Original article


, Volume 40, Issue 3, pp 401-412

First online:

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

  • Samuele AntoniniAffiliated withDipartimento di Matematica, Università di Pavia Email author 
  • , Maria Alessandra MariottiAffiliated withDipartimento di Scienze Matematiche e Informatiche, Università di Siena

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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.


Proof Argumentation Indirect proof Proof by contradiction Proof by contraposition