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A case study of university physics students' conceptualization of sound Linder, Cedric J. 1989

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A C A S E S T U D Y O F UNIVERSITY PHYSICS STUDENTS' CONCEPTUALIZATIONS O F SOUND By CEDRIC J. LINDER B.Sc. (Pure Mathematics; Physics with Electronics), Rhodes University, 1977 B.Sc.Honours (Physics and Electronics), Rhodes University, 1978 Higher Diploma in Education (Postgraduate; Secondary), Rhodes University, 1979 Ed.M. (Science), Rutgers University, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR IN EDUCATION i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MATHEMATICS AND SCIENCE EDUCATION We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A April 1989 © Cedric J. Linder, 1989 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 The University of British Columbia Vancouver, Canada Date ^ / y / g ?  DE-6 (2/88) i i ABSTRACT This study identified some of the conceptual problems which physics students often encounter when asked , to explain their understanding of topics studied in their undergraduate physics programme. In particular, the study focused on the area of sound and the associated conceptualizations held by a group of physics graduates who were enrolled in a secondary physics teacher education programme. Three aspects of their understanding were scrutinized: conceptualizations of sound per se and the consistency of these conceptualizations across a variety of contexts; conceptualizations of the factors affecting the speed of sound propagation; and, factors influencing their conceptualizations of the similarities and differences between the physics concepts of sound and light. The approach taken was one embedded in phenomenography, an experientially based research perspective developed at Gothenburg University in Sweden. In general terms, phenomenography is the study of the qualitatively different ways in which people conceptualize various aspects of reality and phenomena. The data source was a set of interviews conducted with the students which incorporated a variety of different contexts. These contexts included theory, experimentation and demonstration. The interview protocol was developed in an extensive pilot study which involved a similar group of students. The outcomes of the study yielded an identification and description of the students conceptualizations of sound and provided insights into how these were strongly mediated by: microscopic and macroscopic explanatory perspectives, intuition, language, and a tendency to view much of physics as abstract applied mathematics. While some contexts appeared to provide visual cues which evoked certain kinds of conceptualizations, most conceptualizations tended not to be specifically contextually dependent. i i i As part of the consequences of the study, a recommendation was made for university physics educators to re-evaluate both what they teach and how they teach. In particular, for potential physics teachers, a conceptual approach to teaching undergraduate physics was proposed. i v T A B L E OF C O N T E N T S ABSTRACT i i LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS i x CHAPTER I: THE PROBLEM ; 1 1.1 Introduction to the Problem 1 1.2 Background to the Problem: How Physics is Taught 3 1.3 Problem Statement 8 1.3.1 General Statement : ...8 1.3.2 Specific Research Questions.... 9 1.4 Rationale and Delimitations of the Problem 10 1.4.1 Conceptual Understanding of Sound and its Propagation 10 1.4.2 Using Graduate Physics Student Teachers for the Study 12 1.4.2.1 Implications for Potential Physics Teachers 13 1.5 Overview of Layout of Dissertation 15 1.6 Description of Terms 16 1.7 Overview of Chapter I 17 CHAPTER II: LITERATURE REVIEW AND THEORETICAL FRAMEWORK 18 2.1 Introduction....; 18 2.2 The Extensiveness of the Conceptualization Research 18 2.3 Choice of Theoretical Perspective 20 2.4 The Framework of Phenomenography 22 2.4.1 Categories of Interpretation 23 2.4.1.1 Categories of Description 23 2.4.1.2 Categories of Influence 27 2.5 Summary of the Theoretical Perspective: Phenomenography 27 2.6 Overview of Chapter II 28 CHAPTER HI: DESIGN OF STUDY AND METHODOLOGY 29 3.1 Introduction: A Qualitative Naturalistic Case Study 29 3.2 Outcomes of the Study 29 3.3 Generalizability of the Study 30 3.4 The Design of the Study 31 3.4.1 Concept Analysis of the Phenomenon of Sound 31 3.4.2 The Design of the Interview Protocol 31 3.4.2.1 Factors Influencing the Design 31 3.4.2.2 The Structural Format of the Interview Protocol 33 3.5 The Data Analysis 38 3.5.1 Data Analysis: The Categories of Description Characterizing Conceptualizations (Chapter IV) 39 3.5.2 Data Analysis: Looking for Consistency of Conceptualization (Chapter V) 40 3.5.3 Data Analysis: How the Students Managed the Task of Comparing and Contrasting Light and Sound 40 3.6 Overview of Chapter III 41 V CHAPTER IV: DATA ANALYSIS: CONCEPTUALIZATIONS 43 4.1 Introduction to Analytic Method 43 4.2 Data Analysis for Research Question 1: Conceptualizations of the Phenomenon of Sound 44 4.2.1 Introduction. 44 4.2.2 Conceptualizations of Sound: The Microscopic Perspective 45 4.2.2.1 Microscopic Perspective Conceptualization # 1: Sound as an Entity: The Transporting-Molecule Conceptualization 45 4.2.2.2 Microscopic Perspective Conceptualization # 2: Sound as an Entity: The Conducting-Molecule Conceptualization 49 4.2.3 Conceptualizations of Sound: The Macroscopic Perspective 51 4.2.3.1 Macroscopic Perspective Conceptualization # 1: Sound as a Bounded Substance: The Flowing Air Conceptualization 51 4.2.3.2 Macroscopic Perspective Conceptualization # 2: Sound as a Bounded Substance: The Travelling Pattern Conceptualization ...54 4.2.4 The Wave Model Conceptualization: An Intricate Blend of Macro- and Microscopic Perspectives 56 4.2.5 Discussion of Data Analysis for Research Question 1 61 4.3 Data Analysis for Research Question 2: Conceptualizations of Factors Affecting the Speed of Sound 64 4.3.1 Introduction 64 4.3.2 Conceptualization # 1: The Speed of Sound is a Function of the Physical Obstruction that Molecules Present to Sound as it Navigates its Way Through a Medium 64 4.3.3 Conceptualization # 2: The Speed of Sound is a Function of Molecular Separation 67 4.3.4 Conceptualization # 3: The Speed of Sound is a Function of the Compressibility of a Medium 70 4.3.5 Discussion of Data Analysis for Research Question 2 73 4.4 Overview of Chapter IV 75 CHAPTER V: DATA ANALYSIS: CONCEPTUAL CONSISTENCY AND DISPERSION 77 5.1 Data Analysis for Research Question 3: Introduction 77 5.2 Conceptual Dispersion: Patterns of Reasoning In and Across Contexts. 78 5.2.1 Theme (a): Shifting Explanatory Perspectives 83 5.2.2 Theme (b): Gut-Physics Flashbacks 85 5.2.3 Theme (c): Prolonged Gut-Physics Flashbacks 91 5.2.4 Theme (d): Disconnected Mathematical and Physics Thinking. . . . 99 5.2.5 Theme (e): Dissonant Conceptual Dispersion: Examples of Student Reaction to Recognized Inconsistency 103 5.2.5.1 First Example from the Wavelength Probing Scenario 104 5.2.5.2 Second Example from the Wavelength Probing Scenario ....111 5.3 Discussion of Data Analysis for Research Question 3 117 5.4 Overview of Chapter V . 118 vi CHAPTER VL DATA ANALYSIS: FACTORS INFLUENCING CONCEPTUALIZATION: COMPARING AND CONTRASTING LIGHT AND SOUND 120 6.1 Data Analysis for Research Question 4: Introduction 120 6.2 Category of Influence Outcome # 1: The Role of Physics-Based Language in the Comparative-Conceptualization of Light and Sound 123 6.3 Category of Influence Outcome # 2: The Role Played by Everyday-Based Intuition in the Comparative-Conceptualization of Light and Sound 128 6.4 Category of Influence Outcome # 3: The Role of Mathematical and Qualitative Physics Connections in Influencing the Comparative-Conceptualization of Light and Sound 133 6.5 Discussion of Data Analysis for Research Question 4 137 6.6 Overview of Chapter VI 142 CHAPTER VII: CONCLUSIONS, IMPLICATIONS AND RECOMMENDATIONS 144 7.1 Introduction 144 7.2 Specific Conclusions from the Study 144 7.2.1 Introduction 144 7.2.2 Conclusions from Chapter IV 145 7.2.3 Conclusions from Chapter V 147 7.2.4 Conclusions from Chapter VI 150 7.3 General Conclusions, Observations and Discussion Arising from the Study 152 7.3.1 The Functional Context of Language 152 7.3.2 Choice of Explanatory Perspectives 155 7.3.3 Conceptual Dispersion 160 7.4 Implications for Physics Education 165 7.5 A Proposed Physics Undergraduate Programme for Teachers 165 7.5.1 Introduction '. 165 7.5.2 A Proposed Physics Curriculum Structure 168 7.6 Recommendations for Further Research 171 7.6.1 Building a Phenomenography of Physics 171 7.6.2 Research into the Proposed Physics for Teachers Programme 172 7.6.3 Working with Recently Graduated School Physics Teachers 173 7.7 Overview of Chapter VII 174 REFERENCES 175 APPENDIX I: A Concept Map of Sound 188 APPENDIX II: A Sample of a Complete Interview Transcript 189 v i i LIST O F T A B L E S 5.1 Explanatory Perspectives as a Function of Contexts and Students 81 5.2 Students as a Function of Conceptualizations and Interview Contexts 82 v i i i L I S T OF F I G U R E S 3.1 A Travelling Sound Wave Depiction 3.2 Sound Tube Experiment .36 ,37 ix ACKNOWLEDGEMENTS I would like to express my sincere thanks and gratitude to Gaalen Erickson, my research supervisor, and to Walter Boldt, Stuart Donn, and Peter Matthews, my committee members, for all their guidance and encouragement. I would also like to thank Izak van Heerden and Dirk Knoesen of the University of the Western Cape, and Ned Munger of the Cape of Good Hope Foundation, for all their support. Finally, I wish to thank Anne, for her faith in me, and her love and help that made it possible for me to complete this study. Financial assistance for the study was provided by the Cape of Good Hope Foundation, the Institute for Research Development of the Human Sciences Research Council*, and the University of British Columbia, all of which is gratefully acknowledged. * Opinions expressed in this dissertation and conclusions arrived at, are those of the author and are not necessarily to be attributed to the Institute for Research Development or the Human Sciences Research Council. X For Anne 1 C H A P T E R I THE PROBLEM 1.1 Introduction to the Problem The conceptual problems which university physics students typically encounter are often both complex and daunting (for example, see Clement, 1982; diSessa, 1986; McCloskey, 1983, McDermott, 1984; Helm, 1980; Hewson, 1982; Peters, 1981; Viennot, 1979; Warren, 1983), and students are graduating with physics conceptualizations that are considered to be inappropriate (that is, conceptualizations which are at variance with concepts which are defined constructs in physics — see Section 1.6: Description of Terms). Contemporary physics test and examination results are usually considered to be indicative of student understanding, yet these results provide educators with little insight into the nature of their students' understanding. For instance, it may be that some students have conceptualizations which are at variance with the concepts underlying some calculation required in an examination, yet they can still calculate a "correct" answer (Helm, 1983; Hewson, 1980). Working with physics students at Massachusetts Institute of Technology, diSessa (1986), found that while many of the students were able to solve physics problems in quantitative terms they were unable to appropriately analyse them in qualitative terms. Students in such a predicament would seem to lack a coherent physics perspective, which is what their undergraduate studies should be affording them. Depending on students' career decisions, this "predicament" has different implications for different students. It would seem that the most serious implications would be for those students choosing to become school physics teachers. This is because it is unlikely that potential physics teachers could be afforded the conceptual exploration opportunities in education studies that students continuing on in a physics graduate programme would be afforded while in the process of coming to understand at least one physics problem very well. In order for physics educators at the tertiary level to provide a level of education that extends beyond presenting a set of lectures (in the most literal sense) and assigning tutorial problems to be overseen by assistants (whose immediate concerns do not typically extend beyond the students being able to calculate a 2 "correct" answer), then, physics educators require insights into how students conceptualize their physics and what the substance of their conceptualizations are. These kinds of insights are considered to be obtainable from interpretative, experientially based research. Recent research (for example, see Driver and Bell, 1986; Erickson, 1984; Fensham 1983; Novak and Gowin, 1984; Osborne and Freyberg, 1985; Pope and Gilbert 1983; Pope and Keen, 1981) has indicated that many of the conceptual problems which physics students encounter may have their foundation in attitudes to teaching and learning which are based on epistemological beliefs which fail to take any significant account of the prior knowledge, intuitions, beliefs and understandings that students invariably bring with them to class. Essentially there is a lack of cognizance that (non-rote) learning involves a process whereby individuals generate their own meanings in an effort to make sense of their experiences and the information that they receive. Commenting on the importance of the understandings and notions that students have when they come into an instructional setting Novak and Gowin (1984) wrote: How can we help individuals to reflect upon their experience and to construct new, more powerful meanings? Educational programs should provide learners with the basis for understanding why and how new knowledge is related to what they already know (pp. xi - xii). The majority of research done at the post-secondary level into conceptual understanding of physics has been done with undergraduates, primarily at the first year level, and has mainly focused on students' understanding of force and motion. This study considers how a group of physics graduates in a teacher education programme conceptualize the phenomenon of sound from an interpretative experiential perspective called phenomenography ("the study of the qualitatively different ways in which people experience and conceptualize the world around them" — see Section 1.6: Description of Terms) 3 1.2 Background to the Problem: How Physics is Taught There are two main interrelated dynamics which affect physics teaching and learning. On the one hand there are the teachers' perspectives of how students learn and conceptualize their physics. These perspectives form an integral framing of an educators' teaching style in relation to their "personal" philosophy of teaching. As part of the background to this study it will be argued that in much of university physics there is a common teaching style which is driven and perpetuated by an epistemological perspective that pervades much of the Western university physics community. Further, this teaching style facilitates the incorporation of inherited or taken-for-granted methods of physics teaching, which includes the use of analogies, demonstrations etc., which may be inappropriate (because they are often derived from an analysis of the disciplinary knowledge rather than from students' prior knowledge) for providing students with insights into the concepts being taught. On the other hand, there are the students' perceptions of what studying physics is all about, based upon the style in which they are taught. These perceptions are covert and have been characterized in this study as forming part of a "hidden curriculum" of physics. Lecturers who teach university physics courses often make unsubstantiated assumptions about how their students acquire conceptual understanding in the process of learning physics (for example, see McMillen, 1986). As Bruner (1986) has pointed out, these metalearning assumptions are inexplicably intertwined with the instructor's philosophical view of the nature of science: I do not for a minute believe that one can teach even mathematics or physics without transmitting a sense of stance toward nature and the use of mind. (p. 128) The pervasive philosophical view of the nature of science portrayed in science textbooks and professional scientific journals appears to consistently fall under the umbrella of one or another form of philosophical empiricism/positivism; this has been true for most of the 20th Century (Elkana, 1970; Finley, 1983; Gauld, 1982; Hodson, 1985; Marquit, 1978; Mulkay, 1979; Norris, 1984; Otero, 1985; Schon, 1983). Although there are many shades of epistemology under the banner of philosophical empiricism/positivism it is possible to "discuss the main theme 4 without going into the details of variations and still provide a useful analysis" (Nersessian, 1984, p. 5). A useful way of viewing the basic scientific meaning/truth epistemological theme pertaining to the empiricist/positivist umbrella is to describe it as "metaphysical realism" (Glasersfeld, 1984; Putnam, 1981). A metaphysical realist "subscribes to the correspondence theory of truth." (Putnam, 1981, p. 56) In other words, a metaphysical realist views experimentation and observation as direct experiences of physical reality; knowledge is a one-to-one mapping (accurate reflection) of nature's independent reality which exists in our "objective world" (Glasersfeld, 1984). Something is "true" only if it corresponds to this independent objective reality; "truth" is fundamentally "objective validity" (Putnam, 1981). This traditional view of the nature of physics and science has continued to dominate both secondary and post-secondary science educational environments despite severe criticism by leading science educators (see Finley, 1983; Gauld, 1982; Helm, 1983; Hodson, 1985; Holton, 1979; Marquit, 1978; Norris, 1984; Otero, 1985). For example, Finley (1983), in discussing research and curriculum development in science education wrote: A commitment to inductive empiricism pervades the presently held view of science processes. A major tenet of of this commitment is that conceptual knowledge results from the application of science processes in understanding natural phenomena and solving problems .... The alternative is to view the exact nature of science processes as being dependent upon the conceptual knowledge that is used to understand a particular phenomena or problem. (p. 47) Putnam (1981) and Glasersfeld (1984) provide a historical perspective for the pervasiveness of metaphysical realism: The theory that truth is correspondence is certainly the natural one. Before Kant it is perhaps impossible to find any philosopher who did not have a correspondence theory of truth. (Putnam, 1981, p. 56, emphasis his) On the whole, even after Kant the situation did not change. The pressure of philosophical tradition was overwhelming. In spite of Kant's thesis that our mind does not derive laws from nature, but imposes them on it, most scientists today still consider themselves 'discoverers' who unveil nature's secrets and slowly and steadily expand the range of human knowledge .... Now as ever, there reigns the conviction that knowledge is knowledge only if it reflects the world as it is. (Glasersfeld, 1984, p. 20) 5 Although, as Glasersfeld points out, metaphysical realism is still strongly supported by the scientific community not all scientists have embraced it. For example, Einstein and Infeld (1938) described the nature of science epistemology as "a creation of the human mind with its freely invented ideas and concepts ... a link with the world of sense impression", (p. 310) From the discussion so far the question arises: Why should metaphysical realism's epistemological themes present a problem for physics education at university? From the perspective of this study the answer is that metaphysical realism inherently downplays any personal subjective contributions to science, in attitude, historically, and epistemologically. The extension of this attitude into the educational environment contributes to the perception that students have little contribution to make to a physics class beyond "learning" what they are being "taught" and completing their assigned tutorial problem sets. For example, in his criticism of a metaphysical realist type of approach to physics teaching Marquit (1978) wrote: The emphasis which modern empiricists place on the logical structure of scientific knowledge has greatly reduced the dependence of modern sciences on ... speculative and intuitive methods ... to undervalue the contributions of conscious mental or theoretical activity to the process of acquiring an understanding of the physical world, (p. 785) In his book Ideas and Opinions, Einstein (1973) provides an insight into how pervasive the "undervaluing of theoretical activity" in science is: If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds. To him who is a discoverer in this field, the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities. (p. 264) The education problem becomes manifest when one considers the supporting psychological rationale for the dominant adoption of metaphysical realist epistemological themes in current physics class and textbook pedagogy: 6 The psychological rationale which seems to support this type of presentation is the assumption that knowledge of facts provides an adequate psychological foundation for concept learning (Otero, 1985, p. 364). The traditional approach to science teaching which gives overriding importance to "facts" which "match" (Glasersfeld, 1984) ontological reality has foundationally supported a dominant Western teaching perspective which has been termed "cultural transmission" (for example see Pope and Gilbert, 1983, and Pope and Keen, 1981). Cultural transmission characterizes teaching activities which present knowledge as "bundles of truths" in a presumed "logical" order into the "tabula rasa" minds of students — their minds being metaphorical sponges absorbing knowledge. Hence, cultural transmission is naturally open to support from the psychological paradigms of behaviourism and neo-behaviourism. "Facts" and their associated "conceptual understanding" are best learnt by studying hard and the best "reinforcements" for studying hard are examinations, tests and quizzes. In much of university physics "studying hard" manifests itself as solving traditional tutorial problem-sets which are presumed to evoke appropriate conceptualizations of the concepts being taught. The link between solving sets of standard problems and the generation of conceptual understanding appears to be an underlying physics pedagogical assumption which is very widely held by physics educators (Chi, Glaser and Rees, 1981; Larkin and Reif, 1979; Larkin, McDermott, Simon and Simon, 1980; Striley, 1988). For example, Van Harlingen (1985) offers the following advice to introductory physics students: A solid understanding of physics includes the ability to solve a variety of problems .. your ability to successfully solve problems is one way that you (and your teachers) can measure your understanding (p. 30, emphasis mine). However, especially at the introductory physics level, the problem-sets assigned as homework "tutorials" and the problems which are consequently used in physics examinations may be characteristically described as "stereotyped quantitative examples" (Gamble, 1986) requiring "prototypical solutions" (Reif, 1982). For example, see many of the the chapter problems in popular introductory physics textbooks such as Giancoli (1985), Halliday and Resnick (1986), Sears, 7 Zemansky and Young (1985), and Weidner (1985). Linking conceptual understanding with the ability to successfully solve such physics problems is a doubtful pedagogical assumption (diSessa, 1986; Helm, 1983; Hewson 1980; Gamble, 1986; Reif, 1982; Reif and Heller, 1982; Warren, 1986). For example, from the results of their research, Reif and Heller (1982) noted that: The cognitive mechanisms needed for effective scientific problem solving are complex and thus not easily learned from mere examples and practice ....Too little attention is commonly paid to the organization of the knowledge acquired by students ... students are given little help to integrate their accumulating knowledge into a coherent structure facilitating flexible use. (p. 125) Thus it appears that it is of questionable value for physics educators to assign tutorial problems for homework without having an insight into how students are constructing their conceptualizations of the physics being taught (Arons 1983, 1984a, 1984b; Clement, 1981; Faucher, 1981). The metaphysical realist influence on traditional science instruction and epistemology, in its neglect in valuing students' existing conceptions, purposes and motivations, has covertly added another dimension to the conceptual difficulties which university physics students have to face. Instruction which views the lack of "correct" understanding to be a consequence of a lack of "studying hard" (or alternatively lack of required intellect) may proceed at an enormous rate. The amount of course content covered then takes on overriding importance (English language introductory university physics textbooks all offer much the same basic curriculum). This rate of instruction is typically so rapid that any in-class reflection becomes impossible (see for example, McMillen, 1986; Tobias, 1986). Arons (1979) captured the nature of this typical instruction pace with a "length contraction" metaphor (from Einstein's Special Theory of Relativity): It is the premise of the vast majority of introductory physics courses ... that if one takes a huge breadth of subject matter and passes it before the student at sufficiently high velocity, the Lorentz contraction will shorten it to a point at which it drops into the hole which is the students mind .... The students have been 'told' but they have not made the concept part of their own .... they get 'credit' for going through a memorized calculational procedure which happens to give them the 'right' numerical answer ... while they have no understanding of the physics, (p. 650) 8 1.3 Problem Statement 1.3.1 General Statement From the perspective of this study, physics students' conceptualizations are the outcomes resultant from the students' organizing and structuring of what they are taught in terms of their prior knowledge and experiences. Conceptualizations should be recognized in terms of their contextual appropriateness with regards to a coherent physics perspective of the world. In the previous section an argument was presented that university physics education is widely framed by a dominant "standard" empiricist/positivist model of how the teaching of physics should proceed, both in lectures and textbooks. As a direct consequence of this standard model of physics pedagogy it is likely that for many students physics becomes an extremely difficult subject of laws, formulae and problem solving algorithms, all to be mostly rote learnt to pass the final examination with little accompanying appropriate conceptualization construction. Passing contemporary physics examinations is usually equated with the attainment of "correct" conceptual understanding pertinent to the physics being examined, however, students with a deficit of appropriate current physics conceptual understanding often manage to pass physics examinations by memorizing sufficient material (Arons, 1979, 1983; Dahlgren, 1979; Dahlgren and Marton, 1978; Lin, 1982; Lundgren, 1977). It is not surprising, then, to find physics students who have successfully completed their undergraduate physics evoking conceptualizations which are contextually inappropriate, based upon intuition, or confused in abstraction (for example see, Faucher, 1983; Helm, 1980; Hewson, 1982; Sjoberg and Lie, 1981; Villani and Pacca, 1987). The educational concerns associated with students graduating with physics as a major subject and having a relatively wide range of inappropriate conceptualizations are highlighted when considering potential secondary school physics teachers. Research has indicated that secondary physics teachers often hold similar contextually inappropriate conceptualizations as those of their pupils (for example, see Helm, 1980; Sjoberg and Lie, 1981). While a direct link between teachers' and pupils' evoked conceptualizations is not being proposed, it is, 9 however, being suggested that teachers' conceptualizations play a fundamental role in the complex conceptualization construction/reconstruction that takes seed during physics classes. In this regard, it would add a further level of complexity to the recommendation made by Driver and Erickson (1983): We ought to engage in research endeavours which will uncover student frameworks, investigate the ways they interact with instructional experiences and utilize this knowledge in the development of teaching programmes. (p. 40) This study, then, is directed at uncovering the nature of the conceptualizations which a group of ten physics graduates, who are postgraduate students in a physics teacher education programme, have regarding the phenomenon of sound. 1.3.2 Specific Research Questions 1. What are the qualitatively different ways that a group of ten physics graduates from a teacher education programme conceptualize the phenomenon of sound from: - a microscopically based perspective; and, - a macroscopically based perspective? 2. What is the qualitative nature of the students' conceptual understanding of the factors which affect the speed of sound? 3. What is the nature of the consistency of the students' patterns of reasoning about sound in and across the following interview generated contexts: - an example offered by the students from their experiences which had not formed part of their formal physics classes; - an example not commonly used in physics teaching but which would be common to everyday experience; - an example commonly used in physics teaching; - an experimental situation; and, - a hypothetical teaching situation? 4. How do the students deal with a request to qualitatively compare and contrast the physics concepts of light and sound? 10 1.4 Rationale and Delimitations of the Problem 1.4.1 Conceptual Understanding of Sound and its Propagation Physics students are often faced with generating conceptualizations in educational environments which may be doing more to complicate further conceptualization and rationalization than otherwise. Conceptualization difficulties may arise from many factors encountered both in class and in textbooks. Some of these factors include abstractness of examples, implicitness in conceptual connections, ambiguous inferences, counter-intuitiveness and a variety of underlying pedagogical and epistemological assumptions. Examples of textbook generated conceptual difficulties are given by Iona (1987); Aguirre (1981) has exemplified the nature of implicit assumptions in physics texts; and, Tobias (1986) and McMillen (1986) provide insight into some of the underlying pedagogical and epistemological assumptions in a typical university introductory physics course. When faced with situations such as these, students can only try to cope in the best way that they can. For instance, their coping could include adopting one or more of the following strategies: Rote memorization of facts and formulae. Concentrating on problem solving without gaining insight into underlying concepts. Rejecting the presented "correct" conceptual models completely, and constructing conceptualizations which are plausibly based upon intuition, yet which lead some of the time to a "correct" answer. When adopting any of these, or similar strategies, the functional appropriateness of a conceptualization is lost. That is, students will be generating a number of related but inconsistent and disconnected conceptualizations. Consider an example taken from Einstein's Special Theory of Relativity. Suppose a problem of relative velocity is solved for two photons travelling, say, directly away from each other. From the chosen frame of reference the solution of the problem will yield an answer which has a magnitude greater than the speed of light. Many students are deeply concerned when, in similar problems, their calculated answers seemingly contradict one of Einstein's postulates; that is, nothing may travel 11 faster than the speed of light. However, their concern has its foundation in an inadequate conceptualization of what the terms speed and velocity mean in physics. With the appropriate conceptualizations this concern should not arise. From a physics perspective, sound as a primary component of our everyday life has generated a wealth of interesting problems (for instance, see Walker, 1975, pp. 3 - 19). Technological innovations utilizing sound waves are also continuously taking place in fields such as medical physics (see for example, Looker, 1985) and piezoelectric microwave electronics (see for example, Apfel, 1974). Beyond an intrinsic interest in the phenomenon of sound, and despite less and less time being available for the study of sound in introductory physics (for example, see Miller, 1987), the study of sound serves an important introductory role in developing physics wave conceptualizations. For example, "The Feynman Lectures on Physics" chapter entitled "Sound. The Wave Equation" begins with the following introduction: In this chapter we shall discuss the phenomenon of waves. This is a phenomenon which appears in many contexts throughout physics, and therefore our attention should be concentrated on it not only because of the particular example considered here, which is sound, but also because of the much wider application of the ideas in all branches of physics. (Feynman, Leighton, and Sands, 1963, p. 47-1) An example of a related concept from the area of sound and quantum mechanics is: Consider the circumstance in quantum mechanics where the electron lacks sufficient energy to ultimately escape from the proton, its representation is that of confined waves with the solution of the wave equation having definite frequencies (energies). Similarly the solution of the wave equation for a vibrating string rests in confined waves of definite frequencies (harmonics). Some German physics educators are even proposing using similar analogies to teach ideas of quantum mechanics in their secondary schools (Niedderer, 1988). Although some physics lecturers may regard the links between sound and other directly associated fields of physics such as mechanics, hydrodynamics, and thermodynamics as elementary, these links may be quite problematic for physics students. This enhances the rationale for choosing the area of sound to frame this study, for as Dahlgren and Marton (1978) point out: 12 The comprehension of a certain concept (principle, phenomenon) can be seen as a function of the way it appears in the actual context, what the individual has as the object of his attention at the time and what conceptual prerequisites he possesses. This latter view implies that the conception of something may depend on the conception of something else which is more fundamental. ... in order to improve learning we should concentrate our efforts on putting across such basic concepts or structures. But what is basic from the point of view of the learner is not necessarily basic from the point of view of the academic discipline. Of course, it is sensible to start with the content of the actual course, and to derive from this a set of central concepts and principles. Very often, however, the most fundamental assumptions of an academic subject are tacit and taken for granted: one might say that they are not in the academic subject but below it. Consequently, the best way to discover them is to analyse the way which students think about the content of the subject. (p. 27* emphasis theirs) 1.4.2 Using Graduate Physics Student Teachers for the Study Ten physics graduates from a physics teacher education programme were interviewed for the purposes of this study. They were considered ideal interviewees since the results obtained in the pilot study indicated that the students, as potential physics teachers, were naturally interested in the study and saw their participation as contributing to the development of physics teaching. Further, the students' own physics education "method" course was of such a nature that it facilitated an understanding that the interview was not a test of how well they understood their physics but an exploration into how they understood their physics. Consequently they tended to be exceptionally co-operative, honest and open during the course of their interviews, even when they were faced with situations which could have been conceived as questioning the very basics of their own physics understanding. Also, much of the anxiety inherent in such an interview situation was relieved by what may be characterized as peer empathy: both interviewer and interviewee were postgraduates studying in the field of physics education. 1 3 1.4.2.1 Implications for Potential Physics Teachers It is rare for the more advanced courses in undergraduate physics to require students to reflect upon conceptualizations that they constructed in earlier courses (for examples from special relativity see Hewson, 1982; Posner, Strike, Hewson, and Gertzog, 1982; Villani and Pacca, 1987: for examples from mechanics see Faucher, 1983; Helm 1980; Sjoberg and Lie, 1981; Viennot, 1979). Earlier it was pointed out that while students who take postgraduate physics could be provided with opportunities to explore, challenge and refine their conceptualizations, students who intend becoming physics teachers are not afforded such an opportunity. They enter a new academic world of education "methods courses" to graduate as qualified physics teachers (physics authority figures). That they do so with an unknown range of conceptualizations may be considered perturbing, a concern shared by Elton (1980, p. 129): Quite elementary physical concepts are difficult and frequently grossly misunderstood by pupils at school and even by students at university. Evidence for this comes from United States .. France .. South Africa, New Zealand and this country [Great Britain]. Since such misunderstandings are not uncommon even among undergraduates in their final year, some of whom become school teachers, the disquieting possibility must be faced that one cause for these misunderstandings among school pupils may be corresponding misunderstandings among school teachers. If this is so, then the point of attack should shift to the university. Hence, this study has the potential of providing both education and physics lecturers with insights which could allow them to give consideration to "what" and "how" students conceptualize what they are taught. During their education studies, physics student teachers should be provided with insights into the character and origins of their own conceptualizations in order to generate an appreciative system for their own teaching. For example, Erickson has argued that the role of "method" courses in education studies should be primarily aimed at providing: 14 Knowledge in the following of Shulman and Sykes' (1986) categories: (1) curricular knowledge (2) content-specific pedagogical knowledge (3) general knowledge of pedagogical principles. (Erickson, 1987, p. 28) It is anticipated that this research into physics student teachers' conceptual understanding of sound could be described in terms of Shulman and Sykes' (1986) categories of "curricular knowledge" (insight into how knowledge is organized and packaged for instruction in textbooks etc.) and "content-specific pedagogical knowledge" (insight into how, for example physics topics, principles, concepts, strategies etc. are conceptually understood, learnt and forgotten). Fensham (1983) has presented an argument for science teachers to adopt "new" objectives for science teaching "as a means of categorizing some of the research findings that are emerging from probing interviews that get behind the 'correct' answers that most science education expects from its learners", (p. 10) From a physics perspective these objectives may be summarized as follows (from Fensham, 1983, p. 7): (1) To introduce students to examples of how physicists define and use concepts which may conflict with commonsense, experience and everyday language usage. (2) To make explicit students' worldviews of natural phenomena and and to relate these to contemporary and historical scientific worldviews. (3) To enable students to recognize that physicists invent general concepts which idealize actual situations. (4) To help students relate a few examples and concepts to a wide variety of examples and concepts. (5) To help students consider natural phenomena or section of technology and associate several features of it with the corresponding physics concepts. (6) To help students to recognize and use the varieties of^ representations that physicists use to describe physical conditions. 1 5 The author believes that in the education of physics teachers the incorporation of the basic tenets of Fensham's objectives into physics "methods" courses would mean that this study would contribute to the enhancement of physics education students' content specific pedagogical knowledge. 1.5 Overview of Layout of Dissertation This study is a case study using a "phenomenographic" (Marton, 1981) perspective. It involved ten physics graduates from a physics teacher education programme in clinical-like "depth interviews" (Jones, 1985). These interviews incorporated a variety of different contexts regarding the phenomenon of sound. In each of these contexts the students were asked to explain their understanding of sound. The research questions focused on three areas: (1) the generation of categories of description to characterize the students' conceptualizations of the phenomena of sound and of the factors affecting the speed of sound; (2) the consistency of the students' conceptualizations across a variety of contexts; and, (3) how the students' coped with a request to compare and contrast the physics concepts of light and sound. This led to the generation of categories of influence (see Description of Terms below) to characterize factors which influence and mediate the nature of these conceptualizations. There are seven chapters in this dissertation. This chapter has introduced the study and the rationale underlying it. The subsequent chapters deal with: a review of the literature and an overview of the theoretical perspective (Chapter II); the methodology (Chapter III); the analysis of the data (Chapters IV to VI); and, the conclusions, discussions and recommendations arising from the study (Chapter VII). The analysis is done in three chapters coinciding with the three areas of research focus listed above. The qualitative nature of the analysis means that some discussion also occurs in these chapters which is, then, summarized in the conclusions in Chapter VII. 1 6 1.6 Description of Terms Throughout the dissertation several terms are used with a particular meaning in mind, these need to be explicated. This is done logically rather than alphabetically: PHENOMENOGRAPHY: "the study of the qualitatively different ways in which people experience and conceptualize the world around them. The experiential perspective is one of the basic features, various aspects of reality and various phenomena are described in terms of the differing ways in which they appear to people." (Lybeck, Marton, Stromdahl and Tullberg, 1988, p. 5) CONCEPTUALIZATION: this is a term used to broadly reflect how someone sees, visualizes, thinks about, understands or makes sense of experiences and phenomena. It is not meant to represent some structure in a person's mind, rather it is a qualitative description of a person-world relationship. Conceptualizations are the characterization of descriptive categories of peoples' explanations. CATEGORY OF DESCRIPTION: an interpretative descriptive category of explanation which characterizes a conceptualization; an interpretation of another person's interpretation. OUTCOME SPACE: the union of a set of categories of description; an abstract space made up of categories of description "in which individuals move — more or less freely - back and forth" (Marton, 1984, p. 62). CATEGORY OF INFLUENCE: an interpretative descriptive category of influence of conceptualization; a characterization of those factors which mediate and influence what boundaries an outcome space will have. INAPPROPRIATE / APPROPRIATE CONCEPTUALIZATION: a conceptualization which is at variance / synonymous with a concept which is a defined construct within a scientific discipline such as physics. FUNCTIONALLY INAPPROPRIATE CONCEPTUALIZATION: a conceptualization which is evoked in a context where it has little or no functionality. Hence, a functionally inappropriate conceptualization may be an appropriate conceptualization in another frame of reference or context. For example, viewing the relative velocity of particles moving at relativistic speeds from a Galilean perspective. CONCEPTUAL DISPERSION: a characterization of the set of conceptualizations which a person may have regarding some phenomenon; a person's private outcome space. The same phenomenon viewed in different contexts may evoke different conceptualizations of that phenomenon. GUT-PHYSICS: intuition-based conceptualizations that appear to have their foundation in everyday interpretations of how things work; a pervasive, contextually cued reaction to phenomena and experiences. 17 PHYSICS GRADUATE: a student who has graduated with a major or honours degree in physics, or in a field directly connected to physics such as geophysics, astrophysics, or physics-based engineering. LECTURER: a teacher at the university level. TEACHER: a teacher at the secondary level. EDUCATOR: a teacher at any educational level. STUDENT: a person studying at university. PUPIL: a person studying at school. 1.7 Overview of Chapter I This chapter introduced the study and the rationale for the study. Concern was expressed about the metaphysical realism overtones in university physics lecturing and how this may be interpreted by physics students with regards to how they learn and understand their physics. A claim was made that it is important for physics educators to have insights into how their students conceptualize what they are being taught, what the substance of these conceptualizations is, and how this could have important consequences for physics teaching in university physics programmes, in university physics education programmes, and in the school classroom. An overview of the layout of the dissertation indicated that it consisted of seven chapters with the next six chapters reviewing the literature and theoretical perspective; describing the methods of research design, data collection and analysis; describing the data analysis in three chapters; and, a final chapter of conclusions and discussion. An explanation of some technical terms used in the study was also provided in this chapter. 18 C H A P T E R II LITERATURE REVIEW AND THEORETICAL FRAMEWORK 2.1 Introduction As no reported research was found regarding either pupils' or students' conceptualizations of sound, this literature review has two aims. Firstly, it is to give an insight into the extensiveness of the research into science phenomena conceptualization, hence establishing its accorded importance in the science education community. Secondly, it is to introduce the theoretical perspective used to frame the study: the Gothenburg "research specialization" (Marton, 1988) called phenomenography which takes on an interpretative experiential perspective to frame an understanding of knowledge from students' perspectives. 2.2 The Extensiveness of the Conceptualization Research In the field of science education, there has been considerable research into investigating pupils' and students' conceptualizations of scientific phenomena. This body of research has been reviewed several times, the more extensive of which include Driver and Easley (1978); Driver and Erickson (1983); Driver, Guesne and Tiberghien (1985); Fensham (1984); Gilbert and Watts (1983); Hashweh (1988); McDermott (1984); Orton (1985); Osborne and Freyberg (1985); and, White (1987). Also, several books have been written by contributing authors presenting previously unpublished work. These include, Anderson (1981); Gentner and Stevens (1983); Marton, Hounsell and Entwistle (1984); Ramsden (1988); Siegler (1978); and, West and Pines (1985). Specific "students' concepts" conferences have also been held, and their proceedings include Duit, Jung and Rhoneck (1985); Helm and Novak (1983); Novak (1987); and, Sutton and West (1982). Many universities such as Berkeley, Waikato, Leeds, Gothenburg, M.I.T., Kiel, and Paris have an extensive range of inhouse publications dealing with pupils' and students' conceptualizations. Most of the "conceptualization" research efforts have centred on physics, the most popular areas being force and motion, heat, and electricity. For an example of force and motion see Maloney (1988); for heat see Rogan (1988); for electricity 19 see Danusso and Dupre (1987). Further, the focus of much of this research has been in the school arena and has generated terminology such as "children's science" (Gilbert, Osborne and Fensham, 1982) and "children's' dynamics" (Osborne, 1984). Recently the research interest has expanded and other areas have been getting attention. A sample of these are: photosynthesis (Roth, Smith and Anderson, 1983; Wandersee, 1983) the mole concept (Lybeck, Marton, StrOmdahl and Tullberg, 1988), stoichiometry (Mitchell and Gunstone, 1984), covalent bonding (Peterson, Treagust, and Garnett, 1986), changing states of water (Osborne and Cosgrove, 1983), gravity (Stead and Osborne, 1981) and energy (Solomon, 1983; Warren, 1983; Watts, 1983). Far less "conceptualization" research has taken place at the university level, and that which has been carried out has focused on first year students primarily in the areas of force and motion (see diSessa, 1986; McDermott, 1984). A limited amount of work has been done in other areas, for example: Goldberg and McDermott (1987) considered students' conceptualizations of the real image formed by a converging lens or concave mirror; Fredette and Lochhead (1980) and Van Zee, Evans, Greenberg and McDermott (1982) have investigated students' conceptualizations of electric circuits and current; Cros, Amouroux, Chastrette, Fayol, Leber and Maurin (1986) investigated students' preconceptions of the constituents of matter and of acids and bases; and RenstrrJm (1987, 1988) has completed an extensive study of pupils' conceptualizations of matter. Beyond the first year university level very little "conceptualization" research has taken place. Faucher (1983) compared "sophomore and senior" students in limited aspects of force, motion, electricity, electromagnetism, and special relativity. Helm (1980), Sjoberg and Lie (1981), and Viennot (1979) have all completed research which extended from school into senior years of university physics; Sjoberg and Lie, to graduates. Helm, and Sjoberg and Lie extended their studies to physics teachers and found that similar inappropriate conceptualizations were found across the spectrum of their investigations. Sjoberg and Lie, and Viennot focused on force and motion while Helm sampled a variety of topics from a typical first year physics curriculum. One of the conclusions stemming from these studies was that physics teachers may be contributing to the persistence of functionally inappropriate conceptualizations. Gunstone and White (1980) probed physics graduates' understanding of gravity and, then, repeated their research at 20 the first year level (Gunstone and White, 1981). Other studies involving senior undergraduate and graduate physics students have been in the realm of Einstein's special theory of relativity (Hewson, 1982; Posner, Strike, Hewson and Gertzog, 1982; Villani and Pacca, 1987). In the literature review so far an attempt has been made to reflect the diversity of the conceptualization research on the one hand, and on the other hand, the focusing that has taken place in the area of force and motion, particularly at school level. The review also found that there was a comparatively smaller research effort at the senior undergraduate and graduate levels of university physics, and that no research has taken place in the area of sound at either the school or university level. 2.3 Choice of Theoretical Perspective Before choosing the theoretical perspective for this study, the methods and perspectives which had been used in similar studies were carefully considered. It was found, as Driver and Erickson (1983), Gilbert and Watts (1983), West and Pines (1985) and White (1987) have all pointed out, that within the realm of pupil/student conceptualization research there has been little consistency with regards the aims of the research, the methods used in collecting and analysing data, and the utilization of the research outcomes. Gilbert and Watts (1983) and Cobb (1987) have pointed out that this is both covertly and overtly a consequence of what may be characterized as the underlying epistemological spirit supporting the different research efforts. Three general perspectives were subsequently given consideration, namely: - the rule-assessment technique (for instance, see Aguirre, 1981; Maloney, 1985, 1988; and, Siegler, 1976, 1978); - the interview-about-instances technique (for instance, see Gilbert and Watts, 1983; Gilbert, Watts and Osborne, 1985; and, Osborne and Gilbert, 1980); and, - phenomenography (for instance see Johansson, Marton and Svensson, 1985; Lybeck, Marton, Strrjmdahl and Tullberg, 1988; and, Renstrom, 1987, 1988). 21 Phenomenography was considered to be the most suitable perspective to use for the following reasons: - much of the research associated with the first two perspectives has been normatively based. The aim of this study was not to identify "incorrect" conceptualizations but was an attempt to describe how physics students contextually conceptualize the phenomenon of sound: a concern with empathetic meaning and understanding. Phenomenography offers an understanding and interpretative framework which facilitates the description of a person's perceptual world; that is, an interpretative experiential perspective. Phenomenography is not normative but appreciative in the verstehen (Weber, 1949) tradition; - unlike the other two perspectives, phenomenography views conceptualizations as being "relations between the conceptualizing or experiencing individuals and the conceptualized or experienced phenomena" (Lybeck, Marton, Stromdahl and Tullberg, 1988, p. 5) That is, each conceptualization has a how (the act of conceptualization) and a what (the meaning of the conceptualization) aspect which are "dialectically intertwined, neither can exist apart from the other." (Lybeck, Marton, Stromdahl and Tullberg, 1988, p. 5); and - in the author's opinion, phenomenography offered the best support for his belief that the outcomes of this kind of educational research should guide teaching with empathetic insights into how students' conceptualize what is being taught, rather than to prescribe "how" to teach: a belief "that conceptual frameworks can be developed and replaced by new better ones; it is we who create our 'prisons' and we can also, critically demolish them" (Lakatos, 1978, p. 20, emphasis his). Phenomenography was founded at Gothenburg University in Sweden and has been used extensively in Sweden and somewhat in England and Australia to explore a wide spectrum of conceptualizations. Some of these studies are reported in "The Experience of Learning" edited by Marton, Hounsell, and Entwistle (1984). Other studies reported in English include research into student' conceptualizations of: matter (Renstrom, 1987, 1988); the "mole concept" in chemistry (Lybeck, Marton, Stromdahl, and Tullberg, 1988); factors affecting acceleration and velocity (Johansson, Marton, and Svensson, 1985); knowledge (Dahlgren and Pramling, 1985); economic concepts (Dahlgren, 1978); and, factory storemen's ideas about education (Larsson and Helmstad 1985). Recently an international symposium based on phenomenography was held in Australia which reflects the growing interest in the perspective (Bowen, 1986). 2 2 2.4 The Framework of Phenomenography In an invited address to the American Educational Research Association, Marton (1988) introduced phenomenography as a "research specialization" to study "the differing understandings or conceptions of phenomena in the world around us," an "approach to research which takes an experiential perspective" (p. 5). This "experiential perspective" is a cornerstone of phenomenography as it is within the realm of this experiential perspective that phenomenography takes on a subtle and "pragmatic" (Marton, 1981) research distinction. This distinction is made between research which focuses on describing various aspects of the world (called a first-order perspective) and research which describes how people experience various aspects of the world (called second-order perspective). It should be pointed out that: The discerning of these two alternative perspectives has nothing to do with the metaphysical distinction between the real and the apparent, or with arguments for or against as to whether there is a reality as such that is accessible to us. (Marton, 1981, p. 178) Although the Gothenburg Research Group have started to incorporate their "pragmatic" position into a "philosophical" position (Marton, private correspondence, 1988; Marton and Neuman, 1988) the focus of phenomenographic research remains experiential. A useful analogy for phenomenography's first/second order perspectives may be Popper's (1972), first and third worlds (a physical world and a world of ideas) except that which is: Separated from the 'knowing subject' in Popper's case is the body of propositional knowledge regarded as valid at a certain point in the history of science. What we [in phenomenography] want to thematize, on the other hand, is the complex of possible ways of viewing various aspects of the world, the aggregate of basic conceptions underlying not only different, but even alternative and contradictory forms of propositional knowledge, irrespective of whether these forms are deemed right or wrong. (Marton, 1981, p. 197) Gibbs, Morgan and Taylor (1982, p. 140) have thematized the essential pragmatic distinctions between the first and second-order perspectives as follows (second-order versus first-order): 2 3 Qualitative vs. Contextualized vs. Internal vs. Understanding vs. Emancipatory vs. Quantitative Generalized External (Description) (Conceptualization) (Relations) (Forms of comprehension) (Use) Explanation Technical This separation of the first and second-order perspectives is essentially what sets phenomenography apart from phenomenology on the one hand and ethnography on the other. Neither the ethnographic research perspective (Larsson, 1988), nor the phenomenological perspective (Marton, 1981) facilitate a distinction being made between the two perspectives, i.e., there can be no separating of what-is-experienced from the experience-itself. However, Marton (1981) points out: The descriptions we arrive at from the second-order perspective are autonomous in the sense that they cannot be derived from descriptions arrived at from the first-order ... in 'phenomenography,' we suggest, we would deal with both the conceptual and the experiential, as well with what is thought of as that which is lived. (Marton, 1981, pp. 178 - 181) The second-order perspective can thus be thought of in terms of explicating something through the eyes of another -- an interpretative perspective to explore conceptual understanding by careful analysis of the "content" of explanations. 2.4.1 Categories of Interpretation 2.4.1.1 Categories of Description In Chapter I it was argued that physics educators need to have more insight into their students' conceptualizations of what they are being taught; that is, how they see, visualize, understand, think about or make sense of experiences and phenomena. In this study conceptualizations are viewed as reflecting the nature of a contextual person-world relationship. Conceptualizations are thus not specifically inherent to either individuals or to instances of the world, rather they are inherent to both in an intertwined relationship. This phenomenographic interpretation of conceptualization is framed by the implicit "concept of intentionality introduced by the German philosopher Frantz Bretano 1874." (Johansson, Marton and Svensson, 1985, p. 247) That is, the experience of 24 phenomena has a dualism to it, for instance, we do not just hear, we must hear something. Similarly we cannot simply learn we have to learn something. In other words: There are two aspects of the experience of an object, the act of experiencing 'noesis,' and that which is experienced, i.e. the meaning of the object towards which one's attention is directed, the 'noema.' These two aspects jointly form the whole, the experience of the object in question. (Marton, 1984, p. 54) Since the individual and the world are not depicted as separate entities, this does not mean that the relationship between them is fixed. Things can be perceived and experienced in different ways (for example, see Brauner, 1988), and we can argue that one way of perceiving and experiencing some phenomena is better than another. For instance, one might argue that it is better to perceive and experience a "sun rise" as an "earth rotation," while it is certainly possible to do both. Much of what teaching is about concerns better or new ways of perceiving and experiencing -- conceptualizing -- phenomena from different frames of reference. And from this perspective conceptualization may be characterized as sense-making construction manifest as "constitutionalism" (Marton and Neuman, 1988; Renstrom, 1987, 1988): While the emphasis in constructivism is on acts ... constitutionalism has the unity of the act and the acted upon as its point of departure. This latter stance makes it fairly natural to describe different ways of thinking about a certain phenomenon, or different ways of dealing with that phenomenon, in relation to the particular competency we aim at developing in an educational setting. The differences can then be seen as increasingly functional human-world relations. (Marton and Neuman, 1988, pp. 7 - 8 ) An excellent example of different conceptualizations of the same phenomenon is provided by Kuhn (1962) who describes how a "distinguished physicist" and "eminent chemist" replied to the question: Is a single atom of helium an atom or a molecule? For the chemist the atom of helium was a molecule because it behaved like one with respect to the kinetic theory of gases. For the physicist, on the other hand, the helium atom was not a molecule because it displayed no molecular spectrum. (Kuhn, 1962, p. 50) 25 Essentially what is reflected in these two answers is what phenomenography calls a second-order perspective; that is how physicists and chemists may come to conceptualize a molecule rather than what a molecule is. For the purposes of this study the second-order research perspective frames the interpretative exploration of student conceptualization via the careful analysis of the "content" of student explanations. It facilitates the generation of characterizations to depict the "thinker's understanding of that which is thought about" (Johansson, Marton and Svensson, 1985, p. 247). An underlying assumption is that phenomena and experiences are conceptualized in a limited number of qualitatively different ways (Marton, 1986; Johansson, Marton and Svensson, 1985), and the phenomenographic approach involves identifying interpretative categories to characterize these conceptualizations. For instance, in this study the sound-related conceptualizations were characterized from interpretative descriptive categories evolved from the students' thematic explanations. In phenomenography, these interpretative descriptive categories are called "categories of description" (Dahlgren, 1984; Johansson, Marton and Svensson, 1985). In other words, the analytic outcomes, as categories of description, reflect how the students explained the phenomenon of sound. The analytic outcomes, as conceptualizations, reflect how the students "saw" the phenomenon of sound; that is, an interpretation of the students' interpretations. Thus categories of description are said to characterize conceptualizations. They are not the conceptualizations in themselves. The identification of conceptualizations as a phenomenographic analytic outcome is an invention or discovery, whereas the categories of description consists of sets of students' explanations. As Johansson, Marton and Svensson (1985) have pointed out, this is an important but somewhat awkward distinction to maintain. The development of categories of description and their resultant characterization as conceptualizations are primary aims in phenomenographically based research (Dahlgren, 1984; Johansson, Marton, and Svensson, 1985; Lybeck, Marton, Stromdahl and Tullberg, 1988; Marton and Saljo, 1984). The invention or discovery of conceptualizations stem from a rigorous analysis of qualitative differences found in empirical data (Johansson, Marton, and Svensson, 1985), which in this study were the students' thematic explanations. Put in another way, for this study, categories of description portray an empathetically framed recognition and interpretation of sets of student explanation. 2 6 Categories of description may be constructed primarily in terms of the substance of the person's explanations, for example, see Lybeck, Marton, Stromdahl and Tullberg (1988), or they may be constructed primarily in terms of the structure of a person's explanations, for example, see Dahlgren (1984). However, whatever primary characteristics are used to determine the delimitations for the generation of categories of description, they still "refer to whole qualities of human-world relations" (Johansson, Marton and Svensson, 1985, p. 249). When generating the conceptualizations an attempt needs to be made not to impose too much of a personal frame of reference directly onto the students' explanations, yet one must simultaneously link one's personal understanding (in this case, of physics) to the students' understanding, in order to understand and relate to the content of the students' explanations. Dahlgren (1984) describes the data analysis procedure as a process which principally involves: The reduction of unimportant dissimilarities e.g. terminology or other superficial characteristics, and the integration and generalization of important similarities i.e. a specification of the core elements which make up the content and structure of a given category, (p. 24) Constructing categories of description may be depicted as a kind of iterative "hermeneutic circle" procedure which uses the "parts" to evolve the "whole" which in turn delimits the contributing "parts." Once a category of description is constructed, a conceptualization may be generated by framing the category of description as a characterization of a conceptualization. It is important to emphasize that categories of description are not analogous to "concept maps" (Novak and Gowin, 1984) which are representative of individual patterns of reasoning in terms of propositional linkages. Categories of description are rather a kind of collective identification of important explanatory attributes. Categories of description, as the collective outcomes of research into students' conceptualizations in a specific area, represent "an abstract system of description, a gigantic space of categories, in which individuals move — more or less freely — back and forth" (Marton, 1984, p. 62). However, this does not preclude an individual from having such an internal representation, there are simply no claims made in this regard. Nor does it preclude individuals being 27 mapped onto a category of description as is done in the analysis for the second research question. 2.4.1.2 Categories of Influence A Category of influence is a phenomenographic-like construct invented for use in this study to help capture the nature of the students' light/sound comparative-conceptualizations (see Chapter VI). The notion of categories of influence was derived from the notion of categories of description. Just as categories of description are interpretative categories which are used to characterize conceptualization, so categories of influence are interpretative categories which are used to characterize factors which appear to play an important role in mediating and influencing conceptualization, in this instance comparative-conceptualization. For instance, factors such as language, intuition and abstraction are likely candidates in the present study. In this analytic model, categories of description, as subsets of outcome space, are delimited by categories of influence. For example, much of the conceptualizations described in this study could be viewed as reflecting elements of conflict between commonsense and physics thinking, and a useful way of illustrating the notion of a category of influence is to use Feldman's (1980) notion of an idiosyncratic-to-universal knowledge continuum. For the purposes of this illustration, Feldman's knowledge continuum is restructured to fit discipline-based conditions (something similar to which Feldman himself proposes, see pp. 16 - 18). So, as a way of functioning in physics, the idiosyncratic side of the continuum could represent primitive intuition-based conceptualization (which may be quite functional in everyday living) and the universal side of the continuum could represent physics-based conceptualization (bearing in mind that what may now be regarded as primitive could have been contemporary in some past era, for example, see McCloskey, 1983). Intermediary positions along the continuum could, then, be characterized as mediations between these often conflicting ways of conceptualization. 2.5 Summary of the Theoretical Perspective: Phenomenography In summary, phenomenography is an experientially based research perspective which facilitates an interpretative experiential analytic approach to characterize how and what students "see" from their perspective: a figurative mapping of 28 various domains of "categories of interpretation." Hence, the perspective is termed a second-order perspective in that this study represents a shift from studying sound per se, or how much students have learnt about sound (first-order perspective), to studying what kinds of conceptualizations students construct about the phenomenon of sound. The primary outcomes of the study are categories of interpretation, description and influence respectively. Categories of description characterize conceptualizations, and categories of influence characterize factors which influence conceptualization. Developing the categories of interpretation is "not a question of 'simply' reading-off what is in front of us" (Marton, 1984, p. 63). They are painstakingly evolved from repeated scrutiny of thematic interview transcripts where important explanatory attributes are emphasized and insignificant attributes downplayed. No claim is made, however, with regards to the ontological status that the conceptualizations have as students' internal cognitive structures. From a physics viewpoint the conceptualizations that students construct about sound represent a subset of conceptualizations regarding the phenomena of waves thus also providing useful insights into how students conceptualize the physics concept of wave. This outcome is manifested in the analysis for research question 4 (see Chapter VI) where students were asked to compare and contrast light and sound. 2.6 Overview of Chapter II This chapter has reviewed the literature which was used to frame the study. In the first section of the review an effort was made to reflect the importance accorded such research by the science education community; the diversity and convergence of studies done so far; and to point out that no previous studies into pupil or student conceptualization of sound had been reported in the literature. The second section of the review introduced phenomenography as an interpretative second-order experiential research perspective; a perspective that facilitated an interpretation of the students' thematic explanations to characterize their conceptualizations and factors influencing their conceptualization. The next chapter will describe the design of the study and outline the analytic procedure used. 29 C H A P T E R III DESIGN OF STUDY AND METHODOLOGY 3.1 Introduction: A Qualitative Naturalistic Case Study This study has been introduced as a phenomenographically based study; an interpretative experiential second-order study. The aim of the study was to obtain insights into physics students' conceptualizations of sound. As a study of a "bounded system" (Stake, 1978) with a focus on emphasizing the wholeness and unity of those aspects of the system relevant to the research questions, this study may be characterized as a qualitative naturalistic ease study (Lincoln and Guba, 1985; Stake, 1978). The study involved interviewing ten graduate physics students from a physics teacher education programme, about their conceptualizations of the phenomenon of sound. This group of students had graduated from five different universities across Canada with the following four-year physics based undergraduate degrees: four B.Sc. physics; one B.Sc. geophysics; one B.Sc. Honours, physics and astronomy; one B.Sc. physics and oceanography; one B.A.Sc. geophysics engineering; one B.Ed, physics concentration; and one B.E.Sc. Nine of the students were male but to preserve the relationship of trust established prior to and during the interviews all the students are referred to as masculine. 3.2 Outcomes of the Study In any research endeavour, different research perspectives may lead to different knowledge claims, hence a recognized significance, and commonality of understanding, of the research outcomes by all audiences, cannot be assumed. As Shulman (1986) has pointed out: The framing of a research question, like that of an attorney in a court of law, limits the range of permissible responses and prefigures the character of possible outcomes (p. 3). In the evaluation of any qualitative data analysis and its conclusions the basic criteria becomes one of research credibility (Lincoln and Guba, 1985). Research credibility poses the question: Does the research project both as a whole and in its parts generate sufficient credibility to facilitate a consensus that the research 3 0 conclusions are worthy of attention? Focusing on this issue, Lincoln and Guba (1985), in their discussion on "establishing trustworthiness" for qualitative analysis, conclude "it is dubious whether 'perfect' criteria will ever emerge" (p. 331). However, although a generalized significance and commonality of understanding for all audiences cannot be assumed for this study, it does have the potential of helping physics educators obtain an empathetic insight of what is happening in their own educational environments "so that they can change their role in the social interaction [of teaching] to get better results" (Easley, 1982, p. 192). 3.3 Generalizability of the Study The nature of the study and the perspective adopted for the data analysis are such that it should be borne in mind that the analysis is with direct reference to the conceptualizations of the group of students that were involved in this study. Conceptualizations and not students were being sampled (see discussion on phenomenography in Chapter II) and hence generalizability, in the traditional scientific sense, was not part of the logic of the study design. Any generalizations may only be made by readers in the form of what has been termed "naturalistic generalization" (Lincoln and Guba, 1985; Stake, 1978). Stake has argued that the meaning of generalizability must be viewed in relation to the relevant experiences of a potential user of the generalization: Case studies will often be the preferred method of research because they may be epistemologically in harmony with the reader's experience and thus to that person a natural basis for generalization. (Stake, 1978, p. 5) This means that any generalization of the results of a study such as this one must be experientially based: the research outcomes frame reflection eliciting a kind of deja vu for readers with a repertoire of relevant experience. Put another way: to the degree that this framing of reflection leads to new insightful understanding and consequent recognition of the validity of the research outcomes, so the results become generalizable to the reader. From such a naturalistic perspective, generalizability may be characterized as recognition, a "way of knowing" (Stake, 1978), based upon experience. 3 1 3.4 The Design of the Study The design of the study was framed in terms of the following three components: a structural analysis of the concept of sound at an introductory level; the design of a suitable interview protocol based on an extensive pilot study; and, the analysis of the interview data from a phenomenographic perspective. 3.4.1 Concept Analysis of the Phenomenon of Sound An analysis of the nature and the level of complexity of the various physics concepts associated with the phenomenon of sound was undertaken prior to the pilot study. The level of complexity incorporated in the analysis was chosen to be reflective of the level of understanding sought at the first/second year of undergraduate physics. This analysis was carried out in the form of constructing a "concept map" (Novak and Gowin, 1984) which highlights relationships between conceptual attributes in a hierarchical-like network of propositions. The concept map may be found in Appendix I. 3.4.2 The Design of the Interview Protocol 3.4.2.1 Factors Influencing the Design The interview protocol design was based in part upon the results of an extensive pilot study which preceded this study. One of the aims of the pilot study was to develop a "depth interview" (Jones, 1985) which was modelled along the lines of Piaget's (1929) "clinical interview" within a contextually structured protocol Six physics education students with similar backgrounds to the students involved in the main study, volunteered to become involved in the pilot study. The activities which made up the pilot study were extensive and the very rich data generated was only obtainable by virtue of the interest and enthusiasm that the participating students showed in the study. Often interview sessions would last for a complete afternoon. A variety of experiments involving sound were 3 2 performed and the students were also asked to explain their understanding of sound in a variety of different contexts. These contexts were derived from the structural analysis of sound completed prior to the pilot study. The pilot study interviews were audio-recorded and were thoroughly analysed between interviews. This meant that much of the interview protocol was actively evolved during the piloting. Aspects that were deemed unsuitable were dropped and new ideas were introduced into each subsequent interview. When the pilot interviews were completed they were all transcribed verbatim. After repeatedly listening to and reading them, the final protocol was developed and was based upon the following criteria: That the interview must be: interesting enough to engage the interviewees in an honest and open in-depth exploration and reflection of their conceptualizations; seemingly simple enough to validate the claim that the interview was not a "physics test" and to avoid knowledge threatening situations as far as possible; able to provide the richest set of data for the purposes of the study; and, of a reasonable duration from both the interviewees' and interviewer's perspective; about 45 minutes. Over and above the outlined criteria it was felt that the design of the interview protocol needed to reflect an environment which could feasibly maintain an intellectual level of conversation with the students. That is, generating an atmosphere of "talking physics" in a "hand waving" manner. It was hoped that the interview would thus generate explanations which incorporated reasonable approximations in order to provide some sort of generalizable and holistic perspective of sound propagation such as the following: As the molecules rush out of the region of higher density and higher pressure, they give momentum to the molecules in the adjacent region of lower density. For sound to be generated, the regions over which the density and pressure change must be much larger than the distance the molecules travel before colliding with other molecules. This distance is the mean free path and the distance between pressure crests and troughs must be much larger than this. Otherwise the molecules would move freely from the crest to the trough and immediately smear out the wave. It is clear that we are going to describe the gas behavior on a scale large compared with the mean free path, and so the properties of the gas will not be described in terms of 33 the individual molecules. The displacement, for example, will be the displacement of the center of mass of a small element of the gas, and the pressure or density will be the pressure or density in this region. (Feynman, Sands and Leighton, 1963, p. 47-3) It was felt that the advantages of this approach were that it would most naturally facilitate the design objectives and simultaneously not place restrictions on the students' explanations; that is, it would take the form of a "reflective conversation" (Schon, 1983). 3.4.2.2 The Structural Format of the Interview Protocol As already discussed, the design of the interview protocol was to facilitate the elicitation and collection of students' explanations about their understanding of sound framed by various contexts. In such a scenario Jones (1985) has pointed out: An interview is a complicated, shifting, social process occurring between two individual human beings, which can never be exactly replicated (pp. 47 - 48, emphasis hers) Hence, to facilitate the design criteria discussed earlier, a decision was made to introduce identical contexts but not to ask a set list of identical questions. The interview had to be perceived as a discussion and not a test. The interviewer also wanted to be able to ask provocative questions to provide the students with an opportunity repudiate or affirm how the interviewer was interpreting segments of explanation. It was appreciated that the use of provocative questions could be interpreted as "leading the students on," however, the piloting experience had shown provocative questions to be a non-stressful, effective method of validation, especially when a student's articulation had been poor (necessary to guide the nature of future probing). The nature of the study meant that the protocol could not anticipate the flow of dialogue, what issues would be raised by the students, or which explanations would be considered worthy of further probing. This caused some initial difficulty in the written articulation of the protocol. Finally it was decided to produce the protocol in "interview probing units" in an effort to capture some of the essential dynamics of what was being attempted. Examples of possible types of questions were then included to outline the general tone and direction that the 3 4 probing was to take in each context. The final product took on the following form: UNIT 1: The Introductory Phase of the Interview. In this phase the students were chatted to informally and told that the aim of the research was to develop a set of analogies, examples, and demonstrations to enhance students' understanding of sound, and as potential teachers their participation was both appreciated and valued. It was emphasized that the interview was not meant to be a test of their physics knowledge but the interviewer wanted to "see" how the different contexts led them to think about sound. Generally the time was spent developing a relaxed atmosphere in the recognition that both interviewer and interviewee were students with physics backgrounds who were now interested in education. This was considered to be a particularly important stage because as Jones (1985) has pointed out: Human beings present different personae in different situations, to different audiences. In giving accounts to others, they are concerned not only with 'intelligibility' — making their actions comprehensible — but also 'warrantability' — the legitimation of action and the presentation of a credible and legitimate 'self.' (p. 50) UNIT 2: Probing into the nature of the conceptualizations which the students had of sound across four different contexts. First Context: The students were asked to use an example of their own (meaning not a class or textbook example) to explain their understanding of sound. In this context the student were encouraged to draw upon their own experiences of sound outside physics classes, i.e., not typical "teacher" examples. This was initiated with a question such as: Could you give me an example of sound from your own experience, something which teachers don't usually use as an example, and use it to explain how you understand sound? 35 Second Context: A situation not commonly used to demonstrate or personify sound in physics class, yet one which would be very common to everyday experience. A balloon was blown up and then burst. The aim was twofold: to produce a loud source of sound which would rapidly refocus the interview; and to be a source of sound common to everyday experience but not to physics instruction. The initial probing began after asking the students a question such as: Could you use this example to offer an explanation of what sound is and how it travels? After the students had chosen their level of explanation — anticipated to be either a micro- or macroscopic perspective — the probing was directed towards looking for further elaboration. For instance, if a microscopic perspective was introduced a typical question was: What were the air molecules doing before I burst the balloon? [Reply] And after? Third Context: A situation easily identified with the physics class and textbooks. A tuning fork was introduced as being representative of a common teaching demonstration of sound. Explanation was initiated as follows: After providing a box of a variety of tuning forks and encouraging the students to experiment with them for a while, they were presented with a question such as: Could you use one of these tuning forks to explain your understanding of sound? An excellent question to probe micro- and macroscopic connections, and at the same time explore how the students would cope with an exposed inconsistency, was found during the pilot study. During the pilot study all the students estimated the wavelength of sound produced by a tuning fork vibrating at 440Hz to be extremely small (it is actually about 0.75m). In anticipation that a similar outcome would be obtained from the main study students, it was decided to incorporate a section into the "tuning fork" section of protocol where students would be asked to first estimate the wavelength produced by a 440Hz tuning fork and then asked to calculate it. However, because of the potential stress factor involved, the 3 6 interviewer used his judgement at the time to decide whether or not to pursue this line of probing. Fourth Context: A n example based upon a hypothetical teaching situation. The following rather typical depiction of sound waves was shown to the students from an introductory physics textbook: Figure 3.1: A travelling sound wave depiction taken from Weidner (1985, p. 386). " (a) A sinusoidal longitudinal wave. (b) The corresponding wave shape with displacement from equilibrium plotted as a function of distance. " The probing which followed was then embedded in a hypothetical pedagogical situation, for example: Have a look at this figure in this physics textbook. Suppose I was a new undergraduate and I brought this figure to you because I couldn't understand it. Could you help me? 3 7 UNIT 3: Factors affecting the speed of sound in air? The interview then moved to what factors affected the speed of sound and how they affected it? The intention here was to look for explanations which would give insight both into the students' conceptualizations of sound and how this manifested into related conceptualization of factors which affected the speed of sound. It was anticipated that the probing would get the students to reflect on their understanding of related physics concepts such as temperature, nature of a gas, elasticity and inertia. The students were then asked if sound would travel in a vacuum; this line of questioning was pursued only if it was considered to be useful in probing explanations already given in this unit. UNIT 4: Providing a context where further probing could be initiated via an interesting and somewhat unusual demonstration. In this unit the following experimental situation was provided: A metre long hollow glass tube, with one end tapered, was clamped in a set of retort stands. A lighted candle was placed at the tapered end of the tube and two sources of sound were produced at the other end: hand clapping and knocking on a small wooden box with one open end and this end facing the open end of the glass tube, viz: Figure 3.2: Sound Tube Experiment 38 The students were introduced to the experiment. They were asked to observe the experiment, to generate a set of appropriate questions and then to provide the answers to their questions. During the probing the students were typically asked to imagine that the tube was filled with "coloured air" and then to frame their explanations in terms of this coloured air. It was anticipated that this would help discriminate between viewing the sound travelling down the tube as a "puff versus a "pulse." UNIT 5: Ask the students to compare and contrast the physics concepts of light and sound. It was anticipated that this question would enable the students to explore their understanding of waves in two areas that they should be very familiar with. It was also anticipated that conceptualization continuity and rationalization would be highlighted by their explanations and possibly provide a valuable learning experience for the students. 3.5 The Data Analysis Al l the main study interviews were tape recorded and transcribed verbatim. After each interview notes were made regarding any extrinsic factors considered to have the potential of affecting the interpretation of the interview content. For instance, often students "chatted" informally (with the tape recorder off) about their experiences of learning physics. This confidentiality has been respected and these insights have not been reported in this study, however, where appropriate they were used to help frame the students' explanations. The phenomenographic perspective used in this research is extensively discussed in Chapter II and the data analysis for this study is provided in Chapters IV, V , and VI . 3 9 3.5.1 Data Analysis: The Categories of Description Characterizing Conceptualizations (Chapter IV) The data analysis was an extensive task that began by transcribing all the interviews verbatim. Before attempting to answer any of research questions, the interviews were read and listened to repeatedly to obtain an overall insight into the substance of the students' explanations. Once the overall picture began to emerge, notes were taken regarding any themes that were identified. The generation of the categories of description to characterize the students' conceptualizations initially required the use of a set of interview transcripts cut up into pieces and sub-pieces of description. The analytic path, then, involved looking for comprehensive structures of explanation. This process may be characterized as following the kind of "hermeneutic circle" procedure discussed earlier. The cut out extracts were separated into "collections of description" which did not remain static. The collections were continuously rearranged, merged or broken down completely. This approach turned out to be exceedingly problematic as an attempt was being made to characterize parts in terms of a whole while simultaneously the whole was to emerge from the parts. This attempt was confounded by the loss of context as pieces of description became increasingly smaller and the task became exceedingly confusing. Consequently a decision was made to begin again using a complete set of transcripts. However, the initial phase of the analysis was still considered essential, as it now guided the second attempt. The complete set of transcripts were subsequently categorized and cross-referenced with notes and colour codes. This process involved careful reading and re-reading of the transcripts. Eventually the categories of description began to emerge from "explanatory summaries" which were generated by reducing "unimportant dissimilarities ... and the integration and generalization of important similarities ... which make up the content and structure of a given category." (Dahlgren, 1984, p. 24) Each category of description, then, reflected a comprehensive structure with individual student's explanations as subsets of it. Having achieved these analytical outcomes they were set aside and the whole process repeated in an effort to validate the interpretations that had been made. This second round of analytic categorization led to some restructuring of the 4 0 categories of description already evolved and it also led to the merging of two former categories into one. 3.5.2 Data Analysis: Lookine for Consistency of Conceptualization (Chapter V) The phenomenographic perspective characterizes the union of categories of description as "outcome space" (Lybeck, Marton, Stromdahl and Tullberg, 1988). The analysis for Chapter V involved mapping the students' contextual explanations into the outcome space. The aim was to obtain an overall perspective of what conceptualizations were being evoked in the different contexts. This was done by reading through the students' transcripts in contextual segments. (Each segment consisted of the dialogue that occurred in a specific context.) The students' explanations were then mapped into the outcome space. It must be pointed out that in an extract of contextual dialogue a student's explanations could span more than one category of description. This would imply the evocation of more than one conceptualization in some contexts. To provide some sort of internal validity to the mapping decisions, the mapping process was repeated some time later without reference to the original mapping. In this second round only one minor change in interpretation was made. Initially it was anticipated that certain conceptualizations would be characteristic of functioning in a specific context. The analysis indicated that in general this was not so; so although conceptualizations were characteristic of ways of functioning, they were not necessarily characteristic of ways of functioning in specific contexts. Certain themes in the data analysis were, however, identified and these were subsequently discussed using exemplar extracts. 3.5.3 Data Analysis: How the Students Managed the Task of Comparing and Contrasting Light and Sound (Chapter VI) The analysis for the final research question turned out to be rather difficult. Initially an attempt was made to develop categories of description, however, the nature of the students' explanations did not readily lend itself to this approach. Hence a new phenomenographic construct, categories of influence, was developed. In many respects a category of description and a category of influence are similar except that a category of influence is much broader, and as 4 1 such is not envisaged to characterize conceptualization as a category of description would. Since phenomenography reflects a fundamental interest in "how various aspects of the world are seen by different individuals" (Marton, and Neuman, 1988, p. 14) it was envisaged that categories of influence would characterize those factors which appeared to be very influential in how phenomena are conceptualized: a dynamic part of person-world unity. To provide a base of validation for these categories of influence two noted physics educators were contacted by private correspondence, these were Anthony P. French of Massachusetts Institute of Technology, USA, and John W. Warren of Brunei University, England. French kindly agreed to provided a citable description of the kind of explanation he would expect physics graduates to give in the context of the interview. Warren wrote several long letters commenting on the author's interpretations and providing some insights of his own from his many years of experience. These insights were particularly useful in the framing of the students' explanations. The categories of influence were generated in much the same way as the categories of description, the analytic procedure of which is described earlier. 3.6 Overview of Chapter III This chapter has described how the study was designed; outlined the analytic approaches taken to analyse the data; and discussed the nature of the outcomes and generalizability of the study. It was pointed out that the outcomes of the study need to be viewed in terms of the phenomenographic research perspective used to frame the study: that conceptualizations and not students were being sampled. It was in this context that the generalizability of the study was posed in terms of naturalistic generalization: a recognition (a way of knowing) based upon the research outcomes framing a reader's reflections of relevant personal experience. The design of the study occurred in several phases and in part was based upon an extensive pilot study. The first phase involved drawing up a physics structural analysis of the concept of sound at a level deemed appropriate for the study. This analysis, then, guided the pilot study which in turn led to the generation of the interview protocol. The data analysis was based upon a phenomenographic perspective. The analysis was divided up into three chapters: conceptualizations; conceptual consistency and dispersion; and factors influencing conceptualization. The analytic approach taken for each of these chapters was outlined in procedural terms. The following three chapters reflect these analytic approaches and their outcomes. 4 3 CHAPTER IV DATA ANALYSIS: CONCEPTUALIZATIONS 4.1 Introduction to Analytic Method This study has been introduced as a phenomenographically framed case study designed to provide insights into how ten physics graduates from a postgraduate physics teacher education programme think about and make sense of the phenomenon of sound; that is, how they conceptualize sound. This chapter deals with these conceptualizations; it is divided into two sections reflecting the first two research questions. The first section deals with the students' conceptualizations of sound, and the second section deals with their conceptualizations of the factors that affect the speed of sound. As discussed in Chapter II, the conceptualizations presented here are characterizations of categories of students' explanations; that is, characterizations of qualitatively different categories of description. From the perspective of this study, conceptualizations are more characteristic of contextual ways of functioning rather than of individuals and it is important for a reader to appreciate that the interview dialogue excerpts which are provided are only examples and do not in themselves represent the sole source of particular conceptualizations. Also, the dialogue excerpts cannot reflect the interviewer's motives for particular modes of questioning. For instance, sometimes provocative questions were asked in order to help clarify what students may have been alluding to, either at the time or at some time previously. When this is not obvious to a reader the questions may appear to be somewhat "leading." In an effort to avoid this interpretation such questions have been labelled as "provocative questions" in the dialogue. To attempt to supply more detail than has already been supplied would generate labyrinthine discussions that would distract a reader from the outcomes of the study and detract from their qualitative richness. Hence, readers are referred to Appendix II where a fuller appreciation of the kind of interacting-dynamics of the interviews is available from a complete interview transcript. 44 In all the following interview dialogue excerpts the letter "S" represents student dialogue and the letter "I" represents interviewer dialogue. 4.2 Data Analysis for Research Question 1: Conceptualizations of the  Phenomenon of Sound 4.2.1 Introduction The first research question is described in Chapter I as: What are the qualitatively different ways that a group of ten physics graduates from a teacher education programme conceptualize the phenomenon of sound from: a microscopically based perspective; and, a macroscopically based perspective? The analysis involved constructing the categories of description to characterize the students' conceptualizations across the following contexts: a personal experience of sound (students were encouraged to use an exemplar which they had not met in physics classes); when presented with a bursting balloon; when presented with an assortment of "hands-on" tuning forks; when presented with an experimental situation involving a glass tube with a sound source at one end and a candle at the other end. The sound waves travel down the tube and interact with the candle's flame; when presented with a hypothetical situation where a physics freshman requested explanatory help with a schematic and graphical representation of sound from a typical university introductory physics textbook; and, when asked to explain what factors affect the speed of sound in air. While the students were explaining their conceptualizations of sound across and in these contexts they chose to use qualitatively different explanatory perspectives to frame (thematize) their explanations. These explanatory perspectives tended to be: either micro- or macroscopically orientated depending on whether the focus was on actions of discrete molecules or particles (microscopic), or on bulk properties, such as pressure and density (macroscopic); or, an intricate blend of micro- and macroscopic perspectives (see the wave model conceptualization). These explanatory perspective preferences were clearly discernable from the pilot study and thus provided the background for the generation of the first research question in terms of micro- and macroscopic perspectives. 4.2.2 Conceptualizations of Sound: The Microscopic Perspective Two qualitatively different ways of conceptualizing the phenomenon of sound from a microscopic perspective were identified from the group of students participating in the study, these were: Sound is an entity which is carried by individual molecules through a medium. Sound is an entity which is transferred from one molecule to another through a medium. These conceptualizations are now expanded upon with the aid of illustrative excerpts of interview dialogue. 4.2.2.1 Microscopic Perspective Conceptualization # 1: Sound as an Entity:  The Transporting-Molecule Conceptualization. This conceptualization had sound consisting of discrete tiny "things" which make up what we hear. These entities of sound were carried through a medium, such as air, from some source to our ears by individual molecules. There were two depictions of molecular action in the transportation process. FIRST DEPICTION: Molecules were stationary or quasi-stationary when there was no sound. Upon the production of some sound the molecules were provided with the necessary forward movement enabling them to physically carry the sound radially outwards from the source (here there was no clear dimensional conceptualization of this radial movement, see the discussion at the end of the chapter). Consider the following illustrative examples: 4 6 Example 1 for Microscopic Perspective Conceptualization # 1 1 S: When you struck the balloon the air inside the balloon exploded or came out, forced out, which pushed the air molecules around the balloon outwards and that travelled to my ears. 5 I: Okay, to just try and clarify things. Suppose around the area where I created this, the bang, if I spray painted the ring of molecules around it. S: Uhum [affirmative]. I: Okay, and then I burst the balloon, then what happens to 10 those molecules that I have spray painted, what do they do? S: They would spread out radially. I: Okay — so if I could imagine that I am riding on one, I guess in time I would get to the other side of the room? S: Uhum [affirmative]. NOTE: The above final question was an example of a provocative question discussed earlier and in Chapter III. It was asked to give the student an opportunity to affirm or repudiate the interviewer's interpretation of the student's explanations. Example 2 for Microscopic Perspective Conceptualization # 1 This example illustrates how different a student's conceptualization can be from teaching-intent. Here the student was describing molecular action involved in the propagation of a sound such as a hand clap. To do this he introduced an analogical depiction of a gas as a liquid: 1 S: ... I guess I would try to relate things to fluids a lot because I sort of think of a gas like a fluid. I: That's okay. S: So it's almost like you are squishing some of the molecules 5 and moving them, and pointing them in another direction so that they move somewhere else. Like if you have smoke and you don't like it you can make it move; kinda like a fluid you can make it move if you were stirring it or something. So when you go like this [clapping] you are making them 10 [air molecules] move down, and um — 47 I: You told me earlier that they were moving anyway? S: Well, they are moving so I think of them on their sites, like their kinetic energy or whatever. Like it's more a random movement, but when you give something to them it adds 15 on top of it and it gives them like a direction. Um, I don't think of molecules as moving in the air, I just know that they do, so that's why I have to work it in. Like I think of them staying in the same place but I know that they are moving, so that's why I say that they are moving. SECOND DEPICTION: The molecules would be initially moving around randomly. Upon the production of some sound the molecules closest to the sound source would be coerced into giving up their random motion. The molecules, then, would take on a push-pullback motion coincidental with the vibrations of the sound source, and move radially in "jerky" steps through a medium carrying the sound. As in the first depiction the molecular movement was without a clear dimensional conceptualization. Consider the following illustrative examples: Example 3 for Microscopic Perspective Conceptualization # 1 1 S: Before you strike it [a tuning fork] the molecules will just be, just — they are not stationary they are moving around but they are not propagating, they are not travelling to a specific direction, they are just moving randomly. 5 I: Okay, now you strike the tuning fork. S: Now you strike the fork and the forks vibrate which moves, which moves the, um, air molecules around it in a certain direction — like — [to himself: How do I describe that now?] — with, with the movement of the forks. 10 I: Okay, so it moves the air molecule? S: It moves the air molecules [affirmative]. I: Alright, now this is where I am a bit vague. So I can see air molecules being moved, then what happens? S: You spray painted the air molecules around the fork. Now 15 the forks are vibrating — which pushes the air molecules to either side of the fork — I: And then? Is there a partial vacuum left behind them? S: I don't think so. Um, temporarily, um, there will be more, when it pushes out there will be more, like, sort of 20 - - i t will be sort of like — [long pause] I don't know if there is a vacuum, I don't think there is a vacuum but there will be way less molecules behind the front. I: I see. So let's suppose that I put you on one of these molecules then. Could I ask you to describe what happens to 25 you? You are sitting on it. S: I think I will be, be pushed forward, and then since the fork is vibrating there will be like a jerking motion. I will be pushed forward a little more then laid back a bit -I will still be travelling forward. When the fork moves 30 forward again I will be pushed forward by the air molecules behind me, I will be travelling that jerky motion. Example 4 for Microscopic Perspective Conceptualization # 1 1 S: Since the propagation of sound is through air molecules, the more you have the clearer the sound. The more you have the more repetitions you have. Um, each molecule would carry the same portion, same amount of information but you have 5 more of it therefore you hear more, you hear better — So if you have less molecules, one molecule would be carrying just that portion of the, the molecule would be carrying the sound but you would have less of it therefore you wouldn't hear quite as clear. 10 I: Okay, I can see that but why should that make it travel faster or slower? S: Oh — if you have less of them [molecules] then it would have to have, have to travel a further distance before it hits another one, before it shoves another one forward, 15 whereas if you have a whole bunch of them, it wouldn't have to travel as far to push another one. I: How does that help? Suppose I am sitting on a molecule, okay? I am just trying to understand: I have to shove one [molecule] out of the way to keep going or —? 20 S: You know — you shove the one in front of you to, yea, in the direction you are travelling. I: And then what happens? S: Then what happens? I: Yes, after I have shoved the molecule in front of me? 25 S: Sort of like a spring model, you push, give it a push -then you slow down, then the one behind you will push you again and you will move forward, repeat itself ~ You are still moving forward all the time. You are not like the spring model where you go back-and-forth. You are moving 30 forward but you're sort of faster; once you got shoved you would move forward faster. 4.2.2.2 Microscopic Perspective Conceptualization # 2: Sound as an Entity:  The Conducting-Molecule Conceptualization. This conceptualization of sound also depicts sound as consisting of discrete tiny "things" which make up what we hear. However, in this conceptualization, sound was not an entity in itself, it was an abstracted entity. These abstracted entities were given labels such as energy, vibrations, and disturbances (for instance, see line 11 in Example 1 below). Here, sound propagation involved the transferring of "sound entities" by a conduction effect from one molecule to the next. The molecules involved in the propagation of sound did so by giving up their "natural state" and taking on a "sound motion." At the cessation of the sound the molecules returned to their "natural state," for instance: 1 S: ... I also know that after the sound gets to my ear that the sound dies out, so therefore the molecules that were once vibrating have to stop vibrating and go back to random motion. The conduction mechanism was depicted in two ways: FIRST DEPICTION: Molecular interaction involved straight-line, one-on-one molecular collisions in a manner analogous to the so-called "domino-effect;" that is, a whole line of dominos are set standing on edge sufficiently close enough together so that when one domino falls over it will hit the next which will fall over and hit the next and so on. Consider the following illustrative examples: Example 1 for Microscopic Perspective Conceptualization # 2 1 S: The best model, if you recognize that air, like anything else, is made up of tiny particles of things we call molecules, then — at a simpler level just consider a row of beads sitting on the 5 table. And you tap a bead at one end and you knock all the beads along and at the other end you have 5 0 your finger and you can feel the tap. That would be analogous to a book dropping and creating the motion of all these smaller things in the air we 10 call molecules which act the same as the beads and move this disturbance around until your finger at the other end can feel it; in this case with the ear at the other end that is feeling it. Example 2 for Microscopic Perspective Conceptualization # 2 S: ... I would view it [propagation of sound] like a domino effect where the particle it hits against something else which hits against something else which hits against something else and moves — um, therefore energy is lost and that's why sound dissipates, maybe. SECOND DEPICTION: This depiction involved molecules dissipating a vibrational motion through a medium via a resonant coupling between molecules: A sound source vibrated and physically interacted with the molecules adjacent to it. Thus, the source and adjacent molecules vibrated in sympathy with each other. Then, the vibrating molecules would get their nearest neighbours to vibrate in sympathy with each other via the coupling of intermolecular forces to create a resonant effect between the molecules (for instance, see lines 2 - 6 in the third example and lines 1 - 5 in the fourth example). Consider the following illustrative examples: Example 3 for Microscopic Perspective Conceptualization # 2 1 I: Okay. How did they get their neighbour to vibrate? S: [Long pause]. Through the attraction, the, um — the molecules, um, have a certain amount of attraction for each other and then — they would, they would, um, their 5 oscillating would affect their neighbour by causing it to start oscillating as well. Example 4 for Microscopic Perspective Conceptualization # 2 1 S: ... I think it really starts the air molecules to be vibrating and they vibrate in resonance, if you will , or incorporate with the explosion of the balloon. And as each little molecule vibrates out it passes the vibration onto 5 the next molecule and then to the next one until it finally reaches my ear. 5 1 4.2.3 Conceptualizations of Sound: The Macroscopic Perspective Two qualitatively different ways of conceptualizing the phenomenon of sound from a macroscopic perspective were identified from the group of students participating in the study; these were: Sound is a travelling bounded substance with impetus, usually in the form of flowing air. Sound is a bounded substance in the form of some travelling pattern. Before further considering the macroscopic perspective based conceptualizations, a subtle descriptive distinction needs to be pointed out. In the microscopic perspective based conceptualizations sound was depicted as an entity; that is, some small "thing." This entity had no inherent action of its own, it was carried or transferred by molecules. In the macroscopic perspective based conceptualizations sound was depicted as a substance; that is, a continuity of form which was associated with a moving "force"; a continuity of form which had an inherent action of its own. 4.2.3.1 Macroscopic Perspective Conceptualization # 1: Sound as  a Bounded Substance: The Flowing Air Conceptualization. In this conceptualization sound manifested itself as a flowing substance in the form of a bounded volumetric element of flowing air. Inherent to this flowing air was the depiction of sound as a moving force or as a kind of abstraction of moving "force"; sound had "impetus." The conceptualization incorporated two depictions of this flow of air: FIRST DEPICTION: Sound was a type of wind or incorporated a type of wind, the distinction not being clearly demarcated. What was clear was a strong sense of logical implication in the depiction: Sound may be thought of as being a wind but wind was not thought of as being sound. Here, sound was strongly endowed with the property of moving "force," for example, one student described sound as air hitting his ear with noise (see lines 9 - 10 of the first example). 5 2 Example 1 for Macroscopic Perspective Conceptualization # 1 1 S: ... If you are talking to somebody air moves outwards carrying it [sound]. I: Maybe you can be clearer about carrying? S: Alright, maybe that's — so the air moves outwards but I 5 could [waving his hand] ~ I think you could feel air moving outwards towards you now, yet there was no sound. So I am trying to see what is the difference between air just moving outward and that thing that we call sound. That's the way I think about it, it's air hitting the 10 [points to his ears] but it does it with noise. Then, later on in the interview this same student discussed the designing of loud speakers. He had a friend who was an "sound engineer" and they had discussed and argued this topic at length: 1 S: Actually that's where I sort of started thinking, and he had ideas [the sound engineer] ... It became more apparent that what you have to do to create sound is to move air, or to move something that will eventually 5 move the air to hit your ear. Example 2 for Macroscopic Perspective Conceptualization # 1 Before this next excerpt the student had just finished explaining how he would estimate how much air would flow out of a metre long hollow glass tube while sound travelled down the tube. The interviewer, then, proceeded to ask him a provocative question to enable the student to repudiate or confirm the interviewer's interpretation of the student's explanation: 1 I: Okay — [long pause] — would you, then, describe what's happening down this tube as I've set up a wind [by creating sound at one open end of the tube] — blowing down the tube? S: You can, you can say that. 5 I: So on, on a more general scale could I, then, say that sound is a wind? S: [Pause] true. SECOND DEPICTION: In this depiction sound was a substance abstraction which pushed a large segment of air along in propagation. The abstraction was depicted as some sort of waveform which moved air as a type of wind. Example 3 for Macroscopic Perspective Conceptualization # 1 To fully appreciate the richness of these excerpts, some background information needs to be given. The student had observed the "sound tube experiment" and had immediately started to explain his observations before posing any questions (details of the interview protocol are given in in Chapter III). During this phase of his explanation he had provided the following explanation for sound propagation: 1 S: ... a wavefront ... that actually blows -- if I was hearing over there I would have felt the breeze and I would have heard the sound. Hence, when the student paused to attempt to pose his questions, the interviewer decided to probe this depiction of sound as an abstract waveform pushing ("actually blows") air along; generating a "breeze." This involved asking the provocative questions in lines 10 and 2 0 - 2 1 . As was pointed out earlier, this type of provocative questioning was not considered to be "leading" but rather to give students the opportunity to repudiate or confirm the interviewer's interpretation and need to be viewed in the context of the students' academic backgrounds. The excerpt begins about halfway through the student's explanation as he (the student) tried to refocus on what he was asked to do: 1 S: So you are going to ask me what happened there? Or I am going to ask my students what happened there? Or why did it go out? I: Okay. 5 S: Again similar reasons [referring to his earlier explanations of sound propagation]. Sound creates or the, um — [pauses and expresses surprise to himself] — The sound creates a wave that is emitted and is focused on the tube — and so the wave travels down — 10 I: Pushing air in front of it? [Provocative question.] 5 4 S: Uhum [affirmative], yea that's how I visualize it: pushing air in front of it. I: If I speak to you now, how do you see the sound? Doing the same thing? 15 S: Yes, it's pushing things in front of it until it gets to the ear. I: So there's this sound which is — I am just trying to get -- ["S" interrupts] --S: Back to the original? 20 I: So there's a sound wave and it sort of, like a grader pushing the air in front of it? [Provocative question.] S: Yea — that is the picture even that, that we get from, from the textbook, is this grader. These banks of waves that I was trying to define, right? Couldn't really picture 25 exactly what was going on but you have this wave pushing outwards — from an antenna in circular motion or from a speaker — it goes out in all directions. I: So I guess if you have enough sound you could set up quite a wind? 30 S: Yea. In the above example the abstraction was exemplified when the student had sound generating a wave to do the pushing in lines 6 - 9 yet had the sound itself doing the pushing in line 15. In lines 22 - 27 the student explained the framing of his conceptualization on visual representations such as the diverging rings typically drawn in textbook representations (or the common analogy drawn between sound propagation and water waves emanating from a point source) which appear to depict sound as a "wave pushing outwards." 4.2.3.2 Macroscopic Perspective Conceptualization # 2: Sound as a Bounded  Substance: The Travelling Pattern Conceptualization. This conceptualization appeared to have been framed by a conglomeration of "learnt" physics terminology and a retention of disembodied facts. Sound as a substance was incorporated into physics context and language with a consequent overlying sense of vagueness. The substance of sound was described as a kind of "disturbance" which propagated through a medium, of which air was just an 5 5 example. (In some cases there appeared to be a conceptual preference for the propagation medium to be a solid.) This travelling "disturbance" was typically jargon-labelled as: a vibrating medium; a moving density; a moving compression; a propagating pattern; and, a propagating disturbance. Even so, wave terminology was hardly ever used by the students, and when it was, it was only used in passing. In the first example, to follow, note how the association of the concept of sound only with what one hears led to an explicit denial that sound is a wave (see lines 14 - 21), while just prior to this (lines 1 - 13) the student appeared to be confidently depicting his conceptualization in appropriate physics models and language. Further, the student was aware that as a result of his university physics he had changed the conceptualization that he held at school and felt good about his change (see lines 26 - 30). Example 1 for Macroscopic Perspective Conceptualization # 2 1 S: How I see it? Oh, I see the vibrations from the bell being the frequency of the vibrations being propagated through the air through alternating areas of high and low pressure that propagate out from the vibrating bell so that sound is carried by — And what your ear receives is a series of 5 pulsations at a particular frequency of high and low pressure and that's what it responds to. You can draw a picture of a bell. And there it is resonating. And coming out from it is this pattern, coming out radially, a pattern of high and low pressures superimposed on whatever else is 10 happening in the air at that time. That's why you can get a whole bunch of different sounds happening at one time because wave theory allows for the superposition for all kinds of millions of noises, the air is just one great big medium to pass these things all through. So, the bell 15 generates at it's surface these ridges of high and low pressure; these waves. But people get confused, and I got confused, associating sort of sinusoidal waves with sound you start to think of sound as waves but that is not what sound is at all. Sound is pressure and pressure variations, 20 minuscule pressure variations on the human ear. I was amazed to learn in first year physics that, um, the human ear when you are first born is just above, the sensitivity is just above where you could hear random perturbations of pressure in the air. So, if your hearing was more sensitive 25 as a child you would hear this white wash of sound all the time. But it's just above that level. That's how, as I can remember going all the way through school; never really thinking about sound coming at me as little bands of pressure interacting with my ear. That's how I look at it 30 now as pressure variations that my ear reacts to. 5 6 In the following second example another student expressed a sense of vagueness and indifference to sound being a wave (lines 27 - 28). Example 2 for Macroscopic Perspective Conceptualization # 2 1 I: Okay, I am going to [sound of balloon being inflated] — blow it up and I am going to pop it. Now I wonder if you could try and explain to me, um, the mechanism of how sound was propagated from the source, i.e., from the balloon that 5 was popped to your ears, don't worry about how the ears operate. S: Yea, sure. Okay, basically you have an air filled balloon and when the pin penetrates the surface you have a rapid acceleration of the air around that surface. And that rapid 10 acceleration, from the, um, elastic nature of the balloon which causes a motion in the air around that particular area, propagates from that area to your ear. Then, of course it would dilute geometrically, you know, there would be a geometric dilution factor from the distance you 15 are from the source to your ear. I: Okay, I see that, now how would that actually occur? I am trying to — S: Okay, if we presume that the air before the event (I need a pen, being stuck) is, um, is still uniform. There are, 20 you are not basically hearing anything from that particular source because nothing is happening there. There is no, there is no, um, there is nothing there that's moving the air around or producing a wave or a disturbance in the medium you are dealing with, in this case air. So when you 25 pop it, um, because you are moving something ~ you are moving it fast through the air — you are producing a disturbance and that disturbance is propagated in the form of a wave or whatever. You're moving, you are producing a motion in the air which tends to move out from that source, 30 and um --4.2.4 The Wave Model Conceptualization: An Intricate Blend of Macro- and  Microscopic Perspectives This conceptualization of sound identified from the group of students participating in this study was: 5 7 The concept of sound is linked to the concept of waves as part of some universal, mathematically abstract, physics modelling system. The wave model conceptualization was initially considered to consist of two qualitatively different conceptualizations; one framed microscopically and the other framed macroscopically. However, the delimitation of students' explanations that incorporated "waves" as a concept became increasingly more difficult as the wave model conceptualization evolved. This was because both the micro- and macroscopically wave based conceptualizations essentially had the same basic structure: both characterized the wave nature of sound as being a mathematical abstraction that did not exist physically. As already seen in an earlier example, this led some students to insist that sound was not a wave (for example, see macroscopic conceptualization # 2, example 1, lines 17 - 18). This mathematically abstract wave model of sound was depicted as being a subset of some universal physics wave modelling system: a kind of problem solving heuristic perception-set which may be characterized as conceptual "haziness." Here, physics wave concepts appeared to be arbitrarily interlinked and plagued by water wave/sinusoidal wave analogies. The terms used to describe these waves were usually drawn from physics-based terminology, however, their meanings were diverse and often inappropriate. Macroscopically based descriptions were framed by the bulk properties of a medium. Typical examples of the terminology used to describe these properties included: motion of the air; longitudinal; pressure; shock-waves; compressions; transverse; sinusoidal; and, displacement. If the students were asked to elaborate on the meanings of any of these terms they invariably shifted to a microscopic perspective for their explanations. Microscopically based descriptions were framed by a pervasive sense that molecular actions could usefully be described as a mathematical waveform, but no waveform existed in the physical sense. That is, the wave nature of sound that one learnt of in physics was not an inherent property of sound per se. This aspect of the conceptualization had promoted a conceptual separation of "sound" from "sound waves" as quasi-independent concepts. It was this "sound/wave" dichotomy which superseded the micro- and macroscopically based conceptualization distinctions that were initially made, and subsequently facilitated their merging. 5 8 Physics concepts associated with wave theory were often qualitatively conceptualized at the microscopic level, in particular the concepts of wavelength and wave amplitude. For example wavelength was typically depicted as being the displacement that molecules travel between their interactions, and wave amplitude was typically depicted as the speed at which molecules travel between their interactions. Consider the following illustrative examples: Example 1: Illustrating a Wave Model Framed by a Microscopically Based Perspective 1 S: ... as a wave is propagating along it is causing molecules to oscillate from their equilibrium positions. I: Hmm, what is an equilibrium position? S: Equilibrium position will be a position of rest. So if, um, if I am not talking — particles will be, um — Okay, if we are talking about you clapping, before you clap all the particles are in a position of rest and as you clap you are causing to move so particles start jumping all over the place. And as you clap you generate a sinusoidal wave, so what happens initially is the particles closest, the particles begin oscillating. 5 10 Example 2: Illustrating a Wave Model Framed by a Microscopically Based  Perspective 1 I: Is it this vibrating molecule that eventually reaches you? S: [Pause], I guess, yea, in one way I think yes 'cause it will keep moving out and then I have the other idea that it will keep vibrations. And do these vibrations vibrate further out? So it will be like these molecules, these particles will stay here causing the particles in each area to move out. But then again, on the other hand, I got the idea that the particles keep moving. But as far as I rem — as far as my understanding of the way the sound moves is like when you throw a rock into the water you see it hit the water and the waves move out from the central area because it caused an excited, excited area within that area which then excites each area, successive area. 5 10 l 59 Example 3: Illustrating a Wave Model Framed by a Macroscopically Based  Perspective This example illustrates the struggle that some students have with what they perceive to be a kind of universal physics wave modelling system. It appears as though this student has been unable to draw suitable analogies and distinctions between the longitudinal and transverse physics wave models because he was unable to conceptually distinguish between sinusoidal wave representation and a physical wave shape (a common finding with the students involved in this study). 1 I: Any idea what we are talking about when we use the term wavelength? S: The flow of the wave itself [outlining a sinusoidal wave shape in the air with his hand]. 5 I: Okay you drew a --? S: Sinusoidal wave. I: Sinusoidal wave [echoing]. Now in terms of the vibrations that you were talking about, what would a wavelength be? Um, you had the idea — 10 S: The waves would be the crest of the, um, wavelength is h i g h . I: I just have difficulty in trying to picture what a vibrational crest would look like? S: Hmm, yea. [Long pause]. Hmm, could be an answer for that. 15 I guess it would be, um, it's kinda hard to give you a word for that or an explanation for that. The crest would be, I guess, the point that reaches you the soonest ~ I: Point that reaches you soonest? S: Yes, as your wave comes out towards you there is the one 20 point that will be the nearest to you so it appears to be like the crest; the point that is closest to you — or with the strongest signal. I: Okay, that might be one crest? S: Uhum [affirmative]. 25 I: Now when you traced out the wave in the air with your hand you were measuring from one crest to a second crest. Now what would be the second crest? 60 30 35 40 45 50 S: I: S: [Long pause] ~ er, it would be — [long pause] — Does the clapping of my hands produce a wavelength? Yea, it would produce a wavelength. Measured between — crests —? [Long pause] — er, see that is another thing — trying to draw back on my physics — back to first year or so — The wave has to be the upper parts so the next crest should be the next part, er, the next high that reaches you so it would be, it wouldn't be that section there but it would be the next section after that would be the next crest reaching you. Okay, I want to link the idea — Okay, here is a vibration between the tuning fork arms of the air molecules [repeating what he had said earlier]. Now if I can recall correctly you felt it wasn't this group of molecules reaching your ear but this group of molecules somehow molecules ["S" interrupts] — Sending out. Now, in terms of that, how do you conceptualize a wave then? That's all right — so wavelength to me was the sine curve but as I see sound waves they are concentric circles without ever going below the x-axis, they would just be a continuous set of crests with each successive set going out towards you. Example 4: Illustrating a Wave Model Framed by a Macroscopically Based  Perspective In this next example it is interesting to note how this student had made sense of the mathematical representation of sound waves (see lines 6 - 8). The majority of the students indicated that they thought that sound was two dimensional, perhaps this was a conceivable source for this conceptualization. 1 I: It is interesting that here you drew a sinusoidal waveform yet you called it a compressional wave? Are those equivalent? S: A sinusoidal wave is a compressional wave, yes. 5 I: Okay. 61 S: Well — a sinusoidal wave — a compressional wave would be a three dimensional expression of the wave equation, and this is just in two dimensions [referring to his transversal waveform sketch]. 4.2.5 Discussion of Data Analysis for Research Question 1 The qualitatively different ways which the students involved in this study conceptualized the phenomenon of sound were all bounded by a meaning of sound in terms of what a person hears. The conceptualizations have been described in subsets framed by microscopic and macroscopic perspectives since, depending on the context, the students opted to use these qualitatively different modes of explanation. It is interesting to note that in a recent phenomenographic study Lybeck, Marton, Stromdahl and Tullberg (1988) independently identified the framing of "mole concept" conceptualizations from a micro- and macroscopic explanatory perspective by pupils. In this study, the conceptualizations framed by a microscopic perspective represented qualitatively distinct ways which the students depicted the particular role that a proxy-molecule played in the propagation of sound through some medium. Here the molecules were depicted as having a "natural state" which was overridden by the propagation process. This natural state of molecules was typically depicted as being random or quasi-stationary. Sound was, then, conceptualized as a "thing" which was either carried by molecules through a medium or was sequentially passed from one molecule to the next in a collision or conduction-like process. This "carrying" or "transferring" of sound was a mode impressed on the molecules, and after propagation was complete the molecules returned to their natural state. The students' conceptualizations framed by a macroscopic perspective reflected a set of holistically orientated conceptualizations in terms of perceived bulk properties of a medium. Here, sound was a substance made up of a bounded volumetric movement of molecules which travelled as a moving force. This propagation process manifested itself in a variety of ways, the most fundamental being as a wind of some kind. This would seem to reflect elements of primitive 62 intuition. For example, consider the following Aristotelian physics depictions of sound: Sound is a breath with impetus: "Every sound or noise is a breath ... it will cause greater disturbance if it comes in greater quantity or with an unusually violent impact." (Problematica, book VIII - see Forster, 1927, p. 886b) Sound is air set in motion: "Air which travels makes the sound." (Problematica, book XI - see Forster, 1927, p. 899a) Sound has difficulty travelling through media if the "air spaces are too small and so cannot admit the voice or let it pass through, or only with difficulty; for the voice is a kind of air." (Problematica, book XI - see Forster, 1927, p. 905b) On a seemingly more sophisticated level, physics terms were incorporated into the bounded substance conceptualization which was then depicted, for instance, as a travelling pattern (which was qualitatively different to a transferred pattern). What may be considered an interesting counterpart to the macroscopically framed conceptualizations being a substance of moving force was recorded by McCloskey (1983) when working with both physics and non-physics students at John Hopkins University. McCloskey called it a "naive impetus theory": First, the theory asserts that the act of setting an object in motion imparts to the object an internal force or 'impetus' that serves to maintain the motion. Second, the theory assumes that a moving object's impetus gradually dissipates (p. 306). Perhaps physics graduates who hold such a "naive impetus theory" for objects, may extrapolate the theory in their conceptualizations of sound propagation. The wave nature of sound was conceptualized from an intricately intertwined micro- and macroscopic perspective base, and was thus considered to represent a qualitatively different conceptualization which could not be specifically framed by either of the perspectives. The conceptualization of the wave nature of sound was that the wave aspect of sound was a kind of by-product abstraction from the mathematical representation of sound: applied mathematics and not physics. Hence, wave conceptualization tended to be divorced from conceptualization of 6 3 sound, and some students went so far as to claim that they felt that it was a mistake to think of sound as a wave. Interestingly enough, with respect to conceptualizations of sound described in this chapter, Hults (1980) wrote in the Teachers' Pets column of The Physics Teacher: While studying wave behavior, my students found it hard to comprehend that it is not the medium that travels, but only the wave. So to demonstrate, I dipped the bell of a cornet into a shallow pan ... full of soap-bubble solution. Raising the cornet, I then played an entire tune without breaking the bubble formed on the bell.... I had them note that the air with which I played stayed in the quart-sized bubble, but did not travel to the back of the room, yet the 'music' did. (Emphasis his, p. 671) Perhaps the sound conceptualizations described are all manifestations of a primitive conceptualization of a travelling medium in that the wave nature of sound was not conceptualized as sound per se. An underlying theme of all these conceptualizations was that sound production and subsequent propagation was really a two-dimensional process. For example: 1 I: So what kind of dimensional sound would you say we are looking at? S: Two-dimensional. I: Is all sound two-dimensional? 5 S: — [Long pause, and talking softly to himself] ~ I guess I see almost any wave being three-dimensional — it can have — [breaking off to talk softly to himself] — I: Would it be three-dimensional? [Provocative question]. S: — [Long pause during which the student picks up a tuning 10 fork, strikes it several times and looks at it intently] — I don't see it as being three-dimensional, I see it as being two-dimensional. In the above example, the tacit separation of sound from wave can again be seen. Perhaps the depiction of sound as a one or two-dimensional phenomenon (which is how most of the students described the dimensionality of sound) comes from 6 4 one-dimensional textbook illustrations and the teaching practice of reducing mathematical complexity by focusing on the notion of plane waves. The next section in this chapter deals with the students' conceptualizations of the factors affecting the speed of sound propagation. 4.3 Data Analysis for Research Question 2: Conceptualizations of  Factors Affecting the Speed of Sound 4.3.1 Introduction The second research question is described in Chapter I as: What is the qualitative nature of the students' conceptual understanding of the factors which affect the speed of sound? Even though this analysis of research question 2 is presented independently and sequentially to question 1, the analysis should not be viewed independently. The components of the entire conceptualization analysis were intricately interwoven, and the conceptualizations collectively reflect a map of "conceptual space" wherein the students functionally moved around "more or less freely, back-and-forth" (Marton, 1984, p. 62). (In phenomenographic terms such a conceptual map is called the "outcome space" [Dahlgren, 1984].) Three qualitatively different ways of conceptualizing the factors affecting the speed of sound propagation were identified from the group of students participating in this study. These conceptualizations were framed by what the students had been taught in physics and provide fascinating insights into the kind of sense students may make of the content of their physics classes. 4.3.2 Conceptualization # 1: The Speed of Sound is a Function of the Physical Obstruction that Molecules Present to Sound as it Navigates its Way Through a Medium. A logical link may be made between this conceptualization and the physical entity microscopic perspective conceptualizations of sound described earlier. As a physical entity, sound's propagation would be impeded by obstacles in the form of 65 a medium's molecules. The molecular obstruction factor is generated by the following different depictions: FIRST DEPICTION: In this depiction the number of molecules (per unit volume) in a medium reflected a measurement of obstruction to the sound wishing to travel through the medium: The more molecules that there were the greater obstruction that there would be and vice-versa. In this depiction, density and temperature were portrayed as being equivalent since higher temperature was associated with a proportional decrease in density and vice-versa. The depiction may be logically linked to one of the factors that textbooks identify as influencing the speed of sound; namely, density. SECOND DEPICTION: The second depiction may be logically linked to commonsense or intuitive thinking that has had little scientific mediation. In this depiction, the physical size of a medium's molecules was the fundamental determinant of obstruction to sound propagation. The larger the molecules were, the greater the obstructing area that they would present to any sound wishing to propagate through the medium and vice-versa. What follows are some illustrative examples of these depictions. In the first example to follow, the student's conceptualization of what sound was (a small entity) appeared to facilitate his conceptualization that sound could propagate through a vacuum. 1 I: I am interested why —? We were looking at sound travelling through a vacuum, and then travelling in air, and then travelling through a metal. And you felt it would be slower in the metal than in air. Do you have any feeling about why 5 that would be? S: Well, um, I guess I kind of think of it as being energy being transferred and as the waves go through, say a solid, some of the energy will get scattered or whatever by the atoms or absorbed and you would actually loose energy which 10 would be why you get damping and that sort of thing. It would be very difficult to hear something through a solid wall as opposed to hearing something through a vacuum. So I think of the waves (we did a lot of crystallography in materials) so I can sort of picture these lattice 15 structures from metals and the energy going through and getting scattered as it goes through. Whereas in a vacuum you wouldn't have interference it would just keep on going, 6 6 and I guess in air you would have other gases that would interfere, not as often because the molecules would be a lot 20 more distant from each other. Now I am worried, but I think it would be faster in a vacuum, that would be like your zero case. This student's speed of sound conceptualization appeared to have a primitive intuition-base with its plausibility provided by a physics-based conceptualization of crystal scattering (see lines 14 - 16). In this depiction sound would ultimately propagate fastest in a vacuum (for instance, see lines 20 - 22). It is interesting to see that this student presented some conceptual tension between his intuitive ideas and his desire to give the correct answer: "Now I am worried —" (line 20). Perhaps his expressed worry reflected an inkling of some previous conceptual conflict with his intuition when being taught that sound cannot propagate through a vacuum. The next example illustrates the the physical size of the medium's molecules playing the role of sound's obstruction. This example is considered an illustration of how extremely strong intuition-based conceptualizations can be "decorated" with physics terminology. Here the student was explaining why he thought sound would travel faster in air than in wood: The greater molecular density of wood would provide "more of a resistance" to the passage of sound through the wood. In the second part of the example (see lines 17 - 20) the student emphasized sound as being an entity with physical dimensions, and hence, the size of molecules took on an important role as sound attempts to "navigate" through the medium. The extract begins with the student explaining why he thought that sound would propagate more slowly in wood than in air. 1 I: Could you explain why? S: Um, um, it's down to I imagine the wood would provide more of a resistance. It would take more of the initial, I guess — [to himself: what's the word?] — an initial hit or 5 something to produce the initial shock wave. It would take more to elicit a further reaction down the wood than it would in the air, so you are getting a quicker response in the air than you are in the wood. It's hard for me because I have just really thought of sound as moving through the 10 air rather than anywhere else. So with me I've got it set 67 up that's it's due to a vibration of air particles and for me to try and apply that to the wood I am just looking at it being the wood particles, therefore the wood particles would be — harder to produce the sound than the air particles or 15 harder to produce than the air would be because the air seems to provide less resistance. At this point the student digressed, the dialogue continues after the interviewer asked him to summarize what he had been explaining: S: Oh ~ [long pause] — I would say the size of the molecules that make up the medium. Um, the smaller they are the less interference they produce to the sound and 20 the faster the sound will move or be propagated. In the above example it is interesting to note that while the student introduced the idea that sound propagation was associated with molecular vibration (couching his conceptualization in physics terms — see line 11), the rest of his explanation was not framed by a physics perspective. This illustrates how primitive intuition-based conceptualizations may lie just below a level of seemingly reasonable physics explanation (see lines 17 - 20). 4.3.3 Conceptualization # 2: The Speed of Sound is a Function of Molecular Separation. This second conceptualization of the factors that affect the speed of sound has a similar base to that of the previous speed of sound conceptualization in that both have sound being depicted as a physical entity. This second conceptualization can be logically linked to the conceptualization of sound that depicts sound as an entity which is transferred from one molecule to the next (see 4.2.2.2). Consequently the speed of sound was determined by how far molecules have to travel before they can transfer the sound that they carry on to their nearest neighbours and so on. The greater the molecular density of a medium (number per unit volume), the smaller the intermolecular spacing and consequently the shorter the period between molecular "sound transfers." Hence, sound travelled faster in more dense mediums and vice-versa. Consider the following two illustrative examples. In the first example the student considered two factors that contributed to the speed that sound would propagate at: temperature and density. 6 8 1 I: Could you explain to me how those [temperature and pressure] will affect the speed of sound? S: This is going back to the molecular model. If the temperature around the air molecules is low, the air 5 molecules wouldn't be so energetic and it would take more energy to push motion to, sort of, move the air molecules. Whereas, if the air molecules are in a higher temperature they are already energetic so it wouldn't take that much energy to move them. Therefore they sort of, like they 10 are already energetic so they are ready to go. And, if they are cold then you sort of have to warm them up before they go. I: Okay, and the other thing that you spoke about was? S: Pressure. 15 I: How would pressure affect it [speed of sound]? S: Higher pressure would mean denser air molecules, I think. I: Okay, what do you mean by denser air molecules? S: If you have higher pressure the air molecules are more compact, if you have lesser pressure the air molecules are 20 sparse, more diverse, more spread out. I: Okay, how would that affect it? S: Since the propagation of sound is through air molecules, the more you have the clearer the sound. The more you have the more repetitions you have. Um, each molecule would 25 carry the same portion, same amount of information but you have more of it therefore you hear more, you hear better — So if you have less molecules, one molecule, one molecule would be carrying just that portion of the, the molecule would be carrying the sound but you would have less of it 30 therefore you wouldn't hear quite as clear. I: Okay, I can see that, but why should that make it travel faster or slower? S: Oh -- if you have less of them [molecules], then it would have to have, have to travel a further distance before it 35 hits another one, before it shoves another one forward, whereas if you have a whole bunch of them [molecules] it [the sound carrying molecule] wouldn't have to travel as far to push another one. 69 The above example illustrates how students may make sense of physics concepts in terms of the framework of their existing conceptualizations. For instance, in this student's discussion of the temperature factor (see lines 1 - 12) he incorporated an element of physics sophistication into his explanation by introducing the role the molecule's inertia would play in determining the speed of sound (see lines 5 - 6): The air molecules have to be moved in order to carry sound, however, all objects that have to be moved have a certain amount of inertia which first needs to be overcome before the object can be moved. Now, this student depicted higher temperatures reducing this inertial factor by providing the molecules with movement "so that they are ready to go" (line 10). Thus, for this student, higher temperature meant faster propagation of sound (see lines 10 -12). (This seemed to reflect an implicit assumption that inertia reduction was a function of speed.) When turning to the density factor the student emphasized that each molecule transported a certain amount of sound (see lines 24 - 30). In his explanation, more molecules carried proportionally more sound facilitating faster travelling, clearer and louder sound. Note how the student verbalized his decision to view the process microscopically (line 3). In the following, second example, the student described how molecules that are closer together would be able to "react a lot faster" (line 11 - 12). Note how he interpreted the effects of temperature change: higher temperature simply reduced molecular density. However, he did not seem to view temperature change as a significant factor in determining the speed of sound (see lines 11 - 23): 1 I: ... What would change the speed of, what factors affect the speed of sound? S: What it's moving through. I: How-why, would that affect it? 5 S: The density, like we talked about the density of the air. You can transmit sound through walls and the speed of sound through the wall will definitely be different to the speed of sound through air. It will move quicker through a more dense medium. 10 I: Why would that be? 70 S: Because there is more, the molecules don't have to travel so far to hit each other; so that they can react a lot faster. I: Suppose I heated up that media, would that have any effect? 15 S: Well, if you, you know, like with air yes because when you heat it up it becomes less dense and it will not transmit as well. I don't know whether it would make a really appreciable, it should, you know, it should make the same sort of difference with the wall but it may not be as 20 noticeable. Usually when you heat up a wall it becomes less dense which is sort of — although it should, the molecules should move faster and that sort of thing. 4.3.4 Conceptualization # 3: The Speed of Sound is a Function of the Compressibility of a Medium. (The more compressible a medium is the faster the propagation and vice-versa). In this conceptualization the speed of sound was primarily determined by the "compressibility" of a medium; that is, the more compressible a medium was, the faster sound could propagate through it. The next example illustrates the kind of sense making that can take place to accommodate intuitive ideas and result in strong convictions based on powerful conceptualizations. 1 I: Okay, while we were sitting here I was thinking; we spoke about the speed of sound, is this something which is constant? S: It depends upon the medium, whether the sound is travelling 5 down a bar, in a pool, if you clap your hands in the water, or if it's in air. I: Okay, how would the medium affect it? S: [Pause] — okay, the density of the medium is what affects it, and the elasticity would affect it. 10 I: Okay, I am going to ask you what do you mean by the elasticity? S: [Sighing followed by some laughter] Um, this is probably what they should do before you graduate: is that they should put you in a room and ask you all this stuff see 15 if you can really explain it. Um, by elasticity? Okay, I would define elasticity as, in very colloquial terms, um, how easily a group of molecules that are next to each other in a substance; how easily they can move around each other, be jostled around; how strict the bonds are holding these molecules together. If the bonds are more flexible it would be more elastic. Okay, suppose you were in a forest and it was dead quiet, not a sound. Can you imagine that situation? Oh yea, uhum [affirmative]. What are the air molecules doing? They are moving around very quickly. Okay, what would that tell us about the elasticity of the air? Very, very high. The density and the elasticity of the medium were what I was interpreting and I think, elasticity, when I mentioned that I was thinking of solids or liquids. Not solids, I correct myself. [When I mentioned] density I was thinking of solids or gases. Seems to me that the more dense the medium would be the slower the sound would travel. Could you say why? Yes, it would be harder, much harder to compress. I think it's [density] inversely proportional to the elasticity ~ Might help if I wrote this out [jotting down a formula on a piece of paper]. What do I have? I have the speed is proportional to, um, elasticity over density. So, i f you had a higher density material the speed would be slower. If you had a higher modulus of elasticity, meaning it's more flexible, the speed would be higher and intuitively that makes sense to me. So, if we had a very rare medium ["S" interrupts] —? Rare? When I say rare I mean the density is very low so ["S" interrupts] Oh, okay, okay. As we approach a vacuum, then, is the speed of sound going to get progressively more and more rapid? The closer and closer we get to a vacuum? [Pause] ~ I know in a vacuum there is no sound at all because there is no medium. You need a medium to transmit the sound. 72 I: I am using that old idea of a limit; I am getting closer and closer to it. S: So would the speed increase? No, I think the speed is a 60 characteristic of the medium and if you deal with — okay, I see where you are going ~ [long pause] — and you define a medium by the density, for example. So air you get 343 or 333 or whatever it was, and if you had something like a partial vacuum — yea, I would say it would be faster — on the basis of the same idea it would be easier to compress. A plausible basis for this conception that the speed of sound is a function of the compressibility of a medium may be as follows: The inverted interpretation of the physics concept, which is described above appears to be based on the common practice in physics teaching of drawing an analogy between the vibrational behaviour of a simple helical spring and the vibrational behaviour of some bounded section of a liquid, solid or gas medium such as a confined column of air or water, or a vibrating metal rod. Following this type of analogy the speed of sound is typically formulated as being proportional to the square root of the elastic modulus of the medium and inversely proportional to the square root of the density of the medium. It is at this point where common and physics language understandings diverge. In common usage the term "elasticity" conjures up images of how easy it is to extend or compress something which projects "compressibility" as a synonym. In physics, however, the terms "elasticity" and "compressibility" are conceptual antonyms. For example, in physics a measurement of the "elasticity" of air (also known as the bulk modulus), is the inverse of "compressibility" (the fractional change in volume per change in applied pressure). In other words, in physics the "elasticity" of a medium represents a measurement of resistance to compression and extension. A common general speed of sound formula found in physics textbooks has the speed being proportional to the square root of an elastic force factor and inversely proportional to the square root of an inertial factor. In the case of air, the elastic force factor is represented by the adiabatic bulk modulus of air (if we could apply Boyle's Law, which would still give a fair approximation of propagation speed, within 16%, then, pressure would play a "role exactly analogous to an elastic modulus" [French, 1971, p. 58]) and the inertial factor is represented by the density of the air (sound travels fastest in gases, such as 7 3 helium and hydrogen, which have low molecular mass). Interpretation of such formulae using a common language understanding (or intuitive understanding) of the term elasticity (as easily compressed and stretched) could plausibly lead to the conclusion that the more compressible a medium is, the faster sound will travel through it (from a physics perspective the desired interpretation would be to associate highly compressible mediums with low propagation speeds and vice-versa). If the speed of sound formulae are not to end up as rote learnt facts, then, students will have to make some kind of plausible sense of them. For instance, in the given example, in lines 15 - 21, the student explained what he understood by the concept of elasticity (see also lines 25 - 29 and 43 - 44). He was describing a situation which indicated that he perceived elasticity as being a measurement of how easily a part of a medium may be elongated or compressed. After writing down his formula, "I have the speed is proportional to, um, elasticity over density" (lines 40 - 41), he proceeded to explain how he made sense of this formula (see lines 30 - 45). The student did this by linking his conceptualization of elasticity with his conceptualization of compressibility. Then, in turn, he directly linked compressibility with the density term in his formula; that is, from his perspective, density was inversely proportional to compressibility since the less molecules there were in a given volume of a medium the easier it would be to compress the molecules into a smaller volume: "... and intuitively that makes sense to me" (lines 44 - 45). An indication of the strength of the student's conceptualization was illustrated when he accepted that sound would travel progressively faster as one approached a vacuum (lines 63 - 65), even though he knew that sound could not travel in a vacuum (see lines 54 - 56). 4.3.5 Discussion of Data Analysis for Research Question 2 Three qualitatively different conceptualizations of factors affecting the speed of sound identified from the group of students involved in this study have been presented. The first conceptualization had molecules presenting an obstruction to sound propagating through the medium. The second conceptualization had the distance a molecule had to travel before being able to interact with a neighbour as an affecting factor, reflecting the role played by density. The third conceptualization rested on how students had made sense of physics speed of 74 sound formulae to depict greater compressibility of a medium implying faster propagation of sound. Consideration of these three conceptualizations reflects that all have a common theme. It would seem that they are a result of the students having been taught that certain factors (such as density, pressure and temperature) affect the speed of sound without any explanation of how these factors affect the speed of sound. For instance, many introductory physics textbooks simply give formulae for the speed of sound (for example, see Halliday and Resnick, 1988, pp. 419 - 420). The students, then, seem to have made sense of these factors in a manner that seemed the most plausible to them. This claim is made because in this context most of the students seemed quite confident when giving their explanations. That is, they answered with very little hesitation and little indication that they were thinking about the matter for the first time. However, in order to make sense in the most plausible way, it seems as though the students conceptualized these factors microscopically. The inherent difficulty in doing this must consequently account for much of the commonality in, and the nature of, the conceptualizations. The first example for the second conceptualization is a very interesting case. It took some time to decide how to interpret the student's reply regarding the role played by temperature on the speed of sound. Although the student talked about having to "sort of warm up" molecules "before they go," after much consideration this was not considered to be a direct temperature related speed of sound conceptualization. diSessa (1986) has reported on a lot of exploratory work he carried out with Massachusetts Institute of Technology physics students regarding their intuitive modes of thinking about phenomena (what diSessa calls "phenomenological primitives"). He has suggested that, "The situation of bringing an object up to speed, like a car accelerating, seems to be an occasion for abstracting a warming up primitive ..." (p. 31, emphasis his). This is how the student's "warm up" explanation has been interpreted: as an attempt to describe change in molecular speed due to temperature change. In other words, a conceptualization anchored in a quasi-kinetic theory rather than in a speed of sound theory. Even though a logical connection may be drawn between the two, it is felt that this student was not depicting a "mechanism" of sound propagation in his explanation (as he did a little further on in the dialogue), but was 75 explaining his conceptualization of the relationship between temperature and molecule behaviour. 4.4 Overview of Chapter IV This chapter has described qualitatively different conceptualizations identified from the students involved in the study using a phenomenographic perspective. These conceptualizations were of the phenomenon of sound and the factors affecting the speed of sound propagation. Scrutiny of all the conceptualizations described in the previous two sections indicate that they were constructed from a limited set of physical relationships. This finding is in line with other phenomenographic studies (for instance, see the overview by Gibbs, Morgan and Taylor, 1982, and the latest study from the Gothenburg University Group by Lybeck, Marton, Stromdahl and Tullberg, 1988). The implication of this is that while the number of ways for a student to make sense of phenomena is potentially enormous this does not appear to be the case. This greatly enhances the pedagogical and didactical value for phenomenographic studies dealing with students' conceptualizations. The union of the conceptualizations described in this study may be be considered as being representative of some kind of "outcome space" (Dahlgren, 1984), in the sense that the term "space" represents a kind of conceptual delimitation or qualitative map of distinct conceptual variations where each outcome constitutes a distinctly particular way of conceptualizing sound. From this union of conceptual outcomes a theme emerges of qualitative conceptual conflict and mediation between students' intuitive ideas and the models provided by classroom physics. The students' contemporary undergraduate physics appears to only have contributed a dimension of abstraction in the form of mathematical representation to their conceptualizations of sound. This may be because, from general comments made, it appears as if the majority of the students interviewed accepted the mathematical representations encountered in their undergraduate physics at face value. Depending on the context, the students opted to use different modes of explanation. These were characterized as explanatory perspectives which were either macroscopically or microscopically orientated and framed the conceptualizations of sound. A l l the conceptualizations of the factors affecting the speed of sound propagation were framed by microscopic perspectives. Often the students would begin an explanation using a macroscopic perspective but would change to a microscopic perspective when they were asked to elaborate. Also, where the students perceived that they were being very analytical, such as when explaining the speed of sound factors, they opted to frame their explanations from a microscopic perspective. In Chapter VII it is suggested that for many physics students, careful explanation and elaboration means a microscopic "unpacking" because microscopic explanation had formed part of a "hidden curriculum" of physics teaching, both at secondary school and university. That is, physics phenomena and problems should be analysed microscopically for maximum insight and understanding. Further discussions on explanatory perspectives are given in Chapters V and VII. In the next chapter the consistency of the students' conceptualizations will be considered. 7 7 C H A P T E R V DATA ANALYSIS: CONCEPTUAL CONSISTENCY AND DISPERSION 5.1 Data Analysis for Research Question 3: Introduction The third research question is described in Chapter I as: What is the nature of the consistency of the students' patterns of reasoning about sound in and across the following interview generated contexts: - an example offered by the students from their experiences which had not formed part of their formal physics classes; - an example not commonly used in physics teaching but which would be common to everyday experience; - an example commonly used in physics teaching; - an experimental situation; and, - a hypothetical teaching situation? The above contexts were generated during the interviews specifically to explore the nature of the students' conceptualizations about the phenomena of sound. The interview protocol is described in Chapter III, however, for ease of reference the following sequential summary of the contexts is provided: (a) the students being asked to generate their "own example" of sound (i.e., not one taken from their classroom experience) as a basis for their explanations; (b) the students being presented with an inflated balloon which was subsequently burst with a pin; (c) the students being presented with a set of tuning forks and being encouraged to generate their own "hands-on" exploration; (d) the students being asked to observe an experiment with the aim of formulating pertinent questions regarding their observations, and, then, to provide the answers to their questions. The experimental set-up consisted of a hollow, 5cm diameter, metre long, glass tube which tapered at one end. A candle was placed at the tapered end so that the candle's flame was directly opposite the tube's opening. The experiment involved producing a sound, such as hand clapping, at the opposite open end, and observing the effect on the candle flame. (A sketch of the experimental situation may be found in 78 Chapter III in the section dealing with the Interview Protocol); and, (e) the students being asked to imagine the following hypothetical teaching situation: a puzzled first year physics student (the interviewer) comes to them for some help with his physics. His problem is understanding a diagrammatic representation of sound in his physics textbook (this diagrammatic representation is reproduced in Chapter III). The data analysis for this question involved drawing up mappings to reflect the students' patterns of conceptualization, and patterns of framing of conceptualization, across and in the above contexts. These patterns have collectively been characterized as reflecting conceptual dispersion. That is, the notion of conceptual dispersion is used to characterize the array of conceptualizations that may be evoked by a person regarding some phenomenon or related phenomena; their contextual patterns of reasoning. 5.2 Conceptual Dispersion: Patterns of Reasoning In and Across Contexts The nature of the students' patterns of reasoning is illustrated with the aid of two Tables. The first, Table 5.1, represents students' explanatory perspectives, described in Chapter IV, as a function of students and contexts. The second, Table 5.2, represents the students' conceptualizations of the phenomena of sound, also described in Chapter IV, as a function of the contexts. Consideration of Table 5.1 shows that the students' initial explanatory perspectives were often a function of the contexts. This outcome is discussed later in Theme (a). Table 5.2 shows that the students, both individually and as a group, expressed wide qualitative variations in their conceptualizations of sound. Although their conceptualizations tended to be contextually different they did not, on the whole, tend to be contextually dependent. As a case in point, consider the "burst balloon" context in Table 5.2. In this context the full array of the students conceptualizations are represented, with several students holding more than one conceptualization within the same context (see for instance Students 2 and 10). Table 5.2 also shows that the students conceptualizations were well dispersed amongst the various contexts. There are two notable exceptions, these are the 7 9 "textbook" and "sound tube experiment" contexts. Here, more or less the same group of students remain grouped together with the result that conceptual dispersion is not so pervasive within these contexts. These outcomes are discussed later in Themes (b), (c) and (d). Further, the outcomes reflected in Tables 5.1 and 5.2 validated the phenomenographic notion of conceptualization being person-world relationships; a way of contextual functioning rather than a specific attribute of an individual. The first stage of the data analysis for this research question involved the mapping out of segments of interview data to generate Tables 5.1 and 5.2. The second stage involved exploring any patterns identified: Where there appeared to be some sort of identifiable relationship between some specific context and conceptualization or explanatory perspective the appropriate segments of interview dialogue from all the interviews were repeatedly re-read and scrutinized. As a result five themes were constructed to characterize the nature of the students' conceptual dispersions in and across the contexts. These themes were: (a) The students' initial explanatory perspective was often a function of the context. (b) In varying degrees, all the contexts evoked conceptual dispersions which included personal intuition-based conceptualizations which have been characterized as gut-physics. Where gut-physics was only briefly evoked and then suppressed, these occurrences were characterized as gut-physics flashbacks; gut-physics • flashbacks were considered to be conceptual intrusions because the students would typically correct themselves (suppress or override the conceptualization) only to re-use them (gut-physics conceptualizations) again later without any recognition that they were doing so. The "sound tube experiment" and "textbook" contexts had a tendency to evoke much smaller conceptual dispersions than the other contexts did. These trends are discussed in themes (c) and (d): (c) Practically all the students were so influenced by their observations of the "sound tube experiment" that after observing the experiment they almost unanimously depicted sound propagation in terms of a continuous flow of air molecules; a kind of wind. It is proposed that the nature of visual cues available from the experiment evoked a basic, but powerful, 8 0 intuitively primitive conceptualization that had survived years of school and university physics. Since this conceptualization was typically sustained for the complete duration of the context, but not into the next, it has been characterized as a prolonged gut-physics flashback. (d) The students appeared to find the "tutor/textbook" context the most difficult to deal with. The formal physics cues available in this context tended to promote the evocation of an abstract "wave" conceptualization which reflected disconnected mathematics and physics thinking. This "wave" conceptualization, although appearing to be taught-physics orientated, seemed to be of little help to the students in their efforts to make sense of the textbook figure (a figurative analogy of sound coupled with a mathematical representation) that they were presented with. The next theme, theme (e), did not stem directly from trends identified from the mappings reflected in Tables 5.1 and 5.2. Theme (e) did, however, emerge during the mapping to produce the Tables, and it provides what are considered to be important insights into how the students dealt with recognized dissonant conceptual dispersion, and what kind of learning this experience may manifest. (e) During the "tuning fork" section of the interview an opportunity arose for the interviewer to have the students face a situation of recognizable dissonant conceptual dispersion. The students were handed a 440Hz tuning fork and asked to first intuitively estimate the wavelength of the sound produced and, then, to calculate it. The students' micrometre to nanometre order of magnitude intuitive estimations contrasted vividly with their three-quarter metre calculations. This "tuning fork" wavelength context provided insights into how some students cope when faced with dissonance between personal intuition-based and physics-based conceptualizations and what learning was facilitated by the position into which they were manipulated. Also, towards the end of the interview a few students recognized dissonant factors in how they conceptualized and explained sound through the different contexts of the interview. When these students, from their self-initiated reflection, recognized aspects of conflict inherent in their conceptual dispersion, their comments indicated surprise and a very strong desire to "sort out" their conceptualization dissonance (much stronger than when manipulated into such a position). However, in both the manipulated and self-recognized instances of dissonance discovery, the students showed an inability to immediately resolve the dissonance. The themes, (a) - (e), will now be discussed and illustrated by excerpts of interview dialogue. EXPLANATORY PERSPECTIVES FOR CONTEXTS: STUDENT NUMBER Own Example Burst Tuning Text Balloon Forks Book Sound Tube Experiment MAC MIC COM MAC MIC COM MAC MIC COM MAC MIC COM MAC MIC COM 1 * >* * > * * * * * * <* 2 * * * > * * * * * <* 3 * * * * * 4 * * * * * * >* 5 * > * * > * * * * 6 * >* * * * 7 * * * * 8 * * * * > * * * > * * * 9 * * * > * * * * * < * 10 * * * * * * * * * * * * * TABLE 5.1: Explanatory perspectives as a function of contexts and students. MAC = Macroscopic explanatory perspective MIC = Microscopic explanatory perspective COM = Combined perspective referred to in the description of the wave conceptualization < = Direction of perceptible shift in perspective (to left) > = Direction of perceptible shift in perspective (to right) CONTEXTS: CONCEPTUA-LIZATIONS (see below for details) Own Burst Tuning Text Sound Tube Example Balloon Forks Book Experiment MICRO # 1 4;5 3 ;4 ;5 3;4 4 2;4 MICRO # 2 1;6;9 1 ;2 ;3 ;5 1 ;3 ;6 ;8 1;2;8;10 1;9 10 7;9;10 9; 10 MACRO # 1 1 1;2;9 1;7;8 8 1 ; 2 ; 3 ; 4 ; 6 ; 8 ; 9 ; 10 MACRO # 2 2 ; 5 ; 6 ; 8 2 ; 5 ; 8 ; 10 5 ; 10 - 5 10 WAVE 2 ; 3 ; 7 ; 9 6; 7; 10 2;8 1 ;2 ;3 ;4 7; 10 10 9; 10 5; 8; 9; 10 TABLE 5.2: Students (numbered 1 - 10) as a function of conceptualizations and interview contexts pertinent to research question 3. The conceptualizations may be summarized as follows: MICRO # 1: Sound is an entity which is carried by individual molecules through a medium. MICRO # 2: Sound is an entity which is transferred from one molecule to another through a medium. MACRO #1: Sound is a travelling substance with impetus, usually in the form of moving air. MACRO # 2: Sound is a substance in the form of some travelling pattern. WAVE : The concept of sound is linked to a concept of wave as part of some universal* mathematically abstract, physics modelling system. 83 5.2.1 Theme (a): Shifting Explanatory Perspectives In Chapter I the students' micro- and macroscopic perspectives were used to frame the generation of the conceptualizations. Across and in contexts the students often changed their explanatory perspectives, sometimes midstream, as they were faced with the task of articulating their conceptualizations of sound. Table 5.1 traces the students' micro/macro explanatory paths across and in the interview contexts. The mapping reflected in Table 5.1 indicates that besides using different explanatory perspectives in different contexts, the students often utilized more than one explanatory perspective in a given context. This explanatory shifting usually followed a specific direction such as macroscopic to microscopic. At times the students intermingled their explanatory perspectives in such a manner that specific directional perspective . shifting was not discernable. The students were frequently asked to clarify and expand on segments of their explanations and on terminology that they had introduced into the interview. Usually, if they were using a macroscopic explanatory perspective just prior to one of these clarification requests, they would typically respond by shifting to a microscopic explanatory perspective. This directional shifting of explanatory perspective was particularly noticeable during the interview's "own example" and "burst balloon" contexts where there was a strong tendency for the students to begin their explanations on a macroscopic level. For example, consider the following illustrative interview excerpts. In the first, the student had just started explaining how sound propagated from a burst balloon to his ears. He began by using a macroscopic explanatory perspective (see lines 1 - 3 ) and then immediately switched to a microscopic explanatory perspective after he was asked for some clarification (see lines 10 - 12): 1 S: Um, pressure inside the balloon was released and that produced waves, compression waves which transmitted to our ears. I: Okay, now could you try and give a clearer explanation? 5 What do you mean by a compression wave and how did that travel? S: How did they travel? 8 4 I: Let's start off with what you meant by compression waves? 10 S: A wave is produced when pressure is put on — okay ~ the molecules in the air, which are pressed from the pressure towards me, which press the next ones and they propagate The second example comes from the "own example" context where another student was explaining how he conceptualized sound propagation. In lines 1 - 18 he was using a macroscopically based perspective and after a clarification request (lines 18 - 22) he shifted to a microscopic mode for the rest of his explanation: 1 S: Well the most basic theory that I could talk about is, um, going for an example where you can actually see: a speaker or, um, even a voice, a voice diaphragm ~ but, um. Basically what it has to do with is, um, I was going to say 5 a wave but that brings in a lot of other connotations. Um, but that's probably the best; a force of air changing that causes a reaction on your ear drum that you can turn into something. You know, whether it is the drop of a pin causing this noise to reach your ear, this little thing 10 which travels through the air, um, or a voice talking to you vibrating a small diaphragm in your ear which then you can recognize as speech. Any sort of disturbance in air; you need something to propagate this little thing we call sound; whether its dropping a book, talking to someone, 15 turning on your stereo; it all creates a disturbance or a shock to this air around it [the ear] that moves through, then you can proceed with your ear. I: Could you try and clarify a little more for me how this "disturbance" — how it actually reaches my ear? Suppose 20 you are talking over there or drop a book. Could you explain the mechanism: give me a model of what is happening? S: The best model, if you recognize that air like anything else is made up of tiny particles of things we like to call 25 molecules, then — At a simpler level just consider a row of beads sitting on the table. And you tap a bead at one end and you knock the beads all the way along and at the other end [of the beads] you have your finger and you can feel the tap. That would be analogous to a book 30 dropping and creating the motion of all these smaller things in the air we call molecules which act the same as the beads and move this disturbance around until your finger at the other end can feel it; in this case with the ear at the other end that is feeling it. 8 5 This macro- to microscopically based perspective shifting which is illustrated in the above two examples is viewed as being representative of how the students contextually thematized the task of providing articulate explanations. At the same time it is also considered as being reflective conceptualization-shifting — perhaps from intuition-based to physics-based — which in some way, in the context of physics, may be intrinsically linked to enhancing explanatory power. In other words, it is being suggested that the students believed that their explanatory power would be enhanced if they used a microscopically based perspective. The students also tended to associate their microscopic modes of explanation with interview contexts that may be closely associated with their experiences of formal physics teaching: the "tuning fork" and "tutor/textbook" contexts. When explaining in contexts where the students could feasibly be expected to have little or no experiential associations with the content of taught physics -- "own example" and "burst balloon" contexts — there was a tendency for them to start their explanations on a macroscopic level. Here, how an explanation was initially tackled is important because, as was mentioned earlier, most students tended to shift from the macro- to the microscopically perspective when asked to clarify, define, or expand upon aspects of their explanation. Interestingly enough, the "sound tube experiment" context did not generally facilitate a macro-to-micro perspective shift even when the students were asked clarifying questions. 5.2.2 Theme (b): Gut-Physics Flashbacks The term gut-physics was derived from Claxton's (1983) notion of "gut science," and although gut-physics is not being used here in precisely the way that Claxton used gut science, their respective meanings are essentially similar: Gut-physics characterizes personal intuition-based conceptualizations that appear to have their foundations in everyday interpretations of "how things work." In other words, gut-physics is a pervasive, contextually cued, reaction to phenomena and experiences. While gut-physics may or may not accommodate a contemporary physics view, it characterizes a powerful literal way of interpreting phenomena and experiences. The term gut-physics flashbacks is used to characterize these personal intuition-based conceptualizations in the mode that they tended to be presented in the interviews; brief conceptual intruders. In most cases gut-physics 8 6 conceptualizations framed explanations for only short periods and, then, they would typically be denied or suppressed only to be re-evoked and subsequently re-denied or suppressed again. This sequence often occurred several times during an interview. When students come to physics classes with well established sets of gut-physics conceptualizations and they draw upon these in the process of making sense of the physics being taught, then, gut-physics may, in the metaphorical form of a conceptual intruder into taught-physics, be aptly depicted as a "critical barrier" (Hawkins, 1978) to certain types of physics conceptualizations. While gut-physics may be successively discouraged by "layers" of retaught physics (many areas of physics are repeatedly rehashed through school into university at what are considered to be "appropriate" levels of complexity), research at the undergraduate and postgraduate levels of physics education has indicated that students' gut-physics "is highly robust and that it outlives teaching which contradicts it," making "much of our teaching less effective than we usually assume it to be" (Viennot, 1979, p. 205; also see McDermott, 1984; and diSessa, 1986). Gut-physics mediated conceptualizations have been well documented in the context of school physics as children's ideas in science. For a comprehensive set of examples see Driver, Guesne and Tiberghien (1985) and Osborne and Freyberg (1985). What follows are some illustrative examples of what are considered to be gut-physics flashbacks. The first example begins just after the student had explained that sound caused molecules to travel outwards from the source. 1 I: Okay, so that the molecules from here at the tuning fork reach my ear? [With that the interviewer strikes the tuning fork in his hand.] Yes — [long pause and sound of tuning fork] — because — they hit — not the same molecules but they hit others, hit others, hit others, otherwise you wouldn't be able to hear it. If they only got this far or if they hit a wall or something else that doesn't transmit sound you wouldn't be able to hear it because you would need those molecules [in the wall] moving to be able to hear it. 10 8 7 In the above example the student is seen confirming that the molecules travel outwards from the source, in this case continuously so. Then, pausing to reflect upon his (gut-physics) answer while looking intently at a vibrating tuning fork, perhaps recalling some earlier gut-physics suppression that he had been forced to make when studying sound. The result of his reflection was that he effectively suppressed his gut-physics conceptualization and began to evoke another: "... not the same molecules but they hit others, hit others ..." (lines 5 - 6). He, then, attempted to provide some plausibility for his modification: The propagation of sound could not incorporate molecules travelling from source to receiver because, then, sound would be unable to travel through a solid (lines 7 - 10). From his reasoning it seemed as though he had not completely suppressed his gut-physics; see lines 7 - 8, " ... if they [molecules] hit a wall or something else that doesn't transmit sound," which reflects elements of gut-physics (propagation via travelling molecules) in his explanation. The next sequence of interview dialogue with this same student indicates how persistent gut-physics conceptualizations can be. Later, during the same context, he again presented similar gut-physics flashbacks in his molecular collision conceptualization; that is, that the molecules move outwards from the source, except now he has incorporated this into a molecular collision conceptualization; an indication of gut-physics' inherent plausibility. Just prior to the following dialogue the student had been given a "slinky spring" to help clarify part of his explanation. The excerpt begins when the interviewer tried to divert the student from using the slinky to frame all segments of his explanation. 1 S: Okay, well its like if we attach a spring to this fork moving back and forth. I: I can see with the spring, lets just try and think of the air. S: Okay, this fork is moving the air back and forth, just like 5 the spring. So it would be at a maximum at a point where it's moving towards the air — towards compressing — in the direction, well depends [on] where you are listening. Say we are over here, when it moved towards us then the air is compressing [and] we get a high pressure, moving towards 10 whatever is receiving it. When it moves back — 88 I: Why does it move back? S: Why does the fork move back? I: No, you have this molecule — why does it go back? S: Understand that it's the fork [that] moves back and forth, 15 r ight? I: So, if the fork only went in one direction the molecules would — only move in one direction? S: — only move in one direction [voice superimposed over "I's"]. Yea. I: So, when you do that [sound of hand slapping table top], do 20 that [sound of a clap], you only have molecules moving in one direction? S: Well, it's not going back and forth — saying it only goes in one direction is a bit of a misnomer. I: Well, what is it doing? 25 S: Because, like I could, you could be standing over there, over there, anywhere around me: when I do that [sound of clap] you will hear it because it will move in all directions around my hand; but the individual molecules are moving outwards — they are not vibrating back and forth. 30 I: And then what would? — they are moving outward — would there be a vacuum there afterwards? What would happen? S: Well, you move them and they would hit each other and start to move out and then it moves out; if you could sort of picture it, a sphere around where the sound is coming, then, 35 they just bump into each other and move further and further out. The individual molecules don't keep going in that direction they just bump into one next to them, bump into the one next to them, bump into the one next to them. 40 I: When after they have bumped then what do they do? S: They just sort of start doing a fading back to random motion. In the next example (which involved a different student), the student said that he was, "formulating things here" (line 8), giving an indication that his intuition was playing an important role in his explanation. At the same time he also wanted his explanation to be "correct." So, in effect, when reading through the transcript one can almost "feel" the student "stumble through" a range of conceptualizations. The reflectively equivocal nature of his explanation, 89 especially in lines 27 - 42, together with insightful comments such as, "Clarifying these notions is scary" (line 35), seemed to be indicative of an attempt he was making to unscramble his conceptualizations; his gut-physics from physics. In so doing he had to decide what role molecules ought to play in the propagation of sound. When the interviewer tentatively suggested to the student that he may have been presenting different conceptualizations (lines 61 - 64), the student's response portrays what may be described as a "dilemma in conceptualization plausibility." A dilemma between his gut-physics and other conceptualizations: which should, or would, be regarded as the most "correct" physics perspective. 1 I: Could you try and explain to me how the sound travelled from the balloon to your ear — the mechanism? S: [Pause] — okay — balloon ~ pressure — pops [more to • himself than "I"] -- creates a bang, see that's, that's 5 where I am stuck now: it creates a noise, what we will call a noise, the bang, and that, um ~ travelled through the air. I imagine, okay, you ask me to um, so I am formulating things here. It um, does something to air particles which causes them to, um — oscillate — and 10 that moves towards my ear — in the same pattern, in the same way in which they were sent out or in which they were caused to virtually oscillate. I: So you have an oscillating, what should we call it? -- a molecule? 15 S: Uhum [affirmative]. I: And this oscillating molecule eventually — ? S Reaches my ear ["I" interrupts] — I: Reaches your ear? S: [Nods head affirmatively] — And then causes, um — your 20 eardrum or it causes something in your ear to oscillate, it creates a resonance so that you hear the same, the same oscillation, you are able to, um, it causes your eardrum or whatever to oscillate in the same, same manner as picking up the sound as generated there. 25 I: Okay, before that molecule got it's oscillation, what was it doing? S: It's, no, I mean all the molecules in the ~ air right now are all moving, they are — it's oscillating in a certain --[long pause]— it's always going through my head [to 30 himself] — okay it, it will be oscillating. I mean it's moving around, we have — obviously within frequencies and oscillations of particles we have audible and not, things that our ear can't pick up. So it may be, I mean no molecules are static, everything is moving around all the time. Clarifying these notions is scary, um, and so it will be oscillating and then a change in pressure or, well, the balloon breaking — causes everything to — principle behind that — causes everything, it causes, um, it causes a big pressure change. Um, particles start oscillating at a different, I mean at a certain frequency and then I am able to hear that because it's within my audible range. Did I answer what you were asking? You did. There is only one thing which I am not clear on: then is, um, so we have this particle and we started oscillating it separately. How did, if are just looking at one particle, how did that one particle get to my ear? It didn't get to my ear, it in turn causes another molecule to oscillate which causes — and I think it would be a chain reaction, so it would um, I mean just like, um ~ I don't — in my view of sound I wouldn't -- I would view it like a domino effect where that particle, it hits against something else which hits against something else which hits against something else and moves — um, therefore energy is lost and that's why sound dissipates, maybe. What is it hitting? When I say, okay — well, the molecules hitting each other. What does it do after it has hit those molecules? [Long pause] Just wondering, did you change your mind? Earlier on when we were talking there was the idea that the molecule reached you and now we have the idea that the molecule doesn't reach you. No, no I actually, originally I never, in saying I never visualized the molecule hitting — hitting — [pause] — I may have said that in terms of how the sound got there but, um, in my mind I had always envisioned, um — [pause; then softly, more to himself than interviewer: yea, something hitting something and being more like a chain reaction [addressing the interviewer again:] and then, um, once that energy is transferred it is lost, it is transferred to another particle which transfers it to another particle. So that's — so it will return to it's original, um, static frequency or, you know, just the frequency that that molecule oscillates. 91 In the above dialogue gut-physics flashbacks can be easily identified as conceptual intruders. Although the student appeared to deny (see line 65) his gut-physics conceptualization (and possibly lead one to conclude that this dialogue simply represented difficulties with articulation), he generated similar gut-physics flashbacks in other segments of his interview. Here, when the interviewer questioned him further about travelling molecules the student began his reply by indicating dissatisfaction with his explanation, however, this time he did not deny that that was what he meant. From his reply it would seem that although he was giving his explanation a low status in terms of "correctness," it has a higher status in terms of plausibility: how he conceptualized sound: S: Well that don't sit too right with me, but I am trying it in the, in the definition which I have been formulating through the answer to you. I am trying to distinguish how sound is generated and so I see it as having to get some particles going at the same speed. Then, later on in the interview this student again evoked a similar gut-physics conceptualization: in the "sound tube experiment" context he depicted sound as a kind of wind. Based upon these exemplars of gut-physics flashbacks, a reasonable postulate seems to be: it is not unusual for people, in this case students, to have constructed a variety of conceptualizations regarding experiences and phenomena (what has been referred to as conceptual dispersion in this dissertation). What exactly determines the evocation of a conceptualization is obviously multifaceted and complex. However, the results from this and the next theme seem to suggest that the cues which a student takes from a context play an important primary role in the evocation of an appropriate conceptualization. 5.2.3 Theme (c): Prolonged Gut-Physics Flashbacks Earlier it was mentioned that practically all the students that participated in this study essentially "saw" a wind blowing out the candle during the "sound tube experiment" (for details of this experiment see Chapter III). That is, they depicted sound in terms of a continuous flow of molecules. The basis for this theme is the postulate that the perceptual cue of the candle being "blown out" was so powerful that it evoked a kind of prolonged gut-physics flashback. 92 If such a conceptualization is indicative of a very primitive intuition-based conceptualization of sound propagation, then, for the students concerned, it may be feasibly postulated that despite years of formal physics, both at school and university, such conceptualizations often do not get changed but remain more or less intact. It may even be that primitive conceptualizations such as this are suppressed and remain dormant until strong evocative visual cues (such as "sound blowing out" the candle) revitalize the conceptualizations. Support for this view may be found in research reported by Viennot (1979) on "spontaneous reasoning in elementary dynamics" which involved British secondary school pupils, and Belgian, British and French university students. Here Viennot wrote that "intuitive physics" is: Widespread and tenacious. It resists the teaching of concepts which conflict with it, and it reappears even in the expert when he or she lacks time to reflect, (p. 213) The following transcript is a complete excerpt of interview dialogue from the "sound tube experiment" for one of the students. It is offered as a rich exemplar of how the visual cues of the experiment evoked a prolonged gut-physics flashback. Note how, in the second division of the dialogue, when the interviewer modified the experiment, the student reflected upon his explanation and subsequently modified it in an interesting manner (refer back to Viennot's cited comments above). The interview dialogue is presented in three sections to accommodate discussion. It begins when the student took an unusually active role in the experiment by taking the initiative to explore some ideas of his own: 1 I: ... I am going to do the experiment. I would like you to observe what happens and then ask the question or questions, and then answer them. S: Are you going to answer them? 5 I: No, I will let you answer them, okay? S: Augh . I: Sorry to spoil your fun [sound of joint laughter]. 93 The sound tube experiment was set up as described earlier (also see Chapter III) when the student suddenly reached over and moved the candle in front of him. He, then, picked up a tuning fork, struck it to set it vibrating, and held it virtually in the candle's flame. The flame visibly flickered back and forth. The conversation continued: S: See that's what a kid would do, "Look it's not blowing sir." Or it isn't, isn't it? It is, isn't it! Isn't that 15 great, there's something for you! [Striking the tuning fork again and holding it almost in the flame itself] Oh, J....! [Long pause while "S" observes the flame closely: the flame appears to be "stuck" to the tuning fork arm as it vibrates back and forth]. Hey? 20 I: That's kind of interesting. S: Yea, you can see the candle begin to — I wonder [taking another tuning fork of a much lower frequency and again holding it very close to the candle's flame]. There is a surface reaction: the molecules begin to be played around 25 with. I: That's interesting! S: Yea it is. At this point the interviewer continued with the experiment. This initially involved hand-clapping at one end of the 5cm x lm hollow glass tube and simultaneously observing the effect this had on a candle flame situated at the other end of the tube. Note how the student immediately responded to the visual cue of seeing the candle flame extinguished by saying that, "The air blew it out." (see lines 31 - 33). Then, in what appeared to be an exploration of the validity of his conceptualization, he experimented by clapping in the immediate vicinity of the candle (i.e., ignoring the tube). The result was that he, then, rather uniquely offered his explanation from a "kids" perspective. Subsequently his "moving air" conceptualization was explained in terms of what he called a "kid's view" with a powerful, albeit inappropriate, hose nozzle analogy. The dialogue continues: 94 I: Okay, I am going to clap at this end of the tube, let's see what happens [after several claps the candle is 30 extinguished]. S: The candle went out. Why did it go out? Because the air blew it out. Why did the air blow it out? [Long pause.] Well, because you forced the air along when you clapped. And I would ask: Do you think without the tube there that 35 if I clapped it would go out? And if I [was a] smart-ass I would say — ["S" lights the candle again and claps all around the candle] — Doesn't seem to be any way I can put it out without clapping close to it. Without the tube, it looks like we can't put it out without the tube. The kid 40 buys that: without the tube — the tube plays a big part ~ what is going on? I would say it's probably beyond him to be able to explain how the pressure, way it is caught by the tube, transferred along — this is just exactly the same way that we hear sound — the pressure 45 ~ the pressure wave comes down to this end and is then intensified as those molecules, same surface area pushing here [at top of tube] of those molecules is now getting banged on in a smaller and smaller surface area [at the other end of the tube where it narrows]. 50 Those molecules are getting forced, so what you get, you've got a surface area here [at the top of the tube] pushing with the same amount of force, same pressure difference, but that comes out and acts here [other end of tube] so what you get is an actual, um, pulse or pressure of air 55 out this end. It's a, you know, it's a common focusing effect if you — kids can recognize it on a hose, turn a hose on and if you get a little area out at the end you, those things [nozzle] you screw, so that you get the "spsssspt," a real blast out and if you take it off the end 60 it just goes "bloph" but if you put the little thing at the end — I: So what are you saying? You have a higher pressure? S: Yea, you get a focusing and a higher pressure gradient than you would get normally. At this point in the interview the interviewer tried to probe a little further into the student's explanation by asking him what it was "that put out the candle?" The dialogue continues: 70 I: Okay, what is putting out the candle though? S: A i r . 95 I: When you say air, is there a wind? [Provocative question] S: Yes. Essentially we are creating a little wind to blow it out, a pulse of high pressure. 75 I: So, if I could colour the air in this tube in some way, could you explain to me what would happen to this coloured air? 80 S: We would see, starting when you clapped, we would see a bunching of the coloured molecules here [opposite end of tube to candle] and we would see it go right through to here [candle end of tube] and then we would really see them bunch up, down here [end of tube], and then they would spew out and there would be red all over the chair and all over the candle, it would just be everywhere, god it would be awful. Note how in lines 73 - 74 the student made the connection between "a little wind" and a "pulse of high pressure." It is suggested that the student was making an attempt to merge segments of his gut-physics based conceptualization with segments of his taught-physics based conceptualization. In other words, he was making an attempt to sensibly connect the two conceptualizations (in particular see lines 78 - 84), probably for the first time. Following this segment of explanation the interviewer decided to probe what he, at the time, believed was a newly constructed conceptualization (facilitated by the interview process) based upon the merging of two distinctly different "older" conceptualizations (based upon gut-physics and taught-physics respectively). This probing was initiated by removing the hand-clapping visual cue and replacing it with a box which had only one open end (facing the open end of the tube). The box was, then, used to produce sounds similar to hand-clapping by knocking upon it with one's knuckles. That is, part of the perceptual "wind" cue (clapping hands) was effectively removed. Immediately after the modification, the student began to tentatively alter his explanation; a shifting towards a taught-physics based conceptualization. Here he appeared to be trying to decide how the notion of impetus should be manifested in his modified conceptualization (see lines 93 - 120). While it is possible that his shift in explanation may have been the result of him interpreting the experiment modification as an indication that his original explanation was "incorrect," it seems more likely that his change in explanation arose from the removal of a strong perceptual cue which led the student to either evoke a different, or construct a revised, conceptualization. 9 6 The dialogue continues: 85 I: Okay, so, I've got an idea. S: Okay. I: Suppose I — [knocking a small wooden box open at one end] — instead of clapping I bumped this - would the candle still go out? [Facing the open end of the box towards the 90 opposite end of the tube to that of the candle and knocking the box several times: the candle flickers each time and then is extinguished]. What is happening in this case? S: You're generating the same sort of, um, large pressure variation and that you're outputting, um, one impact 100 pressure variation into the air as opposed to um — quite high amplitude because, you know, that's a fairly large sound as opposed to these [tuning forks] — yea it's just a clap or a single shout or an impact on an object, we all know how — we are accustomed to those things being loud as 105 well. A single, um, pulse in your voice called, um, oh god I've forgotten, what's it called? Um, staccato — staccato pulses from a voice, from any sort of object, just one bang, you are used to that being very very loud, and it is because the pressure generation for one pulse is very 110 large. We are used to that for objects too, when you impact an object you are used to that having a really harsh effect. You know? When someone comes up to you and pushes you really hard against something but just sort of gradually builds up the pressure, "eaagh", as opposed to coming up to you and 115 just BANG, you against the wall with the same — We associate impact with high degree and high damaging forces, so, this sort of thing [claps] and that sort of thing [the wooden box] is impact generation of big forces in the air. You get quite a pressure generation to pass along down 120 and blow out that candle. I: So, um, coming back to the coloured air in the tube. I knocked that [the box] several times so that by the time the candle went out could I have emptied the tube of the coloured air? 125 S: Oh, no, I would say not, the only, the only air that's getting, it's not, see it's not really, how do you do this? The, um, air is not getting spewed out, spewed out the end so we have to go back. I have to go back on what I said before. I would not think — [Pause] — hardly any of 130 the, um, air inside the tube would be coming out the end here. What would be happening is the pressure that is built up out to the very end here [of the tube] interacts with the local air and the pressure wave gets passed on. Obviously the air is moving but it does not continue to move, it goes, 9 7 135 as you noticed when you banged it, it went [mimicking the flicker of the candle flame with his hand], it went flush, it went "swooosh" and then it's back to normal instantly, right? A l l you've got is a net pressure gradient in this direction [towards the candle] that interacts with the 140 candle and moves it over but it instantaneously sways back again. Um, I do not think that air is being pushed out that end, what has been happening is the pressure gradient is passed along, I don't think very much — I think there is going to be some amount of bleeding out of this end 145 of some of the red molecules but it's not going to be or isn't going to be "spoosh-spoosh" of red. It's not like turning on a hose and having it come shooting out. This is abstract since we are dealing with the propagation of a wave and not the propagation of the medium itself, so we have to 150 adjust — I was a little hasty in assuming that these red molecules would come shooting out that end. What they were actually doing is passing along, I would think, in the majority, passing the intensified pressure wave to the air outside and as that passed by, that was what [was] 155 interacting with the candle, I would think. [Pause] — Because it looks like there is a pulse of air getting blown over and there is. It is difficult to — I am not sure what you would say, because all you would really feel here — would you do that? [asking "I" to knock the box again while 160 holding his hand at the other end of the tube] ~ you feel a pulse of air hitting your hand — [long pause] — and I am not really sure — yea, I would say it's — I would say it's half-and-half, sort of, I would say that there is some bleeding out of the tube, that there is some air from the 165 tube getting actually pushed out as the pressure wave gets intensified here [end of the tube]. I would also that that is pushing against — see the pressure on the outside, once the pressure wave intensifies, interacts with the air just outside of here [the tube] and pushes it ~ but it's 170 difficult to see it as being fully like a hose, you know, you turn on and the air from inside here pours out. I think the air inside here wants to move but it's not the sort of the effect like "poof-poof". It's not like blowing in totality. I would say it's mostly interaction 175 with the pressure wave with the air just outside here that pushes it along, as opposed to, um, as opposed to this air from inside the tube just blowing out like someone was blowing in at the end of the tube. It's difficult to say, one would have to, um — From the perspective of taught-physics, the student's altered conceptualization provided a far more acceptable explanation in that the candle flame's flickering was manifested in impetus transferred inter alia a pressure wave. However, in this depiction it would seem that the impetus conceptualization, as being manifested as a continuous flow of air, has strength and high plausibility status. 9 8 The strength and plausibility status of this gut-physics conceptualization is exemplified by the student's apparent retreat (see lines 133 - 134 and 160 - 179) back towards his original explanation when he said that, "I would say it's half-and-half." As he continued with his explanation the shift towards his original explanation became increasingly more apparent (see lines 178 - 179). Finally, when the student was asked which of his explanations he believed, he gave ultimate plausibility to his gut-physics based conceptualization (see lines 180 - 187). However, it was strongly mediated by the taught-physics based conceptualization that he appeared to base his post-modification explanations upon. The dialogue continues: 180 I: What do you believe? S: Um, I believe that air is being pushed out from inside to a certain degree and that interacts with the air just on the outside there and moves. I believe that there is a pressure gradient being created here which is moving the 185 air, because the air obviously moves, over the candle. I don't think, I don't think it's pouring out the end like a hose, I don't think. For most of the students involved in this study their observations of the candle flame manifested a conceptualization incorporating impetus, not in terms of the momentum transfer of a sound wave, but in terms of a flow of air. Since this conceptualization is regarded as being part of early gut-physics development, and since the conceptualization typically remained more or less intact for the complete duration of this context, the flow of air conceptualization was characterized as a prolonged gut-physics flashback. Based upon the outcomes illustrated in this theme and the previous gut-physics theme, it would seem plausible to suggest that the context-specific cues which a person picks up, or is sensitive to, play a primary determining role in the evocation of a given conceptualization. Throughout the analysis it appeared as though the contextual cuing influenced the students' choice of theoretical framework, terminology, and analogies. Perhaps a partial explanation of the phenomenon, which has been characterized as conceptual dispersion, is that 9 9 contextual cuing establishes some sort of preferred conceptualization for every context-specific experience; a sort of hierarchy of available conceptualizations based upon previous context-specific experiences. That is, depending on the context, the students appeared to perceive that one, or more, of their conceptualizations were more fruitful than others. For example, when students were asked to estimate the wavelength of sound produced by a vibrating tuning fork, their intuitive conceptualization was very much smaller than the actual (calculated) wavelength (see Theme (e)). Even when students were reluctant to accept the conceptualization of the much larger wavelength they said that they would give the larger (calculated) answer in a physics examination. That is, the larger wavelength conceptualization would be more fruitful in the context of physics examinations (there was no sense that they would be giving an incorrect answer) while the short wavelength conceptualization appeared to be more plausible in the context of how tuning forks produce sound. diSessa (1981; 1986) has proposed similar ideas by suggesting that experts and novices in physics differ in their "control of reasoning" and assign different "cuing priorities", and hence different "reliability priorities," to "concepts" when solving problems. Physics "experts" can recognize specifics of a problem which are context-relevant when deciding on the priority-use of a conceptualization, in particular with the evocation of primitive conceptualizations. diSessa calls these "phenomenological primitives, or p-prims for short" -- which are analogous in many ways to what has been called gut-physics in this dissertation. Physics novices have great difficulty with their conceptualization structuring because their "knowledge system is structurally incapable of supporting any strong, principled commitment to a particular interpretation of a physical phenomenon." (diSessa, 1981, p. 25) 5.2.4 Theme (d): Disconnected Mathematical and Physics Thinking Throughout the interviews most students did not, or could not, distinguish conceptually between, sinusoidal waveforms as a mathematical depiction of essentially nondispersive oscillatory systems, and actual physical waveforms such as water waves. The "tutor/textbook" context supplied visible cues which seemed to reduce conceptual dispersion and evoke conceptualizations whereby the students all explained sound propagation in terms of an abstract wave propagation model (refer to Table 5.2). Perhaps this is a predictable outcome 1 0 0 considering the pedagogical focusing of the context: the students were playing the role of tutor while explaining a physics textbook figure. What was interesting was the manner in which the available textbook cues manifested themselves for the students. To appreciate the nature of this manifestation it is necessary to consider the nature of the textbook figure" and the associated interview scenario (refer to Chapter III). Recall that during the "tutor/textbook" context the students were asked to act as a physics tutor for a hypothetical first year physics student who was confused by the physics textbook figure provided to the students in this context. The figure depicted sinusoidal sound propagation and a mathematical representation thereof. Here a "travelling pressure wave" was used to figuratively depict a "travelling sound wave" by using a common physics wave heuristic: a system of sinusoidally vibrating particles interconnected by elements of helical spring. The relative positions of these particles over one and a half wavelengths are frozen in time in the figure and the mathematical representation given below is a profile of the sound wave's particle displacements plotted in the form of a transverse displacement graph (particle displacement versus propagation direction). In this context the evoked conceptualizations of sound propagation tended to be abstract in the sense that they were "shrouded" by mathematical modelling heuristics. This was in marked contrast to the students' everyday conceptualizations of waves which tended to be framed by experiences and observations of water waves. This abstract/concrete divergence manifested itself in the nature of the diffuse conceptualization linkages that the students expressed while attempting to form linkages between mathematical sinusoidal wave representations and, transverse and longitudinal waves. For example, here is how one student viewed the difficulty he was having making sense of the textbook figure: S: That's where I get into — with my, with the way I looked at it, it would be hard to describe that to someone with my theory because it was my idea that it kept on going and there was no — I knew that it [sound] would be a sine wave but with my theory I would have a hard time 101 explaining the lows [sinusoidal minimums] because it [sound] kept on going at a perpetual pace. So with my understanding I wouldn't be able to explain that [figure] to somebody. None of the students explained the textbook's graphical representation as one depicting the sinusoidal properties of the sound wave vis-a-vis the particle displacements being plotted transversely to propagation direction (which facilitated describing the waveform in terms of sine or cosine function). Prior to the following example, the student had labelled sound as a "longitudinal wave" and had adequately described how the particle displacements, frozen in time, were plotted in the graph below the particle/spring system. The interviewer, then, tentatively asked him: I: But isn't that a definition of a transverse wave? S: Yea. I: Where the particle position is perpendicular — [the student interrupts] S: To the wave motion direction? Yea, sure it is [and laughs a little self-consciously]. I: Any problems with that? S: Yea [laughing self-consciously again], um, hmm — [long pause] — Yea, okay I don't know how to deal with that [laughing self-consciously again]. Another student described his difficulties as a kind of optical illusion; something his mind wanted to impose on the displacement graph: S: Actually they are not too contrary. It's one of those things that are fundamental in that what we are taught, but can be confusing in a situation like this because what you're looking at. What you think you are seeing here is a wave travelling along. You have a picture of a sinusoidal wave just proceeding along. That's not what you've got at all, and that's why you have to read the information. What you've got here is a graph of displacements as at a moment of time — time in your mind is what moves this. 102 To make sense of the textbook figure the students seemed to rely extensively on the visual cues that they could gather from it. These cues appeared to be so powerful that, despite the graph being labelled as a representation of particle displacement and read as such, most of the students either described the graph in terms of particle velocity, or they described the graph as i f displacement amplitude and pressure amplitude were synonymous concepts. That is, they depicted maximum particle displacement as being analogous to maximum sound pressure and vice-versa. Some students treated all three concepts, particle velocity, particle displacement and sound pressure amplitude, synonymously and depicted their respective amplitude changes as being all in phase. The students expressed these conceptualizations when, as part of the hypothetical first year student's understanding difficulty, it was pointed out to them that the maximum and minimum pressures illustrated in the particle/spring system did not correspond to the respective graphical maximums and minimums (particle displacements) below it. Many of the students, then, in their tutor roles, concluded that this was because the textbook figure was poorly drafted. For example: S: ... I am trying to draw, like in drafting, like two views, that's how I am trying to look at it, and nothing lines up, so I don't see what they are — nothing lines up; their symbols aren't consistent. S: Maybe I should just say for the record that I think, you know, that this is terrible and misleading and the authors should change this because I don't think it's a very good illustration, and I remember in my textbooks there was something better than this, I forget what it was, unfortunately, but it was more clear than this. An appreciation of some of the disconnected mathematical and physics thinking depicted in the students' explanations may be found in the way that such typical longitudinal wave representations are introduced to students. For instance, for a travelling sinusoidal sound wave such as that depicted by the textbook figure, the sound pressure and particle velocity functions reflect amplitude changes which are in phase with one another while the sound pressure and particle displacement functions reflect amplitude changes which are ninety degrees out of phase with each other. Such conceptualization connections are not easily made as they are not visually or intuitively obvious. It takes some careful thought and 103 consideration of the respective functions to construct an appreciation of the qualitative relationships between them. This point is taken up further in a discussion of physics teaching in Chapter VII. Longer illustrative extracts from the "textbook/tutor" context have not been provided because the students frequently used the pronouns "this" and "that" while indicating to the textbook figure, making reading of the transcripts difficult to follow. Interested readers are referred to Appendix II where a detailed example is available (it is recommended that this particular section of transcript be read while cross-referencing with the textbook figure which is provided in Chapter III). 5.2.5 Theme (e): Dissonant Conceptual Dispersion: Examples of Student Reaction to  Recognized Inconsistency During the "tuning fork" context the students were presented with a tuning fork vibrating at 440Hz and asked to intuitively estimate the wavelength of the sound waves which were being produced (the frequency, which was stamped on the tuning fork, was pointed out to them). The students were, then, asked to calculate the wavelength. If they had difficulties with this request they were reminded of the relationship: (wavelength)x(frequency) = (speed of sound). In both cases, the initial estimation and subsequent calculation, the students were asked to give an approximate order of magnitude answer. A l l of the students that were presented with this context intuitively estimated the wavelength of sound produced by the vibrating tuning fork to be relatively very small, generally of the order of micro- to nanometres. This was an intriguing outcome because, both in this study and its preceding pilot study, it was essentially the most consistent, contextually-related conceptualization to be evoked. Since the calculation of the wavelength yielded an answer of approximately three quarters of a metre, the anticipation that the students would give intuition-based wavelength estimates several thousand to several million times smaller than the calculated wavelength provided the interviewer with a somewhat unique opportunity to have the students easily come face-to-face with an enormous discrepancy between their conceptualizations (one intuition-based and the other physics-based). The aim of doing this was to observe how the students would react 104 to, and cope with, a situation that evoked immediate, self-recognizable conceptualization dissonance. . Since exposure to this kind of discrepancy could create an undesired sense of anxiety in interviewees and potentially foster a "physics examination" atmosphere, the interviewer made a spontaneous decision during the interview's "tuning fork" context whether or not to proceed with the wavelength probing scenario. This decision was based upon the self-confidence that individual students had exhibited up until that point in the interview, and so in two of the interviews the wavelength probing scenario was glossed over. In many respects how the students responded during the wavelength probing scenario provided a new dimension of insight into the nature of their conceptual dispersions. This is because physics graduates could ostensibly be expected to be able to comfortably draw upon a rich repertoire of synthesized and integrated physics conceptualizations constructed from the content of their undergraduate physics in order to generate reasonable "hand waving physics" explanations and estimations such as the wavelength of the sound waves produced by a vibrating tuning fork (perhaps especially from a selection of good students who have decided to become physics teachers). Two examples from the wavelength probing scenario are provided. The first example is a complete transcript of the wavelength probing scenario. It illustrates the typical manifestation of dissonant wavelength conceptualization and how the students were generally unable to resolve their dissonance. The second example illustrates how difficult the rationalization of conceptions and conceptual change may be. Here, rather uniquely, one of the students presented a personal philosophy of flexibility in his physics thinking and was consequently very receptive to reflecting on dissonant situations. He attempted to restructure his dissonant conceptualizations in search of a rationalization and in doing so illustrated just how intricate reconstruction of a conceptualization may be. 5.2.5.1 First Example from the Wavelength Probing Scenario This first example illustrates how two quite different conceptualizations can be evoked in the same context by the same person. It also illustrates the kind of tension which can exist between competing conceptualizations and how, for example, a physics graduate can, in the space of a few minutes, shift from one 105 conceptualization to another without making any headway in constructing the beginnings of conceptualization consistency or looking for common ground, even when both conceptualizations are based upon the content of physics classes and textbooks. The dialogue begins when the student predictably estimated the wavelength to be extremely small (see lines 10 - 11; 15 - 21; 29 - 31): 1 I: ... I am just looking to see what we've got here [sound of tuning forks being moved around and tapped] — 440 — Well let's have a look a this [sound of tuning fork]. Its frequency is about 440Hz, any idea of the kind of 5 wavelength which we are looking at here? S: [Taking a tuning fork and striking it], ah there is a way of calculating that but you would have, um — er — I: Would you need to calculate it? 10 S: Yea, for myself probably. It's a fairly short, fairly small number. I: From what you have been telling me, from your explanation, there isn't a way that you could, um, give an estimate of the wavelength? 15 S: There probably is if I think about it long enough [continually playing with the tuning fork in question] — oh, yea I know [enthusiastically], the wavelength has to be the same as the — you see each time the fork moves back and forth it creates a new wave so the wavelength is equal 20 to how far the fork moves. That is a very very small number. I: Could you try and put something to it? S: What do you mean? A number? I: A number, a feeling for the size, let's work with this 440 25 [sound of tuning fork]. S: Well, actually the wavelength is, you can't say for sure an accurate number because --I: Are we talking about millimetres, centimetres, or metres? S: Um, the wavelength is of the order of less than 30 millimetres, I would be tempted to say like hundreds of nanometres, four hundred nanometres. 106 I: On all of these [pointing to other tuning forks], on this one as well? [picking out the 128Hz tuning fork because the vibrations of the arms are visible] It is 128Hz. 35 S: Now you are getting closer to, with that, you see, it becomes visible, so you know, you are getting closer to an order of millimetres then. It all depends on, you can only hear through a certain sound range. I: How would you respond to someone if they said to you well 40 — what is this? — 400. If they were saying that the wavelength was much longer how would you convince them in fact — ["S" interrupts]. S: Well, because you are creating a continuous sound which means a continuous wave. It is created out of the fork 45 moving back and forth. So every time the fork hits the same position it's got to be the same position, it's got to be creating like — all the way in and out again that's one whole wave. Every time it [tuning fork prong] goes in and out that's one wave so the distance it travels has to 50 be one wavelength. You know, because with this example you really can't see it [striking the 440Hz fork] moving, although you can feel it moving. Um, it is definitely of the order of less than a millimetre. With this one [picking up and striking the 128Hz fork] you can almost see 55 it moving depending on how hard you want to hit it [sound of tuning fork]. You can see the dimension we are dealing with. Note how this student confidently associated how far the vibrating arm of the tuning fork moves with the wavelength of sound produced (see lines 44 - 57). Warren (1988) has suggested that one source of this conceptualization may be physics textbooks which have "pictures of waves related to bodies [which] normally show wavelengths short compared with the dimensions of the bodies (i.e., ripple tanks, stationary waves on strings, in pipes, etc.)" This appears to be particularly true for depictions of waves emanating from tuning forks. In the next segment of this dialogue the student was asked to calculate the wavelength. At this point he mentioned that he calculated all his "formulas by looking at the units (see lines 70 - 74), an approach which another student referred to as a "survival method in physics." An indication that physics may have manifested itself as applied mathematics for this student (see lines 80 - 86). 107 The dialogue continues: I: Can you remember how you would calculate that? S: Um, the equation for it? 60 I: Yes. S: Well, the reason I say it's variable is because it depends on the speed of sound in air. I: Suppose we took the speed of sound to be 300m/s. S: Okay, we know the frequency so — [talking to himself 70 "seconds"] I tend to do it; I calculate all my formulas by looking at units. I know, I know, what you want to find is the wavelength and you've got the speed of the wave, because the sound travels through at that speed, and the frequency of the wave. So if its going at 300, what did 75 you say? I: 300m/s — that's an approximation actually it's closer to 330m/s but 300 is good enough. S: 300m/s and its 440Hz? I: Oh, use 400Hz. 80 S: Okay, 400 cycles per second. So we want to get something that is going to be in metres, we divide the one by the other which means we divide 300m/s by 400, um, cycles/s, and we get so many metres per cycle which means — one cycle is a wavelength so, so many metres per cycle would be 85 the wavelength. So we are looking at something like .75; three quarters of a metre. Now having completed his calculation the student was suddenly faced with a glaring discrepancy; a state of conceptualization dissonance. At this point in the interview he stood by his "original conceptual idea that the wavelength has to be of the order of the motion of the fork" (see lines 91 - 95), thus affirming the status of his intuition-based conceptualization. The dialogue continues: I: That seems inconsistent with what you were telling me earlier, three quarters of a metre is about that long [indicating with hands]. How would you account for that? 108 90 S: I can't. I: Does it worry you? S: Yea. I still hold by my original conceptual idea that the wavelength has to be of the order of the motion of the fork. I: Which would you prefer to go by, the formula or your — 95 S: I would trust my physical intuition. Following this statement of confidence in his intuition, the student began to shift towards his physics-based conceptualization when he was asked what answer he would give in a physics examination: "I would have to put 0.75m if that's the way the numbers come out" (line 100). In other words, despite having expressed confidence in his intuitive sense making he would not extend that confidence to a physics examination. Perhaps a fruitful speculation could be that his experience with physics examinations has encouraged him not to explore his own sense-making during examinations but rather to rely on mechanical problem solving. At this point in the interview the student began to indicate that he felt uncertain which conceptualization he should be evoking. His uncertainty may have had its roots in. how he perceived the shift in the context: whether he was being tested on his physics or not, which may have left him without any strong sense of conviction of the contextual plausibility of his conceptualizations. Initially, in an effort to account for some of the conflict, he turned to external factors (beyond his control) by suggesting that he may have been given some incorrect information for use in his calculation (see lines 103 - 105): an indication that at this stage he is still favouring his intuition-based conceptualization. However, since the frequency of the tuning fork was stamped on the tuning fork and the interviewer used an introductory physics text as an acceptable source to confirm the approximate speed of sound in air which he had used earlier in his calculation (see lines 110 - 113), at this point the student appeared to begin re-evaluating the plausibility of his intuition-based conceptualization. The dialogue continues: I: So, if they gave that to you in an exam: "Given that the speed of sound in air is 300m/s calculate the wavelength produced by a 400Hz tuning fork": What answer would you give? 109 100 S: I would have to put 0.75m if that's the way the numbers come out. I: How would you feel about it? S: If I assume that is the speed of sound, I have to assume because that is the given, and I know the frequency because 105 that is a given, then the length also has to come. I: Okay I will look up the exact speed of sound for you [looking up in physics text]. In fact it depends upon several factors ~ okay, here they give it as 330. So given that I haven't given you any incorrect information 110 and you have calculated this 3/4 metre, how do you feel about you writing that down in an examination, yet you feel quite confident within yourself that it is closer to millimetres? What does that do to you? At this stage in the interview the student began to consider that there may have been some factor within his control that lay at the root of the discrepancy between his two wavelength conceptualizations. Apparently still wanting to give a higher plausibility to his intuition he proposed that the discrepancy may have arisen because he may have made "a small error" (see lines 122 - 123; 128). However, it was clear that this was not the case and he went on to suggest an interesting way to separate his two answers: into categories of "fact" and "his way of looking at it" (see lines 129-131). The dialogue continues after the interviewer asked the student what affect it would have on him to give an answer in an examination that went against all his understanding (see previous dialogue): S: Well, at that point, looking at the magnitude of the 115 numbers it makes sense that it's almost of the magnitude of a metre. So then I have to look at the way that I was analysing the motion of air around the fork because that's where I must have made the mistake. At that point, once I have looked at that and say gone over it a couple of 120 times, that this is the way it has to be. I: Which is the way it has to be? S: Well, I would have to, you know, upon investigation I would have to default and say I know I'm, I'm within a small error — I know that that is the speed of sound 125 [referring to the 330m/s provided by the physics text] and since these [tuning forks] are calibrated to give a certain frequency, then, I must, again within a small 110 error, then my error must be in my gut-reaction to how the wave is created at the fork. That is a gut-reaction, that 130 is not a fact, it is my way of looking at it. Then I would have to amend my — I: Would you like to try to amend your way of looking at it or --? S: Well, at this time I am sort of — [long hesitation] — 135 I: I don't want to put you on the spot, we can leave it and maybe come back to it later. S: Yea, Yea. I, you know, I still, when I think of the way waves are supposed to propagate, all I know about waves that intuitively makes sense to me, the peak of each sound 140 wave being with the motion of each fork, and the fork definitely doesn't move that far. In the dialogue above, despite having claimed that the calculation represented "fact" and his estimate represented his "way of looking at it" the student ended off by voicing his almost total disbelief in the calculated answer because his intuition-based conceptualizations of waves still had a higher plausibility status. In the discussion around this example it has been proposed that recognizable conceptual dispersion seems to have an element of context specific plausibility; that conceptualizations may be evoked from a kind of context generated hierarchy of plausibility. Hence, for example, in physics examinations intuition-based conceptualizations may be accorded low plausibility while in everyday life they are accorded a much higher plausibility status. In the context of physics class some of the students indicated that they had no faith in their ability to make sense of the concepts being taught. When these students were asked which wavelength conceptualization they had more faith in, typical responses were: S: Well, after going through physics for four years one tends, um — you tend to like equations a lot [laughing self-consciously]. Yea, I would tend to have more faith in a textbook formula than in what I am trying to say at the moment. I: Okay, could I ask you why you would trust it [calculated answer] more? 111 S: Probably because I never had to conceptualize sound on the small level and I just went through it and understood it, and understood my formulas, and was able to calculate things and came up with proper answers that way; proper answers as defined by an exam.... We did a lot of problem solving, and a lot of the times you figured out what the problem was, they gave you the information in the problem, and it was just a matter of rearranging it. If students approach physics with little confidence in their own ability to make sense of what they are being taught, then they would be left with little option but to attempt to rote learn conclusions which are soon forgotten, and would have to fall back on their intuitive sense making. 5.2.5.2 Second Example from the Wavelength Probing Scenario In this study, while developing the notion of conceptual dispersion, examples have been provided which indicated that in some contexts the students accorded their conceptualizations little plausibility and they consequently tended to "flip-flop" between evocation of conceptualizations. Examples have also been provided where the context seemed to be linked to the plausibility status of the students' conceptualizations, suggesting that some sort of plausibility hierarchy was evoked by the context; a kind of contextual conceptualization hierarchical set. In the analysis so far, most of the emphasis has been on the context, however, conceptualizations are considered to be relationships which are constructed by people between themselves and the world. This second wavelength example focuses more on the person than the context. It provides an important insight into how a student's attitude (personal philosophy) plays a significant role in the construction of new or alternative conceptualizations. It also gives an insight into the tenacity of more primitive conceptualizations even when they have been reflected upon and recognized as being flawed. This example is also considered important because it reflects the view presented in this dissertation that physics education should aim at promoting the ongoing construction of phenomena-recognition that leads to the evocation of appropriate contextually functional conceptualizations: A view which perceives "conceptual 1 1 2 change" to be an inadequate description of non-rote learning. This view is further discussed in Chapter VII. The example involves a student who has a strong personal philosophy which makes him open to considering alternative conceptualizations; a kind of sense-making flexibility. This openness, then, reflected a willingness on behalf of the student to construct new, or reconstruct old, conceptualizations. The following example begins with the student providing his intuitive estimate of the tuning fork's wavelength and being faced with his inconsistent calculation: 1 I: Could you intuitively give me an order of magnitude of the wavelength which is produced by this [striking the 440Hz tuning fork]. S: Short. 5 I: Um, millimetres, centimetres, metres - order of magnitude. I am not trying to tell you ~ S: Oh, I understand — to make an intelligent guess — um, less than a millimetre. I: Given that this is just over 400Hz, do you know how to 10 calculate the wavelength, can you remember? S: As far as I know, um, it was a relationship between velocity and, um, wavelength, um, knowing the velocity about 660 MPH I believe ["I" interrupts] -I: That's about 300m/s. 15 S: Okay, then 330 over the, um, because wavelength times frequency gives you the velocity. I: Let's round that off at 400 and round off the speed of sound in air at 300, just for ease of calculation. S: Right, then we have got 300m/s divided by 400Hz, gives us 20 almost a metre. I: Does that surprise you now? S: Oh yea! I: How do you react to that? S: I would — Okay, it's one of those counter-intuitive things 25 because initially you would think of — Okay, the reason it surprises me most is because this thing [tuning fork] is 113 vibrating really fast, right? And you would think that the wavelength, you would think that the pressure variations would be coming very rapidly — [pause] — and in fact 30 they are, it's just that the sound is moving so fast. Do you understand what I mean? What I was ~ in place of speed was putting in frequency. So, we can have long wavelengths like of the order of a metre if the sound is propagating fast enough through the medium. If the sound 35 speed was considerably lower, if it was like 50m/s which is still really going, you know because I couldn't run that fast and that is going pretty quick for a car too, um, then our wavelength would be of the order of 0.2m or something like that. It surprises me because I see this 40 thing [tuning fork] vibrating really fast and really little tiny little pulses, so it's hard of me to think of the pressure wave getting built up in long distances like that. I can't see the pressure wave coming like that [indicating about a metre with his arms] but it is easy to see once you 45 realize how fast it's moving. I mean it's "swishoooooom," these things are propagated through the air very quickly, these little pulses that form, which is the reason that they are stretched out that much. Well you've got a pretty rare system here, right. So, you can't really build up a 50 sensible pulse like that, variation in, um — that's the thing about these kind of intuitive things, right. They: what?! and then aha [indicating first surprise and then making sense of the surprise]. I: So you feel happy with the calculation for the answer? 55 S: Yea, I would say — that's the one thing about being a physicist, you learn to rationalize and adapt very quickly. It's funny people see scientists as being pretty conservative people, right. But in their minds, I mean as far as situations where they are thinking intuitively, they 60 adapt very very fast and in a very liberal way to a new situation. I -mean you tell them something which is totally counter-intuitive and a man in the street will scream night and day that it's not so. A man of science will generally sit, ponder and completely change his world to adapt to 65 what you told him, if necessary: Like quarks come in threes, you know, oh, of course they do ["S" laughs and "I" joins in]. The interesting aspect of this student's dialogue was that although the wavelength discrepancy surprised him (line 22) it did not seem to perturb him unduly (line 24). Not because he had a poor image of his sense making ability (as was seen in the previous example set), but because he was prepared to reflect upon the two outcomes and try and rationalize them. While he began by adopting the position that his physics-based conceptualization was correct he also reflected upon his 114 intuition-based conceptualization in an attempt to identify the source of the inconsistency (see lines 25 - 33), which he successfully did (the only student in this study to do this). The confidence and ease with which he tackled the task was a reflection of his personal accommodation, "... that's one thing about being a physicist, you learn to rationalize and adapt very quickly ... they adapt very very fast and in a very liberal way to a new situation." Although this student's reflection upon his two wavelength outcomes resulted in him recognizing why his intuition-based conceptualization flawed, and having a strong desire to identify the flaw and correct it, his attempts did not lead to his intuition-based conceptualization being revoked. That is, his learning did not involve him changing his conceptualization but recognizing that it was inappropriate. The dialogue continues: I: It is interesting that — why do you have so much confidence in that formula? S: Oh, I've, er, the units work [laughs heartily]. Makes me 70 feel pretty comfortable because I know that something per second times a velocity, I mean a length, gets me a length per, you know what I mean. Yea, you are right, that is where it really rests, it doesn't rest on my fundamental beliefs in the wave function and wave theory, it rests on the fact 75 that the units come out right and that seemed pretty believable, that the units came out right. I: Do they stress that a lot at [naming student's place of undergraduate study]; that the units come out right? S: Well, that's a survival method in physics, I don't know if 80 you learnt that one or not? I mean if your units aren't working chances are you are not doing the calculation right, especially in your intuitive sense of things. So you go by, you intuitively think how a system probably works and by god your units come out so you know that at least you are on the 85 right track — and plus, I mean, okay, when you know your wave theory and you look at the number of times something goes by each second times, the length of that thing — Okay, say ten cars go by every second and each car is 10m long, what is the total accumulated length if the cars were 90 bumper to bumper, what's the distance during this time that the whole lot — If you are an observer, as far as the propagation of the wavefront, the front of the first car so that you can see them, okay?, when each car goes by in one 115 110 105 100 second times the length of the car — you know it's also physically plausible. So, because waves, wave fronts propagating, come on! Kids in grade 9 or 10, wave theory? A wavefront propagating, you can't be serious it doesn't, nothing moves, nothing! Just the molecules to a point, a little song and dance, right. It's just a little more order in their random perturbation than they would normally have when there is no wave being propagated. Doesn't bear up to, see those cars, those cars, right? See those cars are like an electromagnetic wave because electromagnetic waves actually propagate through a vacuum and it's not just — if this is a sound wave, this is an electromagnetic wave, you know the whole package is moving. Don't ask me what it is made of because only Maxwell knows, right. From this section of this student's explanations it would seem as though he constructed a new wavelength conceptualization while leaving his intuition-based conceptualization at least partially in tact (see lines 85 - 100). Thus it would seem that a single conceptual repudiation is probably not sufficient for the rejection of the conceptualization. The reconstruction, or new construction, coupled with rejection of prior conceptualizations would seem to require several, if not many, instances where the original conceptualization is recognized to be defective (perhaps the repudiating instance also needs to become a confirming instance for the new or reconstructed conceptualization: an analogy to scientific thinking, for instance, see Lakatos, 1978, pp. 8 - 101). This scenario is an indication that immediate reflection can be very tentative and fragile even when it resolves serious difficulties, and that depicting learning as "conceptual change" is an inadequate way of capturing the essence of non-rote learning. Consider lines 81 - 91 where he depicted wavelength as an "accumulated" length of many cars (the student was using cars an analogy for the pressure pulses generated by each forward motion of the tuning fork): i.e., no sense of the propagation of a pressure pulse before the generation of the next (this may be reflecting an implicit conceptualization that pressure pulses are pushed along by pulses coming up behind them). Then, in line 92, his new conceptualization seemed to mediate his explanation but it seemed to be more exploratory than definitive. Finally, from line 100 onwards it appears as though the student had started some conceptualization reconstruction but it was awkward and diffuse. Total reconstruction would probably require far more time and diversity of reflection. 116 In the discussion in Chapter VII it is suggested that personal conceptual dispersion may be both a normal and necessary part of multifaceted human functioning. At the same time reconstruction or rejection of inappropriate conceptualizations which are evoked in the arena of physics would seem to be desirable. Rather than educational experiences being aimed specifically at unilateral acceptance of a conception or even generating conceptual change, one of the prime functions of educational experiences should be to generate an environment where students are not afraid to "kick their conceptualizations around;" where they are encouraged to contemplate reconstruction of their conceptualizations to make them more plausible; more functionally appropriate to a context. From this perspective, the apparent reconstruction attempt portrayed in the above transcript excerpt may be interpreted as being indicative of a student in a phase of conceptualization growth. Further support for this notion that in order to develop a rationalization of conceptualizations and appropriate qualitative analysis skills within the field of physics, the educational environment should be structured so as to provide and involve students in experiences, both concrete and abstract (which potentially would provide an adequate base for students to explore-by-reflection their understanding of the concepts being taught), was seen in several instances during the interviews. For instance, one student recognized that he had two conceptualizations of air molecule behaviour which he evoked in different contexts. He had a kinetic conceptualization of air molecules moving randomly yet to explain sound propagation he needed them to be stationary: 1 S: Yea, my idea, initially, the particles remained stationary and [also] they, um, moved out from the area, the central area, or the area that elicited the initial sound and they move outwards towards other areas. So, they remain 5 stationary, so it's not the particle that moves toward you but it's the particles near you that have been vibrated from the particle that set up the reaction towards you. I: If I can recall you told me ["S" interrupts] — S: Yea, I know I said that they were in a constant flow, I 10 know it's sort of contradictory to itself, so I originally said there is a flow of air around you. So when I went to explain sound I said they [the molecules] stayed still, so I would have a hard time sealing the two of them together. 117 I: Which of the two do you believe? 15 S: Um ~ [long pause] — I would have to go with the particles are still moving sp they would have to move from the sound towards you and yet when I explain sound I explain it as particles remaining stationary and causing a reaction that moves everything out towards you. 20 I: Isn't that a problem for you to believe one thing and to have to explain another thing? S: Yea, it is and it's something that never comes to light because you don't think about it. You've got the one idea here and the one idea here and until you really sit down and 25 think about it or are forced to compare them you never notice it, had to compare them before. Until now I never really thought about it in that way before, I never thought that I would think that air is moving constantly but sound causes a stationary [molecule to move] — I never sat down 30 and thought about it before. Right now I would like to sit here and try and find out which is which. Despite recognizing his inconsistent conceptual dispersion this student could not immediately resolve his conflict, an indication that learning requires time and commitment; an ongoing process of construction, mediation and exploration of ideas. 5.3 Discussion of Data Analysis for Research Question 3 The analysis presented in this chapter has exemplified the notion of conceptual dispersion; it has illustrated how the students involved in this study had an array of qualitatively different conceptualizations about sound. This array was, however, limited, i.e., the students presented a limited number of ways of conceptualizing sound. Typically, the students' conceptual dispersion included a number of personal intuition-based conceptualizations which were depicted as gut-physics conceptualizations. There was often a recognizable dimension of tension between the plausibility of the students' physics-based conceptualizations and their intuitive-based conceptualizations. 118 This tension manifested itself along a continuum bound by two extremes: either the students gave a high plausibility status to their ability to make sense of the world around them or they felt inadequate and simply accepted what they were being taught. At the one extreme, when students had simply rote learnt much of what they had been taught it was apparent that they had forgotten elements of it and had to fall back on their intuition, but were willing to downgrade their intuition when challenged. At the other extreme students continued to give high plausibility status to their intuition-based conceptualizations despite evidence to the contrary. For example, in one of the interviews one student recalled having done a laboratory session where he measured the wavelength produced by a mid-range tuning fork, he also recalled the order of magnitude of his measurement. In the interview despite having calculated the wavelength produced by a similar mid-range tuning fork and obtaining an answer with an order of magnitude that agreed with his laboratory experience he still gave higher plausibility to his intuition- based conceptualization which was several thousand times smaller. A l l the students, indicated that for examination purposes they would suppress their intuition-based conceptualizations because as one student said, "It's more important, quote unquote, they want the correct result." This kind of outcome presents an insight into how many students may be perceiving their examinations: as an exercise where, in order to be successful, their intuitive sense making must be temporarily suspended or downgraded. This kind of assessment would feasibly generate a learning style which focused on rote learning physics terminology, definitions, formulae, and problem solving algorithms. 5.4 Overview of Chapter V This chapter has dealt with the nature of the consistency of the students' conceptualizations across and in a number of different contexts. The analysis indicated that while the students' conceptualizations tended to be contextually different they did not tend to be contextually dependent. In some contexts, however, the available visual cues were of such a nature that the students tended to evoke similar conceptualizations. This outcome provides support for the view that teaching is not a matter of facilitating a change in conceptualization but rather of facilitating the recognition of aspects of a situation or problem in such 119 a way that functionally appropriate conceptualizations are evoked from a repertoire of plausible conceptualizations. The next chapter deals with how the students coped when comparing and contrasting light and sound. 120 C H A P T E R VI DATA ANALYSIS: FACTORS INFLUENCING CONCEPTUALIZATION: COMPARING AND CONTRASTING LIGHT AND SOUND 6.1 Data Analysis for Research Question 4: Introduction The fourth research question is described in Chapter I as: How do the students deal with a request to qualitatively compare and contrast the physics concepts of light and sound? In Chapter II the notion of category of influence was introduced as a phenomenographic-like analytic construct which could be used to frame the comparison between the students' conceptualizations of sound and light. Categories of influence were introduced as interpretative categories which characterize factors which appear to mediate and influence conceptualization. Three categories of influence were identified from the students' attempts to compare and contrast light and sound. These were: physics-based language; everyday-based intuition; and, a dichotomy between mathematical and qualitative physics. The sound/light comparisons that the students in this study (and those who participated in the pilot study) provided, indicated, in the context of physics, that they found this kind of task extremely difficult. For example, in the following dialogue a student was attempting to articulate the difficulties that he was having and why he was having these difficulties: 1 S: Well they are waves. They are wave descriptions which are exactly the same in many ways. Physically, a tremendous difference because you, you — what we interpret as being sound, you know, the pressure packets being transferred 5 through the air and light as a wavefront of photons — what you get is -- it happens again and again in science is where interdisciplinary things can be described by the same equations, however, they are worlds apart in appearance. Look a fundamental question, right, I mean, 10 things often look quite different but underlying they operate on the same principles. That's the sort of thing that — you have a really hard time with kids because they 121 30 25 20 15 want to make everything into a specific case because when you ask them to relate ideas, like this one is a very tricky one, we ask them to relate even simply ideas across boundaries, that is difficult, that is high level thinking. Like you are asking me to do right now, to compare sound and light, um, a grade 1 student would have a difficult time with it, a grade 12 student would and, um, a man with his PhD in physics would have a difficult time with it as well because each brings to it their highest level of thought given the knowledge that they have. It is a synthesis question, I mean we are talking about two very very different phenomena that operate in a lot of ways on the same basic fundamental principles. But the degree of your knowledge you bring to it really doesn't affect how good you think as a person, you know; I think your ability to think grows with time as you do more and more to synthesize and to make comparisons, it changes and grows. But what we are not talking about here is comparing knowledge what we are talking about here is trying to compare two phenomena that we seem to treat very similarly on the math table but look a world apart in the physical world. Most of the students readily turned to an everyday-based context "outside of physics" to generate their explanations. Primarily, it seems, because they found it easier and more plausible to conceptualize light and sound in terms of "everyday language" rather than "physics language." In some cases it even seemed as though the students accorded a higher status to their conceptualizations which were embedded primarily in "everyday language." These trends were reflected as a clearly discernable dichotomy in the students' explanations. An excellent illustration of this dichotomy came from the pilot study. The student concerned (a physics honours graduate) appeared to be fascinated by the study and he spent many hours working with the author exploring his conceptualizations of sound in a variety of different experimental situations. One segment of these experiments involved exploring similarities between sound and light reflection by interchanging a candle and a ticking-watch as the "images" and "objects" of large parabolic mirrors. After finding out that the candle and watch could be interchanged with identical image/object predictions, the following dialogue took place (and provided much of the basis for some of the probing strategies used in this study). 1 2 2 1 I: Okay, well I wonder if you see sound being in any way similar to light? S: Yes, um, I guess because of the theory I have done. I — it is hard to say. I can relate and deal with sound and 5 light in a similar way by writing down similar equations. I: Where do the light wave equations come from? S: Well, if you want to go all the way down to Maxwell's laws: electric fields and magnetic fields. I: And sound waves? 10 S: Sound waves would simply be pressure variations. I: Could I apply Newton's laws? S: (Pause) yes, yes because at a molecular level it is just collisions. Conservation of energy and momentum. So in everyday life I see them as completely separate phenomenon 15 — light has different sources than sound, and you can, um, sense it with your eyes rather than with your ears. I see it as completely separate, but in physics I can see the exact same equations apply to both, it is just you have different variables. In one case, or anyways for that 20 matter, on paper you can do the same thing. You can have the Doppler effect with sound waves but it is not very often you have any reason to see a Doppler effect with light waves. So, I guess how I relate to them on paper they are interchangeable, in real life I don't see them as 25 being so. Consequently, the aim of this fourth research question was to attempt to explore the factors which influenced conceptualizations such as this apparent dichotomy between everyday-based intuition and physics-based conceptualization. To pursue this aim different questioning strategies were formulated. These centred around asking the students: (a) if they had ever recognized the similarities in the various wave equations that they had met in physics, and what sense they had made of these similarities; (b) if both sound and light would obey similar laws of reflection, refraction and diffraction; and, (c) if they differentiated between the concepts of light and sound in and outside the formal discipline of physics? 123 Not all of these approaches were used with all the students. Which approach, or combinations of approaches, were utilized depended on the interviewer's perceived dynamics of each interview, in particular the amount of stress that the probing seemed to generate for the interviewees. The category of influence outcomes are characterized by illustrative example sets of interview dialogue. The first example set gives an indication of the level of physics content that the students used in trying to distinguish between light and sound, and hence offers a characterization of the role played by physics-based language in affecting the nature of their comparative-conceptualizations. The second example set illustrates the students reliance on their everyday-based intuitions of light and sound, and hence offers a characterization of the role played by everyday-based intuition in affecting the nature of their comparative-conceptualizations. The third example illustrates a perceived dichotomy between mathematical and qualitative physics and how this affected the nature of their comparative-conceptualizations. 6.2 Category of Influence Outcome # 1: The Role of Physics-Based Language in  the Comparative-Conceptualization of Light and Sound The following excerpts have been chosen from all of the students' interviews. Although their brevity lacks the insights obtainable from a longer segment of dialogue, they do give a rich insight into the role of physics-based language in influencing their comparative-conceptualizations. The excerpts are labelled by student number. Interpretative comments have been included after each set of excerpts. The comments are not meant to be comprehensive but to augment the reader's appreciation of the general level of physics content, vis-a-vis physics-based language, inherent in the students' comparative-conceptualizations. Where appropriate "I" represents interviewer dialogue. SI: They are the same sort of thing with the exception that light moves a lot faster than sound, so that is your main difference. You can't say ... take light and bounce it off a mirror and take sound and bounce it off a mirror. 1 2 4 Sound will propagate through certain things [that] light won't and light will propagate through certain things [that] sound won't. SI did not conceptualize sound and light waves obeying similar laws of reflection while claiming the "main difference" between the two was their respective propagation velocities. Having made these observations it appears as though he had never deduced anything from them. Note how he used an everyday observation to distinguish between the two: that light and sound cannot always propagate through the same medium. Most probably he was conceptualizing light only in terms of "visible light" and thinking of some opaque medium. It would have been interesting to explore how he viewed the microwave protective mesh on the windows of microwave ovens. (Here, light can and cannot propagate through the mesh, the criterion depending on the wavelength of the light trying to propagate through the mesh. While visible light can propagate through the mesh, the mesh acts as a mirror for microwaves.) S2: Okay, from a physics point of view you would have to say that — [pause] — light, okay light is an energy package, you are dealing with photons. And sound — [long pause] — [to himself - ha!] — you are both transmitting energy through a wave but light — When you're dealing with light you are specifically dealing with photons at different frequencies. With sound there is no such component, there is no such particle, or just a unit package of sound. S2, in the fourth line, after having given the matter some consideration, seemed surprised to think of both sound and light "transmitting energy through a wave." He, then, tried to draw a distinction between light and sound by moving from a classical perspective for sound to a quantum perspective for light (an indication that he either had not heard of phonons or had never considered phonons as a kind of photOn isomorphism). For someone to try to rationalize conceptualizations from such a predicament would seem to be an impossible task. S3: They are, they are different — I am sure there are differences that I — What I envisioned here is, I mean, what comes to my mind is there are differences and I am not grasping the differences but I see them as being very analogous to each other — although they are different entities — they are different things. I mean you can't go and say a sound wave is a light wave because sound waves 125 travel and make sound and a light wave is transmitting l ight . S3 could not begin to rationalize any of his conceptualizations of sound and light. His explanation expressed a sense of the frustration that he felt in trying to do so. S4: Light, light is emitted, um -- light is more like a chemical change and sound the result of physical change. Outside physics, um, I would see more sound as a wave than light as a wave. Unfortunately S4 was not asked what he meant by light being "like a chemical change." He may have been thinking of the sun as a source of light and as a giant nuclear reaction, or he may have been couching his answer in what he perceived to be appropriate physics-based language. S4 also was typical of many of the students in that he seemed quite happy to distinguish between sound and light from "inside" and "outside" physics. This was considered as an indication that he had not, or did not, look for relationships between all of his physics knowledge and his everyday experiences which would repudiate the earlier suggestion that he perceived the sun in terms of a giant nuclear reaction. S5: Light is bent — Snell's law — but sound — somehow I think of sound as travelling in the same direction still, it's not bent. S5: Light wave equations come from Maxwell's equations, that's your answer. I: Okay, and sound? S5: Sound? From wave equations, mathematics wave equations — sine waves, cosine waves and that type of stuff. In my mind I don't think that's right [laughs self-consciously]. S5 had indicated earlier that sound and light would obey similar laws for reflection and diffraction. Here he was explaining why he did not include refraction. This appears to be because he had a conceptualization of sound travelling in straight lines from one medium to another. For S5, the respective sound and wave equations appeared not to be tied to any qualitative conceptualization, and he appeared to be self-consciously aware of this. Perhaps 1 2 6 he was now recognizing that he had not put much effort into establishing conceptual connections with his physics mathematics. S7: Light waves are a different kind of energy, there is something different which is causing it. I guess I think of sound waves as closer to water waves, and then light waves I have a really hard time about because I think of discrete and Plank's constant and all that stuff, and photon energy and all that, and I have a hard time visualizing. S7, like S2, was trying to generate an explanation by drawing from classical physics for sound and quantum physics for light, while juxtaposing his physics-based language. It is not surprising that he was having such a difficult time for as Richard Feynman has pointed out, quantum mechanically electrons and photons behave: In their own inimitable way ... in a way that you have never seen before.... There is one simplification ... they are both screwy, but in exactly the same way." (Feynman, 1965, p. 128) S7's explanation was also indicative of what Warren (1988, private correspondence) calls "suffering from the energy cult," where physics students label everything as "energy." S8: They have different velocities as well as different wavelengths. Light has various wavelengths, sound has various wavelengths too, so each has it's own velocity and own wavelength characteristic. I just took it for granted that light is light and sound is sound ~ It's just one of those things that you are exposed to your whole life and nobody's really, you know — you know what light is and you know what sound is and then you just took the formulas they gave you and that was that. S8 appeared to be explaining how physics never came to mean very much to him. He apparently had taken the concepts of light and sound for granted in terms of his everyday experience, and tried to couch his comparative-conceptualization in some physics-based language. S8 also indicated that he had not made any attempt to conceptually connect the mathematics of his physics to his everyday conceptualizations. 1 2 7 S9: Okay — [long pause] — okay, there we are talking in electromagnetic waves and so we are talking in transmission of electromagnetic energy. Whereas in sound waves we are talking in terms of kinetic energy. S9 conceptualized the difference between light and sound in terms of kinds of energy (see energy cult comment earlier). While explaining aspects of sound, S9 used the term "pressure" several times during the interview, yet in this context he depicted the propagation of sound only in terms of kinetic energy and ignored potential energy. An interesting point discussed by Pain (1983, pp. 148 - 151) is that the energy distribution for a sound wave in a gas is such that the average values of the kinetic energy density and potential energy density are equal and that an element of gas, at the same time, has maximum or minimum potential energy and kinetic energy. S10: Asking us graduates and you will get 'package pulses,' you know, you will get photons. You will get actual particles, photons, going along so fast and being so small that they act like waves. S10 seemed to be excusing his explanation; somehow he was restricted in conceptualization by being a graduate. Perhaps this was an indication that he would have liked to use his everyday conceptualizations in his answer but was wary of doing so because they were so different to the abstract notions that he was referring to. In all of the above examples there has been a lack of physics content: a lack of appropriately used physics-based language. What physics-based language was used, appeared to be used more as a kind of "decorative" jargon. It would seem that the students' were uncertain of how to use physics language in the compare and contrast context; uncertain of the meaning of the language. This may be an indication that their conceptualizations tend to exclude physics language as an intrinsic structural component of conceptualization. In Wittgensteinian terms they have not learnt the "language game" of physics and hence cannot play "the game" -- they are deprived of qualitative understanding. 128 6.3 Category of Influence Outcome # 2: The Role Played by Evervdav-Based  Intuition in the Comparative-Conceptualization of Light and Sound The following interview extracts exemplify how many students relied on their everyday-based intuition to distinguish between the concepts of light and sound. They also exemplify the students' need to couple their explanations to everyday analogies. The first extract provides an example of a student relying extensively on his everyday experience to provide an analogical base to conceptualize his physics. It also provides an insight into the kind of difficulty that the students had with this task. 1 I: Okay, one of the last things which I would like to explore with you — We spoke about sound being waves, now, how do you feel, do sound waves arid light waves, do they obey the same laws? For instance, reflection, refraction, 5 diffraction, that the wavelength times frequency equals the speed? S: Uhum, yes. I am trying to think of a, um, diffraction of a sound wave or a refraction, but I would assume that all waves obey the same laws because they are 10 illustrated even through, um, water waves, that's the way illustrations are done to give you some conceptualization of what happens with the waves. I: Okay. Do you have any idea where the wave equations ~ sound wave equations — where they came from? — where 15 they were derived from? — what principles upon which they were based? S: [Long pause] — no, in terms of ~ I: Have you ever noticed that the sound wave equations, for instance, and the light wave equations — they 20 appear, have you — ["S" interrupts] —? S: The constants are different, constants are different. I: I guess I would have said that the variables are different — that would have been the partial differential of something over time times one over c-squared equals 25 partial differential over something — do you remember any of that stuff? S: It's foggy. It's foggy — did you work much with the differential equations in sound? Yea. Okay, and did you ever notice that they were very similar to --? To each other? Yes. I think so. In what way are they really similar? Well, do you know the light wave equations? On what principles are they derived, where do they come from? Not really -- [long pause] — In physics, what is the difference then? Between? Sound and light. [Long pause]. If I'm to explain the difference between sound and light as something, how would I explain it? I'm trying to say — we are in physics now ~ so what is the difference between sound and light? -- what is the difference while you are there in the classroom, what is the difference between the two? In the method in which they are transmitted? — [pause] — or the process? -- [long pause]. What distinguishes the method in which they are transmitted? The properties they have, the various properties --I am on a different wavelength from what you are asking No, that's fine, could you —? Elaborate? What properties would light have which sound doesn't have and vice-versa? [Long pause] — I'm having a hard time thinking about things. 13G I: I am just wondering, in physics, is there a difference? Is there a difference between light waves, sound waves, water waves — any kind of waves that there are? S: They are, they are different — I am sure there are 65 differences that I — what I envision here is, I mean, what comes to my mind is there are differences and I am not grasping the differences but I see them as being very analogous to each other — although they are different entities — they are different things. I mean you can't 70 go and say a sound wave is a light wave because sound waves travel and make sound and a light wave is transmitting light. I: Would sound be able to propagate in a vacuum? S: [long pause] ~ No [very hesitantly] but light -.-75 I: But light? S: Well, I see space, we receive light from space. I mean from stars and I am comparing that as a vacuum, more or less — don't receive sound so light would be able to travel in a vacuum. 80 I: Why wouldn't you --? S: Why wouldn't sound be able to travel? Because it's not part of the — how does light travel then? — it's emitted — how does light travel? [basically talking to himself] — I see it, I mean I see a — I am developing 85 a difference in my mind but I'm not sure exactly how to articulate that difference. I: If I took you out of the physics classroom and asked you what's the difference? Would it be easier? S: I would probably explain it the same way — um, along 90 terms of we see stars, and see the light reflect sent out from those stars, whereas sound does not travel in space. I: But the difference between light and sound: would that be easier to explain outside the physics classroom? [Long pause] i.e., you don't have to use any physics 95 S: Yea, I'm, er — I don't know why I'm having — maybe I'm making it too complicated and I'm not finding the complicated answer — um — so it's quite a difference between light and sound — between light and the sea [talking more to himself, linking sound and sea waves] — light's a reflection and sound? [Very softly to himself] 13 1 I: The reason that I was asking you this: I remember earlier you said one way you did physics was that you made sure you understood the formulae. S: Uhum [affirmative]. 105 I: I was just wondering in what way you made sense of these formulae, I see formula for sound, I see formula for light — they look the same — S: Uhum [affirmative]. I: I wonder how one makes sense of that? 110 S: Perhaps one didn't really try to make sense of that, one just accepted it. I: So then what did formulae really mean to you? When you say you understood it what do you really mean? That you could use it S: Yea, I could apply it to, um, a question — I could, um, 115 know when to use it and when not to use it. I understood, I understood the elements of the, the, um, physics: the frequency and the wavelength, I could visualize that. I: Providing it was a sinusoidal wave? You drew me a sinusoidal wave? 120 S: Uhum [affirmative]. One of the other interesting outcomes in the above example is examined in the next category of influence outcome; note how this student depicted mathematics in physics as formulae to be used to solve physics problems. The following extract offers an example of a student who had vague physics-based conceptualizations while his intuition-based conceptualizations appeared to have both strength and clarity (see lines 16 - 24): 1 S: Light, light is emitted, um — light is more like a chemical reaction, result of chemical change and sound is the result of physical change. I: Once those — once you've had a chemical change and once 5 you've had a physical change, that's happened. Now what is the difference now, between the two? S: There is little difference. They propagate in the form of a wave, they still hold reflection, refraction and all 132 that. You can describe it in terms of the wave equation. 10 I: How about outside physics: do you — see very little difference between light and sound? If you are not in a physics classroom? S: No. Outside physics, um, I would see sound more as a wave than light as a wave. 15 I: Could you explain why? S: Going back to that first example I was giving, the water waves hitting the rocks. Now, something caused the sound, I can see that, I can actually see something doing something to something else and hearing the result of it, 20 whereas when I turn on the lights I just flip the switch and light comes on, there is no one-to-one correspondence between the two. I wouldn't think that turning on the switch would produce light the same way as water waves hitting the rocks producing sound. 25 I: Did that ever used to worry you when you did physics? How did you cope with that? S: Initially yea, because it is not an everyday thing that you think of light as waves. You think of sound as waves by the, by — 30 I: If you don't see light as waves what do you see it as? S: Beams, this is before physics, like a torch or a flashlight, when you turn on the switch -- boom it hits you. There is no delay sort of thing like with sound waves, you can sense from everyday things that there is a 35 delay, that there is a fixed time for sound to travel. I think the prime example would be the echo, it's an everyday thing. You can tell that sound takes time to travel whereas light, once you turn on the switch the beam hits you. I think of it as — just a directing — there is no 40 delay and the, um, the concept of the wave doesn't come into it. One of the interesting factors, exemplified in this excerpt, was that none of the students questioned the validity or meaning of being asked if they wanted to do the light/sound comparison "outside" of physics (see lines 10 - 24). This kind of response was an indication that the students tended to feel that it was acceptable to think differently about phenomena such as light and sound from within a physics context and from within an everyday context. Note, in an "outside physics" context how the student in the example drew an analogy between water waves and sound but had difficulty in thinking about light as a wave: "the concept 133 of wave does not come into it" (line 40) ~ an intuitive idea that could be seen to be very much in line with a quasi-Newtonian view of light as "corpuscles." 6.4 Category of Influence Outcome # 3: The Role of Mathematical and Qualitative  Physics Connections in Influencing the Comparative-Conceptualization of  Light and Sound In the last chapter, one of the analytical themes was called "disconnected mathematics and physics thinking." This outcome may be viewed in similar terms. Most of the students were unable to relate what they did mathematically in physics with the qualitative comparisons that they were attempting to describe. In the following first example the student discussed how he simply "took it for granted that light is light and sound is sound" (line 35) and that this was based primarily upon his everyday experience. In lines 59 - 62 he indicated how important everyday experiences were as an analogical base for his physics sense-making when he says that he had nothing "to base on" whether or not sound could propagate through a medium. 1 I: I want you to cast your mind back and try and recall — when I did physics one thing that I noticed was that the sound wave equations were basically the same as the light wave equations. Do you ever recall thinking 5 about that? S: I can't remember too many equations, no. It's been a while since I've done sound, I know what you are saying, but right off hand I couldn't say what the equations for both were, what the similarities or dissimilarities would be. 10 I: Can you remember where the sound wave equation comes from? S: Um, it came up somewhere when we were doing particle, molecular particle theories, movement, that's the only time I remember taking it? I: Any idea of it's derivation? 15 S: No. I: I don't want you to do the derivation; the basis upon which it was derived? 134 S: It's somebody's equation but I can't remember the name of the person right now — [long pause] — no, I couldn't 20 tell you the basis for it. I: What is the difference between light and sound, if there are any differences? S: They have different velocities as well as different wavelengths. Light has various wavelengths, sound has 25 various wavelengths too, so each has it's own velocity and own wavelength characteristic. I: Would they obey the same laws such as reflection, refraction, diffraction? S: I believe that they obey the same laws, yea. 30 I: You can't remember the equations, but it did seem to me that the equations were the same ["S" interjects] — S: And they obey the same laws. I: I have a little difficulty in physics asking myself what is the difference? Did you ever think about it? 35 S: No, I didn't, I just took it for granted that light is light and sound is sound. I: Both in physics and outside when ["S" interrupts] — S: Yea, I never really thought more. It's just one of these things that you are exposed to all your whole life and 40 nobody's really — you know? You just know what light is and what sound is, and then you just took the formulas they gave you and that was that. I: So you knew what sound was and you knew what light was in your everyday life? 45 S: Uhum [affirmative]. I: What did you know about them? S: You heard one and you saw the other. I: And it never bothered you that everything else seemed the same? 50 S: Well, pretty well the same, no, I never really thought about it or tried to make comparisons as to explain why one is light and one is sound, no, I never tried to question that. I: Okay, can light travel through a vacuum? 135 55 S: Not sure — yes it can. I: Yet sound can't? S: No, I said sound can't so — I: Have you any ["S" interrupts] —? 60 S: No, I am just going by the fact that you see the sunlight; sunlight does pass through space and space is a vacuum and yet I have nothing to base on whether you can hear sound in a vacuum. The dialogue with the above student offers insight into areas beyond a desire, or need, to think in terms of everyday analogies. It presents an insight into the relationship that he generated between mathematics and physics. Firstly, it appears as though he strongly associated the derivation of mathematical relationships in physics with something that other physicists had done (see lines 14 - 20), and despite remembering that the wave equation was derived in his physics classes when they were "doing particle, molecular particle theories," even after giving the matter some thought (lines 11 - 13), he could not even offer any general physics principles that would be applicable in such a derivation. This may be taken further since, to this student, mathematics relationships in physics most probably meant learnt problem-solving algorithms rather than a sense of logically organized and connected reasoning (see lines 41 - 42). In other words, a tool for slotting into stereotypical problem solving rather than a tool for careful thought and reasoning in an array of physics interconnections. In Chapter VII it is suggested that this lack of rationalization between the mathematical and the qualitative is partly a consequence of a "hidden curriculum" of physics which is generated by the typically rapid rate inherent in physics lecturing style described by Arons (1979). The following example illustrates how the rate of introducing new content in a physics course can leave a student with an overriding concern to master certain mathematical techniques and algorithms in order to simply pass the course at the expense of not attempting to begin to rationalize the mathematical content with the qualitative content of the courses. 136 1 I: It just seemed to me when I saw this — one of the other students I interviewed pointed it out to me. He said, "Look they are identical equations — everything is the same" — ["S" interjects affirmative]. If you are 5 working with differentials you solve the problems exactly the same way — ["S" interjects affirmative] — it got me thinking well, it's true, in physics we did that — and now I am interested how one copes with that — what sense you made of it? 10 S: Um, I remember specifically that particular derivation. We were doing that in third year and um, comprehending that wasn't prime on the list of things to do, it was, it was just trying to absorb that material to be able to do problems and pass that course. So, um, that wasn't a big, 15 that wasn't a big concern of mine at the time — [laughs self-consciously] — and so — You know?, I was just like: specifically, here is an example dealing with light and as an aside here is an example dealing with sound — oh yea, what were we talking about then? — transmitting 20 to submarines or something silly like that — and um, you know, in this particular case this is what happens in the sound wave, this is what happens and this is the consequence of this and this and this is the consequence of that and that was nice, um, so we dealt with that and I 25 just learned that in the specifics that this was going to be on a test and this is what we were going to have to know, and the conceptual framework that goes along with that just didn't go along with it. In this excerpt the student poignantly said that in his physics comprehending "wasn't prime on the list of things to do, it was, it was just trying to absorb that material to be able to pass the problems to be able to pass that course" (lines 10 -28). When students do not attempt to rationalize the mathematical and qualitative content of physics, then a kind of physics-based conceptualization deficiency must result. It was also interesting to note that this student did not regard the type of problems that were being done in class, to illustrate the principles being taught, as being of much value; he regarded them as "silly" (line 20). This perception conceivably further reduced his inclination to spend time and effort making his physics conceptualizations logical and consistent. 137 6.5 Discussion of Data Analysis for Research Question 4 The analysis in this chapter was framed by a phenomenographic-like construct termed category of influence; that is, the analysis was framed by a characterization of factors which affected the students' comparative mode of conceptualization of light and sound. An overview of the category of influence outcomes -- physics-based language, everyday intuition, and a dichotomy of physics into the mathematical and the qualitative — indicates that the students' comparative conceptualizations were influenced in ways that resulted in the students generating explanations that lacked mathematical linkages and, explanations which coupled physics content and diffuse classical/quantum distinctions: explanations that did not extend much beyond everyday notions of light and sound. That is, the students tended to generate explanations which were primarily framed by their everyday language meanings and experientially based perceptions of light and sound where light is "seen" and sound is "heard." In particular, several of the students appeared to want to, or need to, be able to draw direct analogies between their everyday experiences and the physics concepts that they were attempting to explain. Perhaps this is why none of the students objected to a line of probing that suggested looking at the sound/light differentiation question "outside of physics," or even questioned what that might mean. . Mathematics appeared to play no role in their comparative-conceptualizations, for instance, when asked how the light wave equations were derived, a standard reply was that they "came from Maxwell's equations," however, the students were unable to elaborate any further. Also, in some cases, despite the students apparently recognizing that their everyday-based intuitive ideas were problematic in the context of physics, they still accorded them high plausibility status. Considering that topics such as "vibrations and waves" and "electromagnetism" form a fundamental part of undergraduate university physics curricula (see Davies, 1982; UNESCO report, 1966), the lack of physics content in the students' explanations was somewhat surprising. For instance, they were inclined to focus on sources of visible light, such as stars, without giving consideration to the sources themselves; to treat the term light only in terms of "visible light." This 13 8 was enigmatic because if the students had been asked, "May we regard X-rays, or infrared waves, or radio waves, as light?" they would have undoubtedly given an affirmative reply. This apparent language confusion is certainly not trivial, for instance, in a public physics lecture at the University of California, 1985, Richard Feynman cautioned members of his audience: I would like to talk a little about understanding. When we have a lecture, there are many reasons why you might not understand the speaker ... another possibility, especially if the lecturer is a physicist, is that he uses ordinary words in a funny way. Physicists often use ordinary words such as 'work' or 'action' or 'energy' or even, as you shall see, 'light' for some technical purpose. (Feynman, 1985, pp. 9 - 10, emphasis mine) What is being suggested is that part of the problem lies in physics being taught without it being made clear in what context aspects of the teaching-language is being used, and without students ever giving the matter explicit consideration. In the face of no alternative meaning being explicitly given to certain words, it is natural for students to work with the everyday meanings that they bring with them to class. Physics textbooks, then, often confound an already complex sense-making situation by defining and using these terms in contradictory ways. This point is explored further in a discussion on the functional context of language in Chapter VII. The issues raised in the discussion so far would seem to indicate that conceptualizations embedded in everyday notions would tend to lack physics content i f students do not reconstruct their everyday conceptualizations with a physics foundation. Overall the analytic outcomes of this study indicate, that for the participating students, this kind of reconstruction was hardly evident. A further complicating factor appeared to be that most of the students had perceived much of their physics in terms of an ensemble of dislocated physics topics or course units. This perception had in turn supported an approach to learning and understanding physics which focused on examinable segments rather than on conceptual construction and rationalization. In other words, while they managed to pass physics course examinations (some receiving very good grades) they avoided conscious, systematic, ongoing efforts to interrelate the various physics courses that they had taken. It seems that this "atomistic" view was nurtured at secondary school and hence naturally formed a continuing 139 learning base for undergraduate study; partially because the structure of their physics courses provided implicit support for their perceptions. For instance, university physics is usually divided up into topics and/or units. A unit would, then, consist of a topic or a range of related topics. Different units or topics are, in most institutions, usually taught by different faculty. This segmented structure is, then, in turn, reflected in and reinforced by, the nature of assigned tutorial problems and topically separated or segmented examinations. Further, many university physics courses tend to focus on the microscopic and what are considered to be more prestigious course topics (for example, some first year courses include quantum physics and Einstein's theory of special relativity while excluding topics such as hydrostatics and hydrodynamics). This microscopic influence appears to have facilitated the students taking "quantum leaps" into a world of photons without having established the appropriate conceptual foundations for such a "leap." It was illustrated earlier how the students also tended to want to frame their conceptualizations in everyday analogies. Part of the problem with such an approach is that appropriate everyday analogies are not readily available for a microscopic perspective. For instance, Feynman (1965) explained that part of the difficulty inherent in understanding light from a quantum perspective lies in the "uncontrolled but utterly vain desire to see it in terms of something familiar" (p. 129). For instance, consider how the following student attempts to use everyday analogy to explain the propagation of photons through a vacuum versus the propagation of sound requiring a medium: 1 S: Okay, when talking about sound, sound needs to propagate, you are moving something, okay. The idea of light is moving as a wave sure enough but it has little photons in it that are carrying 5 this light energy — trying to think of a good comparison. What comes to mind is the thing between — you can spin a rock, well it's not a good example. Throw a rock through a vacuum and you have no problems, you know, this little — 10 it's like a photon going through a vacuum, it has no problem. Now if you don't have that rock or whatever to actually throw through it [a vacuum] and you are relying on what's in between here and there. Um, to move it along, and there is nothing 15 there, there is no way to get it through. That still doesn't make any sense — [sounding very perplexed]. 140 Two noted physicists with strong interests in physics education were requested to help provide validity for some of the interpretations made for this research question. John Warren (author of The Teaching of Physics), kindly provided comments based upon his own physics lecturing experiences and associated education research projects. Anthony French (author of the classic Vibrations and Waves physics textbook produced at the Education Research Center at the Massachusetts Institute of Technology), kindly provided the kind of answer that he would expect a physics graduate to give in a similar context to that generated by the interview. He saw the task as an interesting one and in an attempt to reconstruct the interview context, gave the following answer: Sound can be defined in two related ways. First of all, we have its original, limited meaning, of pressure pulses or waveforms, within a frequency range from about 20 to 15 000 Hz, that are perceived directly by the human ear and brain. Under normal conditions these pulses or waves are carried by the air, but similar signals can be conveyed by pressure waves in a liquid (e.g., when one's head is under water) or (as in a hearing aid) by imposing vibrations on the bones of the head, whence they are conveyed to the inner ear. The source of any sound is a vibrating object — e.g., any musical instrument. The second and broader definition, which includes the first, is that sound is a mechanical vibration of any frequency in a medium (gas, liquid, or solid) associated with motion of the medium back and forth along the direction of travel of the disturbance. Any such vibration is accompanied by corresponding pressure variations within the medium. Sound waves carry energy from a source, through the medium, to a receiver. Sound, in this sense, can have essentially any frequency, or at least up to frequencies thousands of times higher than the upper limit of the human audible range. The essential features are the longitudinal character of the mechanical vibrations, and the necessity of having an elastic material medium in which the vibrations can travel. There can be no transmission of sound through a region of empty space. Light is also a process by which energy is carried from a source to a receiver, but it does not require an intervening medium. The source of light (classically speaking) consists in the accelerated motion of electric charges. This produces time-varying electric and 141 magnetic fields at distant points. The electric and magnetic fields are coupled in such a way that they form a travelling electromagnetic wave in which the electric and magnetic fields are perpendicular (transverse) to the direction of travel of the wave (and to each other). (This then allows for the possibility of different states of polarization of light, which has no counterpart in the longitudinal waves of sound.) As with sound, there is a restricted definition of light, as being within the range of wavelengths or frequencies directly detectable by the human eye (about 450 to 700 nm wavelength). The term is also sometimes applied to vibrations outside this range (e.g., "ultraviolet light") but not, as a rule, to the entire possible range of frequencies, anywhere from zero up to infinity. The detection of a light signal is the result of the action of the electromagnetic field of the wave on electric charges in the receiver. When the concepts of quantum theory are brought in, both sound and light are describable in terms of discrete packets of energy (phonons or photons) equal in magnitude to Planck's constant, h, times the frequency f in Hz. This quantization of the energy is vastly more prominent for light, because the frequencies associated with visible light are higher, by factors of more than 10-to-the-10, than the highest frequency of audible sound, and so the energy quanta are correspondingly bigger. However, the picture of acoustic energy as quanta has become important in the theory of the solid state of matter. (French, 1988, private correspondence) French's explanation was significant for several reasons, even though he is a physicist and not a recent physics graduate. Firstly, he was consciously aware of the restricted meanings that light and sound may have (based on everyday experience of these phenomena) and provides for this in his explanation. However, for both the narrow everyday usage and the broad physics usage of the terms his conceptualizations were grounded in physics. (When Warren noted how the students involved in this study agreed to separate their physics from their "real life" he was deeply concerned and wrote, "Their minds should be open and seeking relationships between all knowledge and all experience." [private correspondence, 1988]) Secondly, French described the phenomena macroscopically and in doing so clearly distinguished between classical and quantum physics. His quantum physics explanation was simple but elegant in that it was essentially a recognition that sound and light could be thought about 142 from somewhat different perspectives, creating different levels of complexity and abstraction. Interestingly enough, one of Warren's comments was that in physics lecturing today, "We are too quick to rush into difficult ideas about quanta" (1988, private correspondence). Something quite evident in the students' explanations. In summary, then, it may be concluded that the students' rather poor comparative-conceptualizations may be viewed as a manifestation of a covert desire to describe phenomena microscopically coupled with an overt desire to anchor conceptualizations in everyday analogies. This, in turn, seemed to have led the students to dichotomize physics into the mathematical and the qualitative. An effective physics education environment would thus need to encourage students to reflect upon both the character and genesis of their conceptualizations; a belief that frames a proposal in Chapter VII for a different undergraduate physics curriculum for potential physics teachers. This kind of reflection would not only potentially enhance their physics understanding but it would also provide some valuable personal insights into how their future pupils may conceptualize what they are trying to teach and consequently facilitate an empathetic mode of better physics teaching. 6.6 Overview of Chapter VI This chapter has considered how the students in this study coped with comparing and contrasting the physics concepts of light and sound. The analysis was done in terms of factors which were seen to be mediating and influencing the students' comparative conceptualizations; the essence of which were framed in everyday terms without much appropriate physics content. This outcome was highlighted by a comparison of light and sound written for this dissertation by Anthony French, of the Massachusetts Institute of Technology. The students' comparative-conceptualizations could also be characterized as disconnected and fragmented pieces of knowledge that manifested themselves as a non-hierarchical conceptual dispersion. Much of this outcome seemed to be a reflection of the students not having conceptualized physics from a holistic perspective and by not having reconstructed their everyday conceptualizations in terms of a rationalization with their physics knowledge. This interpretation 143 was given increased credibility by John Warren of Brunei University who agreed to comment on a sample of the student interview transcripts. The next chapter presents the conclusions of this study and discusses the outcomes of the study as a whole. 144 C H A P T E R VII CONCLUSIONS, IMPLICATIONS AND RECOMMENDATIONS 7.1 Introduction There are two sets of conclusions arising from this study. The first set are specific in that they stem directly from, the research questions. These are presented in an overview without much in-depth discussion as they formed an intricate part of the analysis discussed in Chapters IV, V, and VI. The second set of conclusions are derived mainly from general observations made from the study as a whole and are more fully discussed here. Both sets of conclusions should be viewed tentatively as conjectures or as potential hypotheses generated for future inquiry rather than as generalizations in the traditional scientific sense (cf. Easley, 1982), for as Cronbach has pointed out, there are always unique factors playing a role in research outcomes so that: When we give proper weight to local conditions, any generalization is a working hypothesis, not a conclusion. (Cronbach, 1985, pp. 124 - 125) This, however, does not exclude generalizations being drawn from the outcomes of this study. As discussed in Chapter III, readers of studies such as this may have repertoires of relevant experience which allow them to take local factors into account in such a way as to facilitate the conclusions being given validity within the bounds of their own experience; that is, naturalistic generalizations. As a consequence of the conclusions and observations, educational implications and recommendations for further inquiry, are also discussed in this chapter. 7.2 Specific Conclusions from the Study 7.2.1 Introduction This study has covered a number of areas dealing with physics graduates' conceptualizations of sound. The study was a case study which involved ten physics graduates from a physics teacher education programme in clinical-like depth-interviews which incorporated a variety of different contexts relating to 145 their experiences of sound. The analytic outcomes were framed in terms of a phenomenographic research perspective (Marton, 1981, 1988) in the following related areas: The students' conceptualizations of sound and of factors affecting the speed of sound. The consistency of the students' conceptualizations of sound across and in a selection of contexts from the interviews. The students' comparative-conceptualizations of light and sound. The conclusions arising from these areas are discussed in Chapters IV, V, and VI, which have been summarized as follows: 7.2.2 Conclusions from Chapter IV CONCLUSION 1: The students' conceptualizations of sound from a microscopic based perspective may be summarized as follows: Sound is an entity which is carried by individual molecules through a medium. Sound is an entity which is transferred from one molecule to another through a medium. CONCLUSION 2: The students' conceptualizations of sound from a macroscopic based perspective may be summarized as follows: Sound is a travelling bounded substance with impetus, usually in the form of flowing air. Sound is a bounded substance in the form of some travelling pattern. An interpretation of these results could be that the students' conceptualizations were strongly mediated by primitive intuitions. In conclusions 1 and 2 the subtle but important distinction between "entity" and "substance" needs to be made. The term "entity" is used to characterize a small "thing" relative to molecular dimensions. The term "bounded substance" is used to 146 characterize "a bounded volume," some kind of flowing "form" which is endowed with impetus in the form of "pushing power." CONCLUSIONS: The students' conceptualization of sound from an intricate blend of both micro- and macroscopic perspectives may be summarized as follows: The concept of sound is linked to the concept of waves, as part of some universal, mathematically abstract, physics modelling system. CONCLUSION 4: The students' conceptualizations of the factors affecting the speed of sound may be summarized as follows: The speed of sound is a function of the physical obstruction which molecules present to sound as it navigates its way through a medium. The speed of sound is a function of molecular separation (the closer molecules are to one another in a medium the faster the propagation, and vice-versa). The speed of sound is a function of the compressibility of a medium (the more compressible a medium is the faster sound can travel through it, and vice-versa). CONCLUSION 5: The students' conceptualizations of sound represent a tension in terms of conflict and mediation between intuition and taught physics. CONCLUSION 6: Scrutiny of the data providing for the conceptual outcomes summarized thus far indicates that they were constructed from a limited set of physical relationships. The implication of this conclusion is that while there may potentially be an enormous number of ways for students to conceptualize sound this does not appear to be the case. Consequently the descriptions of the conceptualizations may be of considerable pedagogic value. None of the above conceptualizations were mutually exclusive to students (i.e., not specifically typifying any given student), and the analysis in chapter V deals with the consistency of conceptual evocation across a range of interview contexts. 147 7.2.3 Conclusions from Chapter V CONCLUSION 7: The students' conceptualizations tended to be contextually different but not contextually dependent. That is, while students tended to evoke different conceptualizations in different contexts, the context itself did not determine the evoked conceptualization. There were, however, instances where the available cues in a context were so powerful, in that they provided validity to intuitive ideas, that the cues mediated the students' conceptualizations. The most powerful visual cue was a candle flame being extinguished by a pulse of sound. This manifested itself as "flowing air," a seemingly strong primitive intuition-based conceptualization. From the conceptual consistency analysis a variety of themes were identified and discussed. These themes may be summarized as follows: How the students changed their explanatory perspectives in and across contexts. The role played by powerful intuitive, gut-physics, conceptualizations in the students' interpretations of various phenomena and experiences. Disconnected mathematics and physics thinking leading to abstraction. How the students coped with recognized inconsistencies in their conceptual dispersion (array of conceptualizations). An analytical exploration of these themes in Chapter V gave rise to the following conclusions: CONCLUSIONS: The students tended to use a microscopic explanatory perspective to frame their "scientific" analysis, and to provide what they perceived to be clear insightful explanations; that is, enhancing explanatory power. CONCLUSION!?: The students tended to use a macroscopic explanatory perspective to frame their intuition-based explanations and to explain phenomenon not readily associated with taught physics. 148 CONCLUSION 10: Generally all the contexts evoked some primitive intuition-based conceptualization. These conceptualizations were characterized as gut-physics flashbacks because they were seen as being conceptual intruders into the students' explanations. Typically, after the initial gut-physics evocation the students would suppress or override it, probably because they could recall being taught that their gut-physics was "incorrect." However, at a later stage the students would, then, tend to re-introduce these gut-physics conceptualizations without giving any recognition to the fact that they were doing so. In one context, "the sound tube experiment," the students tended not to suppress their gut-physics because the visual cues (a candle flame being "blown out" by sound) provided validity to the conceptualization that sound consists of flowing air — a kind of wind. This response was characterized as a "prolonged gut-physics flashback." CONCLUSION 11: The physics description and mathematical representation of sound as a wave provided a "critical barrier" (Hawkins, 1978) to understanding. The mathematical representation of sound waves tended to be conceptually constructed by the students in an abstract manner: the mathematics became a heuristic for problem solving and the wave nature of sound was seemingly glossed over. That is, the students had learnt that sound was a wave but this did not mean much to them in their interpretation of sound phenomena; a "critical barrier" to their understanding. This manifested itself in the "tutor/textbook" context where the students exhibited considerable difficulty making sense of a displacement representation of a travelling compression wave. CONCLUSION 12: When the students recognized inconsistencies in their explanations their comments indicated both surprise and an inability to immediately cope with their newly found realization. Inconsistencies that were exposed to them did not have the same effect on the students as when the recognition became self-evident. The students who reflected back on their explanations and could, see inconsistencies expressed an immediate desire to sit down and work it out for themselves. Hence the interview became a significant learning experience for some of the students by providing an environment where they explored some of their own thoughts for the first time. An important implication from this conclusion is that it would seem that in order to develop rationalization skills (i.e., making things logically consistent), and appropriate 149 qualitative analysis skills within the field of physics, the educational environment should be structured so as to provide and involve students in experiences, both concrete and abstract, which would potentially provide an adequate base for students to reflect upon their understanding of the concepts being taught. CONCLUSION 13: A contemporary model of "conceptual change" (for instance, see Driver, 1987; Hewson 1981, 1982; Hewson and Hewson, 1984, 1986; Strike and Posner, 1985) may be considered to inadequately describe non-rote learning because it tends to: ignore the occurrence of conceptual dispersion which was evident in this study, and which has been evident in other studies, for example, Johansson, Marton and Svensson, 1985; and, perceive conceptualization as being a fixed "cognitive structure" in a person's head, rather than being person-world relationships. Hence, remediation focuses on "structure" rather than "relationships." A better description of non-rote learning would be the ability to evoke contextually appropriate conceptualizations so that, for instance, Aristotelian, Newtonian and Einsteinian physics are recognized in terms of their utilities and limitations in different contexts. The occurrence of the phenomenon of conceptual dispersion as described in this study suggests that even if students have their "conceptions changed" it is unlikely that they wi l l discard the rest of their dispersive set of conceptualizations. An example of this predicament is clearly shown in a study by Gunstone, Champagne and Klopfer (1981). They put extensive effort into changing some high school students' conceptualizations regarding force and motion, and after being convinced that they had succeeded, discovered in "post-treatment" interviews that many of the students still retained many of their "pre-treatment" conceptualizations (probably because the students still found them to be functionally appropriate in their everyday life). What the author believes can be realistically expected from a conceptual exploration approach to physics teaching, such as that described in section 7.5.2, is that students will evoke far fewer functionally inappropriate conceptualizations. This would be because their educational experiences have put them in a better position than before to make 150 such judgements. For example, for the purposes of house cleaning it may be functionally appropriate to conceptualize a vacuum cleaner "sucking" up the dirt. However, in the context of a some physics analysis the conceptualization of a vacuum "sucking" would be considered functionally inappropriate. From the physicist's perspective the appropriate conceptualization would be bounded by the level of analysis required. For example, in certain contexts Newtonian conceptualizations are functionally appropriate while in others they are hopelessly inadequate. Further, judgements regarding the functional appropriateness of conceptualizations cannot be viewed in a straightjacket of "correctness" for three important reasons. Firstly, conceptualizations deemed inappropriate today may have been deemed appropriate historically. Secondly, as diSessa (1986) has pointed out, physicists sometimes knowingly chose to use what may be considered as inappropriate or alternate conceptualizations (what diSessa calls "legitimized phenomenology") to reduce unwanted complexity and allow the use of old knowledge: The Newtonian causality of motion, as it is usually taught, is channeled through a single, complex notion — force. However, physicists still use legitimized phenomenology (e.g., force as a mover, rigid body assumptions) to provide high level descriptions that avoid many complexities involved in describing causal relations. (diSessa, 1986, p. 44, emphasis his) Thirdly, conceptualizations deemed inappropriate from a certain perspective should not necessarily be discarded as they may potentially facilitate new insights and perspectives. For example, consider Maxwell's (1861-2) conceptualization of wheels and idlers in space. His conceptualizations, bizarre as they may seem to a modern reader, were functionally appropriate enough for Maxwell to build a model of electrodynamics. 7.2.4 Conclusions from Chapter VI One interpretation of the conclusions presented so far is that the students participating in this study had graduated with a somewhat surprising set of dispersive, unintegrated and inconsistent conceptualizations in an area which may be considered to be fundamental to all physics; that of waves. The final research question extended this interpretation. The students were asked to 151 compare and contrast the concepts of light and sound. The students found this an extremely difficult task. CONCLUSION 14: Three categories of influence characterizing factors influencing and mediating the students' comparative-conceptualizations of light and sound were constructed. These were: the role played by physics-based language; the role played by everyday intuition; and, disconnected mathematical and physics thinking leading to abstraction. The framing of these categories of influence resulted in the following conclusions: CONCLUSION 15: Most of the students attempted to compare and contrast light and sound from an everyday intuition-based perspective, and then buttressed their efforts with physics jargon. In general their explanations reflected a lack of physics knowledge. CONCLUSION 16: The explanations given by the students reflected disconnected and fragmented knowledge. They appeared to be "conceptually unaware" of distinctions between classical and quantum perspectives of light and sound. It appeared as though none of the students had heard of phonons. CONCLUSION 17: Most of the students were uncertain as to whether light and sound would obey similar laws such as reflection, refraction and diffraction. CONCLUSION 18: The students found the mathematical isomorphic structure inherent to light and sound paradoxical. This was because they perceived the isomorphisms as implying that sound and light were physically related. Many of the students expressed a strong sense of frustration with this implication because their everyday experience did not give validity to this conclusion. Consequently many students were happy to consider comparing and contrasting light and sound "in" and "outside" physics. 152 CONCLUSION 19: The students did not have any "feeling" for the derivation of the light and sound wave equations. Most viewed the wave equations as formulae that had been given to them to be used in problem solving. 7.3 General Conclusions. Observations and Discussion Arising from the Study Detailed analysis which framed the conclusions so far is provided in Chapters IV, V, and VI. What follow are broad conclusions which stem from the study as a whole and they are thus discussed as observations. 7.3.1 The Functional Context of Language Physics and everyday language have come to share a number of terms whose meanings can differ quite considerably. While this phenomena may be expected to cause communication "mismatch" (Barnes, 1976; Osborne and Freyberg, 1985; Osborne and Gilbert, 1980) for pupils, it was initially surprising to find physics graduates experiencing difficulty with the functional context of language. During the interviews there were several instances where the students used language in such a way that it became apparent that they either attributed little meaning to terminology in the context of its usage or attributed inappropriate contextual meanings to terminology. From a physics perspective the functional knowledge of language must be fundamental for understanding, for as Buhler and Wittgenstein have reminded us, "we look at the world through spectacles of our conceptual frameworks, which are expressed in our language" (Lakatos, 1978, p. 229). As far as the functional knowledge of physics language is concerned there are important educational implications for students' constructions of conceptualizations. For example, this study has focused on the concept of sound. At first glance sound is a seemingly straightforward concept, yet the students' conceptualizations were far from straightforward. In the discussion to follow, an endeavour will be made to highlight some of the complexity given to the concept of sound by its usage in physics, hence providing a further insight into the difficulties that students must face when constructing an understanding of sound. In introductory physics the functional use of the term sound is both covert and confusing. First of all, the most common meaning attributed to the term sound is 153 one which is shared by ordinary language; that is, the interpretation which our brains construct from a range of eardrum movements. At the same time sound is also given a unique meaning in the context of physics: a subset of the phenomena of waves. This unique meaning is, however, imbued with a sense of ambiguity. For example, consider these two excerpts from highly regarded undergraduate physics texts: Sound waves are longitudinal mechanical waves....There is a large range of frequencies within which longitudinal mechanical waves can be generated, sound waves being confined to the frequency range which can stimulate the human brain to the sensation of hearing. (Fundamentals of Physics: Halliday and Resnick, 1974, p. 323) This is the basic differential equation for compressional waves travelling along one dimension — waves of a type that can be lumped together under the general title of sound, even though only a limited range of their frequencies is detectable by the human ear. (Vibrations and Waves: French, 1971, p. 210, emphasis his) Thus, according to French, but contrary to Halliday and Resnick, compressional waves, regardless of frequency are to be considered as sound. Further ambiguity is accorded to the concept of sound when students read texts such as Pain (1983) who subtly twists the notion of sound even further: "Longitudinal waves propagate as sound waves in all phases of matter" (p. 144). This quote carries the implicit idea that although longitudinal waves and sound waves share a propagation mechanism they are essentially different physical entities. So we see a multiple conceptual segregation: sound from sound waves and sound waves from longitudinal waves. To make the matter even more complex, the transverse waves (shear waves) which are formed when, for instance, a metal bar is struck, are often referred to as sound waves, even though shear waves have a polarization. (Pressure variations often generate both longitudinal and transverse waves in a solid because, unlike a gas, a solid can sustain the necessary transverse shear to propagate a transverse wave). For example, Feynman, Leighton and Sands (1963, p. 51-5) write: A very interesting example of sound waves in a solid, both longitudinal and transverse, are the waves in the solid earth. 154 If introductory students go on to take courses in solid state physics which introduce them to piezoelectric materials, then, they will be introduced to a third concept of a sound wave — the Rayleigh wave or sound surface wave (also called an acoustic surface wave). Apfel (1974) describes a Rayleigh wave as follows: A complex acoustic wave having both longitudinal and transverse components. (p. 110) One of the reasons that the functional context of the term sound in physics is convoluted may be that the common usage of sound is not excluded from physics, as for instance is the common usage of "work." Also, there is a real concrete element about sound -- it is heard -- which there may not be for other basic physics concepts. For instance, Warren (1986) has pointed out: Work is an abstraction from the quantities of displacement and force ... Force is an extremely difficult abstraction which can only be taught on an axiomatic basis. It must be emphasized that forces cannot be felt or seen but can only be deduced mathematically from the results of experiments. (p. 156) So, from a physics perspective sound is something we hear yet simultaneously may or may not be waves which our ears are sensitive to. This manifests itself subtly. A parallel example of this manifestation of functional language problems occurred when the students were asked to compare and contrast light and sound. Here the students appeared to have difficulties conceptualizing the complete spectrum of electromagnetic radiation being referred to as light. The conceptual outcomes of this study suggest that the term sound is conceptualized by the students through a language-bound perspective which essentially does not recognize sound as a term which may be functionally different in physics contexts (as far as physics was concerned sound was still that which is heard). This language restriction on conceptualization may be a reason why the students' conceptualizations of sound tended to be removed from its wave nature. That is, the sound that we hear is essentially a tangible entity, while its wave nature is highly abstract because we have no concrete experience of it, only analogies. This "tangibility" of sound that we hear may provide an explanation for why the students were prepared to consider the existence of sound in a vacuum. If sound that we hear is segregated conceptually from the sound waves 155 encountered mathematically in physics, then, it may become feasible for students to begin to contemplate alternatives, as this student did: S: If I go back to what I said before about sound engineers trying to create something better than a speaker to transmit sound: if you view sound as something other than a wave then you should be able to transmit it some other way. From the above discussion it would seem to be vitally important for physics teachers and lecturers to be clear in their own minds how they are going to use even seemingly straightforward terminology, and, then, to make these interpretations abundantly clear to their students. 7.3.2 Choice of Explanatory Perspectives The following discussion forms an extension of conclusions 8 and 9 since throughout the study it was observed that, depending on the context, the students opted to use different explanatory perspectives -- either macroscopically or microscopically orientated. There was a marked tendency for the students to perceive that phenomena could be better understood if analysed using a microscopic perspective. For instance, the students would often start an explanation using a macroscopic perspective but would change to a microscopic perspective when they were asked to elaborate or clarify aspects of their explanations. This tendency to "unpack" phenomena using a microscopic perspective to provide analytical insight and understanding appears to have two major contributing factors. The first is a metaphysical influence from the history of Newtonian mechanics, and the second is a tacit part of our conceptual system which is tied closely to our use of language. Burt (1954) has proposed that one of the basic postulates of Newtonian mechanics was that "valid explanations must always be in terms of small, elementary units in regularly changing relations." (p. 30) He argues that this postulate now extends beyond just physics to form a basic postulate in all modern science. Thomas Kuhn (1987, private correspondence) has proposed that he would "expect people who knew physics to speak microscopically about macroscopic phenomena when talking to laymen, macroscopically when talking to other physicists." From an educational perspective this would certainly seem to be true. School science may 156 be charaeterized as being almost obsessed with analysing phenomena from a microscopic perspective (consider any school textbook dealing with topics such as chemistry, heat, nature of matter, sound, electricity etc.). At university, even at the introductory level, physics curricula are giving less and less attention to "macroscopic" physics such as hydrostatics, hydrodynamics, elasticity, geometric optics, and sound, all in favour of "modern" particle physics. Also, the teaching of elementary problem solving tends to involve so-called analytical procedure which depicts analysis as breaking the problem down into segments to fit some "prototypical" (Reif, 1982) solution. Consequently it is suggested that much of school and university physics adds to a "hidden curriculum" which encourages students to view phenomena microscopically: developing a keen microscopic perspective is analytical, and hence provides the best framework for the understanding of phenomena. For example, Feynman wrote the following in the forward to The Feynman Lecture Series: If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis ... that all things are made of atoms (Feynman, Leighton and Sands, 1963, p. 1-2, emphasis theirs). From another perspective, the micro- and macroscopic conceptual outcomes of this study may be primarily a product of our conceptual-linguistic system. For instance, Lakoff and Johnson (1980) postulate that a person's conceptual system is "largely metaphorical" and how a person thinks, experiences and acts is "very much a matter of metaphor", (p. 3) An extrapolation of this position is the use of "ontological metaphors." Lakoff and Johnson (1980, p. 25) write: Understanding our experiences in terms of objects and substances allows us to pick out parts of our experience and treat them as discrete entities or substances of a uniform kind. Once we can identify our experiences as entities or substance, we can refer to them, categorize them, group them, and quantify them — and, by this means, reason about them. The micro- and macroscopic conceptual outcomes give face validity to Lakoff and Johnsons' ideas. From the microscopic perspective the students tended to depict sound as an "entity," while from the macroscopic perspective they tended to depict sound as a "substance", both divorced from physical waveforms. 157 From the above discussion, then, it may not be surprising that physics students develop a philosophy that incorporates the assumption that the ability to explain phenomena on a smaller and ever smaller scale indicates better, clearer understanding; better physics. The major problem with "microscopic" physics is that the associated concepts and mathematical representations tend to be very abstract. For instance, undergraduate quantum and statistical physics often tends to be represented in terms of mathematical equations and rules (for example, see Faucher, 1987). For many undergraduates "microscopic" models of "macroscopic" physics are not only inappropriate (in the sense that they lack continuity with other physics knowledge) but they are often conceptually confounding in their simplistic mechanical-like modelling. To illustrate the point being made, consider an example pertinent to this study. Consider the common microscopic school-physics model of sound propagation through air: molecules transfer impulses to neighbouring molecules by vibrating about their (so-called) equilibrium positions and colliding with adjacent molecules (which, then, vibrate a little out of phase with their neighbours and so on). Imagine, then, the conceptual surprise awaiting first year university physics students when, after a typically brief macroscopic introduction to sound related equations, they are given or shown tutorial problems to calculate molecular displacements associated with audible sound (see for example, Halliday and Resnick, 1986; Giancoli, 1985; Sears, Zemansky and Young, 1985). Under standard conditions of temperature and pressure, the molecular displacements (amplitudes) responsible for the propagation of audible sound waves range approximately from pico- to micrometres. These are incredibly small displacements, for instance, at the smaller end of the scale the displacement amplitude may be less than the radius of a nitrogen atom. On the other hand, from kinetic theory we have the average distance that molecules travel between collisions — the mean free path -- to be of the order of ten to a hundred nanometers in air; that is, at least a thousand nitrogen-molecular diameters. This means, in air, that the amount of movement that a molecule undergoes for the propagation of audible sound is very much smaller than the mean free path, as much as ten thousand times smaller for faint sounds! Quite a conceptual surprise 158 for students with conceptualizations of sound propagation via molecular collisions. That is, while on the one hand their visualization involves momentum transfer via molecules colliding with their neighbours, a kind of domino-effect; on the other hand there is the knowledge that much of what we hear could not possibly involve molecules colliding with one another. A large number of general introductory physics textbooks were scrutinized to find out what kinds of conceptual insight they offered which could help a student resolve the apparent paradox between the collision model and the perturbation calculations. Very few offered any kind of insight or explanation. The two best explanations were found in two older "classic" general introductory physics textbooks. These were Sears (1958) and Feynman, Leighton, and Sands (1963). Both of these texts specifically interlinked the macroscopic approach that they took in the construction of the sound wave equations, and a microscopic (kinetic) view of a gas. Thus, in effect, they were explaining, via the incorporation of a microscopic conceptualization, the basis for approaching the propagation of sound from a macroscopic perspective: The molecular nature of a gas has been ignored in the preceding discussion and a gas has been treated as though it were a continuous medium. Actually, we know that a gas is composed of molecules in random motion, separated by distances which are large compared with their diameters. The vibrations which constitute a wave in a gas are superposed on the random thermal motion.... An element of gas in which a sound wave is travelling can be compared to a swarm of gnats, where the swarm as a whole can be seen to oscillate slightly while individual insects move about through the swarm, apparently at random. (Sears, 1958, p. 429) From the point of view of kinetic theory, if we have a higher density of molecules at one place and a lower density adjacent to that place, the molecules would move away from the region of higher density to the one of lower density, so as to equalize this difference. Apparently we would not get an oscillation and there would be no sound. What is necessary to get the sound wave is this situation: as the molecules rush out of the region of higher density and higher pressure, they give momentum to the molecules in the adjacent region of lower density. For sound to be generated, the regions over which the density and pressure change must be much larger than the distance the molecules travel before colliding with other molecules. This distance is the mean free path, and the distance between pressure crests and troughs must be much larger than this. Otherwise the molecules would move freely from the crest to the trough and immediately smear out the wave. It is clear that we are going to describe the gas behavior on a scale large compared 159 with the mean free path, and so the properties of the gas will not be described in terms of the individual molecules. The displacement, for example, will be the displacement of the center of mass of a small element of the gas, and the the pressure or density will be the pressure or density in this region. Feynman, Leighton, and Sands (1963, p. 47-3) From these two excerpts it may be seen that the authors of these texts offered the same sort of conceptual insights but in a somewhat different manner. They were both included here because it was felt that these explanations, in different ways, are indicative of how a physics teacher could use students' existing knowledge and experiences to enable the students to construct physics conceptualizations of sound propagation that would have a high personal plausibility status. In other words, not a new and perhaps largely disconnected conceptualization but a reconstruction of existing conceptualizations. In this case, not for the students to reject or suppress their molecular collision conceptualizations, but rather for the term "collision" to take on a new meaning (in this context of physics) which is rather different to everyday notions of collision, and for "molecule" to be subsumed into a macroscopic notion of particle (i.e., "particle" could represent a "layer" of a medium representing an extremely large number of molecules or atoms): a major part of the reconstruction of the school-taught conceptualization. Then, with a different conceptualization of the term collision and replacement of the "microscopic molecule" with a "macroscopic particle," other associated conceptualizations become subject to reconstruction or even rejection. For example, consider one of the speed-of-sound factors conceptualized by the students in this study: that the speed of sound is inversely related to how far apart molecules are in a gas; the further a molecule has to travel to physically collide with another molecule, the slower the propagation of sound. With the kind of reconstructed conceptualization that is being proposed, this kind of speed-of-sound factor conceptualization must lose much of its viability (under similar conditions of temperature and pressure the speed of sound is actually inversely proportional to the square root of the density of a gas). From the perspective outlined above, it also becomes easier to conceptualize sound propagation in other media, such as in a solid, where a microscopic conceptualization of molecules or atoms in some crystalline structure physically colliding with their neighbours would be quite discordant (in the sense that a physical collision conceptualization for sound propagation would no longer be 160 feasible when molecules and atoms are essentially bound to positions within their crystalline structure), and hence would probably be accorded a low plausibility. Finally, something as simple as a new meaning for "collisions" and "particles" could generate a plausible conceptual basis for the justification and necessity for treating a gas, in this case air, as a continuous medium (that is, macroscopically) in the development of the wave equation. 7.3.3 Conceptual Dispersion The conceptual outcomes that are described in this study reflected both differences between individuals and differences within individuals. In particular the analysis described in Chapter V indicated that: Although the students' conceptualizations tended to be contextually different they were not contextually dependent. This reflects the nature of the conceptualization person-world relationship: people do not necessarily construct the same conceptual relationships for specific phenomena in different contexts. Further, these relationships are often multifaceted reflecting multifaceted conceptualization evocation; The students tended to think about sound in fragmented parts. Each part represented a conceptualization from an array of possible conceptualizations. This was characterized as "conceptual dispersion;" and, In some contexts, students' conceptualizations reflected an inherent hierarchical nature in terms of some contextually related plausibility. Here, conceptual evocation was seemingly sensitized by specific perceptual cues, while i n . other contexts conceptualizations were evoked without any indication of priority or hierarchy. (Perhaps it would be more appropriate to use the term "functionality" in place of "plausibility" in the sense that it supersedes plausibility while simultaneously incorporating a sense of appropriateness). When a group of education students, who are physics graduates, display conceptual dispersion about physics fundamentals the question arises: how is it that their knowledge base appears to be so fragmented? While such a state of affairs may be both conceivable and understandable at school level (for example, see Driver, Guesne and Tiberghien, 1985; Osborne and Freyberg, 1985) it would seem to be enigmatic at a graduate level. There is an implicit assumption that undergraduate study provides a range of experiences which facilitates students' 161 knowledge systems, especially in the realm of fundamentals, to evolve via the broad integration of principles into rational and coherent conceptualizations. From the perspectives of this study, two prominent factors may be seen to be playing important roles in the generation of layers of conceptual dispersion. First of all there is the role which normal socialization plays, and secondly there is the covert support for conceptual dispersion inherent in much undergraduate physics teaching. From the socialization perspective, educationalists, writing from a constructivist worldview influenced by phenomenology (in particular Shutz and Luckmann, 1973, for example see, Solomon, 1983) and even an Einsteinian view of science (for example, see Driver and Erickson, 1983), have described two distinct worlds of conceptualization. The one is primarily generated by the greater part of our everyday life to provide a rich basis for everyday communication, thinking and problem solving. The other is primarily generated in the world of formal physics which in turn provides a rich basis for physics communication, thinking and problem solving. This is not to suggest that these two worlds of conceptualization are mutually exclusive. They are obviously not; however, the relative contributions of the two worlds may, for some students, be diffuse and unrecognizable. Solomon (1983) describes how a conceptual dichotomy may be created between these two worlds of conceptualization ("domains of knowledge"): In the normal or 'natural attitude' we all tend to categorize our experiences rather loosely -- to 'typify' them -- so that they can be absorbed into 'meaning structures'. These are then reinforced by communication with others and by language itself, which gives this 'life-world' knowledge both social value and great persistence. Since each practical situation is only in limited need of explanation, such meaning structures will be fragmentary, not logically integrated with one another and tied to the particular type of experience which prompted them. During a secondary process of socialization, such as schooling, other interpretative systems of knowledge may be learnt. These stand above the life-world structures, seeking to explain our experiences in another province of meaning, and forming what have been called 'symbolic universes' of knowledge (Berger and Luckmann, 1967). The primary life-world structures are not eradicated by such learning since it forms an overarching system with a radically shifted perspective of interpretation which is foreign to the natural attitude and considerably more fragile. Its social currency is also much weaker since it is restricted to a small specialized group, or to certain periods of time within the school [academic] timetable. (Solomon, 1983, p. 50, emphasis hers) 162 Brauner (1988) has proposed similar notions of conceptual or knowledge domains by suggesting that there are "nine modes of perception available for an educated person to use at this time" (pp. 2 - 3). Two of his modes of perception are: a mode of "standard perception" which represents a person's world of "ordinary experience;" and, "theoretic perception" which represents "the non-conventional view of experiences [which is] offered by the sciences" (p. 3). If physics is taught in a manner which does not allow sufficient time for the reflection and consolidation of what is being taught, then it should not be surprising to find students who are content with having fragmented knowledge. During the interviews it became apparent that several of the students were seemingly used to having a low opinion of their ability to make sense of their physics (i.e., construct their conceptualizations to be both logical and consistent). At university, physics topics are usually taught and examined in disconnected sections. Fundamentals are often glossed over in prodigious efforts to cover all of the "prestigious" topics in the curriculum (see Arons, 1979; Champagne, Klopfer and Anderson, 1980; Miller, 1987), essentially robbing students of insights that they w i l l increasingly need to construct coherent and rational conceptualizations. For example, in Chapter VI it was illustrated how the students were unable to effectively compare and contrast the physics concepts of sound and light, even at an elementary level of physics. Warren has suggested that today physics is taught in a mode denying: The idea of principle and insisting] that every idea taught is a 'model.' A l l models are to be regarded as equally true. Nothing must ever be said to imply that anything taught is wrong. If students are taught obvious contradictions they must believe all of them. They must not reason, or ask questions. This is authoritarism run mad. It is not limited to G.B. [Great Britain] (1988, private correspondence, emphasis his) This kind of physics teaching described by Warren could be seen reflected in some of the students' explanations. Many of them seemed to have accorded ontological status to the analogical models of sound propagation that they had been presented with in their physics classes. However, these analogies are only supposed to illustrate a principle, not represent "reality." Hence many students cannot distinguish between principles and analogical models, confounding their ability to rationalize conceptualizations. The Gothenburg research group in 163 Sweden has referred to this phenomenon as "horizontalization." Dahlgren (1984) writes: Examples have a subordinate function, which is to illustrate the principle outlined. In horizontalization, however, this hierarchy is not preserved; no distinction is made between the status of the principle and the the status of the example.... Teachers undoubtedly both hope and believe that the examples or metaphors they use to illustrate a given principle will prove less enduring than the principle itself, but how often this actually occurs is open to doubt, (pp. 27 - 28) The social and educational factors contributing to conceptual dispersion offer a plausible explanation for the gut-physics outcomes outlined in this study. If students' early socialization and educational experiences at school and university encourage the construction of a variety of non-integrated or partially integrated conceptualizations about, say, some physics-related phenomenon or concept, then, it is feasible that these conceptualizations simply become relatively distinct "interpretative systems of knowledge" which are metaphorically spread in layers over early developed intuitive "primary life-world structures." Different contexts and perceptual cues may, then, spontaneously evoke one or more of their conceptualizations, and on reflection they may be able to recognize "gut" flashbacks and draw upon what they perceive to be a more appropriate conceptualization. Claxton (1983) has pointed out that: A successfully 'located' theory is one which is triggered by just that set of environmental cues or features to which its predictions apply accurately. An immature or imperfectly located theory is sometimes triggered by situations to which it is not in fact applicable, and sometimes remains dormant in situations to which it is potentially applicable, (pp. 3 - 4 ) This description of Claxton's illustrates the role cuing may play in the evocation of conceptualizations and may explain why some context-specific conceptualizations were associated with a high plausibility status. If conceptualizations were often "triggered" but were also seemingly non-functional they would feasibly be accorded low plausibility status. 164 Other related research has uncovered what may be called gut-physics conceptual dominance in other areas of introductory university physics, for example, see Gentner and Stevens (1983), and West and Pines (1985), and hence it appears to be a widespread and resilient phenomenon in physics education. A natural question arising from the above discussion may be: Do physicists also hold a variety of conceptualizations about some phenomena or physics concepts? And if they do, why, then, is conceptual dispersion a problem worth attending to in physics education? In all probability physicists do hold a variety of conceptualizations about some phenomena or physics concepts (see diSessa, 1986). What would seem to be educationally critical, then, is not that physics students have a variety of disjointed conceptualizations, nor that they should abandon, or change, their existing repertoire of conceptualizations to accommodate what is currently being taught at their level of education, but rather that they should develop the capability to simultaneously rationalize and distinguish between their conceptualizations in a manner appropriate to a given context: having one's education form a functional base from which to view the world. Starting at school, physics pupils should start developing "physics instincts," depending on the relative complexity in the context, to be able to functionally distinguish between their conceptualizations. In other words, in a given context be able intuitively to recognize, or sense, the functional appropriateness of a domain of conceptualization. This is not an endorsement for students to conceptually distinguish between phenomena "in" and "outside" the realm of physics, but it is a recognition that: A l l language is coupled to conceptualizations, and similar language may have different meanings in everyday life and physics contexts; The conceptualizations associated with ordinary language metaphor and analogy must be different to those of contemporary physics; and, In physics teaching there are different levels of explanation and complexity inherent to different stages of education, and these may manifest themselves quite differently conceptually. If students who graduate with an undergraduate degree in physics go on to become physics teachers while having to operate in a world of disjointed conceptual dispersion, then, the results of this study may imply that their only 165 escape would seem to be one of transmissive teaching: the beginnings of a new cycle of disjointed conceptual dispersion, this time for the next generation of physics students. From this perspective, a fundamental aim of physics education should be to simultaneously create an environment where students' sense making is acknowledged and respected, and to generate a repertoire of experiences that can both individually and collectively provide a functional referential framework to facilitate the evocation of contextually appropriate conceptualizations; thus both recognizing and rationalizing their conceptual dispersion. 7.4 Implications for Physics Education Although there were a limited number of students involved in the study, the fact that they completed their undergraduate physics degrees at a number of different universities indicates that the conceptual problems which were identified in this study are not indicative of any specific undergraduate physics programme but are indicative of their similarities. Warren (1988) has pointed out that many of the problems identified in this study would seem to be just as prevalent in other countries such as Great Britain. 7.5 A Proposed Physics Undergraduate Programme for Teachers 7.5.1 Introduction When one considers that potential secondary school physics teachers complete the physics section of their education in standard physics undergraduate programmes (br programmes considered to be equivalent such as engineering, geophysics etc.) there is room for much concern. Potential physicists do not face quite the same problems because they have to come to understand at least one physics problem very well, and in doing so need to explore and extend their understanding of undergraduate physics. This is not to suggest that students in graduate physics programmes are not prone to similar conceptual difficulties; they certainly are. For example, Hewson (1982) completed some exploratory work with a graduate physics student at Cornell University. The student was teaching a course in Einstein's Special Theory of Relativity. Hewson found that even though this student had successfully completed a course in special relativity and was now 166 teaching it, his conceptualization of many of the concepts pertinent to special relativity were strongly mediated by conceptualizations he had constructed prior to his own studying of the subject. Hence, the proposal to be put forward for a different undergraduate physics programme for prospective teachers could have consequential benefits for the traditional undergraduate programmes. Somehow traditional undergraduate physics programmes always tend to have their focus on their students studying one aspect of physics to facilitate their study of another aspect of physics and so on. Universities whose Physics Departments have strong and diverse research programmes are potentially the most exciting and rewarding places for students to learn physics, be they potential physicists or teachers. However, these same research interests place enormous demands on physics curricula because each group demands that students, as potential new group members, focus on fundamentals considered pertinent to each particular group's field of interest. So, essentially an undergraduate programme's curriculum is greatly influenced by the research interests of the Physics Department. These influences are usually embodied in the array of traditional courses. Very soon after completing their undergraduate physics, potential physics teachers are faced with the enormous responsibility of teaching physics to meet the educational needs of a diverse set of pupils. To do this effectively teachers need to be able to "talk physics," which includes being able to offer some kind of historical context to the growth of physics concepts. What kind of job will they be able to do if they themselves have not reached much beyond a phase of working on physics problems for which they have little feeling; not reached much beyond a stage of conceptual dispersion characterized by no real recognition of the functional appropriateness of their understanding? It is in this context that it is being recommended that concerned physics departments consider introducing an alternative physics major programme (preferably an honours programme): Physics for Teachers. This should not be seen, however, as a service subject, or as an easier, less demanding programme, but as one which is specifically aimed at providing potential teachers with a rich repertoire of physics conceptualizations: conceptualizations which embody both everyday life and an historical appreciation of the development of physics framed by the social and intellectual dynamics of that time. This is not something that can be left to their postgraduate 167 education studies, because there the focus must invariably lean towards pedagogy and didactics. In essence, the author believes that potential physics teachers should graduate with an appreciative sense of what it means to learn physics; that is, beyond the stereotype of rote learning of definitions, laws, formulae, and problem-solving algorithms, which many appear to have constructed from both their school and university physics experiences — a finding also reported in other studies: One of the most striking findings ... is that M.I.T. undergraduates when asked to comment about their high school physics almost universally declared that they could 'solve all the problems' but still felt that they really didn't understand what was going on. (diSessa, 1986, p. 6) The essential ingredients of such a programme would need to be ascertained longitudinally by collaborative education/physics research. Such research could begin by considering suggestions consequential from this and other similar studies. It is from this standpoint that the following ideal model is proposed: Firstly, the most inspiring physicists in the department should be assigned to teach the "basic" courses in the new physics teacher programme. The word "inspiring" is used to characterize the ability to foster interest and intrigue. This would be a necessary starting point since experience has indicated that curiosity, excitement, intrigue and interest on behalf of a lecturer permeates to students, providing an essential ingredient for conceptualization exploration; what has been called "constructivist teaching" (Erickson, 1987). This is particularly true if the initial interest is in our daily world, for research in this area has noted that it is in this realm that the students would have already constructed and validated conceptualizations in their own way (for example, see Driver, Guesne and Tiberghien, 1985; Osborne and Freyberg, 1985). An educational environment is envisaged where students' contributions have perceived value, as their ability to make sense of phenomena and experiences is openly acknowledged and respected. One problem is, however, that the generation of this kind of environment requires a substantial amount of time, together with small classes, to be able to meaningfully explore and discuss ideas in the manner proposed. In many universities small classes would seem to be guaranteed by the relatively small number of students deciding to become physics teachers. More time could be created by reducing the amount of specialized physics taught by offering course options in the senior years specifically for teachers, i.e., drawing up an 168 undergraduate curriculum which is more suited to educating future teachers than future physicists. Such decisions would be sure to generate considerable debate within any Physics Department, and in this respect answers are not straightforward. However, the time factor provided could be partially solved by having less specialized advanced courses than there would be in a traditional programme. 7.5.2 A Proposed Physics Curriculum Structure The specific physics content of an undergraduate curriculum for intending teachers is beyond the scope of this dissertation, but perhaps more important than the content of a curriculum is the structure of it; that is how the physics could be taught to improve the conceptual outcomes. It is anticipated that such a curriculum structure would incorporate the kind of "constructivist teaching" (Erickson, 1987) objectives outlined by physics educators such as Brouwer (1984), Driver (1987), Hewson and Hewson (1984), and Fensham (1983) (see Section 1.4.2.1). From this perspective Brouwer (1984) has written of the hope of: Encouraging more teachers and lecturers to concentrate on the development of a conceptual understanding of physics.... to raise the level of respect of teachers and lecturers for students who enroll in our science courses and convince my fellow instructors that many of what have been labelled misconceptions, are necessary and valuable preconceptions to further learning in physics.... a fundamental element of this method is dialogue or interaction (pp.603 - 604). The source of this proposed curriculum structure came in part from many of the comments which the students made during their interviews. These indicated that they had come to regard physics as "applied mathematics" and had "disconnected" much of their physics thinking from their mathematics thinking. That is, they had perceived their physics courses as courses in problem solving and adapted their learning styles accordingly, for example: S: I never thought more ... you just took the formulas they gave you and that was that. 169 S: We did a lot of problem solving and a lot of times as long as you figured out what the problem was, they gave you the information in the problem, and it was more a matter of rearranging it ... the information was there but you didn't really have to understand it, you just had to understand where it went. S: It doesn't rest on my fundamental beliefs in the wave function and wave theory, it rests on the fact that the units came out right. In this regard Hewitt (1983) and Feynman (1965) make the following point: Physics is easy to teach mathematically, but we make a mistake by then assuming it is easy to learn mathematically. (Hewitt, 1983, p. 305) The physicist has meaning to his phrases. That is a very important thing that a lot of people who come to physics by way of mathematics do not appreciate. Physics is not mathematics and mathematics is not physics. One helps the other. But in physics you have to have an understanding of the connection of words with the real world. It is necessary at the end to translate what you have figured out into English, into the world... This is a problem which is not a problem of mathematics at all. (Feynman, 1965, pp. 55 - 56) Creating an educational environment for conceptualization exploration within a framework of establishing a meaningful relationship between physics and mathematics should, I believe, frame the structuring of a physics-for-teachers programme. Here I envisage that the physics courses would be structured so that all the concepts to be introduced by the course could be dealt with qualitatively before any quantitative problem solving is introduced. In other words, quantitative problem solving is postponed until all the courses' concepts have been explored within the context of students' sense making, and where appropriate, some historical insights. Only, then, would the focus of the course turn to quantitative problem solving. The advantages of such a curriculum structure would be two-fold. Firstly, instead of introductory students beginning their physics study and having their probable stereotypical views of what it means to study physics reinforced, they meet interesting conceptual challenges. Challenges of a nature that they will one day, hopefully, take back with them into their school classrooms. Instead of 170 meeting a rapidly presented maze of formulae and mathematical word problems they will potentially enter an environment that: respects their thinking and invites discussion and reflection; an environment of "hand waving physics" and "thought experiments" (for example, see Helm and Gilbert, 1985; Helm, Gilbert and Watts, 1985); provide some sort of historical context for the concepts being introduced (framed by the social and intellectual dynamics of the time); introduces new ways to fruitfully view the world around them (this includes the relationship of physics to other subjects); and, will largely dispel much of the "hidden curriculum" that was discussed earlier, and thus potentially generate a rather different disposition to learning physics than that which the students involved in this study had fallen prone to. The second major advantage of such a curriculum structure would be that the qualitative exploration of concepts would provide a different and more appropriate conceptualization base for problem solving to be built upon. That is, instead of having the somewhat traditional expectation that after lecturing on a topic, a set of assigned tutorial problems will facilitate the students' construction of appropriate conceptualizations, their construction will potentially have solid foundations before the onset of the quantitative problem solving. Potentially this will give students a "feeling" for what they are solving as they would be viewing the problems from a different conceptualization base than they have in a traditional course. As Hewitt (1983) said in his acceptance speech for his 1982 Millikan Lecture Award, "Let's look at the whole elephant before we begin to measure its tail." (p. 311) Finally, some other suggestions: Firstly, the tutorial classes should ideally be as small as possible to facilitate maximum discussion regarding why an approach was made (rather than "this is how it should be done"). Perhaps students could be divided into small study groups, who could meet weekly with other faculty members for some diversified interaction. From such a perspective, problem solving could realistically represent a further exploration of new conceptualizations and encourage conceptualization mediation, reflection and rationalization. 171 Secondly, the traditional laboratory sessions would need some revision. The author believes that laboratory sessions should focus on phenomena with higher interest profiles than those typically found in undergraduate laboratory sessions. Also, in their restructuring they would need to reflect both the qualitative and quantitative components of the proposed curriculum. In this respect the creativity of the California Institute of Technology School of Physics (who have developed a unique set of undergraduate laboratory sessions) could perhaps be drawn upon. Such a proposal would create enormous curricular challenges to Physics Departments and such a programme would need to be introduced in stages that could be sequentially reviewed and evaluated with a collaborative education and physics research effort. 7.6 Recommendations for Further Research Following the discussions at the end of each analysis chapter, and in this chapter, three recommendations for further research emerge. 7.6.1 Building a Phenomenography of Physics In Chapter II it was pointed out that the major research thrust into students' physics conceptualization has been done at the school level and has often been referred to as "children's science." It was also pointed out that a relatively small number of research projects have investigated university students' conceptualizations. These have tended to focus on freshmen and their elementary mechanics conceptualizations. This study was unique in that it focused on physics graduates. The educational usefulness of these studies is that they provide insights for physics educators into how students make sense of what they are being taught, and how important it is to recognize that students do not make sense of new concepts in isolation, but utilize already well formed prior understandings. From this perspective it would be extremely useful for research to build up and integrate what Johansson, Marton, and Svensson (1985) have referred to as a "phenomenography of physics." That is, a comprehensive description of physics conceptualizations in terms of the content of student thinking. For instance, 172 following on from this study it would be extremely useful to find out how physics graduates conceptualize other areas of their physics. In particular, this study could represent a starting point for further studies into how students conceptualize other related wave concepts, both classical and quantum. While it may be of some interest to know how widespread the conceptualizations described in this study are, it is not recommended as a high priority research activity. There is far more potential usefulness in having insight into how students make sense of what they are being taught than how pervasive a particular conceptualization is. Focusing on the pervasiveness of various conceptualizations which are at variance with contemporary physics, invariably leads to the conclusion that the resolution of the problem lies in changing these conceptions from "incorrect" to "correct," narrowing the description of non-rote learning to one of conceptual change, see Conclusion 13. 7.6.2 Research into the Proposed Physics for Teachers Programme One of the recommendations emanating from this study was for the introduction of a physics-for-teachers undergraduate programme, as a fully recognized physics major or honours programme with a difference. The difference would be the separation of qualitative and quantitative physics with the qualitative component being taught first with some historical insight. The practicalities of setting up such a programme were acknowledged to be complex. Thus it would be useful to carry out several case studies on various courses throughout the undergraduate programme, to see whether such a programme could be usefully implemented. Then, based upon the results of these case studies, improvements and alternatives could be recommended which could eventually lead to some universities implementing an undergraduate programme for physics teachers. What has been proposed is that a different undergraduate programme for teachers is desirable; what needs to be shown is that it would be both useful and viable from both physics and educational perspectives. 173 7.6.3 Working with Recently Graduated School Physics Teachers Earlier in this chapter a case was made for the fundamental importance for all physics educators, irrespective of their level, to have insights into how their students tend to make sense of what they are being taught and how, through what was called "constructivist teaching," educators may have a more meaningful mediatory effect on their students' sense-making. As was mentioned earlier, many physics graduates enter their educational studies with strong beliefs about what it means to learn and teach physics, primarily that teaching physics means teaching problem solving. These beliefs seem to be mainly a direct result of their own school and university physics experiences and as such are. not easily accessible for reconstruction. Earlier on in this chapter the following questions were posed: What kind of physics teachers would these students become if they themselves did not reach much beyond a phase of working on physics problems for which they had little feeling; and, did not reach much beyond a stage of conceptual dispersion without any real recognition of their functional appropriateness? It would seem that a reasonable starting point for such students would be for them to be provided with the opportunity to reflect upon how they personally constructed/reconstructed their own conceptualizations within the context of constructing consistency and rationalization. From this perspective it would be useful to find out how to facilitate new growth in these potential teachers' "content-specific pedagogical knowledge" (Shulman and Sykes, 1986). Some of the interview contexts may provide an excellent framework to facilitate students' exploration and reflection on how their pupils may construct various conceptualizations, by allowing them to review how they constructed their own conceptualizations. For instance, the interview transcripts such as the "wavelength estimation" in this study could be given back to the students concerned (students would review their own transcripts) as a preparation for group seminars to be held before and after the students begin their practical teaching sessions in schools. This could provide a unique forum for an exploration of the conceptualization of what it means to teach physics. 174 7.7 Overview of Chapter VII The conclusions and recommendations discussed in this chapter have reflected a need to sensitize physics educators to the importance of appreciating that students come to class with a dispersive set of conceptualizations. 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S: Well, the most basic theory that I could talk about is, um, going for an example where you can actually see a speaker or, um, even a voice, a voice diaphragm — But, um, basically what it has to do with is, um, I was going to say a wave but that brings in a lot of other connotations. Um, but that's probably the best: a force of air changing that causes a reaction on your ear drum that you can turn into something. You know, whether it is the drop of a pin causing this noise to reach your ear, this little thing which travels through the air, um, or a voice talking to you vibrating a small diaphragm in your ear which then you can recognize as speech. Any sort of disturbance in air: you need something to propagate this little thing we call sound; whether its dropping a book, talking to someone, turning on your stereo: it all creates a disturbance or a shock to this air around it [the ear] that moves through, then you can proceed with your ear. I: Could you try and clarify a little more for me how this "disturbance" - how it actually reaches my ear? Suppose you are talking over there, or drop a book. Could you explain the mechanism: give me a model of what is happening? S: The best model, if you recognize that air like anything else is made up of tiny particles of things we like to call molecules, then — At a simpler level just consider a row of beads sitting on the table. And you tap a bead at one end and you knock the beads all the way along, and at the other end [of the beads] you have your finger and you can feel the tap. That would be analogous to a book dropping and creating the motion of all these smaller things in the air we call molecules which act the same as the beads and move this disturbance around until your finger at the other end can feel it — in this case with the ear at the other end that is feeling it. CONTEXT: BURST BALLOON I: Okay. I am going to try something — [sound of balloon being blown up and then burst] — Okay, I gave you a loud bang there. Could I ask you to explore your explanation a little further for me? Again — what happened between the balloon and your ear. I am not really — I don't want you to go into the intricacies of how the ear works but I am interested in how the sound travelled, or how it was formed initially, and how it travelled to your ear. 190 S: Okay. With the balloon you created a disturbance just like all other sound waves are disturbances, um, in the case of the balloon you are allowing, you put all this air into a pocket and very dramatically, all of a sudden, let it out. That caused a very large disturbance and therefore a very loud noise. So, um, going back to the bead example instead of tapping it with your finger you take a hammer and hit the end of these rows of beads and they all knock into each other and instead of it just tapping your finger at the other end or with the balloon just making a small noise at your ear all of a sudden it hits you fairly hard just like the balloon hit your eardrum fairly dramatically. If you had it close enough it would actually get to the point where it hurt because this disturbance is close enough to your ear that it hits it. The air, the motion of the air hits your ear at such a rate that it hurts. I: I am just er, I would like you to try and clarify a little more for me how this operation — Okay, I can see your analogy with the beads. Could you try and give me a clearer picture in terms of the molecules: what would they be doing? S: Okay. Well in the air you have a group of molecules that act very much as the beads — they are not visible to you but when you create a disturbance with a balloon or a book, um it moves the air around it, you know, and the air being molecules it moves those molecules, those molecules hit other molecules just like one bead hits another. In that way it is like a chain reaction, one hits another hits another. Then, slowly the sound will propagate towards you as those molecules collide with each other — just like the string of beads collide with each other. I: Before I popped the balloon what was happening: what was going on with those molecules? S: They were moving around in a relatively random fashion, um none of these things are totally stagnant. So they were moving in some sort of random fashion and when you popped the balloon you forced them to move in one particular direction so the basic there is instead of having a stationary bead you have a bead that is sort of moving around a bit but you hit it hard enough and you hit enough of them — instead of having one bead you have about twenty in a circle and you hit all, enough of them so the sound starts moving out from there. I: Could you go step by step? I can see quite clearly what you said: you have the circle [indicating a circle with my hands] — what happens to those molecules? [indicating to an area outside the imaginary circle referred to earlier]. S: They are moving around in a relatively random fashion and then you cause a disturbance and force them to move -- the disturbance forces them to move away from wherever that disturbance happened. Like they will move away from where the balloon exploded. They run into the ones that are nearest to them and then those hit others and it [the sound] slowly moves further and further away. I: Okay what happens after they hit the ones nearest to them? S: Well, the molecules will ricochet to a certain extent. They will hit each other and change direction, um, and sort of, the initial bang will hit more and more molecules and as it does that, it ah ~ the initial speed of the first molecules it hit slow down as it goes further and the sound starts to fade because it goes over a 191 larger area and slower. Eventually the whole thing just dies out and then they go back to their sort of random motion. CONTEXT: TUNING FORK I: Have a look at these things [sounds of tuning forks being placed on the table]. Have you ever played with these? S: Oh — [sound of student tapping tuning fork]. I: In class? S: No actually I can't remember specifically -- [more sounds as student investigates the pile of tuning forks given to him]. I: Interesting — just sitting here I noticed a change as you turned the tuning fork. Are you hearing the same thing [phenomenon]? S: Yup. I: Do you have any ideas on that? [sound of several tuning forks as student investigates the phenomenon]. Near your ear the effect is quite dramatic [more sounds of tuning forks]. S: Because the — what's creating the disturbance is the vibration of the bar [referring to a tuning fork leg]. It is moving in this direction [parallel to plane of fork] so the main sound, the main disturbance, is running in those directions. So if you could put your ear fairly close somewhere in here — I: To the gap [between the tuning fork's arms]? S: Yea — you probably wouldn't notice any perceivable sound because it hits what is called a ... it hits what is called a node — [pause] — but I wouldn't — if I was telling a high school student that I wouldn't like to talk about nodes. I: Does that mean — are you describing a sort of one dimensional sound? S: Yea, well actually its sort of two dimensional. The main sound is in the plane that includes the forks. The sound propagates in all directions but because the sound is strongest in that one plane, that is where you will hear it most: it will fade least if you go in either direction from the fork. I: Okay, could you explain how the sound propagates from the fork to my ear? S: Well, you are vibrating the arms of the fork, and its moving the molecules nearer, and its generally hitting ones that are in line with the sides of the fork, but it is also hitting a lot of others. So the sound moves out in all directions from the side of the fork. So the very small movement of the fork where — with the longer one for example you can actually see the vibration happen [referring to a lower frequency tuning fork he had picked up]. With some of the short ones you can't see it so well [referring to higher frequency tuning forks that he picked up]. It is very small, you can feel it if you put your finger on it. That's enough to 192 move the air molecules around the fork and create that thing we call a sound wave. I: Okay I would like to focus ~ when you say "move" could you give me, again, a description of what is happening there. S: Okay. The fork is moving, the arm, if you want to exaggerate it, is moving back and forth in the air and naturally the air starts out being all around it. When it moves one way it has to force the air that on one side of it away from it. Naturally the air occupies the space that it left. When it [the arm of the tuning fork] goes back the other way the exact same thing happens. So you start pushing the air back and forth as the fork vibrates. Now, if we were to have just one vibration it would just push: that was a book example where you have one distinct bang because it moves the air once a certain amount and then it fades: with this [referring to a tuning fork] although it fades a bit because the forks slow down, you can hear an almost continuous sound because it keeps going back and forth. It is almost like, your hand doesn't create sound when you are fanning your face but you can feel it. I: Why not? S: Well, if you move your hand fast enough [waving his hand with great gusto]. Basically the fact that this is metal [pointing to tuning fork] isn't anything special. If I could move my hand as fast as this thing [arm] of the fork you would hear the same sort of buzz. Um, you can feel the air hit your ear if you wave it [hand] by your ear. I: Okay. So, when you say you can feel the air hit your ear when you wave your hand near your ear — ? S: You can feel the air move into the ear cavity. You can hear, although it is not a distinct sound, you can hear something. It is the sound of your hand moving through the air although your hand isn't hitting anything besides the air. So therefore you must assume that I can do that [waves hand]. You don't hear anything from where you are at, but I am moving air. If I move fast enough all of a sudden I can hear something and that must be the fact that I am moving air with my hand. I: Okay. It intrigues me that I can do that [sound of light tapping on table] without moving very fast yet if I move my hand which is moving the air — Why when I move that air don't those molecules, as you were explaining to me earlier on, collide with other molecules and continue ~ ? S: Well, the table for example — the air doesn't have as many molecules whereas the table is what we call a solid. The air is a gas and you are hitting less molecules when you are doing this [waving hand] so you have to move your hand faster to hit — and when we talked about the sound falling off because it hits more and more, if you hit more to begin with the sound will be louder. So when I am hitting the table [hitting table with hand] I am hitting a lot of molecules at once, but when I go like that in the air [waving hand] I am not hitting very many, the density of the air. To follow that example you can even talk about different types of air. Um, an analogy I like to use when talking about this is: on a cold, well, you notice it if you are on Vancouver Island, cold, normally its foggy, but on cold mornings you can hear the fog horns because the cold air has more molecules in 1 9 3 it, it is more dense. So the sound travels further if there is a foghorn going on a day where it is less dense you may not hear it. Like on some days I can hear from my house the ferries leave when they blow their horns because the air is more dense and it gets all the way to me. I: What do you mean when the air is more dense — I can see you saying that's why but I am not really seeing the mechanism? S: If I took a plastic box and I dropped four beads into this box and rattled them around okay. That isn't very dense. Each marble — the number of times something hits one of the walls, say the top wall: I am rattling it back and forth: it doesn't hit that top wall very many times. So, if we were to extend that to the air around it instead of hitting the top wall of the box its hitting another molecule. Okay -- its going to fall off more rapidly because its not hitting other molecules as often. Now if I take it and drop twenty beads in it and rattle it around its hitting all the sides more often and for that reason you can even tell from the example which would make more noise: a plastic box with three beads in it or a plastic box with twenty beads in it, because the beads will make noise just like anything else would that is creating a disturbance. I: Just to make sure — when you are talking about more dense air what are you talking about? S: Well there is more, if I was to take that plastic box and put air in it instead of beads. When the air is more dense there are more molecules of air and when the air is less dense there are less molecules. If you could hear the molecules hitting against the side of the box — . I: Would they hitting now in my box? S: " Oh yea, because they were moving around in that random fashion, right. I: Would they be hitting each other? S: They would be hitting each other. I: Now to get a propagation of sound the molecules must — ? S: Must hit each other in a given direction. When there is no sound all of them are moving around randomly, right, when there is a sound all of a sudden they move to one side or in one direction very rapidly and that's what causes the sound. So what you would have to do is get all those molecules to move in one direction: that's what you do with the fork. I: Okay, when the fork is continuously going, let's listen [sound of tuning fork]: I can see your model of the molecules moving in one direction: do they keep on moving in one direction as long I am hearing the sound? S: Yes. I: If the sound continued for long enough could they reach me? S: Well, they are reaching you. 194 I: Okay, so that the molecules from here at the tuning fork reach my ear? [With that the interviewer strikes the tuning fork in his hand.] S: Yes — [long pause and sound of tuning fork] — because — they hit — not the same molecules but they hit others, hit others, hit others, otherwise you wouldn't be able to hear it. If they only got this far or if they hit a wall or something else that doesn't transmit sound you wouldn't be able to hear it because you would need those molecules [in the wall] moving to be able to hear it. I: The only thing that I still feel confused with in terms of what you told me: what is the difference between a single sound and a continuous sound? S: Well, with a continuous sound you have to be continually disturbing those molecules; the fork is continually moving back and forth and it keeps hitting the molecules back and forth. Now, if I was to just, say, do that [hitting table top with hand] I only — there is only one sound which emanates from that as opposed to if I could do it fast enough: if I kept tapping and I kept making the noise — The difference between [sound of single tap and then rapid tapping] which is basically what the fork is doing [sound of tuning fork] just keeps moving back and forth until it dies. I: The same molecules then that we are talking about: so, as long as there is a continuous sound then those molecules -- give up their random motion and take up some other motion? S: Yup — yea. I: How do they get their random motion back when the sound stops? S: Well, when the impetus or what ever disturbed it dies then they slowly — they slow down and start -- they collide with others and start loosing their energy of motion and they start dying off until they go back to the random motion. I: Do you like sound? [sound of equipment being moved around]. S: Yea [enthusiastically]. I: Did you ever teach it? S: I taught shock waves a lot because I taught flying. I: Oh yes, I remember you telling me. S: Um, the one thing that always — I had a friend who was a sound engineer and the one thing that he always pointed out to me when we were doing all this about electronics and all that sort of thing. The one thing that is still the most archaic thing in creating sound is the speaker. Um, it is basically been unchanged ever since they created the idea of transmitting sound. They've got these electronic and digital HiFi sets, but the idea of the speaker, you find, although it may be, you know, a little nicer and more refined, you know, the individual mechanics may be a little neater than the originals. The idea of that way of creating sound hasn't changed ever since they have been able to do it. Actually that's where I sort of started thinking, and he had ideas, you know, how? 1 9 5 It became more apparent that what you have to do to create sound is to move air, or move something that will eventually move the air to hit your ear. I: You fascinated me: thinking about the loudspeaker, how does the loudspeaker make the sound? S: Same way the fork does, it moves and vibrates the air, but instead of the fork [picking up tuning fork] like this, this will move [pointing to one prong of tuning fork] air in a certain way because there is not, um, it vibrates air in a certain way — it vibrates in a certain frequency. It would be analogous to me taking three or four of these [tuning forks] and tapping them at different times and you would here different sounds. If I was adept at it I could actually make a song out of it or, you know, music just like you would hear out of the speaker. The speaker can change the way it moves, and the frequency that it moves, where a fork can't, so it can create all those different frequencies that your ear can hear. I: How is it actually doing that? S: Well it is vibrating back and forth at a certain frequency just like these forks were vibrating at a certain frequency. The speaker because of the power or whatever you put into it, um, the electricity that is moving it back and forth, you can change the frequency of that and then the speaker will give out the different frequency. You can do this very quickly. I: How does — Okay I can see the speaker moving at a certain frequency, but how does that turn into sound? S: It hits [said very slowly and hesitantly] the molecules just like the fork does. SUBCONTEXT: WAVELENGTH PROBING SCENARIO (Part of Tuning Fork Context) I: That's intriguing I am just looking to see what we've got here [sound of tuning forks being moved around and tapped] — 440 — Well, let's have a look a this [interviewer picking out a 440Hz tuning fork from the selection of tuning forks lying on the table and striking it]. Its frequency is about 440Hz, any idea of the kind of wavelength which we are looking at here? S: [Takes tuning fork and strikes it], you would have, um — er — I: Would you need to calculate it? Ah, there is a way of calculating that but S: Yea, for myself probably. It's a fairly short, fairly small number. I: From what you have been telling me, from your explanation, there isn't a way that you could, um, give a guestimate of the wavelength? S: There probably is if I think about it long enough [continuously playing with the tuning fork in question] -- oh yea, I know [enthusiastically] the wavelength has to be the same as the — you see each time the fork moves back and forth it creates a new wave so the wavelength is equal to how far the fork moves. That is a very very small number. 1 9 6 I: Could you try and put something to it? S: What do you mean? A number? I: A number, a feeling for the size, lets work with this 440 [sound of tuning fork] S: Well, actually the wavelength is, you can't say for say for sure an accurate number because --I: Are we talking about mm, cm or metres? S: Um, the wavelength is of the order of less than millimetres, I would be tempted to say like hundreds of nanometres, four hundred nanometres. I: On all of these [pointing to other tuning forks], on this one as well [picking out the 128Hz tuning fork because the vibrating tongs are vividly visible] it is 128Hz. S: Now you are getting closer to, with that, you see, it becomes visible, so you know, you are getting closer to an order of millimetres then. It all depends on, you can only hear through a certain sound range. I: How would you respond to someone if they said to you, well — what is this? — 400. If they were saying that the wavelength was much longer how would you convince them in fact — ["S" interrupts]. S: Well , because you are creating a continuous sound which means a continuous wave. It is created out of the fork moving back and forth. So, every time the fork hits the same position it's got to be the same position, it's got to be creating like — all the way in and out again that's one whole wave. Every time it [tuning fork arm] goes in and out that's one wave so the distance it travels has to be one wavelength. You know, because with this example you really can't see it [striking the 440Hz fork] moving although you can feel see it moving. Um, it is definitely of the order of less than a millimetre. With this one [picking up and striking the 128Hz fork] you can almost see it moving depending on how hard you want to hit it [sound of tuning fork]. You can see the dimension we are dealing with. I: Can you remember how you would calculate that? S: Um, the equation for it? I: Yes. S: Well, the reason I say its variable is because it depends on the speed of sound in air. I: Suppose we took the speed of sound to be 300m/s. S: Okay, we know the frequency so — [talking to himself "seconds"] I tend to do it; I calculate all my formulas by looking at units. I know, I know, what you want to find is the wavelength and you've got the speed of the wave, because the 197 sound travels through at that speed, and the frequency of the wave. So if its going at 300, what did you say? I: 300m/s — that's an approximation actually it's closer to 330m/s but 300 is good enough. S: 300m/s and its 440Hz? I: Oh, use 400Hz. S: Okay, 400 cycles per second. So we want to get something that is going to be in metres, we divide the one by the other which means we divide 300m/s by 400, um, cycles/s, and we get so many metres per cycle which means — one cycle is a wavelength so, so many metres per cycle would be the wavelength. So we are looking at something like 0.75; three-quarters of a metre. I: That seems inconsistent with what you were telling me earlier, three-quarters of a metre is about that long [indicating with hands]. How would you account for that? S: I can't. I: Does it worry you. S: Yea. I still hold by my original conceptional idea that the wavelength has to be of the order of the motion of the fork. I: Which would you prefer to go by, the formula or your — S: I would trust my physical intuition. I: So if they gave that to you in an exam: "Given that the speed of sound in air is 300m/s calculate the wavelength produced by a 400Hz tuning fork": what answer would you give? S: I would have to put 0.75m if that's the way the numbers come out. I: How would you feel about it? S: If I assume that is the speed of sound, I have to assume because that is the given, and I know the frequency because that is a given, then the length also has to come. I: Okay, I will look up the exact speed of sound for you [looking up in physics text]. In fact it depends upon several factors — okay, here they give it as 330. So given that we haven't given you any incorrect information and you have calculated this 3/4 metre, how do you feel about you writing that down in an examination, yet you feel quite confident within yourself that it is closer to millimetres? What does that do to you? S: Well, at that point, looking at the magnitude of the numbers it makes sense that it's almost of the magnitude of a metre. So then I have to look at the way that I was analysing the motion of air around the fork because that's where I must 198 have made the mistake. At that point, once I have looked at that and say gone over it a couple of times, that this is the way it has to be. I: Which is the way it has to be? S: Well, I would have to, you know, upon investigation I would have to default and say I know I'm, I'm within a small error — I know that that is the speed of sound [referring to the 330m/s provided by the physics text] and since these [tuning forks] are calibrated to give a certain frequency, then, I must, again within a small error, then my error must be in my gut-reaction to how the wave is created at the fork. That is a gut-reaction, that is not a fact, it is my way of looking at it. Then I would have to amend my — I: Would you like to try to amend your way of looking at it or — ? S: Well, at this time I am sort of ~ [long hesitation] — I: I don't want to put you on the spot, we can leave it and maybe come back to it later. S: Yea, Yea. I, you know, I still, when I think of the way waves are supposed to propagate, all I know about waves that intuitively make sense to me, the peak of each sound wave being with the motion of each fork, and the fork definitely doesn't move that far. CONTEXT: TUTOR/TEXTBOOK I: Okay, let's move on to something else. This is a new physics book — I want you to imagine for a moment that I am an undergraduate student and I know that you are in education and are going to become a teacher. I have a bit of a problem. I want you to explain something to me. [Showing an illustration given in the text] they say that the top, (a), is a sinusoidal longitudinal wave and, (b), that's a corresponding wave shape with displacement from equilibrium plotted as a function of distance. I can't make sense of these. Do you want to have a look at it for a moment and then try and — S: Well, um, these are, the model they are trying to show is little springs in between certain points along a wave. What's happening is if we look at any point along wave, take one that's moving. If you have a whole bunch of springs inter-connected, okay, and you start to push the spring at one point that, that — you compress the spring, it will take that compression and then push the next spring along. So, what happens is you get a compression and then an expansion, right, on an individual spring and the next one will do the same and the next one will do the same. Buy that so far? I: Yes, okay. S: Now if we consider — I: I can even get you a spring if that will help. S: Slinkies are great things. I did this in my high school physics classroom: slinky. I am going to move one end [sound of moving slinky on table top]. I force 1 9 9 the spring in, so, if I take a look at where, if I take a look at say this ring [of the slinky] right here. Okay, I push it like that [creating a small pulse] it moves that way, this individual spring moves there and back, and if I kept moving it, it would keep moving forward and back [talking while demonstrating]. So, if all of a sudden I decide: this is sort of hard to keep track of where this particular ring is moving: I am going to say I'm going to make marks on the table [to correspond to the dots in Figure (a)] and say at, um, any given point I'm going to measure, I'm going to take a look which direction this is moving [pointing to the 2nd dot in Figure (a)]. Okay, if it's [a ring of the slinky] moving this way I'm going to draw an arrow up [pointing to Figure (b)] if its moving backwards I'm going to draw an arrow down because we are assuming that we are counting from zero here [first dot in Figure (a)] to some number out there. So that's positive, in the direction of positive, and this is in the direction of negative [+ve toward right on graphs and v.v.] and then we look at how fast it's moving we know how how long to draw that [pointing to upward perpendicular arrows in Figure (b)], how high up to put it. [Sound of slinky moving on table] because when I do that I don't, it's [slinky] not all moving at the same speed it speeds up and it speeds down [sound of slinky moving on table]. I: [Pointing to the first displacement maximum in Figure (b)] so the molecule in the centre there is moving the fastest? S: [Nods affirmative.] I: How do they get that from here [pointing to Figure (a)]? S: Well, the same sort of way we did, looking at any point along here [indicating a position in Figure (a)]. I: Alright, let's take that point there, the first point [Figure (a)]. S: Okay, you see — I: Sorry, I guess this point is stationary, let's go to the second point. S: Second point, okay. Its moving this way [to the right], okay, but it is slowing down because the whole thing is starting to bunch up here [pointing to the section labelled 'Rarefaction' in Figure (a) and then demonstrates using the slinky on the table top]. It's like if I held it right here [about 20cm down stretched out slinky] and started to force every thing that way [pushing the stretched out portion of the slinky towards the section that was held stationary]. It would slow down because the spring would get all cluttered together so this one has not yet reached it's full speed, this one is at full speed; this point, at the next point it's starting to slow down again because its starting to bunch up and this one right here is stationary [looking at four consecutive dots, after the first, in Figure (a)] because it's the point, you see down here [Figure (b) - second node], where the spring stops before it comes back [moves slinky down and up on table top]. I: I can see that but how did they plot that from there to there? [indicating consecutive dots in Figure (a) to consecutive dots in Figure (b)]. S: Well I wouldn't um --200 I: Well how did they take that [Fig. (a)] and get to that [Fig. (b)] - could you give me a neat explanation: remember I am just an undergraduate: how are they getting from figures (a) to (b)? S: Okay, if we take -- [interview inadvertently briefly interrupted.] I: Let's just see if I have your explanation correct. You told me that these arrows represent the speed which the molecules are travelling [Fig. (b) -perpendicular arrows], and there its zero [first node in Fig. (b)], and there it starts to get faster, fastest at the maximum, and then it starts to slow down again, right? S: Aha . I: And then [pointing to the first section of Fig. (b)] where the sinusoidal graph goes below the axis and — [sounding extremely hesitant] which way, er — S: They start moving in the opposite direction. I: Starts going backwards, goes slowly and then faster and faster and then stops? [pointing to third node in Fig. (b)]. S: Yup. I: Now how are they using this [Fig. (a)] to get to this [Fig. (b)]? S: Okay, well first of all this [Fig. (a)] isn't all of this [Fig. (b)]. I: Okay. S: Okay, the easiest thing to know is that we notice that it stops there, there, and there [nodes in Fig. (b)] which correspond to, on this graph, we know it stopped there, there, and there [Fig. (a), beginning, middle, and end]. So, we just take this first part right here [Fig. (a)] — we notice that all, the whole spring is moving to the right over that section. I: Okay, the first three dots [Fig. (a)], right? S: Right. So, that means that it is moving in a positive fashion, so, then the arrows are pointing up in the positive. Okay, because of the stopping here [forth dot Fig. a] the fact, this is slow because, well, lets move, this is slow because it is clustering up here [Fig (a), fourth dot onward]. The fastest point is midway between the two stops, okay, because that's where it has the most speed. Here it is being slowed down because the spring is starting to go as far as it can and here it is being slowed down because the spring is being contracted as much as it can [rarefaction and compression respectively in Fig. (a)]. If we take a look at the next frame — I: Even though they don't line up with each other? [dots in Fig. (a) and arrows in Fig. (b)]. S: No, this um — I: I mean the stationary points line up with each other? ["S" and "I" re-examine the two Figures using a ruler to look for correspondence to plotted points 201 in each Figure. Only the node points in Fig. (b) line up/correspond to dots above in Fig. (a)] S: Their idea of straight isn't quite, isn't quite — in here [Fig. (b)] this distance in between these two arrows [consecutive] is the distance — you know our initial distance is like you are measuring this spring and this spring [Fig. (a): spring elements between the first two dots and second and third dots respectively] but the reason, so, and we are marking them, you know — so what happens is when the motion moves through — these two dots that we are measuring [first two in Fig. (a)] move further apart and closer together. So on this graph [Fig. (a)] these two dots are really far apart and these two dots are really close together. I: What would this represent, the — ? [Pointing to Fig. (a) directly above the first node in Fig. (b)]. S: That's where one of them is stopped. That is this point right here [pointing to node directly below in Fig. (b)]. I: Okay, and if you were looking in terms of a compression and rarefaction: what would this point represent? S: Um, how do you — ["S" appears very uncomfortable with these terms]. I: Would this be where it is all bunched up together or where they are very far apart? S: This, this, well, if we look at — this is where they're at a — on one side it's, everything to the left is really far apart and everything on the right is starting to bunch up. Okay, so it's, it's sort of the halfway point between where it's starting to bunch up and where its really — I: So where it's maximally bunched up you have a zero? S: Yup. I: Okay, here where it is pulled apart as fas as possible you also have a zero? S: Okay, that's the difference between condensing: where it's coming together: and, um, where it's going apart. There are two different types of zero, see, here we notice it's hitting a zero [corresponding to first node in Fig. (b]), and we consider it moving to the right as a progression and it's starting to go backwards. Here [corresponding to second node in Fig. (b)], it's hitting a zero and starting to go forwards. So the entire cycle does not just include two of these its actually three of these [Fig. (b): antinodes]. So a whole wave of this would be all of that [Fig. (b): indicating that the wave length is incorrect and should be extended] and that would include, um, a whole cycle. I: If this [Fig. (a]) is a longitudinal wave, why — what would be the object of drawing it in this sinusoidal form? S: Because longitudinal waves are hard to conceptually understand what is happening in any given point: you can't really instantaneously measure how fast any one of these points is moving, but if we draw it like this [Fig. (b)] and we 202 assume, and we get the sinusoidal form then we don't have -- I could erase all these dots [Fig. (a)] and just treat it as a continuous spring. I: Would we have areas of high and low pressure? S: Yea. I: Okay, lets look at Figure (b) where would the high pressure be and where would the low pressure be? S: Okay, well, the — like we talked about this point [Fig. (b): second node] is where they are all coming together, where, this is where your condensation is happening, so, um, the spring at this point is moving in the negative direction, in fact this way, the spring at this point is moving in the positive direction, this way. So at that point the node is zero with both ends coming towards it. So it would be the same as if I hold this [demonstrating with slinky on table top] and started to squeeze both sides in together that's a high pressure point. Now if we look at the next one here [point in Fig. (a) corresponding to third node in Fig. (b)] we notice that the particle to the left of it is moving away from it and the particle to the right is moving away from it so we are going to have, you are stretching it out. I: I am just thinking ~ high pressure would mean a large force wouldn't it? S: How do you mean? I: How would you explain pressure? What would pressure be? S: Um, good question — I: I was just wondering -- if that's a very high pressure yet it's stationary, and here it is a very low pressure, from what you were telling me, and yet it's moving its fastest. S: That's the difference between velocity and force, well velocity and pressure. Just because it's moving fast it doesn't mean, um, it has any pressure or a specific pressure. You know, if we have two things moving together at high speeds then you would assume at the centre, because you are bringing this all together, then at the centre you are going to get a lot of pressure. When two things are moving apart at a very rapid rate of speed then you would assume in the centre you are going to have a very low pressure because you are stretching it out so it's like [demonstrates using the slinky]. So the speed doesn't mean, because it's fast, I could do the same thing very slowly, I could start moving this out very very slowly [demonstrates using slinky] and start pulling it out — I am still getting a low pressure because I am moving it slowly and the same thing, push it back together, I am getting a higher pressure even though I am moving it slowly. So the speed really doesn't have anything to do with it, as far as how much pressure you get, it's whether it's converging or whether it's diverging. I: In terms of — with sound -- I guess we are talking about the speed of molecules? S: Yup. 2 0 3 I: Okay, so when would that — suppose I tap the table [sound of tapping] or I clap my hands [sound of clapping] continuously or we have this [sound of tuning fork]. When would the molecule be at it's maximum [pressure] and when would it be at it's minimum, in terms of the model which you described earlier? S: Okay, well its like if we attach a spring to this fork moving back and forth. I: I can see with the spring, lets just try and think of the air. S: Okay, this fork is moving the air back and forth, just like the spring. So it would be at a maximum at a point where it's moving towards the air — towards compressing — in the direction, well depends [on] where you are listening. Say we are over here, when it moved towards us then the air is compressing we get a high pressure, moving towards whatever is receiving it. When it moves back — I: Why does it move back? S: Why does the fork move back? I: No, you have this molecule — why does it go back? S: Understand that it's the fork moves back and forth, right. I: So if the fork only went in one direction the molecules would only move in one direction? ["S" superimposes his voice over "I's" - "The molecules only move in one direction"] S Yea. I: So, when you do that [sound of hand slapping table top], do that [sound of a clap], you only have molecules moving in one direction? S: Well, it's not going back and forth, saying it only goes in one direction is a bit of a misnomer. I: Well, what is it doing? S: Because, like I could, you could be standing over there, over there, anywhere around me: when I do that [sound of clap] you will hear it because it will move in all directions around my hand but the individual molecules are moving outwards -- they are not vibrating back and forth. I: And then what would? -- they are moving outward — would there be a vacuum there afterwards? What would happen? S: Well, you move them and they would hit each other and start to move out and then it moves out; if you could sort of picture it, a sphere around where the sound is coming then they just bump into each other and move further and further out. The individual molecules don't keep going in that direction they just bump into one next to them, bump into the one next to them, bump into the one next to them. I: Well, after they have bumped then what do they do? S: They just sort of start doing a fading back to random motion. 204 I: How's your time doing? I've got a couple of other things which I wanted to show you. S: No I'm fine --I: — You may find this interesting — you are going to enjoy teaching I can see that! S: Yea. CONTEXT: SOUND TUBE EXPERIMENT [Small talk as equipment is set up]. I: Okay, I am going to do something different with you. This is a tube and I have a little candle sitting at one end of it ~ I am just going to light it. This time I am going to ask you to ask the question as well as give the answers: what question should I be asking? S: Okay. I: Have a look, I am just going to clap here [at opposite end of tube to candle — sound of clapping — candle flame is extinguished]. What happened; would you like to ask the question and then give me the answer. S: "Why did the candle go out?" would be the question. I: Okay. S: Okay, and what happens is: the sound disturbance that you created, the moving the air we talked about before, at that end [end of tube where clapping took place], because you have this tube here the, we said sound moves in all directions, I could hear it here without having my ear at the end of the tube, but you are constricting the air that you are moving down here [referring to the tube]. It all has to move in one direction and at the end here [of tube] you constrict it even further: you make it move over a smaller area: so it finally comes out here [end of tube closest to candle] moving, its just like blowing out a candle when you just do it with your mouth, just snuff it out. I: So if I filled this [the tube] up with smoke and did it then — what would it look like? Would I get a puff of smoke coming out the end? S: Yes. If you could put a coloured gas in here [the tube], something that you could see. You would see it clear at this end [end of tube where clapping took place] where the air moves in and you would see a little bit of the coloured gas come out at this end. I: Okay. S: There is no vacuum here [end of tube where clapping took place] because air from the outside comes in and it just moves it down and eventually moves out this end. I: If I put this [the tube] at an angle do you think I could get it to keep going? 205 S: How do you mean keep going? I: I have this air moving down the pipe, what stops it from carrying on? S: Well, you give it the initial impetus when you clap, right. That moves it once, and then it moves down. What we would normally consider as the sound dying out at that end — it would move down eventually in this direction [towards the other end of tube where candle was placed]. So when the initial push at that end stops everything goes back to normal, how ever it was before you clapped your hand. So there is nothing to keep the air going. I: Let's go back and look at our molecules, what were the molecules doing before I clapped my hand there. S: They were moving in a random fashion. I: Okay, then I clapped my hand? S: You force some of them to move in the direction down the pipe — I: Which then -- ? S: Hit others down the pipe and then they are a giant bumper car type process right down to the end, they come out and just keep going. I: Okay, what happens to the ones which come out the end? Okay, they blew out the candle and then what happened? S: Okay, they just keep ~ they collide with others and start dying out this time at this side. I: And eventually — ? S: The motion stops, they hit so many that it dies out. I: This always fascinates me. S: Oh it's a cute experiment. CONTEXT: COMPARE AND CONTRAST LIGHT AND SOUND I: Um, I am just wondering if you can try and think back to your physics now, and what you were telling me a little bit earlier on. If I look at the equations for sound - can you ever remember doing equations of sound and writing them down? S: Did do wave equations — I: Yea, okay -S: In so far as you talked about sound as waves, you talk about frequency and amplitude and wavelength. 2 0 6 I: Did you ever talk about sound not being a wave? S: [Large sigh] That's a good question. I can't ever remember talking about it not being a wave, personally. I: It doesn't -- ["S" interrupts]. S: I personally — I am the sort of person that says "never", um — I: Okay, what do you believe within yourself? S: I believe that sound is a wave. I: Okay, I am not trying to corner you into anything. S: But it's an interesting train of thought if I go back to what I said before about sound engineers trying to create something better than a speaker to transmit sound. If you view sound as something other than a wave then you should be able to transmit it some other way than they are, and that's an argument that I got into with my friend that was the sound engineer then — because he didn't have a strong physics background and I was a young and impressionable physicist at that point that was going to swear up and down that sound was a wave. I: Okay. Those wave equations, were did they come from?: how was the sound wave equation derived? S: I can't remember ever covering exactly how it was derived — I, you know, deriving general wave equations, um — I: Principles upon which it was derived? S: Well, um, the way I remember learning it is talking about the spring model of sound. Then you talk about moving back and forth and a sort of pseudo spring constant with his imaginary spring we see. We talked about deriving the equation like that [sounding very hesitant]. I: It appeared to me when I was looking through this physics book, if you look at the wave equations for light and for sound they look identical except for maybe variables. S: Hm, they are. I: How do you account for that? Are they same kind of thing? S: Um, they are not really the same kind of thing but all waves, anything that you want to describe as a wave or that moves as a wave you can describe using the same sort of equation. The only, you know, you can talk about sound waves, light waves, um, even ocean waves -- they have an amplitude, a speed, and a wavelength. You can describe any wave to that extent, so, if, to that point, yes, they are the same sort of thing with the exception that light moves a lot faster than sound, so that is your main difference. I: You started off saying — [pause] — If there was no air could we have sound? 207 S: No. I: If there was no air could we have light? S: Yes. I: You seem very firm about that, but the equations look the same? S: Okay, when talking about sound, sound needs to propagate, you are moving something, okay. The idea of light is, light is moving as a wave sure enough but it has little photons in it that are carrying this light energy and so it is sort of the difference between, um, you know — trying to think of a good comparison. What comes to mind is the thing between, you can spin a rock, well it's not a good example. Throw a rock through a vacuum and you have no problem, you know, this little, it's like a photon going through a vacuum, it has no problem. Now, if you don't have that rock or whatever to actually throw through it and you are relying on what's in between here and there to, um, to move it along and there is nothing there, there is no way it's going to get it through. That still doesn't make any sense but — [sounding perplexed "S" takes this no further]. I: One person that I spoke to previously said that to him, in physics, light and sound were the same thing because the equations were the same, yet in his everyday life he thought that they were separate — ["S" interrupts]. S: Well, you know, any wave can be described by a unique set of equations that are very much similar because all waves act similarly and, but how, what you are talking about, sound and light, how they propagate and what they propagate like, um — For example, light will propagate through a vacuum where sound won't, sound will propagate through solid objects where light won't, like if I hit that wall with a sledge-hammer you could stand on the other side and hear it, but if I took a flashlight up to that wall you would not see the flashlight on the other side, unless we had a very thin wall. So, those waves, because they are waves and they act, you know they are governed by the same equations, they wil l propagate differently through different things. Sound wil l propagate through certain things light won't and light will propagate through certain things sound won't. I: Do you think that you could apply the same laws such as reflection, refraction, diffraction? S: Um, yea. You would have then have to consider what you are reflecting and refracting through, um, you know you tend to want shine a light on mirrors and that will work. Um, I know the other thing that I was talking about, I was trying to think of, about, that was waves: radio waves, microwaves they are all waves, um, and they will transmit through. I've got a scanner in my car and I can receive things that are at high frequencies, relatively well — Yea, true you can take light and shine it through, shine it against a mirror and it will reflect back. Um, you can take sound and it will bounce of walls and things; I wouldn't, you can't say that, you know, take light and bounce it of a mirror and take sound and bounce it off a mirror. You have to consider that they are travelling at different speeds and that they are different. Although they act the same and are governed by the same equations they have different, um, properties, depending on what you want to use: whether you want to use a mirror, which is a shiny metal surface, a wall, a piece of glass. So you have to take that into account, but yes the refraction, reflection, all those laws should hold, yea. 2 0 8 CONTEXT: FACTORS AFFECTING SPEED OF SOUND I: Thank you for the eloquent explanations. I would like to ask you one more thing. Thinking about sound and something which you told me about earlier about the foghorns. Is the speed of sound constant? S: No. I: And light? Is the speed of light constant? S: No. I: They both aren't constant. Okay, lets look at sound for the moment. What would change the speed of, what factors affect the speed of sound? S: What it's moving through. I: How-why would that affect it? S: The density, like we talked about the density of the air. You can transmit sound through walls and the speed of sound through the wall will definitely be different to the speed of sound through air. It will move quicker through a more dense medium. I: Why would that be? S: Because there is more, the molecules don't have to travel so far to hit each other; so that they can react a lot faster. I: Suppose I heated up that media, would that have any effect? S: Well, i f you, you know, like with air, yes, because when you heat it up it becomes less dense and it will not transmit as well. I don't know whether it would make a really appreciable, it should, you know, it should make the same sort of difference with the wall but it may not be as noticeable. Usually when you heat up a wall it becomes less dense which is sort of -- although it should, the molecules should move faster and that sort of thing. I: You mean when I heat it up the molecules are moving faster? S: Yea. I: And — that will that affect the speed of sound? Is that what you are telling me? S: Well, it would affect the density which would affect the speed. I: Okay, if it was hotter it would be — less dense? S: Well, again it depends which medium you are talking about, with air — sure. I: And so, if it was less dense it would travel -209 S: Slower. I: Because the molecules have further to go before they collide with other molecules? S: Yea. I: Okay, just, um, in terms off how we started off with, thinking back to your own experiences. Do you have, um, do you have any other, besides those shock waves, vivid experiences of sound? S: Probably, yea, um, getting rattled when things fall and I guess if I really want to think back that far, um, a lot of the first experiences you have — you hear before you see because a sound over there will drive your attention to it — whatever's happening — I can't really pin point anything other than that. I remember a lot of things falling and, you know, dropping on the floor, hammering, sawing. I: I suddenly thought about something you introduced a bit earlier: you spoke about amplitude. How would you define amplitude of a sound wave? What would the amplitude of a sound wave be? S: How sharp the -- how big — well, how loud the sound was. I: And, how would that relate -- what would be the difference in the propagation of a soft sound and a loud sound? S: Um, well if you want to talk about sound as compression of say a spring or hitting the molecules the initial push would be slower. I: Slower? S: Yea, and that would be quieter. I: Okay, and a very loud sound? S: Would have a very fast jolt, like the balloon. I: Okay, and the next push? So the molecules would be travelling much faster? S: Initially yea. I: Only initially? S: Well, the initial push would be a lot faster over the two and that would correspond to the speed of — of the amplitude of the sinusoidal wave that we would draw because the speeds would be higher and that would follow all the way through the wave. I: So, all the molecules would be moving, down the wave, down the line, that will be moving — ? S: Faster, and also they would go further. 210 I: Okay, so if I am twice as loud, any feeling on how much faster they might be moving? S: Um, has a square law relation. Well, if you want to talk, like if — there is a square in there because if I am sitting lm away from you, for me to be able to hear you just barely, and if I park myself twice as far, 2m away, sound drops off as a square so you would actually have to talk four times as loud to reach twice as far. I: Any idea why it would drop off with the square of the distance? S: Um -- [long pause] — just trying to think of the equations of the sound wave [softly, almost to himself] — not off the top of my head I can't. I: I know that I'm drawing it out now but just one last thing. We spoke about the tuning forks and the intuitive size of the wavelength. Did you resolve that in your mind at all? S: Yea, because we were talking about a compression wave versus, you know, the initial speed of that fork moving back and forth is actually the amplitude of the wave. Okay, if we drew it as as a sinusoidal wave it's the amplitude of the wave and the wavelength is not necessarily just the distance it moves back and forth. I: So this big fork [approx 120Hz: sound of fork] has a much larger amplitude than this one [approx 600Hz: sound of fork]? S: Um, No. I: Oh, I thought that -S: Depends on, see it depends how fast, not how far they [arms of tuning fork] are moving but how fast they are moving. So if I did that [picking up tuning fork and striking it softly] it would be moving back and forth very slowly, that has a very small amplitude, now if I did that [striking the fork viciously] it is moving back and forth faster and like we said with the amplitude it's louder. It's moving back and forth faster so the amplitude increased so it's louder. I: So what would you say that the amplitude of this wave is [sound of tuning fork]. S: On a relative scale you mean? I: Aha . S: Relatively large. I: Yea, but in millimetres, centimetres, metres? S: Well, um, I don't think that you can describe it that way because when you were plotting the amplitude you were talking about the speed verse distance. I: So, what would you measure the amplitude in, metres per second? S: Um, yea, something of that order. 2 1 1 I: Are you uncertain when you say something of that order? S: Well, for a fork, yes, you could measure in speed, it all depends on what sort of sound units you are going to use, but yea with a fork I would describe it in a velocity. 

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