Abstract
Central to the preparation of mathematics teachers is their preparation in mathematics. Consequently, a careful examination of the nature of teachers’ mathematical experiences is warranted. There are many factors that influence the teaching of mathematics including the historical development of mathematics with its inherent formalism. This linkage will be explored along with a review of research on teachers’ beliefs and knowledge of mathematics as beliefs and knowledge relate to teacher change. We conclude that this research suggests that teachers are not always well positioned to adopt a more reform- and process-oriented teaching style that moves beyond the usual formalism in the teaching of mathematics. Grounded in this review of the literature, three principles for teaching preservice teachers mathematics will be presented. These principles are: (a) treating mathematics as a pluralistic subject, (b) providing teachers with opportunities to understand and reflect on school mathematics, and (c) enabling teachers to experience mathematics as a process. We will discuss and illustrate these principles using a specific mathematical problem solved from a variety of perspectives.
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Ball, D. L. (1990a). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21, 132–144.
Ball, D. L. (1990b). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90, 449–466.
Balacheff, N. (1998). Construction of meaning and teacher control of learning. In D. J. Tinsley & D. J. Johnson (Eds.), Information and communication technologies in school mathematics (pp. 111–120). New York: Chapman and Hall.
Benacerraf, P., & Putnam, H. (1964). Philosophy of mathematics. Englewood Cliffs, NJ: Prentice Hall.
Born, M. (1968). My life and my views. New York: Charles Scribners Sons.
Bromme, R. (1994). Beyond subject matter: A psychological topology of teachers’ professional knowledge. In R. Biehler, R. Scholz, R. Strässer & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 73–88). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Brown, S., Cooney, T., & Jones, D. (1990). Mathematics teacher education. In R. Houston (Ed.), Handbook of research on teacher education (pp. 639–656). New York: Macmillan.
Carpenter, T., Fennema, E., & Franke, M. (1996). Cognitively Guided Instruction: A knowledge base for reform in primary mathematics instruction. Elementary School Journal, 97, 3–20.
Chauvot, J. (2000). Conceptualizing mathematics teacher development in the context of reform. Unpublished doctoral dissertation, University of Georgia, Athens.
Cooney, T., Brown, S., Dossey, J., Schrage, G., & Wittmann, E. (1999). Mathematics, pedagogy, and secondary teacher education. Portsmouth, NH: Heinemann.
Cooney, T., Wilson, P., Albright, M., & Chauvot, J. (1998, April). Conceptualizing the professional development of secondary preservice mathematics teachers. Paper presented at the American Educational Research Association annual meeting, San Diego.
Davis, B. (1999). Basic irony: Examining the foundations of school mathematics with preservice teachers. Journal of Mathematics Teacher Education, 2, 25–48.
Davis, P., & Hersh, R. (1981). The mathematical experience. Boston: Birkhäuser.
Dewey, J. (1916). Democracy and education. New York: The Free Press.
Dossey, J. A. (1992). The nature of mathematics: Its role and its influence. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 39–48). New York: Macmillan.
Eggleton, P. J. (1995). The evolving mathematical philosophy of a preservice mathematics teacher. Unpublished doctoral dissertation, University of Georgia, Athens.
Ernest, P. (1991). The philosophy of mathematics education. London: Farmer Press.
Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: D. Reidel Publishing Company.
Frykholm, J. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2, 79–105.
Geliert, U. (2000). Mathematics instruction in safe space: Prospective elementary teachers’ views of mathematics education. Journal of Mathematics Teacher Education, 3, 251–270.
Geometer’s Sketchpad 3.06/PPC [Computer software] (1997). Emeryville, CA: Key Curriculum Press.
Gödel, K. (1931). Über formal unentscheidbare Sätze der principiä mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38, 173–198.
Grant, T. J., Hiebert, J., & Wearne, D. (1998). Observing and teaching reform-minded lessons: What do teachers see? Journal of Mathematics Teacher Education, 2, 217–236.
Graphing Calculator 3.1 [Computer software] (2001). Woodside, CA: Pacific Tech.
Halliday, D., & Resnick, R. (1988). Fundamentals of physics (3rd ed.). New York: John Wiley & Sons.
Hersh, R. (1986). Some proposals for reviving the philosophy of mathematics. In T. Tymoczko (Ed.), New directions in the philosophy of mathematics (pp. 9–28). Boston: Birkhäuser.
House, P. (1980). Interactions of science and mathematics. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Educational Education.
Jaworski, B., & Wood, T. (1999). Themes and issues in inservice programmes. In B. Jaworski, T. Wood & S. Dawson (Eds.), Mathematics teacher education: Critical international perspectives (pp. 125–147). London: Falmer Press.
Krainer, K. (1999). PFL-mathematics: Improving professional practice in mathematics teaching. In B. Jaworski, T. Wood & S. Dawson (Eds.), Mathematics teacher education: Critical international perspectives (pp. 102–112). London: Falmer Press.
Laborde, C. (2001). The use of new technologies as a vehicle for restructuring teachers’ mathematics. In F.-L. Lin & T. Cooney (Eds.), Making sense of mathematics teacher education (pp. 87–110). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Lakatos, I. (1976). Proofs and refutations. New York: Cambridge University Press.
Lerman, S. (2001). A review of research perspectives on mathematics teacher education. In F.-L. Lin & T. Cooney (Eds.), Making sense of mathematics teacher education (pp. 33–52). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Publishers.
Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1, 243–267.
Mathematical Education Sciences Board (2001). Knowing and learning mathematics for teaching. Washington, D. C: Mathematical Education Sciences Board.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA.
Olive, J. (1998). Opportunities to explore and integrate mathematics with the Geometer’s Sketchpad. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 395–418). Mahwah, NJ: Lawrence Erlbaum Associates,
Owens, J. (1987). A study of four preservice teachers’ constructs of mathematics and mathematics teaching. Unpublished doctoral dissertation, University of Georgia, Athens.
Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books Inc.
Ponte, J. (2001). Investigating mathematics and learning to teach mathematics. In F.-L. Lin & T. Cooney (Eds.), Making sense of mathematics teacher education (pp. 53–72). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Schifter, D. (1998). Learning mathematics for teaching: From a teachers’ seminar to the classroom. Journal of Mathematics Teacher Education, 1, 55–87.
Skott, J. (2001). The emerging practices of a novice teacher: The roles of his school mathematics images. Journal of Mathematics Teacher Education, 4, 33–28.
Sowder, J., Armstrong, B., Lamon, S., Simon, M., Sowder, L., & Thompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1, 127–155.
Stacey, K., Helme, S., Steinle, V., Irwin K., Baturo, A., & Bana, J. (2001). Preservice teachers’ knowledge of difficulties in decimal numeration. Journal of Mathematics Teacher Education, 4, 205–225.
Tymoczko, T. (1986). Making room for mathematicians in the philosophy of mathematics. The Mathematical Intelligencer, 8(3), 44–50.
Wilson, M. R., & Goldenberg, M. P. (1998). Some conceptions are difficult to change: One middle school mathematics teacher’s struggle. Journal of Mathematics Teacher Education, 2, 269–293.
Wittmann, E. (1992). One source of the broadcast metaphor: Mathematical formalism. In F. Seeger & H. Steinbring (Eds.), The dialogue between theory and practice in mathematics education: Over coming the broadcast metaphor (pp. 111–119). Bielefeld, Germany: Institut für Didaktik der Mathematik der Universität Bielefeld.
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Cooney, T.J., Wiegel, H.G. (2003). Examining the Mathematics in Mathematics Teacher Education. In: Bishop, A.J., Clements, M.A., Keitel, C., Kilpatrick, J., Leung, F.K.S. (eds) Second International Handbook of Mathematics Education. Springer International Handbooks of Education, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0273-8_26
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