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Issues and Challenges in Instrumental Proof

  • Philippe R. RichardEmail author
  • Fabienne Venant
  • Michel Gagnon
Chapter
  • 119 Downloads
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 14)

Abstract

Our article aims to define the notion of instrumental proof based on didactic, epistemological and cognitive considerations. We raise issues and challenges related to the use of this type of proof in mathematical work and mathematical thinking. The theory of mathematical working spaces serves as a construct on which we address questions about proof, reasoning and epistemic necessity, taking advantage of the possibilities offered by the development geneses and fibrations in an instrumented perspective. The coordination of the semiotic, discursive and instrumental geneses of the working space founds discursive-graphic proofs, mechanical proofs and algorithmic proofs that are activated at school in the subject-milieu interactions. We end with a discussion on some consequences of the computer-assisted modelling of the learning conditions of mathematics, and we conclude on a necessary reconciliation of heuristics and validation.

Keywords

Didactics of mathematics Mathematical working space Discursive-graphic proof Mechanical proof Algorithmic proof Instrumented reasoning Inference and connection of epistemic necessity Subject-milieu interactions Mathematical work and mathematical thinking Genetic developments and fibrations 

Notes

Acknowledgements

We wish sincerely to thank Prof. Annette Braconne-Michoux for her devoted and far-sighted work of linguistic review.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Philippe R. Richard
    • 1
    Email author
  • Fabienne Venant
    • 2
  • Michel Gagnon
    • 3
  1. 1.Université de MontréalMontréalCanada
  2. 2.Université du Québec à MontréalMontréalCanada
  3. 3.École Polytechnique de MontréalMontréalCanada

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