An outcome of debating infinitesimals via primary sources: access to the practice of developing mathematics
Résumé
Building on the work that engagement with primary historical sources provides students with rich
opportunities to reach new understandings about mathematics, we present the case of one university
student’s (Renae) experience with a debate activity in a history of calculus course. Our analysis,
informed by the theory of mathematical transgressions in which transgressive actions propel students
beyond a barrier to outcomes of new upper levels of mathematical understanding revealed several
notable outcomes. For this paper, we focus on one outcome of participating in the debate activity:
access to practitioner practice, grounded in Lave and Wenger’s situated theory of learning. The
dimension of access gained by Renae was insight that mathematics, specifically the concept of
infinitesimals, is developed via critique and argumentation. We conjecture that transgressing via the
debate activity may foster rich connections from the historical to modern perspective.
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