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Reflecting on Good Mathematics Teaching: Knowing, Nurturing, Noticing

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Teaching and Learning Secondary School Mathematics

Part of the book series: Advances in Mathematics Education ((AME))

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Abstract

What does it mean to be a “good” mathematics teacher? Ultimately, the answer to this complex question depends on the goals of mathematics education and on one’s beliefs about teaching and learning. This chapter describes the evolution of one mathematics teacher’s views as practice, research, and changing curricula have influenced her understanding. She reflects on how attention to three particular aspects can support effective mathematics teaching: knowing, not merely the mathematics content, but developing mathematics-knowledge-for-teaching (Shulman 1986; Ball, Thames and Phelps 2008); noticing, as applied to the subject matter, the students, and oneself as teacher (Mason 1998, 2002); and nurturing habits of mind (Cuoco, Goldenberg and Mark 1996; Lim and Selden 2009), in particular fostering a growth mindset in students (Dweck 2006; Boaler 2015). She also advocates for the importance of mathematics teachers holding a growth mindset with respect to their own teaching.

The more you know, the more you know you don’t know. – Aristotle

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References

  • 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: Ablex.

    Google Scholar 

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco: Wiley.

    Google Scholar 

  • British Columbia Ministry of Education. (2013). Transforming curriculum and assessment – Mathematics. Retrieved from https://curriculum.gov.bc.ca/curriculum/Mathematics

  • British Columbia Ministry of Education. (2016). Mathematics: Introduction. Retrieved from https://curriculum.gov.bc.ca/curriculum/mathematics/introduction

  • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175–190.

    Article  Google Scholar 

  • Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for a mathematics curriculum. Journal of Mathematical Behavior, 14(4), 375–402.

    Article  Google Scholar 

  • Dweck, C. (2006). Mindset: The new psychology of success. New York: Ballantine Books.

    Google Scholar 

  • Jacobbe, T., & Millman, R. S. (2009). Mathematical habits of the mind for preservice teachers. School Science and Mathematics, 109(5), 298–302.

    Article  Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.

    Google Scholar 

  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 36, 297–312.

    Google Scholar 

  • Liljedahl, P. (2012). Building thinking classrooms: Conditions for problem solving. In P. Felmer, E. Pekhonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 361–386). New York: Springer.

    Google Scholar 

  • Lim, K., & Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 1576–1583). Atlanta: Georgia State University.

    Google Scholar 

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

    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.

    Article  Google Scholar 

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

    Google Scholar 

  • Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). London: Pearson.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards of school mathematics. Reston: NCTM.

    Google Scholar 

  • Oesterle, S., Olson, M., Hwang, S., Slovin, H., Olson, J., Murawska, J., et al. (2016). Mathematical habits of mind. In L. C. Hart, S. Oesterle, S. Swars Auslander, & A. Kajander (Eds.), The mathematics education of elementary teachers: Issues and strategies for content courses (pp. 51–85). Charlotte: Information Age Publishing.

    Google Scholar 

  • Pirie, S., & Kieren, T. (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23, 505–528.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge.

    Google Scholar 

  • The Western & Northern Canadian Protocol. (2006). The common curriculum framework for K-9 mathematics. Retrieved from https://www.wncp.ca/media/38765/ccfkto9.pdf

  • Yackel, E., & Rasmussen, C. (2002). Beliefs and norms in the mathematics classroom. In G. Leder, E. Pehkonen, & G. Tӧrner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 313–330). London: Kluwer Academic Publishing.

    Google Scholar 

Additional Suggestions for Further Reading

  • Hewitt, D. (1999). Arbitrary and necessary part I: A way of viewing the mathematics curriculum. For the Learning of Mathematics, 19(3), 2–9.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Douglas College, New Westminster, BC, Canada

    Susan Oesterle

Authors
  1. Susan Oesterle
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Correspondence to Susan Oesterle .

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Editors and Affiliations

  1. Lakehead University, Thunder Bay, ON, Canada

    Ann Kajander

  2. Wilfrid Laurier University, Waterloo, ON, Canada

    Jennifer Holm

  3. College of Education, University of Saskatchewan, Saskatoon, SK, Canada

    Egan J Chernoff

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Oesterle, S. (2018). Reflecting on Good Mathematics Teaching: Knowing, Nurturing, Noticing. In: Kajander, A., Holm, J., Chernoff, E. (eds) Teaching and Learning Secondary School Mathematics. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-92390-1_16

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  • DOI: https://doi.org/10.1007/978-3-319-92390-1_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92389-5

  • Online ISBN: 978-3-319-92390-1

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