This chapter draws together the work in this volume, relating it to John and Annie Selden’s interest in theoretical and methodological diversity in our field. It considers work on the details of individual thinking and classroom interactions, on expert mathematical thinking and experience, on constructing and evaluating quantitative measures, and on using constructs from neighboring disciplines. It then considers implications of this diversity for training new researchers in our field, discussing relationships between theory and evidence in qualitative research, and arguing that newer methods are promising for those seeking quantitative methods that are practical to implement and focused on the detail of conceptual content. Finally, it considers how our field might improve reporting standards and build an evidence base around standard tasks, thereby clarifying the scope of theoretical claims and consolidating our now extensive research base.

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Theoretical and Methodological Diversity in Undergraduate Mathematics Education: The Influence of John and Annie Selden on our Field

  • Lara Alcock,
  • Matthew Inglis

摘要

This chapter draws together the work in this volume, relating it to John and Annie Selden’s interest in theoretical and methodological diversity in our field. It considers work on the details of individual thinking and classroom interactions, on expert mathematical thinking and experience, on constructing and evaluating quantitative measures, and on using constructs from neighboring disciplines. It then considers implications of this diversity for training new researchers in our field, discussing relationships between theory and evidence in qualitative research, and arguing that newer methods are promising for those seeking quantitative methods that are practical to implement and focused on the detail of conceptual content. Finally, it considers how our field might improve reporting standards and build an evidence base around standard tasks, thereby clarifying the scope of theoretical claims and consolidating our now extensive research base.