Research: Postgraduate students

Gerrit Stols (University of Pretoria, South Africa)

Associate Professor in the Department of Science, Mathematics and Technology Education, University of Pretoria, South Africa.

Gerrit Stols holds the degrees HED, BSc Hons (North West University), MSc, and PhD (UNISA). He is currently a Associate Professor in the Department of Science, Mathematics and Technology Education, University of Pretoria specialising in mathematical education. He is an NRF-rated researcher. His research interests in mathematics education concern the use of technology in the mathematics classroom as well as mathematical conceptual development. He has supervised more than a dozen postgraduate students to completion and he has obtained numerous grants for his research in the use of technology in Mathematics education.

Structure of a Research Proposal

1. Introduction / Background

2. Literature review: Identify gap in international or national research literature. See summary of theories

3. Theoretical / Conceptual framework: Which theory guides your research and what lens do you use to collect and analyse your data?

4. Rational: Why are you (personally) interested in this topic & what is your contribution?

5. Research question

6. Research design 
6.1 Research method
6.2 Data analysis procedures
6.3 Sample and participants in the study
6.4 Data collection strategies
6.5 Instruments (link framework & instrument)
6.6 Validity & reliability
6.7 Ethical issues

7. References (use APA referencing style)

Structure of a dissertation or thesis

Chapter 1: Introduction

Introduce your research
Discuss the significance and the motivation of your study (research gap)
Explain the objectives of your study
State the research questions
Provide an overview of your research

Chapter 2: Literature review & Conceptual framework

Review the work that has been done in your research area. State and explain the conceptual framework based on the review (what theory guides your research - this is also the lens that you will use to collect and analyse your data).

Start with chapters relevant to your topic:

Clements, M.A. (Ed) (2013). Third international handbook of mathematics education. Springer (EDUN 510.71 THIRD)
Bishop, A. J. (Ed) (2010). Mathematics Education: mayor themes in education. London: Routledge. Volume 1-5 (EDUN 510.71)
English, L. D. (2009).Handbook (SECOND) of International research in Mathematics education: directions for the 21st century.
Mahwah, N.J.; London: Lawrence Erlbaum. Vol 1 & 2 (EDU 510.71 HANDBOOK)
Lester, F. K., & National Council of Teachers of, M. (2007). Second handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics. Charlotte, NC: Information Age Pub. (EDUN 510.71 SECOND)
Gutierrez, A., & Boero, P. (2006). Handbook of research on the psychology of mathematics education: past, present and future. Rotterdam: Sense Publishers. (EDU 510.7 HANDBOOK)
Lester, F. K. (2005). The handbook of research on mathematics education. Greenwich, Conn.; London: Information Age.
Campbell, J.I.D. (2005). Handbook of mathematical cognition. New York: Psychology Press. (EDU 510.71 HANDBOOK)
Bishop, A. J. (2003). Second international handbook of mathematics education. Dordrecht; Boston: Kluwer Academic Publishers.
Grouws, D.A. (1992). Handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics. New York: Macmillan

Google Scholar search (http://scholar.google.co.za): read 30 relevant and recent articles/chapters/books about your topic.

Other resources:
National Academic Press
Free eBooks: Project Gutenberg
Conference proceedings PME-NA (Psychology of Mathematics Education - North America) < br />PME (International Group for the Psychology of Mathematics Education)
NCTM (National Council of Teachers of Mathematics)

Chapter 3: Research methodology

3.1 Research paradigm
3.2 Research design (includes a discussion on the design of other studies)
3.3 Data analysis procedures
3.4 Sample and participants in the study
3.5 Data collection strategies
3.6 Instruments (Explain the link between theoretical framework and instrument)
3.7 Validity & reliability
3.8 Ethical issues

Possible sources:
Cohen, L., Manion, L. & Morrison, K. (2007). Research methods in education. 7th edition. New York: RoutledgeFalmer.
Creswell, J. (2009). Research design: qualitative, quantitative, and mixed methods approaches. Thousand Oaks: Sage Publications
Kelly, A. E., Lesh, R. A., & NetLibrary, I. (2000). Handbook of research design in mathematics and science education.
Punch, K.F. (2009). Introduction to research methods in education. London: SAGE
If your research is about geometry: Lehrer, R. & Chazan, D. 1998. Designing learning environments for developing understanding of geometry and space. N.J.: Lawrence Erlbaum
Design research (If you want to do a design research study) Plomp, T. &
Nieveen, N. (2007). An Introduction to Educational Design Research.
Kelly, A. E., Baek, J. Y., & Lesh, R. A. (2008). Handbook of design research methods in education : innovations in science, technology, engineering, and mathematics. London: Routledge. (EDUN 001.42 HANDBOOK)

Chapter 4 & 5: Results

Explain and present the main results of the research.

Possible data analyses software
Deductive coding: AtlasTI & Official manual or Archer's manual
Inductive coding: Leximancer & manual
Possible data analyses software quantitative analyses: SPSS
Saldaña, J. (2009). Coding manual for qualitative research. London: Sage. (300.72 SALDANA)

Chapter 6: Findings and Summary

The concluding chapter that summarises the study.
How do your findings fit into, and contributes to the current research literature?
How do your findings contradicts the current research literature?
What are the silences in the current research literature? (for future research)
What are your unique contributions to the current research literature?
Limitations of the study
Recommendations for future research

References (use APA referencing style)