i n d of m o t i o n i s t h e c a r t g o i n g t o exhibit? Many s t u d e n t s : Acceleration. Teacher: OK, K e l l y . Kelly: Acceleration. Teacher: Any o t h e r p r e d i c t i o n s ? Kirsten: Deceleration. Teacher: You f i g u r e i t s g o i n g t o slow down. 66  15  Many s t u d e n t s : A f t e r . Yeah, a f t e r . Teacher: OK. I t s g o i n g t o a c c e l e r a t e then d e c e l e r a t e . Kelly: And i f i t has enough room i t s p r o b a b l y g o i n g t o end up stopping. Teacher: K i r s t e n , a r e you s a y i n g i t s g o i n g t o d e c e l e r a t e as soon as I l e t go. Kirsten: Yeah. Teacher: OK. Any o t h e r p r e d i c t i o n s ? No o t h e r p r e d i c t i o n s were f o r t h c o m i n g so the c a r t was  pushed and  released.  20  25  30  35  Teacher: Now, a f t e r I l e t go (of t h e c a r t ) and b e f o r e i t r a n i n t o t h a t desk l e g over t h e r e , what f o r c e s were a c t i n g on i t ? Kelly: You've t o l d us t h a t one ( i n a u d i b l e ) . Teacher: About i n e r t i a . OK, i n e r t i a i s not a f o r c e . I t ' s j u s t a tendency of t h i n g s t o keep on d o i n g whatever they a r e doing before. Kelly: There's f r i c t i o n . There's r o l l i n g f o r c e ( f r i c t i o n ) and, urn, air. Teacher: OK. So's t h e r e ' s j u s t ( p a u s e ) . Kelly: Oh yeah, t h e r e ' s g r a v i t a t i o n a l p u l l . Teacher: OK, but we're o n l y i n t e r e s t e d i n t h o s e f o r c e s t h a t a r e o p e r a t i n g p a r a l l e l t o the d i r e c t i o n of motion. Kelly: OK, then t h e r e i s t h e r o l l i n g and a i r f r i c t i o n . Teacher: So t h e r e ' s j u s t f r i c t i o n . I s t h e push f o r c e s t i l l t h e r e o r not? Dina: No. Not a f t e r you l e f t i t . Not a f t e r you l e t i t go. Teacher: So once I l e t i t go t h e r e ' s j u s t a f r i c t i o n a l f o r c e on i t . I f t h e r e ' s j u s t a f r i c t i o n a l f o r c e o p e r a t i n g on i t , which d i r e c t i o n i s the f r i c t i o n a l f o r c e o p e r a t i n g i n ? Another s t u d e n t : In the o p p o s i t e d i r e c t i o n t o motion.  67  40  45  Teacher: OK. Take a look at t h a t concept map (see F i g u r e 6) over there. I f the o n l y f o r c e o p e r a t i n g on t h i s a f t e r I've l e t i t go i s the f r i c t i o n a l f o r c e , o p e r a t i n g a g a i n s t the d i r e c t i o n of m o t i o n , what t y p e of m o t i o n s h o u l d t h i s e x h i b i t ? Kelly: I t s h o u l d d e c e l e r a t e , (pause) I t s h o u l d but i t doesn't. Teacher: Why s h o u l d i t ? Kelly: Because i f you t h i n k about i t t h e r e ' s o n l y f r i c t i o n ( p a u s e ) , I don't know. K e l l y i s convinced  f o r c e was  removed.  t h a t she saw  the c a r t a c c e l e r a t e a f t e r the push  T h i s i s n ' t t h a t s u r p r i s i n g because t h a t i s what she  p r e d i c t e d would happen (see l i n e 8, p. 66). recognized  On the o t h e r hand she  the l o g i c a l i n c o n s i s t e n c y t h a t she now  because she had  j u s t c o r r e c t l y analyzed  finds herself i n  the f o r c e s o p e r a t i n g on  the  c a r t t o be o n l y f r i c t i o n a l f o r c e s which must slow the c a r t down. t h i s p o i n t , however, she appears t o be u n a b l e t o r a t i o n a l i z e t e n s i o n between her p e r c e p t i o n s this  50  55  60  and her a n a l y s i s .  has  She  At  this  i s not a l o n e i n  conflict.  Teacher: K i r s t e n , why d i d you say i t would d e c e l e r a t e i n the f i r s t place? Kirsten: I don't know why, I j u s t t h i n k i t would. Teacher: You've got t h i s gut f e e l i n g t h a t i t w i l l . Kari. Kari: ( i n a u d i b l e ) I f the net f o r c e i s o p p o s i t e t o the d i r e c t i o n of m o t i o n the o b j e c t i s supposed t o d e c e l e r a t e . Teacher: Now, i f t h a t ' s t h e case - the o n l y f o r c e on here i s the f r i c t i o n a l f o r c e - why would i t a c c e l e r a t e t o b e g i n w i t h ? Kelly: Because of the push f o r c e you gave i t i n the f i r s t p l a c e . If you g i v e i t a push f o r c e and i t s g o i n g t o l a s t f o r a c e r t a i n l e n g t h of t i m e . I t s not g o i n g t o j u s t (pause) Michelle (interjecting): I t s not g o i n g t o j u s t d e c r e a s e because the c o n t a c t f o r c e you've pushed on i t i s g o i n g t o make i t a c c e l e r a t e and then i t ' l l decelerate. 68  65  70  75  80  Teacher: ...Now t h e s u g g e s t i o n ' s been made t h a t what happens t o t h i s c a r t i s t h a t i t speeds up i n i t i a l l y and then i t s t a r t s s l o w i n g down... Now i f i t s g o i n g t o speed up, then how do you make something speed up? What do you have t o do t o i t s n e t force? Brad: Make i t l a r g e r and c o n s t a n t . Teacher: OK. We've got t o make l a r g e r and c o n s t a n t . A t l e a s t cons t a n t . That's t h e bare minimum t h a t we can do. The problem i s , i f I've l e t go of t h a t t h i n g , where i s t h a t l a r g e r f o r c e coming from? Another s t u d e n t : From f r i c t i o n . Teacher: OK, but I don't t h i n k t h a t anybody i s i n disagreement w i t h the f a c t t h a t t h e r e i s f r i c t i o n on here. What's been suggested i s t h a t I move t h i s a l o n g and I l e t i t go and i t s t a r t s s p e e d i n g up. The s u g g e s t i o n ' s been made t h a t t h e r e a s o n i t speeds up i s because I've t r a n s f e r r e d some of my f o r c e on t o t h e c a r t . Michelle: Yup. Teacher: Now, how many p e o p l e t h i n k t h a t i s t h e case? A s t r a w v o t e was t a k e n t o d e t e r m i n e how many s t u d e n t s f e l t  that  some amount of f o r c e had been t r a n s f e r r e d t o t h e c a r t and had caused the i n i t i a l  acceleration.  were o p e r a t i n g  I n o t h e r words, how many of t h e s t u d e n t s  from an 'Impetus Theory' base.  A c l e a r m a j o r i t y of t h e  s t u d e n t s f e l t t h a t t h i s was t h e c a s e .  85  Teacher: Now, i f t h a t ' s t h e c a s e , then i f I remove t h e f r i c t i o n what s h o u l d happen, i f t h e r e i s a t r a n s f e r of f o r c e , i s t h a t i t s h o u l d keep a c c e l e r a t i n g . I s t h a t r i g h t ? Many s t u d e n t s : Right. Teacher: OK. L e t ' s remove t h e f r i c t i o n . T h i s was t h e i n t r o d u c t i o n t o t h e second d e m o n s t r a t i o n .  This,  d e m o n s t r a t i o n used an a i r - t r a c k t o reduce f r i c t i o n t o a n e g l i g i b l e amount.  The method of o p e r a t i o n of t h e a i r - t r a c k and i t s e f f e c t on t h e  69  s l i d i n g f r i c t i o n of the a i r - t r a c k r i d e r was e x p l a i n e d and demonstrated t o the s t u d e n t s .  90  Teacher: Now the s u g g e s t i o n i s t h a t t h e r e i s a t r a n s f e r of f o r c e from whomever or whatever i s d o i n g the p u s h i n g t o the o b j e c t t h a t i s b e i n g pushed. I want you t o remember one t h i n g . I f you're g o i n g t o d e a l w i t h good s c i e n c e what you're g o i n g t o have t o be a b l e t o do i s demonstrate t h a t , a f t e r the i n i t i a l push f o r c e has l e f t , t h e r e i s a f o r c e on the o b j e c t . Otherw i s e , i f you c a n ' t demonstrate t h a t i t i s t h e r e you c a n ' t say that i t i s there. At t h i s p o i n t the a i r - t r a c k was t u r n e d on and t h e r i d e r was g i v e n  an i n i t i a l  95  100  105  110  push f o r c e down the t r a c k .  Teacher: OK. Where i s the push f o r c e on the r i d e r now ( t h e r i d e r was t r a v e l l i n g t h r o u g h the c e n t r a l p o r t i o n of the t r a c k ) ? A Student: The a i r ( f r o m the a i r t r a c k ) i s p u s h i n g i t . Teacher: Now w a i t a minute. The a i r i s g o i n g out t h a t way ( i n d i c a t e s an upwards d i r e c t i o n ) . Melanie: W e l l your f o r c e i s s t i l l on t h e r e . Teacher: OK. I f my f o r c e i s on t h e r e where i s i t ? Dennis: In the a i r . Teacher: No the a i r i s g o i n g up. The m o t i o n i s g o i n g t h a t way ( i n d i c a t e s a d i r e c t i o n 90° t o the a i r f l o w ) . Melanie: I t s p u s h i n g i n the d i r e c t i o n t h a t you pushed. Its s t i l l there. L i k e i t s s t i l l pushing. I t j u s t can't stop (inaudible). Teacher: W e l l my q u e s t i o n t o you i s - where i s i t ? Melanie: I t s i n the r i d e r pushing i t forwards. Teacher: But what's pushing? Melanie: Nothing. Teacher: Can you demonstrate t h a t t h e r e i s something p u s h i n g t h a t rider? Melanie: There's n o t h i n g . I t s from the f r i c t i o n o r something. 70  115  Teacher: But we've reduced t h e f r i c t i o n . Melanie: W e l l I don't know. What had i n i t i a l l y s t a r t e d out as an a n a l y t i c a l debate had q u i c k l y  d e g e n e r a t e d i n t o a c i r c u l a r argument t h a t appeared t o be i r r e s o l v a b l e . T h i s l a c k of r e s o l u t i o n was b e g i n n i n g t o f r u s t r a t e b o t h t h e t e a c h e r and the  students.  I n a f i n a l attempt t o break through t h e c i r c l e , t h e  s t u d e n t s were l e d t h r o u g h a d e t a i l e d f o r c e and motion a n a l y s i s of t h e r i d e r and asked t o c o n s i d e r what k i n d of m o t i o n t h e r i d e r s h o u l d d i s p l a y i f , i n f a c t , i t was c a r r y i n g some form of i n d i g e n o u s f o r c e .  120  125  130  Teacher: Now do you need a l a r g e r f o r c e , i n o t h e r words a n e t f o r c e g r e a t e r than z e r o , t o have something moving? Melanie: Yes. No! You don't. Teacher: I f t h e n e t f o r c e i s z e r o what t y p e of motion do you have? Melanie: Stationary. Teacher: What t y p e of m o t i o n do you have? Melanie: U n i f o r m motion. Teacher: OK. I s t h i s t h i n g ( t h e r i d e r ) e x h i b i t i n g a u n i f o r m motion? Another s t u d e n t : Yeah. Teacher: I f i t s e x h i b i t i n g a u n i f o r m motion what do you know about t h e net f o r c e on i t ? Many s t u d e n t s : Its zero. Teacher: Now i f t h e n e t f o r c e i s z e r o you've got one of two s i t u a t i o n s . There i s a f r i c t i o n a l f o r c e on here ( t h e r i d e r ) t h a t way. Then t h e r e must be an i n h e r e n t f o r c e on here ( t h e r i d e r ) t h a t I gave i t . Melanie: Yeah. That's what I t o l d you. Teacher: But why am I u s i n g t h i s machine? A Student: I t reduces t h e f r i c t i o n . 71  135  140  Teacher: R i g h t ! So i f I've reduced t h e f r i c t i o n t h e r e i s no f o r c e there. Melanie: There's s t i l l f o r c e t h e r e (on t h e r i d e r ) though. Teacher: But i f t h e r e ' s f o r c e on t h e o t h e r s i d e ( o f t h e r i d e r ) i t s h o u l d be a c c e l e r a t i n g . Melanie: No, because your f o r c e i s d y i n g down. I t s n o t a c o n s t a n t force. No amount of argument, l o g i c a l o r o t h e r w i s e , w i l l c o n v i n c e  t h a t t h e r e a r e no m o t i v e f o r c e s a t t a c h e d t o t h e r i d e r . almost c l a s s i c a l statement  Melanie  She espouses an  Impetus Theory when she f i n i s h e s her. argument w i t h t h e  t h a t t h e f o r c e i s " d y i n g down" ( s e e l i n e 140, p. 7 2 ) . F o r  h e r , o b j e c t s o n l y move when they a r e f o r c e d t o move.  I f no r e c o g n i z -  a b l e f o r c e i s p r e s e n t on a moving o b j e c t then i t s because t h e r e has been a t r a n s f e r of f o r c e t o t h e o b j e c t and t h i s f o r c e w i l l g e t used up d u r i n g t h e motion thus c a u s i n g t h e o b j e c t t o slow down and u l t i m a t e l y stop. At t h i s p o i n t o t h e r s t u d e n t s began t o e n t e r t h e debate w i t h t h e i r own e x p l a n a t i o n s f o r t h e movement of t h e r i d e r . Brad:  145  150  There wouldn't be any f r i c t i o n ( r e f e r r i n g t o t h e a i r - t r a c k ) . Teacher: There i s no s l i d i n g f r i c t i o n . You're r i g h t . Brad: So as soon as you l e t i t go t h e r e won't be any f o r c e s a c t i n g on i t a t a l l . So i t w i l l be t r a v e l l i n g w i t h u n i f o r m motion. Teacher: Kelly. Kelly: The f o r c e t h a t you gave i t - l i k e t h e r e ' s no f r i c t i o n o r a n y t h i n g - i t took t h a t f o r c e . I f you gave i t 10 N of f o r c e , - and i t s g o i n g t o keep t h a t . I t s j u s t g o i n g t o keep i t . I t s ( t h e f o r c e ) n o t g o i n g t o r u n o f f . . . . I f t h e r e i s no f r i c t i o n i t ' l l keep g o i n g a t a c o n s t a n t ( p a u s e ) . Teacher: I f you have a c o n s t a n t f o r c e a p p l i e d i n t h e d i r e c t i o n o f m o t i o n a c c o r d i n g t o t h a t ( t h e concept map) i t s h o u l d a c c e l e r ate. 72  155  160  165  170  175  180  185  Kelly: Yeah, but you're n o t g i v i n g i t a c o n s t a n t f o r c e . You j u s t gave i t t h a t one i n i t i a l push...that f i r s t push f o r c e you gave i t 10 N, r i g h t , and you're n o t g i v i n g i t a c o n s t a n t f o r c e so t h a t i t s j u s t g o i n g t o keep t h a t 10 N because t h e r e ' s no f r i c t i o n now. So i t s g o i n g t o keep i t because t h e r e ' s n o t h i n g t o s t o p t h a t 10 N, so i t ' l l keep g o i n g . Teacher: But i s n ' t t h a t a c o n s t a n t f o r c e ? I f t h e r e i s a f o r c e on t h e r e of 10 N a l l t h e time s h o u l d n ' t i t a c c e l e r a t e ? OK. We're g o i n g t o go t o H e i n z y , Tawnia, and then over t o ( i n a u d i b l e ) . OK, H e i n z y . Heinzy: The f o r c e decreases t o z e r o and s i n c e t h e r e ' s no r e s i s t a n c e g o i n g t h e o t h e r way i t keeps g o i n g . Teacher: W i t h what type of motion? Heinzy: Uniform motion. Teacher: So you're s a y i n g t h e n e t f o r c e i s z e r o a f t e r I l e t i t go. Heinzy: I t decreases t o zero. Teacher: OK, and because t h e n e t f o r c e i s z e r o we're d e a l i n g w i t h u n i f o r m motion. Heinzy: Yeah. Teacher: Ok. Tawnia. Tawnia: You s a i d t h a t a c c e l e r a t i o n i s ( a r e s u l t o f ) a push f o r c e g o i n g i n t h e d i r e c t i o n of t h e motion t h a t i s b i g g e r than t h e other force? Teacher: No, I've gone back up t o t h i s concept map r i g h t over here. There's a l a r g e r c o n s t a n t f o r c e a p p l i e d t o moving o b j e c t s i n t h e same d i r e c t i o n as t h e motion and t h a t causes a c c e l e r ation. Tawnia: I know. W e l l t h a t ' s what's happening. The n e t f o r c e i s g o i n g t h e same way as t h e d i r e c t i o n . Teacher: Then t h i s ( t h e r i d e r ) s h o u l d be a c c e l e r a t i n g . Tawnia: Yes. Teacher: Does i t ? Tawnia: No. Teacher: I f i t doesn't ( p a u s e ) . Tawnia: Then t h a t ( t h e concept map) i s a bunch o f c r a p ! 73  190  195  200  Teacher: Then t h e r e i s one of your two o p t i o n s . E i t h e r t h a t t h i n g i s wrong o r Tawnia ( i n t e r j e c t i n g ) : We've l e a r n e d t h i s a l l wrong then. Teacher: Why a r e you assuming t h a t ? D i d t h a t concept map work f o r your o t h e r d e m o n s t r a t i o n s ? Another s t u d e n t : Yeah, i t d i d . Teacher: W e l l i f i t d i d why would you throw i t out j u s t because i t doesn't appear t o work f o r t h i s one. What's your o t h e r o p t i o n here? Kari: That t h i s ( t h e r i d e r ) has no f o r c e s a c t i n g on i t . Teacher: That's t h e o t h e r o p t i o n . R i g h t ! Now once I l e t i t go t h e r e a r e no o t h e r f o r c e s a c t i n g on i t . Kari: And i f t h e r e a r e no f o r c e s then t h e n e t f o r c e i s z e r o , t h e r e f o r e i t has u n i f o r m m o t i o n . The c l a s s ended w i t h K a r i ' s d e s c r i p t i o n o f t h e Newtonian  option.  An o p t i o n t h a t few of t h e s t u d e n t s appeared t o be w i l l i n g t o c o n s i d e r . Throughout  t h i s c l a s s t h e f r u s t r a t i o n l e v e l of b o t h t h e t e a c h e r  and s t u d e n t s had r i s e n t o an almost p a l p a b l e l e v e l .  On t h e one hand,  t h e t e a c h e r f e l t s t y m i e d by h i s i n a b i l i t y t o move t h e m a j o r i t y o f t h e c l a s s towards an a c c e p t a n c e of t h e Newtonian o p t i o n .  On t h e o t h e r  hand, t h e s t u d e n t s appeared f r u s t r a t e d by t h e i r i n a b i l i t y t o o b t a i n v a l i d a t i o n , from t h e t e a c h e r , of t h e i r i n t e r p r e t a t i o n of t h e events t h a t they had j u s t w i t n e s s e d .  An i n t e r p r e t a t i o n t h a t was, t o them,  s t r o n g l y s e l f - e v i d e n t and based on t h e e x p e r i e n t i a l axiom of t h e 'motion i m p l i e s a f o r c e ' c o n c e p t u a l s t r u c t u r e and i t s c o r o l l a r y Theory.  Impetus  A Clue Structure A n a l y s i s of the E f f e c t i v e n e s s of t h e I n s t r u c t i o n a l S t r a t e g y The  c l u e s t r u c t u r e a n a l y s i s of t h e e f f e c t i v e n e s s o f t h e i n s t r u c -  t i o n a l s t r a t e g y was composed o f two phases.  The f i r s t phase c o n s i s t e d  of a n a l y z i n g t h e l e s s o n t r a n s c r i p t s f o r t h e c o n c e p t u a l s t u d e n t s were u s i n g t o i n t e r p r e t t h e f o r c e / m o t i o n p r e s e n t e d t o them.  These c o n c e p t u a l  data that the  e v e n t s t h a t had been  d a t a were then r e c o n s t r u c t e d  into  d i a g r a m m a t i c , i n t e r p r e t a t i o n a l frames on an i n d i v i d u a l and composite basis.  The symbols used t o r e p r e s e n t  t h e v a r i o u s elements and connect-  o r s w i t h i n t h e frame s t r u c t u r e s a r e shown i n F i g u r e 9.  Figure 9. Synbols Used In Frane Constructions  najor Frane designator  car  sub-frane  concept designator  vehicle [  :: :|  )  default value (operational)  [i:i:icari;i;;;j  default value (non-operational)  (  default value (unknown)  )  'isa'  link  concept link  W i t h i n t h e s e t o f elements t h a t have been used f o r t h e r e c o n s t r u c t i o n of t h e i n t e r p r e t a t i o n a l frameworks, t h e concepts o f frames, sub-frames, and d e f a u l t v a l u e s have been d i s c u s s e d d i f f e r e n t i a t i o n of the d e f a u l t values  p r e v i o u s l y . The  i n t o those t h a t a r e o p e r a t i o n a l , 75  non-operational, described.  and unknown , however, have not been p r e v i o u s l y  These d e s c r i p t i o n s w i l l  o c c u r at t h i s  time.  As mentioned p r e v i o u s l y , d e f a u l t v a l u e s are s p e c i f i c , d i s c r e t e , and i d i o s y n c r a t i c d a t a t h a t are a p p l i e d t o the i n t e r p r e t a t i o n of event or o b j e c t . for  an  As an example of t h i s d a t a t y p e , the c o n c e p t u a l  frame  ' c a r ' would c o n t a i n a d e f a u l t v a l u e f o r the number of wheels t h a t  an i n d i v i d u a l p e r c e i v e s a c a r t o have w h i c h , i n most c a s e s , would be 'four'.  For the purposes of t h i s r e s e a r c h , those d e f a u l t v a l u e s  are p l a y i n g an a c t i v e r o l e i n an i n d i v i d u a l ' s i n t e r p r e t a t i o n of event or o b j e c t w i l l  be r e f e r r e d t o as  'operational'.  v a l u e s t h a t are i n t e r p r e t e d (by the r e s e a r c h e r )  that an  Those d e f a u l t  to e x i s t w i t h i n a  s p e c i f i c frame, but are not p l a y i n g an a c t i v e r o l e i n an event or o b j e c t i n t e r p r e t a t i o n w i l l be r e f e r r e d t o as D e f a u l t v a l u e s t h a t are c l a s s i f i e d as b e i n g i n the r e s e a r c h e r ' s  v i e w , are p r e s e n t  'non-operational'. 'unknown' are those t h a t ,  i n an i n d i v i d u a l ' s i n t e r p r e t a t i o n  of an event or o b j e c t but cannot be d i r e c t l y d e r i v e d from the t r a n s criptions. The  second phase c o n s i s t e d of comparing the  'before  instruction'  frame s t r u c t u r e s w i t h those t h a t appeared ' a f t e r i n s t r u c t i o n .  This  1  comparison t h e n a l l o w e d a s u b j e c t i v e assessment t o be made of i n s t r u c t i o n a l s t r a t e g y ' s a b i l i t y t o modify s t u d e n t s ' understanding  conceptual  of the dynamics of m o t i o n t o one more c l o s e l y a p p r o x i -  m a t i n g the Newtonian c o n c e p t i o n s will  the  be d i s c u s s e d  of motion.  Each of t h e s e two  phases  individually.  Student I n t e r p r e t a t i o n a l Frames of M o t i o n Throughout the d i s c u s s i o n s on motion the s t u d e n t s focussed  on two  elements: the i n i t i a l  repeatedly  s t a t e of the o b j e c t t h a t was  be moved or i n m o t i o n , and the f o r c e s t h a t were p e r c e i v e d t o be  to  r e s p o n s i b l e f o r t h e motion.  This b i n a r y nature of the d i s c u s s i o n  suggests that f o r these students,  a t l e a s t , any frame d e a l i n g  with  m o t i o n i s composed of two sub-frames; one sub-frame t o d e a l w i t h t h e o b j e c t and t h e o t h e r t o d e a l w i t h f o r c e s .  T h i s s t a g e of t h e a n a l y s i s  i s d i r e c t e d towards d e l i n e a t i n g t h e components o f t h e s e sub-frames and the i n t e r a c t i o n s between t h e sub-frames. Acceleration The  d i s c u s s i o n s c o n c e r n i n g t h e dynamics of a c c e l e r a t i o n e x p l i c i t l y  i n v o l v e d f o u r s t u d e n t s - K e l l y , Cory, J i m , and M e l a n i e . K e l l y ' s opening arguments as t o why an o b j e c t  ( i n t h i s case a  dynamics c a r t ) would b e g i n t o a c c e l e r a t e and c o n t i n u e  to accelerate  c o n s i s t e d of t h e f o l l o w i n g c o n c e p t s : 1.  The o b j e c t must have a push f o r c e a p p l i e d t o i t ( s e e l i n e s 1  t o 3, p. 3 4 ) . 2.  The a p p l i e d push f o r c e must be l a r g e r than any f r i c t i o n a l  force operating and,  i n t h e o p p o s i t e d i r e c t i o n ( s e e l i n e s 1 t o 3, p. 34)  by i m p l i c a t i o n , t h e push f o r c e must be i n t h e same d i r e c t i o n as  the m o t i o n . 3.  The a p p l i e d push f o r c e must be c o n t i n u o u s ( s e e l i n e 9, p.  4.  The a p p l i e d f o r c e must be c o n s t a n t  34) . ( s e e l i n e s 23 t o 25, p.  35) . K e l l y subsequently modified a p p l i c a t i o n of a constant  h e r f o u r t h p o i n t t o c l a r i f y when an  f o r c e would r e s u l t i n a c c e l e r a t i o n .  This  m o d i f i c a t i o n was based upon t h e s t a t e o f t h e o b j e c t and i n d i c a t e d t h a t i f t h e o b j e c t was i n i t i a l l y s t a t i o n a r y an a p p l i c a t i o n of a f o r c e would a c c e l e r a t e t h a t o b j e c t  constant  ( s e e l i n e 14, p. 3 6 ) . I f , however,  the o b j e c t was a l r e a d y i n motion t h e a p p l i c a t i o n of an a d d i t i o n a l f o r c e 77  would a c c e l e r a t e t h e o b j e c t b u t o n l y f o r a f i n i t e p e r i o d of time. the end o f t h a t p e r i o d whatever a c c e l e r a t i o n had o c c u r r e d degraded t o a c o n s t a n t 39).  velocity  would have  s t a t e ( s e e l i n e s 16 t o 27, pp. 36 and  By i m p l i c a t i o n t h e n , i f one wished t o have a moving  continuously  object  a c c e l e r a t i n g ( l i n e a r a l l y o r otherwise) a continuously  i n c r e a s i n g f o r c e would have t o be a p p l i e d t o t h a t o b j e c t . and  By  F i g u r e s 10  11 diagram t h e p r o b a b l e frame s t r u c t u r e and usage o f t h i s s t r u c -  ture. Another s t u d e n t ' s (Cory) comment t h a t a c o n t i n u a l l y i n c r e a s i n g f o r c e i s r e q u i r e d f o r a c c e l e r a t i o n ( s e e l i n e s 13 t o 22, p. 34) appears t o be d i r e c t e d a t t h e second p a r t o f t h e o r i g i n a l q u e s t i o n  (Why would  Figure 16. Kelly's Acceleration Frane for Stationary Objects  involves i  a.  OBJECT  £  FORCES  ::::::::::t:  STATE  TWE(S)  FWCTIOB men  dynamics' cart  science deno  nationless  *"7^J'•' •' •' J  APPLIED (to object)  ilillllllMI  CHARACTERISTICS  DIRECTION  SOURCE  continuous  sane as notion  78  FRICTION  nZZEZ:  opposes object notion  I HE SIZE  constant  •  »'  1  push) friction"]  Figure 11. Kelly's Acceleration Frane for Hoving Objects  involves i  ,  OBJECT TYPE  STATE  dynamcs cart  FORCES MIS)  FUNCTION science den  (to object)  noving ]: :l  [•'•:•••• CHARACTERISTICS  an o b j e c t c o n t i n u e  continuous  push ) friction  FRICTION opposes object notion  I  DIRECTION  SOURCE  hand  mmm  SIZE  HE  sane as notion  increasing  t o a c c e l e r a t e ? ) asked by t h e t e a c h e r .  have been made w i t h i n t h e c o n t e x t between K e l l y and t h e t e a c h e r  H i s comments  e s t a b l i s h e d during the interchange  t h a t have d e a l t w i t h t h e c o n d i t i o n s  n e c e s s a r y t o keep a moving o b j e c t a c c e l e r a t i n g .  As such he appears t o  be i n agreement w i t h , a t l e a s t , t h a t p a r t o f K e l l y ' s frame t h a t  implies  t h a t i f an o b j e c t i s a l r e a d y moving a c c e l e r a t i o n can o n l y be a c h i e v e d by a p p l y i n g a c o n t i n u a l l y i n c r e a s i n g f o r c e . In a s i m i l a r f a s h i o n M e l a n i e a l s o appears t o agree w i t h a t l e a s t the i m p l i e d p a r t o f K e l l y ' s a c c e l e r a t i o n frame. M e l a n i e ' s comment t h a t a c o n s t a n t  force w i l l 79  As w i t h Cory,  r e s u l t i n a constant  v e l o c i t y ( s e e l i n e s 29 and 30, p. 39) has o c c u r r e d  w i t h i n the context  of a d i s c u s s i o n c o n c e r n i n g t h e a c c e l e r a t i o n of a moving o b j e c t .  As  w i t h K e l l y , M e l a n i e has i m p l i e d t h a t a c c e l e r a t i o n of a moving o b j e c t can o n l y o c c u r w i t h t h e a p p l i c a t i o n of a c o n t i n u o u s l y J i m i s t h e odd man out i n t h i s d i s c u s s i o n .  increasing force.  H i s comments ( s e e  l i n e s 1 t o 11, p. 3 6 ) , made d u r i n g t h e comparison of t h e c l a s s and teacher  produced concept maps, suggest t h a t he i s v i e w i n g  acceleration  from a g e n e r a l i z e d s t a n c e t h a t i s c l o s e t o a Newtonian p o s i t i o n . Jim, a c c e l e r a t i o n w i l l a constant  For  o c c u r no m a t t e r whether t h e a p p l i e d f o r c e i s of  size or increasing.  As long as t h e a p p l i e d f o r c e on an  o b j e c t i s l a r g e r t h a n any opposing f o r c e s t h e o b j e c t w i l l  accelerate.  What cannot be e x p l i c i t l y d e t e r m i n e d from t h e s e comments o r t h e c o n t e x t t h a t they were made i n , i s what, i f any, i n f l u e n c e t h e i n i t i a l s t a t e of the o b j e c t p l a y s .  A p r o b a b l e frame f o r Jim's p e r c e p t i o n s  of a c c e l e r -  a t i o n i s shown i n F i g u r e 12. To t h i s p o i n t , but w i t h t h e p o s s i b l e e x c e p t i o n  of Jim, a l l of t h e  s t u d e n t s t h a t have t a k e n p a r t i n t h i s d i s c u s s i o n have agreed t h a t f o r a moving o b j e c t t o a c c e l e r a t e and c o n t i n u e  t o accelerate a continuously  i n c r e a s i n g f o r c e must be a p p l i e d t o t h a t o b j e c t .  Considering  of o b j e c t i o n t o t h i s s t a n c e by t h e r e s t of t h e s t u d e n t s , disagreement t h a t K e l l y ' s o r i g i n a l s u g g e s t i o n  (continuous  of an o b j e c t can be a c h i e v e d by a p p l y i n g a c o n s t a n t  the lack  the vociferous acceleration  f o r c e ) was met  w i t h , and t h e c o n s e n s u a l agreement w i t h t h e c l a s s produced concept map (see F i g u r e 1) i t appears r e a s o n a b l e t h a t t h i s concept r e p r e s e n t s t h e c o r e of an a c c e l e r a t i o n frame t h a t i s a c c e p t a b l e class.  t o t h e m a j o r i t y of t h e  Such an a c c e l e r a t i o n frame would be almost i d e n t i c a l  K e l l y ' s frame f o r a moving o b j e c t  with  (see F i g u r e 11) but w i t h t h e d e f a u l t  80  Figure 12. Jin's Acceleration Frane  involves  OBJECT  FORCES SEE  TYPE  TVPEIS)  FUNCTION I-:) STATE <•  Moving or rolionless  t 1  (to object)  f *  IIIIMIIttltlMI  >  .!  (MOERISTICS  values  I;  continuous  sane as notion  B  applied > opposing j  0PP05IN6 EHEH: opposes object notion  DIRECTION  SOURCE  •v.  E  1EZ  \  SIZE  constant  increasing  f o r o b j e c t type and f u n c t i o n , and s o u r c e o f t h e f o r c e becoming  unknown q u a n t i t i e s . The  s e t of expectations  c o n c e r n i n g a c c e l e r a t i o n t h a t t h i s type o f  frame engenders i s e x p e r i e n t i a l l y f a m i l i a r t o most i f n o t a l l o f these students.  I f one i s d r i v i n g a c a r o r r i d i n g a b i c y c l e and wishes t o  a c c e l e r a t e more f o r c e must be a p p l i e d t o t h e d r i v i n g wheels. d r i v e r wants t h e a c c e l e r a t i o n t o c o n t i n u e f o r c e s u p p l i e d must a l s o be i n c r e a s e d t h i s frame r e p r e s e n t s  I f the  and/or i n c r e a s e t h e amount o f  i n a continuous fashion.  What  then i s a g u t - l e v e l a p p r e c i a t i o n o f t h e v a r i a b l e  n a t u r e of f r i c t i o n . 81  Following  the d e m o n s t r a t i o n s the s t u d e n t c o n c e p t i o n s of the cause  of a c c e l e r a t i o n appeared t o have a l t e r e d d r a m a t i c a l l y .  The  class  unanimously agreed t h a t , f o r t h e s e d e m o n s t r a t i o n s , a c c e l e r a t i o n caused by the a p p l i c a t i o n of a c o n s t a n t f o r c e as opposed t o a p p l i c a t i o n of a c o n t i n u o u s l y tions.  On  was  the  i n c r e a s i n g f o r c e p r i o r t o the demonstra-  r e f l e c t i o n however, t h i s does not appear t o be the case.  b o t h d e m o n s t r a t i o n s the o b j e c t i n q u e s t i o n As s u c h , t h i s m a j o r i t y  was  initially  motionless.  agreement must be r e s t a t e d t o i n c l u d e  this  c o n d i t i o n , t h a t i s , the a c c e l e r a t i o n of an i n i t i a l l y m o t i o n l e s s was  caused by the a p p l i c a t i o n of a c o n s t a n t f o r c e .  In  object  Again, t h i s  c o n c e p t i o n of the dynamics of a c c e l e r a t i o n i s almost i d e n t i c a l  with  K e l l y ' s frame f o r the a c c e l e r a t i o n of a s t a t i o n a r y o b j e c t  Figure  10).  (see  As a r e s u l t K e l l y ' s frame, w i t h s u i t a b l e changes t o the  default  v a l u e s f o r o b j e c t type and s o u r c e of the a p p l i e d f o r c e , can be as a composite frame f o r most of the  viewed  class.  Deceleration The  d i s c u s s i o n c o n c e r n i n g the dynamics of d e c e l e r a t i o n  i n i t i a t e d by K e l l y . o b j e c t was had  Her  was  view of the cause of d e c e l e r a t i o n of a moving  t h a t the f o r c e s opposing the m o t i o n ( i n t h i s case f r i c t i o n )  t o be l a r g e r than the a p p l i e d f o r c e s  (see l i n e 5, p. 42, and  51 t o 53, p. 45).  A d d i t i o n a l s u p p o r t f o r t h i s c o n c e p t i o n of  a t i o n was  by D i n a (see l i n e s 14 t o 17, pp.  provided  d e f i n i t e l y by Tawnia (see l i n e s 91 t o 125,  pp.  42 and  46 and  47).  c o n c e p t u a l i z a t i o n of d e c e l e r a t i o n i s r e p r e s e n t e d i n F i g u r e Only one surfaced  o t h e r p o s i t i o n c o n c e r n i n g the causes of  during  the i n i t i a l d i s c u s s i o n s .  T h i s was  lines  deceler-  43) and This 13.  deceleration  provided  by  Jim.  Jim's c o n c e p t i o n s of d e c e l e r a t i o n c e n t r e around a need t o keep the  82  very  Figure 13. Kelly's Deceleratifln Frane  DECELERATION  i*  car s  '•]  Having  k  «• •  % ••• I  CHARACTERISTICS  SOURCE  DIRECTION  uheels  sane as ration  opposes object notion  SIZE  a p p l i e d , m o t i v e f o r c e g r e a t e r than any opposing f o r c e s .  To r e a c h t h i s  s t a t e J i m f e e l s t h a t d e c e l e r a t i o n can be a c h i e v e d by s i m p l y the m o t i v e f o r c e w h i l e s t i l l  reducing  r e t a i n i n g t h e above c o n d i t i o n ( s e e l i n e s 7  t o 12, p. 4 2 ) . T h i s p o s i t i o n i s a l s o s t a t e d by Jody ( s e e l i n e s 28 and 29, p. 4 4 ) . A d d i t i o n a l l y , J i m f e e l s t h a t i f t h e magnitude o f t h e m o t i v e f o r c e f a l l s below t h a t of t h e opposing f o r c e s t h e o b j e c t w i l l s t o p  (see l i n e  19, p. 4 3 ) . Jim's c o n c e p t u a l i z a t i o n of d e c e l e r a t i o n i s shown i n F i g u r e 14. Jim's comments c o n c e r n i n g a c c e l e r a t i o n i n d i c a t e t h a t he equates the cause o f t h e motion w i t h t h e a p p l i c a t i o n of a m o t i v e f o r c e i n t h e 83  Figure 14. din's Deceleration Frane  involves ^  3  -  FORCES  OBJECT  33  TYPE '  STATE  car  Hoving  MIS)  science problen  APPLIED (to object) CHARACTERISTICS  SOURCE  DIRECTION [  yteels  sane as notion  same d i r e c t i o n as t h e m o t i o n . t h i s case f r i c t i o n ) o p e r a t e s  Conversely,  FRICTION HHEZil opposes object notion  applied) friction  SIZE  decreasing  i f the larger force ( i n  i n the opposite d i r e c t i o n t o that of the  motion t h e o b j e c t t h a t i s moving must s i m p l y s t o p .  As a r e s u l t of t h i s  'motion i m p l i e s a f o r c e ' frame, i f t h e m o t i o n of t h e o b j e c t i s one o f s l o w i n g down, t h i s can o n l y occur when t h e m o t i v e f o r c e i s reduced, o r reducing, but s t i l l the f r i c t i o n a l  l a r g e r t h a n t h e opposing f r i c t i o n a l  forces.  If  f o r c e s become g r e a t e r than t h e m o t i v e f o r c e t h e o b j e c t  must s t o p . I n t e r e s t i n g l y , J i m sees no c o n f l i c t between h i s c o n c e p t i o n s o f a c c e l e r a t i o n and d e c e l e r a t i o n .  Both of these c o n c e p t u a l 84  sets incorpor-  a t e , as a c o r e i t e m , the i m p l i c a t i o n t h a t the net f o r c e , a c t i n g  on  e i t h e r an a c c e l e r a t i n g or d e c e l e r a t i n g o b j e c t , i s g r e a t e r than zero operating  i n the d i r e c t i o n of m o t i o n .  and  From a p h y s i c a l p o i n t of view,  such a f o r c e c o n d i t i o n can o n l y r e s u l t i n a c c e l e r a t i o n .  For  Jim  however, the key p o i n t i s not the net f o r c e but r a t h e r the d e f a u l t v a l u e f o r the s i z e of the a p p l i e d f o r c e .  I f an o b j e c t i s a c c e l e r a t i n g  t h i s d e f a u l t v a l u e must be e i t h e r c o n s t a n t i s d e c e l e r a t i n g t h i s d e f a u l t v a l u e must be  or i n c r e a s i n g .  I f an  object  decreasing.  In comparison t h e n , the major d i f f e r e n c e between the frame b e i n g used by K e l l y t o i n t e r p r e t the d e c e l e r a t i o n of o b j e c t s and  that  being  employed by J i m l i e s i n the d e f a u l t v a l u e f o r t h e i r p a r t i c u l a r concept i o n of the comparison of the f o r c e s i n v o l v e d .  K e l l y ' s conception  t h i s comparison d i c t a t e s t h a t the t o t a l v a l u e of any a p p l i e d must be l e s s than the t o t a l v a l u e of any Jim's c o n c e p t i o n  frictional  of  forces  f o r c e s , whereas  of t h i s comparison i s e x a c t l y the o p p o s i t e .  For  Jim  d e c e l e r a t i o n o c c u r s when the a p p l i e d f o r c e s are g r e a t e r than the f r i c t i o n a l f o r c e s but are d e c r e a s i n g higher The  ( o r d e c r e a s e d ) from a p r e v i o u s l y  level. hallway  d e m o n s t r a t i o n appeared t o cement the frame,  d e s c r i b e d by K e l l y but w i t h changes t o the d e f a u l t v a l u e s the o b j e c t  initially  describing  (an equipment t r o l l e y ) , i n p l a c e as the i n t e r p r e t a t i o n a l  s t r u c t u r e of c h o i c e f o r the m a j o r i t y of s t u d e n t s (see F i g u r e  15).  A l t h o u g h the a c c e p t a n c e of t h i s frame appeared t o i n d i c a t e t h a t  the  s t u d e n t s had opted f o r a c l o s e a p p r o x i m a t i o n t o the Newtonian model of d e c e l e r a t i o n ( d e c e l e r a t i o n i s a r e s u l t of a net f o r c e o p e r a t i n g d i r e c t i o n opposite  in a  t o t h a t of the motion) subsequent d a t a c o l l e c t e d  from the b a s e b a l l problem suggested t h a t t h i s frame was,  85  in reality, a  Figure 15. Conposite Deceleration Frane Derived Fran Hallway Denonstration  involves t  m OBJECT  TYPE equipfent trolley  STATE  raving  EL  FORCES  .'! i.'  •i ! •  M(S>  FUNCTION science den  ± APPLIED (to object)  !; (MACTERISTICS  SOURCE  DIRECTION  wheels  sate as notion  CWARISOH FRICTION  • • [ friction) posh) i  opposes object notion  SIS  frame t h a t c o u l d be used t o s u p p o r t t h e 'motion i m p l i e s a f o r c e ' s e t conceptualizations. D u r i n g t h e d i s c u s s i o n o f t h e b a s e b a l l problem i t soon became apparent t h a t a m a j o r i t y of s t u d e n t s ( t a k i n g p a r t i n t h e d i s c u s s i o n ) had extreme d i f f i c u l t y w i t h t h e i d e a t h a t a b a l l c o u l d move upwards w i t h o u t a f o r c e ( a p p l i e d i n t h e d i r e c t i o n of motion) t o move i t upwards.  Throughout t h e d i s c u s s i o n s  (contained  on pages 51 t o 57)  student a f t e r student e i t h e r e x p l i c i t l y s t a t e s or i m p l i e s that  there  must be a t r a n s f e r r e d f o r c e ( f r o m t h e b a t ) on t h e b a l l t h a t keeps i t moving upwards.  Only Brad and Tawnia appear t o have a c c e p t e d t h e  s i t u a t i o n t h a t an o b j e c t can move, a l b e i t d e c e l e r a t e , w i t h o u t t h e 86  a p p l i c a t i o n o f some type o f f o r c e i n d i r e c t i o n o f t h e m o t i o n ( s e e l i n e s 57 t h r o u g h 59, p. 54, and l i n e s 95 t h r o u g h 106, p. 5 6 ) . The  concept of ' t r a n s f e r r e d f o r c e ' t h a t i s so p r e v a l e n t  i n these  d i s c u s s i o n s i s a necessary c o n d i t i o n f o r these students i n order t o r e t a i n t h e i n t e g r i t y o f t h e i r i n t e r p r e t a t i o n a l frames.  Up t o t h i s  p o i n t , a l l t h e d e m o n s t r a t i o n s and problems t h a t t h e s e s t u d e n t s have f a c e d have i n v o l v e d some form o f e a s i l y r e c o g n i z a b l e m o t i v e f o r c e d i r e c t l y a s s o c i a t e d w i t h a moving o b j e c t . been c o n s i s t e n t l y i n c o r p o r a t e d  These m o t i v e f o r c e s have  i n t o t h e i r i n t e r p r e t a t i o n a l frames (as  a p p l i e d f o r c e s ) and have been one o f t h e major concepts used f o r t h e i r analyses  o f t h e dynamics o f moving o b j e c t s .  To remove such a major  concept from an i n t e r p r e t a t i o n a l frame t h a t has s e r v e d  them w e l l , j u s t  because t h e concept cannot be e m p i r i c a l l y i d e n t i f i e d , would d e s t r o y t h e frame.  Such a s i t u a t i o n i s u n t e n a b l e f o r t h e s e s t u d e n t s .  As a r e s u l t ,  t h a t r e g i o n w i t h i n t h e i r i n t e r p r e t a t i o n a l frames t h a t had once h e l d t h e concept of ' a p p l i e d f o r c e ( s ) ' must c o n t i n u e  to exist.  This  continued  e x i s t e n c e i s a c h i e v e d by a metamorphosis o f t h e ' a p p l i e d f o r c e ' (from the b a t ) concept t o a ' t r a n s f e r r e d f o r c e ' (on t h e b a l l ) concept w i t h i t s own s e t o f d e f a u l t  values.  In a d d i t i o n t o t h i s metamorphosis, t h a t r e g i o n of t h e i n t e r p r e t a t i o n a l frame t h a t d e a l t w i t h t h e f o r c e ( s ) which opposed motion has had t o be expanded t o r e f l e c t t h e i n c r e a s e d Figure 7).  complexity  of these forces (see  I n b o t h of t h e s e r e g i o n s , however, t h e d e f a u l t v a l u e f o r  the s i z e ( c o n s t a n t ,  i n c r e a s i n g , o r d e c r e a s i n g ) of t h e f o r c e ( o r f o r c e s )  i n v o l v e d cannot be d e t e r m i n e d from t h e t r a n s c r i p t s .  As s u c h , t h e  d e f a u l t v a l u e f o r t h e s i z e concept has been l e f t b l a n k .  This  evolution  of t h e o r i g i n a l composite d e c e l e r a t i o n frame ( s e e F i g u r e 15) i n t o a  87  d e c e l e r a t i o n frame t h a t s u p p o r t s students  t h e type of Impetus Theory t h a t t h e s e  appear t o be u s i n g i s shown i n F i g u r e 16.  Figure 16. Conposite Deceleration Frane Applied to the Baseball Problen  involves  OBJECT  FORCES CMMRISON  TVPE : • : ^ STATE 1;• PrTWCTIflM )• | l]}}}}]}TVPEIS) . . . 7 . . .HZ: i...'...'....V...J.  baseball  mving upwards  i  • • • {opposing > transferred  gane  JO  TRANSFERRED (to object)  0PP0SIN6 CWWCTERISTICS  CHARACTERISTICS SOURCE  DIRECTION  bat  saite as notion  111111  SIZE  DIRECTION  SOURCE E E 1:  parity  • 1111111  friction  SIZE  opposes object notion  Uniform Motion The  i n i t i a l d i s c u s s i o n s o f t h e dynamics o f u n i f o r m m o t i o n were  dominated by Brad and K a r i .  B r a d , d u r i n g t h e s e d i s c u s s i o n s , has put  f o r t h t h e Newtonian p o s i t i o n t h a t u n i f o r m m o t i o n i s t h e r e s u l t of t h e a p p l i c a t i o n of b a l a n c e d f o r c e s t o a moving o b j e c t ( s e e l i n e s 31 t o 33, p. 62, and l i n e s 61 t o 63, p. 6 3 ) . K a r i , however, has suggested t h a t the a p p l i c a t i o n of b a l a n c e d f o r c e s t o a moving o b j e c t w i l l  decelerate  and u l t i m a t e l y s t o p t h a t o b j e c t ( s e e l i n e s 48 t o 51, p. 6 2 ) . She f u r t h e r s u g g e s t s t h a t u n i f o r m motion can o n l y be a c h i e v e d  with the  a p p l i c a t i o n o f a " d e c e l e r a t i n g f o r c e " ( s e e l i n e 2, p. 61) - a f o r c e 88  which i s c o n t i n u o u s l y d e c r e a s i n g i n s i z e . motion c e n t e r s around t h e requirement  K a r i ' s conception of uniform  f o r some type o f m o t i v e f o r c e  and, as s u c h , c a n be viewed as a s u b s e t o f t h e 'motion i m p l i e s a f o r c e ' interpretational  frame.  Both o f t h e s e c o n c e p t i o n s o f u n i f o r m motion have been r e c o n s t r u c t e d i n t o t h e i n t e r p r e t a t i o n a l frames shown i n F i g u r e s 17 and 18. As a r e s u l t o f t h e g e n e r a l n a t u r e o f t h e d i s c u s s i o n s , however, many o f the d e f a u l t v a l u e s f o r s p e c i f i c concepts have not been c l a r i f i e d and have been l e f t b l a n k i n t h e frames.  Figure 17. Brad's Frane for Unifom Hotion  requires OBJECT TYPE UK  air-track rider  FUNCTION TTTTTT7 science dsn  APPLIED (to object) FORCES  STATE TTTTT7; noving  OMRACTERISTICS  TYPE continuous  BALANCED  mm CHARACTERISTICS  ,(net force = 8  89  SOURCE  Figure 18. Kari's Frane for Uniforn Hotion  . .>  r ;\  (. ;> , , , fj • ; ; I i ; • I DURATION f ;  is.:.:.!.:.:.!.1.1.1.i.t.i.i.s.:.:.!. t.i.i.i.i,i.i.t.i.i.i.t.i.t.MI  continuously applied (to object)  K a r i ' s conception  r , SIZE  SOURCE  • • i  ". '. ! . . 1 . . I  •• i  decreasing  • • 1  o f t h e dynamics of u n i f o r m motion appears t o  p r o v i d e some a d d i t i o n a l i n f o r m a t i o n c o n c e r n i n g h e r p r e v i o u s  p o s i t i o n on  the causes of d e c e l e r a t i o n ( a t l e a s t as a p p l i e d t o t h e b a s e b a l l problem) and which c o u l d be a p p l i e d t o t h e composite frame f o r d e c e l e r a t i o n t h a t was a p p l i e d t o t h e b a s e b a l l problem ( s e e F i g u r e 16). conception  This  of d e c e l e r a t i o n i n v o l v e d a ' t r a n s f e r r e d f o r c e ' that operated  i n t h e same d i r e c t i o n as t h e motion of t h e o b j e c t  ( s e e l i n e s 25 t o 27,  p. 53; l i n e s 108 t o 111, p. 56; and l i n e 120, p. 5 7 ) . What was u n c l e a r as f a r as t h i s c o n c e p t i o n the  of d e c e l e r a t i o n was concerned was t h e s i z e of  ' t r a n s f e r r e d f o r c e ' , as such, t h e d e f a u l t v a l u e f o r t h i s concept  was l e f t b l a n k .  Both of t h e s e c o n c e p t i o n s f o r d i f f e r e n t t y p e s of  m o t i o n i n v o l v e t h e a p p l i c a t i o n o f some form of m o t i v e f o r c e , however, K a r i has d e f i n e d t h e s i z e of t h e f o r c e r e s p o n s i b l e f o r u n i f o r m motion. The  s i z e of t h i s f o r c e i s continuously  decreasing.  This suggests t h a t ,  i f K a r i i s making a d i s t i n c t i o n between d e c e l e r a t i o n and u n i f o r m  90  m o t i o n , t h e d e f a u l t v a l u e f o r the s i z e of the ' t r a n s f e r r e d f o r c e ' s h o u l d most p r o b a b l y be c o n s t a n t . F o l l o w i n g t h e d e m o n s t r a t i o n of t h e e f f e c t of b a l a n c e d f o r c e s on a moving equipment t r o l l e y , the t h r e e s t u d e n t s ( H e i n z y , S t e v e , and  Kari;  see l i n e s 64 t o 80, p. 64) p o l l e d f o r the d e s c r i p t i o n of t h e type of r e s u l t a n t motion a l l agreed t h a t the t r o l l e y had uniform motion.  exhibited  T h i s agreement tends t o i n d i c a t e t h a t t h e s e s t u d e n t s ,  a t l e a s t , were e i t h e r i n i n i t i a l  agreement w i t h Brad's  interpretational  frame f o r u n i f o r m motion o r ( c e r t a i n l y i n K a r i ' s case) were moving towards agreement w i t h t h i s  frame.  T h i s was not t h e case f o r o t h e r s t u d e n t s i n t h e c l a s s however. Tawnia's and K i r s t e n ' s comments (see l i n e s 81 t o 94, p. 65) i n d i c a t e a c e r t a i n amount of i n t e r n a l c o n f u s i o n on t h e i r p a r t .  Tawnia's comments  appear t o be an attempt t o o b t a i n a w a r r a n t , from the t e a c h e r , t o v a l i d a t e what she has seen i n t h e p r e c e d i n g d e m o n s t r a t i o n and i n t e r p r e t a t i o n of u n i f o r m motion.  Brad's  Tawnia (and p r o b a b l y K i r s t e n )  appears t o r e q u i r e t h a t warrant b e f o r e she i s w i l l i n g t o r e l i n q u i s h h e r i n t e r p r e t a t i o n a l frame of u n i f o r m motion  (which i s a p p a r e n t l y s i m i l a r  t o K a r i ' s ; see l i n e 53, p. 63) and a c c e p t Brad's.  When t h i s warrant i s  not f o r t h c o m i n g b o t h Tawnia and K i r s t e n i m p l i c i t l y d e c l a r e themselves i n f a v o u r of K a r i ' s o r i g i n a l i n t e r p r e t a t i o n a l frame of u n i f o r m motion when they ask t h e q u e s t i o n 'why  doesn't the o b j e c t s t o p when b a l a n c e d  forces are a p p l i e d to i t ? ' The a i r - t r a c k d e m o n s t r a t i o n , which was  i n p l a c e t o confront those  s t u d e n t s t h a t were u s i n g some form of a 'motion i m p l i e s a f o r c e ' i n t e r p r e t a t i o n a l frame t o e x p l a i n u n i f o r m m o t i o n , produced results.  Without f a i l , a l l s t u d e n t s who  mixed  took p a r t i n the d i s c u s s i o n of  t h i s d e m o n s t r a t i o n agreed t h a t t h e r i d e r t r a v e l l e d w i t h a u n i f o r m 91  motion.  T h i s p o i n t , however, was t h e o n l y p o i n t t h a t c o u l d be agreed  upon as t h i s d e m o n s t r a t i o n appeared t o s p l i t t h e s t u d e n t s i n t o a t l e a s t two groups.  One group appeared t o i n t e r p r e t t h i s d e m o n s t r a t i o n u s i n g a  form of Impetus Theory whereas, t h e o t h e r group opted t o e x p l a i n u n i f o r m m o t i o n u s i n g an expanded v e r s i o n o f Brad's o r i g i n a l i n t e r p r e t a t i o n a l frame ( o r v a r i a n t s of t h a t f r a m e ) . The  group o f s t u d e n t s t h a t appeared t o be u s i n g a form of Impetus  Theory t o e x p l a i n u n i f o r m motion i n c l u d e d M e l a n i e , For a l l three of these students, c a r r i e d an i n h e r e n t  force.  K e l l y , and Tawnia.  t h e a i r - t r a c k r i d e r moved because i t  T h i s f o r c e has been t r a n s f e r r e d t o t h e  r i d e r when i t was g i v e n an i n i t i a l push ( s e e l i n e s 128 t o 141, pp. 71 and  72; l i n e s 147 t o 160, pp. 72 and 73; and l i n e s 182 and 183,  P. 7 3 ) . A l t h o u g h a l l t h r e e o f t h e s e s t u d e n t s appear t o be u s i n g constructed  similarly  i n t e r p r e t a t i o n a l frames f o r t h e i r a n a l y s i s of u n i f o r m  m o t i o n ( a s e x h i b i t e d by t h e a i r - t r a c k r i d e r ) t h e r e a r e d i f f e r e n c e s i n the d e f a u l t v a l u e s the frame.  that are being a p p l i e d t o s p e c i f i c concepts w i t h i n  M e l a n i e ' s frame, w h i c h i s assumed t o r e p r e s e n t  the basic  s t r u c t u r e used by t h e s e s t u d e n t s ( s e e F i g u r e 1 9 ) , i n c l u d e s a d e f a u l t value f o r the t r a n s f e r r e d force that i n d i c a t e s that i t i s c o n t i n u a l l y decreasing.  K e l l y ' s frame, on t h e o t h e r hand would i n c l u d e a d e f a u l t  v a l u e f o r t h e s i z e o f t h e t r a n s f e r r e d f o r c e t h a t would d e s c r i b e f o r c e as r e m a i n i n g c o n s t a n t .  this  Tawnia's frame, as w e l l , would have t h e  same b a s i c d e s i g n as M e l a n i e ' s frame but t h e d e f a u l t v a l u e f o r t h e s i z e of t h e t r a n s f e r r e d f o r c e i s unknown.  The o n l y i n f o r m a t i o n t h a t Tawnia  has s u p p l i e d c o n c e r n i n g t h i s d e f a u l t v a l u e i s t h a t " t h e n e t f o r c e i s g o i n g t h e same way as t h e d i r e c t i o n " ( s e e l i n e s 182 and 183, p. 7 3 ) . Such a s i t u a t i o n i n v o l v i n g t h e a i r - t r a c k r i d e r c o u l d be a c h i e v e d u s i n g 92  Figure 19. Melanie's Uhifom Notion Frane  an i n c r e a s i n g , d e c r e a s i n g ,  or constant  v a l u e f o r t h e s i z e of t h e t r a n s -  ferred force. B r a d , K a r i , and t o a l e s s e r degree, H e i n z y made up t h e group t h a t appeared t o i n t e r p r e t i n g t h e motion of t h e a i r - t r a c k r i d e r u s i n g an expanded v e r s i o n of Brad's o r i g i n a l frame f o r u n i f o r m m o t i o n .  In this  c a s e , Brad has extended h i s i n t e r p r e t a t i o n a l frame, t h a t was based on b a l a n c e d f o r c e s , t o i n c l u d e t h e a l t e r n a t i v e o p t i o n t h a t u n i f o r m motion can be t h e r e s u l t a n t of t h e complete absence of f o r c e s ( s e e l i n e s 144 and  145,  p. 72).  By d o i n g s o h i s i n t e r p r e t a t i o n a l frame of u n i f o r m  motion now r e p r e s e n t s  the general  Newtonian p o s i t i o n t h a t t h i s type o f  m o t i o n ( f o r an i n i t i a l l y moving o b j e c t ) i s t h e r e s u l t of any f o r c e c o n d i t i o n s t h a t r e s u l t i n a n u l l n e t f o r c e (see F i g u r e 2 0 ) . K a r i has a l s o r e c o g n i z e d  t h a t , f o r t h i s demonstration of uniform  m o t i o n , t h e r e a r e no m o t i v e f o r c e s a c t i n g on t h e r i d e r and t h a t t h e n e t f o r c e c o n d i t i o n must be z e r o (see l i n e s 199 t o 203, p. 74). 93  As a  Figure 29. Brad's Expanded Frane for Uniforn Notion  air-track rider  ABSENCE OF FORCES  APPLIED (to object) FORCES  r e s u l t , she appears t o be i n complete agreement tional  frame f o r u n i f o r m motion and, a p p a r e n t l y ,  previous a force'  w i t h Brad's i n t e r p r e t a has abandoned h e r  frame (see F i g u r e 18) t h a t was based upon t h e 'motion i m p l i e s conception.  H e i n z y appears t o have adopted a compromise p o s i t i o n t h a t M e l a n i e ' s 'motion i m p l i e s a f o r c e ' c o n c e p t i o n  w i t h Brad's  melds  Newtonian  p o s i t i o n t h a t u n i f o r m motion i s a r e s u l t of a n u l l n e t f o r c e c o n d i t i o n .  94  H e i n z y f e e l s t h a t t h e r e i s a f o r c e a s s o c i a t e d w i t h t h e i n i t i a l movement of t h e a i r - t r a c k r i d e r (which, by i n f e r e n c e , must be a ' t r a n s f e r r e d f o r c e ' ) but t h a t f o r c e q u i c k l y f a l l s o f f t o z e r o . f e r r e d f o r c e ' has reduced t o zero he r e c o g n i z e s  Once t h e ' t r a n s -  t h a t t h e r e i s no l o n g e r  any f o r c e w h i c h might a c c e l e r a t e t h e r i d e r , n o r a r e t h e r e any opposing f o r c e s which would d e c e l e r a t e  t h e r i d e r ( s e e l i n e s 165 t o 173, p. 7 3 ) .  Thus, t h e r i d e r must be t r a v e l l i n g w i t h a u n i f o r m motion as a r e s u l t of a n u l l net force condition.  T h i s form of an i n t e r p r e t a t i o n a l frame f o r  u n i f o r m m o t i o n i s shown i n F i g u r e 21.  Figure 21. Heinzy's Frane for Uhiforn Notion  .• • .•..' r * \:::::: fTTTTTTT: * I::  air-track rider  science deno  NECCSSARVCOHDITIOH  roving  OPPOSINS FORCES :0  TRANSFERRED (to object) FORCE CHARACTERISTICS  SOURCE  DURATION  iCZDI  decreases to 8  95  Instructional Strategy Effects on Student Interpretational Frames of Motion The determination of the effects that the instructional strategy had on the i n i t i a l conceptions that students were using to explain the dynamics of specific types of motion has been accomplished by comparing their i n i t i a l interpretational frameworks with those that were constructed after the instructional sequence had been completed.  Any  effects that have occurred as a result of the instructional strategy can then be recognized as transformations  to the type and/or sequencing  of concepts within the interpretational framework or to the default values for specific concepts. Acceleration The predominant concept concerning acceleration that became apparent during the i n i t i a l discussions was that a continually increasing force was required to accelerate a moving object.  This concept  represents the core of Kelly's interpretational frame for the acceleration of a moving object (see Figure 11) and was reiterated by the majority of students taking part in these discussions. Following the demonstrations and their attendant discussions, this concept had appeared to be dramatically altered, in a majority of students, to correspond with the minimum Newtonian requirement for acceleration i.e. that a moving body can be accelerated by the application of a constant force in the direction of that body's motion.  As  has already been noted however, the demonstrations that were used involved the acceleration of an i n i t i a l l y stationary object and, as such, what these students were describing were their conditions necessary for the acceleration of this type of object.  This set of  conditions had previously been described by Kelly (see Figure 10) and, 96  i f i t i s assumed t h a t t h i s i n t e r p r e t a t i o n a l frame was a composite frame for  t h e m a j o r i t y of t h e c l a s s , then t h i s frame s h o u l d  nor d i d i t .  T h i s frame i n c o r p o r a t e s  not have changed;  t h e minimum Newtonian c o n d i t i o n s  n e c e s s a r y f o r t h e a c c e l e r a t i o n of a s t a t i o n a r y body and s h o u l d not have changed f o l l o w i n g t h e d e m o n s t r a t i o n s because t h e s e were d e s i g n e d t o i l l u s t r a t e these c o n d i t i o n s . Because t h e r e were no d e m o n s t r a t i o n s p r e s e n t e d t o t h e s e s t u d e n t s t h a t might have i l l u s t r a t e d t h e minimum Newtonian c o n d i t i o n s f o r t h e a c c e l e r a t i o n of an a l r e a d y moving body, i t i s i m p o s s i b l e 'before  and a f t e r ' comparison of t h e s t u d e n t s '  initial  t o make any  conception  that  a c o n t i n u a l l y i n c r e a s i n g f o r c e i s t h e minimum requirement f o r t h e a c c e l e r a t i o n of a moving o b j e c t . Deceleration The i n i t i a l pointed  d i s c u s s i o n s c o n c e r n i n g t h e causes of dynamics p i n -  two c o n f l i c t i n g i n t e r p r e t a t i o n a l frames among t h e s t u d e n t s .  One frame, o u t l i n e d by K e l l y ( s e e F i g u r e 1 3 ) , i l l u s t r a t e s t h e Newtonian p o s i t i o n t h a t d e c e l e r a t i o n i s t h e r e s u l t of t h e n e t f o r c e ( i n d i c a t e d by the d e f a u l t v a l u e f o r t h e 'comparison' c o n c e p t ) on a moving o b j e c t a c t i n g i n t h e o p p o s i t e d i r e c t i o n t o t h e motion of t h e o b j e c t .  The  o t h e r frame, o u t l i n e d by J i m ( s e e F i g u r e 1 4 ) , adopts a 'motion i m p l i e s a f o r c e ' c o n c e p t u a l i z a t i o n of d e c e l e r a t i o n . decelerates  I n t h i s c a s e , an o b j e c t  because i t ' s m o t i v e f o r c e i s d e c r e a s i n g  i n size.  The n e t  f o r c e ( a g a i n i n d i c a t e d by t h e d e f a u l t v a l u e f o r t h e 'comparison' concept),  however, c o n t i n u e s  t o a c t i n t h e d i r e c t i o n of t h e o b j e c t ' s  motion. To b e g i n w i t h , b o t h of t h e s e i n t e r p r e t a t i o n a l frames found supporters w i t h i n the c l a s s .  F o l l o w i n g t h e d e m o n s t r a t i o n s however,the  m a j o r i t y of s t u d e n t s appeared t o agree w i t h K e l l y ' s i n t e r p r e t a t i o n a l 97  framework f o r d e c e l e r a t i o n .  As s u c h , the i n s t r u c t i o n a l  appeared t o have the d e s i r e d e f f e c t of c o n v i n c i n g Newtonian frame f o r d e c e l e r a t i o n was model of the two  frames i n i t i a l l y  strategy  the s t u d e n t s t h a t  the more p o w e r f u l  interpretational  recognized.  I t s h o u l d be n o t e d a t t h i s p o i n t t h a t the i n s t r u c t i o n a l was  the  strategy  not e n t i r e l y s u c c e s s f u l i n t h a t i t f a i l e d t o c o n v i n c e Jim t h a t  he  s h o u l d move away from h i s 'motion i m p l i e s a f o r c e ' i n t e r p r e t a t i o n a l frame.  As a r e s u l t of the s t r a t e g y , Jim d i d make m o d i f i c a t i o n s t o h i s  frame i n t h a t he d i d agree t h a t a net f o r c e a c t i n g i n the  opposite  d i r e c t i o n t o an o b j e c t ' s m o t i o n would cause d e c e l e r a t i o n .  However, he  a l s o f e l t t h a t the d e c e l e r a t i o n would u l t i m a t e l y s t o p and would c o n t i n u e 19, p.  the  object  t o move f o r w a r d s w i t h a u n i f o r m motion (see l i n e s 8 t o  49).  The  b a s e b a l l problem, however, has p o i n t e d out the l i m i t a t i o n s of  the i n s t r u c t i o n a l s t r a t e g y .  A l l the d e m o n s t r a t i o n s i n t h i s  instruc-  t i o n a l sequence i n v o l v e d the a p p l i c a t i o n of a m o t i v e f o r c e t o object.  an  As a r e s u l t , the i n t e r p r e t a t i o n a l frames t h a t were g e n e r a t e d  by t h e s e d e m o n s t r a t i o n s always i n v o l v e d some form of a p p l i e d f o r c e t o the o b j e c t .  The  m o t i v e f o r c e and  b a s e b a l l problem, however, d i d not i n v o l v e any  i t soon became apparent d u r i n g the d i s c u s s i o n of  problem t h a t a m a j o r i t y of s t u d e n t s i n t h i s c l a s s were i n c a p a b l e imagining  m o t i o n w i t h o u t some form of m o t i v e f o r c e .  n e c e s s a r y t o i n v e n t a ' t r a n s f e r r e d f o r c e ' t h a t was m o t i o n of the b a l l and  this of  Thus they f e l t i t r e s p o n s i b l e f o r the  incorporate t h i s invention into t h e i r  p r e t a t i o n a l frame t h a t d e s c r i b e d the b a l l .  form of  inter-  the dynamics of the d e c e l e r a t i o n of  Because t h e r e were no d e m o n s t r a t i o n s i n v o l v e d i n t h i s  i n s t r u c t i o n a l sequence t h a t would e x p l i c i t l y c o n f r o n t  the c o n c e p t i o n  ' t r a n s f e r r e d f o r c e ' , i t i s not p o s s i b l e t o d e t e r m i n e whether the 98  of  i n s t r u c t i o n a l s t r a t e g y might have had any e f f e c t on t h i s t y p e of interpretational  frame.  Uniform Motion The i n i t i a l d i s c u s s i o n s c o n c e r n i n g t h e dynamics of u n i f o r m motion uncovered two i n t e r p r e t a t i o n a l frames t h a t were b e i n g used t o d e s c r i b e t h i s t y p e of m o t i o n .  Brad's frame ( s e e F i g u r e 17) d e s c r i b e s t h e  Newtonian c o n c e p t i o n t h a t u n i f o r m motion i s t h e r e s u l t of t h e a p p l i c a t i o n of b a l a n c e d f o r c e s t o an a l r e a d y moving o b j e c t .  K a r i ' s frame,  however, appears t o based on elements of t h e 'motion i m p l i e s a f o r c e ' conception.  I n t h i s c a s e , K a r i appears t o b e l i e v e t h a t a c c e l e r a t i o n of  a moving o b j e c t i s caused by t h e a p p l i c a t i o n of a c o n t i n u a l l y  increas-  i n g f o r c e , t h a t d e c e l e r a t i o n of an o b j e c t i s a c h i e v e d by a p p l y i n g a c o n s t a n t f o r c e t o t h a t o b j e c t which i s s m a l l e r than t h e t o t a l of any o p p o s i n g f o r c e s , and t h a t u n i f o r m m o t i o n i s t h e r e s u l t of t h e a p p l i c a t i o n of a d e c r e a s i n g f o r c e t o a moving  object.  F o l l o w i n g t h e f i r s t d e m o n s t r a t i o n i n v o l v i n g t h e equipment  trolley  K a r i ' s i n t e r p r e t a t i o n of t h e dynamics of u n i f o r m motion appears t o have changed.  She e x p l i c i t l y agrees t h a t t h e a p p l i c a t i o n of b a l a n c e d f o r c e s  t o t h e moving equipment t r o l l e y has r e s u l t e d i n t h e t r o l l e y  travelling  w i t h a u n i f o r m m o t i o n ( s e e l i n e 80, p. 6 4 ) . As s u c h , she now appears t o be i n agreement  w i t h Brad's o r i g i n a l i n t e r p r e t a t i o n a l frame and has  moved away from h e r own 'motion i m p l i e s a f o r c e ' based frame. Such was n o t t h e case w i t h o t h e r s t u d e n t s i n t h e c l a s s  however.  Tawnia's and K i r s t e n ' s comments ( s e e l i n e s 81 t o 94, p. 65) suggest t h a t , a l t h o u g h t h i s d e m o n s t r a t i o n has p r o b a b l y r a i s e d doubts c o n c e r n i n g t h e i r own p e r s o n a l , i n t e r p r e t a t i o n a l frames f o r u n i f o r m m o t i o n , i t c e r t a i n l y hasn't t r a n s f o r m e d t h e s e frames i n t o ones t h a t i n c o r p o r a t e Newtonian c o n c e p t i o n s of u n i f o r m m o t i o n . 99  T h i s l a c k of t r a n s f o r m a t i o n  becomes even c l e a r e r f o l l o w i n g the a i r - t r a c k d e m o n s t r a t i o n when Tawnia a l i g n s h e r s e l f w i t h the ' t r a n s f e r r e d f o r c e  1  i n t e r p r e t a t i o n a l frame (see  F i g u r e 19) t h a t has been t e n a c i o u s l y defended by M e l a n i e and K e l l y . The a i r - t r a c k d e m o n s t r a t i o n and the d i s c u s s i o n s r e s u l t i n g from i t have p r o v i d e d Brad w i t h an o p p o r t u n i t y t o extend h i s o r i g i n a l , Newtoni a n - b a s e d frame i n t o one t h a t now  represents a t r u l y ,  generalizable  frame f o r u n i f o r m m o t i o n t h a t i s d e f i n i t e l y based on Newtonian p l e s (see F i g u r e 20).  princi-  In a d d i t i o n , t h i s p a r t of t h e i n s t r u c t i o n a l  sequence appears t o have c o n f i r m e d , f o r K a r i , the v a l i d i t y of Brad's i n t e r p r e t a t i o n a l frame.  Her f i n a l  comments (see l i n e s 202 and  p. 74) suggest t h a t she has c o m p l e t e l y abandoned her o r i g i n a l  203, interpre-  t a t i o n a l frame based upon the 'motion i m p l i e s a f o r c e ' c o n c e p t i o n and w h o l e h e a r t e d l y a c c e p t e d t h e d e s c r i p t i o n of u n i f o r m m o t i o n p r o v i d e d by Brad's i n t e r p r e t a t i o n a l  frame.  A l t h o u g h t h e i n s t r u c t i o n a l sequence appeared t o b r i n g about a s u c c e s s f u l t r a n s f o r m a t i o n of K a r i ' s o r i g i n a l , i n t e r p r e t a t i o n a l for  frame  u n i f o r m m o t i o n , t h e same cannot be s a i d f o r H e i n z y ' s i n t e r p r e t a -  t i o n a l frame.  H e i n z y ' s frame (see F i g u r e 21) appears t o s t a k e out the  m i d d l e ground between M e l a n i e ' s and Brad's i n t e r p r e t a t i o n a l frames by i n c o r p o r a t i n g elements of b o t h of t h e s e frames. p r i o r i n t e r p r e t a t i o n a l frame ( o r v e r b a l agreement  Due t o a l a c k of a with a prior  frame)  t h a t c o u l d be used f o r comparison p u r p o s e s , i t i s i m p o s s i b l e t o d e t e r m i n e whether t h i s 'middle ground' frame r e p r e s e n t s a t r a n s i t i o n a l or  f i n a l p o s i t i o n f o r Heinzy.  100  A Summary A n a l y s i s o f t h e M a j o r , Student I n t e r p r e t a t i o n a l Frameworks o f M o t i o n What has become i n c r e a s i n g l y c l e a r from t h e p r e c e d i n g  analysis i s  t h a t many s t u d e n t s i n t h i s c l a s s f i n d i t e x t r e m e l y d i f f i c u l t any  t o imagine  type o f o b j e c t m o t i o n t h a t i s not caused by some form of a p p l i e d  f o r c e operating i n the d i r e c t i o n of motion.  F o r a l a r g e number of  t h e s e s t u d e n t s a c c e l e r a t i o n of an a l r e a d y moving o b j e c t i s a c h i e v e d by a p p l y i n g a m o t i v e f o r c e which c o n t i n u a l l y i n c r e a s e s i n s i z e whereas, the a c c e l e r a t i o n of a s t a t i o n a r y o b j e c t r e q u i r e s o n l y t h e a p p l i c a t i o n of a c o n s t a n t , m o t i v e f o r c e .  Many o f t h e s e same s t u d e n t s a l s o  felt  t h a t d e c e l e r a t i o n o f an o b j e c t c o u l d o c c u r i f , and o n l y i f , t h e a p p l i e d , m o t i v e f o r c e was l e s s than t h e t o t a l magnitude of t h e f o r c e s opposing t h e o b j e c t m o t i o n .  At f i r s t g l a n c e ,  t h i s conception  appears  t o m i r r o r t h e Newtonian c o n d i t i o n f o r d e c e l e r a t i o n which r e q u i r e s the n e t f o r c e on a moving o b j e c t o p e r a t e i n t h e o p p o s i t e the m o t i o n of t h e o b j e c t .  d i r e c t i o n to  T h i s c o n d i t i o n , however, was u n a c c e p t a b l e t o  t h e s e s t u d e n t s when a motion event o c c u r r e d motive f o r c e .  that  t h a t d i s p l a y e d no e x p l i c i t  I n t h i s t y p e o f s i t u a t i o n t h e s e s t u d e n t s found i t  n e c e s s a r y t o i n v e n t an a p p l i e d , m o t i v e f o r c e t h a t had been t r a n s f e r r e d t o t h e moving o b j e c t from some e x t e r i o r s o u r c e .  F i n a l l y , f o r uniform  m o t i o n of an o b j e c t t o o c c u r t h e s e s t u d e n t s f e l t t h a t some form o f a p p l i e d , m o t i v e f o r c e was r e q u i r e d , and one s t u d e n t suggested t h a t i t would have t o be d e c r e a s i n g  i n size.  As was t h e case w i t h  deceler-  a t i o n , i f an a p p l i e d f o r c e was n o t e x p l i c i t l y p r e s e n t when an o b j e c t was t r a v e l l i n g w i t h u n i f o r m m o t i o n , t h e s e s t u d e n t s f e l t i t n e c e s s a r y t o i n v e n t a ' t r a n s f e r r e d f o r c e ' t o account f o r t h e m o t i o n of t h e o b j e c t . The  i n c o r p o r a t i o n of t h e s e c o n c e p t i o n s o f m o t i o n i n t o a gener-  a l i z e d , i n t e r p r e t a t i o n a l framework o f m o t i o n has been a c c o m p l i s h e d by 101  re-ordering the sequence of frames and sub-frames described in the preceding analysis so that they can be connected by 'isa' links.  This  interpretational framework is shown in Figure 22.  Figure 22. An Interpretational Franewrk of Notion Based Upon the 'Notion Inplies a Force' Conception / V  (RESULT OF) > APPLIED FORCE CONDITIONS J  isa  ( I  isa  ( ACCELERATION Y  OBJECT (HOTION)  isa  isa  ( DECELERATION j  (  UNIFORM  \  \  HOTIOH  J  In this framework, the lower levels include frames for the specific types of motion.  Although i t has not been investigated within  this research, i t is conjectured that these frames would contain data that would allow the user to determine which of the three types of motion is being exhibited by the object in question.  The middle level  of this framework is assumed to be a junction point which provides additional pathways to frames that provide specific information about 102  the o b j e c t i n q u e s t i o n .  These frames would c o n t a i n i n f o r m a t i o n  the type of o b j e c t , i t ' s i n i t i a l i t can s u p p l y  about  s t a t e ( s t a t i o n a r y or moving), whether  an i n t e r n a l m o t i v e f o r c e o r whether i t r e q u i r e s an  e x t e r n a l f o r c e f o r m o t i o n , and so on.  The upper l e v e l , a g a i n can be  viewed as a j u n c t i o n p o i n t t h a t , a l l o w s c o n n e c t i o n s t o be made w i t h t h e s p e c i f i c a p p l i e d , m o t i v e f o r c e frames depending upon what type of motion i s b e i n g e x h i b i t e d by t h e o b j e c t .  Data w i t h i n t h e s e frames  would i n c l u d e s u c h items as t h e s i z e and d u r a t i o n of t h e a p p l i e d f o r c e , whether o r not t h e s o u r c e of t h i s f o r c e i s i n t e r n a l t o t h e o b j e c t or e x t e r n a l , and whether or not an a p p l i e d f o r c e has been c o n v e r t e d i n t o a transferred force. For comparison purposes a p o s s i b l e Newtonian i n t e r p r e t a t i o n a l framework i s shown i n F i g u r e 23.  A l l l e v e l s of t h i s framework would  operate i n a s i m i l a r fashion t o t h e i r counterparts i n t e r p r e t a t i o n a l framework.  i n the previous  The upper l e v e l , however, would a l l o w  a c c e s s t o frames d e s c r i b i n g t h e net f o r c e c o n d i t i o n s r e q u i r e d f o r s p e c i f i c motion types.  F o r example, t h e r e c o g n i t i o n t h a t an o b j e c t  was  a c c e l e r a t i n g would a l l o w a c c e s s t o a frame t h a t d e t a i l e d t h a t a p o s i t i v e ( i n t h e d i r e c t i o n of motion) net f o r c e c o n d i t i o n was and how t h a t n e t f o r c e was a c h i e v e d . recognized  a negative  Similarly, i f deceleration  On o n l y two o c c a s i o n s  a n u l l n e t f o r c e frame would  were segments of t h i s type of  Newtonian, i n t e r p r e t a t i o n a l framework u t i l i z e d by s t u d e n t s . occasion  occurred  was  ( o p p o s i n g o b j e c t motion) n e t f o r c e frame would be  a c c e s s e d ; i f u n i f o r m m o t i o n was r e c o g n i z e d be a c c e s s e d .  required  The  first  d u r i n g t h e d i s c u s s i o n of t h e b a s e b a l l problem when  Brad appeared t o be u s i n g Newtonian p r i n c i p l e s t o a n a l y z e t h e f o r c e s operating  on the b a l l and a p p l y t h i s t o d e c e l e r a t i n g m o t i o n (see l i n e s  57 t o 59, p. 5 4 ) .  The second o c c a s i o n  occurred  103  during the d i s c u s s i o n  Figure 23. A Newtonian Interpretational Franewrk  f V  (RESULT OF) \ e FORCE CONDITIONS J , isa  { I  isa  ^ ACCELERATION J  OBJECT (NOTION)  ^ J  isa  isa  ( DECELERATION J  f V  UNIFORM \ NOTION J  of u n i f o r m motion when b o t h Brad and K a r i u t i l i z e d  t h e concept of n u l l ,  net f o r c e t o e x p l a i n t h e u n i f o r m m o t i o n of t h e a i r - t r a c k r i d e r .  104  CHAPTER FIVE  C o n c l u s i o n s , D i s c u s s i o n of R e s u l t s , and  Recommendations  Conclusions The g e n e r a l problem of t h i s r e s e a r c h has been t o d e s i g n an i n s t r u c t i o n a l model t h a t would e x p l i c a t e s t u d e n t s ' c o n c e p t i o n s of dynamics and, i f n e c e s s a r y , t r a n s f o r m these c o n c e p t i o n s i n t o ones t h a t more c l o s e l y a p p r o x i m a t e Newtonian c o n c e p t i o n s of dynamics. w i t h i n t h i s g e n e r a l problem were t h r e e , s p e c i f i c problems.  Included The  first  problem was t h e d e s i g n of an i n s t r u c t i o n a l s t r a t e g y t h a t would i l l u m i n a t e t h e c o n c e p t i o n s b e i n g employed by s t u d e n t s t o e x p l a i n t h e m o t i o n of o b j e c t s and b r i n g about any r e q u i r e d t r a n s f o r m a t i o n s .  The second  problem was t h e development of an a n a l y t i c a l c l u e s t r u c t u r e , based upon a theoretical  p e r s p e c t i v e p r o v i d e d by Frame Theory, which c o u l d be used  t o d e s c r i b e t h e c o n c e p t u a l s t r u c t u r e s employed by s t u d e n t s t o e x p l a i n o b j e c t m o t i o n and w h i c h would s e r v e as a t r a c k i n g mechanism  f o r any  c o n c e p t u a l t r a n s f o r m a t i o n i n i t i a t e d by t h e i n s t r u c t i o n a l s t r a t e g y . F i n a l l y , t h e t h i r d problem was t h e i m p l e m e n t a t i o n  of t h e i n s t r u c t i o n a l  model, w i t h i n an o p e r a t i o n a l c l a s s r o o m , i n o r d e r t o d e t e r m i n e the model's a b i l i t y t o e x p l i c a t e s t u d e n t c o n c e p t i o n s of dynamics and t r a n s f o r m these c o n c e p t i o n s where r e q u i r e d . each of t h e s e problems w i l l  Conclusions  be d i s c u s s e d i n d i v i d u a l l y .  concerning However,  because t h e c o n c l u s i o n s c o n c e r n i n g the f i r s t two problems a r e d i r e c t l y related  t o t h e e f f i c a c y of t h e i n s t r u c t i o n a l model d u r i n g t h e implemen-  t a t i o n phase of t h i s r e s e a r c h , t h e c o n c l u s i o n s r e g a r d i n g the implement a t i o n of t h e i n s t r u c t i o n a l model w i l l  be d i s c u s s e d f i r s t .  105  Conclusions  C o n c e r n i n g the A b i l i t y of the I n s t r u c t i o n a l Model  to E x p l i c a t e Students' The  Concepts of Dynamics  e x p l i c a t i o n of s t u d e n t  binary process  conceptions  of dynamics u s i n g  of concept i l l u m i n a t i o n ( v i a a c o m b i n a t i o n  mapping and c l a s s d i s c u s s i o n t e c h n i q u e s )  the  of concept  and r e c o n s t r u c t i o n of  these  c o n c e p t s i n t o frames and frameworks (by employing the c l u e s t r u c t u r e a n a l y s i s ) must be c o n s i d e r e d process  the f o l l o w i n g s t u d e n t  t o be a s u c c e s s . conceptions  As a r e s u l t of  this  of dynamics have been  identified: 1.  A c c e l e r a t i o n of a s t a t i o n a r y o b j e c t i s the r e s u l t of  a p p l i c a t i o n of a c o n s t a n t 2.  f o r c e t o t h a t o b j e c t (see F i g u r e  the  10).  A c c e l e r a t i o n of a moving o b j e c t i s the r e s u l t of the  appli-  c a t i o n of a c o n t i n u a l l y , i n c r e a s i n g f o r c e t o t h a t o b j e c t i n the d i r e c t i o n of m o t i o n of t h a t o b j e c t (see F i g u r e 3.  11).  D e c e l e r a t i o n of an o b j e c t i s the r e s u l t of an imbalance  between any a p p l i e d , m o t i v e f o r c e s and any o t h e r f o r c e s t h a t oppose the motion of the o b j e c t .  T h i s imbalance i s such t h a t the t o t a l of  the  opposing f o r c e s a r e g r e a t e r than the t o t a l of the a p p l i e d , m o t i v e f o r c e s (see F i g u r e 4.  15).  D e c e l e r a t i o n of an o b j e c t i s the r e s u l t of a p p l i e d , m o t i v e  f o r c e s which a r e d e c r e a s i n g i n magnitude, but which a r e l a r g e r than the t o t a l of any 5.  14).  U n i f o r m motion of an o b j e c t i s the r e s u l t of the a p p l i c a t i o n  of b a l a n c e d 6.  f o r c e s opposing the m o t i o n (see F i g u r e  f o r c e s t o t h a t o b j e c t (see F i g u r e  19).  U n i f o r m m o t i o n of an o b j e c t i s the r e s u l t of the a p p l i c a t i o n  of a c o n t i n u o u s l y , d e c r e a s i n g , m o t i v e f o r c e t o t h a t o b j e c t (see F i g u r e 18).  106  7.  U n i f o r m m o t i o n of an o b j e c t i s the r e s u l t of the a p p l i c a t i o n  of a m o t i v e f o r c e t o an o b j e c t t h a t d e c r e a s e s t o z e r o (see F i g u r e 8.  An a p p l i e d , m o t i v e f o r c e must always be p r e s e n t  d e c e l e r a t i n g and u n i f o r m m o t i o n .  21).  during  I f no a p p l i e d f o r c e can be  recognized  i t i s because the o r i g i n a l , a p p l i e d f o r c e has been t r a n s f e r r e d t o moving o b j e c t .  This  ' t r a n s f e r r e d f o r c e ' i s then r e s p o n s i b l e f o r the  m o t i o n i n a p a r t i c u l a r d i r e c t i o n (see F i g u r e s 16 and W i t h the e x c e p t i o n prevalent, underlying objects.  the  19).  of p o i n t 5, a l l of t h e s e c o n c e p t i o n s i n d i c a t e a  theme f o r s t u d e n t s '  explanations  of the m o t i o n of  T h i s theme i s t h a t a l l motion i n a p a r t i c u l a r d i r e c t i o n , be  i t a c c e l e r a t i o n , d e c e l e r a t i o n , or u n i f o r m m o t i o n , i s the r e s u l t of some type of m o t i v e f o r c e .  T h i s f o r c e can e i t h e r be d i r e c t l y a p p l i e d t o  the  o b j e c t or t r a n s f e r r e d t o the o b j e c t by some o t h e r moving o b j e c t . Conclusions  C o n c e r n i n g the A b i l i t y of the I n s t r u c t i o n a l Model  t o T r a n s f o r m Student C o n c e p t i o n s of Dynamics The  transformation  of s t u d e n t c o n c e p t i o n s of dynamics, t h a t were  e i t h e r p a r t i a l l y or t o t a l l y at odds w i t h Newtonian c o n c e p t i o n s of dynamics, was discordant  t o o c c u r as a r e s u l t of the p r e s e n t a t i o n of (assumed)  e v e n t s t h a t c o u l d not be s a t i s f a c t o r i l y e x p l a i n e d  these student conceptions. marginally The  using  T h i s t e c h n i q u e can o n l y be viewed as  being  successful.  i n i t i a l d i s c u s s i o n s of the causes of a c c e l e r a t i o n had  sug-  g e s t e d t h a t , f o r the m a j o r i t y of s t u d e n t s t a k i n g p a r t i n t h i s d i s c u s s i o n , a c c e l e r a t i o n occurred b e i n g a p p l i e d t o an o b j e c t .  because a c o n t i n u o u s l y  was  In a d d i t i o n , a number of s t u d e n t s a l s o  s u g g e s t e d t h a t the a p p l i c a t i o n of a c o n s t a n t  f o r c e t o an o b j e c t would  r e s u l t i n that object t r a v e l l i n g w i t h a constant confront  increasing force  t h e s e c o n c e p t i o n s and  transform 107  velocity.  In o r d e r  them i n t o ones more c l o s e l y  to  a p p r o x i m a t i n g the Newtonian view of a c c e l e r a t i o n , the s t u d e n t s were p r e s e n t e d w i t h two uniformly  d e m o n s t r a t i o n s i n which s t a t i o n a r y o b j e c t s  accelerated  by the a p p l i c a t i o n of a c o n s t a n t f o r c e .  r e s u l t of t h i s p r e s e n t a t i o n , was  were  apparently  f o r the m a j o r i t y  of  The students,  i n c o r p o r a t i o n of t h i s concept ( a c c e l e r a t i o n r e s u l t s from the  a p p l i c a t i o n of a c o n s t a n t f o r c e ) i n t o t h e s e s t u d e n t s '  c o n c e p t u a l frame  f o r a c c e l e r a t i o n as the n e c e s s a r y c o n d i t i o n f o r the a c c e l e r a t i o n of i n i t i a l l y stationary object.  T h i s c o n c e p t i o n then c o e x i s t e d w i t h  an  the  p r e v i o u s c o n c e p t i o n ( a c c e l e r a t i o n i s a r e s u l t of the a p p l i c a t i o n of a continuously  i n c r e a s i n g f o r c e ) which then assumed the r o l e of  n e c e s s a r y c o n d i t i o n f o r the a c c e l e r a t i o n of a moving o b j e c t Figures  10 and  11).  the (see  Thus, i n t h i s i n s t a n c e , the p r e s e n t a t i o n  were assumed t o be d i s c o r d a n t  of what  events r e s u l t e d i n the i n c o r p o r a t i o n of a  d e s i r e d c o n c e p t i o n i n t o an a l r e a d y  e x i s t i n g and u n d e s i r a b l e  of a c c e l e r a t i o n , r a t h e r than the t r a n s f o r m a t i o n  framework  of the p r e - e x i s t i n g  framework. I t must be n o t e d h e r e t h a t , a t some p o i n t i n s t r u c t i o n a l sequence, a t r a n s f o r m a t i o n  towards the d e s i r e d Newtonian,  c o n c e p t u a l frame f o r a c c e l e r a t i o n d i d o c c u r . of the concept map  ( o r p o i n t s ) i n the  D u r i n g the  f o r a c c e l e r a t i o n and d e c e l e r a t i o n  construction  (see F i g u r e  8)  p r i o r t o t h e d i s c u s s i o n of u n i f o r m m o t i o n , a s t u d e n t consensus had a r r i v e d a t t h a t now  viewed the minimum r e q u i r e m e n t s f o r a c c e l e r a t i o n of  e i t h e r a s t a t i o n a r y or moving o b j e c t t o be one a p p l i c a t i o n of a c o n s t a n t f o r c e .  and  the same - the  J u s t e x a c t l y where and  i n s t r u c t i o n a l sequence t h i s t r a n s f o r m a t i o n for conjecture.  been  why  within  the  o c c u r r e d can o n l y be a t o p i c  What i s known i s t h a t t h i s t r a n s f o r m a t i o n  did  not  o c c u r as a d i r e c t r e s u l t of the a c c e l e r a t i o n d e m o n s t r a t i o n s t h a t were p r e s e n t e d t o the  students. 108  The  initial  student d i s c u s s i o n s concerning  the causes of d e c e l e r -  a t i o n of an o b j e c t suggested t h a t the m a j o r i t y of s t u d e n t s a c o n c e p t i o n of d e c e l e r a t i o n ( d e c e l e r a t i o n i s the r e s u l t of  already  had  the  a p p l i e d , m o t i v e f o r c e s b e i n g l e s s than the t o t a l of the f o r c e s opposing the motion) t h a t was, conception  a t l e a s t , p a r t i a l l y congruent w i t h the Newtonian  of d e c e l e r a t i o n ( d e c e l e r a t i o n i s the r e s u l t of a  net f o r c e o p e r a t i n g on a moving o b j e c t ) .  Only two s t u d e n t s  negative suggested  t h a t the cause of d e c e l e r a t i o n c o u l d be o t h e r w i s e .  For these  d e c e l e r a t i o n was  decreasing i n s i z e  caused by a m o t i v e f o r c e which was  but always remained g r e a t e r than the t o t a l of any m o t i o n (see F i g u r e  c o n f r o n t and t r a n s f o r m any  ation.  In b o t h d e m o n s t r a t i o n s ,  t o the s t u d e n t s i n o r d e r  non-Newtonian c o n c e p t i o n s an o b j e c t was  minimum, Newtonian c o n d i t i o n , a c o n s t a n t d i r e c t i o n t o the o b j e c t ' s m o t i o n . was  f o r c e s opposing the  14).  A g a i n , two d e m o n s t r a t i o n s were p r e s e n t e d to  students  The  of d e c e l e r -  decelerated using  f o r c e a p p l i e d i n the  the  opposite  r e s u l t of these d e m o n s t r a t i o n s  o n l y a p a r t i a l t r a n s f o r m a t i o n of the non-Newtonian c o n c e p t i o n  d e c e l e r a t i o n d e s c r i b e d above. t h i s cause f o r d e c e l e r a t i o n now when a c o n s t a n t  f o r c e was  The  s t u d e n t who  of  had o r i g i n a l l y s u g g e s t e d  agreed t h a t d e c e l e r a t i o n d i d r e s u l t  a p p l i e d t o an o b j e c t i n the o p p o s i t e  direc-  t i o n t o the m o t i o n of the o b j e c t , but he a l s o suggested t h a t the d e c e l e r a t i o n of the o b j e c t would degrade i n t o u n i f o r m m o t i o n . The  i n i t i a l d i s c u s s i o n s of the dynamics of u n i f o r m m o t i o n i l l u m i n -  a t e d one non-Newtonian c o n c e p t i o n  of u n i f o r m m o t i o n .  h e l d , as i t ' s c e n t r a l t e n e t , t h a t u n i f o r m motion was  This  conception  the r e s u l t of  a p p l i c a t i o n of a d e c r e a s i n g , m o t i v e f o r c e t o an o b j e c t (see F i g u r e Two  d e m o n s t r a t i o n s were p r e s e n t e d  t o the s t u d e n t s  c o u n t e r t h i s c o n c e p t i o n , but t h e s e met  18).  i n an attempt t o  w i t h o n l y minimal s u c c e s s .  109  the  Only  one s t u d e n t ( K a r i ) i n d i c a t e d t h a t she now  f e l t t h a t u n i f o r m motion  t h e r e s u l t of b a l a n c e d f o r c e s or a n u l l net f o r c e . s t u d e n t s who  was  For the o t h e r  h e l d t h i s i n i t i a l , non-Newtonian c o n c e p t i o n , t h e demon-  s t r a t i o n s were u n c o n v i n c i n g and no t r a n s f o r m a t i o n s of t h e i r  conceptions  of u n i f o r m motion were apparent. In summary, the attempt  t o t r a n s f o r m s t u d e n t c o n c e p t i o n s of  u s i n g , what were assumed t o be, d i s c o r d a n t , m o t i o n events cannot c o n s i d e r e d t o have been s u c c e s s f u l . u n i f o r m motion) was  In o n l y one case  motion be  (involving  t h e r e a s u c c e s s f u l t r a n s f o r m a t i o n of non-Newtonian  c o n c e p t i o n s i n t o Newtonian c o n c e p t i o n s .  In a l l o t h e r i n s t a n c e s , the  attempts a t t r a n s f o r m a t i o n r e s u l t e d i n e i t h e r i n c o r p o r a t i o n of Newtoni a n concepts i n t o a non-Newtonian c o n c e p t u a l s t r u c t u r e (as was f o l l o w i n g the a c c e l e r a t i o n d e m o n s t r a t i o n s ) , o r a m i n i m a l , t r a n s f o r m a t i o n towards Newtonian concepts  (as was  the case  partial following  t h e d e c e l e r a t i o n d e m o n s t r a t i o n s ) , o r no change of t h e o r i g i n a l t i o n s c o n c e r n i n g a p a r t i c u l a r type of motion t h e u n i f o r m motion  (as was  the case  the case  concepfollowing  demonstrations).  Conclusions Concerning  the Design of the  Instructional Strategy The o r i g i n a l d e s i g n of the i n s t r u c t i o n a l s t r a t e g y can o n l y be c o n s i d e r e d t o be f l a w e d i n b o t h of i t ' s major The use of s t u d e n t - p r o d u c e d  elements.  concept maps as a b a s i s f o r d e l i n e -  a t i n g major s t u d e n t concepts of dynamics, and r e c o g n i z i n g any  altera-  t i o n s t o t h e s e concepts as t h e l e s s o n sequence p r o g r e s s e d , produced of the c l a s s r o o m t e a c h e r s ' worst nightmares  one  - an immense amount of  s t u d e n t p r o d u c t s t h a t had t o be a n a l y z e d and a s s e s s e d b e f o r e t h e next lesson could occur.  As a r e s u l t of t h i s s i t u a t i o n , the o r i g i n a l ,  d e s i g n i n t e n t of t h e s e concept maps s h i f t e d t o become a b a s i s f o r t h e 110  c o n s t r u c t i o n o f c o l l e c t i v e l y - p r o d u c e d concept maps.  The p r o c e s s of  n e g o t i a t i o n and compromise t h a t was r e q u i r e d t o produce t h e s e  collec-  t i v e concept maps o f i n d i v i d u a l f o r c e / m o t i o n events u l t i m a t e l y l e d t o a l o s s of d e t a i l and r i c h n e s s of c o n c e p t u a l u n d e r s t a n d i n g t h a t c o u l d be found i n i n d i v i d u a l l y - p r o d u c e d concept maps.  C e r t a i n l y , the c o l l e c t -  i v e l y - p r o d u c e d concept maps were s u c c e s s f u l i n o u t l i n i n g conceptions of force/motion events. t h e s e maps w i t h t e a c h e r - p r o d u c e d ,  student  I n a d d i t i o n , j u x t a p o s i t i o n of  Newtonian maps of t h e same events was  a b l e t o produce v a r i e d and i n t e r e s t i n g debate c o n c e r n i n g t h e m e r i t s of each map.  However, as a r e s u l t of t h e u n w i e l d y and time-consuming  n a t u r e o f t h e s e concept maps, they were downgraded from t h e i r  original  p o s i t i o n w i t h i n t h e d e s i g n of t h e i n s t r u c t i o n a l s t r a t e g y and r e p l a c e d by a d i r e c t c l u e s t r u c t u r e a n a l y s i s o f s t u d e n t d i s c u s s i o n s of force/motion events. As has a l r e a d y been mentioned, t h e use of what were assumed t o be d i s c o r d a n t , f o r c e / m o t i o n events t o i n i t i a t e t r a n s f o r m a t i o n s of s t u d e n t c o n c e p t i o n s o f t h e s e events t o c o n c e p t i o n s more c l o s e l y a l i g n e d w i t h Newtonian c o n c e p t i o n s of t h e same events met w i t h o n l y minimal  success.  Whether t h i s was because t h e s t u d e n t s d i d n o t r e c o g n i z e t h e s e events as b e i n g t r u l y d i s c o r d a n t , o r because t h e s t u d e n t c o n c e p t i o n s a r e ext r e m e l y r o b u s t and t h e s t u d e n t s a r e l o a t h t o r e l i n q u i s h a s e t of c o n c e p t i o n s t h a t have s e r v e d them s u c c e s s f u l i n t h e p a s t a r e s u b j e c t s for conjecture. C o n c l u s i o n s C o n c e r n i n g t h e Development o f t h e A n a l y t i c a l Clue S t r u c t u r e The use o f Frame Theory as a t h e o r e t i c a l p e r s p e c t i v e f o r t h e development of t h e a n a l y t i c a l c l u e s t r u c t u r e has been e x t r e m e l y successful.  As has a l r e a d y been mentioned, t h e c l u e s t r u c t u r e supIll  p l a n t e d concept mapping as t h e a n a l y t i c a l l e n s of c h o i c e f o r the e x p l i c a t i o n of s t u d e n t c o n c e p t i o n s of f o r c e / m o t i o n events and  tracking  of any changes i n t h e s e c o n c e p t i o n s as t h e l e s s o n sequence p r o g r e s s e d . The use of t h i s c l u e s t r u c t u r e has a l l o w e d the placement of s t u d e n t concepts of f o r c e / m o t i o n events w i t h i n r e a s o n a b l y c o h e s i v e frame s t r u c t u r e s t h a t have proven t o be v i s u a l l y easy t o i n t e r p r e t and have a l l o w e d comparisons  t o be made between c o n c e p t u a l s t r u c t u r e s , used by  d i f f e r e n t s t u d e n t s , t o i n t e r p r e t the same f o r c e / m o t i o n event. t i o n a l l y , t h e s e c o n c e p t u a l frame s t r u c t u r e s have proven t o be  Addisensitive  enough t o a l l o w t r a c k i n g of c o n c e p t u a l change, w i t h i n i n d i v i d u a l s t u d e n t s , t h a t might have o c c u r r e d as a r e s u l t of t h e a p p l i c a t i o n of the i n s t r u c t i o n a l s t r a t e g y . Summary C o n c l u s i o n s C o n c e r n i n g t h e E f f i c a c y of the I n s t r u c t i o n a l Model The i n s t r u c t i o n a l model has proven t o be s u c c e s s f u l i n t h e e x p l i c a t i o n of s t u d e n t c o n c e p t i o n s of dynamics.  T h i s model  has  i n d i c a t e d t h a t , f o r a m a j o r i t y of s t u d e n t s t a k i n g an a c t i v e p a r t i n t h e l e s s o n s , any motion was  viewed as b e i n g the r e s u l t of the a p p l i c a t i o n  of some t y p e of m o t i v e f o r c e .  T h i s e x p l i c a t i o n of s t u d e n t  d i d not occur as a r e s u l t of the o r i g i n a l l y i n t e n d e d use of  conceptions concept  mapping t e c h n i q u e s which proved t o be t o o cumbersome t o be used w i t h i n the c l a s s r o o m environment.  R a t h e r , t h e s u c c e s s f u l e x p l i c a t i o n of  s t u d e n t c o n c e p t i o n s of dynamics was  a c h i e v e d by t h e a p p l i c a t i o n of an  a n a l y t i c a l c l u e s t r u c t u r e , based on Frame Theory, t o t r a n s c r i p t i o n s of s t u d e n t d i s c u s s i o n s of s p e c i f i c f o r c e / m o t i o n events and  problems.  The i n s t r u c t i o n a l model has proven t o be o n l y m i n i m a l l y s u c c e s s f u l i n t r a n s f o r m i n g non-Newtonian, s t u d e n t c o n c e p t i o n s of dynamics i n t o c o n c e p t i o n s t h a t more c l o s e l y approximate  112  Newtonian p r i n c i p l e s of  dynamics.  Attempts a t u s i n g , what were assumed t o be, d i s c o r d a n t  events t o a c c o m p l i s h these t r a n s f o r m a t i o n s have r e s u l t e d i n t h e i n c o r p o r a t i o n o f Newtonian concepts  i n t o non-Newtonian c o n c e p t u a l  frames w i t h o n l y v e r y l i t t l e m o d i f i c a t i o n t o t h e o r i g i n a l , frame, o r v e r y l i t t l e o r no m o d i f i c a t i o n t o t h e o r i g i n a l , frame b e i n g employed by t h e s t u d e n t ( s ) .  conceptual conceptual  I n o n l y one i n s t a n c e , was a  major t r a n s f o r m a t i o n of an o r i g i n a l , s t u d e n t , c o n c e p t u a l frame t o a Newtonian, c o n c e p t u a l  frame r e c o g n i z e d .  The reasons  f o r the l a c k of  s u c c e s s o f t h i s p a r t of t h e i n s t r u c t i o n a l model cannot be  determined  from t h e a v a i l a b l e d a t a and can o n l y be c o n s i d e r e d as s u b j e c t s f o r conjecture.  A D i s c u s s i o n of t h e R e s u l t s The A l t e r n a t e Framework of Dynamics I t has come as no g r e a t s u r p r i s e t o f i n d t h a t t h e 'motion i m p l i e s a f o r c e ' s e t o f c o n c e p t i o n s and i t s c o r o l l a r y Impetus Theory have appeared as t h e c o n c e p t u a l s t r u c t u r e of c h o i c e f o r t h e i n t e r p r e t a t i o n of f o r c e / m o t i o n events by t h e m a j o r i t y o f s t u d e n t s w i t h i n t h i s Numerous o t h e r s t u d i e s t h a t have attempted  class.  to delineate students'  c o n c e p t i o n s o f dynamics have a l s o determined  that t h i s  conceptual  s t r u c t u r e was p r e s e n t , e i t h e r i n whole o r i n p a r t , i n t h e groups of s t u d e n t s t h a t they were i n v e s t i g a t i n g .  As a r e s u l t of t h e prepon-  derance of e v i d e n c e t h a t i n d i c a t e s t h a t t h i s c o n c e p t u a l s t r u c t u r e i s not c o n f i n e d to.any s i n g l e , d e f i n a b l e group o f s t u d e n t s , t h i s s e t o f r e l a t e d c o n c e p t i o n s must be c o n s i d e r e d t o be a form o f ' c o n v e n t i o n a l wisdom' dynamics t h a t has been a r r i v e d a t by u s i n g a 'common  sense'  approach t o e x p l a i n and p r e d i c t t h e m o t i o n of o b j e c t s t h a t a r e so much a p a r t of our everyday  lives.  .113  T h i s 'common sense' approach t o t h e e x p l a n a t i o n o f moving o b j e c t s does not i g n o r e f r i c t i o n n o r does i t a b s t r a c t f r i c t i o n i n t o a form of f o r c e , i t s i m p l y a c c e p t s t h a t f r i c t i o n i s always p r e s e n t and must be dealt with.  H e r e i n l i e s t h e major p o i n t of c o n t e n t i o n between t h e  ' c o n v e n t i o n a l wisdom' dynamics and Newtonian dynamics and one o f t h e p r o b a b l e reasons why t h e 'motion i m p l i e s a f o r c e  1  conceptual s t r u c t u r e  i s so r o b u s t and r e s i s t a n t t o change. The power of Newtonian dynamics stems from i t ' s a b i l i t y t o o e x p l a i n and p r e d i c t t h e m o t i o n o f o b j e c t s w i t h i n b o t h f r i c t i o n - f i l l e d and f r i c t i o n l e s s environments.  I n o r d e r t o r e a c h t h i s s t a t e , however,  Newtonian dynamics t r e a t s f r i c t i o n as a form of a b s t r a c t f o r c e i t opposes m o t i o n .  F o r many i n d i v i d u a l s , however, who have o n l y  w i t h i n a f r i c t i o n - f i l l e d environment and who have d i f f i c u l t y of  because lived  conceiving  a f r i c t i o n l e s s environment, f r i c t i o n i s not a form of f o r c e , but  r a t h e r an impediment  t o motion t h a t can o n l y be overcome by t h e  a p p l i c a t i o n of c o n c r e t e f o r c e s such as pushes and p u l l s .  Thus, motion  becomes i n t i m a t e l y connected t o t h e a p p l i c a t i o n of m o t i v e f o r c e s and e x p e r i e n t i a l l y r e i n f o r c e d by day-to-day l i v i n g on t h e s u r f a c e of t h e Earth.  As a r e s u l t , an e x t r e m e l y c o h e s i v e and p a r s i m o n i o u s ( f o r t h e  s u r f a c e o f t h e E a r t h ) c o n c e p t u a l framework  e v o l v e s around t h e c e n t r a l  t e n e t t h a t , any t i m e an o b j e c t moves i t i s because of t h e a p p l i c a t i o n of  these concrete f o r c e s . The c o h e s i v e n e s s and i n t e r n a l c o n s i s t e n c y o f t h i s c o n c e p t u a l  framework  f o r motion can be seen i n t h e e x p l a n a t i o n s t h a t have been  g i v e n , by t h e s t u d e n t s , f o r t h e causes of t h e v a r i o u s t y p e s o f m o t i o n . 1.  A c c e l e r a t i o n of a moving o b j e c t i s caused by t h e a p p l i c a t i o n  of a c o n t i n u a l l y , i n c r e a s i n g f o r c e i n t h e same d i r e c t i o n as t h e motion of  the object. 114  2.  Acceleration of a stationary object (which is apparently a  different situation than acceleration of a moving object) i s caused by the application of a constant force. 3.  Deceleration of a moving object i s caused by the application  of a constant force in the opposite direction to the motion of the object. 4.  Uniform motion is caused by the application of a continually,  decreasing force in the direction in the direction of the object's motion. Thus, a l l types of motion have their own specific, applied force cause and no cause overlaps with any other cause.  This compartmentalization  of types of motion and their causes ensures that any possible areas of tension within this framework of motion are reduced and the integrity of the framework is maintained. In those cases where no definable force can be located as the cause of some object motion i t becomes necessary to invent some form of pseudo-force ( the 'transferred force ) that is directly related to 1  some previously applied, motive force and incorporate this into the existing framework.  In this fashion the integrity and u t i l i t y of the  existing framework is maintained and the individual is not faced with the disconcerting realization that this conceptual  framework of the  dynamics of moving objects could be incorrect and might require, at the very least, a complete restructuring or, at the very worst, a complete replacement of the existing framework with one that i s new and untried. This latter option is one that few individuals would choose for i t would result i n a period of extreme confusion while the individual sought new causes of the motion of objects and then attempted to  115  c o n s t r u c t t h e s e new causes i n t o a c o m f o r t a b l e and w o r k a b l e framework of dynamics. The  consternation  and c o n f u s i o n  t h a t would r e s u l t from t h e  r e s t r u c t u r i n g and/or replacement of an e x i s t i n g , e x p e r i e n t i a l l y - b a s e d framework p r o b a b l y a c c o u n t s f o r t h e i n a b i l i t y of t h e i n s t r u c t i o n a l s t r a t e g y t o b r i n g about s i g n i f i c a n t t r a n s f o r m a t i o n s i m p l i e s a f o r c e ' conceptual class. provided  i n t h e 'motion  framework t h a t was so p r e v a l e n t  i n this  As an example, i n those cases where t h e i n s t r u c t i o n a l s t r a t e g y discordant  events t h a t s u g g e s t e d t h a t m o t i o n c o u l d  occur  w i t h o u t t h e a p p l i c a t i o n of a m o t i v e f o r c e (as was t h e case w i t h t h e b a s e b a l l problem and t h e a i r - t r a c k d e m o n s t r a t i o n ) t h e m a j o r i t y of s t u d e n t s might have f e l t t h a t i t was p r e f e r a b l e t o opt f o r t h e t r a n s l a t i o n o f t h e n e c e s s a r y ( t o account f o r t h e m o t i o n ) a p p l i e d f o r c e t o a ' t r a n s f e r r e d f o r c e ' r a t h e r than c a l l work i n t o q u e s t i o n s u c h an a c t i o n .  t h e i r e x i s t i n g conceptual  frame-  and a c c e p t t h e consequences t h a t would accompany  I t i s a l s o p o s s i b l e t h a t these s t u d e n t s had a l r e a d y  f a c e d s i t u a t i o n s where o b j e c t s moved w i t h o u t any d e f i n a b l e , m o t i v e f o r c e and had a l r e a d y made t h e n e c e s s a r y adjustments t o t h e i r conceptu a l frameworks t o account f o r t h e s e .  I f t h i s was t h e c a s e , what were  i n i t i a l l y assumed (by t h e r e s e a r c h e r )  t o be d i s c o r d a n t  events were, i n  f a c t , n o t viewed a t a l l (by t h e s t u d e n t s ) t o be d i s c o r d a n t t h e i r conceptual  framework a l r e a d y c o n t a i n e d  ' t r a n s f e r r e d f o r c e ' ) f o r t h i s type of m o t i o n . the i n t e g r i t y of t h e e x i s t i n g c o n c e p t u a l paramount i m p o r t a n c e . w i l l most l i k e l y f a l l  because  an e x p l a n a t i o n ( t h e Thus, t h e p r o t e c t i o n of  framework of dynamics i s of  Any changes t h a t might be made t o t h i s framework i n t o t h e c a t e g o r y of minor m o d i f i c a t i o n s o r  i n c o r p o r a t i o n s t h a t do n o t c a l l i n t o q u e s t i o n  the v a l i d i t y of the  c e n t r a l t e n e t o f t h i s framework - motion i m p l i e s a f o r c e . 116  Major  t r a n s f o r m a t i o n s t o t h i s c o n c e p t u a l framework of dynamics w i l l not o c c u r as l o n g as t h e r i s k s a s s o c i a t e d w i t h r e t a i n i n g t h i s  experientially-  based framework a r e l e s s than t h e r i s k s a s s o c i a t e d w i t h r e p l a c i n g i t w i t h a new and u n t r i e d framework of dynamics. The Elements  o f t h e I n s t r u c t i o n a l Model  The use of t h e t e s t i n g form of t h e t e a c h i n g experiment  as t h e  b a s i s f o r d e t e r m i n i n g t h e e f f i c a c y o f t h e elements of t h e i n s t r u c t i o n a l model has i n d i c a t e d t h a t o n l y t h e a n a l y t i c a l c l u e s t r u c t u r e (and t h e subsequent  r e p r e s e n t a t i o n of s t u d e n t c o n c e p t i o n s of dynamics as frames  and frameworks) can be c o n s i d e r e d t o have been a s u c c e s s i n i t ' s o r i g i n a l form.  The o t h e r element i n t h e i n s t r u c t i o n a l model, t h e  i n s t r u c t i o n a l s t r a t e g y , has undergone s u b s t a n t i a l m o d i f i c a t i o n d u r i n g t h e r e s e a r c h p r o c e s s i n response t o e n v i r o n m e n t a l f a c t o r s w i t h i n t h e classroom. O r i g i n a l l y , t h a t p a r t of t h e i n s t r u c t i o n a l s t r a t e g y t h a t was t o be used f o r t h e e x p l i c a t i o n of s t u d e n t c o n c e p t i o n s of dynamics was t o r e l y h e a v i l y on t h e use o f s t u d e n t - p r o d u c e d concept maps t o p r o v i d e t h e raw data f o r the c l u e s t r u c t u r e a n a l y s i s .  A d d i t i o n a l l y , i t was hoped t h a t  t h e s e concept maps would p r o v i d e an immediate,  c l a s s r o o m window on t o  the type o f concepts and t h e r e l a t i o n s h i p s between t h e s e concepts t h a t s t u d e n t s were u s i n g t o e x p l a i n f o r c e and motion e v e n t s .  T h i s was n o t  t o be t h e case however, as n e i t h e r o f t h e s e two i n t e n t i o n s were a b l e t o be s u c c e s s f u l l y implemented w i t h i n t h e c l a s s r o o m . As has a l r e a d y been mentioned,  t h e attempted i m p l e m e n t a t i o n of  concept mapping t e c h n i q u e t o s p e c i f i c f o r c e and motion events as a method o f p r o v i d i n g an i n i t i a l events produced  e x p l i c a t i o n of s t u d e n t concepts of these  an immense amount of d a t a .  So much s o , t h a t t h e  r e s e a r c h e r found i t i m p o s s i b l e t o a n a l y z e and c o l l a t e t h e s e d a t a f o r 117  s t u d e n t , concept p a t t e r n s and/or concept s h i f t s ( r e s u l t i n g  from  d i s c o r d a n t e v e n t s ) on a day-to-day  basis.  Because of t h i s problem, any  d i s c u s s i o n s c o n c e r n i n g comparisons  between s t u d e n t and Newtonian  c o n c e p t i o n s of t h e s e events had t o w a i t on t h e c o m p l e t i o n of t h e concept map a n a l y s e s and, as a r e s u l t , l e s s o n c o n t i n u i t y and f l o w was reduced. I n a d d i t i o n t o t h e d a t a p r o d u c t i o n and a n a l y s i s problem, a s i g n i f i c a n t number of s t u d e n t s w i t h i n t h e c l a s s were f i n d i n g i t v e r y difficult  (and time-consuming) t o c o n s t r u c t concept maps o f s p e c i f i c  f o r c e and motion e v e n t s .  T h i s d i f f i c u l t y d i d n o t stem from a l a c k o f  f a m i l i a r i t y w i t h concept mapping t e c h n i q u e s f o r t h e s e s t u d e n t s had been s u c c e s s f u l l y c o n s t r u c t i n g concept maps throughout  t h e s c h o o l year on  such d i v e r s e t o p i c s as c u r r e n t e l e c t r i c i t y , c h e m i c a l bonding, and c e l l u l a r reproduction.  R a t h e r , t h e r o o t of t h i s problem appeared t o  l i e w i t h i n t h e s p e c i f i c n a t u r e of t h e concepts and concept  relations  t h a t they had t o r e c o g n i z e i n o r d e r t o c o n s t r u c t a v a l i d map of t h e events t h a t were b e i n g demonstrated.  P r i o r t o t h e dynamics u n i t ,  s t u d e n t concept mapping had been d i r e c t e d a t g e n e r a l i z e d c o n c e p t u a l s t r u c t u r e s such as t h e comparison  and c o n t r a s t i n g o f i o n i c and c o v a l e n t  bonding, and a s e x u a l and s e x u a l c e l l u l a r r e p r o d u c t i o n .  However, w i t h  t h e i n t r o d u c t i o n o f t h e dynamics u n i t they were h a v i n g t o r e c o g n i z e and t e a s e a p a r t v e r y s p e c i f i c concepts c o n c e r n i n g t h e t y p e , s i z e , and d i r e c t i o n o f f o r c e s t h a t were r e s p o n s i b l e f o r t h e motion o f an o b j e c t o r , f o r t h a t m a t t e r , whether any f o r c e s were indeed r e s p o n s i b l e f o r t h e motion.  The d i f f i c u l t y t h a t t h e s e s t u d e n t s e x p e r i e n c e d w h i l e attempt-  i n g t o s i n k down t o t h i s l e v e l of s p e c i f i c i t y s u g g e s t s t h a t  concept  mapping t e c h n i q u e s may n o t be a p p l i c a b l e t o such i s o l a t e d events o r t h a t t h e a n a l y t i c c a p a b i l i t e s of t h e s e s t u d e n t s may n o t y e t be up t o 118  the t a s k o f r e c o g n i z i n g and a b s t r a c t i n g t h e s e t y p e s of s p e c i f i c concepts. Because o f t h e s e two problems w i t h s t u d e n t concept mapping, t h a t p a r t of t h e i n s t r u c t i o n a l s t r a t e g y t h a t d e a l t w i t h t h e e x p l i c a t i o n of s t u d e n t c o n c e p t i o n s o f dynamics was s u b s t a n t i a l l y m o d i f i e d . modification s t i l l  This  i n v o l v e d s t u d e n t concept mapping, however t h e s e maps  were now used as a c a t a l y s t t o i n i t i a t e t h e d i s c u s s i o n and c o n s t r u c t i o n of a c o l l e c t i v e l y - p r o d u c e d concept map f o r a s p e c i f i c type o f m o t i o n . These c o l l e c t i v e l y - p r o d u c e d concept maps were, i n t u r n , used t o provoke f u r t h e r c l a s s d i s c u s s i o n c o n c e r n i n g t h e d i f f e r e n c e s between s t u d e n t and Newtonian c o n c e p t i o n s o f m o t i o n , and t h e a b i l i t y of t h e s t u d e n t conceptual  s t r u c t u r e t o e x p l a i n t h e m o t i o n of o b j e c t s d i s p l a y e d  the d i s c o r d a n t  event d e m o n s t r a t i o n s .  during  The e x p l i c a t i o n and r e p r e s e n t a -  t i o n of t h e s t u d e n t c o n c e p t i o n s of s p e c i f i c types of motion was then a c h i e v e d by d i r e c t l y a p p l y i n g t h e a n a l y t i c a l c l u e s t r u c t u r e t o t h e class discussions.  Thus, by t h e end of t h e u n i t t h a t p a r t o f t h e  i n s t r u c t i o n a l s t r a t e g y that d e a l t w i t h the e x p l i c a t i o n of student c o n c e p t i o n s of motion had e v o l v e d of t a c t i c s t h a t 1.  i n t o a r e a s o n a b l y c o n s i s t e n t sequence  included:  a focus question  (e.g. What would cause t h i s o b j e c t t o  accelerate?). 2.  a d e m o n s t r a t i o n of t h e s p e c i f i c t y p e o f m o t i o n f o l l o w e d by a  c l a s s d i s c u s s i o n of t h e p o s s i b l e causes o f t h e o b j e c t m o t i o n . 3.  c o n s t r u c t i o n o f i n d i v i d u a l concept maps o f t h e c a u s e ( s ) of  the o b j e c t m o t i o n . 4.  c o n s t r u c t i o n of a c o n s e n s u a l , c o l l e c t i v e concept map based  upon d i s c u s s i o n and debate of t h e m e r i t s of i n d i v i d u a l concept maps.  119  5.  a comparison  of t h e elements of t h e c o l l e c t i v e concept  map  f o r a p a r t i c u l a r type of motion w i t h the elements of a Newtonian concept map  f o r t h a t same type of motion.  6.  d i s c o r d a n t event  demonstrations.  7.  a d i s c u s s i o n / d e b a t e of t h e c a u s e ( s ) of the p a r t i c u l a r  type d i s p l a y e d d u r i n g the d i s c o r d a n t event d e m o n s t r a t i o n .  motion  These  d i s c u s s i o n s f o c u s s e d upon t h e r e s p e c t i v e a b i l i t i e s of t h e s t u d e n t and Newtonian c o n c e p t u a l s t r u c t u r e s t o e x p l a i n the c a u s e ( s ) of the p a r t i c u l a r t y p e of motion. 8.  a p o s t hoc c l u e s t r u c t u r e a n a l y s i s of the c l a s s d i s c u s s i o n s  and debates t h a t r e s u l t e d i n the e x p l i c a t i o n of s t u d e n t c o n c e p t i o n s of p a r t i c u l a r t y p e s of motion as  frames.  A l t h o u g h t h i s t a c t i c a l sequence appeared  t o be a g r e e a b l e t o b o t h t h e  s t u d e n t s and r e s e a r c h e r , inasmuch as i t p r o v i d e d a s t i m u l a t i n g room environment,  class-  i t d i d not p r o v i d e the immediate window on t o s t u d e n t  c o n c e p t i o n s of dynamics t h a t had been hoped f o r .  R a t h e r the r e s e a r c h e r  had t o r e l y on a g u t - l e v e l f e e l i n g c o n c e r n i n g whether or not  any  p a r t i c u l a r c l a s s r o o m d i s c u s s i o n was p r o v i d i n g adequate c o n c e p t u a l d a t a t h a t c o u l d be used t o c o n s t r u c t a frame s t r u c t u r e u s i n g the p o s t hoc, clue structure analysis.  As a r e s u l t , t h e e f f e c t s of t h e i n s t r u c t i o n a l  s t r a t e g y on e x p l i c a t i n g s t u d e n t c o n c e p t i o n s of dynamics and  trans-  f o r m i n g t h e s e c o n c e p t i o n s c o u l d not be determined on a day-to-day except on a m a c r o s c o p i c  basis  level.  The o p e r a t i o n of t h i s m o d i f i e d i n s t r u c t i o n a l s t r a t e g y w i t h i n t h e c l a s s r o o m produced  few, i f any, c l a s s management problems.  Because of  t h e s t r a t e g y ' s heavy r e l i a n c e on s t u d e n t a n a l y s i s , d i s c u s s i o n and debate, s t u d e n t on-task t i m e , c o n c e n t r a t i o n and i n t e r e s t appeared  t o be  s i g n i f i c a n t l y h i g h e r than t h a t which would have been g e n e r a t e d by more 120  t r a n s m i s s i v e forms of t e a c h i n g . was  Additionally,  g r a t i f y i n g t o see t h a t these s t u d e n t s  for t h i s researcher, i t  were c a p a b l e of and  inter-  e s t e d i n g r a p p l i n g w i t h the i n t r i c a c i e s of t h e i r p h y s i c a l w o r l d and, e s s e n c e , t a k i n g a c e r t a i n amount of ownership i n t h e i r own  in  education.  Recommendations The  l a r g e number of r e s e a r c h s t u d i e s t h a t have i d e n t i f i e d  'motion i m p l i e s a f o r c e ' c o n c e p t u a l  s t r u c t u r e as the  the  interpretational  model of c h o i c e among t h e i r s u b j e c t s f o r d e a l i n g w i t h the dynamics of moving o b j e c t s s u g g e s t s t h a t f u r t h e r r e s e a r c h i n t o the e x p l i c a t i o n student  conceptions  of dynamics would be redundant.  As a r e s u l t  t h e s e s u c c e s s e s i n i d e n t i f y i n g t h i s major c o n c e p t i o n a l recommended t h a t any instructional framework.  of  of  framework, i t i s  f u t u r e r e s e a r c h be d i r e c t e d towards the d e s i g n  s t r a t e g i e s that w i l l  d i r e c t l y confront t h i s  conceptual  At t h i s p o i n t i t would appear t h a t t h i s r e s e a r c h  c o u l d f o l l o w two p o s s i b l e  of  direction  paths.  F i r s t , the d e s i g n of the f u t u r e i n s t r u c t i o n a l  strategy  could  assume the same s t a n c e as d i d t h i s r e s e a r c h and attempt t o r e p l a c e 'motion i m p l i e s a f o r c e ' c o n c e p t u a l  framework w i t h a new  framework t h a t i s based upon Newtonian p r i n c i p l e s  the  conceptual  of dynamics.  To  accomplish  t h i s r e p l a c e m e n t , however, i t would f i r s t be n e c e s s a r y t o  thoroughly  d i s c r e d i t the e x i s t i n g framework, p r o b a b l y  of d i s c o r d a n t event d e m o n s t r a t i o n s and, r e s e a r c h , t h i s i s not an easy t a s k .  t h r o u g h the  as has been i n d i c a t e d by  Thus, any  research  t e s t i n g of p r o t o t y p e ,  discordant  event d e m o n s t r a t i o n s i n o r d e r t o ensure t h a t they were, i n f a c t ,  121  this  r e s e a r c h t h a t wished t o  f o l l o w t h i s p a t h would have t o b e g i n w i t h an a d d i t i o n a l problem t h a t d e a l t w i t h the d e s i g n and  use  discordant  and had t h e c a p a c i t y t o d i s c r e d i t t h e 'motion i m p l i e s a  f o r c e ' framework. The  second r e s e a r c h p a t h t h a t c o u l d be f o l l o w e d i s a p u r e l y  pragmatic path.  T h i s p a t h would accept t h e premise t h a t , because  e x i s t i n g conceptual  the  framework i s e x p e r i e n t i a l l y based and has e x p l a n -  a t o r y and p r e d i c t i v e c a p a b i l i t i e s t h a t a r e c o n t i n u a l l y r e i n f o r c e d on a day-to-day b a s i s , replacement o f t h i s framework i s n o t p o s s i b l e .  As a  r e s u l t of t h i s p r e m i s e , t h e b e s t t h a t any i n s t r u c t i o n a l s t r a t e g y  could  do, over t h e s h o r t term, i s t h e c o n s t r u c t i o n o f an a d d i t i o n a l Newtonian framework o f m o t i o n t h a t would be d e d i c a t e d explanation  t o t h e i n t e r p r e t a t i o n and  of events that occur w i t h i n t h e school  environment and  which would c o e x i s t w i t h t h e 'motion i m p l i e s a f o r c e Indeed, i f s u c h a c o n s t r u c t i o n and c o e x i s t e n c e  1  framework.  were p o s s i b l e i t i s  d i s t i n c t l y p o s s i b l e t h a t , over t h e long term, s t u d e n t s would the explanatory  recognize  and p r e d i c t i v e power i n h e r e n t w i t h i n t h e Newtonian  framework of dynamics and b e g i n t o r e p l a c e t h e 'motion i m p l i e s a f o r c e ' framework w i t h t h e Newtonian framework i n t e r n a l l y . In a d d i t i o n , i t i s a l s o recommended t h a t as many s c i e n c e  teachers  as p o s s i b l e be made aware o f t h e s t r u c t u r e and c h a r a c t e r i s t i c s o f t h i s conceptual  framework t h a t t h e i r s t u d e n t s a r e b r i n g i n g w i t h them t o  t h e i r c l a s s r o o m s and t h a t l i n e s o f communication be opened between t h e s e t e a c h i n g p r o f e s s i o n a l s and e d u c a t i o n a l science teachers  aware o f t h i s c o n c e p t u a l  researchers.  framework and i t s a t t e n d a n t  problems, t h e number of p r o f e s s i o n a l s s e a r c h i n g problems w i l l be d r a m a t i c a l l y i n c r e a s e d . of d e s i g n i n g will  By making  f o r s o l u t i o n s t o these  Consequently, the p r o b a b i l i t y  an i n s t r u c t i o n a l s t r a t e g y t h a t i s ' c l a s s r o o m o p e r a t i o n a l '  a l s o be i n c r e a s e d .  t h e s e two groups s h o u l d  The opening of l i n e s o f communication between ensure t h a t any i n s t r u c t i o n a l s t r a t e g i e s 122  d e s i g n e d by t e a c h e r s and which appear t o be s u c c e s s f u l the  in  confronting  'motion i m p l i e s a f o r c e ' framework would be f u l l y documented  and  r e c e i v e the r i g o r o u s t e s t i n g r e q u i r e d by the academic community. F i n a l l y , the s u c c e s s f u l  representation  of the a l t e r n a t e framework  of dynamics u s i n g a c l u e s t r u c t u r e a n a l y s i s based on the t h e o r e t i c a l perspective  of frame t h e o r y s u g g e s t s t h a t t h i s form of a n a l y s i s  visual representation  s h o u l d have an e q u a l l y s u c c e s s f u l a p p l i c a t i o n i n  t h o s e a r e a s of the p h y s i c a l s c i e n c e s constructed  and  i n which s t u d e n t s appear t o have  o t h e r s p e c i f i c , a l t e r n a t e frameworks.  recommended t h a t a d d i t i o n a l r e s e a r c h  To t h i s end,  be conducted i n t o the  of u s i n g t h i s form of a n a l y s i s t o r e p r e s e n t s t u d e n t s ' n a t e frameworks i n the a r e a s of h e a t , l i g h t , and  123  i t is  feasibility  possible  electricity.  alter-  References A q u i r r e , Jose M. (1979). C h i l d r e n ' s b e l i e f s about f o r c e s i n e q u i l i brium. U n p u b l i s h e d master's t h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, Vancouver. Champagne, Audrey B., K l o p f e r , L e o p o l d E., & Anderson, John M. (1979). F a c t o r s i n f l u e n c i n g t h e l e a r n i n g of c l a s s i c a l mechanics. Univers i t y o f P i t t s b u r g h , L e a r n i n g Research and Development C e n t r e . Champagne, A.B., K l o p f e r , L.E., & Gunstone, R.F. (1982). C o g n i t i v e r e s e a r c h and t h e d e s i g n of s c i e n c e i n s t r u c t i o n . P r o c e e d i n g s of the I n t e r n a t i o n a l workshop on problems c o n c e r n i n g s t u d e n t s ' r e p r e s e n t a t i o n s of p h y s i c s and c h e m i s t r y knowledge. Ludwigsburg: Padagogische Hochschule, Ludwigsburg, 387-440. C l a x t o n , Guy. ( n . d . ) . School s c i e n c e : f a l l i n g on s t o n y ground o r choked by t h o r n s ? U n p u b l i s h e d m a n u s c r i p t , C e n t r e f o r S c i e n c e and Mathematics E d u c a t i o n , U n i v e r s i t y o f London, C h e l s e a C o l l e g e . Clement, John. (1977). Mapping a s t u d e n t s ' s c o n c e p t i o n s from a problem s o l v i n g p r o t o c o l . Amherst: U n i v e r s i t y o f M a s s a c h u s e t t s , Department o f P h y s i c s and Astronomy. Clement, John. mechanics.  (1981). S t u d e n t s ' p r e c o n c e p t i o n s i n i n t r o d u c t o r y American J o u r n a l o f P h y s i c s , 50(1)> 66-71.  d i S e s s a , Andrea. (1981). U n l e a r n i n g a r i s t o t e l i a n p h y s i c s : a s t u d y of knowledge-based l e a r n i n g . Cambridge: M a s s a c h u s e t t s I n s t i t u t e o f Technology, The D i v i s i o n f o r Study and Research i n E d u c a t i o n . D r i v e r , R o s a l i n d , & E a s l e y , J a c k . (1978). P u p i l s and paradigms: a r e v i e w o f l i t e r a t u r e r e l a t e d t o concept development i n a d o l e s c e n t s c i e n c e s t u d e n t s . S t u d i e s i n S c i e n c e E d u c a t i o n . 5, 61-84. D r i v e r , R o s a l i n d , & E r i c k s o n , Gaalen. (1983). Theories-in-action: some t h e o r e t i c a l and e m p i r i c a l i s s u e s i n t h e s t u d y of s t u d e n t s ' c o n c e p t u a l frameworks i n s c i e n c e . S t u d i e s i n S c i e n c e E d u c a t i o n , 10, 37-60. Fensham, P e t e r J . (1980). A r e s e a r c h base f o r new o b j e c t i v e s of s c i e n c e t e a c h i n g . Research i n S c i e n c e E d u c a t i o n , 10, 22-33. F l e s h n e r , E.A. (1970). P s y c h o l o g y o f t h e mastery and a p p l i c a t i o n by s c h o o l c h i l d r e n o f some concepts i n p h y s i c s . I n E. Stone ( E d . ) , Readings i n E d u c a t i o n a l P s y c h o l o g y , London: Methuen. G i l b e r t , John K., & Watts, D. M i c h a e l . (1983). Concepts, misconcept i o n s and a l t e r n a t e c o n c e p t i o n s : changing p e r s p e c t i v e s i n s c i e n c e e d u c a t i o n . S t u d i e s i n S c i e n c e E d u c a t i o n . 10. 61-98. Gowin, D. Bob. New York.  (1981).  Educating.  Cornell University Press, Ithaca,  124  Gunstone, R i c h a r d F., & White, R i c h a r d T. (1981). gravity. S c i e n c e E d u c a t i o n , 6 5 ( 3 ) , 291-299.  Understanding  of  Helm, H. (1978). M i s c o n c e p t i o n s about p h y s i c a l concepts among South A f r i c a n p u p i l s s t u d y i n g p h y s i c a l s c i e n c e . South A f r i c a n J o u r n a l of S c i e n c e , 74, 285-290. Kalmykova, Z.I. (1967). Methods of s c i e n t i f i c r e s e a r c h i n the p s y c h o l o g y of i n s t r u c t i o n . S o v i e t E d u c a t i o n , 8 ( 6 ) , 13-23. Kuhn, Kenneth C. (1979). C h i l d r e n ' s b e l i e f s about f r e e - f a l l motion. U n p u b l i s h e d master's t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver. K u i p e r s , Benjamin J . (1975). A frame f o r frames: r e p r e s e n t i n g knowledge f o r r e c o g n i t i o n . In D a n i e l G. Bobrow, & A l l a n C o l l i n s ( E d s . ) , R e p r e s e n t a t i o n and u n d e r s t a n d i n g , s t u d i e s i n c o g n i t i v e s c i e n c e (pp. 151-184). New York: Academic P r e s s . L e i t h , S y l v i a G. (1982, J u n e ) . Canadian and B r i t i s h c h i l d r e n ' s a c q u i s t i o n of concepts of motion. Paper p r e s e n t e d a t t h e Canadian S o c i e t y f o r the Study of E d u c a t i o n , Ottawa. L i n c o l n , Y. & Guba E. (1985). CA: Sage P u b l i c a t i o n s .  N a t u r a l i s t i c Inquiry.  M a n i c a s , P e t e r T., and S e c o r d , P a u l F. (1983, A p r i l ) . f o r p s y c h o l o g y of t h e new p h i l o s o p h y of s c i e n c e . P s y c h o l o g i s t , 399-413. McCloskey, M i c h a e l . (1983). 2 4 8 ( 4 ) , 122-130.  Intuitive physics.  Newbury P a r k , Implications American  Scientific  American,  McCloskey, M i c h a e l , Carmozza, A l f o n s o , & Green, B e r t . (1980). C u r v i l i n e a r motion i n t h e absence of e x t e r n a l f o r c e s : n a i v e b e l i e f s about t h e motion of o b j e c t s . S c i e n c e , 2 1 0 ( 5 ) , 1139-1141. M i n s k y , M a r v i n . (1975). A framework f o r r e p r e s e n t i n g knowledge. In P a t r i c k Henry Winston ( E d . ) , The p s y c h o l o g y of computer v i s i o n (pp. 211-277). New York: M c G r a w - H i l l . M i n s t r e l l , J i m . (1981). Conceptual u n d e r s t a n d i n g of p h y s i c s s t u d e n t s and i d e n t i f i c a t i o n of i n f l u e n c i n g f a c t o r s - e x p l a i n i n g the 'at r e s t ' c o n d i t i o n . Unpublished manuscript. M i n s t r e l l , James, ( n . d . ) . Teaching f o r the development of u n d e r s t a n d i n g of i d e a s : f o r c e s on moving o b j e c t s , mimeograph. R o b e r t s , Douglas A., & R u s s e l , Thomas L. (1975). An a l t e r n a t i v e approach t o s c i e n c e e d u c a t i o n r e s e a r c h : drawing from p h i l o s o p h i c a l a n a l y s i s t o examine p r a c t i c e . C u r r i c u l u m Theory Network, 5 ( 2 ) , 107-125.  125  S a l t i e l , E d i t h , & Malgrange, J . L . (1980). 'Spontaneous' ways of r e a s o n i n g i n elementary k i n e m a t i c s . European J o u r n a l o f P h y s i c s , 1, 73-80. S j o b e r g , S v i e n , & L i e S v i e n . (1981). Ideas about f o r c e and movement among Norwegian p u p i l s and s t u d e n t s (Report 81-11). U n i v e r s i t y of O s l o , The C e n t r e f o r School S c i e n c e . S t a k e , Robert E. (1978). The case s t u d y method i n s o c i a l E d u c a t i o n a l R e s e a r c h e r , 7, 5-8.  inquiry.  Trowbridge, D a v i d E., Lawson, Ronald A., & McDermott, L i l l i a n C. (1980, J a n u a r y ) . S t u d e n t s ' c o n c e p t i o n o f dynamics. Paper p r e s e n t e d t o t h e American A s s o c i a t i o n of P h y s i c s Teachers, Chicago. Trowbridge, D a v i d E., & McDermott, L i l l i a n C. (1980a). Investigation of s t u d e n t u n d e r s t a n d i n g of t h e concept o f v e l o c i t y i n one d i m e n s i o n . American J o u r n a l o f P h y s i c s , 4 8 ( 1 2 ) , , 1020-1028. Trowbridge, D a v i d E., & McDermott, L i l l i a n C. (1980b). Investigation of s t u d e n t u n d e r s t a n d i n g o f t h e concept o f a c c e l e r a t i o n i n one d i m e n s i o n . American J o u r n a l of P h y s i c s , 4 9 ( 3 ) , 242-253. Watts, D. M i c h a e l . (1982). G r a v i t y - don't t a k e i t f o r g r a n t e d ! P h y s i c s E d u c a t i o n , 1 7 ( 5 ) , 116-121. Watts, D.M. (1983). A s t u d y of s c h o o l c h i l d r e n ' s a l t e r n a t i v e frameworks o f t h e concept of f o r c e . European J o u r n a l of S c i e n c e E d u c a t i o n , 5 ( 2 ) , 217-230. W a t t s , D.M., & Z y l b e r s z t a j n , A. (1981). A s u r v e y o f some c h i l d r e n ' s i d e a s about f o r c e . P h y s i c s E d u c a t i o n , 16, 360-365. West, Leo H.T., P i n e s , Leon A., & S u t t o n , C l i v e R. (1982). In-depth i n v e s t i g a t i o n of l e a r n e r ' s understandings of s c i e n t i f i c concepts and t h e o r i e s . U n p u b l i s h e d m a n u s c r i p t . Winograd, T. (1975). Frame r e p r e s e n t a t i o n and t h e d e c l a r a t i v e p r o c e d u r a l c o n t r o v e r s y . I n D a n i e l G. Bobrow & A l l e n C o l l i n s ( E d s . ) , R e p r e s e n t a t i o n and u n d e r s t a n d i n g : s t u d i e s i n c o g n i t i v e s c i e n c e . New York: Academic P r e s s . V i e n n o t , L. (1979). Spontaneous r e a s o n i n g i n elementary European J o u r n a l of S c i e n c e E d u c a t i o n , 1, 205-221.  126  dynamics.  Appendix Student Problem Sheets  127  A FEW QUESTIONS ON ACCELERATION  The driver, in the car pictured below, has an extremely heavy, right foot. As a result, the accelerator pedal is pressed to the metal and the car is speeding up. (a) of  Draw all the forces acting on this car that are parallel to the direction motion.  (b)  In which direction is the net force (on this car) operating?  (c)  In one word, describe the forces acting on this car.  A boy isridinga mountain bike along a level street. He is applying and equal and constant force to each pedal so that, in total, the force applied by the rear wheel on the road is greater than the force of friction (both air and rolling friction). (a)  Will this boy be accelerating, decelerating, or travelling with a constant speed. Provide some evidence that will support your answer.  128  (b)  3.  On the diagram below, draw the forces that are operating on this bike (and which are parallel to the direction of motion), and the direction of of the net force.  If acceleration is a result of applying a continuous, constant force to an object, why is it that when you are travelling in a car with a constant speed of 100 km/h, on a flat stretch of highway, you must keep your foot on the accelerator pedal?  129  A FEW QUESTIONS ON DECELERATION  The driver, in the car pictured below, has outfitted his car with a radar detector which, at this very moment, is indicating that the car has just entered a police radar beam. Because he was travelling at a constant speed of 120 km/h and does not want to receive a speeding ticket, the driver has removed his right foot (thaf s right, the heavy one) from the gas pedal and is using it to brake rather heavily. (a)  Draw all the forces acting on this car that are parallel to the direction of motion.  (b)  In which direction is the net force (on this car) operating?  (c)  In one word, describe the forces acting on this car.  A boy is riding a mountain bike along a level street. At present he is not applying any force to the pedals and is just coasting. (a)  Will this boy be accelerating, decelerating, or travelling with a constant speed. Provide some evidence that will support your answer.  130  un the diagram below, draw the forces that are operating on this bike (and which are parallel to the direction of motion), and the direction of the net force.  A baseball player has just hit a foul ball. The ball is travelling vertically upwards. On the diagram below, draw the force (or forces) that are acting on the ball and which are parallel to the direction of motion. In addition, describe how the ball is moving i.e. is it accelerating, decelerating, or travelling with a constant speed?  131  ACCELERATION AND DECELERATION - IS THERE A DIFFERENCE?  Below is a diagram of one of the cans that we used in the lab to investigate acceleration and deceleration. This can is moving from left to right and has two forces acting on it. The largest force is on the left side and the smallest force is on the right side.  > direction of motion (a)  In which direction is the net force acting in?  (b)  Is this cart accelerating or decelerating? Give a reason (or reasons) to support your answer.  Below is a diagram of one of the large trolleys that we were using during the demonstrations. This cart is accelerating from right to left as a result of the force that is being applied to it. Complete this diagram by drawing another force arrow (or force arrows) on it that would slow down (decelerate) the cart. Below the diagram, explain your reasons for completing the drawing as you did.  132  Describe the forces acting on this cart.  A car starts from a rest position (i.e. not moving) and is accelerated to 100 km/h and then is held at 100 km/h. At what points in this sequence of events are the forces on the car in balance.  If you doubled the net force acting on an object, how would its acceleration be affected.  Below is a force diagram of a car. Use this diagram to answer the following questions.  3000 N  500 N  direction of motion  133  (a)  What is the net force acting on this car (please show all your calculations).  (b)  What type of motion will the car exhibit?  Below is a diagram of a car that is moving forwards but decelerating. Assume that the only forces acting on car are (a) the force of the wheels on the road that is moving the car forward, and (b) the frictional force between the wheels and the road surface. Draw force arrows on this car that will account for its deceleration. Make sure that you indicate the initial direction of motion of the car.  If the unbalanced force on an object is doubled, how will the acceleration of the object be affected?  If the net force on an object is kept constant and the mass of an object is doubled, who will the acceleration of the object be affected?  Two boys have skipped their afternoon Science class to go to a baseball game. While at the game, one of the boys tells the other that the the ball actually acclerates after it leaves the pitcher's hand and then begins to decelerate as it approaches the batter. He says this occurs because the pitcher gives the ball some force (when he throws it) causing the ball to accelerate. As the force is used up the ball begins to slow down. 134  The other boy says this is impossible and suggests that his iriend has the intelligence of a small soap dish. He says that the ball begins to slow down as soon as it leaves the pitcher's hand because the only force acting on the ball after this point is fluid friction (from the air) which is acting in the opposite direction to the ball's motion. Which of the two boys do you agree with and why do you agree with him?  135  A FEW QUESTIONS DEALING WITH UNIFORM MOTION  Guess who's back? You're right - its our street version of Mario Andretti. This time however, he's dragging a few speeding tickets with him and, as a result, has changed his driving habits. Analyze the forces acting on his car and  (a)  in one word, describe the forces acting on the car.  (b)  determine the net force acting on the car.  (c)  describe the type of motion that the car is exhibiting.  A boy isridinga mountain bike along a level street. He is applying an equal and constant force to each pedal so that, in total, the force applied by the rear wheel on the road is equal to the force of friction (both air and rolling friction). (a)  Will this boy be accelerating, decelerating, or travelling with a constant velocity. Provide evidence to support your answer.  136  (b)  3.  On the diagram below, draw theforcesthat are operating on this bike (and which are parallel to the direction of motion), and the direction of the net force (if there is no net force state this).  Captain Kirk and the crew of the USS Enterprise have been ordered to proceed to the planetary system of the star Rigel 4 to investigate an outbreak of nibbles. However, 50 light years from Earth and while travelling at warp factor 5, the ship's lithium crystals implode causing an immedioate shutdown of all engines. (a)  Keeping in mind that there is no friction of any kind in space (i)  will the USS Enterprise (and its crew) be accelerating, decelerating, or travelling with a constant velocity 10 seconds after the engines have been shut down. Provide evidence to support your answer.  (ii)  Give your best estimate of fast the ship will be travelling 10 seconds after the engines have been shut down.  137  (b)  Will Captain Kirk and his crew ever be able to reach Rigel 4 and keep their date with the nibbles or are they destined to become a derelict ghost ship forever lost in deep space? Explain your answer.  (c)  Normally it would take the USS Enterprise 3 weeks (from the position where the lithium crystals imploded)to reach Rigel 4 if they were able to maintain a constant velocity of warp factor 4. If you think that they can still reach Rigel 4 without their engines, what is your best estimate as to how long it take them. Explain how you arrived at this estimate.  138  

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