Abstract
Listening to students in productive ways seems to be at the core of teaching practices aligned with the basic tenets of the constructivist world view. We present a definition for productive ways of listening, discuss the challenges involved in implementing it, and propose a way to support the “decentering” needed to learning to listen for teacher education programs. The proposal is based on reading and understanding historical texts as a way to exercising the adoption of the ‘other’s perspective.’ We describe the materials developed for teacher workshops, their implementation and what participants, and we, learned from the experience.
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References
Aharoni, R. (2003). What I learnt in primary school. In Invited talk at the 55th British Mathematics Colloquium (BCM). University of Birmingham, Great Britain, available at http://www.math.technion.ac.il/~ra/education.html
Arcavi, A. (1987). Using historical materials in the mathematics classroom. Arithmetic Teacher, 35(4), 13–16.
Arcavi, A., & Bruckheimer, M. (2000). Didactical uses of primary sources from the history of mathematics. Themes in Education, 1(1), 44–64.
Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373–397.
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners – Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession. Handbook of policy and practice (pp. 3–32). San Francisco, CA: Jossey-Bass.
Confrey, J. (1991). Learning to listen: A student’s understanding of powers of ten. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 111–138). Dordrecht: Kluwer.
Cooney, T., & Krainer, K. (1996). Inservice mathematics teacher education: The importance of listening. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 1155–1185). Dordrecht: Kluwer.
Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3(2), 155–181.
Davis, B. (1997). Listening for differences: An evolving conception of mathematics teaching. Journal for Research in Mathematics Education, 28(3), 355–376.
Even, R., & Wallach, T. (2004). Between student observation and student assessment: A critical reflection. Canadian Journal of Science, Mathematics, and Technology Education, 4(4), 483–495.
Freudenthal, H. (1983). The didactical phenomenology of mathematical structures. Dordrecht: Reidel.
Ginsburg, H., & Opper, S. (1979). Piaget’s theory of intellectual development (2nd ed.). New Jersey: Prentice-Hall.
Henderson, D. W. (1996). I learn mathematics from my students – Multiculturalism in action. For the Learning of Mathematics, 16(2), 46–52.
Isoda, M. (2002). Hermeneutics for humanizing mathematics education (in Japanese). Tsukuba Journal of Educational Studies in Mathematics, 21, 1–10.
Isoda, M., & Kishimoto, T. (2005). A problem solving lesson approach for understanding mathematics in elementary school (in Japanese). Tokyo: Meijitosyo.
Isoda, M., Stephens, M., Ohara, Y., & Miyakawa, T. (2007). Japanese lesson study in mathematics. Singapore: World Scientific.
Jahnke, H. N. (1994). The historical dimension of mathematical understanding – Objectifying the subjective. In J. P. da Ponte, & J. F. Matos (Eds.), Proceedings of the 18th international conference for the psychology of mathematics education, vol. 1 (pp. 139–156). Lisbon, Portugal.
Jahnke, H. N. (1996). Set and measure as an example of complementarity. In H. N. Jahnke, N. Knoche & M. Otte (Eds.), History of mathematics and education: Ideas and experiences (pp. 173–193). Göttingen: Vandenhoeck und Ruprecht.
Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press.
Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Research for Better Schools: Philadelphia.
Moschkovich, J. N. (2004). Appropriating mathematical practices: A case study of learning to use and explore functions through interaction with a tutor. Educational Studies in Mathematics, 55(1–3), 49–80.
Nathan, M. J., & Petrosino, A. (2003). Expert blind spot among preservice teachers. American Educational Research Journal, 40(4), 905–928.
Peet, T. E. (1970). The Rhind mathematical papyrus. University of Liverpool Press.
Sfard, A. (1994). What history of mathematics has to offer to psychology of mathematical thinking. In J. P. da Ponte, & J. F. Matos (Eds.), Proceedings of the 18th international conference for the psychology of mathematics education, vol. 1 (pp. 129–132). Lisbon, Portugal.
Smith, D. E. (1958). History of mathematics, vol. II. New York: Dover.
Smith, T. J. (2003). Pedagogy as conversation: A metaphor for learning together. In Invited keynote address. Mathematics Association of Victoria Annual Conference, Monash University: Melbourne, available at http://www.mav.vic.edu.au/pd/confs/2003/papers/Smith_paper.pdf
Wallach, T., & Even, R. (2002). Teacher hearing students. In A. D. Cockburn, & E. Nardi (Eds.), Proceedings of the 26th international conference for the psychology of mathematics education, vol. 4 (pp. 337–344). Norwich, England.
Acknowledgements
We thank the workshop participants for their enthusiastic involvement and for their openness to share with us their views and criticisms.
We are grateful to Professors Hiroshi Iwasaki and Hitoshi Takahashi, Joetsu University of Education, for inviting us to conduct the second workshop and for their insightful comments on this work.
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Arcavi, A., Isoda, M. Learning to listen: from historical sources to classroom practice. Educ Stud Math 66, 111–129 (2007). https://doi.org/10.1007/s10649-006-9075-8
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DOI: https://doi.org/10.1007/s10649-006-9075-8