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Indirect proof: what is specific to this way of proving?

Abstract

The study presented in this paper is part of a wide research project concerning indirect proofs. Starting from the notion of mathematical theorem as the unity of a statement, a proof and a theory, a structural analysis of indirect proofs has been carried out. Such analysis leads to the production of a model to be used in the observation, analysis and interpretation of cognitive and didactical issues related to indirect proofs and indirect argumentations. Through the analysis of exemplar protocols, the paper discusses cognitive processes, outlining cognitive and didactical aspects of students’ difficulties with this way of proving.

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Notes

  1. 1.

    Valerio and Cristina do not belong to the same class, although they belong to the same school.

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Correspondence to Samuele Antonini.

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This research study was supported by the Italian Ministry of Education and Research (MIUR) Prin 2005 # 2005019721.

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Antonini, S., Mariotti, M.A. Indirect proof: what is specific to this way of proving?. ZDM Mathematics Education 40, 401–412 (2008). https://doi.org/10.1007/s11858-008-0091-2

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Keywords

  • Proof
  • Argumentation
  • Indirect proof
  • Proof by contradiction
  • Proof by contraposition