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Exploring the NATURE OF MATHEMATICAL activity: USING theory, research and `working hypotheses' to broaden conceptions of mathematics knowing

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Abstract

What proficiencies are brought tobear when students work on mathematicsproblems? And to what extent may these becaptured by knowledge categories? These arequestions that I consider in this article,as I explore notions of competency, that gobeyond knowledge to include themathematical `dispositions' that studentsbring to problems and the `practices' withwhich they engage. This exploration willdraw from two frameworks that have recentlybeen introduced in the US. In addition, Iconsider the ways in which researchknowledge is conceived and developed,reflecting upon the important role oftheory and the potential of `workinghypotheses' for connecting with practice innew ways.

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REFERENCES

  • Artigue, M.: 1999, ‘The teaching and learning of mathematics at the university level: Crucial questions for contemporary research in education’, Notices of the AMS 46(11), 1377–1385.

    Google Scholar 

  • Ball, S.J.: 1995, ‘Intellectuals or technicians? The urgent role of theory in educational studies’, British Journal of Educational Studies XXXXIII(3), 255–271.

    Article  Google Scholar 

  • Ball, D. and Bass, H.: 2000, ‘Bridging practices: Intertwining content and pedagogy in teaching and learning to teach’, in J. Boaler (ed.), Multiple Perspectives on Mathematics Teaching and Learning, Ablex Publishing, Westport, CT, pp. 83–104.

    Google Scholar 

  • Ben-Zvi, D. and Arcavi, A.: 2001, ‘Junior high school students’ construction of global views of data and data representations’, Educational Studies in Mathematics 45, 35–65.

    Article  Google Scholar 

  • Boaler, J.: 1997, Experiencing School Mathematics: Teaching Styles, Sex and Setting, Open University Press, Buckingham.

    Google Scholar 

  • Boaler, J.: 2002a, Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and Their Impact on Student Learning (Revised and Expanded Edition ed.), Lawrence Erlbaum Association, Mahwah, NJ.

    Google Scholar 

  • Boaler, J.: 2002b, ‘The development of disciplinary relationships: Knowledge, practice and identity in mathematics classrooms’, For the Learning of Mathematics 22(1), 42–47.

    Google Scholar 

  • Bourdieu, P.: 1982, ‘The school as a conservative force: Scholastic and cultural inequalities’, in E. Bredo and W. Feinberg (eds.), Knowledge and Values in Social and Educational Research, Temple University Press, Philadelphia, pp. 391–407.

    Google Scholar 

  • Bourdieu, P.: 1986, ‘The forms of capital’, in J. Richardson (ed.), Handbook of Theory and Research for the Sociology of Education, Greenwood Press, New York, pp. 241–258.

    Google Scholar 

  • Brown, M.L. (ed.): 1988: Graded Assessment in Mathematics Development Pack: Pupil Materials, Macmillan, Basingstoke, UK.

    Google Scholar 

  • Burton, L.: 1999, ‘The practices of mathematicians: What do they tell us about coming to know mathematics?’ Educational Studies in Mathematics 37, 121–143.

    Article  Google Scholar 

  • Chevallard, Y.: 1990, ‘On mathematics education and culture: Critical afterthoughts’, Educational Studies in Mathematics 21(1), 3–28.

    Article  Google Scholar 

  • Cobb, P., Wood, T., Yackel, E. and Perlwitz, M.: 1992, ‘A follow-up assessment of a second-grade problem-centered mathematics project’, Educational Studies in Mathematics 23, 483–504.

    Article  Google Scholar 

  • Cooney, T.: 1999, ‘Conceptualizing teachers's ways of knowing’, Educational Studies in Mathematics 38, 163–187.

    Article  Google Scholar 

  • Cuoco, A., Goldenberg, E.P. and Mark, J.: 1996, ‘Habits of mind: An organizing principle for mathematics curricula’, Journal of Mathematical Behavior 15, 375–402.

    Article  Google Scholar 

  • Dewey, J.: 1916, Democracy and Education, MacMillan, New York.

    Google Scholar 

  • Dickson, L., Brown, M.L. and Gibson, O.: 1984, Children learning Mathematics: A Teacher's Guide to Recent Research, Holt, Rinehart and Winston, Eastbourne, UK.

    Google Scholar 

  • Dowling, P.: 1996, ‘A sociological analysis of school mathematics texts’, Educational Studies in Mathematics 31, 389–415.

    Article  Google Scholar 

  • Ensor, P.: 2001, ‘From preservice mathematics teacher education to beginning teaching: A study in recontextualizing’, Journal for Research in Mathematic Education 32(3), 296–320.

    Google Scholar 

  • Ernest, P.: 1991, The Philosophy of Mathematics Education, Falmer, New York.

    Google Scholar 

  • Ernest, P.: 1999, ‘Forms of knowledge in mathematics and mathematics education: Philosophical and rhetorical perspectives’, Educational Studies in Mathematics 38(1-3), 67–83.

    Article  Google Scholar 

  • Even, R. and Tirosh, D.: 1995, ‘Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject matter’, Educational Studies in Mathematics 29(1), 1–20.

    Article  Google Scholar 

  • Greeno, J.G., McDermott, R.P., Cole, K., Engle, R., Goldman, S., Knudsen, J., Lauman, B. and Linde, C.: 1999, ‘Research, reform, and aims in education: Modes of action in search of each other’, in E.C. Lagemann and L.S. Shulman (eds.), Issues in Education Research: Problems and Possibilities, Jossey-Bass Publishers, San Francisco.

    Google Scholar 

  • Hart, K.M. (ed.): 1981, Children's Understanding of Mathematics: 11-16, John Murray, London, UK.

    Google Scholar 

  • Hiebert, J.: 1986, Conceptual and Procedural Knowledge: The Case of Mathematics, Lawrence Erlbaum, New Jersey.

    Google Scholar 

  • Joseph, G.G.: 1992, The Crest of the Peacock: Non-European Roots of Mathematics, Penguin, Harmondsworth, UK.

    Google Scholar 

  • Kieran, C., Forman, E.A. and Sfard, A.: 2001, ‘Guest editorial. Learning discourse: Sociocultural approaches to research in mathematics education’, Educational Studies in Mathematics 46(1-3), 1–12.

    Article  Google Scholar 

  • Kilpatrick, J., Swafford, J. and Findell, B. (eds.): 2001, Adding it up: Helping Children Learn Mathematics, National Academy Press, Washington, DC.

    Google Scholar 

  • Kilpatrick, J.: 2001, ‘Understanding mathematical literacy: The contribution of research’, Educational Studies in Mathematics 47(1), 101–116.

    Article  Google Scholar 

  • Lave, J.: 1993, ‘The practice of learning’, in S. Chaiklin and J. Lave (ed.), Understanding Practice: Perspectives on Activity and Context, Cambridge University Press, Cambridge, pp. 3–34.

    Google Scholar 

  • Lave, J. and McDermott, R.P.: 2002, ‘Estranged Learning’, Outlines 1, 19–48.

    Google Scholar 

  • Lerman, S.: 2000, ‘The social turn in mathematics education research’, in J. Boaler (ed.), Multiple Perspectives on Mathematics Teaching and Learning, Ablex Publishing, Westport, CT, pp. 19–44.

    Google Scholar 

  • Lerman, S.: 2001, ‘Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics’, Educational Studies in Mathematics 46(1-3), 87–113.

    Article  Google Scholar 

  • Mead, G.H.: 1899, ‘The working hypothesis in social reform’, American Journal of Sociology 5, 369–371.

    Google Scholar 

  • Morgan, C.: 2000, ‘Better assessment in mathematics education? A social perspective’, in J. Boaler (ed.), Multiple Perspectives on Mathematics Teaching and Learning, Ablex Publishing, Westport, CT, pp. 225–243.

    Google Scholar 

  • National Academy of Education: 1999, Recommendations Regarding Research Priorities: An Advisory Report to the National Educational Research Policy and Priorities Board, NAE, New York.

    Google Scholar 

  • National Council for Teachers of Mathematics (NCTM): 2000, Principles and Standards for School Mathematics, NCTM, Virginia.

    Google Scholar 

  • Noss, R., Healy, L. and Hoyles, C.: 1997, ‘The construction of mathematical meanings: Connecting the visual with the symbolic’, Educational Studies in Mathematics 33, 203–233.

    Article  Google Scholar 

  • RAND Mathematics Study Panel: 2002, October, Mathematical Proficiency for all Students: Toward a Strategic Research and Development Program in Mathematics Education (DRU-2773-OERI), RAND Education and Science and Technology Policy Institute, Arlington, VA.

    Google Scholar 

  • Schoenfeld, A.H.: 1985, Mathematical Problem-Solving, Academic Press, New York, NY.

    Google Scholar 

  • Schoenfeld, A.: 1992, ‘Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics’, in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, MacMillan, New York, pp. 334–371.

    Google Scholar 

  • Sierpinska, A. and Kilpatrick, J. (eds.).: 1998, Mathematics Education as a Research Domain: A Search for Identity. An ICMI study, Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • Simon, M.: 1996, ‘Beyond inductive and deductive reasoning: The search for a sense of knowing’, Educational Studies in Mathematics 30, 197–210.

    Article  Google Scholar 

  • Singh, S.: 1998, Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem, Anchor Books, New York.

    Google Scholar 

  • Skemp, R.: 1976, Relational understanding and instrumental understanding, Mathematics Teaching December, 65–71.

  • Skovsmose, O.: 1994, Towards a Philosophy of Critical Mathematics Education, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Thompson, A.: 1992, ‘Teachers’ beliefs and conceptions: A synthesis of the research’, in D. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 127–146.

    Google Scholar 

  • Tirosh, D.: 1999, ‘Forms of mathematical knowledge: Learning and teaching with understanding’, Educational Studies in Mathematics 38(1-3), 1–9.

    Google Scholar 

  • Valero, P.: 1999, ‘Deliberative mathematics education for social democratization in Latin America’, Zentralblatt fur Didaktik der Mathematik 98(6), 20–26.

    Google Scholar 

  • Van Oers, B.: 2001, ‘Educational forms of initiation in mathematical culture’, Educational Studies in Mathematics 46, 59–85.

    Article  Google Scholar 

  • Vithal, R. and Skovsmose, O.: 1997, ‘The end of innocence: A critique of ethnomathematics’, Educational Studies in Mathematics 34, 131–157.

    Article  Google Scholar 

  • Wenger, E.: 1998, Communities of Practice: Learning, Meaning and Identity, Cambridge University Press, Cambridge.

    Google Scholar 

  • Zevenbergen, R.: 1996, ‘Constructivism as a liberal bourgeois discourse’, Educational Studies in Mathematics 31, 95–113.

    Article  Google Scholar 

Download references

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  1. Mathematics Education, School of Education, Stanford University, 485 Lasuen Mall, Stanford, CA, 94305-3096

    Jo Boaler

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Boaler, J. Exploring the NATURE OF MATHEMATICAL activity: USING theory, research and `working hypotheses' to broaden conceptions of mathematics knowing. Educational Studies in Mathematics 51, 3–21 (2002). https://doi.org/10.1023/A:1022468022549

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