1. Research Design and methodsin
Mathematics Education

2. Overview 2) Research approaches (12-19) Ontology& epistemology
Paradigms
Approaches/strategies
Rigour
Theory
Analysis
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
Barbara Jaworski MEC

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

4. Empirical Research
Data & Analysis
Barbara Jaworski MEC

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

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

7. 1 2 3 4 5 # Research Question Type(s) ofData (Collection)
Why do some students avail themselves to mathematics support whilst others do not?
Qualitative; interviews (+Qu’aire); Numeric (grades etc.) Transcripts, Audio, observation notes, text, researcher reflections 2
Which new technologies are being used in mathematics lectures and how?
Teacher blogs (reflective text). On-line qu’aire. Obs. Of lectures using techn. Open obs. Leading to categories for systematic obs. Interviews (structured) 3
Does expanding the ability to generate examples increase other areas of mathematical ability?
Numeric (raw scores) Scripts 4
Is there a need to improve the teaching of mathematics and to what extent? 5
To what extent is learning mathematics a social activity?
Barbara Jaworski MEC

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?
This will relate to what they have said they want to do.
I will use it to get discussion in the whole group
Barbara Jaworski MEC

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.
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Barbara Jaworski MEC

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
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Barbara Jaworski MEC

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
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Barbara Jaworski MEC

12. What are your epistemological and ontological positions?
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?
This is a repeat slide from our work on paradigms
What questions of bias might arise?
What kinds of ethical issues are likely to be involved?
Barbara Jaworski MEC

13. Paradigms Positivist Interpretivist Critical theorist Constructivist
Post modernist
Pring
Carr and Kemmis
Lincoln and Guba
We discussed all of these in our last session – the slide is intended as a reminder.
Barbara Jaworski MEC

14. Research approaches or strategies
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
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Copy pages from Miles and Huberman?
At this stage I shall be doing no more than introducing the terms and giving a very brief description, just so that the students start to be aware of the multiplicity of strategies and have some ideas about different modes of research.
Barbara Jaworski MEC

15. Symbolic Interactionism
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
Barbara Jaworski MEC

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

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

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

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
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
At this stage I shall be doing no more than introducing the terms and giving a very brief description, just so that the students start to be aware of the multiplicity of strategies and have some ideas about different modes of validation.
Barbara Jaworski MEC

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?
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Barbara Jaworski MEC

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

22. Research Paradigm and Theory
Ontology
Objectivism v. Constructionism
Epistemology
Positivism v. Interpretivism
Theory
Deductive v. Inductive
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Bryman p. 20
Barbara Jaworski MEC

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
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Barbara Jaworski MEC

24. Ethics Legalities Human factors
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
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Barbara Jaworski MEC

25. Relations between researcher and researched
Wagner, 1997
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
Input from me.
Getting students to relate this to their research questions and discuss in the whole group
Barbara Jaworski MEC

26. so, what is research Research is
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

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

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

29. Research Design Research Theoretical paradigm perspectives
Research Research
questions Strategy
Research
Methods
I will use this to review what we have discussed and bring us back to the design stage with a recognition of the inter-relatedness of these elements of research design.
Barbara Jaworski MEC