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

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


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.


Abstract algebra Conjecture mapping Disciplinary practices Preservice and inservice teachers 


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© 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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