Building a Coherent Research Program that Links Abstract Algebra to Secondary Mathematics Pedagogy via Disciplinary Practices
In this commentary, we discuss the contributions of five chapters that explore how disciplinary practices might be used to connect abstract algebra to secondary mathematics pedagogy. We identified four foundational issues that we believe researchers should consider going forward to build a coherent literature base, such as what constitutes a meaningful connection between abstract algebra and pedagogy and how contextual variation between studies should be accounted for. We suggest that an increased theoretical focus on how teachers learn pedagogy in an abstract algebra class can help address these foundational issues. Finally, we propose that Sandoval’s notion of “conjecture mapping” can provide researchers with a research paradigm to focus simultaneously on what they want students to learn, how they think learning occurs, and whether their proposed instruction is effective.
KeywordsAbstract algebra Conjecture mapping Disciplinary practices Preservice and inservice teachers
- Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.Google Scholar
- Heid, M. K., Wilson, P. S., & Blume, G. W. (Eds.). (2015). Mathematical understanding for secondary teaching: A framework and classroom-based situations. Charlotte, NC: IAP.Google Scholar
- Piaget, J., & Garcia, R. (1983/1989). Psychogenesis and the history of science (H. Feider, Trans.). New York, NY: Columbia University Press.Google Scholar