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Educational Studies in Mathematics

, Volume 96, Issue 2, pp 187–205 | Cite as

Affecting the flow of a proof by creating presence—a case study in Number Theory

  • Mika Gabel
  • Tommy Dreyfus
Article

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.

Keywords

Proof teaching Flow of proof Perelman’s New Rhetoric Mathematical argumentation Creating presence 

Notes

Acknowledgements

We would like to thank an anonymous reviewer for encouraging us and helping us to situate our study in the wider research landscape.

Supplementary material

10649_2016_9746_MOESM1_ESM.docx (229 kb)
ESM 1 (DOCX 229 kb)

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Tel Aviv UniversityTel AvivIsrael
  2. 2.Afeka - Tel Aviv Academic College of EngineeringTel AvivIsrael

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