PHYSICS STUDENTS’ DEPICTIONS OF THE QUANTIZATION OF ENERGY

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CHAPTER 3 RESEARCH METHODOLOGY

INTRODUCTION

In chapter 2 the conceptual framework of the present study was presented but apart from the choice of appropriate theories there are also additional methodological considerations to take into account when doing research, for example, how to collect the empirical material and how to establish trustworthiness. Such methodological considerations are the focus of this chapter. This chapter presents justification of the research paradigm, the selected research methodology and provides a detailed description of the phenomenographic research approach and the rationale for its use in this study. The research design is presented, along with details of how the study is implemented, how the empirical data is collected and the reflections involved in the collection and treatment of the data. Furthermore, questions regarding the trustworthiness of the research and ethical considerations are also discussed.

RESEARCH PARADIGM

The word paradigm connotes the ideas of a mental picture or pattern of thought (Kuhn, 1970). According to Henning et al (1974), a paradigm is a framework within which assumptions are built, that fundamentally influences how we visualize the world, determines our perspective, and shapes our picture of how things are related. It is the identification of the underlying basis that is used to construct a scientific investigation; or, “a loose collection of logically held together assumptions, concepts, and propositions that orientates thinking and research” (Bogdan & Biklan, 1982, p. 30). A paradigm, according to Guba and Lincoln (1994), is defined as a system of philosophical beliefs that leads and governs an investigation. So, the research paradigm shapes the whole research process and gives valuable directions and principles about the approach, methods and techniques for conducting a research within its philosophical setting (Guba & Lincoln 1994). In the literature, two leading research paradigms are acknowledged by methodologists in many disciplines; i.e., the positivist and the interpretive paradigms (Patton 1990).
The positivism paradigm believes that human life is governed by generic laws (Denzin & Lincoln, 2000); thus, the people can be studied in a natural scientific manner (Smith, 1983). Positivists believe that reality is stable and can be observed and interpreted from an objective viewpoint, that is without interfering with the phenomena being investigated. Consequently, this epistemological standpoint relies heavily on measurements that epistemological framing needed for investigating some phenomenon (Krauss, 2005; Smith 1983). On the other hand, the interpretive paradigm’s emphasis is on holistic and qualitative information to provide rich insights into components of a phenomenon (Husen, 1988). The interpretive theorist views that the best way to understand the world is from the collective view points of the investigated participants (Husen, 1988). The study of phenomena in their natural environment is key to the interpretivist paradigm, together with the acknowledgement that scientists cannot avoid affecting those phenomena they study. This implies different modes of research to allow us to understand different phenomena and for different reasons (Deetz, 1996). The type paradigm selected depends on what one is trying to do rather than a commitment to a particular paradigm (Cavaye, 1996). Thus, the methodology employed must match the particular phenomenon of interest. Different phenomena may require the use of different methodologies.
The main objective of the principal study in this thesis is to investigate “What depictions of the basic concepts of quantum mechanics do a group of undergraduate physics students have, if any?” Accordingly, the research problem is descriptive rather than prescriptive, which require a theory-building approach (inductive) rather than a theory testing one (deductive). Therefore, the qualitative/interpretive paradigm is more suited than the positivist paradigm (deductive) because the research is concerned with picturing the actual 45 world of investigated phenomena rather than providing statistical details about the cause-effect relationships between variables within the examined phenomena. Constructivist qualitative/interpretivist research avoids the quantification of learning and focuses instead on the categorization of true nature and diversity of individual understanding. It is from this qualitative/interpretivist perspective and the assumptions described above that the study of the depictions of quantum concepts among physics students has its philosophical basis.

QUALITATIVE RESEARCH METHODOLOGY: THE PHENOMENOGRAPHIC PERSPECTIVE

The selection of research methodology is consistent with the selected research paradigm and dependent on the nature of the investigated phenomena, the type of the research questions, the research population and the expected outcomes of the research (Cavaye, 1996; Patton, 1990). The qualitative research methodology is, therefore, selected as having epistemological associations with the philosophical assumptions of the interpretive paradigm explained above. In most cases, qualitative research includes any research that produces findings that are not derived by statistical procedures or other means of quantification. The aim of qualitative research is primarily to gain insight into the individual’s subjective interpretative patterns, experiences and positions (Ueltzhoffer & Ascheberg, 1999). Denzin and Lincoln (2003) also suggest that qualitative research is most interested in processes and meanings that are not experimentally examined. A qualitative approach allows the research participants to speak for themselves as well as their ways of experiencing phenomena. This can be achieved through interviewing individuals and directly asking them questions about how they arrange their world, the researcher enters those persons’ worlds and perspectives, thus, discovering what is on their mind (Patton, 1990).
In this study, the investigation is directed at eliciting undergraduate physics students’ depictions of the basic concepts of quantum mechanics and constructing the description categories which form the basis of their ideas. Explicitly, the study was aimed at exploring the range of qualitatively different ways of depicting the basic concepts of quantum mechanics within a sample group of physics students as a group. As a result, this primary focus on the collective variation made it likely to choose phenomenography as a qualitative research approach. As it has been discussed in section 2.2.4, phenomenography was seen as the most appropriate qualitative approach for this study because it is a research specialization aimed at revealing different ways in which students see, experience, understand and depict various phenomena in the world around them (Marton & Booth, 1997). It is also found that phenomenography can be understood as an analytical framework to gain an empathetic understanding of physics students’ depictions of quantum mechanics. Therefore, the phenomenographic approach was employed in this study. However, it is not a pure phenomenographic approach. Principally, in this study, the interest in phenomenography has much in common with the developmental interest described by Bowden (1995; 2000). Bowden (1995, p.146) elaborates his idea of developmental phenomenography as: “The phenomenographic research that I engage in is situated within a particular kind of context. I focus on research which, through finding out how people experience some aspect of their world, will enable them or others to change the way their world operates, normally in a formal educational setting. My perspective is developmental. My reasons for undertaking the research are concerned with how I can use the research outcomes to affect the world I live and work in.” Therefore, the outcomes of the developmental phenomenographic research, the different conceptions that students grasp (e.g., students depictions of the photon concept, the wave-particle duality, the uncertainty principle) may be informative to teacher-researcher who is developing ways of helping their students understand a phenomenon under investigation from a particular perspective. In this type of research approach, the preferred method of data collection is the semi-structured interview (Bowden, 1995; Marton & Booth, 1997), although other methods have been used (e.g. collecting written comments or filming group work). The semi-structured interview depends on a limited number of predetermined questions, but has an open structure, where the interviewee is encouraged to talk over all thoughts and ideas that come to mind. This type of an interview therefore provides a rich way of exploring the ways in which a set of students conceptualize, depict or conceived the phenomena under investigation. Bowden and his associates have carried out a number of studies into student learning in various topics of physics using a developmental phenomenographic approach (Bowden et al., 1992; Walsh et al., 1993). Bowden et al, for example, used this research methodology to investigate students’ understanding of displacement, velocity, and frames of reference. The researchers interviewed a number of undergraduate students about their conceptual understanding of these particular physics concepts, encouraging the participants to give full descriptions of their conceptual understanding. Participant students’ interviews were then transcribed and subjected to phenomenographic analysis. The description categories that represented the qualitative variations in conceptions were drawn from the data, with the focus on the students’ meaning rather than on particular sentences.
The main emphasis in this study is set in the aim of developmental phenomenography (i.e., to understand the qualitative variation in the ways that undergraduate physics students depict the basic concepts of quantum mechanics so that teaching practice can be meaningfully informed in ways that potentially enhance learning outcomes). This developmental phenomenographic approach, and the methods and procedures used and developed by these researchers (e.g., Bowden et al., 1992; Bowden, 1995; Marton & Booth, 1997), was adapted to undertake the research presented here.

QUALITATVE RESEARCH DESIGN AND PROCEDURE

Kinnear and Taylor (1996) proposed that a research design is a basic plan that guides the data collection and analysis phases of the research project. Research design provides the framework that identifies the type of data to be collected, its sources, and the collection procedure. This study has been introduced as a phenomenographically based study. Bowden (2000) summarizes the phenomenographic study process as having four stages:
plan, data collection, analysis and interpretation. In all of these stages, the researcher must maintain focused on the principal aim of the study. This is vital to consider for obtaining trustworthy results (see Section 3.5). Obviously, what drives the phenomenographic research is an underlying question that the research process tries to address. Thus, describing the research design and procedures are much more tangible. Many pragmatic questions had to be answered during this stage: How will data collection instruments be constructed? From whom will data be collected? How will subjects be selected? How will data be collected? How will data be analyzed? It was well decided that the methods employed in this study are qualitatively-based, and data are collected through in-depth semi-structured interviews with undergraduate physics students taking quantum mechanics. For this reason, it was necessary to plan and organize appropriate research procedures and data collecting instruments (the semi-structured interview questions). To this end a preliminary research project was conducted based on the study setting. The preliminary phase study was implemented for two reasons: First in order to uncover which concepts are considered most important in the undergraduate quantum mechanics so that physics students need to understand to learn quantum mechanics; and secondly, using this earlier work as the basis of a fact finding study, it was expected that the results would provide valuable information, allowing the researchers to make informed judgments concerning the form and content of the instruments (the interview questions) used later in the main study.

Preliminary Study for Designing Interview Questions

This section describes the procedure and setting of the preliminary research project plan. It has already been noted that, the major goal of the preliminary studies were: to identify the key concepts that undergraduate physics students need to understand in order to learn quantum mechanics and from that to determine content areas for preparing and organizing the semi-structured interview questions. In order to uncover which key concepts are considered most important in the undergraduate quantum mechanics, analyses of the current undergraduate physics program course syllabuses ( first year Modern Physics and the second year Quantum Mechanics I courses) from two universities in Ethiopia (Wollo University and Bahir Dar University) were undertaken. The analyses were conducted as follows:
• The key topics which have been taught across the two universities in Modern Physics and Quantum Mechanics I courses were identified.
• The frequency of these key concepts appearing in the syllabuses were ascertained
• These topics were categorized into basic concepts of quantum mechanics
Nevertheless, only analysis of course syllabuses cannot perfectly indicate which key concepts are important for the introductory quantum mechanics. Thus, the Delphi technique was also applied to ask experts from the Department of Physics at Wollo and Bahir Dar Universities considering the significance of these concepts to the teaching and learning of quantum mechanics at tertiary level. From these iterative processes (i.e., the analysis of course syllabuses and consensus among physics experts), the basic concepts that students need to learn quantum mechanics successfully were categorized under two major themes: Light and Matter. The two major themes and these basic quantum mechanics concepts under each theme are presented in Table 3.1.
Consequently, predetermined interview questions used to explore physics students’ depictions of quantum mechanics were organized under the five basic quantum concepts: Quantization of energy, the photon concept, light quanta, matter waves and uncertainty principle. We have conducted pilot interviews on initial versions of the predetermined interview questions with undergraduate students. In this stage, five physics major students with similar backgrounds to the students involved in the main study, volunteered to become involved in the pilot study interviews. These interviews helped us to modify the wording of the predetermined interview questions, understand student thinking, and eliminate some questions that were not serving their intended purpose. Finally, all of the recent versions of the interview questions were reviewed and commented by two experts who have experiences with teaching undergraduate quantum mechanics courses. The final version of the predetermined interview questions are presented in Appendix I. The interview questions were also presented in the analysis in Chapters 4 and 5 to accommodate the results and findings. Section 3.4.3.1 elaborates more on the interview procedures.

Undergraduate Physics Student Sample

The sample sizes reflected in phenomenographic studies are consistent with other qualitative studies. Researchers suggest that qualitative research usually involves much smaller sample sizes than in quantitative research (Strauss & Corbin, 1998). In phenomenographic research, a sample of between 15 and 25 is considered to be sufficient, without becoming unwieldy, to reveal most of the possible viewpoints and allow a defensible interpretation (Trigwell, 2000b). Developmental phenomenographic studies cite larger sample sizes of between 25 to 30 participants that could be interviewed in a block of time (Bowden & Green, 2005). In general, in phenomenographic research, the predominant method for collecting the data is through semi-structured interviews with students, and the researcher must select the students carefully and consider why they are a good choice.
This study involved interviewing 35 second year physics major students from an undergraduate physics program in two government universities (Wollo and Bahir Dar Universities) in Ethiopia, about their depictions of the basic concepts of quantum mechanics. The program is a three-year degree physics program identical across all higher education institutions in Ethiopia. The classroom setting is a predominantly traditional manner (“relying primarily on passive-student lectures, recipe labs, and algorithmic-problem exams” (Hake, 1998), although the lecturers are different (see Section 1.5). In general, ‘Maximum variation sampling’ a strategy for purposeful sampling was considered in selecting these interviewees (Patton, 2002). This approach was taken because phenomenographic methods work best with a variation in understanding. For example, interviewees were carefully selected from two universities (i.e., 18 students from Wollo and 17 from Bahir Dar Universities) to obtain variation and quality in the interviews. All the sample physics students had gone through a course on Modern Physics in their first year based on Beiser’s (2002) well-known textbook on the subject in both universities (see section 1.5). The competency levels of the students in Modern Physics and concurrent physics courses were not tested, but this can be gauged from the following: (a) out of the 35 physics students, thirteen had got “A” grade and twenty two had got “B” grade in the preceding full-semester course on Modern Physics mentioned above and (b) all of them had successfully completed other concurrent undergraduate physics courses in their first year. On average, the interviewees scored marginally higher than the class mean grade on Modern Physics course in both universities, indicating that they were generally better than average students, as might be expected for a group of volunteers. In 2011/12, these students were all enrolled in their second year of a second semester courses in the undergraduate physics program. During this time, they had been exposed to the traditional approach to Quantum Mechanics I, a three-credit quantum mechanics course, for one third of a semester. Thus, before the phenomenographic interviews were conducted, they had been introduced to the basic quantum concepts (i.e., included on the phenomenographic interview questions) and some postulates of quantum mechanics necessary to follow the remaining quantum topics and concurrent physics courses.

Data Collection

The methods selected, in this study, support the developmental phenomenographic orientation. In the developmental phenomenography, the semi-structured interview is regarded as the preferred data collection method, with an emphasis on providing open-ended questions that encourage the participants to express their own perspectives (Bowden, 2000; Bowden & Walsh, 2000). The phenomenographic interviews were designed to obtain a qualitative description of the conceptual understanding of the interviewee. As discussed, in this study, data was collected using the phenomenographic interviews (i.e., semi-structured interviews) since the aim is to find categories of qualitatively different ways of depicting the basic concepts of quantum mechanics. The phenomenographic interview questions were designed based upon the analysis of the preliminary study which preceded this study (see Section 3.4.1). Thus, the major sources of data used for analysis in this study were from the phenomenographic interviews, which included qualitative problem solving, reasoning tasks, explaining the observed phenomena and interpretations for their observations and questions probing student way of using quantum mechanical ontology in explaining microscopic phenomena. In the next section (Interview Protocol), the two themes (i.e., Light and Matter) involving the five basic concepts of quantum mechanics and some of the interview questions are presented.
In both universities, the interviews were held in a physics laboratory and a small meeting room with closed doors to assure privacy. The research interviews were conducted in person, with the interviewee’s consent, and were digitally audio-recorded. The length of the phenomenographic interviews in the various studies has varied. In this study, the interviews took between 45 and 90 minutes to complete. All interviews were conducted in English. It was important to spend time in conversation with the interviewees prior to conducting the formal interview and the audio recording thereof to put the students at ease and to offer them a safe and comfortable atmosphere in which to speak. The time before the main interview allowed for a clarification of the purpose of the study and for the interviewee to obtain a pre-knowledge of the subject matter being investigated, including necessary definitions. For example, in this phase of the interview, it was emphasized that the interview was not meant to be an examination of their quantum mechanics knowledge but the interviewer wanted to characterize how the different contexts led them to think about quantum phenomena.
During the interview, the students’ were allowed to proceed at their own pace, occasionally interjecting prompts or questions to probe students’ thinking. These interjections were usually minimal and clarifying in nature, such as, “what do you mean by that?” or “can you explain that more?” In all times, students were free to explain their understanding of quantum phenomena in written and diagrammatic/graphical forms. But they were urged to think aloud as they answer the interview questions in written explanations and diagrammatic/graphical forms and, in particular, to articulate the reasoning they are using to arrive at their responses. At the end of the interview, the students were also asked to clarify issues they had not made clear in their earlier explanations.

TABLE OF CONTENTS
DECLARATION
ABSTRACT
ACKNOWLEDGMENTS
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
CHAPTER 1 INTRODUCTION
1.1 BACKGROUND OF THE STUDY
1.2 THE RESEARCH PROBLEM OF THE STUDY
1.3 RESEARCH QUESTIONS
1.4 SIGNIFICANCE OF THE STUDY
1.5 CONTEXT AND SCOPE OF THE STUDY
1.6 TERMINOLOGY USED IN THE THESIS
1.7 LAYOUT OF THE THESIS
CHAPTER 2 LITERATURE REVIEW AND FRAMEWORK OF THE STUDY
2.1 LITERATURE REVIEW
2.2 THEORETICAL FRAMEWORK OF THE STUDY
CHAPTER 3 RESEARCH METHODOLOGY
3.1 INTRODUCTION
3.2 RESEARCH PARADIGM
3.3 QUALITATIVE RESEARCH METHODOLOGY: THE PHENOMENOGRAPHIC PERSPECTIVE
3.4 QUALITATVE RESEARCH DESIGN AND PROCEDURE
3.5 TRUSTWORTHINESS IN THE STUDY
3.6 ETHICAL CONSIDERATIONS
CHAPTER 4 PHYSICS STUDENTS’ DEPICTIONS OF QUANTIZATION, THE PHOTON CONCEPT AND LIGHT QUANTA INTERFRENCE
4.1 INTRODUCTION
4.2 PHYSICS STUDENTS’ DEPICTIONS OF THE QUANTIZATION OF ENERGY
4.3 PHYSICS STUDENTS’ DEPICTIONS OF THE PHOTON CONCEPT
4.4 PHYSICS STUDENTS’ DEPICTIONS OF LIGHT QUANTA INTERFERENCE
4.5 DESCUSSION OF THE DESCRIPTION CATEGORIES
4.6 PHYSICS STUDENTS’ WAYS OF DEPICTIONS OF QUANTA AS THE CONTEXT OF EXPLAINING CHANGES
4.7 CHAPTER SUMMARY, CONCLUSIONS AND IMPLICATIONS
CHAPTER 5 PHYSICS STUDENTS’ DEPICTIONS OF MATTER WAVES AND THE UNCERTAINTY PRINCIPLE
5.1 INTRODUCTION
5.2 PHYSICS STUDENTS’ DEPICTIONS OF THE QUANTUM MODEL OF MATTER WAVES
5.3 PHYSICS STUDENTS’ DEPICTIONS OF THE UNCERTAINTY PRINCIPLE
5.4 DISCUSSION OF THE DESCRIPTION CATEGORIES
5.5 CHAPTER SUMMARY AND CONCLUSIONS
CHAPTER 6 ADDRESSING CONCEPTUAL DIFFICULTIES BY INTRODUCING MULTIPLE REPRESENTATIONS OF QUANTUM PHENOMENA AND USING INTERACTIVE TUTORIALS
6.1 INTRODUCTION
6.2 THE CASE STUDY
6.3 THE COURSE STRUCTURE, CONTENT AND STUDY CONTEXT
6.4 EMPHASIS AND SEQUENCE OF THE MULTIPLE REPRESENTSIONS-BASED INSTRUCTIONS AND THE INTERACTIVE QUANTUM TUTORIALS
6.5 METHODS AND PROCEDURES FOR DATA COLLECTION
6.6 DATA ANALYSIS
6.7 RESULTS AND FINDINGS
6.8 STUDENTS’ TYPES OF CONCEPTUAL UNDERSTANDING
6.9 The Nature of Physics Students’ Conceptual Pathways of Quantum Mechanics
6.10 DISCUSSIONS AND CONCLUSIONS
CHAPTER 7 CONCLUSIONS, IMPLICATIONS AND FUTURE CONSIDERATIONS
7.1 INTRODUCTION
7.2 CONCLUSIONS TO PART I OF THE STUDY
7.3 CONCLUSIONS TO PART II OF THE STUDY
7.4 IMPLICATIONS OF THE STUDY
7.5 FUTURE CONSIDERATIONS OF THE STUDY
REFERENCES
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