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Building a Coherent Research Program that Links Abstract Algebra to Secondary Mathematics Pedagogy via Disciplinary Practices

  • James Cummings
  • Elise Lockwood
  • Keith Weber
Chapter
Part of the Research in Mathematics Education book series (RME)

Abstract

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.

Keywords

Abstract algebra Conjecture mapping Disciplinary practices Preservice and inservice teachers 

References

  1. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  2. 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
  3. Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15(4), 375–402.CrossRefGoogle Scholar
  4. DiSessa, A. A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. Journal of the Learning Sciences, 13(1), 77–103.CrossRefGoogle Scholar
  5. Dubinsky, E., Dautermann, J., Leron, U., & Zazkis, R. (1994). On learning fundamental concepts of group theory. Educational Studies in Mathematics, 27(3), 267–305.CrossRefGoogle Scholar
  6. 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
  7. Piaget, J., & Garcia, R. (1983/1989). Psychogenesis and the history of science (H. Feider, Trans.). New York, NY: Columbia University Press.Google Scholar
  8. Sandoval, W. (2014). Conjecture mapping: An approach to systematic educational design research. Journal of the Learning Sciences, 23(1), 18–36.CrossRefGoogle Scholar
  9. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.CrossRefGoogle Scholar
  10. Ticknor, C. S. (2012). Situated learning in an abstract algebra classroom. Educational Studies in Mathematics, 81(3), 307–323.CrossRefGoogle Scholar
  11. Wasserman, N. H., Fukawa-Connelly, T., Villanueva, M., Mejia-Ramos, J. P., & Weber, K. (2017). Making real analysis relevant to secondary teachers: Building up from and stepping down to practice. PRIMUS, 27(6), 559–578.CrossRefGoogle Scholar
  12. 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

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA
  3. 3.Graduate School of EducationRutgers UniversityNew BrunswickUSA

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