What Kind of Opportunities Do Abstract Algebra Courses Provide for Strengthening Future Teachers’ Mathematical Knowledge for Teaching?
The previous two chapters drew insights from studies featuring very different methodologies, but focused on very similar types of connections between abstract algebra and preservice teacher education. A central idea of each chapter was the way that preservice teachers’ learning of abstract algebra could both reinforce and build on their knowledge of secondary mathematics. We focus our commentary primarily on this idea. First, we will characterize the possible benefits of this bidirectional relationship in terms of supporting the development of preservice teachers’ mathematical knowledge for teaching. Then, we will critically consider whether such benefits are worthy of being intentionally pursued by teacher education programs and (if so) how they might be best realized.
KeywordsMathematical knowledge for teaching Backward transfer Preservice teacher education Mathematical preparation of teachers
- Ball, D. L., & Bass, H. (2009). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners’ mathematical futures. Paper presented at the 43rd Jahrestagung der Gesellschaft für Didaktik der Mathematik, Oldenburg. Retrieved from www.mathematik.uni-dortmund.de/ieem/BzMU/BzMU2009/BzMU2009-Inhalt-fuer-Homepage.htm
- Dubinsky, E., & Leron, U. (1994). Learning abstract algebra with ISETL. New York, NY: Springer.Google Scholar
- Kieran, C. (1979). Children’s operation thinking within the context of bracketing and the order of operations. In D. Tall (Ed.), Proceedings of the third international conference for the psychology of mathematics education (pp. 128–133). Coventry: Warwick University, Mathematics Education Research Centre.Google Scholar
- Larsen, S. (2010). Struggling to disentangle the associative and commutative properties. For the Learning of Mathematics, 30(1), 37–42.Google Scholar