yess4 barbara jaworski
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Becoming a researcher in Becoming a researcher in mathematics education – mathematics education –
what what do we need to think about?do we need to think about?
Barbara JaworskiBarbara Jaworski
Barbara Jaworski YERME 2006Barbara Jaworski YERME 2006 22
Two main goals Two main goals
of research in mathematics educationof research in mathematics education
To enhance To enhance knowledgeknowledge in the field in the field • knowledge about mathematics, learning knowledge about mathematics, learning
mathematics, teaching mathematics, doing mathematics, teaching mathematics, doing research in learning mathematics …research in learning mathematics …
To enhance To enhance practicepractice in the field in the field • to enable to enable betterbetter learning and teaching of learning and teaching of
mathematics, mathematics, betterbetter researching … researching …
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MathematicsMathematics
What is special about mathematics?What is special about mathematics?
Beauty
Functionality
Power to express succinctly
Power to generalise
Abstraction
GeometricNumeric
InfinityLogic
Statistical
LimitsSimplicity
Complexity
A language
Algebraic
Infinitessimals
Graphs
Power to explain
Proof
Probability
Calculus
Structures
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Mathematics EducationMathematics Education
How mathematical topics can be made How mathematical topics can be made accessible for learners;accessible for learners;
How we learn mathematics How we learn mathematics successfully;successfully;
How we teach mathematics in order How we teach mathematics in order that learning can be successful;that learning can be successful;
How we develop mathematics teaching How we develop mathematics teaching and educate mathematics teachers;and educate mathematics teachers;
How research in the field informs and How research in the field informs and promotes development.promotes development.
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Research DesignResearch Design
ResearchResearch TheoreticalTheoreticalparadigmparadigm perspectivesperspectives
Research Research ResearchResearchquestions questions StrategyStrategy
Research Research MethodsMethods
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ParadigmsParadigms
PositivistPositivist
InterpretivistInterpretivist
Critical theoristCritical theorist
ConstructivistConstructivist
Post modernistPost modernistPring
Carr and KemmisLincoln and Guba
How does mathematics education
fit within here?
Davis & Hersch
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What are your epistemological and What are your epistemological and ontological positions?ontological positions?
What kinds of ethical What kinds of ethical issues are likely to issues are likely to be involved?be involved?
What kinds of What kinds of knowledge? knowledge?
What IS?What IS?Do you seek objectivity?Do you seek objectivity?
What kinds of What kinds of interpretationinterpretations are likely to s are likely to be involved be involved and how do and how do you expect to you expect to deal with deal with them?them?
What What questions questions of bias of bias might might arise?arise?
Do you expect to Do you expect to address human address human issues and values, issues and values, and if so what is and if so what is your stance on your stance on these?these?
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TheoryTheory
Naïve empiricismNaïve empiricism
The literatureThe literature
Grand theoryGrand theory
Local theoryLocal theory
Personal theoryPersonal theory
BrymanMason & Waywood
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Position of theoryPosition of theory
Theory that guides research Theory that guides research (deductive)(deductive) Theory that emerges from research Theory that emerges from research
(inductive)(inductive) … … principles …principles … … … assumptions …assumptions …
What kind of theory are we talking about?What kind of theory are we talking about?
What do we mean by theory?What do we mean by theory?
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Research Paradigm and TheoryResearch Paradigm and Theory
OntologyOntology ObjectivismObjectivismv. Constructionismv. Constructionism
EpistemologyEpistemologyPositivism v.Positivism v. Interpretivism Interpretivism
TheoryTheoryDeductive v. InductiveDeductive v. Inductive
BrymanSierpinska & Lerman
Pring
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so, what so, what isis research research Research isResearch is
””systematic inquiry made public” systematic inquiry made public” (1984, p. 77).(1984, p. 77).
Action research might be defined asAction research might be defined as ‘ ‘the study of a social situation with a view to improving the study of a social situation with a view to improving the quality of action within it’. It aims to feed practical the quality of action within it’. It aims to feed practical judgement in concrete situations, and the validity of the judgement in concrete situations, and the validity of the ‘theories’ or hypotheses it generates depends not so much ‘theories’ or hypotheses it generates depends not so much on ‘scientific’ tests of truth, as on the usefulness in helping on ‘scientific’ tests of truth, as on the usefulness in helping people to act more intelligently and skillfully …. In action people to act more intelligently and skillfully …. In action research ‘theories’ are not validated independently and then research ‘theories’ are not validated independently and then applied to practice. They are validated through practice’ applied to practice. They are validated through practice’ (1991, p. 69).(1991, p. 69).
StenhouseStenhouse
ElliottElliott
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Formal Educational ResearchFormal Educational Research
We want to know We want to know Research Questions Research Questions
Research Design (Methodology+Methods) Research Design (Methodology+Methods) Data Collection Data Collection Data Analysis Data Analysis Validation Validation Ethics Ethics
Results/Findings Results/Findings New Knowledge (Dissemination)New Knowledge (Dissemination)[New Practice?][New Practice?]
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Practitioner (action) ResearchPractitioner (action) Research
We want to know We want to know Research Questions Research Questions Plan for action Plan for action Action (new practice?) Action (new practice?) Reflection Reflection onon action action
New knowledge [Dissemination?]New knowledge [Dissemination?]New PracticeNew Practice
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Research questionsResearch 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 Are there specific questions I want
answers toanswers to RefiningRefining RefiningRefining RefiningRefining ……..
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Collecting suitable dataCollecting suitable data
Do you want to find out how many, or Do you want to find out how many, or what percentage or proportion?what percentage or proportion?
Do you want to find out what people know, Do you want to find out what people know, or think, their beliefs or attitudes?or think, their beliefs or attitudes?
Do you want to explore the impact of Do you want to explore the impact of some learning and/or teaching approach, some learning and/or teaching approach, methods or materials?methods or materials?
Do you want to design materials or models Do you want to design materials or models to achieve better learning or teaching?to achieve better learning or teaching?
Do you envisage a documentary study?Do you envisage a documentary study?
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Quantitative or Qualitative or both?Quantitative or Qualitative or both?
Quantitative: where you quantify your Quantitative: where you quantify your data and analyse it using statistical data and analyse it using statistical techniquestechniques
Qualitative: where you describe, Qualitative: where you describe, characterise, look deeply into human characterise, look deeply into human actions, thinking, values …actions, thinking, values …
Both: where you use methods of both Both: where you use methods of both sorts, or where the boundaries are sorts, or where the boundaries are blurred.blurred.
GorardBasseyTeppo
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Relations between researcher and Relations between researcher and researchedresearched
Data extraction agreementsData extraction agreements• Externally objectiveExternally objective• SubjectsSubjects of research of research
Clinical partnershipsClinical partnerships• Outsider and insider Outsider and insider participantsparticipants with with
mutual respectmutual respect Co-learning agreementsCo-learning agreements
• All participants are both insiders and All participants are both insiders and outsidersoutsiders
WagnerWagner
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Research strategiesResearch strategies Survey or testSurvey or test ExperimentExperiment Action researchAction research Case studyCase study EthnographyEthnography Life historyLife history Document analysisDocument analysis
PhenomenologyPhenomenology EthnomethodologyEthnomethodology Symbolic Symbolic
interactionisminteractionism PhenomenographyPhenomenography Democratic Democratic
researchresearch Feminist researchFeminist research
Miles & HubermanMiles & Hubermanmaps from maps from
Wolcott and TeschWolcott and Tesch
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Where do your data come from?Where do your data come from?
Population: the set of sources of data Population: the set of sources of data from which you draw a suitable samplefrom which you draw a suitable sample
Sample: the set of sources within your Sample: the set of sources within your population from which you collect data:population from which you collect data:• RandomRandom• RepresentativeRepresentative• ConvenienceConvenience• Focused or purposiveFocused or purposive• SpecificSpecific
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EthicsEthics Human factorsHuman factors
• Avoidance of causing hurt or disadvantage to Avoidance of causing hurt or disadvantage to any participants in the research – anonymityany participants in the research – anonymity
• Decisions about openness and inclusion in the Decisions about openness and inclusion in the researchresearch
LegalitiesLegalities• 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 GuidelinesBERA Ethical Guidelines
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How do/will you collect your dataHow do/will you collect your data
Methods of data collectionMethods of data collection• Surveys: questionnairesSurveys: questionnaires• Experiments: control groupsExperiments: control groups• TestsTests• Ethnographic approachesEthnographic approaches
ObservationObservation• SystematicSystematic• ParticipantParticipant
InterviewsInterviews• StructuredStructured• Semi structuredSemi structured• ConversationsConversations• Focus groupsFocus groups
• Documentary dataDocumentary data
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How will you analyse your data?How will you analyse your data?
Relates directly to your research Relates directly to your research strategy and paradigmatic positionstrategy 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
BrymanMiles & Huberman
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Rigour: validation and evidenceRigour: validation and evidence
Validity: Validity: construct, internal, construct, internal,
external, external, ecologicalecological
ReliabilityReliability
ReplicabilityReplicability
GeneralizabilityGeneralizability
BrymanLincoln & Guba
Trustworthiness:Trustworthiness:
CredibilityCredibility
TransferabilityTransferability
DependabilityDependability
ConfirmabilityConfirmability
RelevanceRelevance
TriangulationTriangulation
Respondent validationRespondent validation
Member checksMember checks
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Writing a research paper/article/reportWriting 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 What is your research design, why and how
(methodology)?(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 What conclusions do you draw – how does
your research add to knowledge in the field?your research add to knowledge in the field?
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ReferencesReferencesBassey, M. (1999) Bassey, M. (1999) Case Study Research in Educational Case Study Research in Educational
Settings.Settings. Buckingham: Open University Press Buckingham: Open University PressBERA (2004). BERA (2004). Revised Ethical Guidelines for educational Revised Ethical Guidelines for educational
research.research. On-line. On-line. http://www.bera.ac.uk/publications/pdfs/ETHICA1.PDFhttp://www.bera.ac.uk/publications/pdfs/ETHICA1.PDF [01.03.06][01.03.06]
Bryman, A. (2001) Bryman, A. (2001) Social Research MethodsSocial Research Methods. Oxford: Oxford . Oxford: Oxford University Press.University Press.
Carr, W. and Kemmis, S. (1986) Carr, W. and Kemmis, S. (1986) Becoming Critical: Education, Becoming Critical: Education, Knowledge and Action ResearchKnowledge and Action Research. London: Falmer Press. London: Falmer Press
Davis, P. J. And Hersh, R. (1981) Davis, P. J. And Hersh, R. (1981) The Mathematical The Mathematical Experience.Experience. London: Penguin London: Penguin
Elliott, J. (1991) Elliott, J. (1991) Action Research for Educational ChangeAction Research for Educational Change. . Buckingham: Open University PressBuckingham: Open University Press
Gorard, S. (2001) Gorard, S. (2001) Quantitative Methods in Educational Quantitative Methods in Educational ResearchResearch. London: Continuum. London: Continuum
Lincoln, Y. S. & Guba, E. G. (2000).Paradigmatic controversias, Lincoln, Y. S. & Guba, E. G. (2000).Paradigmatic controversias, contradictions and emerging confluences. contradictions and emerging confluences. In N. K. Denzin & In N. K. Denzin & Y. S. Lincoln (Eds.) Y. S. Lincoln (Eds.) Handbook of Qualitative ResearchHandbook of Qualitative Research, 2nd , 2nd Edition pp. 163-188. London: Sage. Edition pp. 163-188. London: Sage.
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ReferencesReferencesMason, J. & Waywood, A. (1996). The Role of Theory in Mathematics Mason, J. & Waywood, A. (1996). The Role of Theory in Mathematics
Education and Research. In A. Bishop et al., Education and Research. In A. Bishop et al., International International Handbook of Mathematics EducationHandbook of Mathematics Education. Dordrecht: Kluwer. Dordrecht: Kluwer
Miles, M. B. & Huberman, A. N. (1994Miles, M. B. & Huberman, A. N. (1994).Qualitative Data Analysis: An ).Qualitative Data Analysis: An expanded sourcebookexpanded sourcebook. Second Edition. London: Sage. Second Edition. London: Sage
Pring, R. (2000) Pring, R. (2000) Philosophy of Educational ResearchPhilosophy of Educational Research. London: . London: ContinuumContinuum
Sierpinska, A. & Lerman, S. (1996). Epistemologies of Mathematics Sierpinska, A. & Lerman, S. (1996). Epistemologies of Mathematics and Mathematics Education. In A. Bishop et al., and Mathematics Education. In A. Bishop et al., International International Handbook of Mathematics EducationHandbook of Mathematics Education. Dordrecht: Kluwer. Dordrecht: Kluwer
Stenhouse, L. (1979). Research as a basis for teaching: Inaugural Stenhouse, L. (1979). Research as a basis for teaching: Inaugural Lecture, University of East Anglia, February, 1979. In L. Stenhouse Lecture, University of East Anglia, February, 1979. In L. Stenhouse (1983) Authority,Education and Emancipation. London: (1983) Authority,Education and Emancipation. London: Heinemann Educational, pp. 177-195. Reprinted in Ruddock, J. Heinemann Educational, pp. 177-195. Reprinted in Ruddock, J. and Kopkins, D. (1985). Research as a basis for teaching: and Kopkins, D. (1985). Research as a basis for teaching: Readings from the work of Lawrence Stenhouse. Pp 113-128.Readings from the work of Lawrence Stenhouse. Pp 113-128.
Teppo, A. (1998) (Ed.) Qualitative Research Methods in Mathematics Teppo, A. (1998) (Ed.) Qualitative Research Methods in Mathematics Education. Education. Journal for Research in Mathematics Education, Journal for Research in Mathematics Education, Monograph Number 9Monograph Number 9. Reston, Va: National Council of Teacher of . Reston, Va: National Council of Teacher of Mathematics.Mathematics.
Wagner, J. (1997). The unavoidable intervention of educational Wagner, J. (1997). The unavoidable intervention of educational research: a framework for reconsidering researcher-practitioner research: a framework for reconsidering researcher-practitioner cooperation. Educational Researcher, 26 (7) pp. 13-22cooperation. Educational Researcher, 26 (7) pp. 13-22