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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 this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Mathematics & Science Education The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date October 7, 1988 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 if 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 i i 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 i i List of Figures v i i 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 4 Rationale for the Problem 7 Educational Significance of the Problem 7 Theoretical Considerations 8 Limitations 9 2. 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 page 3. 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 30 4. 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 101 v Chapter page 5. 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 I l l Summary Conclusions Concerning the Efficacy of the Instructional Model 112 A Discussion of the Results 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 37 2. Teacher-Constructed Map of Newtonian 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 53 8. Redesigned Concept Map of Acceleration and Deceleration 60 9. Symbols Used in Frame Constructions 75 10. Kelly's Acceleration Frame for Stationary Objects 78 11. 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 86 16. Composite Deceleration Frame Applied to the Baseball Problem 88 17. Brad's Frame for Uniform Motion 89 18. Kari's Frame for Uniform Motion 90 vi i 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 95 22. An Interpretational Framework of Motion Based Upon the 'Motion Implies a Force' Conception 102 23. A Newtonian Interpretational Framework of Motion 104 v i i i 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 all 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 first, motion implies an application of force; second, force is 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 is 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 its 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 all forms of motion require an application of force. The Specific Problems The general problem can be subdivided into three specific problems or objectives. These are: 1. 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 is 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 in orderly and meaningful patterns (Tyler, 1972)", as cited by Roberts & Russell (1975). Clue Structure A clue structure is 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 imple-mentation 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 is 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 , all 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 'it 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 idiosyn-cratic, many similarities among the expectations and beliefs of individuals have been recognized by researchers. This apparent anomaly arises from, at least, two possibilities. These are: first, 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 is neces-sary to accept the previous assumption that individuals process information and construct meaning in similar ways. Once this assump-tion is 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 - for the effectiveness of common sense thought" (p. 211). 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 is a remembered framework to be adapted to f i t reality by changing as necessary ... A frame is 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 if the individual per-ceives 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 is 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, idio-syncratic 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 similar-ity 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 is 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 informa-tion about both events. As a result, these levels are fixed and probably represent a conceptualization of the events in question. Further 'successful' applications of this dynamic structure to other contextually similar events result in an increase to the complex-ity of the frame. This increasing complexity can be represented as a continued expansion of the frame to include increasingly more general-ized 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, in turn, subsume even more specific frames. In this fashion a "generalization hierarchy" (Winograd, 1975, p. 196) of frames is constructed. This conceptualization of personal, inductive, domain-related knowledge as a collection of mental frames arranged in a generalization hierarchy provides a theoretical perspective for the representation of personally constructed knowledge. This representation will be more fully discussed in Chapter Three. 6 R a t i o n a l e f o r the Problem Educational S i g n i f i c a n c e of the Problem Many teachers and researchers have recognized that l a r g e numbers of students hold views of f o r c e and motion that can best be described as p r e - O a l i l e a n . I t has been assumed (and i s assumed f o r the purposes of t h i s research) that these views represent an impediment to the a c q u i s i t i o n of Newtonian concepts of dynamics. This stance i s most s t r o n g l y s t a t e d by Viennot (1979): The i n t u i t i v e scheme i s , thus, widespread and tenacious. I t r e s i s t s the teaching of concepts which c o n f l i c t w i t h i t , and i t reappears even i n the expert when he or she l a c k s time to r e f l e c t . Such t e n a c i t y i s probably connected w i t h the s e l f -consistency of the scheme ... a major teaching e f f o r t i s needed which goes beyond the conventional teaching of the Newtonian scheme alone ... students should be helped to make e x p l i c i t t h e i r own i n t u i t i v e reasoning w i t h a l l i t s conse-quences, and to compare t h i s w i t h what they are taught (p. 213). This research has set i t s e l f the task of transforming the i n t u i t i v e scheme ( a l t e r n a t i v e framework) by developing an i n s t r u c t i o n a l model that does go beyond the teaching of the Newtonian scheme alone. By doing so, i t was conjectured that a more complete understanding of Newtonian concepts of dynamics, by students, might be achieved. The i n s t r u c t i o n a l s t r a t e g y , although designed e x t e r n a l l y to the classroom, has been developed and assessed w i t h i n an o p e r a t i o n a l classroom. This form of p r a c t i c a l e v o l u t i o n has attempted to ensure that the i n s t r u c t i o n a l s t r a t e g y i s responsive to the demands of c l a s s -room systems. This responsiveness, combined w i t h the inherent f l e x i -b i l i t y of the model, should ensure that the i n s t r u c t i o n a l model can be adapted by teachers to meet t h e i r own unique se t s of requirements. This research represents an i n i t i a l step i n the movement of a well-documented body of research data from a n a l y s i s to f u l l - f l e d g e d 7 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 device d e r i v e d from i n f o r m a t i o n processing theory. As such, t h i s research provides a double p e r s p e c t i v e f o r f u t u r e research. F i r s t , the form of the i n q u i r y w i l l provide the b a s i s f o r more systematic i n v e s t i g a t i o n s of the i n s t r u c t i o n a l model's a b i l i t y to r e s o l v e the 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 the classroom. Second, the use of frame theory as an a n a l y t i c a l t o o l f o r deciphering classroom i n t e r a c t i o n s should provide f u t u r e researchers 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 assessing the e f f i c a c y of other i n s t r u c t i o n a l models. In summary, t h i s research 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 both educational p r a c t i c e and research. This research provides an i n s t r u c t i o n a l model that i s designed t o in c r e a s e students' understanding of Newtonian dynamics, and, at the same time, remain responsive to the demands of the classroom and the 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 research provides a base f o r f u t u r e systematic research concerning the e f f i c a c y of the i n s t r u c t i o n a l model, and the use of frame theory 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 -i n g classroom i n t e r a c t i o n s and student knowledge s t r u c t u r e s . T h e o r e t i c a l Considerations This research deviates from the standard p r a c t i c e of 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 defined educational theory. This 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 , to t h i s p o i n t , the general area of research i n which t h i s study 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 the elements of students' p e r s o n a l l y constructed knowledge, w i t h i n p a r t i c u -l a r phenomenological contexts, and not i n developing theory or u t i l -8 i z i n g theory to e x p l a i n the r e s u l t s . As West, Pines, and Sutton (1982) have pointed out: We cannot 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 Ausubelians, f o r example, and by doing so, d i s c r i m i n a t e t h e i r research from those who c l a i m t o be Brunerians or K e l l i a n s (P. I D -Second, the acts of l e a r n i n g and understanding by an i n d i v i d u a l , w i t h i n a classroom environment, are " a r t i f a c t u a l " (Gowin, 1982, p. 26) events unique to the 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 theory can adequately account f o r the m u l t i p l i c i t y of l e a r n i n g modes present i n the classroom. Hanicas and Secord (1983) e x p l i c i t l y recognize t h i s 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 that s p e c i f i c behaviors - l i k e most events i n the world - cannot be explained as the simple m a n i f e s t a t i o n of some s i n g l e law or p r i n c i p l e ... Indeed, the acts of persons are open-systemic events i n which a v a r i e t y of systems and s t r u c t u r e s are i n v o l v e d , systems that are 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 of these c o n s i d e r a t i o n s , the 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 considered to be immutable. Rather, the s t r a t e g y i s open to m o d i f i c a t i o n by the demands of the classroom environment. In t h i s way the g u l f between educational theory and p r a c t i c e might be bridged. L i m i t a t i o n s This research i s l i m i t e d i n two ways. F i r s t , i t does not conform w i t h the c l a s s i c a l view of g e n e r a l i z a b i l i t y i n which e x t e r n a l v a l i d i t y i s e s t a b l i s h e d through the random s e l e c t i o n of a sample from a w e l l -d e f i n e d p o p u l a t i o n . Rather, t h i s research 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 " (Stake, 1978, p. 5). Second, the problem of attempting to e s t a b l i s h equivalence between the co n s t r u c t s of a frame 9 as a mental knowledge s t r u c t u r e , and the 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 using elements of frame theory as an a n a l y t i c device i s open to question. Neither of these l i m i t a t i o n s i s , however, considered to 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 research has attempted to develop an i n s t r u c t i o n a l model based on student b e l i e f s and c o g n i t i v e processing techniques, i t has been c r u c i a l that these b e l i e f s and techniques be e x p l i c i t l y and 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 research 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 order to o b t a i n the high q u a l i t y , r i c h d e s c r i p t i o n s that have been necessary f o r the development and assessment of the i n s t r u c t i o n a l model. Secondly, as has already been mentioned, t h i s research has been d i r e c t e d at developing a p r a c t i c a l i n s t r u c t i o n a l model that could be adapted by p r a c t i c i n g teachers to meet t h e i r own s e t s of requirements. This d i r e c t i o n , however, r e q u i r e s that t h i s research be placed w i t h i n a classroom context that i s both recognizable and empathetic t o them, f o r as L i n c o l n and Guba (1985) have pointed out . . . i f you want people t o understand b e t t e r than they other-wise might, provide them i n f o r m a t i o n i n the form i n which they u s u a l l y experience i t . They w i l l be a b l e , both t a c i t l y and p r o p o s i t i o n a l l y , to 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 that w i l l prove to be u s e f u l extensions of t h e i r understand-ings (p. 120). The developmental nature of t h i s research i s a l s o apparent i n the attempt to develop an a n a l y t i c a l device, 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 theory and the students' a l t e r n a t e frameworks. At t h i s stage, i t i s not c l e a r whether or 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 Minsky (1975). C e r t a i n l y , there 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 these c o n s t r u c t s ; that i s , frames are considered to 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 are g e n e r a l i z e d representations of commonalities 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 preva-lence of the commonalities that have l e d to the c o n s t r u c t i o n of the a l t e r n a t e framework, however, i n d i c a t e that the i n d i v i d u a l s i n v o l v e d have constructed knowledge from experience i n remarkably s i m i l a r ways. This 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 to the 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 research can only be considered to be at a hypothesis 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 addressed 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 the Related L i t e r a t u r e Over the past decade an i n c r e a s i n g amount of science education research has been d i r e c t e d towards uncovering and c a t a l o g i n g students' b e l i e f s concerning s p e c i f i c p h y s i c a l phenomena. I t has been hoped that such research would e v e n t u a l l y lead to an improvement i n the q u a l i t y of understanding of these phenomena by students i n the sciences and technologies ( G i l b e r t and Watts, 1983). To date, the research t o p i c s have been e c l e c t i c w i t h probes being launched at areas such as f o r c e , uniform and a c c e l e r a t e d motion, energy, e l e c t r i c i t y , heat, l i g h t , and the p a r t i c u l a t e nature of matter. 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 targeted the a s s o c i a t e d areas of f o r c e and motion as being e s p e c i a l l y f r u i t f u l f o r the d e l i n e a t i o n of students* b e l i e f s . The r a t i o n a l e f o r t h i s choice has probably best been s t a t e d by Champagne, K l o p f e r , and Gunstone (1982, p. 399): 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 neces-sary f o r coping w i t h the moving objects that are encountered i n d a i l y l i f e . Thus, a l l students begin the formal study 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 set of p r i n c i p l e s that a l l o w them t o p r e d i c t the r e a l world. In a d d i t i o n , the same words that are used to de s c r i b e and e x p l a i n motion i n everyday language a l s o are used by p h y s i c i s t s . W i t h i n the set of research s t u d i e s that have i n v e s t i g a t e d s t u -dents' b e l i e f s concerning f o r c e and motion, i . e . dynamics, two sub-sets of research c a t e g o r i e s have been recognized. These are: f i r s t , those s t u d i e s that have catalogued student b e l i e f s of dynamics on the b a s i s of t h e i r own merits and "without assessment against 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 & Easley, 1978, p. 63), and second, those s t u d i e s that have assessed student b e l i e f s of dynamics r e l a t i v e to 1 2 t h e i r congruence w i t h accepted s c i e n t i f i c concepts. These two categor-i e s are r e f e r r e d t o , r e s p e c t i v e l y , as the ideographic and the nomo-t h e t i c ( D r i v e r & Easley, 1978). I t i s these two c a t e g o r i e s that 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 research strands w i t h i n the l i t e r a t u r e . The Ideographic Approach A g u i r r e (1978), Kuhn (1979), Trowbridge, 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 students' 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 motion, 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 general. The terminologies used by these researchers to 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 ideographic approach. A g u i r r e (1978) and Kuhn (1979) both seek to describe student b e l i e f s . T h e i r p r o p o s i -t i o n i s that these b e l i e f s are e x p e r i e n t i a l l y based and, to a great degree, formed e x t e r n a l l y to formal i n s t r u c t i o n . Trowbridge, Lawson, and McDermott (1980a, b) seek to e l i c i t the students' "naive 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 or precon-c e p t i o n s . 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 to reconstruct a students' a l t e r n a t i v e framework which they d e f i n e as a set of "coherent ideas of the world based on t h e i r own experiences" (p. 360). C l e a r l y , these researchers 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 s i m i l a r assumptions. F i r s t , students are 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 concerning s c i e n t i f i c concepts. Second, t h i s knowledge has been constructed on an e x p e r i e n t i a l foundation. F i n a l l y , t h i s knowledge has been acquired p r i o r to formal i n s t r u c t i o n i n the concept(s) i n ques-t i o n . 13 These assumptions are r e f l e c t e d i n the methodology and subjects u t i l i z e d by the m a j o r i t y of these researchers. With the exception of the s t u d i e s by Watts (1983, 1982), and Watts and Z y l b e r s z t a j n (1981), a l l researchers have employed some form of c l i n i c a l i n t e r v i e w that would r e f l e c t the i d i o s y n c r a t i c nature of the knowledge being i n v e s -t i g a t e d . 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 "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) from a l a r g e sample of students and thus opted f o r a paper and p e n c i l t e s t . In a d d i t i o n , a l l researchers have used s u b j e c t s who have had l i t t l e or no exposure to formal physics i n s t r u c t i o n i n order to i n v e s t i g a t e the e x p e r i e n t i a l nature of t h i s knowledge. Re s u l t s Although a number of d i f f e r e n t contexts are employed i n these 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 occur. A l l researchers found that 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 that i f an object i s moving a f o r c e must be a c t i n g upon that o b j e c t . The converse of t h i s p o s i t i o n was a l s o h e l d to be t r u e . V a r i a t i o n s of t h i s p o s i t i o n were recognized by Kuhn "(1979) who found a number of h i s subjects equating constant speed w i t h constant f o r c e , and by A g u i r r e (1978), Watts and Z y l b e r s z t a j n (1981), and Trowbridge, Lawson and McDermott (1980) who a l l found that 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 that motion due to the i n t e r a c t i o n of two bodies was due to the body with the greater f o r c e . A g u i r r e ' s (1978) r e s u l t s i n d i c a t e that s u b j e c t s below twelve years of age 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 recognize only one f o r c e i n the system thus suggesting that t h i s b e l i e f may be age dependent. Both s t u d i e s by Watts (1982, 1983) and that by Watts and Z y l b e r s z t a j n (1981) i n d i c a t e that some c h i l d r e n r e q u i r e that there be a medium, such as a i r , through which a f o r c e can a c t . In the case of the 14 l a t t e r study 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 to support the sub-j e c t s ' contention that the moon lacked a g r a v i t a t i o n a l f i e l d . These researchers 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 that 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 . The 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 the r e s u l t a n t a c t i v i t y . The b e l i e f that g r a v i t a t i o n a l f o r c e increases w i t h height was common to a s u b s t a n t i a l number of subjects i n the s t u d i e s of A g u i r r e (1978), Kuhn (1979), Watts (1982), 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 erception most prevalent i n subjects l e s s than eleven years of age suggesting that i t may be age dependent. Other b e l i e f s were recognized i n s i n g l e s t u d i e s . Watts (1983) reported 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 to complete an a c t i o n against some form of r e s i s t a n c e , objects that are r e s t r a i n e d i n p o s i t i o n have an inherent f o r c e , objects that can or might cause events to occur have an inherent f o r c e , and moving objects have inherent f o r c e . A g u i r r e (1978) a l s o reported the existence of a b e l i e f i n the inherent f o r c e of r e s t r a i n e d o b j e c t s . In t h i s case, the inherent f o r c e could only 'hold' and not ' p u l l ' . A g u i r r e (1978) a l s o recognized that a l a r g e number of h i s subjects could only i d e n t i f y a f o r c e e q u i l i b r i u m c o n d i t i o n 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 that g r a v i t a t i o n a l f o r c e only operates when objects f a l l . Viewed i n t o t a l i t y these b e l i e f s and perceptions appear to represent a mixture of A r i s t o t e l i a n - l i k e and Impetus t h e o r i e s of dynamics. The r e p r e s e n t a t i v e sample of subjects of these s t u d i e s views f o r c e and motion from a pre-Newtonian p o s i t i o n but, as Watts and Z y l b e r s z t a j n (1981) noted at the beginning of t h e i r paper: 15 I t i s no news that 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 motion, and o f t e n r e j e c t , or f a i l to ap p r e c i a t e , the substance 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 students' b e l i e f s of for c e and motion have occurred along the nomothetic s t r a n d . Researchers operating from t h i s p e r s p e c t i v e are Champagne, R l o p f e r , and Anderson (1979), Clement (1981, 1977), diSessa (1981), Fleshner (1970), Gunstone and White (1981), Helm (1978), L e i t h (1982), McCloskey (1983), McCloskey, Carmozza, and Green (1980), M i n s t r e l 1 (1981), S a l t i e l and Malgrange (1980), Sjoberg and L i e (1981), Trowbridge and McDermott (1980a, b ) , and Viennot (1979). These researchers have attempted to 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 concepts w i t h i n the f o l l o w i n g contexts: c l a s s i c a l mechanics (Champagne, K l o p f e r , and Anderson, 1979, Sjoberg and L i e , 1981), computer-simulated motion i n two dimensions (diSessa, 1981), f o r c e (Fleshner, 1970), g r a v i t a t i o n a l f o r c e (Gunstone and White, 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 motion (McCloskey, 1983 and McCloskey, Carmozza, and Green, 1980), the 'at r e s t ' c o n d i t i o n of an object ( 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 reference ( 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 motion (Viennot, 1970). The terminology, methodology, and subjects used i n these s t u d i e s a l l r e f l e c t the nomothetic p e r s p e c t i v e . The terminologies used by these researchers to 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 connotations. Champagne, K l o p f e r , and Anderson (1979), Clement (1981), Helm (1978), L e i t h (1982), McCloskey (1983), Sjoberg and L i e (1981), and Trowbridge and McDermott (1980a, b) 16 a l l attempt to i d e n t i f y students' concepts and/or misconcepts. The i m p l i c a t i o n i s that these w i l l not, i n a l l p r o b a b i l i t y , match the accepted s c i e n t i f i c concept. DiSessa (1981) attempts to de f i n e students' "naive knowledge" (p. 1) that has yet to reach the 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 to describe student "naive b e l i e f s " (p. 1139). Fleshner (1970) speaks of determining how "formerly acquired knowledge" (p. 201) i s r a t i o n a l i z e d w i t h newly acquired school knowledge. Gunstone and White (1981) wish to assess students' p r e d i c t i v e and explanatory c a p a b i l i t i e s when faced w i t h formal physics problems. M i n s t r e l 1 (1981) attempts to e l i c i t student pre- or a l t e r n a t e conceptions p r i o r to i n s t r u c t i o n i n the accepted s c i e n t i f i c concept. Viennot (1979) wishes to r e c o n s t r u c t student reasoning p a t t e r n s i n an attempt to determine how they i n t e r a c t w i t h teaching. What seems to be i m p l i c i t i n these terminologies i s that student b e l i e f s are somehow at odds w i t h accepted s c i e n t i f i c thought. In a s i m i l a r f a s h i o n , the methodologies u t i l i z e d r e f l e c t the nomothetic approach. In order to con t r a s t student b e l i e f s w i t h s c i e n t i f i c concepts the m a j o r i t y of researchers 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. Exceptions to t h i s methodological format are found i n the i n v e s t i g a t i o n s of Clement (1977), diSessa (1981), Fleshner (1970), McCloskey (1983), M i n s t r e l 1 (1981) , and Trowbridge and McDermott (1980a, b ) . A l l of these r e -searchers, w i t h the exception of M i n s t r e l 1, have used some form of c l i n i c a l i n t e r v i e w i n order to observe t h e i r s u bjects i n p h y s i c a l s i t u a t i o n s . M i n s t r e l ! ' s research occurs w i t h a classroom s e t t i n g , where the researcher i s the teacher, and thus, 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 subjects i n v e s t i g a t e d , w i t h the exception of one study, have been exposed to some type of formal physics i n s t r u c t i o n . The use of these s u b j e c t s has allowed the e x p l i c i t j u x t a p o s i t i o n of the students' b e l i e f s of dynamics w i t h the Newtonian concepts of dynamics. The exception to the use of the subject group has occurred i n the study by L e i t h (1982). In t h i s i nstance the researcher was attempting to v a l i d a t e a set of tasks d e r i v e d from a P i a g e t i a n study and used a group of school c h i l d r e n , 7-12 years of age. In g e n e r a l , researchers i n v e s t i g a t i n g students' b e l i e f s of dynamics from a nomothetic 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 given to students that have been exposed to some l e v e l of formal i n s t r u c t i o n s . R e s u l t s The r e s u l t s from those s t u d i e s employing the nomothetic approach have, f o r the most p a r t , been deduced from e r r o r analyses of student responses to questions ( e i t h e r w r i t t e n or v e r b a l ) concerning Newtonian mechanics. These r e s u l t s w i l l be discussed under two c a t e g o r i e s : f i r s t , those that deal w i t h concepts of dynamics, and second, those that deal w i t h kinematics. A b e l i e f that appears to be pervasive among subjects s t u d i e d by a l a r g e number of researchers (Champagne, K l o p f e r and Anderson, 1979, Gunstone and White, 1981, M i n s t r e l l , 1981, S a l t i e l and Malgrange, 1980, and Viennot, 1979) i s that a body at r e s t i s devoid of any a p p l i e d f o r c e s . The converse 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 i n a number of forms. Champagne, K l o p f e r and Anderson (1979), and M i n s t r e l l (1981) report that a number of t h e i r s u b j e c t s held 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 motion 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 uniform motion (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 to the a p p l i e d f o r c e (Champagne, K l o p f e r and Anderson, 1979) and that 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, Clement, 1981, L e i t h , 1982). Clement (1981), diSessa (1981), McCloskey (1983), Carmozza and Green (1980), Sjoberg and L i e (1981), and Viennot (1979) a l s o i d e n t i -f i e d s u b j e c t s who b e l i e v e d that when two or more for c e s are present any 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 . A l l of these b e l i e f s c o n t r i b u t e to a s t r u c t u r e that Clement (1981) c a l l s the "motion i m p l i e s a f o r c e misconception" (p. 67). This s t r u c t u r e , as McCloskey (1983) has pointed out, i s reminiscent of the p r e - G a l i l e a n Impetus Theory. Related to t h i s s t r u c t u r e i s the lack of c o n s i d e r a t i o n given by some sub j e c t s to frames of reference (McCloskey, 1983, S a l t i e l and Malgrange, 1980) and a c t i o n / r e a c t i o n combinations (Sjoberg and L i e , 1981, Viennot, 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 that a p p l i e d f o r c e occurs as only a push or p u l l (Fleshner, 1970) which might lead to the b e l i e f , reported by M i n s t r e l l (1981) that only animate objects can apply a f o r c e . S p e c i f i c b e l i e f s concerning motion due to g r a v i t a t i o n a l f o r c e have been i d e n t i f i e d . Gunstone and White (1981) reported that a m i n o r i t y of s u b j e c t s thought that 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 a f u n c t i o n of an object's weight and weight was a f u n c t i o n of the object's height above a reference s u r f a c e . Sjoberg and L i e (1981) reported that approxi-mately 15% of t h e i r s u b j e c t s thought that a g r a v i t a t i o n a l f i e l d r e q u i r e s some form of medium f o r i t to be e f f e c t i v e . Observations concerning s u b j e c t s ' b e l i e f s of kinematics have been made by L e i t h (1982), and Trowbridge and McDermott (1980a). A l l of 19 these researchers found that t h e i r s u b j e c t s tended to compare the spe e d / v e l o c i t y of two objects on the ba s i s of p o s i t i o n (when two obje c t s are si d e - b y - s i d e they have the same speed) or d i s t a n c e t r a v e l -l e d (the greater the d i s t a n c e , the greater the speed). L e i t h (1982) a l s o found that absolute speed of an object was equated w i t h l e a s t t r a v e l time without regard to d i s t a n c e t r a v e l l e d . Trowbridge and McDermott (1980a, b) observed that a s u b s t a n t i a l m i n o r i t y (up to 30%) of t h e i r s u bjects judged r e l a t i v e a c c e l e r a t i o n on the ba s i s of p o s i -t i o n , i . e . i f one object passed another i t had greater a c c e l e r a t i o n . The r e s u l t s of the i n v e s t i g a t i o n s concerning students' b e l i e f s of mechanics that have taken the nomothetic approach are probably best summed up by McCloskey (1983), and Sjoberg and L i e (1981). F i r s t , McCloskey: Indeed, the ideas about motion h e l d by most people 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 at l e a s t one physics course, are much c l o s e r to the account g i v e n by the Impetus Theory than they are to Newtonian mechanics (p. 125) ... The s t r i k i n g s i m i l a r i t y between the views of the medieval philosophers and those of our sub j e c t s suggests that the Impetus Theory i s a n a t u r a l outcome of experience w i t h t e r r e s t r i a l motion (p. 127). F i n a l l y , Sjoberg and L i e : This r a t h e r depressing p i c t u r e " f o r c e s " (!) on us an under-standing that the foundation of 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 textbooks more or l e s s assume. On the c o n t r a r y , Newton's laws are contrary to common sense ideas developed i n t u i t i v e l y and spontaneously by p u p i l s (and ad u l t s ) (p. 18). A Comparison of Re s u l t s A comparison of the r e s u l t s of each research 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 of congruence between both strands. This congruence was evident i n s u b j e c t s ' b e l i e f s concerning the e f f e c t s of f o r c e s , p o s s i b l e sources of f o r c e , and the types of f o r c e s . 20 The most commonly e l i c i t e d b e l i e f from subjects i n both research strands was that motion i s the r e s u l t of a continuous a p p l i c a t i o n of f o r c e . This b e l i e f , or i t s converse, was recognized by a l l researchers operating along the ideographic s t r a n d and by Champagne, K l o p f e r and Anderson (1979), Clement (1981), Gunstone and white (1981), McCloskey (1983), McCloskey, Carmozza, and Green (1980), M i n s t r e l l (1981), S a l t i e l and Malgrange (1980), Sjoberg and L i e (1981), and Viennot (1979) from the nomothetic group. 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 the b e l i e f that an a p p l i c a t i o n of constant f o r c e produced uniform motion (Kuhn, 1978, Champagne, K l o p f e r and Anderson, 1979), or as the b e l i e f that an a p p l i c a t i o n of 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 boundaries appear i n v i s i b l e to these 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 reported i n s t u d i e s from both strands suggest that t h i s c l a s s of b e l i e f s may be prevalent at many educational l e v e l s . Clement (1981) reported that 88% of the f i r s t year and approximately 70% of the second, t h i r d , and f o u r t h year engineering students t e s t e d at an American u n i v e r s i t y found i t d i f f i c u l t "to t h i n k about an object c o n t i n u i n g to move i n one d i r e c t i o n w i t h the t o t a l net for 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. 67). McCloskey (1983) found that more than 33% of the American high school and c o l l e g e students he i n v e s t i g a t e d explained motion i n terms of an Impetus Theory. Approxi-mately o n e - t h i r d of the Norwegian high school and c o l l e g e students u t i l i z e d by Sjoberg 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 of motion of a pendulum bob. Watts and Z y l b e r s z t a j n (1981) reported that 85% of the B r i t i s h , fourteen year o l d sub 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 motion. Results such as these tend 21 to suggest that the b e l i e f that motion i m p l i e s a f o r c e i s not only common but pervasive. 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 forces were a l s o found to correspond c l o s e l y . Using the ideographic approach A g u i r r e (1978), Trowbridge, Lawson, and McDermott (1980), Watts and Z y l b e r s z t a j n (1981) reported that t h e i r s ubjects a t t r i b u t e d any r e s u l t a n t motion only to the l a r g e s t f o r c e . S i m i l a r l y , diSessa (1981), McCloskey (1983), McCloskey, Carmozza, and Green (1980), Sjoberg and L i e (1981), and Viennot (1979), using the nomo-t h e t i c approach, reported that t h e i r s ubjects b e l i e v e d than any r e s u l t a n t motion would 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 . D i r e c t l y a s s o c i a t e d w i t h these b e l i e f s i s the f a i l u r e of sub j e c t s to consider a c t i o n / r e a c t i o n combinations (Sjoberg and L i e , 1981, Viennot, 1979). Subjects from both strands a t t r i b u t e d f o r c e to only those objects that had motive c h a r a c t e r i s t i c s . W i t h i n the ideographic s t r a n d Watts (1983) and A g u i r r e (1978) found that subjects a t t r i b u t e d an inherent f o r c e to those objects that can or might cause events to occur. M i n s t r e l l (1981), operating from a nomothetic p o s i t i o n , found that h i s students b e l i e v e d that only animate objects can apply a f o r c e . These b e l i e f s s t r o n g l y 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 p r e v i o u s l y , that 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 , are not recognized by some subj e c t s i n v e s t i g a t e d under e i t h e r research approach. Studies by Watts (1983, 1982), Watts and Z y l b e r s z t a j n (1981), and Sjoberg and L i e (1981) found that subjects r e q u i r e d g r a v i t y to act through some form of connecting medium. As a r e s u l t g r a v i t y i s transformed i n t o an ex t e r n a l surface 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 reported that h i s sub j e c t s b e l i e v e d that f o r c e could only be a p p l i e d by a i n d i r e c t push or p u l l . These reported b e l i e f s suggest that only e x t e r n a l surface f o r c e s (pushes or p u l l s ) are recognized. These congruent, or 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 that the subj e c t s i n v o l v e d i n these s t u d i e s view the e f f e c t s , sources, and types of f o r c e s from a reasonably common p o s i t i o n . Clement (1981) suggests that t h i s viewpoint i s a r e s u l t of a common, e x p e r i e n t i a l i n t e r p r e t a -t i o n of f o r c e : In the r e a l world, where f r i c t i o n i s present, one must push an object to keep i t moving. Since f r i c t i o n i s oft e n not r e c o g n i z e d as a f o r c e by the beginner, the student may b e l i e v e that c o n t i n u i n g motion i m p l i e s the presence of a con t i n u i n g f o r c e i n the same d i r e c t i o n , as a necessary cause of the motion (p. 66). If t h i s common viewpoint i s v a l i d , i t appears to represent an a l t e r n a t e framework of dynamics constructed from three b a s i c t e n e t s : f i r s t , motion i m p l i e s an a p p l i c a t i o n of f o r c e , second, f o r c e i s as s o c i a t e d only w i t h motive o b j e c t s , and t h i r d , e x t e r n a l surface forces are the only types of for c e s a v a i l a b l e . In order to e x p l i c a t e and transform (where d e s i r e a b l e and pos-s i b l e ) the a l t e r n a t e framework of dynamics t h i s research has adopted c h a r a c t e r i s t i c s from both of the previous research strands. I t assumes, as does the ideographic s t r a n d , that the presence of an a l t e r n a t e framework of dynamics i s the r e s u l t of an a c t i v e construc-t i o n , on the part of an i n d i v i d u a l , to e x p l a i n personal movement and the motion of o b j e c t s . F u r t h e r , t h i s research assumes, as does the nomothetic s t r a n d , that t h i s a l t e r n a t e framework w i l l be, to some degree, at odds with accepted s c i e n t i f i c explanations of motion. 23 M e t h o d o l o g i c a l l y , however, t h i s research has diverged from these two strands. In order to e x p l i c a t e the a l t e r n a t e framework of dynamics that i n d i v i d u a l s have constructed t h i s research 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 classroom d i s c u s s i o n s and debates (concerning the motion of objects) r a t h e r than c l i n i c a l i n t e r v i e w s or 'paper and p e n c i l ' t e s t s . A d d i t i o n a l l y , t h i s clue s t r u c t u r e has been incorp 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 that has attempted to transform the a l t e r n a t e framework of dynamics to one that more c l o s e l y approximates the Newtonian framework of dynamics. The design of t h i s i n s t r u c t i o n a l model and i t s implementation w i t h i n an o p e r a t i o n a l classroom are the subject of Chapter Three - The Research Design. 24 CHAPTER THREE The Research Design The design base f o r t h i s study i s de r i v e d from a set of procedures d e s c r i b e d , i n i t i a l l y i n the Russian l i t e r a t u r e , as a teaching 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 study has used pers p e c t i v e s from one of the two forms of the teaching experiment - the t e s t i n g (or searching) form. This form of the teaching experiment i s used ...at the beginning stage of research, when the experimenter, having o u t l i n e d a hypothesis, does not yet conceive w i t h s u f f i c i e n t c l a r i t y the o r g a n i z a t i o n a l forms of i t s v e r i f i -c a t i o n and i s working them out i n the process of the e x p e r i -ment i t s e l f , or 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 of the method and wants to determine the most e f f e c t i v e of them (Kalmykova, 1966, p. 18). Inherent w i t h i n t h i s design are two major components. The f i r s t of these i s the i n s t r u c t i o n a l model that acts as an experimental nucleus f o r the research. The second component i n v o l v e s the implementation of the model, w i t h i n an o p e r a t i o n a l classroom, i n order to assess i t s a b i l i t y to provoke the d e s i r e d conceptual change w i t h i n the students. The c h a r a c t e r i s t i c s of both of these design components w i l l be d i s c u s -sed i n t h i s chapter. 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, the 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 these two elements w i l l be described i n d i v i d -u a l l y . 25 The I n s t r u c t i o n a l Strategy The i n s t r u c t i o n a l s t r a t e g y has four o b j e c t i v e s . These are: 1. to e x p l i c a t e the a l t e r n a t e framework that students use when d e a l i n g w i t h force/motion (dynamics) events. 2. to have students compare the concepts comprising t h e i r a l t e r n a t e framework of dynamics w i t h the Newtonian concepts of dynamics and (a) recognize conceptual d i f f e r e n c e s , and (b) c l a r i f y the p o t e n t i a l sources of these d i f f e r e n c e s . 3. to have students recognize (a) the 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 of i n t e r p r e t i n g force/motion events. (b) Newtonian conceptions of dynamics as more p l a u s i b l e and productive i n t e r p r e t a t i o n s of force/motion events. 4. to have students transform t h e i r e x i s t i n g mental s t r u c t u r e to one more c l o s e l y approximating the Newtonian framework of dynamics, and use t h i s framework f o r the i n t e r p r e t a t i o n of force/motion events. In order to achieve these o b j e c t i v e s , three complementary t a c t i c s have been used. F i r s t , i n order to achieve the e x p l i c a t i o n of the components of the a l t e r n a t e framework of dynamics the students were asked to analyze, and draw concept maps (Gowin, 1982) - e i t h e r i n d i v i d u a l l y or c o l l e c t -i v e l y - of a s e r i e s of la b o r a t o r y force/motion events that are r e l a t e d to dynamics events that occur w i t h i n the normal, c u l t u r a l context. These concept maps then served as a f o c a l point f o r the comparison of student conceptions of dynamics w i t h Newtonian conceptions. 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 student con-s t r u c t e d concept maps with a teacher constructed Newtonian concept map of the same event. This j u x t a p o s i t i o n was then used to generate c l a s s d i s c u s s i o n s i n which students were challenged to 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 that were i n c o n f l i c t w i t h Newtonian conceptions and encouraged to question the Newtonian concepts and t h e i r p o s i t i o n s w i t h i n the map. The 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 discordant ( i n the researcher's opinion) events that could not l o g i c a l l y or e m p i r i c a l l y be explained using t h e i r a l t e r n a t e framework(s). These discordant events then served 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 concerning the a b i l i t y of both conceptual schemes to provide an adequate explana-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 that the Newtonian framework would appear to the students as a more powerful base f o r the i n t e r p r e t a t i o n of force/motion events. This f i n a l t a c t i c was intended to i n i t i a t e the transformation of the mental s t r u c t u r e (represented by the a l t e r n a t e framework) by p r o v i d i n g the students w i t h a c l a s s of exemplary phenomena that could best be i n t e r p r e t e d using the Newtonian framework. These phenomena were a l l presented as demonstrations and i n v o l v e d the uniform, p o s i t i v e or negative, l i n e a r a c c e l e r a t i o n of objects as a r e s u l t of the a p p l i c a -t i o n of a constant f o r c e , and objects which t r a v e l l e d w i t h l i n e a r , uniform motion as a r e s u l t of balanced f o r c e s . I n i t i a l l y , the pheno-mena used were divorced from the students' normal, c u l t u r a l experiences and i n v o l v e d apparatus a s s o c i a t e d w i t h a school science l a b o r a t o r y . However, as the students became more f a m i l i a r w i t h the Newtonian conceptual scheme, motion problems more c l o s e l y a l l i e d to the students' normal, e x p e r i e n t i a l base were used (see Appendix I - Student Problem 27 Sheets). In t h i s way, the transformed mental s t r u c t u r e should 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 to the o r i g i n a l 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 Clue 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 student's i n d u c t i v e 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 set of frames (Minsky,1975) arranged 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 constructed by connecting each of these frames ( r e p r e s e n t i n g a s p e c i f i c concept) to the next, more general frame, by an ' i s a' l i n k which represents a sub-c l a s s / s u p e r - o r d i n a t e c l a s s r e l a t i o n s h i p . Attached to each of the con-ceptual frames, then, w i l l be sub-classes of concepts, or events which are s p e c i a l i z a t i o n s of that 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 to consider the general concept 'pa r t ( s ) of a house'. Attached to t h i s concept, 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 types 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 data that would allow an observer to recognize each room type. F u r t h e r , these data could i n c l u d e s p e c i f i c , subordinate frames (again attached to the immediate, super-ordinate frame by an ' i s a ' l i n k ) that would allow the observer to d i f f e r e n t i a t e , f o r example, between formal l i v i n g rooms and 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 type of a n a l y s i s a s t r u c t u r e evolves that repre-sents a template that could be used to determine whether or not a s t r u c t u r e could be considered to be a house. Conversely, when t h i s type 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 i n d u c t i v e knowledge of houses a clue s t r u c t u r e develops that provides an i n t e r p r e t a t i v e window i n t o what that i n d i v i d u a l perceives a house to be. The process of adding substance to and r e f i n i n g the s k e l e t a l clue s t r u c t u r e , w i t h i n the context of t h i s research, i n v o l v e s successive a p p l i c a t i o n s of the e v o l v i n g clue s t r u c t u r e to student responses to a v a r i e t y of force/motion events. The student responses to these events are q u a l i t a t i v e l y analyzed f o r a d d i t i o n a l conceptual i n f o r m a t i o n that i s r e l a t e d to the p r e v i o u s l y constructed c l u e s t r u c t u r e . This addi-t i o n a l conceptual i n f o r m a t i o n i s then incorporated i n t o the previous clue s t r u c t u r e as e i t h e r sub-classes of e x i s t i n g frames or as new frames. 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 e v o l u t i o n a r y process that 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 research, 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 occurred at the l e v e l of the i n d i v i d u a l student. However, where there has been s u b s t a n t i a l congruence between cl u e s t r u c t u r e s d e r i v e d from a group of students, or where a group of students has been i n agreement concerning the s p e c i f i c frames and sequencing of the frames w i t h i n a c l u e s t r u c t u r e , that 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 being g e n e r a l l y r e p r e s e n t a t i v e of that 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 occurred w i t h i n the researcher's own tenth grade science c l a s s . W i t h i n t h i s c l a s s , there were 12 males and 19 females aged 14 and 15 years. Membership i n t h i s c l a s s was by computer assignment based p r i m a r i l y upon the students' t e n t h grade course s e l e c t i o n s . These students had not had any p r i o r , 29 formal i n s t r u c t i o n i n Newtonian dynamics. As a r e s u l t of these environmental c h a r a c t e r i s t i c s , t h i s component of the research design represents a case study of the e f f i c a c y of the 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 study environment, the researcher assumed the r o l e of an a c t i v e p a r t i c i p a n t observer. The assessment of the e f f i c a c y of the 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 the students' a l t e r n a t e framework of dynamics and, i f necessary, produce the d e s i r e d conceptual changes w i t h i n the students. The determination of whether or not these conceptual changes occurred was based upon the research-er's judgement and cl u e s t r u c t u r e a n a l y s i s of classroom t r a n s c r i p t i o n s and student concept maps. These forms of analyses served as a t r a c k i n g mechanism f o r conceptual change w i t h i n the students and, i n t h i s regard, provided a q u a l i t a t i v e measure of the e f f e c t i v e n e s s of the i n s t r u c t i o n a l s t r a t e g y . Methods of Data C o l l e c t i o n and A n a l y s i s Video taping of a l l classroom sessions provided the primary data. These data were subsequently reduced to 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 the research sequence. The t r a n s c r i p t i o n s were then analyzed f o r the major conceptual content and patterns employed by i n d i v i d u a l s w i t h i n the c l a s s , and a hi e r a r c h y of these conceptual data was constructed. These data forms then became the b a s i s f o r the cl u e s t r u c t u r e a n a l y s i s . As the 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 to the conceptual data frame s t r u c t u r e s were generated that were intended to represent the major conceptual knowledge p a t t e r n ( s ) that i n d i v i d u a l students were using to i n t e r p r e t the force/motion events. Where there was substan-t i a l support by members of the c l a s s f o r a p a r t i c u l a r set of conceptual 30 data, the r e s u l t i n g frame was assumed to represent a composite s t r u c -t u r e that was agreeable to a m a j o r i t y of the c l a s s . These frame s t r u c -t ures were then used to t r a c k the e f f e c t that the i n s t r u c t i o n a l s t r a t e g y was having on the conceptual knowledge patterns of the students. Secondary data were obtained i n the form of student generated concept maps and worksheet answers. These data forms were used as a cross-check on the v a l i d i t y of the 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 conceptual s t r u c t u r e s w i t h those contained i n the frame s t r u c t u r e . In summary, t h i s research represents a case study of the e f f e c t s that an e x t e r n a l l y designed i n s t r u c t i o n a l s t r a t e g y has had on the conceptual knowledge patterns that students use to make sense of f o r c e and motion events. These e f f e c t s have been tracked using a cl u e s t r u c t u r e a n a l y s i s of the concepts and conceptual 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 the a n a l y s i s of classroom video tapes, that students have e x h i b i t e d when attempting to e x p l a i n a v a r i e t y of f o r c e and motion events. 31 CHAPTER FOUR The Classroom Case Study The case study covers eight c l a s s periods that spanned a t o t a l time p e r i o d of t h i r t e e n school days. W i t h i n t h i s p e r i o d , f i v e s p e c i f i c lessons were presented to the students. These were: LESSON 1 - An I n t r o d u c t i o n to Dynamics and Dynamics Terminology. LESSON 2 - Force A n a l y s i s Techniques. 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 Uniform Motion. Because t h i s case study i s p r i m a r i l y concerned w i t h the a n a l y s i s of the i n i t i a l conceptual s t r u c t u r e s that the students were using to i n t e r p r e t dynamics events and any subsequent a l t e r a t i o n to these s t r u c t u r e s as a r e s u l t of the i n s t r u c t i o n a l s t r a t e g y , only the l a s t three lessons w i l l be presented i n t h i s chapter. I t should a l s o be noted at t h i s point t h a t , i n a p h y s i c a l sense, there i s no verbal 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 d i s t i n c t i o n w i t h d e c e l e r a t i o n appearing as a negative a c c e l e r a t i o n . Due to the age of these students and t h e i r l a ck 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 d i s t i n c t i o n has been s u b s t i t u t e d f o r the v e c t o r i a l . Although most physics t e x t s present Newton's Laws of Motion i n sequ e n t i a l order, f o r the purposes of t h i s study, the order was reversed. This d e c i s i o n was based upon previous classroom s t u d i e s by M i n s t r e l l (n.d., p. 61), who found 32 i n every c l a s s , on every t e s t , the p r o p o r t i o n of the c l a s s g i v i n g Newtonian answers f o r the a c c e l e r a t i n g cases was great e r than that f o r the constant v e l o c i t y cases. Why were the a c c e l e r a t i n g cases e a s i e r f o r the students to handle? P i a g e t ' s t h e o r y (1958) suggests that reasoning from the concrete to the a b s t r a c t i s e a s i e r than from the a b s t r a c t to the c o n c r e t e . The concrete f i r s t h a n d experience i n the i n s t r u c t i o n d e a l t w i t h s i t u a t i o n s i n v o l v i n g a c c e l e r a t i o n , Newton's Second Law. I t seemed l o g i c a l that the constant v e l o c i t y case, i n v o l v i n g Newton's F i r s t Law, should be taught as a l o g i c a l consequence of the a c c e l e r a t i o n case. Because the focus of t h i s research i s the e l i c i t a t i o n and a l t e r a -t i o n ( i f necessary and p o s s i b l e ) of students' conceptions of motion, the case study was concentrated on data c o l l e c t e d from the l a s t three lessons. The data from these lessons w i l l be introduced i n two formats. The f i r s t data 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 concerning motion events that are presented to provide a f l a v o u r of the classroom environment, and a macroscopic view of i n i t i a l student conceptions and any subsequent a l t e r a t i o n s to these conceptions. Included w i t h i n these t r a n s c r i p t i o n s are concept maps constructed by the c l a s s as a r e s u l t of t h e i r d i s c u s s i o n s of force and motion events. These concept maps are presented to allow a v i s u a l examination of the major concepts being employed by these students to i n t e r p r e t these events. The second form of data to be presented i s i n t e r p r e t a t i o n a l , conceptual frames constructed by the researcher to account f o r attempts by i n d i v i d u a l students and/or the c l a s s to i n t e r p r e t s p e c i f i c types of motion. The use of these i n t e r p r e t a t i o n a l frames allows a more i n -depth examination of the elements of the a l t e r n a t e framework and provides 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 to t h i s framework as a r e s u l t of the i n s t r u c t i o n a l s t r a t e g y . The method of 33 c o n s t r u c t i n g these 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 discussed l a t e r i n t h i s chapter. The Lessons The Dynamics of A c c e l e r a t i o n The l e s s o n was begun by asking the students why an ob j e c t , such as a dynamics c a r t , would begin to a c c e l e r a t e and continue to a c c e l e r a t e ? K e l l y : Because there i s more f o r c e pushing i t than there i s f r i c t i o n going against i t . The reason i s (pause) f r i c t i o n i s t r y i n g t o stop i t . . . ( i n a u d i b l e ) . Teacher: Is that f o r c e always there? K e l l y : 5 No (pause) Yes, i t would have to be, depending on how long, how f a r you wanted to a c c e l e r a t e i t f o r . Teacher: We're going to keep the t h i n g a c c e l e r a t i n g f o r as long as we want. K e l l y : Then the f o r c e always has to be there. Teacher: 10 So there has to be a continuous f o r c e a p p l i e d to the ob j e c t , and the f o r c e has to be l a r g e r than (pause)? K e l l y : than the f r i c t i o n . Teacher: What do the r e s t of you t h i n k about that? Is that the cause of a c c e l e r a t i o n ? (pause) Any other ideas about a c c e l e r a t i o n ? 15 Is i t caused by a continuous force? Cory: I t i n c r e a s e s . Teacher: So, the 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 the time (pause) so the f o r c e i s always g e t t i n g l a r g e r , 20 and l a r g e r , and l a r g e r ? Another student: Yeah. Cory: Yes. At t h i s p o i n t , student idea generation tended to abate. In order to refocus them, both 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 the c o n t i n -34 uous a p p l i c a t i o n of a constant force) and Cory's ( 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 an i n c r e a s i n g force) concepts of the cause of a c c e l e r a t i o n , were w r i t t e n on the blackboard. 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 her concept. Teacher: K e l l y , c o r r e c t me i f I'm wrong, that f o r c e i s always the same s i z e i s that r i g h t ? K e l l y : 25 Yeah. This c l a r i f i c a t i o n caused many of the students to become a g i t a t e d and v o c a l l y disagree with K e l l y ' s concept of a constant, continuous f o r c e causing a c c e l e r a t i o n . In the face of t h i s unsubstantiated disagreement, K e l l y volunteered a f u r t h e r c l a r i f i c a t i o n . K e l l y : I t ' s s t i l l continuous f o r c e . I f you keep the f r i c t i o n on at the same l e v e l , then i t ' s s t i l l continuous f o r c e but, ah, the continuous f o r c e i s g e t t i n g harder. I t ' s pushing more. Teacher: Is that what you mean by t h i s statement ( r e f e r r i n g to K e l l y ' s 30 o r i g i n a l concept of the cause of a c c e l e r a t i o n that had been w r i t t e n on the blackboard). K e l l y : Yeah. Teacher: So your continuous f o r c e i s a continuous, i n c r e a s i n g f o r c e . K e l l y , however, was not completely w i l l i n g to cast aside her o r i g i n a l idea that a c c e l e r a t i o n might be caused by a continuously a p p l i e d , constant f o r c e . She f i n i s h e d the debate with a f u r t h e r q u a l i f i c a t i o n . K e l l y : ...or you can have a continuous f o r c e w i t h a decrease i n the 35 f r i c t i o n f o r c e . 35 At t h i s p o i n t i n the le s s o n , there was o v e r a l l c l a s s agreement wi t h the idea that an object ( 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 , continuous f o r c e was a p p l i e d to an object as long as the f r i c t i o n a l f o r c e remained constant and sm a l l e r than the a p p l i e d f o r c e . This s p i r i t of classroom consensus was c a r r i e d over to the c o n s t r u c t i o n of an embryonic concept map that attempted to r e l a t e a c c e l e r a t e d motion to f o r c e (see Figure 1 ). The next c l a s s began with a review of the a c c e l e r a t i o n concept map that the students had generated at the end of the previous c l a s s . This map was then juxtaposed w i t h a teacher-constructed map of Newtonian concepts of a c c e l e r a t i o n (see Figure 2) and the students were asked to compare and comment upon the two maps. Teacher: The r e a l d i f f e r e n c e (between the two maps) i s , i f you apply a constant 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 apply an i n c r e a s i n g f o r c e , w i l l you get a c c e l e r a t i o n ? Jim: Yeah. Teacher: 5 Yes? In both cases? Jim: Yeah. Teacher: Why? Jim: Because you're s t i l l a p p l y ing a f o r c e . Teacher: So even i f the f o r c e I'm applying i s constant, i t i s s t i l l 10 going t o a c c e l e r a t e ? 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 yesterday (see l i n e s 23 to 25, p. 35) what do you th i n k about that? K e l l y : Yeah, e s p e c i a l l y on the s t a t i o n a r y one. Teacher: 15 So you're going to agree w i t h t h i s too. Even i f the f o r c e i s constant? K e l l y : W e l l , ah (pause), what I don't t h i n k i s (pause) i t ' s the moving o b j e c t , r i g h t , (pause) You s a i d they were doing t h i s 36 Figure 1. A Map of Students' Concepts of A c c e l e r a t i o n f o r c e s are balanced a p p l i e d i n same d i r e c t i o n as motion causes a c c e l e r a t i o n 37 Figure 2. Teacher-constructed Map of Newtonian Concepts of A c c e l e r a t i o n f o r c e s are balanced unbalanced - i . e . net f o r c e > 0 moving obj e c t s i n same d i r e c t i o n as motion and the l a r g e r , constant f o r c e a p p l i e d to s t a t i o n a r y objects causing a c c e l e r a t i o n 38 f o r as long as they wanted to go f o r , r i g h t ? (obtains 20 c o n f i r m a t i o n from the teach e r ) , (pause) I f you pushed 50 N on something f o r ah (pause) l i k e a length of time, i t s f i r s t b i t i s going to a c c e l e r a t e and then stop. Melanie ( i n t e r j e c t i n g ) : I f i t ' s a constant f o r c e , i t w i l l stay constant! Teacher (addressing K e l l y ) : So you f e e l that there i s going to be a point where, even 25 though that f o r c e i s constant, you're going to back o f f to a constant v e l o c i t y a f t e r awhile. K e l l y : Yeah. Teacher: Melanie, you had something to say. Melanie: I f you have a constant f o r c e , then y o u ' l l have a constant 30 v e l o c i t y . Teacher: So you're going back to t h i s theory that we came up w i t h yesterday, that constant f o r c e ends up with constant 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 to come up w i t h a c c e l e r a t i o n . Melanie: 35 Yeah. I t appeared, at t h i s p o i n t , that the students were wedded to the concept t h a t , i f an object was to a c c e l e r a t e continuously, a c o n s t a n t l y i n c r e a s i n g f o r c e would have to be a p p l i e d to that o b j e c t . The union, however, was not without i t s flaws f o r both Jim and K e l l y had suggested that a c c e l e r a t i o n would occur i f a constant f o r c e was a p p l i e d to an obj e c t . Although, i n K e l l y ' s case, q u a l i f i c a t i o n s had been a p p l i e d to the concept. Two demonstrations were presented to the c l a s s i n order to provide them with p h y s i c a l s i t u a t i o n s that would emulate both conceptual schemes. The f i r s t demonstration c o n s i s t e d of an equipment t r o l l e y that was being p u l l e d by a student. The f r i c t i o n on the t r o l l e y had been estimated by measuring the amount of fo r c e r e q u i r e d to j u s t begin the t r o l l e y moving. The f o r c e that the student was applying to the 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 graduated i n newtons. The c l a s s was asked to c l o s e l y observe the motion of the t r o l l e y . 39 Three t r i a l s were made wi t h t h i s equipment. The f i r s t two t r i a l s i n v o l v e d s t a r t i n g the t r o l l e y from a motionless p o s i t i o n and then p u l l i n g i t w i t h (a) a continuously 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. The t h i r d t r i a l i n v o l v e d the a p p l i c a t i o n of a constant f o r c e of 20 N once the t r o l l e y was moving. In a l l cases, the students unanimously agreed that the t r o l l e y a c c e l e r a t e d . The second demonstration i n v o l v e d applying a constant f o r c e of approximately 5 N to a dynamics c a r t using a system of p u l l e y s that allowed a 500 g mass to f a l l under the i n f l u e n c e of g r a v i t y (see Figure 3). Again, the c l a s s unanimously agreed that the a p p l i c a t i o n of t h i s constant f o r c e caused the c a r t to 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 the i n s t r u c t i o n a l s t r a t e g y appeared to have the d e s i r e d e f f e c t s . The i n i t i a l demonstration (of an a c c e l e r a t i n g dynamics c a r t ) and the subsequent d i s c u s s i o n of the cause(s) of t h i s a c c e l e r a t i o n had exposed the students' general conception of a c c e l e r a -t i o n . This was that a c c e l e r a t i o n was caused by a continuously i n c r e a s -i n g f o r c e a p p l i e d i n the same d i r e c t i o n as the i n i t i a l motion. Addi-40 t i o n a l l y , t h i s conception suggested that the m a j o r i t y of students would a l s o adhere to the g e n e r a l i z e d b e l i e f that any form of motion must imply some a p p l i c a t i o n of fo r c e f o r , i f a c c e l e r a t i o n was caused by a continuous 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 uniform motion should l o g i c a l l y be caused by an a p p l i c a t i o n of constant f o r c e . Whether t h i s , i n f a c t , would be the case would have to wait f o r the lessons d e a l i n g w i t h uniform motion. That part of the i n s t r u c t i o n a l s t r a t e g y that was intended to a l t e r the student's g e n e r a l i z e d conception of the dynamics of a c c e l e r a t i o n appeared to proceed f l a w l e s s l y . When faced w i t h e m p i r i c a l evidence from the demonstrations there was unanimous agreement that a c c e l e r a t i o n would be caused the a p p l i c a t i o n of a constant f o r c e a p p l i e d i n the same d i r e c t i o n as the i n i t i a l motion. What was d i s t u r b i n g about t h i s event was that the conversion from the f i r s t b e l i e f s t r u c t u r e to the second appeared to occur without any form of mental dissonance on the part of the students. Considering the v o c i f e r o u s disagreement that had r e s u l t e d from K e l l y ' s o r i g i n a l suggestion that a c c e l e r a t i o n was a r e s u l t of the a p p l i c a t i o n of a constant f o r c e (see l i n e s 23 through 25, p. 35), i t was d i f f i c u l t to b e l i e v e that the students 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 conceptual 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 that the demonstrations had convinced the students that the minimum c o n d i t i o n necessary f o r a c c e l e r a t i o n to occur was an a p p l i c a -t i o n of a constant f o r c e and that t h e i r o r i g i n a l conception was a subset of t h i s , or were these two conceptual s t r u c t u r e s now co e x i s t e n t i n the minds of the students and context s e n s i t i v e ? One s t r u c t u r e , a c c e l e r a t i o n r e q u i r e s a continuously i n c r e a s i n g f o r c e , to be used f o r e x p e r i e n t i a l / r e a l world circumstances, and the other, a c c e l e r a t i o n only r e q u i r e s a constant a p p l i c a t i o n of f o r c e , to be used f o r t h e i r science 41 c l a s s . The r e s o l u t i o n of the p o s s i b l e i n t e r p r e t a t i o n s had to wait u n t i l the cl 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 . 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 to the motion of a car i f the f o r c e s u p p l i e d to the d r i v e wheels was reduced by h a l f while keeping the f r i c t i o n a l f o r c e s constant (but l e s s than the f o r c e s u p p l i e d by the d r i v e wheels), the question was posed - how could you get t h i s car to begin to slow down. In other words, under what c o n d i t i o n s would the car decelerate? 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 to a diagram of a c a r , on the board, w i t h the f o r c e from the d r i v i n g wheels being l a r g e r than the f r i c t i o n a l f o r c e ) , how do you get de c e l e r a -t i o n ? How do you get the car to slow down? K e l l y : 5 Make the f r i c t i o n l a r g e r than the f o r c e . (Teacher draws another diagram of a car on the blackboard and r e i t e r -ates the question.) Teacher: How do you get d e c e l e r a t i o n ? You want to slow t h i s guy down. Jim: Decrease your push f o r c e . Teacher: How much are you going to decrease i t ? I f I was going to draw a push forc e up here ( r e f e r r i n g to the diagram) would i t 10 be sm a l l e r than t h i s ( r e f e r r i n g to the f r i c t i o n a l f o r c e ) , l a r g e r than t h i s , or the same s i z e ? Jim: I t ' s going to be l a r g e r . Teacher: I t ' s going to be l a r g e r . Any other ideas? Dina: ( i n a u d i b l e ) . . . i t ' l l be sm a l l e r so that f r i c t i o n w i l l 15 slow i t down. Teacher: Why does i t have to be smaller? 42 Dina: So that the f r i c t i o n overpowers the push f o r c e . Teacher: Jim, what do you t h i n k about that? Jim: ( i n a u d i b l e ) . . . i t w i l l stop i t . Teacher: 20 I f I draw t h i s arrow up here ( r e f e r r i n g to the push fo r c e ) to be l a r g e r than the f r i c t i o n a l f o r c e , am I going to end up wi 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 to the a c c e l e r a t i o n diagram)? Jim: Yeah. Teacher: 25 Am I s t i l l going to 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 constant speed . . . ( i n a u d i b l e ) . . . y o u ' r e not going to 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 concepts of the 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 that d e c e l e r -r a t i o n occurs when the f r i c t i o n a l (or opposing) fo r c e s on an object become l a r g e r than the motive f o r c e , whereas Jim f e e l s that d e c e l e r -a t i o n occurs when the motive f o r c e decreases i n magnitude, but s t i l l remains l a r g e r than the f r i c t i o n a l f o r c e s . K e l l y ' s and Dina's idea that the net force on the object must be i n the opposite d i r e c t i o n r e l a t i v e to an object's motion i s a l o g i c a l extension of the conclu-s i o n s , p r e v i o u s l y a r r i v e d at by the students, concerning the cause of a c c e l e r a t i o n . Jim's i d e a , on the other hand, i s i n d i r e c t c o n t r a d i c -t i o n w i t h these conclusions but i n keeping w i t h the 'motion i m p l i e s a fo 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, Jim apparently doesn't see any c o n t r a d i c t i o n between the p o s i t i o n he has taken on d e c e l e r a t i o n and h i s previous statements on a c c e l e r a t i o n (see l i n e s 1 through 11, p. 36). Jim i s r e s o l u t e i n h i s b e l i e f and suggests that K e l l y ' s and Dina's concept w i l l cause the object to stop. When asked to r e c o n c i l e h i s concept w i t h the agreed upon f o r c e diagram of a c c e l e r a t i o n Jim f u r t h e r suggests that a red u c t i o n of the motive forc e . 4 3 ( a l b e i t , keeping the net fo r c e i n the same d i r e c t i o n as the 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 not stop the obj e c t . Jim's b e l i e f appears to be a c o n s i s t e n t subset of the concept that 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 . I f an ever i n c r e a s i n g f o r c e i s replaced by a decreasing f o r c e s u r e l y d e c e l e r a t i o n must r e s u l t . The robustness of t h i s b e l i e f suggests that Jim i s basing h i s concept on perso n a l , e x p e r i e n t i a l evidence. This type of evidence could be c o l l e c t e d while d r i v i n g a car. I f the car was a c c e l e r a t i n g and the gas pedal was then s l i g h t l y released (the motive f o r c e was reduced) the r a t e of a c c e l e r a t i o n would decrease. This decrease 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 the motive forc e s t i l l being a p p l i e d i n the d i r e c t i o n of motion. The r e s t of the c l a s s had, so f a r , not entered i n t o the debate on the p o s s i b l e causes of d e c e l e r a t i o n . In order to e l i c i t any f u r t h e r ideas or arguments, both concepts, regarding a c c e l e r a t i o n , were r e s t a t e d and the students' opinions were s o l i c i t e d . Jody: The push f o r c e i s going to be l a r g e r (than the f r i c t i o n a l f o r ce) but sma l l e r than i t was before. (Teacher draws a diagram of a car on the blackboard, next t o the diagram that the c l a s s has agreed represents a c c e l e r a t i o n , w i t h the motive f o r c e reduced i n magnitude but s t i l l l a r g e r than the f r i c t i o n a l f o r c e.) Teacher: 30 There's the push f o r c e . Is i t l a r g e r than the f r i c t i o n a l force? Is the net fo r c e s t i l l i n the same d i r e c t i o n of the motion? The question i s - i s that ( p o i n t i n g to the new diagram) going to have the same e f f e c t as t h i s ( p o i n t i n g to the a c c e l e r a t i o n diagram)? This 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 to the a c c e l e r a t i o n diagram). What does t h i s ( p o i n t i n g to the new diagram) r e s u l t in? Jim: D e c e l e r a t i o n and then a c c e l e r a t i o n . Teacher: Any other ideas? 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 40 t h i s and slo w l y slow i t down (Jim demonstrates with h i s pen on the lab bench) and you're s t i l l moving; so, you took o f f some of the push f o r c e but you don't stop i t . Teacher: Suppose I took t h i s push f o r c e and I shortened i t up (makes the m o d i f i c a t i o n to the diagram). I made i t smaller than the 45 f r i c t i o n a l f o r c e . (At t h i s p o i n t , a number of u n i d e n t i f i e d students volunteered answers to the question that hadn't yet been asked. They suggested that the car would (a) stop, or (b) dec e l e r a t e . ) K e l l y : I t s going to d e c e l e r a t e . The f r i c t i o n f o r c e becomes stronger than the push f o r c e and then, sooner or l a t e r , i t s going to stop i f you keep i t at t h a t , and i t s going to stop and i t w i l l be a balanced f o r c e . . . ( i n a u d i b l e ) . . . a f t e r i t stops. Teacher: 50 I n t e r e s t i n g ! Why do you t h i n k that i s going to occur? K e l l y : Because the push f o r c e i s l e s s than the f r i c t i o n f o r c e and (pause) unless (pause) i f i t ' s going along a l e v e l road i t can't keep i t s motion up. Jim: Urn, I t h i n k that i f you weren't moving there wouldn't be 55 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 to zero. Teacher: So, the slower you are moving, the l e s s w i l l be the f r i c t i o n f o r c e . Jim: Yeah. Teacher: 60 I j u s t want to get back to something that K e l l y s a i d a minute ago. Ah (pause) she s a i d that t h i s ( p o i n t i n g to diagram i n which the motive f o r c e i s l e s s than the f r i c t i o n a l f o rce) i s going to 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 going on, t h i s i s going to stop and reverse i t s d i r e c t i o n . 65 Is that c o r r e c t ? K e l l y : Reverse i t s d i r e c t i o n ? No! I t w i l l j u s t stop! 45 Teacher: In t h i s s i t u a t i o n ( r e f e r r i n g to the previous diagram), what i s the d i r e c t i o n of the net force going to be? Jim: What do I think? Teacher: 70 No, what i s i t going to be? The way i t ' s drawn r i g h t now. Tawnia: I t ' l l be one way f o r awhile then, when i t s t a r t s d e c e l e r a t i n g (pauses). Teacher: Let's put some numbers on t h i s . This might help you. Let's say that the f r i c t i o n , i n t h i s case, i s 100 N. The push 75 f o r c e from the wheels i s 50 N. What i s the a c t u a l s i z e of the net force going to be? K e l l y : 50 N. Teacher: OK. 50 N. Which d i r e c t i o n i s i t going to be i n ? Many students: L e f t to r i g h t ! Teacher: 80 Going that way ( i n d i c a t i n g a d i r e c t i o n opposite to the motion d i r e c t i o n ) . Many students: Yeah! Another student: Opposite to the d i r e c t i o n . Teacher: So the net fo r c e i s 50 N, and i t i s i n that d i r e c t i o n (makes 85 adjustment to diagram on the blackboard). Now, you've got two competing p o s s i b i l i t i e s here. E i t h e r t h i s ( p o i n t i n g to the diagram w i t h the net fo r c e a p p l i e d i n the opposite d i r e c t i o n to the motion d i r e c t i o n ) causes d e c e l e r a t i o n or, the other s i t u a t i o n , which had the push forc e being l a r g e r 90 (than the f r i c t i o n a l f o rce) causes d e c e l e r a t i o n . Tawnia: How could that ( r e f e r r i n g to the l a t t e r case) cause d e c e l e r a t i o n ? Teacher: W e l l , t h a t ' s what we're going to t e s t out. Jim: W e l l , f r i c t i o n can't be stronger than the push f o r c e because 95 e v e r y t h i n g . . . ( i n a u d i b l e ) . Teacher: Brad, 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 the push forc e because, when you put your foot on the brake i t stops because of f r i c t i o n . Teacher: OK. Tawnia, then C a r l a . Tawnia: 100 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 the push f o r c e being l a r g e r (than the f r i c t i o n a l f o r c e s ) . Does that work by when (pause) the fo r c e i s a p p l i e d but 46 i t i s not constant. I mean, you have to have a constant f o r c e to keep i t a c c e l e r a t i n g but, i f you j u s t have a 105 push f o r c e l a r g e r t h a t ' s not constant then you're going 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 sm a l l e r and then l a r g e r and smaller? Tawnia: I f i t ' s constant i t ' s going to stay (pause), i t ' s going 110 to a c c e l e r a t e but, i f i t ' s not constant i t ' s going to eventu-a l l y d e c e l e r a t e . Teacher: What I'm i n t e r e s t e d i n i s what you mean by 'not constant'? Tawnia: Um, OK. When you j u s t push something and you j u s t l e t i t go. Is that what you mean by the push forc e being l a r g e r because 115 i t ' s not a constant f o r c e but i t i s going to d e c e l e r a t e . Teacher: See, i n that case, when you l e t i t go, I would say that there i s no push f o r c e on i t at a l l . Tawnia: Then how can i t d e c e l e r a t e i f a constant f o r c e i s a p p l i e d to i t , w i t h the push f o r c e being l a r g e r ? Teacher: 120 The push forc e being l a r g e r Tawnia ( i n t e r j e c t i n g ) : and a constant f o r c e , how can i t decelerate? Teacher: That's my quest i o n ! Tawnia: You s a i d that we were going to t e s t that out. Teacher: That's r i g h t . Tawnia: 125 But that can't happen! Jim i s not without supporters i n the c l a s s . Jody, f o r one, appears to agree w i t h Jim's conception that d e c e l e r a t i o n r e q u i r e s a redu c t i o n i n the motive forc e while s t i l l keeping i t l a r g e r than any opposing fo r c e s (see l i n e s 28 and 29, p. 44). In a d d i t i o n , some other students agree w i t h Jim's idea t h a t , i f the motive forc e becomes l e s s than the opposing f o r c e s , an object w i l l stop moving. K e l l y and Dina a l s o f i n d support w i t h i n the c l a s s . Tawnia, i n an attempt to r a t i o n a l i z e her acceptance of the idea that a c c e l e r a t i o n i s achieved through an a p p l i c a t i o n of constant f o r c e , p o i n t s out the 47 l o g i c a l i n c o n s i s t e n c y of Jim's argument (see 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 that a c c e l e r a t i o n can occur during those times when the net force i s opposite to the d i r e c t i o n of motion - "But that can't happen!". What i s n ' t c l e a r at t h i s stage i s , which of these two views represents a m a j o r i t y p o s i t i o n w i t h i n the c l a s s . In order to c r y s t a l -l i z e the debate, the students were presented w i t h another hallway demonstration. As with the a c c e l e r a t i o n demonstration, an equipment t r o l l e y was used as the moving object w i t h the forces being s u p p l i e d by the students. This demonstration began with a r e c r e a t i o n of the 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 student began p u l l i n g i t w i t h a constant f o r c e of approximately 20 N. When i t was c l e a r that the 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 the opposite d i r e c t i o n , w i t h f o r c e of approximately 20 N. This retrograde f o r c e , when combined with the f r i c t i o n a l f o r c e of approximately 8 N, provided a net f o r c e of 8 N a p p l i e d i n the opposite d i r e c t i o n to the i n i t i a l motion (see Figure 4). When asked to describe the type of motion that 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 of students agreed that the t r o l l e y d ecelerated. The c l a s s ended w i t h t h i s demonstration and any f u r t h e r d i s c u s s i o n was deferred to the next c l a s s . The next c l a s s began with a diagram of the previous demonstration (see Figure 4). The students were then asked to comment on the type of motion that r e s u l t e d from the 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 that t r o l l e y e x h i b i t at that point? Cindy: D e c e l e r a t i o n . 48 F i g u r e 4 . D e c e l e r a t i o n D e n o n s t r a t i o n # 1 < i n i t i a l d i r e c t i o n o f n o t i o n p u l l f o r c e ^^^^ p u l l f o r c e ( 2 8 N ) ( 2 0 H ) — • f r i c t i o n ( 8 N ) Teacher: Now, before we go any f u r t h e r , i s there any disagreement on the observation? Did everyone see that ( r e f e r r i n g to the 5 t r o l l e y ) d e c e l e r a t i n g or, d i d anyone e l s e see one of the other of the two other types of motion - 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: Well,ah, (pause) i t was d e c e l e r a t i n g but, 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 at a constant v e l o c i t y . Teacher: 10 OK. So you saw i t d e c e l e r a t i n g and, then 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 didn't go long enough. I t was s t a r t i n g at the end. Teacher: So, i f we had allowed i t to go longer, you t h i n k i t would 15 have s t a r t e d to t r a v e l w i t h a constant v e l o c i t y . So do you agree w i t h Cindy, w i t h the f i r s t p a r t , that there 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 other observations? In the face of dwindling peer support and e m p i r i c a l evidence to the c o n t r a r y , Jim 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 to h i s theory 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 that decelerated motion 49 was a f u n c t i o n of a reduced motive f o r c e , however, the net f o r c e s t i l l remained i n the same d i r e c t i o n as motion. A d d i t i o n a l l y , t h i s f o r c e s i t u a t i o n would not, 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 of motion but, r a t h e r , some form of forward motion would s t i l l be i n e f f e c t . A f t e r t h i s demonstration, he has now grudgingly adopted the p o s i t i o n that d e c e l e r a t i o n i s a r e s u l t of the net fo r c e opposing the o r i g i n a l d i r e c t i o n of motion. However, he i s not w i l l i n g to completely abandon hi s previous i n t e r p r e t a t i o n a l frame. He f i n i s h e s t h i s d i s c u s s i o n of d e c e l e r a t i o n by suggesting t h a t , under these new set of c o n d i t i o n s , uniform motion w i l l be the r e s u l t when the 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 pressed on t h i s observation he equivocates, but s t r o n g l y suggests that the demonstration wasn't allowed t o continue to i t s l o g i c a l end. The c l a s s consensus appeared to favour the concept that d e c e l e r -a t i o n occurred when the net fo r c e was i n the opposite d i r e c t i o n to the motion of an ob j e c t . This consensus appeared ra t h e r v i g o r o u s l y during the next demonstration. This demonstration was a v a r i a t i o n on the second a c c e l e r a t i o n demonstration (see Figure 3). In t h i s case, however, a mass had been added i n such a way that a net fo r c e was a p p l i e d i n the opposite d i r e c t i o n to the c a r t ' s motion (see Figure 5). When asked to p r e d i c t what type of motion would be d i s p l a y e d by the c a r t under these condi-t i o n s , a number of students r e p l i e d , w i t h some i n d i g n a t i o n , that the c a r t must d e c e l e r a t e . A f t e r the demonstration concluded, these same students suggested (with an 'I t o l d you so' a i r ) that 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 these c o n d i t i o n s and that f u r t h e r demonstrations were p o i n t l e s s . 50 Figure 5. Deceleration Dertonstration #2 roof nass gravity f r i c t i o n i n i t i a l direction of notion-Note: nass 1 < nass 2 nass 2 gravity mi r 4 An episode occurred towards the end of t h i s c l a s s , however, that i l l u s t r a t e d how 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 students understand-i n g of d e c e l e r a t i o n dynamics r e a l l y was and how c l o s e to the surface the concept of 'motion i m p l i e s a f o r c e 1 e x i s t e d . 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 students had been assigned a d e c e l e r a t i o n worksheet which was to be due f o r t h i s c l a s s . The questions on t h i s worksheet were discussed a f t e r the f i n a l d e c e l e r a t i o n demonstration and, w i t h the exception of the f i n a l problem, appeared to present few d i f f i c u l t i e s to the students. The f i n a l problem (shown below as Figure 6) was a d i f f e r e n t matter. Teacher: What are the f o r c e s a c t i n g on that b a l l K a r i ? K a r i : G r a v i t y . Teacher: Is that the only force? K a r i : No. Teacher: 5 Is there another force? K a r i : F r i c t i o n . Teacher: The d i r e c t i o n that g r a v i t y i s operating i n K a r i ? 51 Figure 6. The Final Deceleration Problen A baseball player has Just h i t a foul ball. The b a l l is travelling vertically upwards. On the diagram below, draw the Force (or Forces) that are acting on the b a l l and which are parallel to the direction of notion. In addition, describe how the b a l l is Rowing i.e. is i t accelerating, decelerating, or travelling with a constant 1 speed? K a r i : Um, down. Teacher: The d i r e c t i o n that f r i c t i o n i s operating i n ? K a r i : 10 In the opposite (pause) as g r a v i t y . Teacher: G r a v i t y i s operating down, the b a l l i s going 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 ? K a r i : Oh, the b a l l i s going up. Down. Teacher: OK. F r i c t i o n i s operating i n that d i r e c t i o n . Can I 15 s i m p l i f y t h i s diagram any r i g h t now? 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 provided a c o r r e c t f o r c e a n a l y s i s of the 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 re c o g n i z i n g that m u l t i p l e f o r c e s operating i n the 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 (see Figure 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 that K a r i (and other students) subsequently s t r i p p e d o f f to reveal an e x p e r i e n t i a l core based upon Impetus Theory. K a r i : 52 F i g u r e 7 . K a r i ' s F o r c e A n a l y s i s f r i c t i o n 4 f r i c t i o n + g r a v i t y Teacher: Ok, so we have a net fo r c e downward? K a r i : Yeah. Teacher: Does everybody see what I'm doing with t h a t . Just combining 20 the two because they're i n the same d i r e c t i o n . Another student: What about the push force? Teacher: OK. Just hang on. (The teacher makes the necessary a d j u s t -ments to the diagram on the blackboard.) OK, K a r i , any other forces on there? K a r i : 25 Yeah. The push f o r c e going up. Teacher: What push force? K a r i : Urn, urn, from the b a l l . Teacher: Is there anything pushing the b a l l ? Another student: The bat! Teacher: 30 The bat i s down here ( i n d i c a t i n g a region below the black-board). At t h i s p o i n t , the c l a s s became very a g i t a t e d and many students attempted to provide an answer to t h i s problem. 53 Teacher: Hold i t ! Now wait a minute! Wait a minute! I ' l l get too each of you, one at a time. Melody: Mr. Brace! L i s t e n to t h i s ! (Melody begins to read out the 35 problem, but slo w l y t r a i l s o f f and stops before f i n i s h i n g i t . ) Teacher: Has the b a l l l e f t the bat? Many students ( i n c l u d i n g Melody): Yeah. Teacher: Are there any other forces on the b a l l ? Melody: 40 No, there are no other f o r c e s . Just the forces going downward. Teacher: M i c h e l l e . M i c h e l l e : A push f o r c e . Teacher: Where i s the push f o r c e coming from? Melody ( i n t e r j e c t i n g ) : 45 Well what are you going to c a l l the f o r c e ( d i r e c t e d at M i c h e l l e ) ? Teacher: Hold i t . Wait a minute. Is there a contact f o r c e i n v o l v e d here? Another student: Yeah, there was. Teacher: 50 You're saying there i s a contact force? Another student: Was! There was! Teacher: Past tense? Is that contact f o r c e s t i l l there? Many students: No! M i c h e l l e : The push f o r c e i s s t i l l t here, but the contact i s n ' t . Teacher: 55 Now wait a minute. How can you have a push f o r c e without a contact? Brad: As the soon as the b a l l l e f t the bat, the f o r c e , urn, there was no more f o r c e and the b a l l immediately s t a r t e d to de c e l e r a t e . Teacher: 60 So you're saying at t h i s p o i n t there are no other forces on here ( r e f e r r i n g to Figure 6)? We have a motion going upwards, and the only forces are g r a v i t y and f r i c t i o n o perating downward. Another student: Then how can i t be going upwards? 54 Another student: 65 That's impossible! B a l l s being batted or thrown i n t o the a i r have been common, childhood experiences f o r the m a j o r i t y , i f not a l l , of these students. I t i s c l e a r from the debate that has taken place that almost a l l of these students have constructed an explanation f o r the upwards movement of objects (under these c o n d i t i o n s ) that 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 suggests that i t i s almost i n c o n c e i v a b l e to them that some object could move upwards against the combined forces of g r a v i t y and f l u i d f r i c t i o n without some k i n d of f o r c e to p u s h . i t . This e x p e r i e n t i a l l y constructed explanation i s so concrete to these students that they appear to not have heard and/or accepted the force and motion a n a l y s i s of t h i s system but, i n s t e a d , have immediately opted f o r t h e i r own i n t e r n a l presumption of the dynamics of the system. Only Brad appears to have heard the i n i t i a l 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. Aside from t h i s one comment, however, he d i d not enter i n t o the debate that continued to rage around him. Teacher: Hold i t ! Wait! Wait! C a r l a you were next. We're going to go C a r l a , K e l l y , and then back to you guys. C a r l a : ( i n a u d i b l e ) when you s l o w l y press on the brakes i t ' l l s l o w l y go to a stop. When the bat h i t s the b a l l , the b a l l w i l l go 70 up and s l o w l y (pause), e v e n t u a l l y ( i n a u d i b l e ) . Teacher: So you agree that there i s d e c e l e r a t i o n . C a r l a : Yeah. Teacher: Do you agree w i t h t h i s type of diagram, that the only forces operating on here are g r a v i t y and f r i c t i o n and they 75 operate as a net f o r c e v e r t i c a l l y downward? 55 C a r l a : ( i n a u d i b l e ) Yeah. Teacher: OK. K e l l y . K e l l y : The b a l l moving i s the end r e s u l t of the contact f o r c e . I don't know what you c a l l that though. What do you (pause). 80 You t e l l us. Is there a name f o r a force a f t e r the contact force? The b a l l ' s s t i l l moving. The b a l l ' s going i s the end r e s u l t of the contact f o r c e . But the contact f o r c e i s over w i t h but i t s not going ( i n a u d i b l e ) . Teacher: What has been the r e s u l t of the contact force? Let's t r y and 85 (pause). K e l l y : The motion of the b a l l upwards. Teacher: OK. So th a t ' s taken care of r i g h t here ( r e f e r r i n g to the diagram), and your p o s i t i o n r i g h t now i s that there i s no longer any contact f o r c e . That has been t r a n s l a t e d i n t o a 90 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 the net f o r c e opposing the d i r e c t i o n of motion) i n so f a r as the other forces? K e l l y : Yeah. Teacher: OK. A couple of more p o i n t s . Tawnia. Tawnia: 95 When the b a l l leaves the bat there's a contact f o r c e . I t s j u s t l i k e pushing and p u l l i n g down the hallway ( r e f e r r i n g to the hallway demonstrations). You l e t i t go and i t j u s t keeps going and the f r i c t i o n acts on i t and i t d e c e l e r a t e s . I t s going to happen w i t h the b a l l . There was a contact f o r c e . 100 I t ' l l move because of the contact f o r c e and i t w i l l slow down because of f r i c t i o n . So the only f o r c e s that were a c t i n g on i t was the contact f o r c e , at the beginning, then the f r i c t i o n a cts on i t r i g h t away. And a f t e r the contact f o r c e there i s only a f r i c t i o n f o r c e . ,. Teacher: i05 Is g r a v i t y operating on there or not? Tawnia: Yeah. Teacher: OK. So you want to i n c l u d e g r a v i t y . OK, you guys. K a r i : I don't understand. I f there's no force now how come i t s s t i l l going upwards? I t w i l l e v e n t u a l l y go down but there 110 s t i l l has to be some s o r t of f o r c e on i t to make i t continue to go upwards. Teacher: Can you come up w i t h some place where there i s an upwards force on the b a l l ? Are there any f i e l d f orces or contact f o r c e s pushing upwards? K a r i : 115 Not at the moment. 56 Melody: What are you going to c a l l i t ? There has to be some force pushing i t up. Teacher: Why does there have to be a force? Melody: I t wouldn't move anywhere! K a r i : 120 Don't forces cause motion? Teacher: D e f i n i t e l y ! K a r i , Melody, and Tannis ( t o g e t h e r ) : W e l l , i t s moving! K e l l y ( i n t e r j e c t i n g ) : W e l l , there was a f o r c e . There was a contact f o r c e that caused the motion ( i n a u d i b l e ) . K a r i : 125 I know t h a t ! Teacher: K e l l y I want you to e x p l a i n that p o s i t i o n to those guys. K a r i and Tannis: We know t h a t ! Melody: What are you going to c a l l i t ? K a r i : Say that you were t o l d that there was f r i c t i o n f o r c e and 130 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 that i t was going down. But no i t s not, i t s s t i l l going up! Teacher: Remember what you s a i d before about the i n i t i a l motion. Now once you s t a r t the i n i t i a l motion and then apply a f o r c e i n the opposite d i r e c t i o n what type of motion do you come up 135 with? A student: D e c e l e r a t i o n . Teacher: OK, l e t ' s f o l l o w t h i s r i g h t through to the end. Melody: I t s d e c e l e r a t i n g when i t s going up. K a r i : I understand i t S i r . I'm j u s t saying what do you c a l l i t . Teacher: 140 I know. I'm t r y i n g to stay away from the l a b e l f o r a minute. I want to go r i g h t through t h i s process. Melody: Then we understand i t . In so f a r as t h i s context i s concerned, the '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, are f i r m l y en-trenched i n these students. Only Tawnia (see l i n e s 95 through 106, p. 56) and Brad (see l i n e s 57 to 59, p. 54) appear to have analyzed the 57 s i t u a t i o n i n the l i g h t of the previous demonstrations and lessons, and can accept that there can be motion without a continuous motive f o r c e . For the remainder of the students who took part i n t h i s debate however, i f a b a l l i s moving upwards there must be some force pushing i t upwards. These students do, however, appear to be w r e s t l i n g w i t h an i n t e r e s t i n g dichotomy. On the one hand there i s t h e i r almost unshak-able b e l i e f that motion i s d i r e c t l y t i e d to a continuous motive f o r c e . While on the other hand they have been provided w i t h e m p i r i c a l evidence that a p p l i e d , net for c e s can be operating i n the opposite d i r e c t i o n to the motion of an obj e c t . Compounding t h i s paradoxical s i t u a t i o n i s the r e a l i z a t i o n (among some of the students) that they have stumbled i n t o a l o g i c a l t r a p . They have agreed w i t h the a n a l y s i s of the forces a c t i n g on the b a l l but now must f i n d some other phantom force to b u t t r e s s t h e i r contention t h a t , i n t h i s case, the b a l l can only move upwards i f there i s a f o r c e pushing i t upwards. Th e i r c r i e s f o r help i n r e s o l v i n g t h i s c o n f l i c t are c l e a r throughout the l a t t e r stages of t h i s debate. K e l l y ( l i n e s 78 through 83, p. 56), Melody ( l i n e s 116 and 128, p. 57), and K a r i ( l i n e 139, p. 57) a l l ask f o r a name f o r the fo r c e that they assume i s causing the motion of the b a l l . I t s as i f a name, provided by the teacher, would provide them with a warrant that 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 theory concerning the upward motion of the b a l l . When that name i s not forthcoming, c l o s u r e to the debate i s provided by Melody (see l i n e 142, p. 57) who appears to be g i v i n g n o t i c e that she i s now prepared to play the school game. The game, i n t h i s case, i s that there are ' r i g h t ' answers to school questions, but the r e a l answers are to be found elsewhere. 58 The Dynamics of Uniform Motion The emergence of the 'motion i m p l i e s a f o r c e ' b e l i e f as the predominant conceptual 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 d e c e l e r -a t i o n d i d not provide an auspicious entrance to a study of uniform motion. The 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 study had been to u t i l i z e the students' a p p r e c i a t i o n of Newtonian concepts 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 against the emergence of the 'motion i m p l i e s a f o r c e ' b e l i e f during the d i s c u s s i o n s concern-in g uniform motion. The premature (from an i n s t r u c t i o n a l point of view) appearance of t h i s s t r u c t u r e however, tended to throw t h i s s t r a t e g y i n t o d i s a r r a y . A f t e r a number of attempts to redesign the s t r a t e g y to f i t t h i s new environment, i t was decided to r e t a i n the 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 . This m o d i f i c a t i o n i n v o l v e d an attempt to r e i n f o r c e the Newtonian concepts of a c c e l e r a t i o n / d e c e l e r a -t i o n (and by doing so, deemphasize the 'motion i m p l i e s a f o r c e ' frame) by engaging the c l a s s i n an extension of t h e i r e x i s t i n g a c c e l e r a t i o n concept map to i n c l u d e the d e c e l e r a t i o n concepts. Student d i s c u s s i o n leading up to and during the redesign of the a c c e l e r a t i o n concept map was perfunctory. I t was as i f the debate i n the previous c l a s s had never occurred, and i t was an i n s u l t to t h e i r i n t e l l i g e n c e to be d i s c u s s i n g , again, a set of concepts that was so s e l f - e v i d e n t . The redesign of the a c c e l e r a t i o n concept map (see Figure 8) was achieved 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 uniform motion began with a d e f i n i t i o n - uniform motion i s t r a v e l l i n g w i t h a constant speed. Again the v e c t o r i a l component of t h i s concept was ignored due to age and lack of mathemat-i c a l s o p h i s t i c a t i o n of these students. The students were then asked f o r 59 Figure 8. Redesigned Concept Map of Acceleration and Deceleration forces are balanced unbalanced - i .e . net force > 0 and the larger, constant force i s applied to moving objects stationary objects i n opposite direction as motion same direction as motion causing causing deceleration acceleration 60 t h e i r ideas concerning what set of c o n d i t i o n s could r e s u l t i n an object t r a v e l l i n g w i t h a constant speed. Dina: When a constant f o r c e i s a p p l i e d . I t was pointed out that t h i s s i t u a t i o n , according to the concept map that the students 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 that the f o r c e was being a p p l i e d i n . Again the question was posed. K a r i : A d e c e l e r a t i n g f o r c e . Teacher: You mean i t s g e t t i n g s m a l l e r and smaller and smaller? ( K a r i nods her head i n agreement). W e l l , i f one f o r c e (the l a r g e r 5 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 to the net force? Brad: I t becomes equal. Teacher: U l t i m a t e l y i t w i l l become equal. Equal to what? Brad: ( i n a u d i b l e ) a car won't dece l e r a t e or a c c e l e r a t e . I t 10 w i l l j u s t stay at one speed. Teacher: OK, but i f you have one f o r c e here and one f o r c e there, and they're are both the same what's the net force? Many students: Zero. Teacher: Is that going to cause uniform motion? Brad: 15 Yes. Teacher: So you f e e l that i f the net f o r c e i s equal to zero then y o u ' l l end up w i t h uniform motion. (Brad nods h i s head i n agreement.) So what your saying then i s that i f there i s no f o r c e , no net f o r c e operating on an object (pause). Brad: 20 W e l l , there was. Now there i s n ' t , so i t stays at the same speed. Teacher: So i f i t t r a v e l s at a constant speed net f o r c e i s zero. 61 Brad has e x h i b i t e d a high 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 analogic reasoning to a r r i v e at h i s c o n c l u s i o n concerning the dynamics of uniform motion. Whether h i s s o l u t i o n i s pervasive among or accept-able to the r e s t of the c l a s s remains to be seen. K a r i : I don't b e l i e v e t h a t . I f you have balanced forces then i t won't be moving. Teacher: 25 OK. Why do you t h i n k i t won't be moving? K a r i : Because i t has an equal amount of f o r c e pushing against each other. I f they're the same s t r e n g t h they're not going to push each other. Teacher: Brad, you were p r e t t y d e f i n i t e that they were not going 30 to move ( s i c ) . Why not? Brad: I s a i d i t was gonna - i t won't dec e l e r a t e or a c c e l e r a t e . I t has to a c c e l e r a t e before uniform motion and then the forces w i l l balance out and stay at uniform speed. Teacher: Are you two t a l k i n g about the same set of c o n d i t i o n s ? 35 When you're t a k i n g about t r a v e l l i n g w i t h uniform motion, that object that's going to be t r a v e l l i n g w i t h uniform motion, was i t moving to begin w i t h or was i t stopped to begin with? Brad: I t would be moving to begin w i t h . Teacher: 40 Then your p o s i t i o n i s then that i f you take a moving object and you apply balanced forces to i t then you end up w i t h uniform motion. Brad: Yes. Teacher: K a r i was your object K a r i ( i n t e r j e c t i n g ) : 45 S t i l l . Teacher: I t was s t i l l to begin w i t h . So we have a d i f f e r e n t set of c o n d i t i o n s . K a r i : But I t h i n k i f we have balanced forces i t ' l l d e c e l e r a t e . Teacher: Why w i l l i t decelerate? K a r i : 50 Because the forces are equal and they're, I don't know, they're going to want to stop. Brad: They're not going to stop. 62 Tawnia: That's r i g h t (apparently agreeing w i t h K a r i ) . Teacher: So, i n essence, what you're saying i s that there i s a 55 requirement f o r a constant f o r c e to keep something moving. Is there a problem w i t h t h i s then ( r e f e r r i n g to the concept map)? In t h i s case i t appears that a constant 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 or d e c e l e r a t i o n . K a r i : Maybe I don't b e l i e v e i n uniform motion then. Teacher: 60 Brad d i d you want to say something. Brad: W e l l , when an object moves w i t h uniform motion i t can't speed up or i t can't slow down so there are no for c e s ( i n a u d i b l e ) to speed i t up or slow i t down. Brad i s apparently 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 the c l a s s i n so f a r as h i s ex p l a n a t i o n of the causes of uniform motion. K a r i , Dina, and Tawnia represent the (supposed) m a j o r i t y view that a n u l l net forc e c o n d i t i o n does not c o n t r i b u t e to uniform motion and, by i n f e r e n c e , i f there i s motion (uniform or otherwise) there must be a dominant f o r c e present. In an attempt to break the hold that the 'motion i m p l i e s a f o r c e ' b e l i e f had over the c l a s s a demonstration was presented. This demon-s t r a t i o n was given i n two p a r t s . The f i r s t part of the demonstration was designed to demonstrate the e f f e c t of balanced f o r c e s on a s t a t i o n a r y object - 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 the students were able to cor-r e c t l y p r e d i c t and accept the outcome of t h i s event. The second part of the demonstration was designed to demonstrate the e f f e c t of balanced f o r c e s on a moving o b j e c t , again an equipment t r o l l e y . In t h i s case the 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 student and then a second student s u p p l i e d an equal f o r c e i n the opposite d i r e c t i o n . Before the demonstration began the students were asked to p r e d i c t the motion of the t r o l l e y when only one student was 63 p u l l i n g i t . A l l of those students that r e p l i e d i n d i c a t e d that the t r o l l e y should a c c e l e r a t e . A f t e r a number of p r a c t i c e attempts to f a m i l i a r i z e the students who were supplying the forces w i t h what was expected of them, and to ensure that the t r o l l e y would f o l l o w a s t r a i g h t path, the c l a s s was asked to c l o s e l y observe the motion of the t r o l l e y a f t e r the second, equal but opposing f o r c e had been a p p l i e d . Teacher: Heinzy, what type of motion d i d you t h i n k i t was t r a v e l l i n g 65 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 lying the f o r c e i n the opposite d i r e c t i o n . Heinzy: I t slowed down. Teacher: As i t moved that way towards the camera d i d i t continue to get slower and slower? Heinzy: 70 I t stopped at one point and stayed at that p o i n t . Teacher: I'm sor r y ? Heinzy: Or, i t kept at a constant speed. Teacher: So there was a p e r i o d where i t appeared to slow down and then i t t r a v e l l e d w i t h a constant speed. Heinzy: 75 Yeah. Teacher: Steve, what do you think? You f e l t i t slowed down f i r s t and then (pause) Steve: kept going at the same speed. Teacher: K a r i ? K a r i : 80 Yup. Uniform motion. The c l a s s was almost at an end. I t had been a c l a s s that had s i n g u l a r l y lacked the energy and v i t a l i t y that had been so evident 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 the m a j o r i t y of the c l a s s was p l a y i n g Melody's 'school game'. Although the demonstration appeared to have convinced the students that balanced f o r c e s a p p l i e d to a moving object r e s u l t e d i n uniform 64 motion there was a sense of unease i n the c l a s s . This uneasiness was perhaps t y p i f i e d by the comments that Tawnia and her lab partner K i r s t e n made as they were preparing to leave the c l a s s . Tawnia: Is that 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 apply balanced f o r c e s then you t r a v e l at a constant speed? Teacher: 85 What d i d you see happening? Tawnia: Well I don't know? I don't even know i f they (the students who were applying the forces to the t r o l l e y ) were applying balanced f o r c e s . Teacher: Well they were being p r e t t y c a r e f u l . I t h i n k you can assume 90 that they were applying balanced f o r c e s . Tawnia: So t h a t ' s r i g h t then. K i r s t e n : Then why wouldn't i t stop? Tawnia: Yeah. The 'motion i m p l i e s a f o r c e ' b e l i e f was l u r k i n g j u s t below the surface and Tawnia was on the verge of succumbing to i t ' s s eductive a t t r a c t i o n (as were, probably, many other s t u d e n t s ) . Her attempt to ob t a i n a warrant from the teacher concerning the 'Tightness' of the concept that balanced f o r c e s would produce uniform motion was an attempt to reduce the t e n s i o n and uneasiness that 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 uneasiness that stemmed from the c o n f l i c t between what her experience suggested was true and the conceptual path that her teacher wanted to lead her down. When that warrant was not e x p l i c i t l y forthcoming and, i n s t e a d she was asked to reexamine her own observations, she has r e p l i e d (with 65 K i r s t e n ' s support) w i t h an apparent acceptance of the 'motion i m p l i e s a f o r c e 1 b e l i e f . The l a s t c l a s s i n the dynamics u n i t was devoted to t a c k l i n g , head-on, t h i s underlying sense among the students that a l l motion, and s p e c i f i c a l l y uniform motion, must be caused by some form of a p p l i e d or indigenous f o r c e . The c l a s s was begun by reviewing the demonstration from the previous day and randomly s e l e c t i n g students to e x p l a i n what they thought caused uniform motion. C o n s i s t e n t l y the students res-ponded that uniform motion r e s u l t e d when the net fo r c e on an object became zero. A c l a s s straw vote r e s u l t e d i n unanimous agreement with t h i s concept. The sense of unease, prevalent i n the previous c l a s s however, remained. I t was as i f the students were p a r r o t i n g back what they thought was expected of them. In an attempt to draw out and confront what was assumed to be an almost s u b l i m i n a l , i n t u i t i v e b e l i e f i n the 'motion i m p l i e s a f o r c e ' concept the students were presented with one f i n a l s e r i e s of demonstrations. The f i r s t demonstration c o n s i s t e d simply of pushing a dynamics c a r t across the f l o o r and then removing the push f o r c e . Teacher: I f I push t h i s c a r t along the f l o o r and I l e t i t go, the question i s what would the fo r c e or forces be a c t i n g on the c a r t ? Before we get to the fo r c e or forces one t h i n g I'd l i k e to know i s what k i n d of motion i s the c a r t going to 5 e x h i b i t ? Many students: A c c e l e r a t i o n . Teacher: OK, K e l l y . K e l l y : A c c e l e r a t i o n . Teacher: Any other p r e d i c t i o n s ? K i r s t e n : 10 D e c e l e r a t i o n . Teacher: You f i g u r e i t s going to slow down. 66 Many students: A f t e r . Yeah, a f t e r . Teacher: OK. I t s going to a c c e l e r a t e then d e c e l e r a t e . K e l l y : And i f i t has enough room i t s probably going to end up 15 stopping. Teacher: K i r s t e n , are you saying i t s going to d e c e l e r a t e as soon as I l e t go. K i r s t e n : Yeah. Teacher: OK. Any other p r e d i c t i o n s ? No other p r e d i c t i o n s were forthcoming so the c a r t was pushed and released. Teacher: 20 Now, a f t e r I l e t go (of the c a r t ) and before i t ran i n t o that desk l e g over there, what forces were a c t i n g on i t ? K e l l y : You've t o l d us that 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 things to keep on doing whatever they are 25 doing before. K e l l y : 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, a i r . Teacher: OK. So's there's j u s t (pause). K e l l y : Oh yeah, there's g r a v i t a t i o n a l p u l l . Teacher: 30 OK, but we're only i n t e r e s t e d i n those f o r c e s that are operating p a r a l l e l to the d i r e c t i o n of motion. K e l l y : OK, then there i s the r o l l i n g and a i r f r i c t i o n . Teacher: So there's j u s t f r i c t i o n . Is the push f o r c e s t i l l there or not? Dina: 35 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 there'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 there's j u s t a f r i c t i o n a l f o r c e operating 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 operating i n ? Another student: In the opposite d i r e c t i o n to motion. 67 Teacher: 40 OK. Take a look at that concept map (see Figure 6) over there. I f the only f o r c e operating 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 , operating against the d i r e c t i o n of motion, what type of motion should t h i s e x h i b i t ? K e l l y : I t should d e c e l e r a t e , (pause) I t should but i t doesn't. Teacher: 45 Why should i t ? K e l l y : Because i f you t h i n k about i t there's only f r i c t i o n (pause), I don't know. K e l l y i s convinced that she saw the c a r t a c c e l e r a t e a f t e r the push force was removed. This i s n ' t that s u r p r i s i n g because that i s what she p r e d i c t e d would happen (see l i n e 8, p. 66). On the other hand she has recognized the l o g i c a l i n c o n s i s t e n c y that she now f i n d s h e r s e l f i n because she had j u s t c o r r e c t l y analyzed the f o r c e s operating on the c a r t to be only 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. At t h i s p o i n t , however, she appears to be unable to r a t i o n a l i z e t h i s t e n s i o n between her perceptions and her a n a l y s i s . She i s not alone i n t h i s c o n f l i c t . 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? K i r s t e n : 50 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 that i t w i l l . K a r i . K a r i : ( i n a u d i b l e ) I f the net f o r c e i s opposite to the d i r e c t i o n of motion the object i s supposed to d e c e l e r a t e . Teacher: Now, i f t h a t ' s the case - the only f o r c e on here i s the f r i c -55 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 to begin with? K e l l y : 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 . I f you give i t a push f o r c e and i t s going to l a s t f o r a c e r t a i n length of time. I t s not going to j u s t (pause) M i c h e l l e ( i n t e r j e c t i n g ) : I t s not going to j u s t decrease because the contact f o r c e 60 you've pushed on i t i s going to make i t a c c e l e r a t e and then i t ' l l d e c e l e r a t e . 68 Teacher: ...Now the suggestion's been made that what happens to t h i s c a r t i s that i t speeds up i n i t i a l l y and then i t s t a r t s slowing down... Now i f i t s going to speed up, then how do you 65 make something speed up? What do you have to do to i t s net force? Brad: Make i t l a r g e r and constant. Teacher: OK. We've got to make l a r g e r and constant. At l e a s t con-s t a n t . That's the bare minimum that we can do. The problem 70 i s , i f I've l e t go of that t h i n g , where i s that l a r g e r f o r c e coming from? Another student: From f r i c t i o n . Teacher: OK, but I don't t h i n k that anybody i s i n disagreement w i t h the f a c t that there i s f r i c t i o n on here. What's been 75 suggested i s that I move t h i s along and I l e t i t go and i t s t a r t s speeding up. The suggestion's been made that the reason i t speeds up i s because I've t r a n s f e r r e d some of my force on to the c a r t . M i c h e l l e : Yup. Teacher: 80 Now, how many people t h i n k that i s the case? A straw vote was taken to determine how many students f e l t that some amount of fo r c e had been t r a n s f e r r e d to the c a r t and had caused the i n i t i a l a c c e l e r a t i o n . In other words, how many of the students were operating from an 'Impetus Theory' base. A c l e a r m a j o r i t y of the students f e l t that t h i s was the case. Teacher: Now, i f t h a t ' s the case, then i f I remove the f r i c t i o n what should happen, i f there i s a t r a n s f e r of f o r c e , i s that i t should keep a c c e l e r a t i n g . Is that r i g h t ? Many students: Right. Teacher: 85 OK. Let's remove the f r i c t i o n . This was the i n t r o d u c t i o n to the second demonstration. This, demonstration used an a i r - t r a c k to reduce f r i c t i o n to a n e g l i g i b l e amount. The method of operation of the a i r - t r a c k and i t s e f f e c t on the 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 explained and demonstrated to the students. Teacher: Now the suggestion i s that there i s a t r a n s f e r of f o r c e from whomever or whatever i s doing the pushing to the object that i s being pushed. I want you to remember one t h i n g . I f you're going to deal w i t h good science what you're going to 90 have to be able to do i s demonstrate t h a t , a f t e r the i n i t i a l push for c e has l e f t , there i s a forc e on the object. Other-wise, i f you can't demonstrate that i t i s there you can't say that i t i s there. At t h i s point the a i r - t r a c k was turned on and the r i d e r was given an i n i t i a l push for 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 (the r i d e r was 95 t r a v e l l i n g through 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 (from the a i r t r a c k ) i s pushing i t . Teacher: Now wait a minute. The a i r i s going out that way ( i n d i c a t e s an upwards d i r e c t i o n ) . Melanie: Well your forc e i s s t i l l on there. Teacher: 100 OK. I f my f o r c e i s on there where i s i t ? Dennis: In the a i r . Teacher: No the a i r i s going up. The motion i s going that way ( i n d i c a t e s a d i r e c t i o n 90° to the a i r f l o w ) . Melanie: I t s pushing i n the d i r e c t i o n that you pushed. I t s s t i l l 105 there. L i k e i t s s t i l l pushing. I t j u s t can't stop (inaud-i b l e ) . Teacher: Well my question to 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: 110 Nothing. Teacher: Can you demonstrate that there i s something pushing that r i d e r ? Melanie: There's nothing. I t s from the f r i c t i o n or something. 70 Teacher: But we've reduced the f r i c t i o n . Melanie: 115 Well 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 degenerated i n t o a c i r c u l a r argument that appeared to be i r r e s o l v a b l e . This lack of r e s o l u t i o n was beginning to f r u s t r a t e both the teacher and the students. In a f i n a l attempt to break through the c i r c l e , the students were l e d through 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 the r i d e r and asked to consider what k i n d of motion the r i d e r should 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 indigenous f o r c e . Teacher: Now do you need a l a r g e r f o r c e , i n other words a net f o r c e greater than zero, to have something moving? Melanie: Yes. No! You don't. Teacher: I f the net force i s zero what type of motion do you have? Melanie: 120 S t a t i o n a r y . Teacher: What type of motion do you have? Melanie: Uniform motion. Teacher: OK. Is t h i s t h i n g (the r i d e r ) e x h i b i t i n g a uniform motion? Another student: Yeah. Teacher: 125 I f i t s e x h i b i t i n g a uniform motion what do you know about the net f o r c e on i t ? Many students: I t s zero. Teacher: Now i f the net f o r c e i s zero 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 (the r i d e r ) -130 that way. Then there must be an inherent f o r c e on here (the r i d e r ) that I gave i t . Melanie: Yeah. That's what I t o l d you. Teacher: But why am I using t h i s machine? A Student: I t reduces the f r i c t i o n . 71 Teacher: 135 R i g h t ! So i f I've reduced the f r i c t i o n there i s no f o r c e there. Melanie: There's s t i l l f o r c e there (on the r i d e r ) though. Teacher: But i f there's f o r c e on the other s i d e (of the r i d e r ) i t should be a c c e l e r a t i n g . Melanie: 140 No, because your f o r c e i s dying down. I t s not a constant f o r c e . No amount of argument, l o g i c a l or otherwise, w i l l convince Melanie that there are no motive forces attached to the r i d e r . She espouses an almost c l a s s i c a l Impetus Theory when she f i n i s h e s her. argument w i t h the statement that the force i s "dying down" (see l i n e 140, p. 72). For her, objects only move when they are forced to move. I f no recogniz-able f o r c e i s present on a moving object then i t s because there has been a t r a n s f e r of force to the object and t h i s f o r c e w i l l get used up during the motion thus causing the object to slow down and u l t i m a t e l y stop. At t h i s point other students began to enter the debate w i t h t h e i r own explanations f o r the movement of the r i d e r . Brad: There wouldn't be any f r i c t i o n ( r e f e r r i n g to the 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 there won't be any forces a c t i n g 145 on i t at 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 uniform motion. Teacher: K e l l y . K e l l y : The f o r c e that you gave i t - l i k e there's no f r i c t i o n or anything - i t took that f o r c e . I f you gave i t 10 N of f o r c e , - and i t s going to keep t h a t . I t s j u s t going to keep i t . I t s 150 (the force) not going to run o f f . . . . I f there i s no f r i c t i o n i t ' l l keep going at a constant (pause). Teacher: I f you have a constant f o r c e a p p l i e d i n the d i r e c t i o n of motion according to that (the concept map) i t should a c c e l e r -ate. 72 K e l l y : 155 Yeah, but you're not g i v i n g i t a constant f o r c e . You j u s t gave i t that one i n i t i a l push...that f i r s t push for c e you gave i t 10 N, r i g h t , and you're not g i v i n g i t a constant forc e so that i t s j u s t going to keep that 10 N because there's no f r i c t i o n now. So i t s going to keep i t because 160 there's nothing to stop that 10 N, so i t ' l l keep going. Teacher: But i s n ' t that a constant force? I f there i s a f o r c e on there of 10 N a l l the time shouldn't i t a c c e l e r a t e ? OK. We're going to go to Heinzy, Tawnia, and then over to ( i n a u d i b l e ) . OK, Heinzy. Heinzy: 165 The f o r c e decreases to zero and s i n c e there's no r e s i s t a n c e going the other way i t keeps going. Teacher: With what type of motion? Heinzy: Uniform motion. Teacher: So you're saying the net f o r c e i s zero a f t e r I l e t i t go. Heinzy: 170 I t decreases to zero. Teacher: OK, and because the net force i s zero we're d e a l i n g w i t h uniform motion. Heinzy: Yeah. Teacher: Ok. Tawnia. Tawnia: 175 You s a i d that a c c e l e r a t i o n i s (a r e s u l t of) a push f o r c e going i n the d i r e c t i o n of the motion that i s bigger than the other force? Teacher: No, I've gone back up to t h i s concept map r i g h t over here. There's a l a r g e r constant f o r c e a p p l i e d to moving objects i n 180 the same d i r e c t i o n as the motion and that causes a c c e l e r -a t i o n . Tawnia: I know. Well t h a t ' s what's happening. The net f o r c e i s going the same way as the d i r e c t i o n . Teacher: Then t h i s (the r i d e r ) should be a c c e l e r a t i n g . Tawnia: 185 Yes. Teacher: Does i t ? Tawnia: No. Teacher: I f i t doesn't (pause). Tawnia: Then that (the concept map) i s a bunch of crap! 73 Teacher: 190 Then there i s one of your two options. E i t h e r that t h i n g i s wrong or Tawnia ( i n t e r j e c t i n g ) : We've learned t h i s a l l wrong then. Teacher: Why are you assuming that? Did that concept map work f o r your other demonstrations? Another student: 195 Yeah, i t d i d . Teacher: Well i f i t d i d why would you throw i t out j u s t because i t doesn't appear to work f o r t h i s one. What's your other option here? K a r i : That t h i s (the r i d e r ) has no forc e s a c t i n g on i t . Teacher: 200 That's the other o p t i o n . Right! Now once I l e t i t go there are no other forces a c t i n g on i t . K a r i : And i f there are no forces then the net fo r c e i s zero, t h e r e f o r e i t has uniform motion. 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 of the Newtonian option. An option that few of the students appeared to be w i l l i n g to consider. Throughout t h i s c l a s s the f r u s t r a t i o n l e v e l of both the teacher and students had r i s e n to an almost palpable l e v e l . On the one hand, the teacher f e l t stymied by h i s i n a b i l i t y to move the m a j o r i t y of the c l a s s towards an acceptance of the Newtonian o p t i o n . On the other hand, the students 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 to obt a i n v a l i d a t i o n , from the teacher, of t h e i r i n t e r p r e t a t i o n of the events that they had j u s t witnessed. An i n t e r p r e t a t i o n that was, to them, s t r o n g l y s e l f - e v i d e n t and based on the e x p e r i e n t i a l axiom of the 'motion i m p l i e s a f o r c e ' conceptual 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 Clue S t r u c t u r e A n a l y s i s of the E f f e c t i v e n e s s  of the I n s t r u c t i o n a l Strategy The clue s t r u c t u r e a n a l y s i s of the e f f e c t i v e n e s s of the i n s t r u c -t i o n a l s t r a t e g y was composed of 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 the lesson t r a n s c r i p t s f o r the conceptual data that the students were using to i n t e r p r e t the force/motion events that had been presented to them. These conceptual data were then reconstructed i n t o diagrammatic, 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 b a s i s . The symbols used to represent the various elements and connect-ors w i t h i n the frame s t r u c t u r e s are shown i n Figure 9. Figure 9. Synbols Used In Frane Constructions najor Frane designator :: :| sub-frane vehicle concept designator [ car ) 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 the set of elements that have been used f o r the recon-s t r u c t i o n of the i n t e r p r e t a t i o n a l frameworks, the concepts of frames, sub-frames, and d e f a u l t values have been discussed p r e v i o u s l y . The 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 i n t o those that are o p e r a t i o n a l , 75 non-operational, and unknown , however, have not been p r e v i o u s l y described. These d e s c r i p t i o n s w i l l occur 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 values 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 data that are a p p l i e d to the i n t e r p r e t a t i o n of an event or o b j e c t . As an example of t h i s data type, the conceptual frame f o r 'car' would cont a i n a d e f a u l t value f o r the number of wheels that an i n d i v i d u a l perceives a car to have which, i n most cases, would be 'four'. For the purposes of t h i s research, those d e f a u l t values that 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 an event or object w i l l be r e f e r r e d to as ' o p e r a t i o n a l ' . Those d e f a u l t values that are i n t e r p r e t e d (by the researcher) 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 object 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 to as 'non-operational'. Default values that are c l a s s i f i e d as being 'unknown' are those t h a t , i n the researcher's view, are present 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 object but cannot be d i r e c t l y d erived from the t r a n s -c r i p t i o n s . The second phase c o n s i s t e d of comparing the 'before i n s t r u c t i o n ' frame s t r u c t u r e s w i t h those that appeared ' a f t e r i n s t r u c t i o n 1 . This comparison then allowed a s u b j e c t i v e assessment to be made of the 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 to modify students' conceptual understanding of the dynamics of motion to one more c l o s e l y approxi-mating the Newtonian conceptions of motion. Each of these two phases w i l l be discussed i n d i v i d u a l l y . Student I n t e r p r e t a t i o n a l Frames of Motion Throughout the d i s c u s s i o n s on motion the students repeatedly focussed on two elements: the i n i t i a l s t a t e of the object that was to be moved or i n motion, and the forces that were perceived to be r e s p o n s i b l e f o r the motion. This binary nature of the d i s c u s s i o n suggests that f o r these students, at l e a s t , any frame d e a l i n g with motion i s composed of two sub-frames; one sub-frame to deal w i t h the object and the other to deal w i t h f o r c e s . This stage of the 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 the components of these sub-frames and the i n t e r a c t i o n s between the sub-frames. A c c e l e r a t i o n The d i s c u s s i o n s concerning the 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 four students - K e l l y , Cory, Jim, and Melanie. K e l l y ' s opening arguments as to why an object ( i n t h i s case a dynamics c a r t ) would begin to a c c e l e r a t e and continue to a c c e l e r a t e c o n s i s t e d of the f o l l o w i n g concepts: 1. The object must have a push forc e a p p l i e d to i t (see l i n e s 1 to 3, p. 34). 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 f o r c e operating i n the opposite d i r e c t i o n (see l i n e s 1 to 3, p. 34) and, by i m p l i c a t i o n , the push f o r c e must be i n the same d i r e c t i o n as the motion. 3. The a p p l i e d push f o r c e must be continuous (see l i n e 9, p. 34) . 4. The a p p l i e d f o r c e must be constant (see l i n e s 23 to 25, p. 35) . K e l l y subsequently modified her f o u r t h point to c l a r i f y when an a p p l i c a t i o n of a constant 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 the s t a t e of the object and i n d i c a t e d that i f the object 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 constant f o r c e would a c c e l e r a t e that object (see l i n e 14, p. 36). I f , however, the object was already i n motion the 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 the object but only f o r a f i n i t e p e r i o d of time. By the end of that p e r i o d whatever a c c e l e r a t i o n had occurred would have degraded to a constant v e l o c i t y s t a t e (see l i n e s 16 to 27, pp. 36 and 39). By i m p l i c a t i o n then, i f one wished to have a moving object continuously a c c e l e r a t i n g ( l i n e a r a l l y or otherwise) a continuously i n c r e a s i n g f o r c e would have to be a p p l i e d to that o b j e c t . Figures 10 and 11 diagram the probable frame s t r u c t u r e and usage of t h i s s t r u c -t u r e . Another student's (Cory) comment 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 required f o r a c c e l e r a t i o n (see l i n e s 13 to 22, p. 34) appears to be d i r e c t e d at the second part of the o r i g i n a l question (Why would Figure 16. Kelly's Acceleration Frane for Stationary Objects involves i OBJECT £ a. ::::::::::t: FORCES STATE dynamics' cart FWCTIOB m e n TWE(S) science deno nationless APPLIED (to object) i l i l l l l l l M I *"7^ J'•' •' •' J • »'1 FRICTION nZZEZ: push) friction"] CHARACTERISTICS SOURCE opposes object notion DIRECTION I continuous sane as notion SIZE HE constant 78 Figure 11. Kelly's Acceleration Frane for Hoving Objects involves i , OBJECT TYPE FORCES STATE FUNCTION MIS) mmm dynamcs cart science den (to object) noving ]: :l [•'•:•••• SOURCE CHARACTERISTICS DIRECTION FRICTION push ) friction opposes object notion I SIZE HE hand continuous sane as notion increasing an object continue to ac c e l e r a t e ? ) asked by the teacher. His comments have been made w i t h i n the context e s t a b l i s h e d during the interchange between K e l l y and the teacher that have d e a l t w i t h the c o n d i t i o n s necessary to keep a moving object a c c e l e r a t i n g . As such he appears to be i n agreement w i t h , at l e a s t , that part of K e l l y ' s frame that i m p l i e s that i f an object i s already moving a c c e l e r a t i o n can only be achieved by applying 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 Melanie a l s o appears to agree w i t h at l e a s t the i m p l i e d part of K e l l y ' s a c c e l e r a t i o n frame. As with Cory, Melanie's comment that a constant f o r c e w i l l r e s u l t i n a constant 79 v e l o c i t y (see l i n e s 29 and 30, p. 39) has occurred w i t h i n the context of a d i s c u s s i o n concerning the a c c e l e r a t i o n of a moving ob j e c t . As wit h K e l l y , Melanie has i m p l i e d that a c c e l e r a t i o n of a moving object can only occur w i t h 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 . Jim i s the odd man out i n t h i s d i s c u s s i o n . His comments (see l i n e s 1 to 11, p. 36), made during the comparison of the c l a s s and teacher produced concept maps, suggest that he i s viewing a c c e l e r a t i o n from a g e n e r a l i z e d stance that i s c l o s e to a Newtonian p o s i t i o n . For Jim, a c c e l e r a t i o n w i l l occur no matter whether the a p p l i e d f o r c e i s of a constant s i z e or i n c r e a s i n g . As long as the a p p l i e d f o r c e on an object i s l a r g e r than any opposing fo r c e s the object w i l l a c c e l e r a t e . What cannot be e x p l i c i t l y determined from these comments or the context that they were made i n , i s what, i f any, i n f l u e n c e the i n i t i a l s t a t e of the object p l a y s . A probable frame f o r Jim's perceptions of a c c e l e r -a t i o n i s shown i n Figure 12. To t h i s p o i n t , but w i t h the p o s s i b l e exception of Jim, a l l of the students that have taken part i n t h i s d i s c u s s i o n have agreed that f o r a moving object to a c c e l e r a t e and continue to a c c e l e r a t e 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 to that o b j e c t . Considering the lack of o b j e c t i o n to t h i s stance by the r e s t of the students, the vo c i f e r o u s disagreement that K e l l y ' s o r i g i n a l suggestion (continuous a c c e l e r a t i o n of an object can be achieved by applying a constant f o r c e ) was met w i t h , and the consensual agreement with the c l a s s produced concept map (see Figure 1) i t appears reasonable that t h i s concept represents the core of an a c c e l e r a t i o n frame that i s acceptable to the m a j o r i t y of the c l a s s . 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 w i t h K e l l y ' s frame f o r a moving object (see Figure 11) but wi t h the d e f a u l t 80 TYPE Figure 12. Jin's Acceleration Frane involves OBJECT FUNCTION I-:) STATE FORCES S E E <• \ Moving or t 1 f * rolionless TVPEIS) 1EZ E B I I I IMIIt t l t lMI > .! (to object) 0PP05IN6 EHEH: applied > opposing j (MOERISTICS SOURCE •v. opposes object notion DIRECTION continuous I; sane as notion SIZE constant increasing values f o r object type and f u n c t i o n , and source of the force becoming unknown q u a n t i t i e s . The set of expectations concerning a c c e l e r a t i o n that t h i s type of 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 to most i f not a l l of these students. I f one i s d r i v i n g a car or r i d i n g a b i c y c l e and wishes to ac c e l e r a t e more force must be a p p l i e d to the d r i v i n g wheels. I f the d r i v e r wants the a c c e l e r a t i o n to continue and/or increase the amount of for c e s u p p l i e d must a l s o be increased i n a continuous f a s h i o n . What t h i s frame represents then i s a g u t - l e v e l a p p r e c i a t i o n of the v a r i a b l e nature of f r i c t i o n . 81 F o l l o w i n g the demonstrations the student conceptions of the cause of a c c e l e r a t i o n appeared to have a l t e r e d d r a m a t i c a l l y . The c l a s s unanimously agreed t h a t , f o r these demonstrations, a c c e l e r a t i o n was caused by the a p p l i c a t i o n of a constant f o r c e as opposed to 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 p r i o r to the demonstra-t i o n s . On r e f l e c t i o n however, t h i s does not appear to be the case. In both demonstrations the object i n question was i n i t i a l l y motionless. As such, t h i s m a j o r i t y agreement must be r e s t a t e d to i n c l u d e t h i s c o n d i t i o n , that 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 motionless object was caused by the a p p l i c a t i o n of a constant f o r c e . Again, t h i s conception 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 w i t h 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 object (see Figure 10). 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 to the d e f a u l t values f o r object type and source of the a p p l i e d f o r c e , can be viewed as a composite frame f o r most of the c l a s s . D e c e l e r a t i o n The d i s c u s s i o n concerning the dynamics of d e c e l e r a t i o n was i n i t i a t e d by K e l l y . Her view of the cause of d e c e l e r a t i o n of a moving object was that the f o r c e s opposing the motion ( i n t h i s case f r i c t i o n ) had to be l a r g e r than the a p p l i e d forces (see l i n e 5, p. 42, and l i n e s 51 to 53, p. 45). A d d i t i o n a l support f o r t h i s conception of d e c e l e r -a t i o n was provided by Dina (see l i n e s 14 to 17, pp. 42 and 43) and very d e f i n i t e l y by Tawnia (see l i n e s 91 to 125, pp. 46 and 47). This 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 represented i n Figure 13. Only one other p o s i t i o n concerning the causes of d e c e l e r a t i o n surfaced during the i n i t i a l d i s c u s s i o n s . This was provided by Jim. Jim's conceptions of d e c e l e r a t i o n centre around a need to keep the 82 Figure 13. Kelly's Deceleratifln Frane DECELERATION i* k car '•] Having s «• • % • • • I CHARACTERISTICS SOURCE opposes object notion DIRECTION SIZE uheels sane as ration a p p l i e d , motive forc e greater than any opposing f o r c e s . To reach t h i s s t a t e Jim f e e l s that d e c e l e r a t i o n can be achieved by simply reducing the motive f o r c e while s t i l l r e t a i n i n g the above c o n d i t i o n (see l i n e s 7 to 12, p. 42). This p o s i t i o n i s a l s o s t a t e d by Jody (see l i n e s 28 and 29, p. 44). A d d i t i o n a l l y , Jim f e e l s that i f the magnitude of the motive f o r c e f a l l s below that of the opposing forces the object w i l l stop (see l i n e 19, p. 43). 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 Figure 14. Jim's comments concerning a c c e l e r a t i o n i n d i c a t e that he equates the cause of the motion with the a p p l i c a t i o n of a motive forc e i n the 83 TYPE ' car Figure 14. din's Deceleration Frane involves OBJECT ^ 3 -STATE FORCES 3 3 MIS) Hoving science problen APPLIED (to object) CHARACTERISTICS SOURCE FRICTION HHEZil applied) friction opposes object notion DIRECTION [ SIZE yteels sane as notion decreasing same d i r e c t i o n as the motion. Conversely, i f the l a r g e r f o r c e ( i n t h i s case f r i c t i o n ) operates i n the opposite d i r e c t i o n to that of the motion the object that i s moving must simply stop. 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 the motion of the object i s one of slowing down, t h i s can only occur when the motive f o r c e i s reduced, or reducing, but s t i l l l a r g e r than the opposing f r i c t i o n a l f o r c e s . I f the f r i c t i o n a l f orces become greater than the motive for c e the object must stop. I n t e r e s t i n g l y , Jim sees no c o n f l i c t between h i s conceptions 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 . Both of these conceptual s e t s i n c o r p o r -84 a t e , as a core item, the i m p l i c a t i o n that 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 greater than zero and operating i n the d i r e c t i o n of motion. From a p h y s i c a l point of view, such a fo r c e c o n d i t i o n can only 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 point 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 value 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 object 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 value must be e i t h e r constant or i n c r e a s i n g . I f an object 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 value must be decreasing. In comparison then, the major d i f f e r e n c e between the frame being used by K e l l y to i n t e r p r e t the d e c e l e r a t i o n of objects and that being employed by Jim l i e s i n the d e f a u l t value f o r t h e i r p a r t i c u l a r concep-t i o n of the comparison of the forces i n v o l v e d . K e l l y ' s conception of t h i s comparison d i c t a t e s that the t o t a l value of any a p p l i e d forces must be l e s s than the t o t a l value of any f r i c t i o n a l f o r c e s , whereas Jim's conception of t h i s comparison i s e x a c t l y the opposite. For Jim d e c e l e r a t i o n occurs when the a p p l i e d forces are greater than the f r i c t i o n a l f o r c e s but are decreasing (or decreased) from a p r e v i o u s l y higher l e v e l . The hallway demonstration appeared to cement the frame, i n i t i a l l y d e scribed by K e l l y but w i t h changes to the d e f a u l t values d e s c r i b i n g the object (an equipment t r o l l e y ) , i n place 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 choice f o r the m a j o r i t y of students (see Figure 15). Although the acceptance of t h i s frame appeared to i n d i c a t e that the students had opted f o r a c l o s e approximation to 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 operating i n a d i r e c t i o n opposite to that of the motion) subsequent data c o l l e c t e d from the b a s e b a l l problem suggested that t h i s frame was, i n r e a l i t y , a 85 Figure 15. Conposite Deceleration Frane Derived Fran Hallway Denonstration involves t TYPE OBJECT m .'! i.' •i ! • EL FORCES STATE FUNCTION equipfent trolley raving science den ± M(S> CWARISOH APPLIED (to object) FRICTION • • [ friction) posh) i !; (MACTERISTICS SOURCE opposes object notion DIRECTION SIS wheels sate as notion frame that could be used to support the 'motion i m p l i e s a f o r c e ' set co n c e p t u a l i z a t i o n s . During the d i s c u s s i o n of the bas e b a l l problem i t soon became apparent that a m a j o r i t y of students ( t a k i n g part i n the 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 the idea that a b a l l could move upwards without a force ( a p p l i e d i n the d i r e c t i o n of motion) to move i t upwards. Throughout the d i s c u s s i o n s (contained on pages 51 to 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 (from the bat) on the b a l l that keeps i t moving upwards. Only Brad and Tawnia appear to have accepted the s i t u a t i o n that an object can move, a l b e i t d e c e l e r a t e , without the 86 a p p l i c a t i o n of some type of f o r c e i n d i r e c t i o n of the motion (see l i n e s 57 through 59, p. 54, and l i n e s 95 through 106, p. 56). The concept of ' t r a n s f e r r e d f o r c e ' that i s so prevalent 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 to r e t a i n the i n t e g r i t y of t h e i r i n t e r p r e t a t i o n a l frames. Up to t h i s p o i n t , a l l the demonstrations and problems that these students have faced have i n v o l v e d some form of e a s i l y recognizable motive 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 object. These motive forces have been c o n s i s t e n t l y incorporated 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 of the major concepts used f o r t h e i r analyses of the dynamics of 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 that has served them w e l l , j u s t because the 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 destroy the frame. Such a s i t u a t i o n i s untenable f o r these students. As a r e s u l t , that region 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 that had once he l d the concept of 'applied f o r c e ( s ) ' must continue to e x i s t . This continued existence i s achieved by a metamorphosis of the 'applied f o r c e ' (from the bat) concept to a ' t r a n s f e r r e d f o r c e ' (on the b a l l ) concept w i t h i t s own set of d e f a u l t values. In a d d i t i o n to t h i s metamorphosis, that region of the i n t e r p r e t a -t i o n a l frame that d e a l t w i t h the f o r c e ( s ) which opposed motion has had to be expanded to r e f l e c t the increased complexity of these forces (see Figure 7). In both of these regions, however, the d e f a u l t value f o r the s i z e (constant, i n c r e a s i n g , or decreasing) of the fo r c e (or for c e s ) i n v o l v e d cannot be determined from the t r a n s c r i p t s . As such, the d e f a u l t value f o r the s i z e concept has been l e f t blank. This e v o l u t i o n of the o r i g i n a l composite d e c e l e r a t i o n frame (see Figure 15) i n t o a 87 d e c e l e r a t i o n frame that supports the type of Impetus Theory that these students appear to be using i s shown i n Figure 16. Figure 16. Conposite Deceleration Frane Applied to the Baseball Problen involves OBJECT TVPE HZ: FORCES : • : ^ STATE 1;• PrTWCTIflM )• | l]}}}}]} . . . 7 . . . i . . . ' . . . ' . . . . V . . . J . i TVPEIS) baseball mving upwards gane JO CMMRISON • • • {opposing > transferred TRANSFERRED (to object) 0PP0SIN6 CHARACTERISTICS SOURCE CWWCTERISTICS 1 1 1 1 1 1 • 1 1 1 1 1 1 1 DIRECTION SIZE bat saite as notion SOURCE E E DIRECTION SIZE parity 1 : friction opposes object notion Uniform Motion The i n i t i a l d i s c u s s i o n s of the dynamics of uniform motion were dominated by Brad and K a r i . Brad, during these d i s c u s s i o n s , has put f o r t h the Newtonian p o s i t i o n that uniform motion i s the r e s u l t of the a p p l i c a t i o n of balanced forces to a moving object (see l i n e s 31 to 33, p. 62, and l i n e s 61 to 63, p. 63). K a r i , however, has suggested that the a p p l i c a t i o n of balanced forces to a moving object w i l l d e c e l e r a t e and u l t i m a t e l y stop that object (see l i n e s 48 to 51, p. 62). She f u r t h e r suggests that uniform motion can only be achieved w i t h the a p p l i c a t i o n of a " d e c e l e r a t i n g f o r c e " (see l i n e 2, p. 61) - a fo r c e 88 which i s continuously decreasing i n s i z e . K a r i ' s conception of uniform motion centers around the requirement f o r some type of motive f o r c e and, as such, can be viewed as a subset of the '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. Both of these conceptions of uniform motion have been recon-s t r u c t e d i n t o the i n t e r p r e t a t i o n a l frames shown i n Figures 17 and 18. As a r e s u l t of the general nature of the d i s c u s s i o n s , however, many of the d e f a u l t values 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 blank i n the frames. Figure 17. Brad's Frane for Unifom Hotion OBJECT TYPE UK FUNCTION TTTTTT7 air-track rider science dsn requires STATE TTTTT7; noving continuous APPLIED (to object) FORCES OMRACTERISTICS TYPE BALANCED CHARACTERISTICS mm ,(net force = 8 SOURCE 89 Figure 18. Kari's Frane for Uniforn Hotion . .> r ;\ (. ;> , , , fj • ; ; I r , is.:.:.!.:.:.!.1.1.1.i.t.i.i.s.:.:.!. t.i.i.i.i,i.i.t.i.i.i.t.i.t.MI i ; • I DURATION f ; SIZE continuously applied (to object) decreasing SOURCE • • i ". '. ! . . 1 . . I • • i • • 1 K a r i ' s conception of the dynamics of uniform motion appears to provide some a d d i t i o n a l i n f o r m a t i o n concerning her previous p o s i t i o n on the causes of d e c e l e r a t i o n (at l e a s t as a p p l i e d to the bas e b a l l problem) and which could be a p p l i e d to the composite frame f o r d e c e l e r -a t i o n that was a p p l i e d to the bas e b a l l problem (see Figure 16). This conception 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 the same d i r e c t i o n as the motion of the object (see l i n e s 25 to 27, p. 53; l i n e s 108 to 111, p. 56; and l i n e 120, p. 57). What was unclear as f a r as t h i s conception of d e c e l e r a t i o n was concerned was the s i z e of the ' t r a n s f e r r e d f o r c e ' , as such, the d e f a u l t value f o r t h i s concept was l e f t blank. Both of these conceptions f o r d i f f e r e n t types of motion i n v o l v e the a p p l i c a t i o n of some form of motive f o r c e , however, K a r i has defined the s i z e of the force r e s p o n s i b l e f o r uniform 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 uniform 90 motion, the d e f a u l t value 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 ' should most probably be constant. Fo l l o w i n g the demonstration of the e f f e c t of balanced forces on a moving equipment t r o l l e y , the three students (Heinzy, Steve, and K a r i ; see l i n e s 64 to 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 the type of r e s u l t a n t motion a l l agreed that the t r o l l e y had e x h i b i t e d uniform motion. This agreement tends to i n d i c a t e that these students, at l e a s t , were e i t h e r i n i n i t i a l agreement with Brad's i n t e r p r e t a t i o n a l frame f o r uniform motion or ( c e r t a i n l y i n K a r i ' s case) were moving towards agreement with t h i s frame. This was not the case f o r other students i n the 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 to 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 confusion on t h e i r p a r t . Tawnia's comments appear to be an attempt to o b t a i n a warrant, from the teacher, to v a l i d a t e what she has seen i n the preceding demonstration and Brad's i n t e r p r e t a t i o n of uniform motion. Tawnia (and probably K i r s t e n ) appears to r e q u i r e that warrant before she i s w i l l i n g to r e l i n q u i s h her i n t e r p r e t a t i o n a l frame of uniform motion (which i s apparently s i m i l a r to K a r i ' s ; see l i n e 53, p. 63) and accept Brad's. When t h i s warrant i s not forthcoming both 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 favour 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 uniform motion when they ask the question 'why doesn't the object stop when balanced fo r c e s are a p p l i e d to i t ? ' The a i r - t r a c k demonstration, which was i n place to confront those students that were using 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 to e x p l a i n uniform motion, produced mixed r e s u l t s . Without f a i l , a l l students who took part i n the d i s c u s s i o n of t h i s demonstration agreed that the r i d e r t r a v e l l e d w i t h a uniform 91 motion. This p o i n t , however, was the only p o i n t that could be agreed upon as t h i s demonstration appeared to s p l i t the students i n t o at l e a s t two groups. One group appeared to i n t e r p r e t t h i s demonstration using a form of Impetus Theory whereas, the other group opted to e x p l a i n uniform motion using an expanded v e r s i o n of 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 (or v a r i a n t s of that frame). The group of students that appeared to be using a form of Impetus Theory to e x p l a i n uniform motion i n c l u d e d Melanie, K e l l y , and Tawnia. For a l l three of these students, the a i r - t r a c k r i d e r moved because i t c a r r i e d an inherent f o r c e . This f o r c e has been t r a n s f e r r e d to the r i d e r when i t was given an i n i t i a l push (see l i n e s 128 to 141, pp. 71 and 72; l i n e s 147 to 160, pp. 72 and 73; and l i n e s 182 and 183, P. 73). Although a l l three of these students appear to be using s i m i l a r l y constructed 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 uniform motion (as e x h i b i t e d by the a i r - t r a c k r i d e r ) there are d i f f e r e n c e s i n the d e f a u l t values that are being a p p l i e d to s p e c i f i c concepts w i t h i n the frame. Melanie's frame, which i s assumed to represent the b a s i c s t r u c t u r e used by these students (see Figure 19), 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 f o r c e 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 the other hand would i n c l u d e a d e f a u l t value 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 that would describe t h i s f o r c e as remaining constant. Tawnia's frame, as w e l l , would have the same b a s i c design as Melanie's frame but the d e f a u l t value 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 i s unknown. The only i n f o r m a t i o n that Tawnia has s u p p l i e d concerning t h i s d e f a u l t value i s that "the net fo r c e i s going the same way as the d i r e c t i o n " (see l i n e s 182 and 183, p. 73). Such a s i t u a t i o n i n v o l v i n g the a i r - t r a c k r i d e r could be achieved using 92 Figure 19. Melanie's Uhifom Notion Frane an i n c r e a s i n g , decreasing, or constant value 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 . Brad, K a r i , and to a l e s s e r degree, Heinzy made up the group that appeared to i n t e r p r e t i n g the motion of the a i r - t r a c k r i d e r using an expanded v e r s i o n of Brad's o r i g i n a l frame f o r uniform motion. In t h i s case, Brad has extended h i s i n t e r p r e t a t i o n a l frame, that was based on balanced f o r c e s , to in c l u d e the a l t e r n a t i v e o p t i o n that uniform motion can be the r e s u l t a n t of the complete absence of forces (see l i n e s 144 and 145, p. 72). By doing so h i s i n t e r p r e t a t i o n a l frame of uniform motion now represents the general Newtonian p o s i t i o n that t h i s type of motion ( f o r an i n i t i a l l y moving object) i s the r e s u l t of any fo r c e c o n d i t i o n s that r e s u l t i n a n u l l net fo r c e (see Figure 20). K a r i has a l s o recognized t h a t , f o r t h i s demonstration of uniform motion, there are no motive forces a c t i n g on the r i d e r and that the net for c e c o n d i t i o n must be zero (see l i n e s 199 to 203, p. 74). As a 93 Figure 29. Brad's Expanded Frane for Uniforn Notion air-track rider APPLIED (to object) FORCES ABSENCE OF FORCES r e s u l t , she appears to be i n complete agreement with Brad's i n t e r p r e t a -t i o n a l frame f o r uniform motion and, apparently, has abandoned her previous frame (see Figure 18) that was based upon the 'motion i m p l i e s a f o r c e ' conception. Heinzy appears to have adopted a compromise p o s i t i o n that melds Melanie's 'motion i m p l i e s a f o r c e ' conception w i t h Brad's Newtonian p o s i t i o n that uniform motion i s a r e s u l t of a n u l l net fo r c e c o n d i t i o n . 94 Heinzy f e e l s that there i s a fo r c e a s s o c i a t e d w i t h the i n i t i a l movement of the 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 that f o r c e q u i c k l y f a l l s o f f to zero. Once the 'trans-f e r r e d f o r c e ' has reduced to zero he recognizes that there i s no longer any f o r c e which might a c c e l e r a t e the r i d e r , nor are there any opposing for c e s which would dec e l e r a t e the r i d e r (see l i n e s 165 to 173, p. 73). Thus, the r i d e r must be t r a v e l l i n g w i t h a uniform motion as a r e s u l t of a n u l l net force c o n d i t i o n . This form of an i n t e r p r e t a t i o n a l frame f o r uniform motion i s shown i n Figure 21. Figure 21. Heinzy's Frane for Uhiforn Notion .• • .•..' r * \:::::: fTTTTTTT: * I:: air-track rider science deno roving NECCSSARVCOHDITIOH TRANSFERRED (to object) FORCE OPPOSINS FORCES :0 CHARACTERISTICS DURATION decreases to 8 SOURCE iCZDI 95 Instructional Strategy Effects on Student  Interpretational Frames of Motion The determination of the effects that the instructional strategy had on the initial conceptions that students were using to explain the dynamics of specific types of motion has been accomplished by comparing their initial interpretational frameworks with those that were con-structed 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 initial discussions was that a continually increas-ing force was required to accelerate a moving object. This concept represents the core of Kelly's interpretational frame for the acceler-ation 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 applic-ation 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 initially 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 that 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 f o r the m a j o r i t y of the c l a s s , then t h i s frame should not have changed; nor d i d i t . This frame incorporates the minimum Newtonian c o n d i t i o n s necessary 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 body and should not have changed f o l l o w i n g the demonstrations because these were designed to i l l u s t r a t e these c o n d i t i o n s . Because there were no demonstrations presented to these students that might have i l l u s t r a t e d the minimum Newtonian c o n d i t i o n s f o r the a c c e l e r a t i o n of an already moving body, i t i s impossible to make any 'before and a f t e r ' comparison of the students' i n i t i a l 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 the minimum requirement f o r the a c c e l e r a t i o n of a moving ob j e c t . D e c e l e r a t i o n The i n i t i a l d i s c u s s i o n s concerning the causes of dynamics p i n -pointed 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 the students. One frame, o u t l i n e d by K e l l y (see Figure 13), i l l u s t r a t e s the Newtonian p o s i t i o n that d e c e l e r a t i o n i s the r e s u l t of the net f o r c e ( i n d i c a t e d by the d e f a u l t value f o r the 'comparison' concept) on a moving object a c t i n g i n the opposite d i r e c t i o n to the motion of the object. The other frame, o u t l i n e d by Jim (see Figure 14), 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 . In t h i s case, an object d e c e l e r a t e s because i t ' s motive forc e i s decreasing i n s i z e . The net fo r c e (again i n d i c a t e d by the d e f a u l t value f o r the 'comparison' concept), however, continues to act i n the d i r e c t i o n of the ob j e c t ' s motion. To begin w i t h , both of these i n t e r p r e t a t i o n a l frames found sup-po r t e r s w i t h i n the c l a s s . F o l l o w i n g the demonstrations however,the m a j o r i t y of students appeared to 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 such, the i n s t r u c t i o n a l s t r a t e g y appeared to have the d e s i r e d e f f e c t of convincing the students that the Newtonian frame f o r d e c e l e r a t i o n was the more powerful i n t e r p r e t a t i o n a l model of the two frames i n i t i a l l y recognized. I t should be noted at t h i s point that the i n s t r u c t i o n a l s t r a t e g y was not e n t i r e l y s u c c e s s f u l i n that i t f a i l e d to convince Jim that he should 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 to h i s frame i n that he d i d agree that 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 to an object's motion would cause d e c e l e r a t i o n . However, he a l s o f e l t that the d e c e l e r a t i o n would u l t i m a t e l y stop and the object would continue to move forwards with a uniform motion (see l i n e s 8 to 19, p. 49). The b a s e b a l l problem, however, has pointed 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 demonstrations i n t h i s i n s t r u c -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 motive f o r c e to an o b j e c t . 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 that were generated by these demonstrations always i n v o l v e d some form of a p p l i e d f o r c e to the o b j e c t . The b a s e b a l l problem, however, d i d not i n v o l v e any form of motive f o r c e and i t soon became apparent during the d i s c u s s i o n of t h i s problem that a m a j o r i t y of students i n t h i s c l a s s were incapable of imagining motion without some form of motive f o r c e . Thus they f e l t i t necessary to invent a ' t r a n s f e r r e d f o r c e ' that was r e s p o n s i b l e f o r the motion of the b a l l and i n c o r p o r a t e t h i s i n v e n t i o n 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 frame that described the dynamics of the d e c e l e r a t i o n of the b a l l . Because there were no demonstrations 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 that would e x p l i c i t l y confront the conception of ' 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 to determine whether the 98 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 type of i n t e r p r e t a t i o n a l frame. Uniform Motion The i n i t i a l d i s c u s s i o n s concerning the dynamics of uniform motion uncovered two i n t e r p r e t a t i o n a l frames that were being used to describe t h i s type of motion. Brad's frame (see Figure 17) describes the Newtonian conception that uniform motion i s the r e s u l t of the a p p l i c a -t i o n of balanced forces to an already moving ob j e c t . K a r i ' s frame, however, appears to based on elements of the 'motion i m p l i e s a f o r c e ' conception. In t h i s case, K a r i appears t o b e l i e v e that a c c e l e r a t i o n of a moving object i s caused by the 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 , that d e c e l e r a t i o n of an object i s achieved by applying a constant f o r c e to that object which i s smaller than the t o t a l of any opposing f o r c e s , and that uniform motion i s the r e s u l t of the a p p l i c a -t i o n of a decreasing f o r c e to a moving object. F o l l o w i n g the f i r s t demonstration i n v o l v i n g the equipment t r o l l e y K a r i ' s i n t e r p r e t a t i o n of the dynamics of uniform motion appears to have changed. She e x p l i c i t l y agrees that the a p p l i c a t i o n of balanced forces to the moving equipment t r o l l e y has r e s u l t e d i n the t r o l l e y t r a v e l l i n g w i t h a uniform motion (see l i n e 80, p. 64). As such, she now appears to be i n agreement with 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 her own 'motion i m p l i e s a f o r c e ' based frame. Such was not the case with other students i n the 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 to 94, p. 65) suggest t h a t , although t h i s demonstration has probably r a i s e d doubts concerning t h e i r own pe 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 uniform motion, i t c e r t a i n l y hasn't transformed these frames i n t o ones that i n c o r p o r a t e Newtonian conceptions of uniform motion. This lack of transformation 99 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 demonstration 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 Figure 19) that has been t e n a c i o u s l y defended by Melanie and K e l l y . The a i r - t r a c k demonstration 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 provided Brad w i t h an opportunity to extend h i s o r i g i n a l , Newton-ian-based frame i n t o one that now represents a t r u l y , g e n e r a l i z a b l e frame f o r uniform motion that i s d e f i n i t e l y based on Newtonian p r i n c i -p l e s (see Figure 20). In a d d i t i o n , t h i s part of the i n s t r u c t i o n a l sequence appears to have confirmed, 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 203, p. 74) suggest that she has completely abandoned her 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 based upon the 'motion i m p l i e s a f o r c e ' conception and wholeheartedly accepted the d e s c r i p t i o n of uniform motion provided by Brad's i n t e r p r e t a t i o n a l frame. Although the i n s t r u c t i o n a l sequence appeared to b r i n g about a s u c c e s s f u l transformation 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 f o r uniform motion, the same cannot be s a i d f o r Heinzy's i n t e r p r e t a -t i o n a l frame. Heinzy's frame (see Figure 21) appears to stake out the middle ground between Melanie'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 both of these frames. Due to a lack of a p r i o r i n t e r p r e t a t i o n a l frame (or verbal agreement w i t h a p r i o r frame) that could be used f o r comparison purposes, i t i s impossible to determine whether t h i s 'middle ground' frame represents 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 of the Major, Student I n t e r p r e t a t i o n a l Frameworks of Motion What has become i n c r e a s i n g l y c l e a r from the preceding a n a l y s i s i s that many students i n t h i s c l a s s f i n d i t extremely d i f f i c u l t to imagine any type of object motion that 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. For a la r g e number of these students a c c e l e r a t i o n of an already moving object i s achieved by applying a motive f o r c e which c o n t i n u a l l y increases 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 object requires only the a p p l i c a t i o n of a constant, motive f o r c e . Many of these same students a l s o f e l t that d e c e l e r a t i o n of an object could occur i f , and only i f , the a p p l i e d , motive f o r c e was l e s s than the t o t a l magnitude of the forces opposing the object motion. At f i r s t glance, t h i s conception appears to m i r r o r the 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 req u i r e s that the net fo r c e on a moving object operate i n the opposite d i r e c t i o n to the motion of the obj e c t . This c o n d i t i o n , however, was unacceptable to these students when a motion event occurred that d i s p l a y e d no e x p l i c i t motive f o r c e . In t h i s type of s i t u a t i o n these students found i t necessary to invent an a p p l i e d , motive f o r c e that had been t r a n s f e r r e d to the moving object from some e x t e r i o r source. F i n a l l y , f o r uniform motion of an object to occur these students f e l t that some form of a p p l i e d , motive f o r c e was r e q u i r e d , and one student suggested that i t would have to be decreasing i n s i z e . As was the case with d e c e l e r -a t i o n , i f an a p p l i e d f o r c e was not e x p l i c i t l y present when an object was t r a v e l l i n g w i t h uniform motion, these students f e l t i t necessary to invent a ' t r a n s f e r r e d f o r c e ' t o account f o r the motion of the object. The i n c o r p o r a t i o n of these conceptions of motion 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 of motion has been accomplished 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 / (RESULT OF) > APPLIED FORCE V CONDITIONS J isa ( OBJECT I (HOTION) isa isa isa ( ACCELERATION Y ( 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 object i n question. These frames would conta i n i n f o r m a t i o n about the type of o b j e c t , i t ' s i n i t i a l s t a t e ( s t a t i o n a r y or moving), whether i t can supply an i n t e r n a l motive forc e or whether i t r e q u i r e s an ex t e r n a l f o r c e f o r motion, and so on. The upper l e v e l , again can be viewed as a j u n c t i o n point t h a t , allows connections to be made with the s p e c i f i c a p p l i e d , motive forc e frames depending upon what type of motion i s being e x h i b i t e d by the ob j e c t . Data w i t h i n these frames would i n c l u d e such items as the s i z e and d u r a t i o n of the a p p l i e d f o r c e , whether or not the source of t h i s f o r c e i s i n t e r n a l to the object 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 converted i n t o a t r a n s f e r r e d f o r c e . 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 Figure 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 f a s h i o n to t h e i r counterparts i n the previous i n t e r p r e t a t i o n a l framework. The upper l e v e l , however, would allow access to frames d e s c r i b i n g the 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. For example, the r e c o g n i t i o n that an object was a c c e l e r a t i n g would allow access to a frame that d e t a i l e d that a p o s i t i v e ( i n the 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 required and how that net f o r c e was achieved. S i m i l a r l y , i f d e c e l e r a t i o n was recognized a negative (opposing object motion) net f o r c e frame would be accessed; i f uniform motion was recognized a n u l l net f o r c e frame would be accessed. On only two occasions 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 students. The f i r s t occasion occurred during the d i s c u s s i o n of the baseball problem when Brad appeared to be using Newtonian p r i n c i p l e s to analyze the forces operating on the b a l l and apply t h i s to d e c e l e r a t i n g motion (see l i n e s 57 to 59, p. 54). The second occasion occurred during the d i s c u s s i o n 103 Figure 23. A Newtonian Interpretational Franewrk f (RESULT OF) \ e FORCE V CONDITIONS J , isa { OBJECT ^ I (NOTION) J isa isa isa ^ ACCELERATION J ( DECELERATION J f UNIFORM \ V NOTION J of uniform motion when both Brad and K a r i u t i l i z e d the concept of n u l l , net f o r c e t o e x p l a i n the uniform motion of the a i r - t r a c k r i d e r . 104 CHAPTER FIVE Conclusions, D i s c u s s i o n of R e s u l t s , and Recommendations Conclusions The general problem of t h i s research has been to design an i n s t r u c t i o n a l model that would e x p l i c a t e students' conceptions of dynamics and, i f necessary, transform these conceptions i n t o ones that more c l o s e l y approximate Newtonian conceptions of dynamics. Included w i t h i n t h i s general problem were three, s p e c i f i c problems. The f i r s t problem was the design of an i n s t r u c t i o n a l s t r a t e g y that would i l l u m i n -ate the conceptions being employed by students to e x p l a i n the motion of objects and b r i n g about any r e q u i r e d transformations. The second problem was the development of an a n a l y t i c a l clue s t r u c t u r e , based upon a t h e o r e t i c a l p e r s p e c t i v e provided by Frame Theory, which could be used to describe the conceptual s t r u c t u r e s employed by students to e x p l a i n object motion and which would serve as a t r a c k i n g mechanism f o r any conceptual transformation i n i t i a t e d by the 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 , the t h i r d problem was the implementation of the 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 classroom, i n order to determine the model's a b i l i t y to e x p l i c a t e student conceptions of dynamics and transform these conceptions where re q u i r e d . Conclusions concerning each of these problems w i l l be discussed i n d i v i d u a l l y . However, because the conclusions concerning the f i r s t two problems are d i r e c t l y r e l a t e d to the e f f i c a c y of the i n s t r u c t i o n a l model during the implemen-t a t i o n phase of t h i s research, the conclusions regarding the implemen-t a t i o n of the i n s t r u c t i o n a l model w i l l be discussed f i r s t . 105 Conclusions Concerning 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' Concepts of Dynamics The e x p l i c a t i o n of student conceptions of dynamics using the binary process of concept i l l u m i n a t i o n ( v i a a combination of concept mapping and c l a s s d i s c u s s i o n techniques) and r e c o n s t r u c t i o n of these concepts 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 considered to be a success. As a r e s u l t of t h i s process the f o l l o w i n g student conceptions of dynamics have been i d e n t i f i e d : 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 object i s the r e s u l t of the a p p l i c a t i o n of a constant f o r c e to that object (see Figure 10). 2. A c c e l e r a t i o n of a moving object 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 a l l y , i n c r e a s i n g f o r c e to that object i n the d i r e c t i o n of motion of that object (see Figure 11). 3. D e c e l e r a t i o n of an object i s the r e s u l t of an imbalance between any a p p l i e d , motive forces and any other f o r c e s that oppose the motion of the object. This imbalance i s such that the t o t a l of the opposing forces are greater than the t o t a l of the a p p l i e d , motive forces (see Figure 15). 4. D e c e l e r a t i o n of an object i s the r e s u l t of a p p l i e d , motive forces which are decreasing i n magnitude, but which are l a r g e r than the t o t a l of any forces opposing the motion (see Figure 14). 5. Uniform motion of an object i s the r e s u l t of the a p p l i c a t i o n of balanced f o r c e s to that object (see Figure 19). 6. Uniform motion of an object i s the r e s u l t of the a p p l i c a t i o n of a continuously, decreasing, motive f o r c e to that object (see Figure 18). 106 7. Uniform motion of an object i s the r e s u l t of the a p p l i c a t i o n of a motive forc e to an object that decreases to zero (see Figure 21). 8. An a p p l i e d , motive f o r c e must always be present during d e c e l e r a t i n g and uniform motion. 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 to the moving object. 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 motion i n a p a r t i c u l a r d i r e c t i o n (see Figures 16 and 19). With the exception of point 5, a l l of these conceptions i n d i c a t e a p r e v a l e n t , underlying theme f o r students' explanations of the motion of o b j e c t s . This theme i s that 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 uniform motion, i s the r e s u l t of some type of motive f o r c e . This 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 to the object or t r a n s f e r r e d to the object by some other moving ob j e c t . Conclusions Concerning 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 Transform Student Conceptions of Dynamics The transformation of student conceptions of dynamics, that 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 with Newtonian conceptions of dynamics, was to occur as a r e s u l t of the p r e s e n t a t i o n of (assumed) discordant events that could not be s a t i s f a c t o r i l y explained using these student conceptions. This technique can only be viewed as being m a r g i n a l l y s u c c e s s f u l . The 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-gested t h a t , f o r the m a j o r i t y of students t a k i n g part 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 because a continuously i n c r e a s i n g f o r c e was being a p p l i e d to an o b j e c t . In a d d i t i o n , a number of students a l s o suggested that the a p p l i c a t i o n of a constant f o r c e to an object 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 v e l o c i t y . In order to confront these conceptions and transform them i n t o ones more c l o s e l y 107 approximating the Newtonian view of a c c e l e r a t i o n , the students were presented with two demonstrations i n which s t a t i o n a r y objects were uniformly a c c e l e r a t e d by the a p p l i c a t i o n of a constant f o r c e . The r e s u l t of t h i s p r e s e n t a t i o n , apparently f o r the m a j o r i t y of students, was 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 constant force) i n t o these students' conceptual frame f o r a c c e l e r a t i o n as the necessary 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 an i n i t i a l l y s t a t i o n a r y o b j e c t . This conception then c o e x i s t e d w i t h the previous conception ( 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 force) which then assumed the r o l e of the necessary 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 object (see Figures 10 and 11). 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 of what were assumed to be discordant 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 conception i n t o an already e x i s t i n g and undesirable framework of a c c e l e r a t i o n , r a t h e r than the transformation of the p r e - e x i s t i n g framework. I t must be noted here t h a t , at some point (or p o i n t s ) i n the i n s t r u c t i o n a l sequence, a transformation towards the d e s i r e d Newtonian, conceptual frame f o r a c c e l e r a t i o n d i d occur. During the c o n s t r u c t i o n of the concept map 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 (see Figure 8) p r i o r to the d i s c u s s i o n of uniform motion, a student consensus had been a r r i v e d at that now viewed the minimum requirements 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 object to be one and the same - the a p p l i c a t i o n of a constant f o r c e . Just e x a c t l y where and why w i t h i n the i n s t r u c t i o n a l sequence t h i s transformation occurred can only be a t o p i c f o r conjecture. What i s known i s that t h i s transformation d i d not occur 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 demonstrations that were presented to the students. 108 The i n i t i a l 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 object suggested that the m a j o r i t y of students already had a conception 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 the a p p l i e d , motive fo r c e s being l e s s than the t o t a l of the forces opposing the motion) that was, at l e a s t , p a r t i a l l y congruent w i t h the Newtonian conception 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 negative net f o r c e operating on a moving o b j e c t ) . Only two students suggested that the cause of d e c e l e r a t i o n could be otherwise. For these students d e c e l e r a t i o n was caused by a motive f o r c e which was decreasing i n s i z e but always remained greater than the t o t a l of any forces opposing the motion (see Figure 14). Again, two demonstrations were presented to the students i n order to confront and transform any non-Newtonian conceptions of d e c e l e r -a t i o n . In both demonstrations, an object was decelerated using the minimum, Newtonian c o n d i t i o n , a constant f o r c e a p p l i e d i n the opposite d i r e c t i o n to the object's motion. The r e s u l t of these demonstrations was only a p a r t i a l t ransformation of the non-Newtonian conception of d e c e l e r a t i o n described above. The student who had o r i g i n a l l y suggested t h i s cause f o r d e c e l e r a t i o n now agreed that d e c e l e r a t i o n d i d r e s u l t when a constant f o r c e was a p p l i e d to an object i n the opposite d i r e c -t i o n to the motion of the o b j e c t , but he a l s o suggested that the d e c e l e r a t i o n of the object would degrade i n t o uniform motion. The i n i t i a l d i s c u s s i o n s of the dynamics of uniform motion i l l u m i n -ated one non-Newtonian conception of uniform motion. This conception h e l d , as i t ' s c e n t r a l tenet, that uniform motion was the r e s u l t of the a p p l i c a t i o n of a decreasing, motive f o r c e to an object (see Figure 18). Two demonstrations were presented to the students i n an attempt to counter t h i s conception, but these met w i t h only minimal success. Only 109 one student ( K a r i ) i n d i c a t e d that she now f e l t that uniform motion was the r e s u l t of balanced f o r c e s or a n u l l net f o r c e . For the other students who h e l d t h i s i n i t i a l , non-Newtonian conception, the demon-s t r a t i o n s were unconvincing and no transformations of t h e i r conceptions of uniform motion were apparent. In summary, the attempt to transform student conceptions of motion using, what were assumed to be, d i s c o r d a n t , motion events cannot be considered to have been s u c c e s s f u l . In only one case ( i n v o l v i n g uniform motion) was there a s u c c e s s f u l transformation of non-Newtonian conceptions i n t o Newtonian conceptions. In a l l other i n s t a n c e s , the attempts at transformation 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 Newton-i a n concepts i n t o a non-Newtonian conceptual s t r u c t u r e (as was the case f o l l o w i n g the a c c e l e r a t i o n demonstrations), or a minimal, p a r t i a l t r ansformation towards Newtonian concepts (as was the case f o l l o w i n g the d e c e l e r a t i o n demonstrations), or no change of the o r i g i n a l concep-t i o n s concerning a p a r t i c u l a r type of motion (as was the case f o l l o w i n g the uniform motion demonstrations). Conclusions Concerning the Design of the  I n s t r u c t i o n a l Strategy The o r i g i n a l design of the i n s t r u c t i o n a l s t r a t e g y can only be considered to be flawed i n both of i t ' s major elements. The use of student-produced concept maps as a b a s i s f o r d e l i n e -a t i n g major student concepts of dynamics, and r e c o g n i z i n g any a l t e r a -t i o n s to these concepts as the lesson sequence progressed, produced one of the classroom teachers' worst nightmares - an immense amount of student products that had to be analyzed and assessed before the 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 , design i n t e n t of these concept maps s h i f t e d to become a b a s i s f o r the 110 c o n s t r u c t i o n of c o l l e c t i v e l y - p r o d u c e d concept maps. The process of n e g o t i a t i o n and compromise that was required to produce these c o l l e c -t i v e concept maps of i n d i v i d u a l force/motion events u l t i m a t e l y l e d to a lo s s of d e t a i l and richness of conceptual understanding that could 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 -ively-produced concept maps were s u c c e s s f u l i n o u t l i n i n g student conceptions of force/motion events. In a d d i t i o n , j u x t a p o s i t i o n of these maps with teacher-produced, Newtonian maps of the same events was able to produce v a r i e d and i n t e r e s t i n g debate concerning the merits of each map. However, as a r e s u l t of the unwieldy and time-consuming nature of these concept maps, they were downgraded from t h e i r o r i g i n a l p o s i t i o n w i t h i n the design of the i n s t r u c t i o n a l s t r a t e g y and replaced by a d i r e c t clue s t r u c t u r e a n a l y s i s of student d i s c u s s i o n s of force/motion events. As has already been mentioned, the use of what were assumed to be di s c o r d a n t , force/motion events to i n i t i a t e transformations of student conceptions of these events to conceptions more c l o s e l y a l i g n e d w i t h Newtonian conceptions of the same events met with only minimal success. Whether t h i s was because the students d i d not recognize these events as being t r u l y d i s c o r d a n t , or because the student conceptions are ex-tremely robust and the students are l o a t h to r e l i n q u i s h a set of conceptions that have served them s u c c e s s f u l i n the past are subjects f o r c o n j e c t u r e . Conclusions Concerning the Development of the A n a l y t i c a l Clue S t r u c t u r e The use of 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 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 been extremely s u c c e s s f u l . As has already been mentioned, the clue s t r u c t u r e sup-I l l planted concept mapping as the a n a l y t i c a l lens of choice f o r the e x p l i c a t i o n of student conceptions of force/motion events and t r a c k i n g of any changes i n these conceptions as the lesson sequence progressed. The use of t h i s c l u e s t r u c t u r e has allowed the placement of student concepts of force/motion events w i t h i n reasonably cohesive frame s t r u c t u r e s that have proven to be v i s u a l l y easy to i n t e r p r e t and have allowed comparisons to be made between conceptual s t r u c t u r e s , used by d i f f e r e n t students, t o i n t e r p r e t the same force/motion event. Addi-t i o n a l l y , these conceptual frame s t r u c t u r e s have proven to be s e n s i t i v e enough to allow t r a c k i n g of conceptual change, w i t h i n i n d i v i d u a l students, that might have occurred as a r e s u l t of the 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 Conclusions Concerning the 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 to be s u c c e s s f u l i n the e x p l i c a t i o n of student conceptions of dynamics. This 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 students t a k i n g an a c t i v e part i n the lessons, any motion was viewed as being the r e s u l t of the a p p l i c a t i o n of some type of motive f o r c e . This e x p l i c a t i o n of student conceptions 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 intended use of concept mapping techniques which proved to be too cumbersome to be used w i t h i n the classroom environment. Rather, the s u c c e s s f u l e x p l i c a t i o n of student conceptions of dynamics was achieved by the 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, to t r a n s c r i p t i o n s of student d i s c u s s i o n s of s p e c i f i c force/motion events and problems. The i n s t r u c t i o n a l model has proven to be only minimally s u c c e s s f u l i n transforming non-Newtonian, student conceptions of dynamics i n t o conceptions that more c l o s e l y approximate Newtonian p r i n c i p l e s of 112 dynamics. Attempts at using, what were assumed to be, discordant events to accomplish these transformations have 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 Newtonian concepts i n t o non-Newtonian conceptual frames with only very l i t t l e m o d i f i c a t i o n to the o r i g i n a l , conceptual frame, or very l i t t l e or no m o d i f i c a t i o n to the o r i g i n a l , conceptual frame being employed by the s t u d e n t ( s ) . In only one i n s t a n c e , was a major tran s f o r m a t i o n of an o r i g i n a l , student, conceptual frame to a Newtonian, conceptual frame recognized. The reasons f o r the lack of success of t h i s part of the i n s t r u c t i o n a l model cannot be determined from the a v a i l a b l e data and can only be considered as subjects f o r conject u r e . A D i s c u s s i o n of the Results  The A l t e r n a t e Framework of Dynamics I t has come as no great s u r p r i s e to f i n d that the 'motion i m p l i e s a f o r c e ' set of conceptions and i t s c o r o l l a r y Impetus Theory have appeared as the conceptual s t r u c t u r e of choice f o r the i n t e r p r e t a t i o n of force/motion events by the m a j o r i t y of students w i t h i n t h i s c l a s s . Numerous other s t u d i e s that have attempted to d e l i n e a t e students' conceptions of dynamics have a l s o determined that t h i s conceptual s t r u c t u r e was present, e i t h e r i n whole or i n p a r t , i n the groups of students that they were i n v e s t i g a t i n g . As a r e s u l t of the prepon-derance of evidence that i n d i c a t e s that t h i s conceptual s t r u c t u r e i s not confined to.any s i n g l e , d e f i n a b l e group of students, t h i s set of r e l a t e d conceptions must be considered to be a form of 'conventional wisdom' dynamics that has been a r r i v e d at by using a 'common sense' approach to e x p l a i n and p r e d i c t the motion of objects that are so much a part of our everyday l i v e s . .113 This 'common sense' approach t o the explanation of moving objects does not ignore f r i c t i o n nor 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 simply accepts that f r i c t i o n i s always present and must be d e a l t w i t h . Herein l i e s the major point of contention between the 'conventional wisdom' dynamics and Newtonian dynamics and one of the probable reasons why the '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 robust and r e s i s t a n t to change. The power of Newtonian dynamics stems from i t ' s a b i l i t y too e x p l a i n and p r e d i c t the motion of objects w i t h i n both 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. In order to reach 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 because i t opposes motion. For many i n d i v i d u a l s , however, who have only l i v e d 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 c onceiving of 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 rath e r an impediment to motion that can only be overcome by the a p p l i c a t i o n of concrete forces such as pushes and p u l l s . Thus, motion becomes i n t i m a t e l y connected to the a p p l i c a t i o n of motive fo 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 the surface of the Earth. As a r e s u l t , an extremely cohesive and parsimonious ( f o r the surf a c e of the Earth) conceptual framework evolves around the c e n t r a l tenet t h a t , any time an object moves i t i s because of the a p p l i c a t i o n of these concrete f o r c e s . The cohesiveness and i n t e r n a l consistency of t h i s conceptual framework f o r motion can be seen i n the explanations that have been giv e n , by the students, f o r the causes of the various types of motion. 1. A c c e l e r a t i o n of a moving object i s caused by the 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 the same d i r e c t i o n as the motion of the obj e c t . 114 2. Acceleration of a stationary object (which is apparently a different situation than acceleration of a moving object) is caused by the application of a constant force. 3. Deceleration of a moving object is 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, all 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 1) that is directly related to some previously applied, motive force and incorporate this into the existing framework. In this fashion the integrity and utility 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 is new and untried. This latter option is one that few individuals would choose for i t would result in a period of extreme confusion while the individual sought new causes of the motion of objects and then attempted to 115 construct these new causes i n t o a comfortable and workable framework of dynamics. The c o n s t e r n a t i o n and confusion that would r e s u l t from the 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 probably accounts f o r the i n a b i l i t y of the i n s t r u c t i o n a l s t r a t e g y to b r i n g about s i g n i f i c a n t transformations i n the 'motion i m p l i e s a f o r c e ' conceptual framework that was so prevalent i n t h i s c l a s s . As an example, i n those cases where the i n s t r u c t i o n a l s t r a t e g y provided discordant events that suggested that motion could occur without the a p p l i c a t i o n of a motive f o r c e (as was the case with the bas e b a l l problem and the a i r - t r a c k demonstration) the m a j o r i t y of students might have f e l t that i t was p r e f e r a b l e to opt f o r the t r a n s l a -t i o n of the necessary (to account f o r the motion) a p p l i e d f o r c e to a ' t r a n s f e r r e d f o r c e ' rather than c a l l t h e i r e x i s t i n g conceptual frame-work i n t o question and accept the consequences that would accompany such an a c t i o n . I t i s a l s o p o s s i b l e that these students had already faced s i t u a t i o n s where objects moved without any d e f i n a b l e , motive f o r c e and had already made the necessary adjustments to t h e i r concept-ual frameworks to account f o r these. I f t h i s was the case, what were i n i t i a l l y assumed (by the researcher) to be discordant events were, i n f a c t , not viewed at a l l (by the students) to be discordant because t h e i r conceptual framework already contained an explanation (the ' 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 motion. Thus, the p r o t e c t i o n of the i n t e g r i t y of the e x i s t i n g conceptual framework of dynamics i s of paramount importance. Any changes that might be made to t h i s framework w i l l most l i k e l y f a l l i n t o the category of minor m o d i f i c a t i o n s or in c o r p o r a t i o n s that do not c a l l i n t o question the v a l i d i t y of the c e n t r a l tenet of t h i s framework - motion i m p l i e s a f o r c e . Major 116 transformations to t h i s conceptual framework of dynamics w i l l not occur as long as the 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 e x p e r i e n t i a l l y -based framework are l e s s than the 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 of the I n s t r u c t i o n a l Model The use of the t e s t i n g form of the teaching experiment as the ba s i s f o r determining the e f f i c a c y of the elements of the i n s t r u c t i o n a l model has i n d i c a t e d that only the a n a l y t i c a l c l u e s t r u c t u r e (and the subsequent r e p r e s e n t a t i o n of student conceptions of dynamics as frames and frameworks) can be considered to have been a success i n i t ' s o r i g i n a l form. The other element i n 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 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 during the research process i n response to environmental f a c t o r s w i t h i n the classroom. O r i g i n a l l y , that part of the i n s t r u c t i o n a l s t r a t e g y that was to be used f o r the e x p l i c a t i o n of student conceptions of dynamics was to r e l y h e a v i l y on the use of student-produced concept maps to provide the raw data f o r the cl 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 that these concept maps would provide an immediate, classroom window on to the type of concepts and the r e l a t i o n s h i p s between these concepts that students were using to e x p l a i n f o r c e and motion events. This was not to be the case however, as n e i t h e r of these two i n t e n t i o n s were able to be s u c c e s s f u l l y implemented w i t h i n the classroom. As has already been mentioned, the attempted implementation of concept mapping technique to s p e c i f i c f o r c e and motion events as a method of p r o v i d i n g an i n i t i a l e x p l i c a t i o n of student concepts of these events produced an immense amount of data. So much so, that the researcher found i t impossible to analyze and c o l l a t e these data f o r 117 student, concept patterns and/or concept s h i f t s ( r e s u l t i n g from discordant events) on a day-to-day b a s i s . Because of t h i s problem, any di s c u s s i o n s concerning comparisons between student and Newtonian conceptions of these events had to wait on the completion of the concept map analyses and, as a r e s u l t , lesson c o n t i n u i t y and flow was reduced. In a d d i t i o n t o the data production and a n a l y s i s problem, a s i g n i f i c a n t number of students w i t h i n the c l a s s were f i n d i n g i t very d i f f i c u l t (and time-consuming) to construct concept maps of s p e c i f i c f o r c e and motion events. This d i f f i c u l t y d i d not stem from a lack of f a m i l i a r i t y w i t h concept mapping techniques f o r these students 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 the school year on such d i v e r s e t o p i c s as current e l e c t r i c i t y , chemical bonding, and c e l l u l a r reproduction. Rather, the root of t h i s problem appeared to l i e w i t h i n the s p e c i f i c nature of the concepts and concept r e l a t i o n s that they had to recognize i n order to construct a v a l i d map of the events that were being demonstrated. P r i o r to the dynamics u n i t , student concept mapping had been d i r e c t e d at g e n e r a l i z e d conceptual s t r u c t u r e s such as the comparison and c o n t r a s t i n g of i o n i c and covalent bonding, and asexual and sexual c e l l u l a r reproduction. However, with the i n t r o d u c t i o n of the dynamics u n i t they were having to recognize and tease apart very s p e c i f i c concepts concerning the type, s i z e , and d i r e c t i o n of for c e s that were r e s p o n s i b l e f o r the motion of an object or, f o r that matter, whether any forces were indeed r e s p o n s i b l e f o r the motion. The d i f f i c u l t y that these students experienced while attempt-i n g to s i n k down to t h i s l e v e l of s p e c i f i c i t y suggests that concept mapping techniques may not be a p p l i c a b l e to such i s o l a t e d events or that the a n a l y t i c c a p a b i l i t e s of these students may not yet be up to 118 the task of r e c o g n i z i n g and a b s t r a c t i n g these types of s p e c i f i c concepts. Because of these two problems with student concept mapping, that part of the 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 conceptions of dynamics was s u b s t a n t i a l l y modified. This m o d i f i c a t i o n s t i l l i n v o l v e d student concept mapping, however these maps were now used as a c a t a l y s t t o i n i t i a t e the 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 of motion. 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 to provoke f u r t h e r c l a s s d i s c u s s i o n concerning the d i f f e r e n c e s between student and Newtonian conceptions of motion, and the a b i l i t y of the student conceptual s t r u c t u r e to e x p l a i n the motion of objects d i s p l a y e d during the discordant event demonstrations. The e x p l i c a t i o n and representa-t i o n of the student conceptions of s p e c i f i c types of motion was then achieved by d i r e c t l y a p p lying the a n a l y t i c a l c l u e s t r u c t u r e to the c l a s s d i s c u s s i o n s . Thus, by the end of the u n i t that part of the 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 conceptions of motion had evolved i n t o a reasonably c o n s i s t e n t sequence of t a c t i c s that i n c l u d e d : 1. a focus question (e.g. What would cause t h i s object to a c c e l e r a t e ? ) . 2. a demonstration of the s p e c i f i c type of motion followed by a c l a s s d i s c u s s i o n of the p o s s i b l e causes of the object motion. 3. c o n s t r u c t i o n of i n d i v i d u a l concept maps of the cause(s) of the object motion. 4. c o n s t r u c t i o n of a consensual, 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 the merits of i n d i v i d u a l concept maps. 119 5. a comparison of the elements of the 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 that same type of motion. 6. discordant event demonstrations. 7. a discussion/debate of the cause(s) of the p a r t i c u l a r motion type d i s p l a y e d during the discordant event demonstration. These d i s c u s s i o n s focussed upon the r e s p e c t i v e a b i l i t i e s of the student and Newtonian conceptual s t r u c t u r e s to e x p l a i n the cause(s) of the p a r t i -c u l a r type of motion. 8. a post hoc clue 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 that r e s u l t e d i n the e x p l i c a t i o n of student conceptions of p a r t i c u l a r types of motion as frames. Although t h i s t a c t i c a l sequence appeared to be agreeable to both the students and researcher, inasmuch as i t provided a s t i m u l a t i n g c l a s s -room environment, i t d i d not provide the immediate window on to student conceptions of dynamics that had been hoped f o r . Rather the researcher had to r e l y on a g u t - l e v e l f e e l i n g concerning whether or not any p a r t i c u l a r classroom d i s c u s s i o n was p r o v i d i n g adequate conceptual data that could be used to construct a frame s t r u c t u r e using the post hoc, clue s t r u c t u r e a n a l y s i s . As a r e s u l t , the e f f e c t s of the 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 student conceptions of dynamics and t r a n s -forming these conceptions could not be determined on a day-to-day b a s i s except on a macroscopic l e v e l . The operation of t h i s modified 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 the classroom produced few, i f any, c l a s s management problems. Because of the s t r a t e g y ' s heavy r e l i a n c e on student a n a l y s i s , d i s c u s s i o n and debate, student on-task time, c o n c e n t r a t i o n and i n t e r e s t appeared to be s i g n i f i c a n t l y higher than that which would have been generated by more 120 t r a n s m i s s i v e forms of teaching. A d d i t i o n a l l y , f o r t h i s researcher, i t was g r a t i f y i n g to see that these students were capable of and i n t e r -ested 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 world and, i n essence, 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 education. Recommendations The l a r g e number of research s t u d i e s that have i d e n t i f i e d the 'motion i m p l i e s a f o r c e ' conceptual s t r u c t u r e as the i n t e r p r e t a t i o n a l model of choice among t h e i r s ubjects f o r d e a l i n g w i t h the dynamics of moving objects suggests that f u r t h e r research i n t o the e x p l i c a t i o n of student conceptions of dynamics would be redundant. As a r e s u l t of these successes i n i d e n t i f y i n g t h i s major conceptional framework, i t i s recommended that any f u t u r e research be d i r e c t e d towards the design of i n s t r u c t i o n a l 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 framework. At t h i s point i t would appear that t h i s research d i r e c t i o n could f o l l o w two p o s s i b l e paths. F i r s t , the design of the f u t u r e i n s t r u c t i o n a l s t r a t e g y could assume the same stance as d i d t h i s research and attempt to replace the 'motion i m p l i e s a f o r c e ' conceptual framework w i t h a new conceptual framework that i s based upon Newtonian p r i n c i p l e s of dynamics. To accomplish t h i s replacement, however, i t would f i r s t be necessary to thoroughly d i s c r e d i t the e x i s t i n g framework, probably through the use of discordant event demonstrations and, as has been i n d i c a t e d by t h i s research, t h i s i s not an easy task. Thus, any research that wished to f o l l o w t h i s path would have to begin w i t h an a d d i t i o n a l research problem that d e a l t w i t h the design and t e s t i n g of prototype, discordant event demonstrations i n order to ensure that they were, i n f a c t , 121 discordant and had the ca p a c i t y to d i s c r e d i t the 'motion i m p l i e s a f o r c e ' framework. The second research path that could be followed i s a purely pragmatic path. This path would accept the premise t h a t , because the e x i s t i n g conceptual framework i s e x p e r i e n t i a l l y based and has explan-atory and p r e d i c t i v e c a p a b i l i t i e s that are 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 of t h i s framework i s not p o s s i b l e . As a r e s u l t of t h i s premise, the best that 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 the short term, i s the c o n s t r u c t i o n of an a d d i t i o n a l Newtonian framework of motion that would be dedicated to the i n t e r p r e t a t i o n and expl a n a t i o n of events that occur w i t h i n the school environment and which would c o e x i s t w i t h the 'motion i m p l i e s a f o r c e 1 framework. Indeed, i f such a c o n s t r u c t i o n and coexistence 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 the long term, students would recognize the explanatory and p r e d i c t i v e power inherent w i t h i n the Newtonian framework of dynamics and begin to replace the 'motion i m p l i e s a f o r c e ' framework w i t h the 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 that as many science teachers as p o s s i b l e be made aware of the 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 of t h i s conceptual framework that t h e i r students are b r i n g i n g w i t h them to t h e i r classrooms and that l i n e s of communication be opened between these teaching p r o f e s s i o n a l s and educational researchers. By making science teachers aware of t h i s conceptual framework and i t s attendant problems, the number of p r o f e s s i o n a l s searching f o r s o l u t i o n s to these problems w i l l be d r a m a t i c a l l y increased. Consequently, the p r o b a b i l i t y of designing an i n s t r u c t i o n a l s t r a t e g y that i s 'classroom o p e r a t i o n a l ' w i l l a l s o be increased. The opening of l i n e s of communication between these two groups should ensure that 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 designed by teachers and which appear to be s u c c e s s f u l i n c o n f r o n t i n g the '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 rigorous 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 r e p r e s e n t a t i o n of the a l t e r n a t e framework of dynamics using a clue 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 p e r s p e c t i v e of frame theory suggests that t h i s form of a n a l y s i s and v i s u a l r e p r e s e n t a t i o n should 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 those areas of the p h y s i c a l sciences i n which students appear to have constructed other s p e c i f i c , a l t e r n a t e frameworks. To t h i s end, i t i s recommended that a d d i t i o n a l research be conducted i n t o the f e a s i b i l i t y of using t h i s form of a n a l y s i s to represent students' p o s s i b l e a l t e r -nate frameworks i n the areas of heat, l i g h t , and e l e c t r i c i t y . 123 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 forces i n e q u i l i - brium. 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West, Leo H.T., Pines, Leon A., & Sutton, 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 . Unpublished manuscript. Winograd, T. (1975). Frame r e p r e s e n t a t i o n and the d e c l a r a t i v e -procedural controversy. In Daniel G. Bobrow & A l l e n C o l l i n s (Eds.), Representation and understanding: 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 Press. Viennot, L. (1979). Spontaneous reasoning i n elementary dynamics. European Journal of Science Education, 1, 205-221. 126 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) 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. 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) 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. 3. 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. 500 N 3000 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 is riding a 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) 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 the net force (if there is no net force state this). 3. 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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