Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem
Francisco Vargas 1 2 * , Keith Stenning 3
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1 Universidad el Bosque, Bogotá, COLOMBIA2 Ludwigsburg University of Education, Ludwigsburg, GERMANY3 University of Edinburgh, UK* Corresponding Author

Abstract

We report on a study conceived with the idea that the use of logic in regard to mathematical reasoning as it actually occurs in practice is not limited to its prominent role in formal deductions and proofs. Interpretation of different mathematical situations elicits in fact the use of mostly unconscious forms of reasoning, close to those of narrative processing, which do not coincide with the expectations of traditional logic. This is pervasive, in particular, in educational situations at different levels, as we illustrate with interpretations which can emerge alongside an apparently obvious mathematical statement, namely, Pythagoras Theorem. We defend the position that analyses of “errors”, should start by understanding their prevalence and non arbitrariness. Accordingly, we use a nonclassical logics whose features may give new insights to the kind of learning obstacles often found in the literature, as well as in our results.

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2020, Volume 15, Issue 1, Article No: em0547

https://doi.org/10.29333/iejme/5883

Publication date: 21 Aug 2019

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