appendix 2 - school of physics · web viewall of the physics lecturers had previously taught...

Please cite as: Fletcher, P.R., (2004) PhD Thesis - How Tertiary Level Physics Students Learn and Conceptualise Quantum Mechanics (School of Physics, University of Sydney)

APPENDIX 2GROUNDED THEORY INVESTIGATION – STAGE 1

This Appendix contains the data and detailed analysis for the initial grounded theory based investigations.

The appendix contains six sections

Concept Map Results and Analysis – 67 Concept Maps Expert Group Discussions/Interviews Results and Analysis – 18

participants Examination Script Results and Analysis – 137 Scripts Preliminary Interview Results and Analysis – 17 Interviews

Development of the Final Instrument Associated Literature Reviews

The first four sections were exploratory investigations which grounded the final interview protocol in the setting. At the conclusion of each section a set of emerging categories were listed and formed the primary data source for the selective coding phase carried out in the ‘Development of the Final Instrument’ section. In order to appropriately identify the main underlying phenomena which were carried forward a preliminary selective coding process involving two researchers was performed. This coding process involved the use of constant comparison techniques between all other related data/analysis and drew upon the researchers developing theoretical sensitivity.

Refer to Chapter 4 for a summary and discussion of these results.

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A2.1 CONCEPT MAP RESULTS AND ANALYSISIn 1999 a concept mapping exercise was distributed to 67

intermediate (second year) University of Sydney physics students who had just completed their second year quantum mechanics lecture series. The exercise was developed by Associate Professor Ian Johnston as a formative assessment task to examine the relationships between key concepts associated with quantum mechanics. Preliminary examination of these concept maps by the researcher in December 1999 revealed they contained interesting features and were selected as a data source for this study.

A2.1.1 Concept Mapping ExerciseThe exercise asked the students to draw a concept map showing

how they think the provided listed concepts related to one another. The exercise was distributed to 67 students at the commencement of the final lecture in their second year quantum mechanics course.

Students were provided with a ‘general concept mapping instruction sheet’ to assist students who were not familiar with or had not previously drawn a concept map, a ‘concept map answer cover sheet’, a ‘concept map answer sheet’ and were given 20 minutes to prepare a response.

The concept mapping exercise required the construction of a concept map using the nineteen labels provided. It 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.

Please refer to the following sections to view a set of reduced copies of all exercise handouts and a typical finished concept map.

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General Concept Mapping Instruction SheetCONCEPT MAPS

A good way to explore understanding is by drawing a concept map

Concept maps are useful for:

Students Lecturers Helps focus on important ideas

in a course Helps to focus lecture on key

learning areas Helps recognise relationships

between key ideas and concepts in the course

Can use student maps to focus lectures on students’ weaknesses

Useful as a revision tool, providing a schematic summary

As a research tool

Helps conceptual understanding

How to draw a map

Below is an example of a concept map for mechanics. Concept maps have three features:

1. Concept Labels2. Links3. Link Labels

To draw a concept map you simply connect concept labels with links and then label the links. A concept map is a personal representation of your ideas about a topic. Unlike other aspects of physics, there is more than one concept map and there is no correct concept map for a given topic.

Figure A2-1 : Concept Map Instruction Sheet (Printed A4 Portrait)

Example “Newtonian Concept Map”

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Figure A2-2 : Example “Newtonian Concept Map” provided with Concept Map Instruction Sheet (Printed A4 Landscape on reverse)

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Concept Map Answer Cover Sheet Layout

QUANTUM PHYSICS1998

Concept MapAnswer Booklet

Student ID : _______________________

PLEASE NOTE: This exercise is intended only for diagnostic purposes. It will NOT be used for any kind of assessment.

We require your Student ID so that we may compare and correlate responses as part of the teaching research.

This Concept Map Answer Booklet cover sheet will be separated and your student ID encoded to ensure your privacy.

Figure A2-3 : Concept Map Cover Sheet (Printed A4 Portrait)

Concept Map Answer Sheet Layout

On this page please draw a concept map showing how you think these following concepts are related to one another

AtomDiffractionElectronEnergyEnergy levelFrequencyIntensityInterferenceLightMassMatterMomentumOrbitParticlePhotonProbabilityUncertainty PrincipleWaveWavelength

Figure A2-4 : Concept Map Answer Sheet (Printed A3 Landscape)

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Example of Student Concept Map

Figure A2-5 : 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 (Refer to Figure A2-4))

A2.1.2 Results - Concept Map StructuresThe concept maps were examined and discussed by the researcher

and two colleagues in order to formulate an analysis strategy. The following two investigations were proposed and conducted: A structural analysis and a nodal analysis.

Structural and Nodal AnalysisBased upon the work by Cronin, Dekkers and Dunn (1982) and

Bailey and Butcher (1997) a set of concept map structural types were developed. The researchers examined each concept map and determined the most prominent structural features and a preliminary list of categories developed.

These categories were discussed with two colleagues and refined. Nine map structure types were revealed string, string with a wheel attached, hierarchy, complex, complex with a wheel attached, wheel, wheel linked to another wheel, bubble loops, and disjoint. The nine categories are illustrated and described in Table A2-1

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These categories of description were then used by the researcher and another colleague to code and tabulate all concept maps. The tabulated coding was compared, discussed and the finalised data is presented in the right hand column of Table A2-1. (Refer to Table A2-3 and Table A2-4 for dataset)

Next the researcher 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 would provide information about which concepts the students considered as key focus ideas that they linked to other concepts.

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Concept Map Structure Types

Map Type

Illustration Description (n) %

String Three or more concepts are linked in a single chain

(1)1%

Wheel A number of single concepts emanate from a single concept

(2)3%

String with a wheel attached

Four or more concepts are linked in a single chain with a wheel structure attached at one end

(7)10%

Hierarchy Concepts are arranged in a simple tree type structure.

(16)24%

Complex Cross-linking between the concepts to form an associative network

(6)9%

Complex with a wheel attached

And associative structure with an obvious wheel structure attached

(20)30%

Wheel linked to another wheel

Two concepts with wheel structures which are connected by a number of joining radial links

(12)18%

Bubble Loops

Several string structures that form closed loops

(2)3%

Disjoint The concepts are arranged into two or more separate structures

(3)4%

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Table A2-1 : Concept Map Structural Types and Results Summary (not mutually exclusive)

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Summary of Results from Structural and Nodal Analysis The most striking trend to emerge from the analysis was that over

two thirds of the students drew concept maps that described quantum mechanics as a subject of two parts, one part based on waves and the other on particles.

By studying the nodes in relation to the three largest structure categories (hierarchy, wheel linked to another wheel and complex with wheel attached) this duality trend is evident. Over a fifth of the students drew a hierarchical structure of quantum mechanics concepts. The highest or primary concept was predominantly light (in 11 of the 16 maps) and then split into two secondary concepts usually wave and particle (in 12 of the 16 maps). The wheel linked to another wheel structure showed a clear separation of concepts into two sections. The central concepts or nodes in the two wheels were once again wave and particle (in 10 of the 12 maps). The complex with wheel attached structure also illustrated separation into two sections, the majority (15 out of 20 maps) also split along wave/particle nodes.

Other Interesting Features that Emerged from the Concept MapsDuring the preliminary interviews with students the term

‘uncertainty’ was brought up by the students in a number of different contexts, for example, measurement uncertainty, the uncertainty principle (with related formula), determining momentum and probability distributions. As part of the ongoing constant comparison process, the concept maps were revisited and analysed with respect to the concept of uncertainty.

The concept label provided to the students was ‘Uncertainty Principle’, the way students used this label on their maps fell into three groups. The first group (5 maps) did not link uncertainty to their map of quantum mechanics. Either the label did not appear on their map or the label was present without links. The second group (13 maps) made only one link to uncertainty, for the most part it appeared that uncertainty had been added as an afterthought. The concept label hung off the edge of the map and was not important to the overall structure.

The third group of 49 maps had from two to four links between the concept uncertainty and the rest of the map. In these maps the concept

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of uncertainty was integrated into the structure of quantum mechanics, in one case the label ‘uncertainty principle’ formed the node of a wheel structure. All maps in this group linked uncertainty to particle. Other popular links were wave, probability and momentum. (Refer to Table A2-2)

Links to ‘Uncertainty Principle’

Linked to Particle

Linked to Wave

Linked to Probability

Linked to Momentum

Number of Maps

49100%R

3878%R

3776%R

1735%R

Note : Maps that included momentum in a link label to uncertainty have been coded as linked to momentum

Table A2-2 : Maps with two or more links to ‘Uncertainty Principle’

On 5 concept maps the students had written label links or explanatory notes indicating that uncertainty was related to measurement or the inability to make accurate measurements. On 4 different maps students had annotated the link between uncertainty and momentum with the formula .

Summary of Results from Concept Map AnalysisThe concept of uncertainty was isolated in one group of concept

maps and strongly linked in another. The majority of students see it as closely linked to concepts such as wave, particle, probability and momentum and their link labels suggest that uncertainty means different things to different students.

Just under a quarter of students used mathematical formula on their concept map either on the links or as labels. For example the formula E = hf was used to label the link between frequency and energy. Some students used it multiple times. No mathematics was given as stimulus material for the concept maps. For these students a conceptual structure of quantum mechanics requires mathematics.

A2.1.3 Results Carried Forward – Concept MapsThe following three categories emerged from the concept map

analysis and were carried forward to the selective coding phase.

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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 is weak and others associate uncertainty with a range of other concepts and contexts.

3. Mathematics - For some students mathematics is an integral component of the structure of quantum mechanics.

A2.1.4 Concept Mapping Data SetsThe following tables contain the coding for the concept map

analysis. Table A2-3 shows the Linking Structures, Map Structures, the associations for Uncertainty and the presence of Mathematics. Table A2-4 shows the Primary Nodes within the Wheel, Complex and Hierarchical Structures.

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Second Year Physics – Concept Mapping

Table A2-3 : Concept Map Coding – Linking and Map Structures (1of 2)

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Second Year Physics – Concept Mapping

Table A2-4 : Concept Map Coding – Primary Nodes within Wheel, Complex and Hierarchical Structures (2 of 2)

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A2.2 EXPERT GROUP DISCUSSIONS/INTERVIEWS RESULTS AND ANALYSISSeveral focus group discussions with physics and chemistry

lecturers from the University of Sydney were planned. The knowledge, experience and insights of these teachers and practioners of quantum mechanics were a valuable contribution to the grounded theory stage of the study. Whilst we received positive responses to our discussion invitations, time tabling constraints meant that only one focus group discussion was ever conducted. Instead fourteen individual interviews were scheduled to ensure the views of all the experts were heard.

The Expert Focus Group DiscussionThe focus group consisted of four lecturers, all of whom were from

the School of Chemistry, and the interviewer. The chemistry lecturers’ area of research is theoretical chemistry. All of the lecturers have taught senior chemistry options which include components of quantum chemistry. The discussion was held between 10:00am and 11:00am in an office in the School of Chemistry. The group sat comfortably around a table which had a tape recorder in the centre. Prior to commencing the discussion the lecturers were provided with a list of discussion points which were developed from diary entries from preliminary discussions (Refer to Figure A2-5 below). 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.

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Focus Group Discussion - Quantum MechanicsPoints for Discussion

What are the key aspects you want your students to learn?

A description of the role, types and use of experiments? analogies? mathematics? models? assessment strategies?

What are the difficulties students have when learning quantum mechanics?As a lecturer what difficulties do you have teaching quantum mechanics?

Figure A2-6 : Focus Group Discussion 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 in SUPER and SCIFER assisted the researcher in developing a theoretical sensitivity towards this type of data.

The Individual Expert InterviewsIt was not possible to schedule any more focus group discussions

so two chemistry lecturers and twelve physics lecturers were interviewed individually. The two chemistry lecturers had a research background in theoretical chemistry. The physics lecturers had a variety of research backgrounds including theoretical physics, applied physics, high energy physics, physical optics, astrophysics and physics education. All of the physics lecturers had previously taught quantum mechanics at junior, intermediate or senior level. Five of the physics lecturers had less than 5 years experience and are referred to as junior lecturers, the remaining seven lecturers had more than 5 years experience and are referred to as senior lecturers. Although the dynamics and debate of a group discussion was lost, the interviews produced fourteen detailed and rich

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responses as a data source. For these interviews a more structured interview guide (Refer to Figures A2-6 and A2-7) was constructed and followed.

PHYSICS QUANTUM - ACADEMIC GUIDE QUESTIONSSetting the Scene- From you own experience. Do you feel that the teaching of quantum

mechanics has changed since your undergraduate studies?- From your perspective. What is the importance of teaching quantum

mechanics today?Teaching Key Concepts- If you were given the task to map out a quantum physics curriculum

spanning from secondary school through to postgraduate.- What key concepts would you introduce and reinforce at each

stage?Expert/Novice- Briefly describe a barrier and a well.- What are the key ideas a student should understand?Difficulties- From a students perspective. What difficulties do you anticipate they

might have learning quantum mechanics? - What Analogies/Models do you use to explain quantum physics

concepts. For example: Wave/Particle duality, Probability, Uncertainty, Potential Wells and Barriers.

- From you own personal experience. What sorts of difficulties have you encountered teaching quantum mechanics?

Expert/Novice- 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.

- What are the key quantum concepts a student should address when answering this hypothetical problem?

- What difficulties do you feel a student might encounter whilst answering this type of question?

Discussion points and questions- Importance of philosophical aspects.- The role of analogy in the learning process.- What does it mean to learn quantum mechanics?Epilogue- At the end of the course what do you want the student to take away?

- First year student that uses physics as a service course toward their degree

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- Physics majors

Figure A2-7 : Physics Lecturer Guide Interview Questions

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CHEMISTRY QUANTUM - ACADEMICGUIDE QUESTIONS

Setting the Scene- From you own experience. Do you feel that the teaching of quantum

mechanics has changed since your undergraduate studies?- From your perspective. What is the importance of teaching quantum

mechanics today?Teaching Key Concepts- If you were given the task to map out a quantum mechanics

curriculum spanning from secondary school through to postgraduate.- What key concepts would you introduce and reinforce at each

stage?

Expert/Novice - Briefly describe a barrier and a well.- What are the key ideas a student should understand?Difficulties- From a students perspective. What difficulties do you anticipate they

might have learning quantum mechanics? - What Analogies/Models do you use to explain quantum mechanical

concepts. For example: Wave/Particle duality, Probability, Uncertainty, Potential Wells and Barriers.

- From you own personal experience. What sorts of difficulties have you encountered teaching quantum mechanics?

Expert/Novice - 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.

- What are the key quantum concepts a student should address when answering this hypothetical problem?

- What difficulties do you feel a student might encounter whilst answering this type of question?

Discussion points and questions- Importance of philosophical aspects.- The role of analogy in the learning process.- What does it mean to learn quantum mechanics?Epilogue- At the end of the course what do you want the student to take away?

- First year student that uses chemistry as a service course toward their degree

- Chemistry majors

Figure A2-8 : Chemistry Lecturer Guide Interview Questions

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These guides were constructed at the request of the lecturers who wished to provide considered responses in the interview. To produce the guides the researcher returned to existing data sources (concept maps, examination scripts, focus group interview and discussions) and from existing categories produced an overview using an axial coding process. The guides were given to the lecturers at least two days before the scheduled interview.

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 conversational style. All interviews were relaxed and free-flowing however the junior physics lecturers tended to cover each point on the interview guide in turn while the senior physics lecturers tended to produce a reflective and global response. At times the researcher prompted and narrowed the conversation to probe specific issues.

Results – Expert Group Discussions/InterviewsThe tapes were immediately transcribed so the researcher could

read through the transcripts and make reflective notes. Reflective notes gave the researcher 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 eight categories. 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. The following table summarises the depth of the lecturer’s response in each category (Refer to Table A2-5).

Please cite as: Fletcher, P.R., (2004) PhD Thesis - How Tertiary Level Physics Students Learn and Conceptualise Quantum Mechanics (School of Physics, University of Sydney)

Expert Group – Depth of Response

PHYSICS CHEMISTRYLectures of 3rd year and honours

Lectures of 2nd year

Lectures of 1st year Lecturers of 3rd year and above in quantum chemistry

Individual Individual Individual Focus Group IndividualLecturer ID >

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Teaching Approach D M M D D M D D M D S NR D D M D M DKey Concepts D D S M D D M M M D M D D D D D S DAssessment D S NR S D S D D NR NR M NR M M D D NR NRPerceivedDifficulties D M NR D D M D D D D D D D D D D D DMaths NR D M D D M D D D D M M M D D D D DAnalogies D D D D D D D D D D D D D D D D M DComputer Simulations D NR NR M D D NR D NR NR NR S M D D D M MExperiments D D S NR NR NR NR D M NR NR NR D D D D M M

Depth of Response (This was a measure of the level of discussion. For example a Deep response involved extensive thoughtful comments concerning the topic under discussion) :: S – Surface M – Middle D – Deep NR – No Response

Table A2-5 : Expert Interview/Group Discussions - The depth of response against each identified category

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Teaching ApproachesSeveral approaches to teaching quantum mechanics were

articulated by the lecturers; their approaches differed depending on their research background, level of experience and personal preferences. A number of lecturers adopted an historical approach to the subject but others rejected this approach entirely. One lecturer suggested “a balance between the historical and axiomatic approaches” (Lecturer ID 7) was preferable. The majority of lecturers felt it was necessary for the students to make a conceptual shift from classical ideas of waves and particles to a probabilistic understanding of wave functions. They suggested a number of approaches for achieving this shift, for example, visualisation of wave functions, analogies, real world examples and mathematics. Two lecturers in particular preferred a teaching approach that had a strong mathematical emphasis. The mathematics was covered “step-by-step and then tie in the physics” (Lecturer ID 2). The lecturers were unanimous in their support of including applications or examples of quantum mechanics. Some lecturers attempted to teach quantum mechanics in a concrete context while others attempted to consistently link theory, experiment and applications during their course.

Key ConceptsThe lecturers identified concepts or issues which they felt were

critical to students understanding of quantum mechanics, they have been compiled into a list of eighteen concepts in Table A2-6 below.

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Expert Group - Concepts Identified

Concept identified Number of lecturers

Duality 4Linking Quantum Mechanics to ‘real world’ 4Uncertainty 4Bonding 3Spectroscopy 3Waves 3Energy Levels 2Energy Quantisation 2Probability 2Schrödinger Equation 2Double slit experiment 1Harmonic Oscillators 1Mathematical tools 1Matrices and Operators 1Perturbation 1Photoelectric effect 1Tunnelling 1Wave functions 1Wells 1

Table A2-6 : Expert Group - Key concepts identified by lecturers

AssessmentThe primary summative assessment tools of student learning used

in the School of Physics and the School of Chemistry are formal examinations, assignments and quizzes. Some of the lecturers interviewed do make use of formative assessment tools (for example concept maps, interactive lecturing, questioning, predict-observe-explain and 1 minutes papers).

Emerging from the interviews was the view that student learning is motivated by the examination1. Students use a recipe approach to solving questions, often-different recipes for different sections of the course. They develop these recipes during the course (often imitating the lecturers) and then use them in assignments and examinations. The lecturers are aware of this aspect of student learning and see evidence of it when they set unfamiliar problems in assessments. Some lecturers acknowledge that since the teaching approach encourages

1 Three lecturers suggested that student examination scripts could be valuable resource for this study.

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compartmentalisation and isolation of ideas student failure at unfamiliar problems is to be expected. Other lecturers deliberately set assessment problems that discourage a recipe approach by students.

The majority of lecturers would like the assessment tasks to reflect their conceptual teaching approach. There was a tendency to ask quantitative questions rather than qualitative or interpretative questions and most would like this balance to change.

Perceived DifficultiesThe lecturers identified a range of difficulties students and

teachers had with teaching and learning quantum mechanics. The difficulties have been grouped into common categories, refer to Table A2-7.

MathsAll of the lecturers felt that good mathematical skills were essential

to a student’s success in quantum mechanics. None of the lecturers felt progress could be made in the subject without the necessary mathematics skills (these skills were not specifically articulated, it is inferred by the researcher that mathematical skills to the level of multi-variable calculus is preferred). Some of the lecturers saw mathematics as the tool kit for quantum mechanics; others saw it as the essential underpinning of the subject, an essential language needed for communication and understanding. One lecturer saw mathematics as a barrier to student understanding in all physics subjects not just quantum mechanics. Two lecturers felt mathematics, while important, was a secondary problem to understanding the abstract concepts of quantum mechanics.

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Expert Group – Difficulties Identified

Difficulty Number of

lecturersPrior experiences of students

Weak physics background (force and electrostatics)

Weak mathematics Students have preconceptions Weak understanding of waves

8

Teaching approach causes difficulties Teachers do not provide resolutions to paradoxes Teachers don’t link things together or revisit Introductory course is very complex Not enough time for students to gain

understanding Teachers don’t explicitly address underlying issues

4

Terminology Terms in quantum mechanics have common and

scientific meanings

3

Abstract nature of Quantum Mechanics Quantum mechanics is abstract Hard to visualise Conceptually difficult

4

Problem solving Cannot extend to unfamiliar situations Can’t use tools to explain things Cannot critically analyse models Don’t have a deep understanding they have

isolated chunks Don’t see relationships between models Difficulties understanding what has been

calculated in a physics sense Problems generalising

7

Specific Topics Energy levels Wave functions Probability Operators Eigen values/vectors Potentials diagrams (well and barriers) Waves Harmonics Uncertainty Expectation

8

Table A2-7 : Expert Group – Difficulties Identified by the 18 lecturers

Analogies

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The attitude of lecturers towards the use of analogies was split. Half of the lecturers were positive about analogies in quantum mechanics and used them in their teaching. These lecturers felt that analogies could be a starting point for students into an abstract subject, an analogy could help them picture and link quantum ideas for themselves. One lecturer stated “we think fundamentally in terms of analogies, we tie things to things” (Lecturer ID 7). Two lecturers felt analogies could be used to generate valuable discussions amongst students about the nature of quantum mechanics.

The lecturers who had a negative attitude to analogies felt that they confused students and did not help learning. One lecturer commented; “introducing weird scenarios and discussions is not pedagogically helpful” (Lecturer ID 3). Other lecturers felt there were “no true analogies for quantum mechanics” (Lecturer ID 6) and use of real examples or experiments was more useful. The limitations of analogies was also a point of criticism, some felt that analogies were sadly inadequate for all but surface comparisons, others felt that students were unable to recognise the limitations in analogies and so became more confused.

Analogies used by lecturers included:

Charged plates or walls Vibrating strings Gravitational wells Fourier analogies Refractive index Quantaroo Frogs and apples Fences (barriers)

Computer SimulationsHalf of the physics lecturers used computer simulations to teach

quantum mechanics. They felt that the simulations helped students to visualise abstract concepts and gave them confidence. One lecturer commented that computer simulations were wonderful tools for the teachers or experts but he suspected students “just see a bunch of lines” (Lecturer ID 8). Although the simulations provided visual information he was not convinced it actually helped their understanding.

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ExperimentsMost lecturers considered the use of experiments in teaching and

learning quantum mechanics important and two lecturers in particular stated that linking theory to experiment was the basis of their teaching approach. All of the chemistry lecturers interviewed made use of spectra observations, conjugated chain experiments and molecular bonding models as a part of teaching quantum chemistry. The junior physics course in quantum mechanics uses experiments (standing waves, double slit interference, spectra observation and photoelectric effect) interactively in lectures and hands-on in tutorials. The intermediate and senior physics laboratories have quantum mechanics experiments (semiconductors, double slit experiment, photoelectric effect, electron spin resonance and radioactivity) that lecturers usually refer to, but students do not necessarily complete these experiments concurrently with lectures.

Lecturers stated different reasons for using or referring to experiments in quantum mechanics. Some lecturers felt experiments were important in that they demonstrated “oddity in nature” (Lecturer ID 1) to the students. Others felt that experiments gave students concrete experiences to link abstract concepts to. Another group used experiments as the basis of problems the students had to solve, the aim being for students to link experiment and theory.

A2.2.2 Results Carried Forward – Expert Discussions/Interviews

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

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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.

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.

5. Mathematics – Experts feel that students must have the necessary mathematics skills to succeed at quantum mechanics.

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A2.3 EXAMINATION SCRIPT RESULTS AND ANALYSISDuring the expert interviews, several lecturers referred to students

having difficulties with qualitative or interpretative questions in examinations and assignments. Three lecturers suggested a review of student examination scripts might be of use to this study. Junior and Intermediate physics examination scripts were made available for analysis. A senior academic from the School of Physics who was unconnected with this study randomly selected 137 examination scripts from the archive (total number of scripts in archive unknown, selection - 46 Junior First Year Technological, 45 Intermediate Second Year Technological and 46 Intermediate Second Year Advanced). 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.

Six questions were selected for analysis, three from the junior physics examination and three from the intermediate physics examination. The questions were selected in consultation with senior lecturers from the School of Physics who had a role in setting and marking the examination. The six questions had qualitative and quantitative sub-components and covered a range of key concepts identified by the expert interviews. An overview of the type and number of scripts as well as the questions selected appear in Table A2-8.

Examination Script Data Sources

Year Group Number of Scripts

Questions Selected

Junior Technological 46 Q9Q10Q11

Intermediate Technological 45 QA1 (a), (b) & (d)QA2 (a), (b) & (c)

Intermediate Advanced 46 QB1 (a) & (c)Note : Question A1 (a) and Question B1 (a) are basically the same question.

Table A2-8 : Examination Script – Questions selected for analysis

Each question was analysed using a phenomenographic approach to reveal aspects of variation within the student responses. The

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responses to each section of the questions were reviewed, coded, categorised and tabulated. Refer to Tables A2-9 through A2-34 for the coded datasets. 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 provide a framework in which to group and present the finalised categories.

The following pages show each examination question as it appeared to the students (Refer to Figures A2-6 through A2-14) and is followed by a description of the features revealed in data analysis of students’ responses.

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First Year – Question 9

First Year Physics 1003 & 1203 – Technological

Question 9

Consider the de Broglie wavelengths of an electron and a proton. Which has the smaller wavelength if the two particles have the same

(a) speed(b) kinetic energy,(c) momentum?

Explain your answers. (5 marks/100)

Figure A2-9 : Examination Script – First Year Question 9

Observed featuresThe 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 parts a) and c) but only one third gave a correct answer for part b). 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.

Students displayed confidence in working with and describing the formula and not calculating the actual values. For parts a) and c) they were capable of clearly explaining the relationship between variables in the formula.

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Question 10

Consider an electron confined to a microscopic region.The results of quantum mechanics state that the energy of the confined electron is quantised.

(a) What is meant by the term(i) quantised(ii) ground state(iii) excited state(iv) zero point energy ?

b) What does the quantisation of energy of confined electrons imply about the attainability of the absolute zero of temperature?

(5 marks/100)


Observed FeaturesApproximately 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.

In part b) the students were required to use a quantised model of a confined electron to explain a related example. 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.

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Question 11

(a) Write down the Heisenberg uncertainty relation for position and momentum.

State briefly its physical significance. Do not write more than about 5 lines.

(b) Imagine playing baseball in a universe (not ours) where Planck's constant is 0.6 J.s.

An 0.5kg ball is thrown with a velocity of 20m/s and an uncertainty of 1m/s

(i) What is the uncertainty in its momentum along the direction of motion?

(ii) What is the uncertainty in its position along the direction of motion?

(iii) Would the uncertainty in its position be the same along the direction that is at right angles to the direction of motion? Explain your answers.

(c) In our universe the uncertainty relation is mostly applied to very small objects such as electrons and protons. Why don't we use the uncertainty relation on

larger objects (such as cars, tennis balls, etc)? Does it apply in these cases? Explain your answers.

(10 marks/100)


Observed FeaturesStudents do not seem to know the formulaic representation of

Heisenberg’s Uncertainty Principle, 20% of students did not include a formula in their answer to part a) 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 the formula stated (or not) 76% of students gave an answer to part a) 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 are unclear what meaning is given to these terms.

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In part b) the students needed to manipulate formulae and make some calculations, students experienced difficulties with arithmetic, formula and units.

The final part of question 11 asked students 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 is 42%. This compares to only 4% when the students were describing the uncertainty formula.

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Second Year – Question A1

Second Year Intermediate Physics 2001& 2101– Technological & Environmental

Question A1 (20 marks/100)

Write brief answers (about 5 lines plus diagrams if appropriate) to each of the following parts (a) to (d). If you use formulas and/or diagrams, define the symbols and terms.

(a) Describe the Compton scattering experiment and how it illustrates the particle nature of light

(b) What is a de Broglie wavelength of a particle? Describe an experiment that can determine its value.

(c) State in words the meaning of the term expectation value as used in quantum mechanics. How is it determined from the wave function of an eigenstate?

(d) Explain the meaning of the terms tunnelling, reflection coefficient and transmission coefficient as used in quantum mechanics

Figure A2-12 : Examination Script – Second Year Question A1

Observed FeaturesPart a)

Analysis of this question revealed that students were not overly familiar with the Compton scattering experiment, 37% of students confused it with another experiment (e.g. photoelectric effect or double slit). The remaining students gave a variety of responses all describing the collision of a type of electromagnetic radiation (photon, light, x-ray, gamma ray) with a target (e.g. atom, electron, carbon, gold, crystal, lattice).

When they described the interaction that occurs between photons and electrons in Compton Shifting 63% of students described classical wave behaviour (reflection, diffraction, scattering etc) then they used this to justify the particle nature of light. Only 17% of students gave evidence of particle behaviour (collision or momentum change) as an argument for the particle nature of light.

Part b)

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All students attempted the first section of this question and described de Broglie’s wavelength. 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 in their response.

Describing an experiment to measure de Broglie’s wavelength was more troublesome for students, 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.

Part d) 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.

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Second Year – Question B1

Second Year Intermediate Physics 2901– Advanced

Question B1 (20 marks/100)

Briefly answer each of the following questions, using about 5 lines for each subject, plus a diagram if applicable(a) Describe the process of Compton Scattering and explain its significance in the discussion of wave-particle duality(b) Describe the main properties required of the Schrödinger Wave Equation.(c) Explain the significance of Quantum Mechanical tunnelling to nuclear reactions inside stars.(d) Describe the difference between e versus k diagrams for a free particle an=d that of an electron in the Kronig-Penny model of a 1-dimensional lattice.(e) Where s the Fermi Energy in an n-type semiconductor at

(i) low temperature(ii) high temperature?

Figure A2-13 : Examination Script – Second Year Question B1

Observed FeaturesPart a)

This question was basically the same question that appeared on the intermediate technological examination paper (Question A1, refer to Figure A2-12). The advanced students were similarly unfamiliar with Compton scattering, 29% of students confused it with another experiment and others gave a variety of experimental descriptions including in their responses a range of electromagnetic waves and a range of targets.

The advanced students were marginally more successful at describing the interaction that occurs between photons and electrons in Compton Shifting with 24% describing classical particle phenomena (collisions transferring momentum and transferring kinetic energy) and only 37% described classical wave phenomena (reflection, diffraction, scattering etc).

Part c)This question requires 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

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fusion. Most students attempted to reconstruct the four-step hydrogen fusion process and this made up the bulk of their answer.

Second Year – Question A2

Second Year Intermediate Physics 2001& 2101– Technological & Environmental

Question A2 (15 marks/100)

An investigation of the eigenstates of an electron in a triangular wellyields an eigenfunction of the form [W] shown in figure 1. The potential has a maximum depth of 1.2 keV and a width of 0.12 nm. The eigenvalues for all thebound eigenstates are given in the table.

(a) Counting the lowest energy eigenstate as state n=1, which is the eigen state seen in the diagram?

(b) Explain what is meant by the term normalisation constant as applied to the wave function.

(c) Draw a copy of the potential well shown in figure 1 and using the same x scale, sketch the probability density distribution of the particle in this eigenstate.

d) Sketch the probability density distributions for the lowest and highest energy level

Figure A2-14 : Examination Script – Second Year A2

Observed FeaturesStudents found this question relatively straightforward. Given

stimulus material on wave functions and potential diagrams they could interpret the material and determine the eigenstate and the probability distribution. 70% of students could give a correct definition of normalisation constant.

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A2.3.2 Results Carried Forward – Examination ScriptsThe 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. 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/particle view to a wave function view.

3. 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 hides their lack of understanding of the physical situation.

A2.3.3 Examination Script Data SetsFollowing twenty-six tables contain the coded data sets for the five

examination script questions (Refer to Tables A2-9 through A2-34).

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First Year Physics – Question 9 /1

Table A2-9 : Examination Script Coding - First Year Question 9 (1 of 2). Note: The 2nd column coded for the order in which the coded information was presented. The T prefix means that the information coded was presented prior to response working (ie. In a common area on the examination script)

A2-51First Year Physics – Question 9 /2

Table A2-10 : Examination Script Coding - First Year Question 9 (2 of 2)

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A2-55First Year Physics – Question 10 /4


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Second Year Advanced Physics – Question B1 /1

Table A2-20 : Examination Script Coding - Second Year Advanced Question B1 (1 of 6)

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Second Year Physics – Question A1 /1

Table A2-26 : Examination Script Coding - Second Year Question A1 (1 of 8)

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A2-75Second Year Physics – Question A2 /1


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A2.4 PRELIMINARY INTERVIEWS RESULTS AND ANALYSISThe preliminary interviews served two purposes; 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. The second of these two purposes is discussed in section A2.5.

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 interviews). The initial preliminary interviews were unstructured or recursive in nature and as more were completed they became semi-structured, the aim being to progressively focus the interview towards the final interview instrument. The preliminary interview was used to:

explore ideas and issues deeply, trial question types and question order, experiment with opening and closing sections of the interview establish suitable time lengths for different sections

A2.4.1 Analysis of Data CollectedThe interviews were transcribed from tape immediately and

annotated with reflective notes. A detailed personal and analytical log was written for each interview. Key features of each interview were noted on the cover page. A representative transcript document for one particular preliminary interview consisting of the cover page, transcript and reflective notes (selected pages only - pages 1-6, 29-31) (Refer to Figures A2-15 through A2-23), detailed personal log and detailed analytical log follows.

Figure A2-15 : Representative Preliminary Interview Transcript – TED Page 1 Cover Page (1 of 9)

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Figure A2-16 : Representative Preliminary Interview Transcript – TED Page 2 (2 of 9)

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Following is the detailed personal log for the interview with Ted and is based upon the information recorded in the first column of the transcript.

Personal Log – SID 06Interview 6/10/00 - TED

Participant and Interview DetailsThe participant chosen for the purpose of in-depth analysis (second postgraduate student) was known to the interviewer via contact through School of Physics activities including tutoring and the Physics Society. The participant is nearing the completion of his thesis in theoretical physics. He is involved in the School’s teaching program in both the First Year tutorials and the computational physics laboratories as a tutor/demonstrator. The participant responded to the email interview invitation, an interview was arranged via a telephone call and scheduled for 3:00pm on 6 October 1999. The participant indicated that he could spare 1 hour. The interview was conducted in Physics A28 Room 105, which has been specifically setup as a dedicated interview laboratory. The interview was audio-taped and no additional notes were taken by the interviewer.

Interview ProcessOverall the interview went smoothly and a good rapport existed between the interviewer and participant. The smoothness could certainly be attributed to the prior working relationship formed during previous tutorial sessions. Additionally the participant was very familiar with the interview topic having taught quantum mechanics for the past three years in the physics computational laboratory.

The participant arrived on time, was dressed in casual attire, appeared relaxed and chatty prior to the commencement of the interview. The participant was seated on the opposite side of a medium sized table located centrally in the interview room. The participant treated the interview process as a professional activity and appeared to be reasonably relaxed and at ease with the environment. As an interviewer I perceived the participant as a very practically orientated teacher with considerable expertise and experience in teaching quantum mechanics to tertiary level students. This opinion was based mainly upon the very reflective manner in which he responded to questions during the interview.

Suitability of SettingThe interview setting is not ideal because the laboratory is located in the basement area of the Physics Building. This poses a number of problems the most critical of these being the resonant noise generated from other equipment located in the basement area. The earlier interviews which used a standard audiotape recorder were swamped by low frequency hash that drowned out softer speech. This problem was overcome during this interview by using a filter and a more sophisticated tape deck with noise reduction features. These changes to the environment (i.e. it now looks like a sound studio) might upset some participants and the interview laboratory will require a little remodelling to combat this likely problem. The good news though was that the audio quality is readable. These issues did not seem to upset the participant and he actually commented favourably on the lighting and pictures present in the room.

A Brief Reflective Analysis

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The interview was meant to be open-ended from a question viewpoint and thus timing was not a concern. One hour was allotted and this proved satisfactory. There was no list of prepared questions.

Upon examination of the transcript my interview technique was weak in a number of aspects which are outlined below.

The opening question concerning the participant’s experiences was a disaster. It was meant to clearly convey to the participant that the interview was reasonably open, this was attempted by asking a wide range of “What do you think?” questions in one massive blob. Although the participant got the idea of the intended openness of the interview by responding to the first question with “I was hoping for something more specific”. It was felt that a softer start would have been less traumatic and provided a similar result.

The participant was quite reflective in all his responses and thus minimal prompting was required. For example, the participant often referred to his own learning experiences then related these to his own teaching experiences. Note that in the other three interviews conducted the participants were less reflective and a considerable level of prompting was required. The questions posed were mainly opinion value or nudging in nature. This strategy was adopted consciously in an attempt to maintain an open flowing dialogue throughout the interview. The experiment seemed to have worked in this case. A better constructed strategy is required to generate a working environment where the participant is very relaxed but aware that we are interested in their story, and not some sort of ‘correct’ answer.

Several of the questions were malformed in the sense that they tended to either be too complex (i.e. too many sub-parts) or were just ‘way left of field’ and did not really fit into the conversational flow. Both these weaknesses are founded in inexperience and a number of mechanisms to combat this over enthusiasm in moving the questioning along will need to be explored. (Overall I felt the questions were on the whole effective and kept the dialogue moving along).

During the interview the interviewer felt that a number of leading questions were posed, asking a question and half answering it. For example “Does the student recognise when they see say given the Bohr atom or something, do they recognise that (it is) a model or do they take it as said fact?” (0198). The question would have been better phrased as “What do you think the Bohr model of the atom represents to the students?”. This problem was in some sense an artefact of the type and form of the interview combined with the interviewer’s inexperience. There were no set questions and thus questions were constructed as the interview progressed. A watch will need to be kept on this and a series of strategies practiced in order to construct more concise questions on the ‘fly’ as the interview progresses.

Interview CloseThe interview was concluded in an orderly manner on time. The participant commented that he would be interested in participating in any further research. The following week a rough copy of the analysis was provided to the participant. He was surprised that he had said so many intelligent things. He commented on some of the problems he experienced with the questions he had been asked (these have been addressed in the preceding section). His main criticisms centred on

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making sure that questions are single questions (as opposed to multifaceted) and suggested that a more Socratic dialogue be applied.

ConclusionIn conclusion the information provided by the participant was reflective in nature and he generally supported his viewpoint by providing evidence based on his personal experiences. Thus it was felt that the information he provided was valid and relevant to the research topic and therefore the process did get to the truth of the participant’s feelings and experience. The factors that might have influenced the information given mainly centred around the working relationship that had developed between the participant and the interviewer while working together on several prior occasions in tutorials. Given a scenario where the participant was not known to the interviewer, it was felt that the interview would not run quite as smoothly and more difficulties would have been encountered when formulating questions on the ‘fly’.

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Following is the detailed analytical log for the interview with Ted and is based upon the information recorded in the fourth and fifth columns of the transcript.

Analytical Code Description – SID 06for Interview 6/10/00 - TED

OverviewSix 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.

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.

Category DefinitionsDefinitions of these initial primary categories are tabulated below, refer Table 1. Table 2 contains a set of brief definitions for the secondary categories and includes an occurrence summary.

Primary Category DefinitionsCATEGORY DESCRIPTIONConcept (C) An idea, concept or theme that stands alone and

primarily relates to quantum mechanicsPersonal Comment (PC)

Comment relating to the teaching/ learning process

Personal Experience (PE)

Comment based upon the participant’s personal experiences or knowledge

Student Experience (SE)

Description of the student’s experience

Self Reflection (SR) A comment based upon a personal reflective thought or experience and is some what philosophical in nature

Time Frame (WH) The time related context in which statements are

Personal Comment

Personal Experience

Concept

Student Experience

Self ReflectionTime Frame

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being madeTable 1 : Primary category definitions for interview

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Primary and Secondary Coding

CATEGORY SECONDARY KEY WORDS TotCONCEPT (C) C – Analogy 3

C – Bohr Model /Bohr model of the atom 2C – Duality / Wave particle nature of matter 6C – Ideas / Underlying ideas 2C – Key Conc / Key underlying concepts 3C – Lagrangian / Energy used to solve a problem 1C – Maths / Mathematics 3C – Matter Waves / Wave nature of matter 3C – Model 5C – Photo Elec / Photoelectric Experiment 2C – Potential / Usually electric potential 6C – Probability / Statistical understanding 5C – Quantisation / Discreteness found in nature 1C – Quantum Mech / Quantum mechanics 3C – Schrödinger / Wave equation for matter 2C – Tunnelling / Non classical phenomena 1C – Unc Principle / Heisenberg’s uncertainty principle 2C – Waves / Wave phenomena 1C – Well / An electrical potential 1

PERSONAL COMMENT (PC) PC – Teach Early / Teach the topic earlier 4PC – Teach HS / Teach topic at High School 3PC – Teach Qual / Teaching quality questioned 8

PERSONAL EXPERIENCE (PE) PE – Analogy / Metaphor to describe phenomena 3PE – Difficult 4PE – Engagement / Activity involved 3PE – Lack Under / Surface knowledge 12PE – Mis Interp / Misinterpretation of … 1PE – Not Engaged / Lack of involvement 1PE – Requirement / Necessary to understand 1PE – Taught 1stY 1PE – Taught Later 1PE – Understood / Good understanding of … 7

STUDENT EXPERIENCE (SE ) SE – Solar / Example Solar Panel 1SELF REFLECTION (SR) SR – Lack Under / Surface knowledge 2

SR – Math vs Con / Mathematics vs Concept 3SR – Math vs Phys / Mathematics vs Physics 4SR – Newt vs Quan / Newtonian vs Quantum mechanics

1

SR – Not Sure 2SR – Phys vs Chem / Physics vs Chemistry 1SR – Phys vs Con / Physics vs Concept 2SR – Shift Focus / Change of emphasis 1

TIME FRAME (WH) WH – 1stY 1WH – 2ndY 2WH – 3ndY 1WH – Early 1WH – HS / High School 3

Table 2 : Primary and secondary category summary

The set of categories described above are preliminary and are designed to form a useful launching and reference point for the early stages of this study. The researcher anticipates that another ten interviews should provide sufficient understanding of the topic to undergo a process of modification and reclassification of the categories into a set of more logical structures.

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AnalysisSeveral threads are clearly visible through the interview – student’s background knowledge; the order and timing in which concepts can be taught; teaching strategies and methods; the level of student understanding; and the participant’s perspective on how physics fits into education.

Student’s background knowledgeThe participant made reference to a number of areas in a student’s knowledge that he felt were weak and offered probable reasons in a number of cases. For clarity the probable reasons will be detailed first followed by a list of specific areas.

The participant was initially concerned with the quality of teaching provided in high schools in regards to quantum concepts. The participant described two problems.

His first point related to the experience levels of high school science teachers,

“I am slightly concerned with quantum mechanics that when people do teach sort of it a little bit of it at school … that it can actually be quite easily taught sort of wrong … People don’t understand it and you know high school teachers have not necessarily had that good a physics training …” (P008)

and the second related to students not understanding the concept of a model sufficiently.

“I don’t feel that many students, coming out of high school have the idea of what you are being presented is possibly a model for how something works and not necessarily what’s going on.” (P024)

He went on to explain that these issues are compounded by out of school influences such as science popularisation. One example discussed by the participant related to the concept of uncertainty.

“Uncertainty principle I am using because it is something that in particular, that, is likely that has been popularised and I think, and in some cases popularised not well, people don’t quite have it … I remember people sort of vaguely discussing this when I was at school, and I realised from the stuff they were saying that it wasn’t right.. it’s not what it means, and … what they were saying was something else entirely.” (P030)

At several junctures in the interview the concept of probability was discussed and it was clear by the interview’s conclusion that the participant felt that more familiarity with statistics would assist students in understanding quantum concepts. He clearly articulated his feelings in this matter quite early on in the interview and this theme continued strongly throughout.

“… I think the whole area of probabilities, uncertainties comes into everything I don’t think they are well understood. … not just by quantum physics students but just generally … they still don’t have a good grasp, of what a probability means.” (P080)

In addition to the aforementioned concepts of a model, the terms uncertainty and probability; the participant was also concerned with the level of understanding in the areas of potential, tunnelling and wells. Most

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interestingly the participant commented that students do not understand the links between physics concepts and the physical world in both quantum and Newtonian mechanics.

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(Quantum)“I think they get what potential is, like they link that what they see is fine with the mathematics. They don’t link see potential with … sort of what physical situation it is.” (P046)

and

(Newtonian)“that when they come to this idea of a particle bouncing around and then actually measuring how fast it is going and working out … some sort of inverse relationship between how fast it is going and how long it spends in a particular region. They have trouble … making that connection” (P072)

The order and timing in which concepts can be taughtOne line of questioning investigated the participant’s thoughts on which concepts he thought were key to learning quantum mechanics and which of these should be taught earlier in a students education.

The participant stated clearly on several occasions that quantum mechanics should be introduced to students early in their high school education.

“… I do think that students should be introduced to it reasonably early ‘cause it is sort of a bit freaky interesting.” (P008)He believes that the students should not be shielded from the concepts and that they already have experiences with a number of quantum concepts.

“I think to some extent some of the ideas from a principle sense could be taught, as I said things like the photoelectric effect can be discussed… in a junior science course. … the principle that pretty much every kid probably has seen a solar panel they have got some idea that you can shine light on something and get electricity out.. anything just to discuss basically.. some ideas behind it but I don’t think that you could do… much beyond, that sort of thing in junior science… But in an HSC level I think you could do a bit, like some of the mathematics …” (P014)

He also indicates a number of abstract concepts that could be explored by high school students including quantisation, duality (the wave particle nature of matter) and from the previous section more statistics especially probability.

“I think quantisation… I think getting the idea … like that waves of light can be treated as a particle can probably be … you can see it as a wave or its you can treat it as a particle with photons with a particular energy. I think that that could be taught at quite an early stage. ... and possibly some of the ideas of matter being treated as waves and streams could also work, but I’m not sure how much you can get out of that.” (P012)

Teaching strategies and methodsTwo teaching strategies were prominent in the participant’s discussions. Engagement of the students with the material and the use of analogies to convey quantum mechanics concepts.

In relation to engagement the participant considered that hands on activities and mental engagement are key to understanding. The participant reflected both upon his learning experiences and those he has observed in the classroom.

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“I feel … from my point of view, from when I was a student …. I didn’t really have a good grip of what the Schrödinger equations was about until I actually saw it demonstrated and we solved it and we actually did stuff with it in the computational lab. … I don’t know whether that’s a general thing. The students I have had … [it] … does seem to help them.. “ (P034)

The participant discussed a number of analogies that he uses while teaching quantum mechanics including the vibrating string and a ball caught between two hills. He considered that analogies were key components in the learning activity and that weaker students could use an analogy to focus their thoughts and solve problems.

“I have always found to get across best is just the actually talk about… There are two things you talk about … One there is the idea of a ball rolling in some sort of valley and can’t get out of.. and can just roll back and forwards.. and the other is that of a wave on a string. So you sort have got I suppose a particle and a wave model. You have a wave on a string and you can have certain values in between how where it is tied off. One gives you the idea of the energy and not having enough energy to get out and the other one gives you the discretisation of the levels that are allowed sort of sort values modes of how it vibrates.” (P056)

“… of analogies I’d say the idea of a wave on a string. Quite a few students if they haven’t got that down you can make them understand that, that makes things a reasonably bit easier for understanding why you get … discrete bound states” (P080)

The level of student understandingThe participant believed that students will by second year have grasped and understood a number of concepts quite well up to a certain level. He considers that a second year student understands the smeared out nature of matter, wave particle duality and bound states.

“I think they have the idea.. I actually think, a lot of them have the idea that the thing is smeared out. And the fact that it is smeared out and that they almost loose completely that it is a particle or could be considered that it is a particle. A question that often throws them is based upon some sort of stepped well. (P072)”

“I would say the key concepts you get are the wave particle sort of duality that you can get…. Treat both things as waves or particles. The idea that you get the you get states which are bound you can have sort of entrapped when you get that then you them you can get discrete levels. … And how they interact …” (P094)

The participant’s perspective on how physics fits into educationAn interesting point raised by the participant was the relationship of physics to chemistry. The participant feels that Chemistry simply presents a model whereas Physics describes the underlying framework.

“it seems to me chemistry if you present it that way saying this is the model and this is how we and these are the calculations for the energy levels and then do things with that, seems like chemistry rather than physics where you would want to say this is the model and you got it based upon these principles. ..” (P018)

Discussion

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The discussion outlines what information has been found by making a number of propositions and then provides several future focus questions relating to information that should be explored in future interviews.

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PropositionsThe analysis identified a number of potential propositions that could be tested using information gathered in subsequent interviews.

The use of analogies as a teaching strategy assists students in conceptualising quantum mechanical phenomena.

Students have difficulty in connecting quantum mechanical concepts to physical applications.

A number of key concepts exist that will facilitate a student’s learning experience.

Students possess a number of preconceptions that could inhibit the formation of consistent conceptual mental models.

Future Focus Questions

The analysis identified a number of refined and additional questions that should be incorporated into future interviews. These have been listed below under the sub-headings Academic Staff and Students.

Academic Staff

What are the emphases, prerequisites and outcomes they expect across the years?

When and what concepts should be taught? What types of analogies can be used to teach quantum mechanics? What key tools do students require to be successful? How and when should students be taught to understand modelling?

Students

Do students perceive that quantum mechanics is taught differently in chemistry to physics?

Check the student perception of the computational laboratory experience.

Design some probing questions to elicit student conceptions on potential wells and barriers.

Need to research further the links that student have in connection with mathematics, physics, terminology, analogies and the physical world.

Do students comprehend the limitations associated with analogies?

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A2.4.2 Coding and ResultsEach 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.

AnalogiesEight 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)

AssessmentThe 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 SimulationsThis 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

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Student comments on course structure were predominantly related to the integration of lecture and laboratory components of the course. For example one 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)

DifficultiesOnce 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

DualityThroughout the preliminary interviews the students used a variety

of words to describe the quantum entity including: wave, particle,

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wave/particle, wave packet, smeared particle, wave function and probability density. The students 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 thought 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.

MathematicsThe 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 “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 3rd year when you do it again its much easier.” (PrelimSID13)

Potential Energy DiagramsThe 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

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describing other more complicated diagrams. “The wells steps always confuse me … I get the wave function shape wrong” (PrelimSID02)

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 WorldThe 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 ThoughtsThroughout 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.

TunnellingWhen describing or discussion 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)

A2.4.3 Results Carried Forward – Preliminary InterviewsThe following five categories emerged from the preliminary

interview analysis and were carried forward to the selective coding phase.

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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. Their perception of their strengths and weaknesses could influence future learning.

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.

A2.4.4 Chemistry InterviewsAt 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 thesis and so the development of the chemistry interview instrument, its implementation and subsequent data analysis are not reported here. The research on quantum learning in chemistry provided additional theoretical sensitivity to the study.

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A2.5 DEVELOPMENT OF THE FINAL INTERVIEW INSTRUMENTTo develop the final interview instrument we must bring together

the interview protocol established in Chapter 3, and the categories that were brought forward from the data in the grounded theory study.

A2.5.1 Constraints of the ProtocolThe interviewer conformed to the interview protocol established for

this study (see Chapter 3 for details). Requirements of the protocol that govern interview development are listed below.

The interview will be focussed or semi-structured and consist of open-ended questions

Consideration is to be given to data validity and reliability during interview construction and administration

The interview begins with questions designed to relax the subject and form a rapport

The interview is brought to a close with a series of reflective questions

The interview will be approximately 1 hour in duration

The questions would revisit key concepts during the interview using different modes of questioning, contexts and styles. The interviewer has the flexibility and the freedom to follow up issues that emerge unexpectedly; he may change the order of the questions or leave out questions if deemed necessary.

A2.5.2 Categories Brought Forward from the Grounded StudyCombining 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. 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

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examples tended to highlight gaps, inconsistencies and misconceptions in student’s understanding of quantum mechanics. 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/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 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.

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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 which 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.

The primary focus for the interviews was students’ conceptual understanding of quantum mechanics. It was found during the preliminary interviews that asking specific mathematics questions focussed the students’ attention upon that aspect and appeared to put them off conceptual descriptions. Information was available about the student’s mathematics background and was collected, but otherwise the interview left out specific mathematical discussions. If the student brought it up it was discussed otherwise not.

The seven categories Real World, Duality, Uncertainty, Analogies, Tunnelling, Difficulties and Reflections would become the topics for the final interviews.

A2.5.3 Selective CodingThe seven categories were further analysed using selective coding

to identify three underlying themes (Refer to Table A2-35). These themes carried forward and informed the sequencing process.

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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 A2-35 : Interview Themes

A2.5.4 Sequencing TopicsTo provide a workable and logical sequence for the seven interview

topics the format of the interview needs to be considered. The protocol required the interview to comprise three parts; an opening, a body and a close.

OpeningTo 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, be answerable at a number of levels and consist of a range of aspects that could be discussed. It would have a depth of complexity, a range of applications and could re-emerge later in the interview.

A number of topics were trialed for the opening during the preliminary interviews. They are listed in Table A2-36 on the following page, along with the advantages and disadvantages revealed in analysis.

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Interview Opening Topics

Opening Topic

Advantages Disadvantages

Double Slit Experiment

Familiar topic Students were relaxed

and confident Depth of complexity Later link to analogy

Some students saw it linked to optics but not quantum mechanics

Photoelectric Effect

Familiar topic Depth of complexity

Most students could not recall the details or significance of the photoelectric effect

Did not relax the studentsRole of Mathematics in Quantum Mechanics

Familiar topic Students were relaxed

and confident Gave good overview of

maths ability

Gave the entire interview a strong maths flavour

Too open and hard to control

Wave/Particle Duality

Familiar topic Depth of complexity Stimulated a range of

ideas and feelings

Too open and hard to control

Did not relax students Was unsettling rather than

setting the sceneTable A2-36 : 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.

CloseTo close the interview we need a topic that sums up the issues

raised during the body and gives the students a relaxed opportunity to reflect back on their responses. The interview should end with the student feeling relaxed and appreciated. A number of closure topics were tested during the preliminary interviews they are listed in Table A2-37 below along with the advantages and disadvantages revealed in analysis.

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Interview Closure Topics

Closure Topic

Advantages Disadvantages

Reflection on course

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

Responses may be destructive or personal

Difficulties Students have considered the topic in part prior to the closure

Allows students to identify their difficulties


Some students may feel defensive

Interview closes with students focussing on low points

Real world Students have considered the topic in part prior to closure

Links quantum mechanics to useful applications


Many students may not be able to identify and discuss real world applications

Table A2-37 : 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.

BodyThe 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 trialed and so we have data to inform the sequencing. In addition the topics can be classified according to the predominant learning domains2 with which each is associated. The 2 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)

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domains of Skill, Affective and Cognitive were addressed in addition to the content. The results of the trials and the learning aspect classification appear in Table A2-38.

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.

Interview Body Topics

Body Topic Advantages Disadvantages DomainAnalogies Reveal students’ ability to visualise, and shift

context Helps students understand abstract concepts

Students often don’t see limitations of analogies

Some students don’t like them Some lecturers don’t use them

Cognitive & Skill

Difficulties Allows students to identify their own difficulties

Students describe a range of difficulties

Could make students defensive Affective

Real World In a detailed answer student shows how quantum mechanics is linked to real world

Links between theory, experiment and application

Highlights student difficulties

Students often do not see any link between quantum mechanics and the real world

This topic puts off weak students

Cognitive

Tunnelling 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

Weak students cannot give a detailed response without prompting

Students can get tangled and confused in their answers

Cognitive & Skill

Uncertainty Identified as a key concept of quantum mechanics

Students give a range of descriptions Strong links to other topics

Student responses can vary depending on the context used

Cognitive

Wave/Particle Duality

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

Very broad topic and students can get off track

Concept is not revisited in senior and honours level courses

Cognitive

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Strong links to other topicsTable A2-38 : Interview Body Topics

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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 where ever 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 ask an application question on tunnelling later 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 trailed 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 A2-39 provides a summary of the final interview instrument. The interview guide with complete and detailed questions appears in Appendix 3.

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Final Interview Instrument Structure

Interview Protocol

Timeline

(minutes)

Learning Domain

Topic Questions Theme Addressed

Rapport 0 Cognitive Wave/Particle Duality

Double Slit Wave or Particle? Uncertainty

Concept & LinkingConceptConcept

Body 10 Evidence of Wave/Particle duality Applications/Examples/

Experiments

LinkingLinking

Revisit key concepts

15 Cognitive & Skill

Tunnelling Draw a well and a barrier Compare and contrast Discuss terminology

ToolsTools, Linking & ConceptTools & Concept

Different modes of questioning

30 Affective Difficulties Learning difficulties in quantum mechanics

What tools do you need? Analogies and models you use?

Concept & Tools ToolsTools & Linking

Different contexts 40 Cognitive Real World Explain Electromagnetic shielding or radioactivity in terms of quantum mechanics

Linking

Different styles 45 Cognitive & Skill

Analogies Quantaroo (macroscopic analogy of double slit)

Concept, Tools & Linking

Closure 55

60

Affective Reflection Changes in understanding What did you need to understand? Expectation of lecturer Advice to new lecturer

Concept, Tools & LinkingConcept, Tools & Linking

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Concept, Tools & LinkingConcept, Tools & Linking

Table A2-39 : Structure of the Final Interview Instrument

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A2.6 ASSOCIATED LITERATURE REVIEWSA2.6.1 Concept Mapping

To assist in the analysis of the concept maps a literature review was undertaken. The following informed this study and is provided as a resource.

Concept mapping - Educational research

Al-Kunifed, A., Wandersee, J.H., (1990) One hundred references related to concept mapping, Journal of Research in Science Teaching, 27(10), 1069-1075

Bagno, E., Eylon, B.S., (1997) From problem solving to a knowledge structure: an example from the domain of electromagnetism, American Journal of Physics, 65(8), 726-736

Brumby, M., (1983) Concept mapping: structure or process?, Research in Science Education, 13, 9-17

Cronin, P.J., Dekkers, J., Dunn, J.G., (1982) A procedure for using and evaluating concept maps, Research in Science Education, 12, 17-24

De Jong, T., Ferguson-Hessler, M.G.M., (1986) Cognitive structures of good and poor novice problem solvers in physics, Journal of Educational Psychology, 78(4), 279-288

Domin, D.S., (1996) Comment: concept mapping and representational systems, Journal of Research in Science Teaching, 33(8), 935-936

Dorough, D.K, Rye, J.A., (1997) Mapping for Understanding, The Science Teacher, 64(1), 37-41

Edwards, J., Fraser, K., (1983) Concept maps as reflectors of conceptual understanding, Research in Science Education, 13, 19-26

Halloun, I., (1996) Schematic modelling for meaningful learning of physics, Journal of Research in Science Teaching, 33(9), 1019-1041

Hegarty-Hazel, E., Prosser, M., (1991) Relationship between students’ conceptual knowledge and study strategies – part1: student learning in physics, International Journal of Science Education, 13(3), 303-312

Hegarty-Hazel, E., Prosser, M., (1991) Relationship between students’ conceptual knowledge and study strategies – part2: student learning in biology, International Journal of Science Education, 13(4), 421-429

Lawless, C., (1994) Investigating the cognitive structure of students studying quantum theory in an open-university history of science course: a pilot study, British Journal of Educational Technology, 25(3), 198-216

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Liu, X., Hinchey, M., (1996) The internal consistency of a concept mapping scoring scheme and its effect on prediction validity, International Journal of Science Education, 18(8), 921-937

Markham, K.M., Mintzes, J.J., (1994) The concept map as a research and evaluation tool: Further evidence of validity, Journal of Research in Science Teaching, 31, 91-101

Nakhleh, M.B., Krajcik, J.S., (1996) Reply to Daniel S. Domin’s comment on concept mapping and representational systems, Journal of Research in Science Teaching, 33(8), 937-938

Novak, J.D., Gowin, D.B., Johansen, G., (1983) The use of concept mapping and knowledge vee mapping with junior high school science students, Science Education, 67, 625-645

Novak, J.D., Gowin, D.B., (1984) Learning How to Learn. (New York, Cambridge University Press)

Novak, J.D., (1990) Concept mapping: A useful tool for science education, Journal of Research in Science Education, 27(10), 937-949

Roth, W.M., Roychoudhury, A., (1993) The concept map as a tool for the collaborative construction of knowledge: a microanalysis of high school physics students, Journal of Research in Science Teaching, 30(5), 503-534

Vazquez, O.V., Caraballo, J.N, (1993) Mega-analysis of the effectiveness of concept mapping as a learning strategy in science education, The proceedings of the third international seminar on misconceptions and educational strategies in science and mathematics, Ithaca, New York

Von Glasersfeld , E., (1991) A constructivist’s view of teaching and learning, In Duit, Goldberg and Niedderer (Eds.), Research in physics learning: Theoretical issues and empirical studies, Proceedings of an International Workshop, University of Bremen

White, R., Gunstone, R., (1992) Probing Understanding. London, The Falmer Press

Wilson, J.M., (1993) The predictive validity of concept-mapping: relationships to measures of achievement, The proceedings of the third international seminar on misconceptions and educational strategies in science and mathematics, Ithaca, New York

Wilson, J.M., (1994) Network representation of knowledge about chemical equilibrium: Variations with achievement, Journal of Research in Science Teaching, 31, 1133-1147

Concept mapping - Teaching

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Adamczk, P., Wilson, M., Williams, D., (1994) Concept mapping: a multi-level and multi-purpose tool, School Science Review, 76(275), 116-124

Adamczk, P., Wilson, M., (1996) Using concept maps with trainee physics teachers, Physics Education, 31(6), 374-381

Anderson, E.J., (1997) Active learning in the lecture hall, Journal of College Science Teachers, 26(6), 428-429

Anderson-Inman, L., Zeitz, L., (1993) Computer-based concept mapping: active study for active learners, The Computing Teacher, 20, 6-11

Malone, J., Dekkers, J., (1984) The concept map as an aid to instruction in science and mathematics, School Science and Mathematics, 84(3), 220-231

Nakhleh, M.B., Krajcik, J.S., (1994) Influence of levels of information as presented by different technologies on students’ understanding of acid, base and pH concepts, Journal of Research in Science Teaching, 31(10), 1077-1096

Concept mapping - Assessment

Araceli Ruiz-Primo, M., Shavelson, R.J., (1996) Problems and issues in the use of concept maps in science assessment, Journal of Research in Science Teaching, 33(6), 569-600

Austin, L.B., Shore, B.M., (1995) Using concept mapping for assessment in physics, Physics Education, 30(1), 41-45

Liu, X., Hinchey, M., (1993) The validity and reliability of concept mapping as an alternative science assessment, The proceedings of the third international seminar on misconceptions and educational strategies in science and mathematics, Ithaca, New York

McClure, J.R., Sonak, B., Suen, H.K., (1999) Concept Map Assessment of Classroom Learning: Reliability, Validity and Logical Practicality, Journal of Research in Science Teaching, 36(4), 475-492

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APPENDIX 2................................................................................................................................ 11

GROUNDED THEORY INVESTIGATION – STAGE 1................................................................11A2.1 CONCEPT MAP RESULTS AND ANALYSIS.................................................................12

A2.1.1 Concept Mapping Exercise.................................................................................................12A2.1.2 Results - Concept Map Structures.......................................................................................15

Structural and Nodal Analysis..........................................................................................................15Summary of Results from Structural and Nodal Analysis.............................................................18

Other Interesting Features that Emerged from the Concept Maps......................................................18Summary of Results from Concept Map Analysis........................................................................19

A2.1.3 Results Carried Forward – Concept Maps...........................................................................19A2.1.4 Concept Mapping Data Sets................................................................................................20

A2.2 EXPERT GROUP DISCUSSIONS/INTERVIEWS RESULTS AND ANALYSIS................23The Expert Focus Group Discussion.................................................................................................23The Individual Expert Interviews......................................................................................................24Results – Expert Group Discussions/Interviews................................................................................27

Teaching Approaches...................................................................................................................29Key Concepts...............................................................................................................................29Assessment..................................................................................................................................30Perceived Difficulties..................................................................................................................31Maths...........................................................................................................................................31Analogies.....................................................................................................................................33Computer Simulations.................................................................................................................33Experiments.................................................................................................................................34

A2.2.2 Results Carried Forward – Expert Discussions/Interviews...................................................34A2.3 EXAMINATION SCRIPT RESULTS AND ANALYSIS.....................................................36

First Year – Question 9.....................................................................................................................38Observed features........................................................................................................................38

First Year – Question 10...................................................................................................................39Observed Features........................................................................................................................39

First Year – Question 11...................................................................................................................40Observed Features........................................................................................................................40

Second Year – Question A1..............................................................................................................42Observed Features........................................................................................................................42

Second Year – Question B1..............................................................................................................44Observed Features........................................................................................................................44

Second Year – Question A2..............................................................................................................45Observed Features........................................................................................................................45

A2.3.2 Results Carried Forward – Examination Scripts..................................................................46A2.3.3 Examination Script Data Sets..............................................................................................46

A2.4 PRELIMINARY INTERVIEWS RESULTS AND ANALYSIS............................................73A2.4.1 Analysis of Data Collected..................................................................................................73A2.4.2 Coding and Results.............................................................................................................92

Analogies.....................................................................................................................................92Assessment..................................................................................................................................92Computer Simulations.................................................................................................................92Course structure...........................................................................................................................92Difficulties...................................................................................................................................93Duality.........................................................................................................................................93Mathematics................................................................................................................................94Potential Energy Diagrams...........................................................................................................94Real World..................................................................................................................................95Reflective Thoughts.....................................................................................................................95Tunnelling...................................................................................................................................95

A2.4.3 Results Carried Forward – Preliminary Interviews..............................................................95A2.4.4 Chemistry Interviews..........................................................................................................96

A2.5 DEVELOPMENT OF THE FINAL INTERVIEW INSTRUMENT....................................97A2.5.1 Constraints of the Protocol..................................................................................................97A2.5.2 Categories Brought Forward from the Grounded Study.......................................................97A2.5.3 Selective Coding.................................................................................................................99A2.5.4 Sequencing Topics............................................................................................................100

Opening..........................................................................................................................................100Close..............................................................................................................................................101

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Body...............................................................................................................................................102A2.6 ASSOCIATED LITERATURE REVIEWS......................................................................107

A2.6.1 Concept Mapping..............................................................................................................107Concept mapping - Educational research........................................................................................107Concept mapping - Teaching..........................................................................................................108Concept mapping - Assessment......................................................................................................109

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Figure A2-1 : Concept Map Instruction Sheet (Printed A4 Portrait)................................................13Figure A2-2 : Example “Newtonian Concept Map” provided with Concept Map Instruction Sheet

(Printed A4 Landscape on reverse).........................................................................................13Figure A2-3 : Concept Map Cover Sheet (Printed A4 Portrait).......................................................14Figure A2-4 : Concept Map Answer Sheet (Printed A3 Landscape)................................................14Figure A2-5 : 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 (Refer to Figure A2-4))..........................................................................15

Figure A2-6 : Focus Group Discussion Points.................................................................................24Figure A2-7 : Physics Lecturer Guide Interview Questions.............................................................25Figure A2-8 : Chemistry Lecturer Guide Interview Questions........................................................27Figure A2-9 : Examination Script – First Year Question 9..............................................................38Figure A2-10 : Examination Script – First Year Question 10..........................................................39Figure A2-11 : Examination Script – First Year Question 11..........................................................40Figure A2-12 : Examination Script – Second Year Question A1.....................................................42Figure A2-13 : Examination Script – Second Year Question B1.....................................................44Figure A2-14 : Examination Script – Second Year A2....................................................................45Figure A2-15 : Representative Preliminary Interview Transcript – TED Page 1 Cover Page (1 of 9)

.............................................................................................................................................. 74Figure A2-16 : Representative Preliminary Interview Transcript – TED Page 2 (2 of 9).................75Figure A2-17 : Representative Preliminary Interview Transcript – TED Page 3 (3 of 9).................76Figure A2-18 : Representative Preliminary Interview Transcript – TED Page 4 (4 of 9).................77Figure A2-19 : Representative Preliminary Interview Transcript – TED Page 5 (5 of 9).................78Figure A2-20 : Representative Preliminary Interview Transcript – TED Page 6 (6 of 9).................79Figure A2-21 : Representative Preliminary Interview Transcript – TED Page 29 (7 of 9)...............80Figure A2-22 : Representative Preliminary Interview Transcript – TED Page 30 (8 of 9)...............81Figure A2-23 : Representative Preliminary Interview Transcript – TED Page 31 (9 of 9)...............82

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Table A2-1 : Concept Map Structural Types and Results Summary (not mutually exclusive).........17Table A2-2 : Maps with two or more links to ‘Uncertainty Principle’.............................................19Table A2-3 : Concept Map Coding – Linking and Map Structures (1of 2)......................................21Table A2-4 : Concept Map Coding – Primary Nodes within Wheel, Complex and Hierarchical

Structures (2 of 2).................................................................................................................. 22Table A2-5 : Expert Interview/Group Discussions - The depth of response against each identified

category................................................................................................................................. 28Table A2-6 : Expert Group - Key concepts identified by lecturers..................................................30Table A2-7 : Expert Group – Difficulties Identified by the 18 lecturers..........................................32Table A2-8 : Examination Script – Questions selected for analysis.................................................36Table A2-9 : Examination Script Coding - First Year Question 9 (1 of 2).......................................47Table A2-10 : Examination Script Coding - First Year Question 9 (2 of 2).....................................48Table A2-11 : Examination Script Coding - First Year Question 10 (1 of 5)...................................49Table A2-12 : Examination Script Coding - First Year Question 10 (2 of 5)...................................50Table A2-13 : Examination Script Coding - First Year Question 10 (3 of 5)...................................51Table A2-14 : Examination Script Coding - First Year Question 10 (4 of 5)...................................52Table A2-15 : Examination Script Coding - First Year Question 10 (5 of 5)...................................53Table A2-16 : Examination Script Coding - First Year Question 11 (1 of 4)...................................54Table A2-17 : Examination Script Coding - First Year Question 11 (2 of 4)...................................55Table A2-18 : Examination Script Coding - First Year Question 11 (3 of 4)...................................56Table A2-19 : Examination Script Coding - First Year Question 11 (4 of 4)...................................57Table A2-20 : Examination Script Coding - Second Year Advanced Question B1 (1 of 6)..............58Table A2-21 : Examination Script Coding - Second Year Advanced Question B1 (2 of 6)..............59Table A2-22 : Examination Script Coding - Second Year Advanced Question B1 (3 of 6)..............60Table A2-23 : Examination Script Coding - Second Year Advanced Question B1 (4 of 6)..............61Table A2-24 : Examination Script Coding - Second Year Advanced Question B1 (5 of 6)..............62Table A2-25 : Examination Script Coding - Second Year Advanced Question B1 (6 of 6)..............63Table A2-26 : Examination Script Coding - Second Year Question A1 (1 of 8)..............................64Table A2-27 : Examination Script Coding - Second Year Question A1 (2 of 8)..............................65Table A2-28 : Examination Script Coding - Second Year Question A1 (3 of 8)..............................66Table A2-29 : Examination Script Coding - Second Year Question A1 (4 of 8)..............................67Table A2-30 : Examination Script Coding - Second Year Question A1 (5 of 8)..............................68Table A2-31 : Examination Script Coding - Second Year Question A1 (6 of 8)..............................69Table A2-32 : Examination Script Coding - Second Year Question A1 (7 of 8)..............................70Table A2-33 : Examination Script Coding - Second Year Question A1 (8 of 8)..............................71Table A2-34 : Examination Script Coding - Second Year Question A2 (1 of 1)..............................72Table A2-35 : Interview Themes..................................................................................................100Table A2-36 : Interview Topics....................................................................................................101Table A2-37 : Interview Closure Topics.......................................................................................102Table A2-38 : Interview Body Topics...........................................................................................104Table A2-39 : Structure of the Final Interview Instrument............................................................106

appendix 2 - school of physics · web viewall of the physics lecturers had previously taught...

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