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