International Electronic Journal of Mathematics Education

Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Vargas F, Stenning K. Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem. INT ELECT J MATH ED. 2020;15(1), em0547. https://doi.org/10.29333/iejme/5883
APA 6th edition
In-text citation: (Vargas & Stenning, 2020)
Reference: Vargas, F., & Stenning, K. (2020). Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem. International Electronic Journal of Mathematics Education, 15(1), em0547. https://doi.org/10.29333/iejme/5883
Chicago
In-text citation: (Vargas and Stenning, 2020)
Reference: Vargas, Francisco, and Keith Stenning. "Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem". International Electronic Journal of Mathematics Education 2020 15 no. 1 (2020): em0547. https://doi.org/10.29333/iejme/5883
Harvard
In-text citation: (Vargas and Stenning, 2020)
Reference: Vargas, F., and Stenning, K. (2020). Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem. International Electronic Journal of Mathematics Education, 15(1), em0547. https://doi.org/10.29333/iejme/5883
MLA
In-text citation: (Vargas and Stenning, 2020)
Reference: Vargas, Francisco et al. "Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem". International Electronic Journal of Mathematics Education, vol. 15, no. 1, 2020, em0547. https://doi.org/10.29333/iejme/5883
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Vargas F, Stenning K. Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem. INT ELECT J MATH ED. 2020;15(1):em0547. https://doi.org/10.29333/iejme/5883

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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License

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.