Abstract
The notion of flow of a proof encapsulates mathematical, didactical, and contextual aspects of proof presentation. A proof may have different flows, depending on the lecturer’s choices regarding its presentation. Adopting Perelman’s New Rhetoric (PNR) as a theoretical framework, we designed methods to assess aspects of the flow of a proof. We present a case study from a Number Theory class at the beginning undergraduate level, focusing on an intervention concerning one lesson given in two consecutive years. The intervention consisted of a discussion with the lecturer about findings from Year-1 and potential changes in the flow of the proof before the Year-2 lesson. We analyze two aspects of the flow of the proof: the scope and organization of the argumentation and the presence (in the PNR sense) of different elements. Our analysis revealed that the intervention caused global and local changes in the flow and that PNR enables us to capture these changes.
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Notes
In the Toulmin schemes, the sequence of data and claims is numbered logically, e.g., claim C1 is derived from data D, claim C2 is derived from C1, and so on. However, the warrants, backups, and refutations are numbered in chronological order, in order to emphasize the temporal dimension of the argumentation.
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We would like to thank an anonymous reviewer for encouraging us and helping us to situate our study in the wider research landscape.
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Gabel, M., Dreyfus, T. Affecting the flow of a proof by creating presence—a case study in Number Theory. Educ Stud Math 96, 187–205 (2017). https://doi.org/10.1007/s10649-016-9746-z
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DOI: https://doi.org/10.1007/s10649-016-9746-z