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On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education

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Theories of Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

The current infatuation in the U.S. with “what works” studies seems to leave education researchers with less latitude to conduct studies to advance theoretical and model-building goals and they are expected to adopt philosophical perspectives that often run counter to their own. Three basic questions are addressed in this article: What is the role of theory in education research? How does one’s philosophical stance influence the sort of research one does? And, What should be the goals of mathematics education research? Special attention is paid to the importance of having a conceptual framework to guide one’s research and to the value of acknowledging one’s philosophical stance in considering what counts as evidence.

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References

  • Anderson, J. R., Reder, L. M., & Simon, H. A. (1996). Situated learning and education. Educational Researcher, 25(4), 5–11.

    Google Scholar 

  • Boaler, J. (2000). Exploring situated insights into research and learning. Journal for Research in Mathematics Education, 31, 113–119.

    Article  Google Scholar 

  • Churchman, C. W. (1971). The Design of Inquiring Systems: Basic Concepts of System and Organization. New York: Basic Books.

    Google Scholar 

  • Cobb, P. (1995). The relevance of practice: A reply to Orton. Journal for Research in Mathematics Education, 26, 230–253.

    Article  Google Scholar 

  • Cobb, P. (2007). Putting philosophy to work: Coping with multiple theoretical perspectives. In F. Lester (Ed.), Handbook of Research on Teaching and Learning Mathematics (2nd ed.). Greenwich, CT: Information Age Publishing.

    Google Scholar 

  • Cook, T. (2001, Fall). Sciencephobia: Why education researchers reject randomized experiments. Education Next. Retrieved September 18, 2005, from www.educationnext.org/20013/62.pdf.

  • Davis, R. B. (1967). The range of rhetorics, scale and other variables. Proceedings of National Conference on Needed Research in Mathematics Education in the Journal of Research and Development in Education, 1(1), 51–74.

    Google Scholar 

  • Davis, R. B., Maher, C. A., & Noddings, N. (Eds.) (1990). Constructivist view on the teaching and learning of mathematics. Journal for Research in Mathematics Education Monograph No. 4. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Denzin, N. (1978). The Research Act: A Theoretical Introduction to Sociological Methods. New York: McGraw Hill.

    Google Scholar 

  • diSessa, A. A. (1991). If we want to get ahead, we should get some theories. In Proceedings of the 13 th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 220–239). Blacksburg, VA.

    Google Scholar 

  • Eisenhart, M. A. (1991). Conceptual frameworks for research circa 1991: Ideas from a cultural anthropologist; implications for mathematics education researchers. In Proceedings of the 13 th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 202–219). Blacksburg, VA.

    Google Scholar 

  • Garrison, J. W. (1988). The impossibility of atheoretical educational science. Journal of Education Thought, 22(1), 21–26.

    Google Scholar 

  • Gravemeijer, G. (1994). Educational development and developmental research. Journal for Research in Mathematics Education, 25, 443–471.

    Article  Google Scholar 

  • Greeno, J. G. (1997). On claims that answer the wrong questions. Educational Researcher, 26(1), 5–17.

    Google Scholar 

  • Hammersley, M. (1990). From ethnography to theory: A programme and paradigm in the sociology of education. In M. Hammersley (Ed.), Classroom Ethnography (pp. 108–128). Milton Keynes: Open University Press.

    Google Scholar 

  • Hiebert, J., Kilpatrick, J., & Lindquist, M. M. (2001). Improving U.S. doctoral programs in mathematics education. In R. Reys & J. Kilpatrick (Eds.), One Field, Many Paths: U.S. Doctoral Programs in Mathematics Education (pp. 153–159). Washington, DC: Conference Board of the Mathematical Sciences.

    Google Scholar 

  • Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 3–38). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Kuhn, T. S. (1962). The Structure of Scientific Revolutions. Chicago: University of Chicago Press.

    Google Scholar 

  • Lesh, R. A. (2002). Research design in mathematics education: Focusing on design experiments. In L. English (Ed.), Handbook of International Research in Mathematics Education (pp. 27–49). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R. A., & Doerr, H. (Eds.) (2003). Beyond Constructivism: A Models and Modeling Perspective on Mathematical Problem Solving. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R. A., & Kelly, E. A. (Eds.) (2000). Handbook of Research Design in Mathematics and Science Education. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R. A., & Sriraman, B. (2005). Mathematics Education as a design science. International Reviews on Mathematical Education (ZDM), 37(6), 490–504.

    Google Scholar 

  • Lester, F. K., & Lambdin, D. V. (2003). From amateur to professional: The emergence and maturation of the U.S. mathematics education research community. In G. M. A. Stanic & J. Kilpatrick (Eds.), A History of School Mathematics (pp. 1629–1700). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Lester, F. K., & Wiliam, D. (2000). The evidential basis for knowledge claims in mathematics education research. Journal for Research in Mathematics Education, 31, 132–137.

    Article  Google Scholar 

  • Lester, F. K., & Wiliam, D. (2002). On the purpose of mathematics education research: Making productive contributions to policy and practice. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (pp. 489–506). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Orton, R. E. (1995). Ockham’s razor and Plato’s beard: Or, the possible relevance of the philosophy of mathematics, and the problem of universals in particular, to the philosophy of mathematics education, and the problem of constructivism in particular. Journal for Research in Mathematics Education, 26, 204–229.

    Article  Google Scholar 

  • Scandura, J. M. (Ed.) (1967). Research in Mathematics Education. Washington, DC: National Council of Teachers of Mathematics.

    Google Scholar 

  • Scriven, M. (1986). Evaluation as a paradigm for education research. In E. House (Ed.), New Directions in Education Evaluation (pp. 53–67). London: Falmer Press.

    Google Scholar 

  • Silver, E. A., & Herbst, P. (2004, April). “Theory” in mathematics education scholarship. Paper presented at the research presession of the annual meeting of the National Council of Teachers of Mathematics, Philadelphia, PA.

    Google Scholar 

  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.

    Article  Google Scholar 

  • Singer, E. A., Jr. (1959). Experience and Reflection. Philadelphia: University of Pennsylvania Press.

    Google Scholar 

  • Steffe, L. P., & Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 267–306). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Stokes, D. E. (1997). Pasteur’s Quadrant: Basic Science and Technological Innovation. Washington, DC: Brookings Institution Press.

    Google Scholar 

  • United States Department of Education (2002). Strategic Plan: 2002–2007. Washington, DC: Author.

    Google Scholar 

  • Van Maanen, J. (1988). Tales of the Field: On Writing Ethnography. Chicago, IL: University of Chicago Press.

    Google Scholar 

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Correspondence to Frank K. Lester Jr. .

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Lester, F.K. (2010). On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-00742-2_8

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