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Triangulation is the use of two or more methods of data collection in the study of human behaviour (Cohen and Manion 1994 p233). Triangulation in social research has the same aim as in navigation or surveying – to improve validity and overcome bias, but the type of triangulation used is dependent on the nature of the research project. Denzin (1970) defines six types of triangulation that can be used in research as time triangulation, space triangulation, combined levels triangulation, theoretical triangulation, investigator triangulation and methodological triangulation. Three of these types were used in this study and they are described below.
Time Triangulation

A social system changes with time and time triangulation collects data to reflect this. A study with a cross sectional design collects data concerned with time related processes from different groups at one point in time. This study attempted to follow the development of students’ ideas in quantum mechanics throughout their university studies. Data was collected from groups of students from four different levels of university study.
Combined Levels Triangulation

A social system can be divided into three broad levels, being individual, group and collective. Combined levels triangulation collects data from more than one level to show that human behaviour encompasses these three levels of a social system. This study collected data from individual participants and small groups.
Methodological Triangulation

There are two subdivisions of methodological triangulation: within methods and between methods (Holloway 1997 p157). Within methods aims to increase reliability by repetition of single method whilst between methods focuses on validity by using multiple methods and looking for convergence in the data collected. This study employed a range of data collection techniques (e.g. interviews, examination scripts, concept maps) in its initial stage that resulted in several data sets converging and revealing a set of common themes. This led to the development of an interview protocol and set of guide questions that was implemented with 60 subjects.


Finally, the preliminary research plan was reviewed and separated into two distinct stages and another column was appended containing pertinent notes associated with methodological aspects of the study.

  • Stage 1 - Grounded Theory approach which would develop a set of interview questions (refer Table 3-3)

  • Stage 2 - Phenomenological Approach which would seek to reveal underlying themes (refer Table 3-4)

This plan performed two important roles within the study, as a guide for the research and as a point of reference for discussing the research project with colleagues and students.

^ Research Plan - Stage 1 - Grounded Theory Approach - Development of a Set of Interview Questions

^ Proposed Strategy



Methodology Guide Notes

^ Identify Initial Research Questions

Focus group discussions and unstructured interviews

Lecturers, research staff, post-graduate students

Identification of key concepts.

Identification of a set of preliminary codings.

Refine interview protocol. Use memoing and audiotape to record discussions. Transcribe audiotapes and include notes. Commence analysis of the data immediately using open and axial coding techniques

^ Literature Review

Review a wide selection of related research articles in physics and chemistry educational research

Library databases, research articles

Clear understanding of the scope of related research

Primarily use this material to develop theoretical sensitivity

^ Identify Key Themes, Ideas and Concepts

Enter the field with open and responsive research outlook

Mentors within the Faculty of Education

Fine tune grounded theory research methodology to meet requirements

Continually seek advice concerning the management and handling of the coding and categorisation.

Collect and analyse data from a wide range of sources

Lecturers, students, researchers, examination scripts, lectures, tutorials and laboratories

Adaptation of appropriate data collection and analysis tools

Quantitative analysis techniques should compliment the qualitative coding if deemed appropriate.

Ensure constant comparison across all datasets.

Identify key categories

Analysis software

Awareness of emerging concepts.

Identification of a set of key categories

Upon review of available data analysis software the decision to develop an MSAccess and MSExcel based data storage and analysis system was taken.

Preliminary Interviews

(Carries into next section)

10 Students

Honing of interviewing skills and trialling questions.

Fine tuning of the interview protocol in preparation for next stage

^ Develop and Refine an Interview Based Research Instrument

Isolate the key areas of interest and the key aspects of quantum mechanics

All datasets, coding and categorisation.

Development of a set of interview questions

Adapt the selective coding process to isolate core categories and themes.

Continue Preliminary Interviews

Remainder of 10 students

Final set of Guide Interview questions

Develop questions, trail and review in preparation for Stage 2

Table 3-3 : Research Project Plan – Stage 1

^ Research Plan - Stage 2 – Phenomenological Approach – Conduct Student Interviews

^ Proposed Strategy



Methodology Guide Notes

^ Conduct Interviews

Interview students

60 Students

2nd Year – Postgraduate

Interview transcripts

Continue to fine tune interview procedures and progressively focus research

Analyse interview

Interview transcripts

Adaptation of appropriate research methodology and analysis tools

Identification of categories and emerging themes

Transcribe and analyse interview within 5 days

Identify a Set of Underlying Themes

Step back from the data and refocus on isolating a set of key concepts relating to the teaching and learning of quantum mechanics

Interview transcripts

Clustered themes

Identification of a set of underlying themes to be used as the basis of a focused reanalysis of the transcripts

Extract significant statements

Cluster themes

Perform member checks

Reanalyse Interview Transcripts

Revisit all transcripts and develop a detailed analytical description for each theme

Identified Themes

Interview Transcripts

Develop an exhaustive description of each theme in relation to both the individual student and across the entire data sample.

Revisit the dataset with a focused view on the data and use the identified themes as a point of reference

Extract significant statements

Cluster themes

Perform member checks

Investigate and map the variations in student understanding

Report Findings against Themes

Report findings

Themes and descriptions

Report the findings and significance of each theme

Recommendations concerning Teaching and learning quantum mechanics

Table 3-4 : Research Project Plan – Stage 2


Baker, C., Wuest. J. and Stern, P.N., (1992) Method slurring Journal of Advanced Nursing 17, 1355-1360

Bransden, B.H. and Joachain, C.J., (1989) Introduction to Quantum Mechanics (Longman Scientific and Technical, New York), p31

Brousseau, G., (1992) Didactique: What can it do for the teacher? In ^ Research in Didactique of Mathematics (eds) R.Doudy and A Mercier (La Pensée Sauvage, Paris), pp7-19

Burrell, G. and Morgan, G., (1979) Sociological Paradigms and Organisational Analysis (Heinemann Educational Books, London)

Cohen, L. and Manion, L., (1994) ^ Research Methods in Education (Routledge, London), p233

Colaizzi, P.F., (1978) Psychological research as the phenomenologist views it. Existential Phenomenological Alternatives for Psychology (eds) R.S. Valle and M. King (Oxford University Press, New York), pp48-71

Denzin, N.K., (1970) ^ The Research Act in Sociology: A Theoretical Introduction to Sociological Method (The Butterworth Group, London)

Eisberg, R. and Resnick, R., (1985) Quantum physics of atoms, molecules, solids, nuclei and particles second edition (John Wiley & Sons, Brisbane)

French, A.P. and Taylor, E.F., (1990) ^ An Introduction to Quantum Physics (Van Nostrand Reinhold, UK)

Gill. J., (1996) Beyond the baby and the bathwater, Australian Educational Researcher 23(1), 31-46

Giorgi, A., Fischer, W.F. and Von Eckartsberg, R., (1971) (eds) Duquesne Studies in Phenomenological Psychology, Volume 1 (Duquesne University Press, Pittsburgh, PA)

Halliday, D., Resnick, R. and Walker, J., (1999) ^ Fundamentals of Physics sixth edition (John Wiley & Sons, Brisbane)

Hecht, E., (1990) Physics:Calculus Volume 2, second edition (Brooks/Cole, Australia), pp1136-1163

Holloway, I., (1997) Basic Concepts for Qualitative Research (Blackwell Science Pty Ltd, Carlton)

Marton, F., (1981) Phenomenography-describing conceptions of the world around us, ^ Instructional Science, 10, 177-200

Melia, K.M., (1996) Rediscovering Glaser Qualitative Health Research, 6(3), 368-78.

Moustakas, C., (1994) Phenomenological Research Methods (Sage, Thousand Oaks), p28

Prosser, M., (1993) Phenomenography and the Principles and Practices of Learning, ^ Higher Education Research & Development, 12(1), 21-31

Ridge, D., (1995) Assembling and organising the data, in V. Minichiello, R. Aroni, E. Timewell and L. Alexander (Eds) In-depth Interviewing (Addison Wesley Longman, Melbourne), pp220-246

Stern, P.N., (1994) Eroding grounded theory. In ^ Critical Issues in Qualitative Research Methods (ed) J.M. Morse (Sage, Thousand Oaks), pp212-23.

Strauss, A. and Corbin, J., (1990) Basics of Qualitative Research: Grounded Theory Procedures and Techniques (Sage, Newbury Park)

Taylor, S.J. and Bogdan, R., (1984) ^ Introduction to Qualitative Research Methods (Wiley, New York)

van Manen, M., (1984) Practising phenomenological writing, Phenomenology and Pedagogy, 2(1), 36-69

Walsh, E., Dall’Alba, G., Bowen, J., Martin, E., Marton, F., Masters, G., Ramsden, P. and Stephanou, A., (1993) Physics Students’ Understanding of Relative Speed: A Phenomenographic Study, Journal of Research in Science Teaching, 30(9), 133-1148

Young, H.H., (1992) University Physics eighth edition (Addison-Wesley Publishing Company, Australia), pp1161-1180

^ CHAPTER 3 23





3..1 The School of Physics 27

Description of Junior Physics Courses 27

Description of Intermediate Physics Courses 28

Description of Senior Physics Courses 30

3..2 The School of Chemistry 30

Description of Junior Chemistry Courses 31

Description of Intermediate and Senior Chemistry Courses 31



3..1 Foundations for Selecting Appropriate Educational Research Methodologies 34

Ontology 34

Epistemology 35

Human nature 35

Methodology 35


3..1 Grounded Theory Approach – Stage 1 37

Selection Criteria 39

Developing Theoretical Sensitivity 39

Data Collection 39

Theoretical Sampling 40

Data Analysis 40

Open Coding 40

Axial Coding 40

Selective Coding 41

3..2 Phenomenological Approach – Stage 2 41

3..3 Phenomenographic Influence – Capturing Variation 43

3..4 Interview Protocol 44

3..5 Triangulation 49

Time Triangulation 49

Combined Levels Triangulation 49

Methodological Triangulation 49


Figure 3-1 : Example page from preliminary interview transcript showing layout 48

^ Table 3-1 : Preliminary Research Project Plan 33

Table 3-2 : Description of Interview Question Types 45

Table 3-3 : Research Project Plan – Stage 1 51

Table 3-4 : Research Project Plan – Stage 2 52

1 For example, in two undergraduate texts; (Young (1992) and Hecht (2000)) only the Copenhagen interpretation of quantum mechanics is presented without any hint that alternative interpretations exist and continue to be debated.

2 At the School of Physics, University of Sydney between 50% and 90% of a student’s assessment is by formal written examination.

3 Based on discussions with students and lecturers at the University of Sydney, 2000.

4 For example, calculus of many variables and the concept of an operator.

5 The textbooks required are Serway Moses and Moyer, Modern Physics, Saunders College Publishing, 2e 1997 for the Normal streams and Eisberg & Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, J.Wiley 2e, 1985 for the Advanced stream. The recommended references are Halliday, Resnick and Walker, Fundamentals of Physics; French and Taylor, An Introduction to Quantum Physics; Kittel, Introduction to Solid State Physics; Schiff, Quantum Mechanics (Advanced) and Omar, Elementary Solid State Physics (Advanced). Two popular level books on the interpretation of quantum theory are also recommended Gamow, The new world of Mr. Tompkins and Whitaker, Einstein, Bohr and the Quantum Dilemma.


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