Research Design and methods

1. Research Design and methods in Mathematics Education

2. 1) Empirical research (1-11) Research questions Data collection Quantitative/qualitative data Data sources Methods of data collection 3) Macro perspectives (20-25) Ethics Researcher and researched So, what is research? Formal research Practitioner research Research design Overview 2) Research approaches (12-19) • Ontology& epistemology • Paradigms • Approaches/strategies • Rigour • Theory • Analysis Barbara Jaworski MEC 2008 2

3. 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 … Barbara Jaworski MEC 2008 2

4. Empirical Research Data & Analysis Barbara Jaworski MEC 2008 2

5. 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. Barbara Jaworski MEC 2008 2

6. Research Questions Why do some students avail themselves to mathematics support whilst others do not? Which new technologies are being used in mathematics lectures and how? Does expanding the ability to generate examples increase other areas of mathematical ability? Is there a need to improve the teaching of mathematics and to what extent? To what extent is learning mathematics a social activity? Barbara Jaworski MEC 2008 2

7. Barbara Jaworski MEC 2008 2

8. 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 explain certain classroom phenomena • 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? Barbara Jaworski MEC 2008 2

9. Quantitative or Qualitative or both? • Quantitative: where you quantify your data and analyse it (possibly) 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. Barbara Jaworski MEC 2008 2

10. 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 Barbara Jaworski MEC 2008 2

11. 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 Barbara Jaworski MEC 2008 2

12. What are your epistemological and ontological positions? What kinds of ethical issues are likely to be involved? What kinds of knowledge? What IS? What kinds of interpretations are likely to be involved and how do you expect to deal with them? Do you seek objectivity? Do you expect to address human issues and values, and if so what is your stance on these? What questions of bias might arise? Barbara Jaworski MEC 2008 2

13. Paradigms • Positivist • Interpretivist • Critical theorist • Constructivist • Post modernist Pring Carr and Kemmis Lincoln and Guba Barbara Jaworski MEC 2008 2

14. Survey Experiment Intervention Action research Design research Case study Ethnography Document analysis e.g. Miles & Huberman maps from Wolcott and Tesch Life history Phenomenology Ethnomethodology Symbolic interactionism Phenomenography Democratic research Feminist research Developmental research Research approaches or strategies Barbara Jaworski MEC 2008 2

15. Phenomenology A philosophy that is concerned with the question of how individuals make sense of the world around them and how in particular the philosopher should bracket out preconceptions concerning his or her grasp of that world Ethnomethodology A sociological perspective concerned with the way in which social order is accomplished through talk and interaction. It provides the intellectual foundations of conversation analysis Symbolic Interactionism A theoretical perspective in sociology and social psychology that views social interaction as taking place in terms of the meanings actors attach to action and things. Bryman, pp 539-544 Barbara Jaworski MEC 2008 2

16. Phenomenography The unit of phenomenographic research is a way of experiencing something, … and the object of the research is the variation in ways of experiencing phenomena. .. An interest in describing the phenomena in the world as others see them, and in revealing and describing the variation therein, especially in an educational context. (Marton & Booth, p.111) Barbara Jaworski MEC 2008 2

17. Democratic research [asks] the question, ‘information for whom and for what purpose?’ and it was in attempting to answer this that negotiated success, shared data collection, negotiated meanings, feedback of both transcribed interviews and writing up were developed. (Herbert, 1989, p.49/50) Feminist research The research methods developed by feminist inspired researchers arose out of a realisation that in the past most research projects had been conducted from a male-dominated perspective and that men’s version of events had been accepted as the ‘real’ version. One of the fiercest challenges came from anthropologists who felt that women’s lives had been excluded or ignored – [there is] no one ‘right’ way of operating nor one exclusive use of techniques. (Herbert, 1989, p. 53) Barbara Jaworski MEC 2008 2

18. … quantitative research was bound up with male values of control that can be seen in the general orientation of the research strategy – control of the research subject/respondent and control of the research context and situation. Moreover the research process was seen as one-way traffic, in which researchers extracted information from the people being studied and give little or more usually nothing in return. For many feminists, such a strategy bordered on exploitation and was incompatible with feminism’s values … (Bryman, p. 22) Barbara Jaworski MEC 2008 2

19. Rigour: validation and evidence • Validity (Quantitative research) • Construct (measurement), Internal (causal), External (generalizable), Ecological (related to everyday life) • Reliability (linked to construct validity) • Replicability • Generalizability • Trustworthiness (Qualitative research) • Credibility (internal validity) • Transferability (external validity) • Dependability (reliability) • Confirmability (replicability) • Relevance (ecological) • Triangulation • Respondent validation • Member checks Read Bryman Chapter 2 Barbara Jaworski MEC 2008 2

20. 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? Barbara Jaworski MEC 2008 2

21. Theory • Naïve empiricism • The literature • Grand theory • Local theory • Personal theory Bryman p. 1-7 Barbara Jaworski MEC 2008 2

22. Research Paradigm and Theory Ontology Objectivism v. Constructionism Epistemology Positivism v. Interpretivism Theory Deductive v. Inductive Bryman p. 20 Barbara Jaworski MEC 2008 2

23. 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 • Grounded theory Content Analysis Predetermined categories Emergent categories Semiotic analysis Barbara Jaworski MEC 2008 2

24. Ethics • Legalities • Protecting the ownership of the research • Honesty in the reporting of results etc. • Plagiarism • Human factors • Avoidance of causing hurt or disadvantage to any participants in the research – anonymity • Decisions about openness and inclusion in the research process – democracy e.g., BERA Ethical Guidelines Barbara Jaworski MEC 2008 2

25. Relations between researcher and researched • Data extraction agreements • Externally objective • Subjects/informants of research • Clinical partnerships • Outsider and insider participants with mutual respect • Co-learning agreements • Participants can be both insiders and outsiders • Sharing of power and responsibility Wagner, 1997 Barbara Jaworski MEC 2008 2

26. so, what is research Stenhouse • 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). Elliott Barbara Jaworski MEC 2008 2

27. 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?] Burton 2002 “Where is the WHY?” Barbara Jaworski MEC 2008 2

28. Practitioner (action) Research We want to know  Research Questions  Plan for action  Action (new practice?)  Reflection on action  New knowledge [Dissemination?] New Practice Barbara Jaworski MEC 2008 2

29. Research Design Research Theoretical paradigm perspectives Research Research questions Strategy Research Methods Barbara Jaworski MEC 2008 2