Becoming a researcher in mathematics education – what do we need to think about? Barbara Jaworski
Two main goals of research in mathematics education
To enhance knowledge in the field
knowledge about mathematics, learning mathematics, teaching mathematics, doing research in learning mathematics …
To enhance practice in the field
to enable better learning and teaching of mathematics, better researching …
What is special about mathematics?
Beauty Functionality Power to express succinctly Power to generalise Abstraction Geometric Numeric Infinity Logic Statistical Limits Simplicity Complexity A language Algebraic Infinitessimals Graphs Power to explain Proof Probability Calculus Structures
How mathematical topics can be made accessible for learners;
How we learn mathematics successfully;
How we teach mathematics in order that learning can be successful;
How we develop mathematics teaching and educate mathematics teachers;
How research in the field informs and promotes development.
Pring Carr and Kemmis Lincoln and Guba How does mathematics education fit within here? Davis & Hersch
What are your epistemological and ontological positions?
What kinds of ethical issues are likely to be involved?
What kinds of knowledge? What IS? Do you seek objectivity? What kinds of interpretations are likely to be involved and how do you expect to deal with them? What questions of bias might arise? Do you expect to address human issues and values, and if so what is your stance on these?
Bryman Mason & Waywood
Position of theory
Theory that guides research (deductive)
Theory that emerges from research (inductive)
… principles …
… assumptions …
What kind of theory are we talking about?
What do we mean by theory?
Research Paradigm and Theory
Objectivism v. Constructionism
Positivism v. Interpretivism
Deductive v. Inductive
Bryman Sierpinska & Lerman Pring
so, what is research
” systematic inquiry made public” (1984, p. 77).
Action research might be defined as
‘ the study of a social situation with a view to improving the quality of action within it’. It aims to feed practical judgement in concrete situations, and the validity of the ‘theories’ or hypotheses it generates depends not so much on ‘scientific’ tests of truth, as on the usefulness in helping people to act more intelligently and skillfully …. In action research ‘theories’ are not validated independently and then applied to practice. They are validated through practice’ (1991, p. 69).
Formal Educational Research
We want to know
Research Design (Methodology+Methods)
New Knowledge (Dissemination)
Practitioner (action) Research
We want to know
Plan for action
Action (new practice?)
Reflection on action
New knowledge [Dissemination?]
What do I want to find out?
What is my field of research?
Can I express this more succinctly?
Are there specific questions I want answers to
Collecting suitable data
Do you want to find out how many, or what percentage or proportion?
Do you want to find out what people know, or think, their beliefs or attitudes?
Do you want to explore the impact of some learning and/or teaching approach, methods or materials?
Do you want to design materials or models to achieve better learning or teaching?
Do you envisage a documentary study?
Quantitative or Qualitative or both?
Quantitative: where you quantify your data and analyse it using statistical techniques
Qualitative: where you describe, characterise, look deeply into human actions, thinking, values …
Both: where you use methods of both sorts, or where the boundaries are blurred.
Gorard Bassey Teppo
Relations between researcher and researched
Data extraction agreements
Subjects of research
Outsider and insider participants with mutual respect
All participants are both insiders and outsiders
Survey or test
Miles & Huberman maps from Wolcott and Tesch
Where do your data come from?
Population: the set of sources of data from which you draw a suitable sample
Sample: the set of sources within your population from which you collect data:
Focused or purposive
Avoidance of causing hurt or disadvantage to any participants in the research – anonymity
Decisions about openness and inclusion in the research
Protecting the ownership of the research
Honesty in the reporting of results etc.
process – democracy
BERA Ethical Guidelines
How do/will you collect your data
Methods of data collection
Experiments: control groups
How will you analyse your data?
Relates directly to your research strategy and paradigmatic position
Bryman Miles & Huberman
Rigour: validation and evidence
construct, internal, external, ecological
Bryman Lincoln & Guba
Triangulation Respondent validation Member checks
Writing a research paper/article/report
What is your research area and why?
What are your research questions?
What theory underpins your research?
What is your research design, why and how (methodology)?
What did you find and how?
What evidence or justification do you have?
What conclusions do you draw – how does your research add to knowledge in the field?
Bassey, M. (1999) Case Study Research in Educational Settings. Buckingham: Open University Press
BERA (2004). Revised Ethical Guidelines for educational research. On-line. http://www.bera.ac.uk/publications/pdfs/ETHICA1.PDF [01.03.06]
Bryman, A. (2001) Social Research Methods . Oxford: Oxford University Press.
Carr, W. and Kemmis, S. (1986) Becoming Critical: Education, Knowledge and Action Research . London: Falmer Press
Davis, P. J. And Hersh, R. (1981) The Mathematical Experience. London: Penguin
Elliott, J. (1991) Action Research for Educational Change . Buckingham: Open University Press
Gorard, S. (2001) Quantitative Methods in Educational Research . London: Continuum
Lincoln, Y. S. & Guba, E. G. (2000).Paradigmatic controversias, contradictions and emerging confluences. In N. K. Denzin & Y. S. Lincoln (Eds.) Handbook of Qualitative Research , 2nd Edition pp. 163-188. London: Sage.
Mason, J. & Waywood, A. (1996). The Role of Theory in Mathematics Education and Research. In A. Bishop et al., International Handbook of Mathematics Education . Dordrecht: Kluwer
Miles, M. B. & Huberman, A. N. (1994 ).Qualitative Data Analysis: An expanded sourcebook . Second Edition. London: Sage
Pring, R. (2000) Philosophy of Educational Research . London: Continuum
Sierpinska, A. & Lerman, S. (1996). Epistemologies of Mathematics and Mathematics Education. In A. Bishop et al., International Handbook of Mathematics Education . Dordrecht: Kluwer
Stenhouse, L. (1979). Research as a basis for teaching: Inaugural Lecture, University of East Anglia, February, 1979. In L. Stenhouse (1983) Authority,Education and Emancipation. London: Heinemann Educational, pp. 177-195. Reprinted in Ruddock, J. and Kopkins, D. (1985). Research as a basis for teaching: Readings from the work of Lawrence Stenhouse. Pp 113-128.
Teppo, A. (1998) (Ed.) Qualitative Research Methods in Mathematics Education. Journal for Research in Mathematics Education, Monograph Number 9 . Reston, Va: National Council of Teacher of Mathematics.
Wagner, J. (1997). The unavoidable intervention of educational research: a framework for reconsidering researcher-practitioner cooperation. Educational Researcher, 26 (7) pp. 13-22