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Teachers’ Opportunities to Learn Mathematics Through Teaching

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Learning Through Teaching Mathematics

Part of the book series: Mathematics Teacher Education ((MTEN,volume 5))

Abstract

In this chapter we discuss theoretical and empirical grounds for teachers’ learning through teaching (LTT). We review several theories on teachers’ knowledge and the potential changes in this knowledge, and then focus on learning mathematics. We consider several specific examples of teachers’ learning in a variety of instructional situations and identify the types of learning that have occurred. We further identify the sources of LTT, the types of knowledge acquired through teaching, and consider factors that support teachers’ learning.

Every teacher’s greatest opportunity for further learning in mathematics education is her classroom teaching. (Simon, 2006, p. 137).

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References

  • Artzt, A. F., & Armour-Thomas, E. (2002). Becoming a reflective mathematics teacher. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Atkinson, T., & Claxton, G. (Eds.) (2000). The intuitive practitioner: On the value of not always knowing what one is doing. Philadelphia, PA: Open University Press.

    Google Scholar 

  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 14–17, 20–22, 43–46.

    Google Scholar 

  • Berliner, D. C. (1987). Ways of thinking about students and classrooms by more and less experienced teachers. In J. Calderhead (Ed.), Exploring teachers’ thinking (pp. 60–83). Great Britain: Cassell Educational Limited.

    Google Scholar 

  • Berliner, D. C. (1994). Teacher expertise. In B. Moon & A. S. Mayes (Eds.), Teaching and learning in the secondary school (pp. 107–113). Routledge.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. The Netherlands: Kluwer.

    Google Scholar 

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

    Google Scholar 

  • Chazan, D., Yerushalmy, M., & Leikin, R. (2008). An analytic conception of equation and teachers’ views of school algebra. Journal of Mathematical Behavior, 27, 87–100.

    Article  Google Scholar 

  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Research design in mathematics and science education (pp. 307–333). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Cobb, P., & McClain, K. (2001). An approach for supporting teachers’ learning in social context. In F.-L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 207–231). Dordrecht, The Netherlands: Kluwer.

    Chapter  Google Scholar 

  • Dewey, J. (1933). How we think: A restatement of the relation of reflective thinking to the educative process. Boston: D.C. Heath and Co.

    Google Scholar 

  • Fischbein, E. (1984). The interactions between the formal, the algorithmic, and the intuitive components in a mathematical activity. In R. Biehler, R. W. Scholz, R. Sträßer & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 231–245). The Netherlands: Kluwer.

    Google Scholar 

  • Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38, 653–689.

    Article  Google Scholar 

  • Hewitt, D. (1992). Train spotters’ paradise. Mathematics Teaching 140, 6–8.

    Google Scholar 

  • Jaworski, B. (1998). Mathematics teacher research: Process, practice, and the development of teaching. Journal of Mathematics Teacher Education, 1(1), 3–31.

    Article  Google Scholar 

  • Kennedy, M. M. (2002). Knowledge and teaching. Teacher and Teaching: theory and practice, 8, 355–370.

    Article  Google Scholar 

  • Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven: Yale University Press.

    Google Scholar 

  • Lampert, M., & Ball, D. L. (1999). Aligning teacher education with contemporary K-12 reform visions. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 33–53) San Francisco: Jossey-Bass.

    Google Scholar 

  • Leikin, R. (2005). Qualities of professional dialogue: Connecting graduate research on teaching and the undergraduate teachers’ program. International Journal of Mathematical Education in Science and Technology, 36(1–2), 237–256.

    Google Scholar 

  • Leikin, R. (2006). Learning by teaching: The case of Sieve of Eratosthenes and one elementary school teacher. In R. Zazkis & S. Campbell (Eds.), Number theory in mathematics education: perspectives and prospects (pp. 115–140). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Leikin, R., & Dinur, S. (2007). Teacher flexibility in mathematical discussion. Journal of Mathematical Behavior, 26, 328–347.

    Article  Google Scholar 

  • Leikin, R., & Levav-Waynberg, A.(2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66, 349–371.

    Article  Google Scholar 

  • Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics.

    Google Scholar 

  • Leikin, R., & Rota, S. (2006). A case study on the development of teacher’s proficiency through teaching. Mathematics Education Research Journal, 18(3), 44–68.

    Article  Google Scholar 

  • Lesh, R., & Kelly, A. E. (1994). Action-theoretic and phenomenological approaches to research in mathematics education: Studies on continually developing experts. In R. Biehler, R. W. Scholz, R. Sträßer, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 277–286). The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Lloyd, G. M., & Wilson, M. S. (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, 248–274.

    Article  Google Scholar 

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

    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(3), 243–267.

    Article  Google Scholar 

  • Mason, J. (2002). Researching your own practice: The discipline of noticing. New York: Falmer.

    Google Scholar 

  • McNeal, B., & Simon M. A. (2000) Mathematics culture clash: Negotiating new classroom norms with prospective teachers. Journal of Mathematical Behavior, 18, 475–509.

    Article  Google Scholar 

  • Nathan, M. J., & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21, 175–207.

    Article  Google Scholar 

  • Perrin-Glorian, M.-J., DeBlois, L., and Robert, A. (2008). Chapter 2: Individual practicing mathematics teachers: Studies on their professional growth. In T. Wood & K. Krainer (Eds.), International handbook of mathematics teacher eduation. Participants in mathematics teacher education: individuals, teams, communities, and networks (Vol.3, pp. 35–59). Rotterdam, the Netherlands: Sense Publishers.

    Google Scholar 

  • Piaget, J. (2001). Studies in reflecting abstraction. Sussex, England: Psychology Press.

    Google Scholar 

  • Pressley, M., & McCormick, C. (1995). Cognition, teaching and assessment. New York: Harper Collins College Publishers

    Google Scholar 

  • Scheffler, I. (1965). Conditions of knowledge. An introduction to epistemology and education. Glenview, IL: Scott, Foresman & Company.

    Google Scholar 

  • Schifter, D. (Ed.) (1996) What’s happening in math class? Envisioning new practices through teacher narratives (Vols. I and II). New York: Teacher College Press.

    Google Scholar 

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

    Article  Google Scholar 

  • Schön, D. A. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books.

    Google Scholar 

  • Schwartz, J. L., Yerushalmy, M., & Shternberg, B. (2000). Geometric Supposer [Computer software]. Israel: CET.

    Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15 (2), 4–14.

    Google Scholar 

  • Simon, M. A. (1997). Developing new models of mathematics teaching: An imperative for research on mathematics teacher development. In E. Fennema & B. Scott-Nelson (Eds.), Mathematics teachers in transition. (pp. 55–86). Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Simon, M. A. (2007). Constrains on what teachers can learn from their practice: Teachers’ assimilatory schemes. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 137–142). Korea: The Korea Society of Educational Studies in Mathematics.

    Google Scholar 

  • Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1(2), 157–189.

    Article  Google Scholar 

  • Sternberg, R. J., & Horvath, J. A. (1995). A prototype view of expert teaching. Educational Researcher, 24(6), 9–17.

    Google Scholar 

  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education, (pp. 267–307). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Stigler J. W., & Hiebert J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.

    Google Scholar 

  • Thompson, P. (1979, March). The constructivist teaching experiment in mathematics education research. Paper presented at the Annual Meeting of the National Council of Teachers of Mathematics, Boston.

    Google Scholar 

  • Tzur, R. (2001). Becoming a mathematics teacher educator: Conceptualizing the terrain through self-reflective analysis. Journal of Mathematics Teacher Education, 4, 259–283.

    Article  Google Scholar 

  • Voigt, J. (1995). Thematic patterns of interactions and sociomathematical norms. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning: Interactions in classroom culture (pp. 163–201). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Wilson, S., Shulman, L., & Richert, A. E. (1987). “150” Different ways of knowledge in teaching. Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teachers’ thinking. (pp. 1–37). London: Cassell.

    Google Scholar 

  • Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Zazkis, R. (1998). Divisors and quotients: Acknowledging polysemy. For the Learning of Mathematics, 18(3), 27–30.

    Google Scholar 

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Correspondence to Roza Leikin .

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Leikin, R., Zazkis, R. (2010). Teachers’ Opportunities to Learn Mathematics Through Teaching. In: Leikin, R., Zazkis, R. (eds) Learning Through Teaching Mathematics. Mathematics Teacher Education, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3990-3_1

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