Skip to main content
SpringerLink
Log in

Examining the Mathematics in Mathematics Teacher Education

  • Chapter
  • First Online:
Second International Handbook of Mathematics Education

Part of the book series: Springer International Handbooks of Education ((SIHE,volume 10))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 429.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ball, D. L. (1990a). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21, 132–144.

    Google Scholar 

  • Ball, D. L. (1990b). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90, 449–466.

    Google Scholar 

  • 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.

    Google Scholar 

  • Benacerraf, P., & Putnam, H. (1964). Philosophy of mathematics. Englewood Cliffs, NJ: Prentice Hall.

    Google Scholar 

  • Born, M. (1968). My life and my views. New York: Charles Scribners Sons.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Chauvot, J. (2000). Conceptualizing mathematics teacher development in the context of reform. Unpublished doctoral dissertation, University of Georgia, Athens.

    Google Scholar 

  • Cooney, T., Brown, S., Dossey, J., Schrage, G., & Wittmann, E. (1999). Mathematics, pedagogy, and secondary teacher education. Portsmouth, NH: Heinemann.

    Google Scholar 

  • 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.

    Google Scholar 

  • Davis, B. (1999). Basic irony: Examining the foundations of school mathematics with preservice teachers. Journal of Mathematics Teacher Education, 2, 25–48.

    Google Scholar 

  • Davis, P., & Hersh, R. (1981). The mathematical experience. Boston: Birkhäuser.

    Google Scholar 

  • Dewey, J. (1916). Democracy and education. New York: The Free Press.

    Google Scholar 

  • 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.

    Google Scholar 

  • Eggleton, P. J. (1995). The evolving mathematical philosophy of a preservice mathematics teacher. Unpublished doctoral dissertation, University of Georgia, Athens.

    Google Scholar 

  • Ernest, P. (1991). The philosophy of mathematics education. London: Farmer Press.

    Google Scholar 

  • Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: D. Reidel Publishing Company.

    Google Scholar 

  • Frykholm, J. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2, 79–105.

    Google Scholar 

  • Geliert, U. (2000). Mathematics instruction in safe space: Prospective elementary teachers’ views of mathematics education. Journal of Mathematics Teacher Education, 3, 251–270.

    Google Scholar 

  • Geometer’s Sketchpad 3.06/PPC [Computer software] (1997). Emeryville, CA: Key Curriculum Press.

    Google Scholar 

  • Gödel, K. (1931). Ăśber formal unentscheidbare Sätze der principiä mathematica und verwandter Systeme I. Monatshefte fĂĽr Mathematik und Physik, 38, 173–198.

    Google Scholar 

  • 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.

    Google Scholar 

  • Graphing Calculator 3.1 [Computer software] (2001). Woodside, CA: Pacific Tech.

    Google Scholar 

  • Halliday, D., & Resnick, R. (1988). Fundamentals of physics (3rd ed.). New York: John Wiley & Sons.

    Google Scholar 

  • 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.

    Google Scholar 

  • House, P. (1980). Interactions of science and mathematics. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Educational Education.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Lakatos, I. (1976). Proofs and refutations. New York: Cambridge University Press.

    Google Scholar 

  • 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.

    Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Publishers.

    Google Scholar 

  • 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.

    Google Scholar 

  • Mathematical Education Sciences Board (2001). Knowing and learning mathematics for teaching. Washington, D. C: Mathematical Education Sciences Board.

    Google Scholar 

  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA.

    Google Scholar 

  • 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,

    Google Scholar 

  • Owens, J. (1987). A study of four preservice teachers’ constructs of mathematics and mathematics teaching. Unpublished doctoral dissertation, University of Georgia, Athens.

    Google Scholar 

  • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books Inc.

    Google Scholar 

  • 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.

    Google Scholar 

  • Schifter, D. (1998). Learning mathematics for teaching: From a teachers’ seminar to the classroom. Journal of Mathematics Teacher Education, 1, 55–87.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Tymoczko, T. (1986). Making room for mathematicians in the philosophy of mathematics. The Mathematical Intelligencer, 8(3), 44–50.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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 fĂĽr Didaktik der Mathematik der Universität Bielefeld.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Georgia, USA

    Thomas J. Cooney & Heide G. Wiegel

Authors
  1. Thomas J. Cooney
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heide G. Wiegel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Monash University, Australia

    Alan J. Bishop

  2. Universiti Brunei Darussalam, Brunei

    M. A. Clements

  3. Free University of Berlin, Germany

    Christine Keitel

  4. University of Georgia, Athens, USA

    Jeremy Kilpatrick

  5. The University of Hong Kong, Hong Kong

    Frederick K. S. Leung

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

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

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0273-8_26

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3951-2

  • Online ISBN: 978-94-010-0273-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation