Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers pp 175-185 | Cite as

# Making Mathematical Connections Between Abstract Algebra and Secondary Mathematics Explicit: Implications for Curriculum, Research, and Faculty Professional Development

## Abstract

This commentary chapter examines the four chapters in this section, which focus on connecting abstract algebra to secondary mathematics, from both practitioner and research-based viewpoints of their interrelated themes and implications for curriculum, research, and faculty professional development. In the context of making mathematical connections between abstract algebra and secondary mathematics explicit, this commentary reflects on the learning goals for preservice secondary mathematics teachers (PSMTs), curricular goals for PSMTs, and the implications of these efforts that include calls both for further research and for addressing the professional development needs of faculty.

## Keywords

Mathematical knowledge for teaching Preservice secondary mathematics teacher preparation Abstract algebra for teachers## References

- Blanton, M. L., & Stylianou, D. A. (2009). Interpreting a community of practice perspective in discipline specific professional development in higher education.
*Innovative Higher Education, 34*(2), 79–92.CrossRefGoogle Scholar - Cofer, T. (2015). Mathematical explanatory strategies employed by prospective secondary teachers.
*International Journal of Research in Undergraduate Mathematics Education, 1*(1), 63–90.CrossRefGoogle Scholar - Conference Board of the Mathematical Sciences. (2001).
*The mathematical education of teachers*. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America.CrossRefGoogle Scholar - Conference Board of the Mathematical Sciences. (2012).
*The mathematical education of teachers II*. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America.CrossRefGoogle Scholar - Cuoco, A., & Rotman, J. J. (2013).
*Learning modern algebra: From early attempts to prove Fermat's last theorem*. Washington, DC: Mathematical Association of America.Google Scholar - Epperson, J. A. M., & Rhoads, K. (2015). Choosing high-yield tasks for the mathematical development of practicing secondary teachers.
*Journal of Mathematics Education at Teachers College, 6*(1), 37–44.Google Scholar - Hausberger, T. (2018). Structuralist praxeologies as a research program on the teaching and learning of abstract algebra.
*International Journal of Research in Undergradraduate Mathematics Education, 4*(1), 74–93.CrossRefGoogle Scholar - Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester Jr. (Ed.),
*Second handbook of research on mathematics teaching and learning*(Vol. 2, pp. 707–762). Reston, VA: National Council of Teachers of Mathematics (NCTM).Google Scholar - Kondratieva, M., & Winsløw, C. (2018). Klein’s plan B in the early teaching of analysis: Two theoretical cases of exploring mathematical links.
*International Journal of Research in Undergraduate Mathematics Education, 4*(1), 119–138.CrossRefGoogle Scholar - Lave, J., & Wenger, E. (1991).
*Situated learning: Legitimate peripheral participation*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Mathematical Association of America. (2015).
*2015 CUPM curriculum guide to majors in the mathematical sciences*. Washington, DC: Mathematical Association of America Author.Google Scholar - Pimm, D. (1995).
*Symbols and meanings in school mathematics*. London: Routledge.Google Scholar - Wasserman, N. (2014). Introducing algebraic structures through solving equations: Vertical content knowledge for K-12 mathematics teachers.
*PRIMUS, 24*(3), 191–214.CrossRefGoogle Scholar - Wenger, E. (1998).
*Communities of practice: Learning, meaning, and identity*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Wheeler, D. (1996). Backwards and forwards: Reflections on different approaches to algebra. In N. Bernarz, C. Kieran, & L. Lee (Eds.),
*Mathematics education library*,*Approaches to algebra*(Vol. 18, pp. 317–325). Dordrecht, The Netherlands: Springer.Google Scholar - Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers.
*Mathematical Thinking and Learning, 12*(4), 263–281.CrossRefGoogle Scholar