1. Becoming a researcher in mathematics education – what do we need to think about? From a theoretical perspective

2. 2 Two main goals of research in mathematics education To enhance knowledge in the field To enhance knowledge in the field knowledge about mathematics, learning mathematics, teaching mathematics, doing research in learning mathematics, teaching …knowledge about mathematics, learning mathematics, teaching mathematics, doing research in learning mathematics, teaching … To enhance practice in the field To enhance practice in the field to enable better learning and teaching of mathematics, better researching …to enable better learning and teaching of mathematics, better researching …

3. 3 Mathematics What is special about mathematics? Beauty Functionality Power to express shortly Power to generalise Abstraction Geometric Numeric Infinity Logic Statistical Limits Simplicity Complexity A language Algebraic Infinitessimals Graphs Power to explain Proof Probability Calculus Structures Numbers Derivation Functions Sets

4. 4 Mathematics Education How mathematical topics can be made accessible for learners; How mathematical topics can be made accessible for learners; How we learn mathematics successfully; How we learn mathematics successfully; How we teach mathematics in order that learning can be successful; How we teach mathematics in order that learning can be successful; How we develop mathematics teaching and educate mathematics teachers; How we develop mathematics teaching and educate mathematics teachers; How research in the field informs and promotes development. How research in the field informs and promotes development.

5. 5 Research Design ResearchTheoretical paradigmperspectives Research Research questions Strategy Research Research Methods Methods

6. 6 Paradigms Positivist Positivist Interpretivist Interpretivist Critical theorist Critical theorist Constructivist Constructivist Post modernist Post modernist How does mathematics education fit within here? Davis & Hersch

7. 7 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?

8. 8 Theory Naïve empiricism Naïve empiricism The literature The literature Grand theory Grand theory Local theory Local theory Personal theory Personal theory Bryman Mason & Waywood

9. 9 Position of theory Theory that guides research and researcher (deductive)……tümdengelimli Theory that guides research and researcher (deductive)……tümdengelimli Theory that emerges from research (inductive) Theory that emerges from research (inductive) … principles … … principles … … assumptions … … assumptions … What kind of theory are we talking about? What do we mean by theory?

10. 10 Research Paradigm and Theory Ontology Objectivismv. Constructionism Epistemology Positivism v. Interpretivism Theory Deductive v. Inductive Bryman Sierpinska & Lerman Pring

11. 11 so, what is research Research is Research is ”systematic inquiry made public” (1984, p. 77). Action research might be defined as 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). ‘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). Stenhouse Elliott

12. 12 Formal Educational Research We want to know  Research Questions  Research Design (Methodology+Methods)  Research Design (Methodology+Methods)  Data Collection  Data Analysis  Validation  Ethics  Results/Findings  New Knowledge (Dissemination) [New Practice?]

13. 13 Practitioner (action) Research We want to know  Research Questions  Plan for action  Action (new practice?)  Reflection on action  New knowledge [Dissemination?] New Practice

14. 14 Research questions What do I want to find out? What do I want to find out? What is my field of research? What is my field of research? Can I express this more succinctly? Can I express this more succinctly? Are there specific questions I want answers to Are there specific questions I want answers to Refining Refining …. ….

15. 15 Collecting suitable data Do you want to find out how many, or what percentage or proportion? 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 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 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 want to design materials or models to achieve better learning or teaching? Do you envisage a documentary study? Do you envisage a documentary study?

16. 16 Quantitative or Qualitative or both? Quantitative: where you quantify your data and analyse it using statistical techniques Quantitative: where you quantify your data and analyse it using statistical techniques Qualitative: where you describe, characterise, look deeply into human actions, thinking, values … 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. Both: where you use methods of both sorts, or where the boundaries are blurred. Gorard Bassey Teppo

17. 17 Relations between researcher and researched Data extraction agreements Data extraction agreements Externally objectiveExternally objective Subjects of researchSubjects of research Clinical partnerships Clinical partnerships Outsider and insider participants with mutual respectOutsider and insider participants with mutual respect Co-learning agreements Co-learning agreements All participants are both insiders and outsidersAll participants are both insiders and outsiders Wagner

18. 18 Research strategies Survey or test Survey or test Experiment Experiment Action research Action research Case study Case study Ethnography Ethnography Life history Life history Document analysis Document analysis Phenomenology Phenomenology Ethnomethodology Ethnomethodology Symbolic interactionism Symbolic interactionism Phenomenography Phenomenography Democratic research Democratic research Feminist research Feminist research Miles & Huberman maps from Wolcott and Tesch

19. 19 Where do your data come from? Population: the set of sources of data from which you draw a suitable sample 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: Sample: the set of sources within your population from which you collect data: RandomRandom RepresentativeRepresentative ConvenienceConvenience Focused or purposiveFocused or purposive SpecificSpecific

20. 20 Ethics Human factors Human factors Avoidance of causing hurt or disadvantage to any participants in the research – anonymityAvoidance of causing hurt or disadvantage to any participants in the research – anonymity Decisions about openness and inclusion in the researchDecisions about openness and inclusion in the research Legalities Legalities Protecting the ownership of the researchProtecting the ownership of the research Honesty in the reporting of results etc.Honesty in the reporting of results etc. PlagiarismPlagiarism process – democracyprocess – democracy BERA Ethical Guidelines

21. 21 How do/will you collect your data Methods of data collection Methods of data collection Surveys: questionnairesSurveys: questionnaires Experiments: control groupsExperiments: control groups TestsTests Ethnographic approachesEthnographic approaches Observation Observation SystematicSystematic ParticipantParticipant Interviews Interviews StructuredStructured Semi structuredSemi structured ConversationsConversations Focus groupsFocus groups Documentary dataDocumentary data

22. 22 How will you analyse your data? Relates directly to your research strategy and paradigmatic position Relates directly to your research strategy and paradigmatic position Statistical analysisStatistical analysis Experimental analysisExperimental analysis Comparative analysisComparative analysis Interpretative analysisInterpretative analysis Discourse analysisDiscourse analysis Reflective analysisReflective analysis Critical analysisCritical analysis Documentary analysisDocumentary analysis Bryman Miles & Huberman

23. 23 Rigour: validation and evidence Validity: construct, internal, external, ecological ReliabilityReplicabilityGeneralizability Bryman Lincoln & Guba Trustworthiness:CredibilityTransferabilityDependabilityConfirmabilityRelevance Triangulation Respondent validation Member checks

24. 24 Writing a research paper/article/report What is your research area and why? What is your research area and why? What are your research questions? What are your research questions? What theory underpins your research? What theory underpins your research? What is your research design, why and how (methodology)? What is your research design, why and how (methodology)? What did you find and how? What did you find and how? What evidence or justification do you have? What evidence or justification do you have? What conclusions do you draw – how does your research add to knowledge in the field? What conclusions do you draw – how does your research add to knowledge in the field?

25. 25 References 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] http://www.bera.ac.uk/publications/pdfs/ETHICA1.PDF 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.

26. 26 References 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