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The Future of the Teaching and Learning of Algebra The 12th ICMI Study pp 265–290Cite as

Teachers’ Knowledge and the Teaching of Algebra

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Part of the book series: New ICMI Study Series ((NISS,volume 8))

Abstract

In this chapter an analysis of the research on teachers’ knowledge and practice and its development with respect to the teaching of algebra is presented. The chapter begins with a brief discussion of four dilemmas that were confronted during this analysis. The findings from research on teachers’ knowledge are reported in three areas: (a) teachers’ subject matter knowledge and pedagogical content knowledge, (b) teachers’ conceptualisations of algebra, and (c) teachers learning to become teachers of algebra. The chapter concludes with a discussion of critical issues and suggestions for further research.

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References

  • Agudelo-Valderrama, C. (2000). Una innovación curricular que enfoca el proceso de transición entre el trabajo aritmético y el algebraico. [A curricular innovation that focuses on the transition between arithmetical and algebraic work.] Tunja, Colombia: Universidad Pedagógica y Tecnológica de Colombia.

    Google Scholar 

  • Arens, S., & Meyer, R. (2000). Algebraic thinking: Implications for rethinking pedagogy and professional development. Aurora, CO: Mid-Continent Research for Education and Learning. (ERIC Document Reproduction Service No. ED 449 983).

    Google Scholar 

  • Artigue, M., Assude, T., Grugeon, B., & Lenfant, A. (2001). Teaching and learning algebra: Approaching complexity through complementary perspectives. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 21–32). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.

    Google Scholar 

  • Ball, D., Lubienski, S., & Mewborn, D. (2002). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). Washington, DC: American Educational Research Association.

    Google Scholar 

  • Bednarz, N., Kieran, C., & Lee L. (Eds.) (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht, The Netherlands: Kluwer Academic.

    Google Scholar 

  • Belfort, E., Guimaraes, L., & Barbastefano, R. (2001). Tertiary algebra and secondary classroom practices in number and algebra: Closing the gap. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 79–86). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Bishop, J. W., & Stump, S. L. (2000). Preparing to teach in the new millennium: Algebra through the eyes of pre-service elementary and middle school teachers. In M. Fernandez (Ed.), 22ndannual conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 107–113). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

    Google Scholar 

  • Blanton, M., & Kaput, J. (2001). Algebrafying the elementary mathematics experience Part II: Transforming practice on a district-wide scale. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 87–95). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Brown, C., & Smith, M. (1997). Supporting the development of mathematical pedagogy. The Mathematics Teacher, 90(2), 138–143.

    Google Scholar 

  • Chazan, D. (1999). On teachers’ mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra International Journal of Computers for Mathematical Learning, 4(2–3), 121–149.

    Google Scholar 

  • Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College Press.

    Google Scholar 

  • Chazan, D., Larriva, C., & Sandow, D. (1999). What kind of mathematical knowledge supports teaching for “conceptual understanding”? Preservice teachers and the solving of equations. In O. Zaslavsky (Ed.), Proceedings of the 23rdannual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 197–205). Haifa, Israel: Program Committee.

    Google Scholar 

  • Chinnappan, M., & Thomas, M. (2001). Prospective teachers’ perspectives on function representation. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and beyond (Proceedings of the 24th annual conference of the Mathematics Education Research Group of Australasia, pp. 155–162). Sydney: MERGA.

    Google Scholar 

  • Cooney, T. (1999). Conceptualizing teachers’ ways of knowing. Educational Studies in Mathematics, 38, 163–187.

    Article  Google Scholar 

  • Cooney, T. J., & Wilson, M. R. (1993). Teachers’ thinking about functions: Historical and research perspectives. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.), Integrating research on the graphical representation of functions (pp. 131–158). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Doerr, H. M., & Bowers, J. S. (1999). Revealing pre-service teachers’ thinking about functions through concept mapping. In F. Hitt & M. Santos (Eds.), Proceedings of the 21stannual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 364–369). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

    Google Scholar 

  • Doerr, H. M., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspective on mathematics teaching, learning and problem solving (pp. 125–139). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Doerr, H. M., & Zangor, R. (1999). The teacher, the tasks and the tool: The emergence of classroom norms. International Journal of Computer Algebra in Mathematics Education, 6(4), 267–279.

    Google Scholar 

  • Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143–163.

    Article  Google Scholar 

  • Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521–544.

    Article  Google Scholar 

  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94–116.

    Google Scholar 

  • Even, R., & 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 

  • Even, R., Tirosh, D., & Robinson, N. (1993). Connectedness in teaching equivalent algebraic expressions: Novice versus expert teachers. Mathematics Education Research Journal, 5(1), 50–59.

    Google Scholar 

  • Gadanidis, G. (2001). Web-based multimedia activities as pedagogical models. In W. Yang, S. Chu, Z. Karian, & G. Fitz-Gerald (Eds.), Proceedings of the Sixth Asian Technology Conference in Mathematics (pp. 223–232). Melbourne, Australia: RMIT University.

    Google Scholar 

  • Haimes, D. H. (1996). The implementation of a “function” approach to introductory algebra: A case study of teacher cognitions, teacher actions, and the intended curriculum. Journal for Research in Mathematics Education, 27(5), 582–602.

    Google Scholar 

  • Heid, M. K. (1995). Impact of technology, mathematical modeling, and meaning on the content, learning, and teaching of secondary-school algebra. Journal of Mathematical Behavior, 14(1), 121–137.

    Google Scholar 

  • Heid, M. K., Blume, G. W., Zbiek, R. M., & Edwards, B. S. (1999). Factors that influence teachers learning to do interviews to understand students’ mathematical understandings. Educational Studies in Mathematics, 37(3), 223–249.

    Google Scholar 

  • Hitt, F. (1994). Teachers’ difficulties with the construction of continuous and discontinuous functions. Focus on Learning Problems in Mathematics, 16(4), 10–20.

    Google Scholar 

  • Johnson, S. (2001). Learning to teach algebra in the UK: Trainee teachers’ experiences. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 336–343). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Kaput, J., & Blanton, M. (2001). Algebrafying the elementary mathematics experience Part I: Transforming task structures. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 344–351). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). New York: Macmillan Publishing Company.

    Google Scholar 

  • Kieran, C., & Sfard, A. (1999). Seeing through symbols: The case of equivalent expressions. Focus on Learning Problems in Mathematics, 21(1), 1–17.

    Google Scholar 

  • Leikin, R., Chazan, D., & Yerushalmy, M. (2001). Understanding teachers’ changing approaches to school algebra: Contributions of concept maps as part of clinical interviews. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25thannual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 289–296). Utrecht, Netherlands: Program Committee.

    Google Scholar 

  • Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.

    Google Scholar 

  • Lloyd, G. M., & Wilson, M. (1998). Supporting innovation: The impact of a teacher’s conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248–274.

    Google Scholar 

  • McGowen, M., & Davis, G. (2001). Changing pre-service teachers’ attitudes to algebra. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 438–445). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Menzel, B. (2001). Language conceptions of algebra are idiosyncratic. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 446–453). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Menzel, B., & Clarke, D. (1998). Teachers interpreting algebra: Teachers’ views about the nature of algebra. In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching mathematics in new times (Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australasia, pp. 365–372). Gold Coast, Australia: MERGA.

    Google Scholar 

  • Mesa, V. (2001, April). Conceptions of function present in seventh-and eighth-grade textbooks from fifteen countries. Paper presented at the annual meeting of the American Educational Research Association. Seattle, WA.

    Google Scholar 

  • Miller, L. D. (1992). Teacher benefits from using impromptu writing prompts in algebra classes. Journal for Research in Mathematics Education, 25(4), 329–340.

    Google Scholar 

  • Munby, H., Russell, T., & Martin, A. (2002). Teachers’ knowledge and how it develops. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 877–904). Washington, DC: American Educational Research Association.

    Google Scholar 

  • Nathan, M. J., & Koedinger, K. R. (2000a). An investigation of teachers’ beliefs of students’ algebra development. Cognition and Instruction, 18(2), 209–237.

    Article  Google Scholar 

  • Nathan, M. J., & Koedinger, K. R. (2000b). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168–190.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

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

    Google Scholar 

  • Norman, A. (1992). Teachers’ mathematical knowledge of the concept of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (Vol. 25, MAA Notes, pp. 215–232). Washington, DC: Mathematical Association of America.

    Google Scholar 

  • Norman, A. (1993). Integrating research on teachers’ knowledge of functions and their graphs. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.), Integrating research on the graphical representation of functions (pp. 159–187). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Penglase, M., & Arnold, S. (1996). The graphics calculator in mathematics education: A critical review of recent research. Mathematics Education Research Journal, 8(1), 58–90.

    Google Scholar 

  • Pirie, S. E. B., & Martin, L. (1997). The equation, the whole equation, and nothing but the equation! One approach to the teaching of linear equations. Educational Studies in Mathematics, 34(2), 159–181.

    Google Scholar 

  • Raymond, A. M., & Leinenbach, M. (2000). Collaborative action research on the learning and teaching of algebra: A story of one mathematics teacher’s development. Educational Studies in Mathematics, 41(3), 283–307.

    Article  Google Scholar 

  • Schmidt, S., & Bednarz, N. (1997). Raisonnements arithmetiques et algebriques dans un contexte de resolution des problemes: difficultes rencontrees par les futurs enseignants [Arithmetical and algebraic reasoning within a problem-solving context: Difficulties encountered by future teachers]. Educational Studies in Mathematics, 32(2), 127–155.

    Article  Google Scholar 

  • Slavit, D. (1996). Graphing calculators in a “hybrid” Algebra II classroom. For the Learning of Mathematics, 16(1), 9–14.

    Google Scholar 

  • Stacey, K., & MacGregor, M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18(2), 149–167.

    Google Scholar 

  • Stein, M. K., Baxter, J., & Leinhardt, G. (1990). Subject-matter knowledge and elementary instruction: A case from functions and graphing. American Educational Research Journal, 27(4), 639–663.

    Google Scholar 

  • Stump, S. (1999). Secondary mathematics teachers’ knowledge of slope. Mathematics Education Research Journal, 11(2), 124–144.

    Google Scholar 

  • Stump, S. L. (2001). Developing preservice teachers’ pedagogical content knowledge of slope. Journal of Mathematical Behavior, 20, 207–227.

    Article  Google Scholar 

  • Stump, S., & Bishop, J. (2001). Framing the future: Inventing an algebra course for preservice elementary and middle school teachers. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference, pp. 564–570). Melbourne, Australia: University of Melbourne.

    Google Scholar 

  • Sutherland, R., Rojano, T., Bell, A., & Lins, R. (Eds.) (2001). Perspectives on school algebra. Dordrecht, The Netherlands: Kluwer Academic.

    Google Scholar 

  • Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford (Ed.), The ideas of algebra, K-12 (pp. 8–19). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Tharp, M. L., Fitzsimmons, J. A., & Ayers, R. L. B. (1997). Negotiating a technological shift: Teacher perception of the implementation of graphing calculators. Journal of Computers in Mathematics and Science Teaching, 16(4), 551–575.

    Google Scholar 

  • Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51–64.

    Article  Google Scholar 

  • van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers’ content knowledge on their evaluation of students’ strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319–351.

    Google Scholar 

  • Wilson, M. R. (1994). One pre-service secondary teacher’s understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 25(4), 346–370.

    Google Scholar 

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Authors and Affiliations

  1. Syracuse University, New York State, USA

    Helen M. Doerr

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  1. Helen M. Doerr
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Editors and Affiliations

  1. The University of Melbourne, Australia

    Kaye Stacey , Helen Chick  & Margaret Kendal ,  & 

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Doerr, H.M. (2004). Teachers’ Knowledge and the Teaching of Algebra. In: Stacey, K., Chick, H., Kendal, M. (eds) The Future of the Teaching and Learning of Algebra The 12th ICMI Study. New ICMI Study Series, vol 8. Springer, Dordrecht. https://doi.org/10.1007/1-4020-8131-6_10

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  • DOI: https://doi.org/10.1007/1-4020-8131-6_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8130-9

  • Online ISBN: 978-1-4020-8131-6

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