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CHAPTER 4 DEVELOPMENT OF RESEARCH QUESTIONS : GROUNDED THEORY APPROACH 4.1 INTRODUCTION This chapter describes the investigation that lead to the development of the set of interview questions that formed the primary research instrument for this study. The grounded theory approach with its constant comparison techniques was adopted, which allowed emerging ideas to guide the study. The final questions and their sequencing were grounded in the data collected from a range of sources including concept maps, expert interviews, examination scripts and preliminary student interviews. Through the recursive processes of open and axial coding each data source provided a set of categories which were carried forward to the selective coding phase. The selective coding phase was adapted to isolate underlying themes, identify question topics and allow informed judgements to be made on the appropriate sequencing of the interview questions in the final instrument. For a detailed account of this stage of the study please refer to Appendix 2. Once a set of interview questions was agreed upon the analysis shifted from a grounded approach to a more focused study that employed a phenomenological approach reported in Chapter 5. 4.2 SOURCES OF GROUNDED DATA This study was conducted within the Schools of Chemistry and Physics at the University of Sydney. These Schools contained many potential sources of data that could be used to ground this study. The researcher drew upon four main data sources some of which already existed and others that could be readily collected. 1) The first source was a formative assessment task that had been used with intermediate physics students during a quantum mechanics course. Associate Professor Ian Johnston had designed a concept mapping task to examine the links 54 55 students made between key concepts in quantum mechanics and 67 student concept maps were selected as a data source for this study. 2) It was recognised that the academic staff from the Schools of Physics and Chemistry were a valuable source of knowledge and experience. A large proportion of academics were involved with research and possessed industry links as well as curriculum design, course delivery and assessment of student learning in quantum mechanics or related fields. A number of academics were invited to participate in expert group discussion/interviews and these became the second data source for the study. 3) The third data source was based on the strong recommendation of a number of academics involved with teaching quantum mechanics. A collection of existing summative assessment tasks on quantum mechanics examinations completed by junior and intermediate physics students were made available. Of these tasks 137 examination scripts were selected and used in the study. 4) The final source of data consisted of the experiences and knowledge of students studying quantum mechanics. Students were invited to participate in preliminary interviews and their observations, responses, discussions and opinions were used to inform the study. Also the interviews provided a testing platform for the development of the final instrument. The analysis phase of these four data sources resulted in a small number of identified categories, which emerged from the open and axial coding process; to be fed into the third selective coding step of the grounded approach. The selective coding process identified three core categories which became the overarching themes that linked the final set of categories to one another. 4.2.1 Concept Maps In 1999 a concept mapping exercise was distributed to 67 intermediate University of Sydney physics students who had just completed their second year quantum mechanics lecture series. The exercise asked the students to draw a concept map showing how they think the provided list of concepts related to one another. The exercise required the construction of a concept map using the nineteen labels provided. Students were given a general concept mapping instruction sheet 56 to assist those who were not familiar with or had not previously drawn a concept map, and were given 20 minutes to prepare a response. The exercise was designed to elicit the students’ understanding of the relationships between the terms used in the context of quantum mechanics. The nineteen concept labels were presented in alphabetical order and they were: atom, diffraction, electron, energy, energy level, frequency, intensity, interference, light, mass, matter, momentum, orbit, particle, photon, probability, uncertainty principle, wave and wavelength. Figure 4-1 shows an example of a student’s concept map. Example of Student Concept Map Figure 4-1 : Copy of Student Concept Map (Student ID 21). This map shows the “wheel linked to another wheel” structural type. Reduced from original A3 with the labels and header instructions cropped (Please refer to Appendix 2, Figures A2-1 through A2-4 for details of the complete concept mapping exercise) The analysis of the concept maps focussed on classifying the structure of each map and identifying nodes. Drawing upon the work of Cronin, Dekkers and Dunn (1982) and Bailey and Butcher (1997) a set of nine concept map structural types were identified. The maps were then classified using these types. The nine types are illustrated and described in Table 4-1 along with the number of maps. 57 Concept Map Structure Types Map Type String String with a wheel attached Hierarchy Illustration Description Three or more concepts are linked in a single chain Four or more concepts are linked in a single chain with a wheel structure attached at one end Concepts are arranged in a simple tree type structure. Complex Cross-linking between the concepts to form an associative network Complex with a wheel attached And associative structure with an obvious wheel structure attached Wheel A number of single concepts emanate from a single concept Wheel linked to another wheel Two concepts with a number of joining radial links Bubble Loops Several string structures that form closed loops Disjoint The concepts are arranged into two or more separate structures Table 4-1 : Concept Map Structural Types and Results Summary (n=67) (n) % (1) 1% (7) 10% (16) 24% (6) 9% (20) 30% (2) 3% (12) 18% (2) 3% (3) 4% 58 The nodal analysis process examined the number of links emanating from each concept label. The majority of the maps possessed one or more concept label nodes which had a large number of links to other concept labels. The identification of these nodes provided information about which concepts the students considered as key focus ideas that they linked to other concepts. For a full description of the data collection and analysis please refer to Appendix 2 (pages A2-2 through A2-12). Following is a summary of the three categories that emerged from the concept map analysis, and were carried forward to the selective coding phase. 1. Wave Particle Duality - Concept maps showed a strong separation between particle and wave. This suggests that the idea of wave/particle duality is a dominant feature of students’ understanding of quantum mechanics. 2. Uncertainty - A significant variation in where students see uncertainty fitting into quantum mechanics was evident. For some students their understanding appeared weak and others associated uncertainty with a range of different concepts and contexts. 3. Mathematics - For some students mathematics is an integral component of the structure of quantum mechanics. 4.2.2 Expert Group Discussions/Interviews Several focus group discussions with physics and chemistry lecturers from the University of Sydney were planned. Whilst I received positive responses to my discussion invitations, timetabling constraints meant that only one focus group discussion was conducted. Instead fourteen individual interviews were scheduled to ensure the views of all the experts were heard. The Expert Focus Group Discussion The focus group consisted of four lecturers, all of whom were from the School of Chemistry, and the interviewer. All of the lecturers have taught senior chemistry options which encompassed components of quantum chemistry. Prior to commencing the discussion the lecturers were provided with a list of discussion points which included learning, teaching, difficulties, experiments, analogies, 59 mathematics, models and assessment strategies. These were developed from diary entries from preliminary discussions (Please refer to Appendix 2 - Figure A2-6 for a copy of the discussion points). A free-flowing group conversation followed with only a minimum of guidance required to cover the discussion points. The discussion was at times lively as the lecturers debated their views of various points. The tape recording of the discussion was immediately transcribed and the researcher reviewed the data and made a series of reflective notes. These reflective notes along with selected extracts of the transcript were the basis of presentations given to the Sydney University Physics Education Research (SUPER) group and the Science Faculty Education Research (SCIFER) group. The discussions that followed these SUPER and SCIFER presentations assisted the researcher in developing a theoretical sensitivity towards this type of data. The Individual Expert Interviews A total of fourteen individual interviews were conducted. The two chemistry lecturers have a research background in theoretical chemistry. The physics lecturers have a variety of research backgrounds including theoretical physics, applied physics, high energy physics, physical optics, astrophysics and physics education. All lecturers had previously taught quantum mechanics at junior, intermediate or senior level. Although the dynamics and debate of a group discussion was lost, the interviews produced fourteen detailed and rich responses as a data source. At the request of the lecturers who wished to provide considered responses at the interview, a set of guide questions was developed. The questions were developed from the grounded theory analysis of the existing data sources including the concept maps, examination scripts, focus group interview and discussions. The results comprising categories, emerging ideas and themes identified formed the interview questions topics. These guides were provided to the lecturers at least two days prior to the scheduled interview. (Please refer to Appendix 2 - Figures A2-7 and A2-8 for copies of the Lecturer Guide Questions) The interviews were conducted at a time convenient to the lecturer in their own office. A portable tape recorder was used to record the interview. Interviews were scheduled for approximately 50 minutes duration, the actual time taken varied from 40 to 92 minutes. Each interview was slightly different in its tone, pace and 60 conversational style. All interviews were relaxed and free-flowing. At times the researcher prompted and narrowed the conversation to probe specific issues. The tapes were immediately transcribed so I could read through the transcripts and make reflective notes providing me with cues and reference points in the data for later perusal. Each transcript was open coded producing many categories, and then axial coding was employed to reveal the following eight categories: Teaching Approach, Key Concepts, Assessment, Perceived Difficulties, Maths, Analogies, Computer Simulations and Experiments. Some of the categories were attitudinal, others were quantitative (contained a list). For example Maths contained the lecturers’ views on the importance of mathematics to quantum mechanics, while Key Concepts contained a list of concepts identified by the lecturer as important to quantum mechanics. For a full description of the data collection and analysis associated with these eight categories please refer to Appendix 2 (pages A2-23 through A2-35). Upon further analysis, comparison and consolidation the following five categories emerged from the expert interview analysis, and were carried forward to the selective coding phase. 1. Real world – Students experience difficulties solving unfamiliar problems and linking theory, experiment and application. Experts agree the purpose of quantum mechanics is to understand and explain ‘real world’ phenomena and students should be able to do this. The experts identified linking quantum mechanics to the real world as a key concept and as a teaching approach. 2. Duality – Identified as a key concept in quantum mechanics. Students have difficulties progressing past a classical view of either a wave or a particle. The experts feel that teaching does not provide a resolution to the duality paradox and the concept is not revisited in later years. 3. Uncertainty – Identified as a key concept in quantum mechanics. 4. Analogies – Some experts find analogies to be a useful teaching and learning tool in quantum mechanics. Others find analogies inadequate and confusing and prefer to use examples of experiments instead. 61 5. Mathematics – Experts feel that students must have the necessary mathematics skills to succeed at quantum mechanics. 4.2.3 Examination Scripts During the expert interviews, several lecturers referred to students having difficulties with qualitative or interpretative questions in examinations and assignments. Three lecturers strongly suggested a review of student examination scripts might be of use to this study. A senior academic from the School of Physics who was unconnected with this study randomly selected 137 Junior and Intermediate examination scripts. These scripts were then photocopied so there was no student identification remaining. The scripts were analysed on their contents only, cross-referencing to other student details was not possible. In consultation with senior lecturers from the School of Physics who had a role in setting and marking these examinations, six questions were selected for analysis. Three from the junior physics examination and three from the intermediate physics examination. The six questions had qualitative and quantitative sub-components and covered a range of key concepts identified by the expert interviews. These were basically back-of-chapter textbook in style and content and addressed the following: de Broglie wavelength; quantisation; ground state; tunnelling; normalisation constant; Heisenberg’s uncertainty principle; Compton scattering; and the interpretation of graphical and tabulated data. As researcher I was not concerned with the correctness of the responses instead I was interested in the question “What does the student think is important for the examiner to see?” and how much variation in responses was present. Each question was analysed using a phenomenographic approach to reveal aspects of variation within the student responses. The responses to each section of the questions were reviewed, coded, categorised and tabulated. (Please refer to Appendix 2 - Tables A2-9 through A2-34 for the coded datasets, commencing on page A2-47). The correctness of the student response was tabulated along with other features that emerged from the analysis. This did not influence the phenomeographic approach, however it did provided a framework in which to group and present the finalised tabulated categories. 62 Following are a selection of interesting observed features identified in the responses provided by the First and Second Year students. First Year examination Scripts de Broglie Students were asked to compare the de Broglie wavelength for an electron and a proton with the same speed, kinetic energy and momentum. The students demonstrated two ways of presenting their answer: 1. using mathematical formulae and inequality signs to show mathematical relationships for the electron and proton 2. using a written description to articulate the differences between the electron and proton. Many students had difficulties with the relationship between momentum and kinetic energy. Approximately three quarters of the students successfully answered in relation to speed and momentum but only one third gave a correct answer for kinetic energy. Most students had difficulties manipulating the formulae for de Broglies’s wavelength into a form that allowed them to see a relationship between kinetic energy and wavelength. Terminology Approximately one quarter of students did not give a meaning for the terms quantised and zero point energy. The concept of quantised energy was identified as a key concept in the expert interviews and from the data it appears that only 43% of students can correctly define the term either in terms of energy or more generally. All but two students were able to give a meaning for the terms ground state and excited state. Students seem to recognise these terms and can successfully define them. 63 Application of Quantised Energy Students were required to use a quantised model of a confined electron to explain a related example concerning the ability to obtain absolute zero. Just over half of the students successfully linked electron energy and motion at absolute zero, but 30% of the students did not respond to this part at all. Heisenberg’s Uncertainty Principle Students do not seem to know the formulaic representation of Heisenberg’s Uncertainty Principle, 20% of students did not include a formula in their response and 65% gave a formula that was incorrect. Most of the mistakes came from the equality/inequality sign of the formula with students using , , and =. This suggests there is some confusion with the relationship between momentum, position and Planck’s constant. Regardless of whether the formula was stated or not 76% of students gave an answer that suggested a connection between momentum and position of a particle and how this limited the measurement of either quantity. Only two students suggested that a classical meaning of uncertainty related to an error in measurement. The terms ‘accurately’ and ‘precisely’ were used by 30% of students but it was unclear what meaning is given to these terms. Students were asked to extend the concept of uncertainty to the macroscopic world and explain it in this context. The student responses suggest that 63% think that uncertainty relates to all objects regardless of size, while 20% think it only relates to microscopic objects. In the macroscopic context the proportion of students relating uncertainty to classical measurement error was 42%. This compares to only 4% when the students were describing the uncertainty formula. Second Year Examination Scripts de Broglie All students within the sample attempted the question asking them to describe de Broglie’s wavelength of a particle. Written descriptions included references to the wave/particle nature of electrons and the motion of particles and waves. Some students linked the de Broglie wavelength to electron orbitals. Some students drew sketches of wave packets and 53% of students included the formula h in their response. p 64 The second part of the question which asked for a description of an experiment to measure de Broglie’s wavelength proved to be more troublesome, 29% did not state an experiment at all and 12% described another quantum mechanics experiment (e.g. photoelectric effect). The most popular group of experiments described were ones that caused wave interference (e.g. double slit or single slit diffraction), 30% of students gave this response. Compton Scattering Analysis of this question revealed that students were not overly familiar with the Compton scattering experiment, 37% of Normal and 29% of the Advanced stream students confused Compton Scattering with another experiment (e.g. photoelectric effect or double slit) others gave a variety of experimental descriptions including in their responses a range of electromagnetic waves and a range of targets. When asked to describe the interaction that occurs between photons and electrons in Compton shifting, 63% of Normal stream students described classical wave behaviour (reflection, diffraction, scattering etc) then they used this to justify the particle nature of light. 24% of Advanced stream students described the classical particle phenomena (collisions transferring momentum and transferring kinetic energy) and 37% described classical wave phenomena (reflection, diffraction, scattering etc). Tunnelling In describing tunnelling, students gave somewhat mixed answers. The majority of responses (65%) described particles as the entity doing the tunnelling a particle ‘penetrates’, ‘burrows’ or ‘leaks’. Some students (10%) referred to the wave function tunnelling and 4% described electrons tunnelling. All students stated that either a well or a barrier was what was tunnelled through. To accompany their descriptions 50% of the students drew pictures. The pictures they drew in some cases contradicted their written description, for example, 28% of students drew pictures of wave functions tunnelling and only 13% drew pictures of particles tunnelling. The Advanced Stream were asked to explain the significance of tunnelling to nuclear reactions in stars. This question required the application of tunnelling to a real world example. The students’ description or explanation of tunnelling was in terms of a proton or alpha particle crossing a potential barrier to result in fusion. 65 Most students attempted to reconstruct the four-step hydrogen fusion process and this made up the bulk of their answer. Wells Students, when provided with graphical and tabulated stimulus material on wave functions and potential diagrams, could without difficulty interpret the material and determine the eigenstate and the probability distribution. For a full description of the data collection and analysis please refer to Appendix 2 (pages A2-36 through A2-72). The following three categories emerged from the examination script analysis, and were carried forward to the selective coding phase. 1. Real world – Use of real world examples illustrated gaps, inconsistencies and misconceptions in student’s understanding of quantum mechanics. These problems were not noticeable when students were asked similar questions in a theoretical context. In futher studies, real world examples (e.g. radioactivity) could be used as a tool to probe student understanding in an interview. 2. Duality – Students do not seem to match the correct classical behaviour to waves and particles. Many of them use wave behaviour as evidence of particle nature. There appears to be no conceptual shift from a wave-orparticle view to a wave function view. 3. Tunnelling – Students appear to be familiar with the terms, diagrams and graphs, associated with potential wells and barriers diagrams and wave functions. However their explanation of tunnelling which brings together all of these tools, is patchy and expressed in terms of a particle model rather than a wave function or probability model. Their proficiency with the tools hides their lack of understanding of the physical situation. 66 4.2.4 Preliminary Interviews The preliminary interviews served two purposes; as a source of data for the grounded theory stage of the study, and an opportunity to trial and refine the interview protocol leading to the development of the final interview instrument. In all, 17 preliminary interviews were conducted. These interviews drew on issues that were emerging from the other data sources (concept maps, examination scripts and expert discussion/interviews). The initial preliminary interviews were unstructured or recursive in nature and, as more were completed, they became semi-structured, with the aim of progressively focusing the interview towards the final interview instrument. This section describes and reports the grounded theory analysis and the identification of categories to be carried forward to the selective coding phase. The analysis relating to the development and refining of the interview protocol including trialling question types, question order, selection of opening and closing questions is reported in Section 4.3 ‘Development of the Final Interview Instrument’. 4.2.5 Analysis of Data Collected Each interview was transcribed from tape immediately following the interview and formatted according to the protocol defined in Chapter 3. The interview transcript was first annotated with reflective notes in the Personal Log column and then analysed using the grounded theory iterative process of open and axial coding to reveal categories. Key statements, preliminary ‘in vivo codes’ and emerging ideas identified during this phase of analysis were recorded in the Analytical Log Major Point column. Once the final iteration of axial coding was complete the final set of major categories was used to re-code the entire transcript. These codes were recorded in the Analytical Log Category Coding column. Please refer to Figure 4-2 for and example of a Preliminary Interview Transcript Cover Page and Figure 4-3 Preliminary Interview Transcript Page. 67 Preliminary Interview - Transcript Cover Page Figure 4-2 : Representative Preliminary Interview Transcript – TED Page 1 Cover Page Preliminary Interview - Transcript Page Figure 4-3 : Representative Preliminary Interview Transcript – TED Page 4 68 A detailed personal log and analytical log was then written for each interview. The personal log is an instrument for recording reflective notes and highlights areas for improvement and development of the interview process. The analytical log is an instrument which provides a format and forum in which to identify trends and ideas; then allow for common elements to be identified and condensed, the identification of relationships between categories and the isolation of core categories. An excerpt from a Detailed Analytical Log follows: Analytical Code Description – SID 06 for Interview 6/10/00 - TED Overview Six primary categories were used to code the transcript – Concept, Personal Comment, Personal Experience, Student Experience, Self Reflection and Time Frame. A secondary set of key-words were selected to provide a greater level of context during this preliminary analysis exercise. The primary categories could be represented in a number ways and for the purpose of this study it is convenient to adopt a hub structure that is centrally linked to the category of Concept, refer Figure 1. Personal Comment Student Experience Concept Time Frame Self Reflection Personal Experience Figure 1 : Primary categories This structure although in some sense is arbitrary directly relates to the research project question of conceptual development. Thus the structure provides a useful natural theme without constraining the data-set. … … … 69 Please refer to Appendix 2 - Figures A2-15 through A2-23 (page A2-74ff) for a representative transcript document for one particular preliminary interview. Each interview was coded and then compared with prior interviews and ten common categories were identified: Analogies; Assessment; Computer Simulations; Course Structure; Difficulties; Duality; Mathematics; Potential Diagrams; Real World; Reflective Thoughts; and Tunnelling. The categories will be briefly discussed. Analogies Eight students indicated that they found analogies helpful to their learning, two of these students in particular really liked them and wished they were used in courses more often. Six students did not like analogies and said they were confusing. The remaining two students commented that analogies were occasional useful but often they were inadequate. The students mentioned a limited set of analogy examples, for example “a ball rolling in some sort of valley” (PrelimSID06) Assessment The focus of student discussion regarding assessment was the end of semester examination. Students emphasised the importance of mathematics to doing well in examinations. Students described their preparation for examinations in terms of remembering recipes for solving different problems. “To study I try to learn all of the examples given in lectures” (PrelimSID02). “I memorise the steps so hopefully I can do it in the exam” (PrelimSID10). Computer Simulations This category was covered in detail by the physics students as a computational lab forms part of their course in intermediate physics. The chemistry students referred briefly to computer generated models of orbitals and molecular shapes. The majority of students found computer simulations useful for visualising abstract ideas (e.g. the mathematics of potential diagrams and wave functions). A number of students felt computer simulations could be more powerful if preceded by a ‘real experiment’. Three students felt the link between the simulation and the physical meaning was not made clear enough. “I didn’t understand Schrödinger’s equation and wells until I saw it in the computational lab…” (PrelimSID04) Course structure Student comments on course structure were predominantly related to the integration of lecture and laboratory components of the course. For example one 70 student said “the lectures and computer lab got out of sync ...” (PrelimSID11), another said “it is not clear what the lab has to do with the lecture bit …” (PrelimSID07). Some students commented on the teaching approach within the course. Four students said they enjoyed the historical approach used and three students appreciated seeing all of the steps described in the lecture examples “if I get down all the steps I am more confident of figuring it out later” (PrelimSID03) Difficulties Once a rapport was established between student and interviewer, the students were more than willing to articulate their difficulties with quantum mechanics. One student said “it is good to be asked …how long have you got?” (PrelimSID07). Students were open about their strength and weaknesses: “I am good at the maths (long pause) but I couldn’t tell you what it all means.” (PrelimSID05) “I find the maths overwhelming at times … what is the point, what is it for?” (PrelimSID11) “When they want us to explain anything, in assignments, I am stuck….” (PrelimSID03) The following list summarises the difficulties identified by students in the preliminary interviews: Conceptual explanations Duality Mathematics Probability Uncertainty Unfamiliar problems Wave functions Wells Duality Throughout the preliminary interviews the students used a variety of words to describe the quantum entity including: wave, particle, wave/particle, wave packet, smeared particle, wave function and probability density. The students 71 appear to view the entity in different ways depending on the situation. “I guess I don’t think about it, I don’t let it worry me, whatever works.” (PrelimSID17) One student described how he thinks about a wave function shape for a particular potential well. “I think of the particle in the well and how it moves for that potential energy, then I think of where abouts it is going slow or fast and then I work back to the wave function shape.” (PrelimSID08) This comment demonstrates how students use multiple entities to solve problems in quantum mechanics and they need to shift between them. This particular student demonstrated a strong conceptual understanding of all aspects of quantum mechanics covered in the interview but it appears from the transcripts that other weaker students have serious difficulties with multiple entities. Mathematics The students interviewed split into two distinct groups regarding mathematics in quantum mechanics. One group (5 students) felt that the mathematics was “straight-forward” or “easy” once you were shown the steps. The other group (12 students) found the mathematics “more difficult” or “hard” and at times “overwhelming”. All students felt you needed mathematics in order to succeed at quantum mechanics. Four students felt that your understanding improved with time as your mathematics skills improved. “When you solve Schrödinger’s equation the first time, its like, ‘oh my god’ … really hard, but in 3 rd year when you do it again its much easier.” (PrelimSID13) Potential EnergyDiagrams The students discussed a variety of potential diagrams used in quantum mechanics including infinite wells, finite wells, square wells, parabolic wells, ramp wells, step wells, an array of wells, barriers and humps. Five students recognised that all of these examples have the same basic structure associated with kinetic and potential energy and could describe in detail 3 examples. “The wells describes the energy in the system.” (PrelimSID06). The remaining students were very familiar with the simple examples (e.g. square wells) but had difficulties working with and describing other more complicated diagrams. “The wells steps always confuse me … I get the wave function shape wrong” (PrelimSID02) 72 While most students were familiar with potential diagrams as important tools in problem solving only three students could clearly explain the relationship between potential diagrams and physical systems. Most students saw potential diagrams as useful but isolated tools. Real World The students were asked to describe three examples of quantum mechanics applied to the real world. Only two students were able to do so, most other students could name one but three students could not give a single example. “I can’t think of any examples … it’s too abstract.” (PrelimSID01). Reflective Thoughts Throughout the preliminary interviews students made reflective comments on a range of topics including: high school physics experiences, course structures, teaching approaches, sequencing of ideas, learning styles and their attitude towards learning quantum mechanics. Tunnelling When describing or discussing tunnelling, students use potential diagrams and wave functions as tools. Ten students drew diagrams of the barrier with a decaying wave function superimposed. Most students described the wave function of being in a classically forbidden region, probing this idea revealed a variation in the depth of understanding. Most students conceptualise a ‘particle’ as the entity doing the tunnelling but cannot easily link this to their drawing. “I can see how it works when the wave function overlaps the barrier but what does this mean in terms of particles?” (PrelimSID10) Role of Chemistry Student Interviews At this point the categories that were identified from each of the four data sources were used to develop two final interview instruments for the study. One interview instrument focused on quantum mechanics learning in Chemistry and the other on learning in Physics. At a later date it was decided the learning issues in chemistry were beyond the scope of this dissertation and so the development of the chemistry interview instrument, its implementation and subsequent data analysis are not reported here. The research into learning in quantum chemistry provided additional theoretical sensitivity for this study. 73 For a full description of the data collection and analysis please refer to Appendix 2 (pages A2-73 through A2-96). Upon further analysis, comparison and consolidation the following five categories emerged from the preliminary interview analysis, and were carried forward to the selective coding phase. 1. Analogies – Some students find analogies useful to their learning of quantum mechanics, other students dislike analogies and find them confusing. 2. Tunnelling – This concept links a group of problem solving tools (e.g. potential diagrams and wave functions) to real world examples of quantum mechanics. Discussion of this concept can reveal students difficulties with the tools and how they interpret what the tools do. 3. Difficulties – Students are aware of and can identify the difficulties they experience in learning quantum mechanics. Difficulties students discussed included Conceptual Explanations, Duality, Mathematics, Probability, Uncertainty, Unfamiliar problems, Wave Functions and Potential Wells. It was recognised that a student’s perception of their strengths and weaknesses could influence future learning experiences. 4. Reflection – Given the opportunity students will reflect on their learning in and experiences in quantum mechanics. Through reflective processes students come to see relationships and connections in the subject. 5. Duality – Students view the quantum mechanics entity as a wave or particle or wave function depending on the situation. They often shift between entities. 74 4.3 DEVELOPMENT OF THE FINAL INTERVIEW INSTRUMENT 4.3.1 Categories Brought Forward from the Grounded Study Combining the results from the four data sources, concept maps, expert group discussions/interviews, examination script and preliminary interviews, eight categories emerged. They are summarised below. 1. Real world – The experts identified linking quantum mechanics to the real world as a key concept and as a teaching approach. However they were concerned that most students were unable to do this. Analysis of student responses in examinations and interviews indicated students had difficulties with unfamiliar problems and applications of quantum mechanics to the real world. Real world examples tended to highlight gaps, inconsistencies and misconceptions in student’s understanding of quantum mechanics. In future investigations, real world examples (e.g. radioactivity) could be used as a tool to probe student understanding in an interview. 2. Duality – Student concept maps suggest that students see a clear separation between the concepts of particle and wave; however their responses to examination questions suggest they cannot connect the correct classical behaviour to waves and particles. There also appears to be no conceptual shift from a wave-or-particle view to a wave function view following formal instruction. Instead students view the quantum mechanics entity as a wave or particle or wave function depending on the situation. The experts feel that teaching does not provide a resolution to the duality paradox and the concept is not revisited in senior years. 3. Uncertainty – The experts identify uncertainty as a key concept in quantum mechanics, however many students appear to have difficulties with it. Students can use Heisenberg’s Uncertainty Principle to solve mathematical problems but they cannot link it to other aspects of quantum mechanics or explain its significance in real word examples. Some students continue to confuse uncertainty with measurement error. 4. Analogies – Some experts find analogies to be a useful teaching and learning tool in quantum mechanics. Others find analogies inadequate and 75 confusing and prefer to use examples of experiments instead. Students also expressed a range of attitudes to their use. 5. Tunnelling – Students appear to be familiar with the terms, diagrams and graphs associated with potential diagrams and wave functions. However their explanation of tunnelling which brings together all of these tools is patchy and expressed in terms of a particle model rather than a wave function or probability model. Their proficiency with the tools appears to hide their lack of understanding of the conceptual/physical situation. 6. Difficulties - Students are aware of and can identify the difficulties they experience in learning quantum mechanics. Their perception of their strengths and weaknesses could influence future learning. Experts also identify difficulties students in general have with quantum mechanics based on their teaching and assessment experiences. 7. Reflection – Given the opportunity, students will reflect on their learning in and experiences in quantum mechanics. Through reflective processes students come to see relationships and connections in the subject. 8. Mathematics – Students and experts both see mathematics as an integral part of quantum mechanics that must be mastered in order to succeed and progress in the subject. As outlined in Chapter 1, the purpose of this investigation is to explore the teaching and learning processes associated with delivering a tertiary level quantum mechanics curriculum. The investigation aimed to isolate key concepts, identify learning difficulties, identify teaching difficulties and so provide both teachers and curriculum developers with a valuable resource. The primary focus for the second stage interviews was to explore the students’ attitude and conceptual understanding of quantum mechanics. It was found during the preliminary interviews that asking specific mathematics questions focussed the student’s attention upon that aspect and appeared to put them off conceptual descriptions. Information was available about the students mathematics background and was collected, but otherwise it was decided that the interview 76 should leave out specific mathematical discussions. If the student brought it up it was discussed otherwise not. The seven remaining categories Real World, Duality, Uncertainty, Analogies, Tunnelling, Difficulties and Reflections would become the topics for the final series of interviews. 4.3.2 Selective Coding The seven categories were further analysed using selective coding to identify three underlying core codes. These core codes became the themes that overarched the grounded theory categories and were carried forward to inform the interview question sequencing process. (Refer to Table 4-2). Interview Themes 1. Concepts Basic ideas and definitions used to describe or explain quantum mechanics. “What they know” 2. Tools Methods, recipes, mathematics, examples and analogies used to solve problems in quantum mechanics. “What they do” 3. Linking The process of tying together different aspects of quantum mechanics to make a connected and coherent whole. “How they make sense of it” Table 4-2 : Interview Themes 4.3.3 Sequencing Topics To provide a workable and logical sequence for the seven interview topics the format of the interview needed to be considered. The protocol required the interview to comprise three parts; an opening, a body and a close. Opening To open the interview we needed a familiar quantum mechanics topic that the students were comfortable discussing. The ideal topic would be something the students had previously experienced. It would also be answerable at a number of levels and consist of a range of aspects that could be discussed. It would have a 77 depth of complexity, a range of applications and could re-emerge later in the interview. A number of topics were trialled for the opening during the preliminary interviews. They are listed in Table 4-3 below along with the advantages and disadvantages revealed in analysis. Interview Opening Topics Opening Topic Double Slit Experiment Photoelectric Effect Role of Mathematics in Quantum Mechanics Wave/Particle Duality Advantages Familiar topic Students were relaxed and confident Depth of complexity Later link to analogy Familiar topic Depth of complexity Familiar topic Students were relaxed and confident Gave good overview of maths ability Familiar topic Depth of complexity Stimulated a range of ideas and feelings Disadvantages Some students saw it linked to optics but not quantum mechanics Most students could not recall the details or significance of the photoelectric effect Did not relax the students Gave the entire interview a strong maths flavour Too open and hard to control Too open and hard to control Did not relax students Was unsettling rather than setting the scene Table 4-3 : Interview Topics From this analysis the topic Double Slit Experiment” was selected for the opening as it best met the stated criteria. To address the possible disadvantage of this topic the researcher used a follow up question mentioning wave/particle duality with those students who could not see a link to quantum mechanics. Close To close the interview we needed a topic that summed up the issues raised during the body and gave the students a relaxed opportunity to reflect back on their responses. appreciated. The interview should end with the student feeling relaxed and A number of closure topics were tested during the preliminary interviews they are listed in Table 4-4 below along with the advantages and disadvantages revealed in analysis. 78 Interview Closure Topics Closure Topic Reflection on course Difficulties Real world Advantages Students have considered the topic in part prior to closure All students have an opinion to offer on the course A range of issues to discuss Students have considered the topic in part prior to the closure Allows students to identify their difficulties A range of issues to discuss Students have considered the topic in part prior to closure Links quantum mechanics to useful applications A range of issues to discuss Disadvantages Responses may be destructive or personal Some students may feel defensive Interview closes with students focussing on low points Many students may not be able to identify and discuss real world applications Table 4-4 : Interview Closure Topics The topic Reflection was chosen as a closure topic as it best fitted the selection criteria. Care was taken in designing specific questions and prompts for this topic to address the possibility of destructive or personal criticism emerging. Body The body of the interview is approximately 45 minutes in length and will need to include six topics. It is important to sequence the topics and specific questions in order get the most out of the interview instrument. During the preliminary interviews a number of questions associated with the topics were trialled and so we have data to inform the sequencing. In addition the topics can be classified according to the predominant learning domains1 with which each is associated. The domains of Skill, Affective and Cognitive were addressed in addition to the content. The results of the trials appear in Table 4-5. Psychologists distinguish between three kinds of learning or domains based on the type of performance involved. Psychomotor or Skill domain (both motor and cognitive skills) Affective domain (involves feelings and emotions) Cognitive domain (information and ideas) For example see Lefrancois, G.R., (1999) Psychology for teaching, (Wadsworth/Thompson Learning Belmont CA) p118. 1 Interview Body Topics Body Topic Analogies Difficulties Real World Tunnelling Uncertainty Wave/Particle Duality Advantages Reveal students’ ability to visualise, and shift context Helps students understand abstract concepts Allows students to identify their own difficulties Students describe a range of difficulties In a detailed answer student shows how quantum mechanics is linked to real world Links between theory, experiment and application Highlights student difficulties In a detailed answer students refer to tools such as potential diagrams and wave functions Tunnelling is a bridging concept between theory and real world examples Identified as a key concept of quantum mechanics Students give a range of descriptions Strong links to other topics Identified as a key concept in quantum mechanics It can be used to indicate conceptual change (from wave/particle to wave function) Students give a range of descriptions Strong links to other topics Disadvantages Students often don’t see limitations of analogies Some students don’t like them Some lecturers don’t use them Could make students defensive Domain Cognitive & Skill Students often do not see any link between quantum mechanics and the real world This topic puts off weak students Cognitive Weak students cannot give a detailed response without prompting Students can get tangled and confused in their answers Student responses can vary depending on the context used Cognitive & Skill Very broad topic and students can get off track Concept is not revisited in senior and honours level courses Cognitive Table 4-5 : Interview Body Topics 79 Affective Cognitive 80 The advantages and disadvantages given for each topic suggest preferred sequencing options. Wave/Particle Duality is best positioned directly following the opening. Wave/Particle Duality is strongly linked to Double Slit Experiment and should allow the discussion to broaden after a focussed introduction. In some cases the interviewer will prompt a connection between Double Slit Experiment and quantum mechanics by mentioning the idea of wave/particle duality so it naturally follows the opening. Students’ answers to the topic Uncertainty will be strongly influenced by the preceding context wherever it is placed. With this in mind Uncertainty will be addressed in the interview as two separate questions connected with the topics Wave/Particle Duality and Analogies. As many students have difficulties describing tunnelling without prompting familiar questions on potential diagrams and wave functions will precede any direct questions on tunnelling. It would be ideal to later ask an application question on tunnelling in the Real World topic. The Difficulties topic would sit well in the middle of the interview once students are relaxed and so it can be reflected upon in the later part of the interview. Many students have difficulties with the Real World topic so it needs to be placed between two topics that students have confidence in. Questions associated with Analogies can be easily imbedded in other topics. Discussion of a specific analogy should be considered late in the interview in case the student does not provide adequate information. The questions selected for each topic came from several sources. Questions that were trialled and worked well in the preliminary interviews were considered and usually selected. Some questions were modified and new questions written to address the advantages and disadvantages that were highlighted by the preliminary interviews. Questions were reviewed to ensure there was a variety of modes, learning styles and learning aspects addressed. In addition the questions needed to address the three themes that tied the grounded data together. Table 4-6 provides a summary of the final interview instrument. The physics interview guide follows in Section 4.4 and the complete and detailed questions for the study appears in Appendix 3. Final Interview Instrument Structure Interview Protocol Rapport Timeline (minutes) 0 Learning Domain Cognitive Topic Wave/Particle Duality Questions Body 10 Revisit key concepts 15 Cognitive & Skill Tunnelling Different modes of questioning 30 Affective Difficulties Different contexts 40 Cognitive Real World Different styles 45 Analogies Closure 55 Cognitive & Skill Affective Reflection 60 Double Slit Wave or Particle? Uncertainty Evidence of Wave/Particle duality Applications/Examples/Experiments Draw a well and a barrier Compare and contrast Discuss terminology Learning difficulties in quantum mechanics What tools do you need? Analogies and models you use? Explain Electromagnetic shielding or radioactivity in terms of quantum mechanics Quantaroo (macroscopic analogy of double slit) Changes in understanding What did you need to understand? Expectation of lecturer Advice to new lecturer Table 4-6 : Structure of the Final Interview Instrument 81 Theme Addressed Concept & Linking Concept Concept Linking Linking Tools Tools, Linking & Concept Tools & Concept Concept & Tools Tools Tools & Linking Linking Concept, Tools & Linking Concept, Tools & Linking Concept, Tools & Linking Concept, Tools & Linking Concept, Tools & Linking 82 4.4 FINAL INTERVIEW INSTRUMENT PHYSICS SECOND/THIRD/HONS/POST GRADUATE Wave/particle duality - Double Slit Experiment - Describe what occurs if you shine the light on the slits? - Draw/describe - What features of this relate to quantum mechanics? - What separates a wave and a particle? - What is meant by Uncertainty? Duality - Evidence of wave particle duality - Key ideas, experiments Tunnelling - Barriers and Wells - Compare and contrast - Discuss Wave Function, Eigen Functions/Values, Probability Distribution Functions TUTORS (*) Difficulties - What difficulties do you anticipate the students might have learning quantum mechanics? - What tools do you expect students to have? - What Analogies/Models do you use to explain quantum physics concepts? Linking - What links do quantum mechanics concepts have outside, EM shielding, Radioactive decay - Application - Name three things quantum mechanics has given us? Discussion Question - Imagine you live in a universe in which the value of Planck’s Constant, h, is much greater than 10-34 – say of order 1000. In this universe you would observe quantum phenomena in everyday life. Now imagine you are a hunter. Every evening a mob of Quantaroos (Quantum kangaroos) bound along a path that passes through a densely packed grove of tall thin trees (River Gums) into a clearing. You would like to capture a Quantaroo as it exits the grove into the clearing. You have a shovel to dig a hole or a trench, a tranquiliser gun and a net. Epilogue - Sequence of major concepts, changes in understanding. - During the delivery of the course what did you feel you needed to understand? - What do you feel the lecturer wanted you to again from the course? - What would you advise a new lecturer about teaching the course? 83 CHAPTER 4 ........................................................................................................................................54 DEVELOPMENT OF RESEARCH QUESTIONS : GROUNDED THEORY APPROACH ...............54 4.1 INTRODUCTION ..................................................................................................................54 4.2 SOURCES OF GROUNDED DATA......................................................................................54 4.2.1 Concept Maps ..............................................................................................................................55 4.2.2 Expert Group Discussions/Interviews ..........................................................................................58 The Expert Focus Group Discussion .........................................................................................................58 The Individual Expert Interviews ..............................................................................................................59 4.2.3 Examination Scripts .....................................................................................................................61 First Year examination Scripts ..................................................................................................................62 de Broglie ..............................................................................................................................................62 Terminology ..........................................................................................................................................62 Application of Quantised Energy ..........................................................................................................63 Heisenberg’s Uncertainty Principle.......................................................................................................63 Second Year Examination Scripts .............................................................................................................63 de Broglie ..............................................................................................................................................63 Compton Scattering...............................................................................................................................64 Tunnelling .............................................................................................................................................64 Wells .....................................................................................................................................................65 4.2.4 Preliminary Interviews .................................................................................................................66 4.2.5 Analysis of Data Collected ...........................................................................................................66 Analogies ..............................................................................................................................................69 Assessment ............................................................................................................................................69 Computer Simulations...........................................................................................................................69 Course structure ....................................................................................................................................69 Difficulties ............................................................................................................................................70 Duality ..................................................................................................................................................70 Mathematics ..........................................................................................................................................71 Potential EnergyDiagrams.....................................................................................................................71 Real World ............................................................................................................................................72 Reflective Thoughts ..............................................................................................................................72 Tunnelling .............................................................................................................................................72 Role of Chemistry Student Interviews ...........................................................................................................72 4.3 DEVELOPMENT OF THE FINAL INTERVIEW INSTRUMENT .........................................74 4.3.1 Categories Brought Forward from the Grounded Study ...............................................................74 4.3.2 Selective Coding ..........................................................................................................................76 4.3.3 Sequencing Topics .......................................................................................................................76 Opening .....................................................................................................................................................76 Close..........................................................................................................................................................77 Body ..........................................................................................................................................................78 4.4 FINAL INTERVIEW INSTRUMENT .....................................................................................82 Figure 4-1 : Copy of Student Concept Map (Student ID 21). This map shows the “wheel linked to another wheel” structural type. Reduced from original A3 with the labels and header instructions cropped (Please refer to Appendix 2, Figures A2-1 through A2-4 for details of the complete concept mapping exercise) ........................................................................................................... 56 Figure 4-2 : Representative Preliminary Interview Transcript – TED Page 1 Cover Page................... 67 Figure 4-3 : Representative Preliminary Interview Transcript – TED Page 4 ...................................... 67 Table 4-1 : Concept Map Structural Types and Results Summary (n=67) ........................................... 57 Table 4-2 : Interview Themes............................................................................................................... 76 Table 4-3 : Interview Topics ................................................................................................................ 77 Table 4-4 : Interview Closure Topics ................................................................................................... 78 Table 4-5 : Interview Body Topics....................................................................................................... 79 Table 4-6 : Structure of the Final Interview Instrument ....................................................................... 81