Note on paraconsistency and reasoning about fractions

In mathematics education, one can get around predicament by avoiding the concepts of numerator and denominator, viewing fractions as a heterogeneous subject, or accepting cognitive conflicts. Here, Bergstra and Bethke propose the application of a paraconsistent strategy to reasoning about fractions....

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Published inJournal of applied non-classical logics Vol. 25; no. 2; pp. 120 - 124
Main Authors Bergstra, Jan A., Bethke, Inge
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.04.2015
Taylor & Francis Ltd
Subjects
Cognition & reasoning
Fractions
Logic
Mathematics
Mathematics education
paraconsistent reasoning
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ISSN1166-3081
1958-5780
DOI10.1080/11663081.2015.1047232

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Summary:In mathematics education, one can get around predicament by avoiding the concepts of numerator and denominator, viewing fractions as a heterogeneous subject, or accepting cognitive conflicts. Here, Bergstra and Bethke propose the application of a paraconsistent strategy to reasoning about fractions. A paraconsistent logic is a way to reason about inconsistent information without exploding in the sense that if a contradiction is obtained, then everything can be obtained. Paraconsistent logics come in a broad spectrum, ranging from logics for which it is the case that if a contradiction were true, then everything would be true, to logics which claim that some contradictions really are (non-trivially) true.
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ISSN:1166-3081
1958-5780
DOI:10.1080/11663081.2015.1047232