Collaboration is central to the practice of proving for professional mathematicians. Given the collaborative nature of proving in the discipline and the benefits of collaboration for student learning, instructors are increasingly designing instruction to incorporate collaboration among students within proof-based courses. Yet, most extant research on proving with undergraduate students is not conducted within collaborative settings nor within classroom-based contexts. In this manuscript, we make a call for research to focus upon collaborative proving in real classrooms. Although this type of research is messy and challenging, it is increasingly important in order to impact change and improvement within undergraduate mathematics education. To effectively study these complex proving spaces, we argue the importance of meaningful theoretical framing to ground the work. We provide examples from our own research that illustrate both the role and utility of theoretical framing when studying collaborative proving in real classrooms.

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Researching Collaborative Proving in Real University Classrooms: The Role and Utility of Theoretical Framing

  • Amanda Lake Heath,
  • Sarah K. Bleiler-Baxter

摘要

Collaboration is central to the practice of proving for professional mathematicians. Given the collaborative nature of proving in the discipline and the benefits of collaboration for student learning, instructors are increasingly designing instruction to incorporate collaboration among students within proof-based courses. Yet, most extant research on proving with undergraduate students is not conducted within collaborative settings nor within classroom-based contexts. In this manuscript, we make a call for research to focus upon collaborative proving in real classrooms. Although this type of research is messy and challenging, it is increasingly important in order to impact change and improvement within undergraduate mathematics education. To effectively study these complex proving spaces, we argue the importance of meaningful theoretical framing to ground the work. We provide examples from our own research that illustrate both the role and utility of theoretical framing when studying collaborative proving in real classrooms.