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Learning Through Teaching Mathematics pp 49–67Cite as

How and What Might Teachers Learn Through Teaching Mathematics: Contributions to Closing an Unspoken Gap

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

Abstract

My thesis in this chapter is that in order to decrease the gap between the potential and actual teacher learning through teaching (LTT), how and what teachers might learn needs to be further articulated. I begin with a rationale for the need to promote LTT and suggest reasons for that gap. Next, I propose using the reflection on activity–effect framework, originally developed for mathematics learning and teaching, to also address the problem of how LTT may occur. Then, I build on a previous distinction among three perspectives of mathematic teaching to propose a novel, three-prong pedagogical approach for answering the “what” question. Applying this approach to LTT, I discuss three issues that, integrated, constitute essential goals for LTT: Mathematics knowledge for teaching, task (or lesson) design and adjustment, and epistemological stance toward the nature of knowledge. I conclude with a few key questions for further research on LTT.

This chapter extends the discussion of Teacher Learning Through Teaching Research Forum, PME-31, Seoul.

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Notes

  1. 1.

    The research was conducted as part of the NSF Project No. REC-9600023, Mathematics Teacher Development. All opinions expressed are solely those of the author.

References

  • Adler, J., & Huillet, D. (2008). The social production of mathematics for teaching. In P. Sullivan & T. Wood (Eds.), The international handbook of mathematics teacher education: Knowledge and beliefs in mathematics teaching and teaching development (Vol. 1, pp. 195–221). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Baars, B. J. (2007). Mind and brain. In B. J. Baars & N. M. Gage (Eds.), Cognition, brain, and consciousness: Introduction to cognitive neuroscience (pp. 3–29). Amsterdam, The Netherlands: Elsevier.

    Google Scholar 

  • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.

    Google Scholar 

  • Bereiter, C. (1985). Toward a solution of the learning paradox. Review of Educational Research, 55(2), 201–226.

    Google Scholar 

  • Borba, M. C. (2007). Integrating virtual and face-to-face practice: A model for continuing teacher education. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st annual meeting of the international group for the psychology of mathematics education (Vol. 1, pp. 128–131). Seoul, Korea: The Korean Society of Educational Studies in Mathematics.

    Google Scholar 

  • Clarke, D. (2008). The mathematics teacher as curriculum maker: Developing knowledge for enacting curriculum. In P. Sullivan & T. Wood (Eds.), The International handbook of mathematics teacher education: Knowledge and beliefs in mathematics teaching and teaching development (Vol. 1, pp. 133–151). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Cohen, D. K., & Ball, D. L. (1990). Policy and practice: An overview. Educational Evaluation and Policy Analysis, 12(3), 233–239.

    Google Scholar 

  • Davis, B. (1996). Teaching mathematics: Toward a sound alternative. New York: Garland.

    Google Scholar 

  • Dewey, J. (1933).How we think: A Restatement of the relation of reflective thinking to the educative process. Lexington, MA: D.C. Heath.

    Google Scholar 

  • Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children’s mathematics. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (Vol. 2, pp. 257–281). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht, The Netherlands: Freudenthal Institute.

    Google Scholar 

  • Heinz, K., Kinzel, M., Simon, M. A., & Tzur, R. (2000). Moving students through steps of mathematical knowing: An account of the practice of an elementary mathematics teacher in transition. Journal of Mathematical Behavior, 19, 83–107.

    Article  Google Scholar 

  • Herbst, P. (2008). The teacher and the task. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the 32nd annual conference of the international group of psychology of mathematics education (Vol. 1, pp. 125–132). Morelia, Michoacán, Mexico: Michoacán University of Saint Nicholas of Hidalgo.

    Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Article  Google Scholar 

  • Ingersoll, R. M. (2001). Teacher turnover and teacher shortage: An organizational analysis. American Educational Research Journal, 38(3), 499–534.

    Article  Google Scholar 

  • Krainer, K. (2008a). Individuals, teams, communities and networks: Participants and ways of participation in mathematics teacher education – An Introduction. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Participants in mathematics teacher education (Vol. 3, pp. 1–10). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Krainer, K. (2008b). Reflecting the development of a mathematics teacher educator and his discipline. In B. Jaworski & T. Wood (Eds.), The international handbook of mathematics teacher education: The mathematics teacher educator as a developing professional (Vol. 4, pp. 177–199). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Lambert, M. A. (2008). From counting-on to number: Analysis of manipulative-based tasks. Unpublished Masters Thesis Purdue, West Lafayette, IN.

    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. (2008). Teams of prospective mathematics teachers: Multiple problems and multiple solutions. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Participants in mathematics teacher education (Vol. 3, pp. 63–88). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Leikin, R., & Zazkis, R. (2007). A view on the teachers’ opportunities to learn mathematics through teaching. Paper presented at the Thirty-First Annual Conference of the International Group for the Psychology of Mathematics Education, Seoul, Korea.

    Google Scholar 

  • Leinhardt, G. (1989). Math lessons: A contrast of novice and expert competence. Journal for Research in Mathematics Education, 20(1), 52–75.

    Article  Google Scholar 

  • Lerman, S. (2006). Socio-cultural research in PME. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, Present, and Future (pp. 347–366). Rotterdam, The Netherlands: Sense.

    Google Scholar 

  • Lewis, C., & Tsuchida, I. (1998). A lesson is like a swiftly flowing river: How research lessons improve Japanese education. American Educator, 22, 12–52.

    Google Scholar 

  • Liljedahl, P. (2007). Teachers’ learning reified: The professional growth of inservice teachers through numeracy task design. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st annual meeting of the international group for the psychology of mathematics education (Vol. 1, pp. 132–137). Seoul, Korea: The Korean Society of Educational Studies in Mathematics.

    Google Scholar 

  • Livingston, C., & Borko, H. (1990). High school mathematics review lessons: Expert-novice distinctions. Journal for Research in Mathematics Education, 21(5), 372–387.

    Article  Google Scholar 

  • Lompscher, J. (2002). The category of activity as a principal constituent of cultural-historical psychology. In D. Robbins & A. Stetsenko (Eds.), Voices within Vygotsky’s non-classical psychology: Past, Present, Future (pp. 79–99). New York: Nova Science.

    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.

    Google Scholar 

  • Ma, Y., Zhao, D., & Tuo, Z. (2006). Difference within communalities: How is mathematics taught in rural and urban regions in Mainland China? In L. Fan, N.-Y. Wong, J. Cai, & L. Shiqi (Eds.), How chinese learn mathematics: Perspectives from insiders (pp. 413–442). Singapore: World Scientific Publishing.

    Google Scholar 

  • Markovits, Z., & Smith, M. (2008). Cases as tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (Vol. 2, pp. 39–64). Rotterdam, the Netherlands: Sense.

    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. (2001). Knowing and learning mathematics for teaching: Proceedings of a workshop. Journal of Mathematics Teacher Education, 4(4), 339–348.

    Article  Google Scholar 

  • Mason, J. (2008). Being mathematical with and in front of learners: Attention, Awareness, and Attitude as sources of differences between teacher educators, teachers, and learners. In B. Jaworski & T. Wood (Eds.), The international handbook of mathematics teacher education: The mathematics teacher educator’s as a developing professional (Vol. 4, pp. 31–55). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Paine, L. W., & Ma, L. (1993). Teachers working together: A dialogue on organizational and cultural perspectives of Chinese teachers. International Journal of Educational Research, 19(8), 675–697.

    Article  Google Scholar 

  • Pascual-Leone, J. (1976). A view of cognition from a formalist’s perspective. In K. F. Riegel & J. A. Meacham (Eds.), The developing individual in a changing world: Vol. 1 Historical and cultural issues (pp. 89–110). The Hague, The Netherlands: Mouton.

    Google Scholar 

  • Perrin-Glorian, M.-J., Deblos, L., & Robert, A. (2008). Individual practising mathematics teachers: Studies on their professional growth. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Participants in mathematics teacher education (Vol. 3, pp. 35–59). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Piaget, J. (1964). Development and learning. In R. E. Ripple & V. N. Rockcastle (Eds.), Piaget rediscovered: Report of the conference on cognitive studies and curriculum development (pp. 7–20). Ithaca, NY: Cornell University.

    Google Scholar 

  • Piaget, J. (1970). Genetic epistemology (E. Duckworth, Trans.). New York: Columbia University.

    Google Scholar 

  • Piaget, J. (1971). Biology and knowledge (B. Walsh, Trans.). Chicago: The University of Chicago.

    Google Scholar 

  • Piaget, J. (1985). The equilibration of cognitive structures: The central problem of intellectual development (T. Brown & K. J. Thampy, Trans.). Chicago: The University of Chicago.

    Google Scholar 

  • Pirie, S. E. B., & Kieren, T. E. (1994). Beyond metaphor: Formalising in mathematical understanding within constructivist environments. For the Learning of Mathematics, 14(1), 39–43.

    Google Scholar 

  • Sánchez, V., & García, M. (2008). What to teach and how to teach it: Dilemmas in primary mathemaics teacher education. In B. Jaworski & T. Wood (Eds.), The international handbook of mathematics teacher education: The mathematics teacher educator as a developing professional (Vol. 4, pp. 281–297). Rotterdam, the Netherlands: Sense.

    Google Scholar 

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

    Article  Google Scholar 

  • Schön, D. A. (1987). Educating the reflective practitioner: Toward a new design for teaching and learning in the professions (1 edn.). San Francisco: Jossey-Bass.

    Google Scholar 

  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.

    Article  Google Scholar 

  • Simon, M. A. (2006a). Key developmental understandings in matheamtics: A direction for investigating and establishing learning goals. Mathematical Thinking and Learning, 8(4), 359–371.

    Article  Google Scholar 

  • Simon, M. A. (2006b). Pedagogical concepts as goals for teacher education: Towards an agenda for research in teacher development. In S. Alatorre, J. L. Cortina, S. Mariana, & A. Méndez (Eds.), Proceedings of the twenty eighth annual meeting of the north american chapter of the international group for the psychology of mathematics education (Vol. 2, pp. 730–735). Merida, Yucatán, Mexico: Universidad Pedagógica Nacional.

    Google Scholar 

  • Simon, M. A. (2007). Constraints on what teachers can learn from their practice: Teachers’ assimilatory schemes. Paper presented at the Thirty-First Conference of the International Group for the Psychology of Mathematics Education, Seoul, Korea.

    Google Scholar 

  • Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104.

    Article  Google Scholar 

  • Simon, M. A., Tzur, R., Heinz, K., & Kinzel, M. (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for Research in Mathematics Education, 35(3), 305–329.

    Article  Google Scholar 

  • Simon, M. A., Tzur, R., Heinz, K., Kinzel, M., & Smith, M. S. (2000). Characterizing a perspective underlying the practice of mathematics teachers in transition. Journal for Research in Mathematics Education, 31(5), 579–601.

    Article  Google Scholar 

  • Steffe, L. P. (1995). Alternative epistemologies: An educator’s perspective. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 489–523). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

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

    Article  Google Scholar 

  • Stolzenberg, G. (1984). Can inquiry into the foundations of mathematics tell us anything interesting about mind? In P. Watzlawick (Ed.), The invented reality: How do we know what we believe we know (pp. 257–309). NY: Norton.

    Google Scholar 

  • Sullivan, P. (2008a). Designing task based mathematics lessons as teacher learning. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd annual conference of the international group of psychology of mathematics education (Vol. 1, pp. 133–138). Morelia, Michoacán, Mexico: Michoacán University of Saint Nicholas of Hidalgo.

    Google Scholar 

  • Sullivan, P. (2008b). Knowledge for teaching mathematics: An introduction. In P. Sullivan & T. Wood (Eds.), The international handbook of mathematics teacher education: Knowledge and beliefs in mathematics teaching and teaching development (Vol. 1, pp. 1–9). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Sullivan, P., Mousley, J., & Zevenbergen, R. (2003). Being explicit about aspects of mathematics pedagogy. In N. A. Pateman, B. J. Dougherty & J. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PME-NA (Vol. 4, pp. 267–274). Honolulu, Hawai’i: University of Hawai’i.

    Google Scholar 

  • Tzur, R. (1996). Interaction and children’s fraction learning. Ann Arbor, MI: UMI Dissertation Services (Bell & Howell).

    Google Scholar 

  • Tzur, R. (2004). Teacher and students’ joint production of a reversible fraction conception. Journal of Mathematical Behavior, 23, 93–114.

    Article  Google Scholar 

  • Tzur, R. (2007). Fine grain assessment of students’ mathematical understanding: Participatory and anticipatory stages in learning a new mathematical conception. Educational Studies in Mathematics, 66(3), 273–291.

    Article  Google Scholar 

  • Tzur, R. (2008a). A researcher perplexity: Why do mathematical tasks undergo metamorphosis in teacher hands? . In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd Annual conference of the international group of psychology of mathematics education (Vol. 1, pp. 139–146). Morelia, Michoacán, Mexico: Michoacán University of Saint Nicholas of Hidalgo.

    Google Scholar 

  • Tzur, R. (2008b). Profound awareness of the learning paradox (PALP): A journey towards epistemologically regulated pedagogy in mathematics teaching and teacher education. In B. Jaworski & T. Wood (Eds.), The international handbook of mathematics teacher education: The mathematics teacher educator’s as a developing professional (Vol. 4, pp. 137–156). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Tzur, R. (accepted for publication). Brain-mind theory-driven task design. In E. Kelly, S. Jensen, & J. Baek (Eds.), Neuro Math Education. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Tzur, R., & Simon, M. A. (2004). Distinguishing two stages of mathematics conceptual learning. International Journal of Science and Mathematics Education, 2, 287–304.

    Article  Google Scholar 

  • Tzur, R., Simon, M., Heinz, K., & Kinzel, M. (2001). An Account of a teacher’s perspective on learning and teaching mathematics: Implications for teacher development. Journal of Mathematics Teacher Education, 4(3), 227–254.

    Article  Google Scholar 

  • Tzur, R., Zaslavsky, O., & Sullivan, P. (2008). Examining teachers’ use of (non-routine) mathematical tasks in classrooms from three complementary perspectives: Teacher, teacher educator, researcher. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd annual conference of the international group of psychology of mathematics education (Vol. 1, pp. 123–125). Morelia, Michoacán, Mexico: Michoacán University of Saint Nicholas of Hidalgo.

    Google Scholar 

  • von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. Washington, DC: Falmer.

    Book  Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (Vol. 1). Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Watson, A. (2008). Task transformation is the teacher’s responsibility. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd annual conference of the international group of psychology of mathematics education (Vol. 1, pp. 146–153). Morelia, Michoacán, Mexico: Michoacán University of Saint Nicholas of Hidalgo.

    Google Scholar 

  • Watson, A., & Sullivan, P. (2008). Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (Vol. 2, pp. 109–134). Rotterdam, the Netherlands: Sense.

    Google Scholar 

  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. NY: Cambridge University.

    Google Scholar 

  • Wertsch, J. V., & Toma, C. (1995). Discourse and learning in the classroom: A sociocultural approach. In L. P. Steffe & J. Gale (Eds.), Constructivism in education(Vol. 1, 1 edn., pp. 159–174). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Yoshida, M. (2008). Exploring ideas for a mathematics teacher educator’s contribution to lesson study. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in matheamtics teacher education (Vol. 2, pp. 85–106). Rotterdam, The Netherlands: Sense.

    Google Scholar 

  • Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through Practice. Journal of Mathematics Teacher Education, 7(1), 5–32.

    Google Scholar 

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  1. University of Colorado Denver, Denver, CO, USA

    Ron Tzur

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  1. Ron Tzur
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Correspondence to Ron Tzur .

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  1. Faculty of Education, University of Haifa, Haifa, 31905, Israel

    Roza Leikin

  2. Fac. Education, Simon Fraser University, University Drive 8888, Burnaby, V5A 1S6, British Columbia, Canada

    Rina Zazkis

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Tzur, R. (2010). How and What Might Teachers Learn Through Teaching Mathematics: Contributions to Closing an Unspoken Gap. 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_3

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