Abstract
In this chapter, I share three stories of my personal learning that was triggered by interaction with students. I analyze these stories using disaggregated perspective on learning, considering how the instructor’s mathematics and pedagogy is implemented to consider mathematical and pedagogical issues with prospective teachers. In the first story, I present a novel pedagogical approach in order to enhance teachers’ mathematics related to a translation of a parabola. In the second story, I share my learning of mathematics related to Affine transformations triggered by students’ errors that lead to correct results. In the third story, I explore several examples of numerical variation, presenting it as a powerful pedagogical tool.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For a triangle with sides a, b, c, the area A is determined by \(A = \sqrt {s(s - a)(s - b)(s - c)}\), where s is a semiperimeter of the triangle, \(s = \frac{{a + b + c}}{2}\).
References
Baker, B., Hemenway, C., & Trigueros, M (2000). On transformations of basic functions. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12th ICMI study conference on the future of the teaching and learning of Algebra (Vol. 1, pp. 41–47). Melbourne: University of Melbourne.
Borba, M. C., & Confrey, J. (1996). A students’ construction of transformations of functions in a multirepresentational environment. Educational Studies in Mathematics, 31(3), 319–337.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (2000). How people learn: Brain, mind, experience and school. Washington, DC: National Academy Press.
Eisenberg, T., & Dreyfus, T. (1994). On understanding how students learn to visualize function transformations. In E. Dubinsky. A. Schoenfeld, & J. Kaput (Eds.), Research in collegiate mathematics education (Vol. 1, pp. 45–68). Providence, RI: American Mathematical Society.
Fehr, H., Fey, J., & Hill, T. (1973). Unified mathematics. Menlo Park, CA: Addison Wesley.
National Council of Teachers of Mathematics [NCTM]. (2002). Principles and standards for school mathematics. Reston, VA: NCTM.
Liljedahl, P., Chernoff. E., & Zazkis, R. (2007). Interweaving mathematics and pedagogy in task design: A tale of one task. Journal of Mathematics Teacher Education, 10(4–6), 239–249.
Mason, J. (2001). Tunja Sequences as example of employing students; power to generalize. Mathematics Teacher, 94(3), 164–169.
Mason, J. (2007). Structured variation grids. Available: http://msc.open.ac.uk/jhm3/
Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277–289.
Stein, S. (1999). Archimedes: What did he do besides cry Eureka. Mathematical Association of America Washi.
Zazkis, R. (1999). Divisibility: A problem solving approach through generalizing and specializing. Humanistic Mathematics Network Journal, (21), 34–38.
Zazkis, R., Liljedahl, P., & Gadowsky, K. (2003). Students’ conceptions of function translation: Obstacles, intuitions and rerouting. Journal of Mathematical Behavior, 22, 437–450.34.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Zazkis, R. (2010). What Have I Learned: Mathematical Insights and Pedagogical Implications. 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_5
Download citation
DOI: https://doi.org/10.1007/978-90-481-3990-3_5
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3989-7
Online ISBN: 978-90-481-3990-3
eBook Packages: Humanities, Social Sciences and LawEducation (R0)