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Abstract

‘Teachers must know the subject they teach. Indeed, there may be nothing more foundational to teacher competency’ (Ball et al. in Journal of Teacher Education 59:389–407, 2008). In this article, the complex relationship between mathematics, mathematics for teaching, and pedagogy is explored, together with implications for teacher education programmes in Canada.

Résumé

« Les enseignants doivent connaître la matière qu’ils enseignent. En effet, il n’y a peut-être rien de plus fondamental pour la compétence des enseignants» (Ball et al. in Journal of Teacher Education 59:389–407, 2008). Dans cet article, on explore la relation complexe qui existe entre les mathématiques, le rôle que joue cette matière dans son enseignement et la pédagogie, ainsi que les implications qu’a cette relation sur les programmes de formation des enseignants au Canada.

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Notes

  1. teachers college, formerly known as normal school, is a post-secondary educational institution dedicated to the training and professional development of teachers—teaching teachers how to teach. Originating in France, these institutions were established to provide specialised educational programme for those learning to become teachers. Many teachers colleges today have been amalgamated into universities and colleges to form departments of education. (New World Encyclopedia).

References

  • Ball, D. L. & Bass, H. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3). pp. 241 – 247. https://doi.org/10.1177/00224871000510030

    Article  Google Scholar 

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching what makes it special? Journal of Teacher Education59(5), 389-407.

    Article  Google Scholar 

  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A. Klusmann, U., Krauss, S., Neubrand, M., & Tsai, Y. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), p. 33-180.

    Article  Google Scholar 

  • Drake, G., Walsh, K., Pomerance, L. & Rickenbrode, R. (2018) 2018 Teacher Prep Review. National Council on Teacher Quality, Washington, DC.

    Google Scholar 

  • Hart, L., Oesterle, S., Swars, S. & Kajander, A. (Eds.). (2016). The mathematics education of elementary teachers: Issues and strategies for content courses. Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education35(5), 330–351;

    Article  Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal42(2), 371–406.

    Article  Google Scholar 

  • Holm, J. & Kajander, A. (2020). Seeking intersections: Math degrees, beliefs, and elementary teacher knowledge. Canadian Journal of Science, Mathematics and Technology Education, 20(1), 27-41. https://doi.org/10.1007/s42330-019-00069-3

    Article  Google Scholar 

  • Kajander. A. (2010). Mathematics teacher preparation in an era of curriculum change: The development of mathematics for teaching. Canadian Journal of Education. 33(1), 228-255.

    Google Scholar 

  • Kajander, A. (2023). Mathematics for intermediate teachers: From models to methods. Newcastle upon Tyne, United Kingdom: Cambridge Scholars Press.

    Google Scholar 

  • Kajander, A. and Boland, T. (2014). Mathematical models for teaching: Reasoning without memorization. Toronto, ON: Canadian Scholars’ Press.

    Google Scholar 

  • Kajander, A., & Holm, J. (2016). What math matters? Types of mathematics knowledge and relationships to methods course performance. Canadian Journal of Science, Mathematics and Technology Education, 16(3), 273-283. DOI: https://doi.org/10.1080/14926156.2016.1183837.

    Article  Google Scholar 

  • Kajander, A., Kotsopoulos, D., Martinovic, D., & Whiteley, W. (2013). Mathematics pre-service teacher education in Ontario: Consultation brief regarding the extended pre-service program. Fields Mathematics Education Journal. 1(1). 62-67

    Google Scholar 

  • Kajander, A. & Jarvis, D. (2009). Report of the working group of elementary mathematics for teaching. Canadian Mathematics Education Forum. Simon Fraser University, Vancouver, B.C. pp.1-14. http://math.ca/Events/CMEF2009/reports/wg2-report.pdf

  • Mitchell, R., Charalambous, C. Y., & Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17(1), 37-60.

    Article  Google Scholar 

  • Putman, H., & Lubell, S. (2016). Teacher prep review: Undergraduate elementary education. National Council on Teacher Quality. https://www.nctq.org/publications/Teacher-Prep-Review:-Undergraduate-Elementary-Education

  • Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, Vol. 15, No. 2 (Feb., 1986), pp. 4–14.

  • Sinclair, M. (2005). Submission to the Ontario College of Teachers Review of Teacher Qualifications. [Unpublished report]. Sub-Committee of the Education Forum of the Fields Institute of Mathematical Sciences. University of Toronto.

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Correspondence to Ann Kajander.

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Kajander, A., Colgan, L. What Does It Mean to Know Mathematics for Teaching?. Can. J. Sci. Math. Techn. Educ. (2024). https://doi.org/10.1007/s42330-024-00311-7

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