APPENDIX 2
GROUNDED 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
Refer to Chapter 4 for a summary and discussion of these results.
A2-11
A2-12
A2.1 CONCEPT MAP RESULTS AND ANALYSIS
In 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 Exercise
The 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.
A2-13
General Concept Mapping Instruction Sheet
CONCEPT MAPS
A good way to explore understanding is by drawing a concept map
Concept maps are useful for:
Students

Helps focus on important ideas in a
course

Helps recognise relationships
between key ideas and concepts in
the course

Useful as a revision tool, providing
a schematic summary

Helps conceptual understanding
How to draw a map



Lecturers
Helps to focus lecture on key
learning areas
Can use student maps to focus
lectures on students’ weaknesses
As a research tool
Below is an example of a concept map for mechanics. Concept maps have three features:
1. Concept Labels
2. Links
3. 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”
Figure A2-2 : Example “Newtonian Concept Map” provided with Concept Map Instruction
Sheet (Printed A4 Landscape on reverse)


A2-14
Concept Map Answer Cover Sheet Layout
QUANTUM PHYSICS
1998
Concept Map
Answer 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
Atom
Diffraction
Electron
Energy
Energy level
Frequency
Intensity
Interference
Light
Mass
Matter
Momentum
Orbit
Particle
Photon
Probability
Uncertainty Principle
Wave
Wavelength
Figure A2-4 : Concept Map Answer Sheet (Printed A3 Landscape)
A2-15
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 Structures
The 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 Analysis
Based 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
A2-16
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.
A2-17
Concept Map Structure Types
Map Type
String
String with
a wheel
attached
Hierarchy
Illustration
Description
Three or more concepts
are linked in a single
chain
Four or more concepts
are linked in a single
chain with a wheel
structure attached at
one end
Concepts are arranged
in a simple tree type
structure.
(n) %
(1)
1%
(7)
10%
(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
A number of single
concepts emanate from
a single concept
Wheel
linked to
another
wheel
Two concepts with a
number of joining
radial links
Bubble
Loops
Several string
structures that form
closed loops
Disjoint
The concepts are
arranged into two or
more separate
structures
Table A2-1 : Concept Map Structural Types and Results Summary
(2)
3%
(12)
18%
(2)
3%
(3)
4%
A2-18
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 Maps
During 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 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
A2-19
linked uncertainty to particle.
Other popular links were wave, probability and
momentum. (Refer to Table A2-2)
Links to ‘Uncertainty Principle’
Number of Maps
Linked to
Particle
49
100%R
Linked to
Wave
38
78%R
Linked to
Probability
37
76%R
Linked to
Momentum
17
35%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 xp   .
Summary of Results from Concept Map Analysis
The 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 Maps
The following three categories emerged from the concept map analysis and
were carried forward to the selective coding phase.
1.
Wave Particle Duality - Concept maps showed a strong separation between
particle and wave. This suggests that the idea of wave/particle duality is a
dominant feature of students’ understanding of quantum mechanics.
2.
Uncertainty - A significant variation in where students see uncertainty
fitting into quantum mechanics was evident.
For some students their
A2-20
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 Sets
The 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.
A2-21
Second Year Physics – Concept Mapping
Table A2-3 : Concept Map Coding – Linking and Map Structures (1of 2)
A2-22
Second Year Physics – Concept Mapping
Table A2-4 : Concept Map Coding – Primary Nodes within Wheel, Complex and
Hierarchical Structures (2 of 2)
A2-23
A2.2 EXPERT GROUP DISCUSSIONS/INTERVIEWS RESULTS AND
ANALYSIS
Several 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 Discussion
The 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.
A2-24
Focus Group Discussion - Quantum Mechanics
Points 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 Interviews
It 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 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.
A2-25
PHYSICS QUANTUM - ACADEMIC GUIDE 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 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
- Physics majors
Figure A2-7 : Physics Lecturer Guide Interview Questions
A2-26
CHEMISTRY QUANTUM - ACADEMIC
GUIDE 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
A2-27
Figure A2-8 : Chemistry Lecturer Guide Interview Questions
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/Interviews
The 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).
Expert Group – Depth of Response
PHYSICS
Lectures of 3rd year and honours
Individual
Lecturer ID >
Teaching
Approach
Key
Concepts
Assessment
Perceived
Difficulties
Maths
Analogies
Computer
Simulations
Experiments
Lectures of
2nd year
Lectures of
Individual
Individual
1st
CHEMISTRY
Lecturers of 3rd year and above in
quantum chemistry
year
Focus Group
Individual
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
D
M
M
D
D
M
D
D
M
D
S
NR
D
D
M
D
M
D
D
D
S
M
D
D
M
M
M
D
M
D
D
D
D
D
S
D
D
S
NR
S
D
S
D
D
NR
NR
M
NR
M
M
D
D
NR
NR
D
M
NR
D
D
M
D
D
D
D
D
D
D
D
D
D
D
D
NR
D
M
D
D
M
D
D
D
D
M
M
M
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
M
D
D
NR
NR
M
D
D
NR
D
NR
NR
NR
S
M
D
D
D
M
M
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
A2-28
A2-29
Teaching Approaches
Several 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 Concepts
The 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.
A2-30
Expert Group - Concepts Identified
Concept identified
Duality
Linking Quantum Mechanics to ‘real world’
Uncertainty
Bonding
Spectroscopy
Waves
Energy Levels
Energy Quantisation
Probability
Schrödinger Equation
Double slit experiment
Harmonic Oscillators
Mathematical tools
Matrices and Operators
Perturbation
Photoelectric effect
Tunnelling
Wave functions
Wells
Number of lecturers
4
4
4
3
3
3
2
2
2
2
1
1
1
1
1
1
1
1
1
Table A2-6 : Expert Group - Key concepts identified by lecturers
Assessment
The 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
compartmentalisation and isolation of ideas student failure at unfamiliar problems
Three lecturers suggested that student examination scripts could be valuable resource for
this study.
1
A2-31
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 Difficulties
The 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.
Maths
All 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.
A2-32
Expert Group – Difficulties Identified
Difficulty
Prior experiences of students
 Weak physics background (force and electrostatics)
 Weak mathematics
 Students have preconceptions
 Weak understanding of waves
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
Terminology
 Terms in quantum mechanics have common and scientific
meanings
Abstract nature of Quantum Mechanics
 Quantum mechanics is abstract
 Hard to visualise
 Conceptually difficult
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
Specific Topics
 Energy levels
 Wave functions
 Probability
 Operators
 Eigen values/vectors
 Potentials diagrams (well and barriers)
 Waves
 Harmonics
 Uncertainty
 Expectation
Number of
lecturers
8
Table A2-7 : Expert Group – Difficulties Identified by the 18 lecturers
4
3
4
7
8
A2-33
Analogies
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 Simulations
Half 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.
A2-34
Experiments
Most 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
were carried forward to the selective coding phase.
1.
Real world – Students experience difficulties solving unfamiliar problems
and linking theory, experiment and application. Experts agree the purpose
of quantum mechanics is to understand and explain ‘real world’ phenomena
and students should be able to do this.
The experts identified linking
quantum mechanics to the real world as a key concept and as a teaching
approach.
2.
Duality – Identified as a key concept in quantum mechanics. Students have
difficulties progressing past a classical view of either a wave or a particle.
The experts feel that teaching does not provide a resolution to the duality
paradox and the concept is not revisited.
A2-35
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.
A2-36
A2.3 EXAMINATION SCRIPT RESULTS AND ANALYSIS
During 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.
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
Junior
Group
Technological
Number of Scripts
46
Intermediate
Technological
45
Intermediate
Advanced
46
Questions Selected
Q9
Q10
Q11
QA1 (a), (b) & (d)
QA2 (a), (b) & (c)
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 responses to each section of
the questions were reviewed, coded, categorised and tabulated. Refer to Tables A29 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
A2-37
influence the phenomeographic approach, however it did provided 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.
A2-38
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)
Figure A2-9 : Examination Script – First Year Question 9
Observed features
The students demonstrated two ways of presenting their answer:
1.
using mathematical formulae and inequality signs to show mathematical
relationships for the electron and proton
2.
using a written description to articulate the differences between the electron
and proton.
Many students had difficulties with the relationship between momentum
and kinetic energy.
Approximately three quarters of the students successfully
answered 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.
A2-39
First Year – Question 10
First Year Physics 1003 & 1203 – Technological
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)
Figure A2-10 : Examination Script – First Year Question 10
Observed Features
Approximately one quarter of students did not give a meaning for the terms
quantised and zero point energy. The concept of quantised energy was identified as a
key concept in the expert interviews and from the data it appears that only 43% of
students can correctly define the term either in terms of energy or more generally.
All but two students were able to give a meaning for the terms ground state
and excited state. Students seem to recognise these terms and can successfully define
them.
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.
A2-40
First Year – Question 11
First Year Physics 1003 & 1203 – Technological
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)
Figure A2-11 : Examination Script – First Year Question 11
Observed Features
Students 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.
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
A2-41
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.
A2-42
Second Year – Question A1
Second Year Intermediate Physics 2001& 2101– Technological & Environmental
Question A1
(20 marks)
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 Features
Part 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)
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
A2-43
students linked the de Broglie wavelength to electron orbitals. Some students drew
sketches of wave packets and 53% of students included the formula  
h
in their
p
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.
A2-44
Second Year – Question B1
Second Year Intermediate Physics 2901– Advanced
Question B1
(20 marks)
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 Features
Part a)
This question was basically the same question that appeared on the
intermediate technological examination paper (Question A1 refer to Figure A2-11).
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) and Part c).
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 fusion.
Most students
attempted to reconstruct the four-step hydrogen fusion process and this made up
the bulk of their answer.
A2-45
Second Year – Question A2
Second Year Intermediate Physics 2001& 2101– Technological & Environmental
Question A2
(15 marks)
An investigation of the eigenstates of an electron in a triangular well
yields 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 the
bound 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 Features
Students 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.
A2-46
A2.3.2 Results Carried Forward – Examination Scripts
The following three categories emerged from the examination script analysis
and were carried forward to the selective coding phase.
1.
Real world – Use of real world examples illustrated gaps, inconsistencies
and misconceptions in student’s understanding of quantum mechanics.
These problems were not noticeable when students were asked similar
questions in a theoretical context. 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 Sets
Following twenty-six tables contain the coded data sets for the five
examination script questions (Refer to Tables A2-9 through A2-34).
A2-47
First Year Physics – Question 9 /1
Table A2-9 : Examination Script Coding - First Year Question 9 (1 of 2)
A2-48
First Year Physics – Question 9 /2
Table A2-10 : Examination Script Coding - First Year Question 9 (2 of 2)
A2-49
First Year Physics – Question 10 /1
Table A2-11 : Examination Script Coding - First Year Question 10 (1 of 5)
A2-50
First Year Physics – Question 10 /2
Table A2-12 : Examination Script Coding - First Year Question 10 (2 of 5)
A2-51
First Year Physics – Question 10 /3
Table A2-13 : Examination Script Coding - First Year Question 10 (3 of 5)
A2-52
First Year Physics – Question 10 /4
Table A2-14 : Examination Script Coding - First Year Question 10 (4 of 5)
A2-53
First Year Physics – Question 10 /5
Table A2-15 : Examination Script Coding - First Year Question 10 (5 of 5)
A2-54
First Year Physics – Question 11 /1
Table A2-16 : Examination Script Coding - First Year Question 11 (1 of 4)
A2-55
First Year Physics – Question 11 /2
Table A2-17 : Examination Script Coding - First Year Question 11 (2 of 4)
A2-56
First Year Physics – Question 11 /3
Table A2-18 : Examination Script Coding - First Year Question 11 (3 of 4)
A2-57
First Year Physics – Question 11 /4
Table A2-19 : Examination Script Coding - First Year Question 11 (4 of 4)
A2-58
Second Year Advanced Physics – Question B1 /2
Table A2-20 : Examination Script Coding - Second Year Advanced Question B1 (1 of 6)
A2-59
Second Year Advanced Physics – Question B1 /2
Table A2-21 : Examination Script Coding - Second Year Advanced Question B1 (2 of 6)
A2-60
Second Year Advanced Physics – Question B1 /3
Table A2-22 : Examination Script Coding - Second Year Advanced Question B1 (3 of 6)
A2-61
Second Year Advanced Physics – Question B1 /4
Table A2-23 : Examination Script Coding - Second Year Advanced Question B1 (4 of 6)
A2-62
Second Year Advanced Physics – Question B1 /5
Table A2-24 : Examination Script Coding - Second Year Advanced Question B1 (5 of 6)
A2-63
Second Year Advanced Physics – Question B1 /6
Table A2-25 : Examination Script Coding - Second Year Advanced Question B1 (6 of 6)
A2-64
Second Year Physics – Question A1 /1
Table A2-26 : Examination Script Coding - Second Year Question A1 (1 of 8)
A2-65
Second Year Physics – Question A1 /2
Table A2-27 : Examination Script Coding - Second Year Question A1 (2 of 8)
A2-66
Second Year Physics – Question A1 /3
Table A2-28 : Examination Script Coding - Second Year Question A1 (3 of 8)
A2-67
Second Year Physics – Question A1 /4
Table A2-29 : Examination Script Coding - Second Year Question A1 (4 of 8)
A2-68
Second Year Physics – Question A1 /5
Table A2-30 : Examination Script Coding - Second Year Question A1 (5 of 8)
A2-69
Second Year Physics – Question A1 /6
Table A2-31 : Examination Script Coding - Second Year Question A1 (6 of 8)
A2-70
Second Year Physics – Question A1 /7
Table A2-32 : Examination Script Coding - Second Year Question A1 (7 of 8)
A2-71
Second Year Physics – Question A1 /8
Table A2-33 : Examination Script Coding - Second Year Question A1 (8 of 8)
A2-72
Second Year Physics – Question A2 /1
Table A2-34 : Examination Script Coding - Second Year Question A2 (1 of 1)
A2-73
A2.4 PRELIMINARY INTERVIEWS RESULTS AND ANALYSIS
The 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 semistructured, 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 Collected
The interviews were transcribed from tape immediately and annotated with
reflective notes.
interview.
A detailed personal and analytical log was written for each
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)
A2-74
Figure A2-16 : Representative Preliminary Interview Transcript – TED Page 2 (2 of 9)
A2-75
Figure A2-17 : Representative Preliminary Interview Transcript – TED Page 3 (3 of 9)
A2-76
Figure A2-18 : Representative Preliminary Interview Transcript – TED Page 4 (4 of 9)
A2-77
Figure A2-19 : Representative Preliminary Interview Transcript – TED Page 5 (5 of 9)
A2-78
Figure A2-20 : Representative Preliminary Interview Transcript – TED Page 6 (6 of 9)
A2-79
Figure A2-21 : Representative Preliminary Interview Transcript – TED Page 29 (7 of 9)
A2-80
Figure A2-22 : Representative Preliminary Interview Transcript – TED Page 30 (8 of 9)
A2-81
Figure A2-23 : Representative Preliminary Interview Transcript – TED Page 31 (9 of 9)
A2-82
A2-83
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 06
Interview 6/10/00 - TED
Participant and Interview Details
The 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 senior 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 Process
Overall 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 Setting
The 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
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.
A2-84
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 Close
The 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 making sure that
questions are single questions (as opposed to multifaceted) and suggested that a more
Socratic dialogue be applied.
Conclusion
In 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
A2-85
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’.
A2-86
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 06
for Interview 6/10/00 - TED
Overview
Six primary categories were used to code the transcript – Concept, Personal Comment,
Personal Experience, Student Experience, Self Reflection and Time Frame. A secondary set
of key-words were selected to provide a greater level of context during this
preliminary analysis exercise.
The primary categories could be represented in a number ways and for the purpose of
this study it is convenient to adopt a hub structure that is centrally linked to the
category of Concept, refer Figure 1.
Personal Comment
Student
Experience
Concept
Time Frame
Self Reflection
Personal Experience
Figure 1 : Primary categories
This structure although in some sense is arbitrary directly relates to the research
project question of conceptual development. Thus the structure provides a useful
natural theme without constraining the data-set.
Category Definitions
Definitions 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 Definitions
CATEGORY
Concept (C)
DESCRIPTION
An idea, concept or theme that stands alone and
primarily relates to quantum mechanics
Personal 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 being
made
Table 1 : Primary category definitions for interview
A2-87
Primary and Secondary Coding
CATEGORY
CONCEPT (C)
PERSONAL COMMENT (PC)
PERSONAL EXPERIENCE (PE)
STUDENT EXPERIENCE (SE )
SELF REFLECTION (SR)
TIME FRAME (WH)
SECONDARY KEY WORDS
C – Analogy
C – Bohr Model /Bohr model of the atom
C – Duality / Wave particle nature of matter
C – Ideas / Underlying ideas
C – Key Conc / Key underlying concepts
C – Lagrangian / Energy used to solve a problem
C – Maths / Mathematics
C – Matter Waves / Wave nature of matter
C – Model
C – Photo Elec / Photoelectric Experiment
C – Potential / Usually electric potential
C – Probability / Statistical understanding
C – Quantisation / Discreteness found in nature
C – Quantum Mech / Quantum mechanics
C – Schrödinger / Wave equation for matter
C – Tunnelling / Non classical phenomena
C – Unc Principle / Heisenberg’s uncertainty principle
C – Waves / Wave phenomena
C – Well / An electrical potential
PC – Teach Early / Teach the topic earlier
PC – Teach HS / Teach topic at High School
PC – Teach Qual / Teaching quality questioned
PE – Analogy / Metaphor to describe phenomena
PE – Difficult
PE – Engagement / Activity involved
PE – Lack Under / Surface knowledge
PE – Mis Interp / Misinterpretation of …
PE – Not Engaged / Lack of involvement
PE – Requirement / Necessary to understand
PE – Taught 1stY
PE – Taught Later
PE – Understood / Good understanding of …
SE – Solar / Example Solar Panel
SR – Lack Under / Surface knowledge
SR – Math vs Con / Mathematics vs Concept
SR – Math vs Phys / Mathematics vs Physics
SR – Newt vs Quan / Newtonian vs Quantum mechanics
SR – Not Sure
SR – Phys vs Chem / Physics vs Chemistry
SR – Phys vs Con / Physics vs Concept
SR – Shift Focus / Change of emphasis
WH – 1stY
WH – 2ndY
WH – 3ndY
WH – Early
WH – HS / High School
Tot
3
2
6
2
3
1
3
3
5
2
6
5
1
3
2
1
2
1
1
4
3
8
3
4
3
12
1
1
1
1
1
7
1
2
3
4
1
2
1
2
1
1
2
1
1
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.
A2-88
Analysis
Several 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 knowledge
The 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 interestingly the participant commented
that students do not understand the links between physics concepts and the physical
world in both quantum and Newtonian mechanics.
A2-89
(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 taught
One 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 methods
Two 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.
“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
A2-90
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 understanding
The 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 education
An 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
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.
A2-91
Propositions
The 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 subheadings 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?
A2-92
A2.4.2 Coding and Results
Each interview was coded and then compared with prior interviews and ten
common categories were identified: Analogies; Assessment; Computer Simulations;
Course Structure; Difficulties; Duality; Mathematics; Potential Diagrams; Real
World; Reflective Thoughts; and Tunnelling.
The categories will be briefly
discussed.
Analogies
Eight students indicated that they found analogies helpful to their learning,
two of these students in particular really liked them and wished they were used in
courses more often.
Six students did not like analogies and said they were
confusing. The remaining two students commented that analogies were occasional
useful but often they were inadequate. The students mentioned a limited set of
analogy examples, for example “a ball rolling in some sort of valley” (PrelimSID06)
Assessment
The focus of student discussion regarding assessment was the end of
semester examination.
Students emphasised the importance of mathematics to
doing well in examinations. Students described their preparation for examinations
in terms of remembering recipes for solving different problems. “To study I try to
learn all of the examples given in lectures” (PrelimSID02). “I memorise the steps so
hopefully I can do it in the exam” (PrelimSID10).
Computer Simulations
This category was covered in detail by the physics students as a
computational lab forms part of their course in intermediate physics. The chemistry
students referred briefly to computer generated models of orbitals and molecular
shapes. The majority of students found computer simulations useful for visualising
abstract ideas (e.g. the mathematics of potential diagrams and wave functions). A
number of students felt computer simulations could be more powerful if preceded
by a ‘real experiment’. Three students felt the link between the simulation and the
physical meaning was not made clear enough. “I didn’t understand Schrödinger’s
equation and wells until I saw it in the computational lab…” (PrelimSID04)
Course structure
Student comments on course structure were predominantly related to the
integration of lecture and laboratory components of the course. For example one
A2-93
student said “the lectures and computer lab got out of sync ...” (PrelimSID11),
another said “it is not clear what the lab has to do with the lecture bit …”
(PrelimSID07).
Some students commented on the teaching approach within the course.
Four students said they enjoyed the historical approach used and three students
appreciated seeing all of the steps described in the lecture examples “if I get down
all the steps I am more confident of figuring it out later” (PrelimSID03)
Difficulties
Once a rapport was established between student and interviewer, the
students were more than willing to articulate their difficulties with quantum
mechanics. One student said “it is good to be asked …how long have you got?”
(PrelimSID07). Students were open about their strength and weaknesses:
“I am good at the maths (long pause) but I couldn’t tell you what it all means.”
(PrelimSID05)
“I find the maths overwhelming at times … what is the point, what is it for?”
(PrelimSID11)
“When they want us to explain anything, in assignments, I am stuck….”
(PrelimSID03)
The following list summarises the difficulties identified by students in the
preliminary interviews:








Conceptual explanations
Duality
Mathematics
Probability
Uncertainty
Unfamiliar problems
Wave functions
Wells
Duality
Throughout the preliminary interviews the students used a variety of words
to describe the quantum entity including: wave, particle, wave/particle, wave
packet, smeared particle, wave function and probability density.
The students
A2-94
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.
Mathematics
The students interviewed split into two distinct groups regarding
mathematics in quantum mechanics.
One group (5 students) felt that the
mathematics was “straight-forward” or “easy” once you were shown the steps. The
other group (12 students) found the mathematics “difficult” or “hard” and at times
“overwhelming”. All students felt you needed mathematics in order to succeed at
quantum mechanics. Four students felt that your understanding improved with
time as your mathematics skills improved.
“When you solve Schrödinger’s
equation the first time, its like, ‘oh my god’ … really hard, but in 3 rd year when you
do it again its much easier.” (PrelimSID13)
Potential EnergyDiagrams
The students discussed a variety of potential diagrams used in quantum
mechanics including infinite wells, finite wells, square wells, parabolic wells, ramp
wells, step wells, an array of wells, barriers and humps. Five students recognised
that all of these examples have the same basic structure associated with kinetic and
potential energy and could describe in detail 3 examples. “The wells describes the
energy in the system.” (PrelimSID06).
The remaining students were very familiar with the simple examples (e.g.
square wells) but had difficulties working with and describing other more
complicated diagrams. “The wells steps always confuse me … I get the wave
function shape wrong” (PrelimSID02)
A2-95
While most students were familiar with potential diagrams as important
tools in problem solving only three students could clearly explain the relationship
between potential diagrams and physical systems. Most students saw potential
diagrams as useful but isolated tools.
Real World
The students were asked to describe three examples of quantum mechanics
applied to the real world.
Only two students were able to do so, most other
students could name one but three students could not give a single example. “I
can’t think of any examples … it’s too abstract.” (PrelimSID01).
Reflective Thoughts
Throughout the preliminary interviews students made reflective comments
on a range of topics including: high school physics experiences, course structures,
teaching approaches, sequencing of ideas, learning styles and their attitude towards
learning quantum mechanics.
Tunnelling
When describing or 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 Interviews
The following five categories emerged from the preliminary interview
analysis and were carried forward to the selective coding phase.
1.
Analogies – Some students find analogies useful to their learning of
quantum mechanics, other students dislike analogies and find them
confusing.
2.
Tunnelling – This concept links a group of problem solving tools (e.g.
potential diagrams and wave functions) to real world examples of quantum
mechanics. Discussion of this concept can reveal students difficulties with
the tools and how they interpret what the tools do.
A2-96
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 Interviews
At this point the categories that were identified from each of the four data
sources were used to develop two final interview instruments for the study. One
interview instrument focused on quantum mechanics learning in Chemistry and the
other on learning in Physics. At a later date it was decided the learning issues in
chemistry were beyond the scope of this 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.
A2-97
A2.5 DEVELOPMENT OF THE FINAL INTERVIEW INSTRUMENT
To 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 Protocol
The 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 Study
Combining the results from the four data sources, concept maps, expert group
discussions/interviews, examination script and preliminary interviews, eight
categories emerged. They are summarised below.
1.
Real world – The experts identified linking quantum mechanics to the real
world as a key concept.
As a teaching approach however they were
concerned that most students were unable to do this. Analysis of student
responses in examinations and interviews indicated students had difficulties
with unfamiliar problems and applications of quantum mechanics to the
real world. Real world examples tended to highlight gaps, inconsistencies
A2-98
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.
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.
A2-99
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
understanding of quantum mechanics.
interviews
was
students’
conceptual
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 Coding
The 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.
A2-100
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 Topics
To 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.
Opening
To open the interview we needed a familiar quantum mechanics topic that
the students were comfortable discussing. The ideal topic would be something the
students had previously experienced, 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.
A2-101
Interview Opening Topics
Opening
Topic
Double Slit
Experiment
Advantages


Photoelectric
Effect




Role of
Mathematics
in Quantum
Mechanics


Wave/Particle
Duality




Familiar topic
Students were relaxed and
confident
Depth of complexity
Later link to analogy
Familiar topic
Depth of complexity
Familiar topic
Students were relaxed and
confident
Gave good overview of maths
ability
Familiar topic
Depth of complexity
Stimulated a range of ideas
and feelings
Disadvantages

Some students saw it linked
to optics but not quantum
mechanics

Most students could not recall
the details or significance of
the photoelectric effect
Did not relax the students
Gave the entire interview a
strong maths flavour
Too open and hard to control






Too open and hard to control
Did not relax students
Was unsettling rather than
setting the scene
Table 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.
Close
To 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.
appreciated.
The interview should end with the student feeling relaxed and
A number of closure topics were tested during the preliminary
interviews they are listed in Table A2-37 below along with the advantages and
disadvantages revealed in analysis.
A2-102
Interview Closure Topics
Closure Topic
Reflection on
course


Difficulties



Real world




Advantages
Students have considered
the topic in part prior to
closure
All students have an opinion
to offer on the course
A range of issues to discuss
Students have considered
the topic in part prior to the
closure
Allows students to identify
their difficulties
A range of issues to discuss
Students have considered
the topic in part prior to
closure
Links quantum mechanics to
useful applications
A range of issues to discuss




Disadvantages
Responses may be
destructive or personal
Some students may feel
defensive
Interview closes with
students focussing on low
points
Many students may not be
able to identify and discuss
real world applications
Table 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.
Body
The body of the interview is approximately 45 minutes in length and will
need to include six topics.
It is important to sequence the topics and specific
questions in order get the most out of the interview instrument.
During the
preliminary interviews a number of questions associated with the topics were
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 domains of Skill, Affective and Cognitive were addressed in
Psychologists distinguish between three kinds of learning or domains based on the type of
performance involved.
 Psychomotor or Skill domain (both motor and cognitive skills)
 Affective domain (involves feelings and emotions)
 Cognitive domain (information and ideas)
For example see Lefrancois, G.R., (1999) Psychology for teaching, (Wadsworth/Thompson
Learning Belmont CA) p118.
2
A2-103
addition to the content.
The results of the trials and the learning aspect
classification appear in Table A2-38.
Interview Body Topics
Body Topic
Analogies

Real World




Tunnelling



Difficulties

Uncertainty
Wave/Particle
Duality







Advantages
Reveal students’ ability to visualise, and shift
context
Helps students understand abstract concepts
Allows students to identify their own difficulties
Students describe a range of difficulties
In a detailed answer student shows how quantum
mechanics is linked to real world
Links between theory, experiment and application
Highlights student difficulties
In a detailed answer students refer to tools such as
potential diagrams and wave functions
Tunnelling is a bridging concept between theory
and real world examples
Identified as a key concept of quantum mechanics
Students give a range of descriptions
Strong links to other topics
Identified as a key concept in quantum mechanics
It can be used to indicate conceptual change (from
wave/particle to wave function)
Students give a range of descriptions
Strong links to other topics











Disadvantages
Students often don’t see limitations of analogies
Some students don’t like them
Some lecturers don’t use them
Could make students defensive
Domain
Cognitive &
Skill
Students often do not see any link between
quantum mechanics and the real world
This topic puts off weak students
Cognitive
Weak students cannot give a detailed response
without prompting
Students can get tangled and confused in their
answers
Student responses can vary depending on the
context used
Cognitive &
Skill
Very broad topic and students can get off track
Concept is not revisited in senior and honours
level courses
Cognitive
Table A2-38 : Interview Body Topics
A2-104
Affective
Cognitive
A2-105
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.
Final Interview Instrument Structure
Interview Protocol
Rapport
Timeline
(minutes)
0
Learning
Domain
Cognitive
Topic
Wave/Particle
Duality
Questions
Body
10
Revisit key concepts
15
Cognitive &
Skill
Tunnelling
Different modes of
questioning
30
Affective
Difficulties









Different contexts
40
Cognitive
Real World



Different styles
45
Analogies

Closure
55
Cognitive &
Skill
Affective
Reflection




60
Double Slit
Wave or Particle?
Uncertainty
Evidence of Wave/Particle duality
Applications/Examples/Experiments
Draw a well and a barrier
Compare and contrast
Discuss terminology
Learning difficulties in quantum
mechanics
What tools do you need?
Analogies and models you use?
Explain Electromagnetic shielding or
radioactivity in terms of quantum
mechanics
Quantaroo (macroscopic analogy of
double slit)
Changes in understanding
What did you need to understand?
Expectation of lecturer
Advice to new lecturer
Table A2-39 : Structure of the Final Interview Instrument
A2-106
Theme Addressed
Concept & Linking
Concept
Concept
Linking
Linking
Tools
Tools, Linking & Concept
Tools & Concept
Concept & Tools
Tools
Tools & Linking
Linking
Concept, Tools & Linking
Concept, Tools & Linking
Concept, Tools & Linking
Concept, Tools & Linking
Concept, Tools & Linking
A2-107
A2.6 ASSOCIATED LITERATURE REVIEWS
A2.6.1 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), 279288
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
A2-108
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
Adamczk, P., Wilson, M., Williams, D., (1994) Concept mapping: a multi-level and
multi-purpose tool, School Science Review, 76(275), 116-124
A2-109
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
A2-110
APPENDIX 2 ...................................................................................................................................... 11
GROUNDED THEORY INVESTIGATION – STAGE 1 .................................................................... 11
A2.1 CONCEPT MAP RESULTS AND ANALYSIS ..................................................................... 12
A2.1.1
Concept Mapping Exercise ....................................................................................................... 12
A2.1.2
Results - Concept Map Structures ............................................................................................ 15
Structural and Nodal Analysis................................................................................................................. 15
Summary of Results from Structural and Nodal Analysis .................................................................. 18
Other Interesting Features that Emerged from the Concept Maps........................................................... 18
Summary of Results from Concept Map Analysis .............................................................................. 19
A2.1.3
Results Carried Forward – Concept Maps ................................................................................ 19
A2.1.4
Concept Mapping Data Sets ..................................................................................................... 20
A2.2
EXPERT GROUP DISCUSSIONS/INTERVIEWS RESULTS AND ANALYSIS .................. 23
The Expert Focus Group Discussion ....................................................................................................... 23
The Individual Expert Interviews ............................................................................................................ 24
Results – Expert Group Discussions/Interviews ..................................................................................... 27
Teaching Approaches ......................................................................................................................... 29
Key Concepts ..................................................................................................................................... 29
Assessment ......................................................................................................................................... 30
Perceived Difficulties ......................................................................................................................... 31
Maths.................................................................................................................................................. 31
Analogies............................................................................................................................................ 33
Computer Simulations ........................................................................................................................ 33
Experiments........................................................................................................................................ 34
A2.2.2
Results Carried Forward – Expert Discussions/Interviews ....................................................... 34
A2.3
EXAMINATION SCRIPT RESULTS AND ANALYSIS ........................................................ 36
First Year – Question 9 ........................................................................................................................... 38
Observed features ............................................................................................................................... 38
First Year – Question 10 ......................................................................................................................... 39
Observed Features .............................................................................................................................. 39
First Year – Question 11 ......................................................................................................................... 40
Observed Features .............................................................................................................................. 40
Second Year – Question A1 .................................................................................................................... 42
Observed Features .............................................................................................................................. 42
Second Year – Question B1 .................................................................................................................... 44
Observed Features .............................................................................................................................. 44
Second Year – Question A2 .................................................................................................................... 45
Observed Features .............................................................................................................................. 45
A2.3.2
Results Carried Forward – Examination Scripts ....................................................................... 46
A2.3.3
Examination Script Data Sets ................................................................................................... 46
A2.4
PRELIMINARY INTERVIEWS RESULTS AND ANALYSIS ............................................... 73
A2.4.1
Analysis of Data Collected ....................................................................................................... 73
A2.4.2
Coding and Results ................................................................................................................... 92
Analogies............................................................................................................................................ 92
Assessment ......................................................................................................................................... 92
Computer Simulations ........................................................................................................................ 92
Course structure ................................................................................................................................. 92
Difficulties.......................................................................................................................................... 93
Duality................................................................................................................................................ 93
Mathematics ....................................................................................................................................... 94
Potential EnergyDiagrams .................................................................................................................. 94
Real World ......................................................................................................................................... 95
Reflective Thoughts ........................................................................................................................... 95
Tunnelling .......................................................................................................................................... 95
A2.4.3
Results Carried Forward – Preliminary Interviews ................................................................... 95
A2.4.4
Chemistry Interviews ................................................................................................................ 96
A2.5
DEVELOPMENT OF THE FINAL INTERVIEW INSTRUMENT ....................................... 97
A2.5.1
Constraints of the Protocol ....................................................................................................... 97
A2.5.2
Categories Brought Forward from the Grounded Study ........................................................... 97
A2.5.3
Selective Coding ....................................................................................................................... 99
A2.5.4
Sequencing Topics .................................................................................................................. 100
Opening ................................................................................................................................................. 100
Close ..................................................................................................................................................... 101
A2-111
Body ...................................................................................................................................................... 102
A2.6
ASSOCIATED LITERATURE REVIEWS .......................................................................... 107
A2.6.1
Concept Mapping ................................................................................................................... 107
Concept mapping - Educational research .............................................................................................. 107
Concept mapping - Teaching ................................................................................................................ 108
Concept mapping - Assessment............................................................................................................. 109
A2-112
Figure A2-1 : Concept Map Instruction Sheet (Printed A4 Portrait) .................................................... 13
Figure A2-2 : Example “Newtonian Concept Map” provided with Concept Map Instruction Sheet
(Printed A4 Landscape on reverse) .............................................................................................. 13
Figure A2-3 : Concept Map Cover Sheet (Printed A4 Portrait) ........................................................... 14
Figure A2-4 : Concept Map Answer Sheet (Printed A3 Landscape) .................................................... 14
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)) .............................................................................. 15
Figure A2-6 : Focus Group Discussion Points ..................................................................................... 24
Figure A2-7 : Physics Lecturer Guide Interview Questions ................................................................. 25
Figure A2-8 : Chemistry Lecturer Guide Interview Questions ............................................................. 27
Figure A2-9 : Examination Script – First Year Question 9 .................................................................. 38
Figure A2-10 : Examination Script – First Year Question 10 .............................................................. 39
Figure A2-11 : Examination Script – First Year Question 11 .............................................................. 40
Figure A2-12 : Examination Script – Second Year Question A1 ......................................................... 42
Figure A2-13 : Examination Script – Second Year Question B1 ......................................................... 44
Figure A2-14 : Examination Script – Second Year A2 ........................................................................ 45
Figure A2-15 : Representative Preliminary Interview Transcript – TED Page 1 Cover Page (1 of 9) . 74
Figure A2-16 : Representative Preliminary Interview Transcript – TED Page 2 (2 of 9) .................... 75
Figure A2-17 : Representative Preliminary Interview Transcript – TED Page 3 (3 of 9) .................... 76
Figure A2-18 : Representative Preliminary Interview Transcript – TED Page 4 (4 of 9) .................... 77
Figure A2-19 : Representative Preliminary Interview Transcript – TED Page 5 (5 of 9) .................... 78
Figure A2-20 : Representative Preliminary Interview Transcript – TED Page 6 (6 of 9) .................... 79
Figure A2-21 : Representative Preliminary Interview Transcript – TED Page 29 (7 of 9) .................. 80
Figure A2-22 : Representative Preliminary Interview Transcript – TED Page 30 (8 of 9) .................. 81
Figure A2-23 : Representative Preliminary Interview Transcript – TED Page 31 (9 of 9) .................. 82
A2-113
Table A2-1 : Concept Map Structural Types and Results Summary .................................................... 17
Table A2-2 : Maps with two or more links to ‘Uncertainty Principle’ ................................................. 19
Table A2-3 : Concept Map Coding – Linking and Map Structures (1of 2) .......................................... 21
Table A2-4 : Concept Map Coding – Primary Nodes within Wheel, Complex and Hierarchical
Structures (2 of 2) ........................................................................................................................ 22
Table A2-5 : Expert Interview/Group Discussions - The depth of response against each identified
category ....................................................................................................................................... 28
Table A2-6 : Expert Group - Key concepts identified by lecturers ...................................................... 30
Table A2-7 : Expert Group – Difficulties Identified by the 18 lecturers .............................................. 32
Table A2-8 : Examination Script – Questions selected for analysis ..................................................... 36
Table A2-9 : Examination Script Coding - First Year Question 9 (1 of 2) ........................................... 47
Table A2-10 : Examination Script Coding - First Year Question 9 (2 of 2) ......................................... 48
Table A2-11 : Examination Script Coding - First Year Question 10 (1 of 5) ....................................... 49
Table A2-12 : Examination Script Coding - First Year Question 10 (2 of 5) ....................................... 50
Table A2-13 : Examination Script Coding - First Year Question 10 (3 of 5) ....................................... 51
Table A2-14 : Examination Script Coding - First Year Question 10 (4 of 5) ....................................... 52
Table A2-15 : Examination Script Coding - First Year Question 10 (5 of 5) ....................................... 53
Table A2-16 : Examination Script Coding - First Year Question 11 (1 of 4) ....................................... 54
Table A2-17 : Examination Script Coding - First Year Question 11 (2 of 4) ....................................... 55
Table A2-18 : Examination Script Coding - First Year Question 11 (3 of 4) ....................................... 56
Table A2-19 : Examination Script Coding - First Year Question 11 (4 of 4) ....................................... 57
Table A2-20 : Examination Script Coding - Second Year Advanced Question B1 (1 of 6)................. 58
Table A2-21 : Examination Script Coding - Second Year Advanced Question B1 (2 of 6)................. 59
Table A2-22 : Examination Script Coding - Second Year Advanced Question B1 (3 of 6)................. 60
Table A2-23 : Examination Script Coding - Second Year Advanced Question B1 (4 of 6)................. 61
Table A2-24 : Examination Script Coding - Second Year Advanced Question B1 (5 of 6)................. 62
Table A2-25 : Examination Script Coding - Second Year Advanced Question B1 (6 of 6)................. 63
Table A2-26 : Examination Script Coding - Second Year Question A1 (1 of 8) ................................. 64
Table A2-27 : Examination Script Coding - Second Year Question A1 (2 of 8) ................................. 65
Table A2-28 : Examination Script Coding - Second Year Question A1 (3 of 8) ................................. 66
Table A2-29 : Examination Script Coding - Second Year Question A1 (4 of 8) ................................. 67
Table A2-30 : Examination Script Coding - Second Year Question A1 (5 of 8) ................................. 68
Table A2-31 : Examination Script Coding - Second Year Question A1 (6 of 8) ................................. 69
Table A2-32 : Examination Script Coding - Second Year Question A1 (7 of 8) ................................. 70
Table A2-33 : Examination Script Coding - Second Year Question A1 (8 of 8) ................................. 71
Table A2-34 : Examination Script Coding - Second Year Question A2 (1 of 1) ................................. 72
Table A2-35 : Interview Themes ........................................................................................................ 100
Table A2-36 : Interview Topics ......................................................................................................... 101
Table A2-37 : Interview Closure Topics ............................................................................................ 102
Table A2-38 : Interview Body Topics ................................................................................................ 104
Table A2-39 : Structure of the Final Interview Instrument................................................................. 106