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 …

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 …

Mathematics 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

What is special about mathematics?

Mathematics Education 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.

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.

Research Design Research Theoretical paradigm perspectives Research Research questions Strategy Research Methods

Research Theoretical

paradigm perspectives

Research Research

questions Strategy

Research

Methods

Paradigms Positivist Interpretivist Critical theorist Constructivist Post modernist Pring Carr and Kemmis Lincoln and Guba How does mathematics education fit within here? Davis & Hersch

Positivist

Interpretivist

Critical theorist

Constructivist

Post modernist

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?

What kinds of ethical issues are likely to be involved?

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

Naïve empiricism

The literature

Grand theory

Local theory

Personal theory

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?

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 Ontology Objectivism v. Constructionism Epistemology Positivism v. Interpretivism Theory Deductive v. Inductive Bryman Sierpinska & Lerman Pring

Ontology

Objectivism v. Constructionism

Epistemology

Positivism v. Interpretivism

Theory

Deductive v. Inductive

so, what is research Research is ” 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). Stenhouse Elliott

Research is

” 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 Questions  Research Design (Methodology+Methods)  Data Collection  Data Analysis  Validation  Ethics  Results/Findings  New Knowledge (Dissemination) [New Practice?]

We want to know 

Research Questions 

Research Design (Methodology+Methods) 

Data Collection 

Data Analysis 

Validation 

Ethics 

Results/Findings 

New Knowledge (Dissemination)

[New Practice?]

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

We want to know 

Research Questions 

Plan for action 

Action (new practice?) 

Reflection on action 

New knowledge [Dissemination?]

New Practice

Research questions 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 Refining Refining Refining … .

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

Refining

Refining

Refining

… .

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?

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

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.

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

Data extraction agreements

Externally objective

Subjects of research

Clinical partnerships

Outsider and insider participants with mutual respect

Co-learning agreements

All participants are both insiders and outsiders

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

Survey or test

Experiment

Action research

Case study

Ethnography

Life history

Document analysis

Phenomenology

Ethnomethodology

Symbolic interactionism

Phenomenography

Democratic research

Feminist research

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: Random Representative Convenience Focused or purposive Specific

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:

Random

Representative

Convenience

Focused or purposive

Specific

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

Human factors

Avoidance of causing hurt or disadvantage to any participants in the research – anonymity

Decisions about openness and inclusion in the research

Legalities

Protecting the ownership of the research

Honesty in the reporting of results etc.

Plagiarism

process – democracy

How do/will you collect your data Methods of data collection Surveys: questionnaires Experiments: control groups Tests Ethnographic approaches Observation Systematic Participant Interviews Structured Semi structured Conversations Focus groups Documentary data

Methods of data collection

Surveys: questionnaires

Experiments: control groups

Tests

Ethnographic approaches

Observation

Systematic

Participant

Interviews

Structured

Semi structured

Conversations

Focus groups

Documentary data

How will you analyse your data? Relates directly to your research strategy and paradigmatic position Statistical analysis Experimental analysis Comparative analysis Interpretative analysis Discourse analysis Reflective analysis Critical analysis Documentary analysis Bryman Miles & Huberman

Relates directly to your research strategy and paradigmatic position

Statistical analysis

Experimental analysis

Comparative analysis

Interpretative analysis

Discourse analysis

Reflective analysis

Critical analysis

Documentary analysis

Rigour: validation and evidence Validity: construct, internal, external, ecological Reliability Replicability Generalizability Bryman Lincoln & Guba Trustworthiness: Credibility Transferability Dependability Confirmability Relevance Triangulation Respondent validation Member checks

Validity:

construct, internal, external, ecological

Reliability

Replicability

Generalizability

Trustworthiness:

Credibility

Transferability

Dependability

Confirmability

Relevance

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?

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?

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] 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.

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.

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

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