Resolver problemas envolvendo prova e demonstração: uma dificuldade para professores de ensino básico

Abstract : In the last decade, the importance attributed to proofs and demonstrations in Mathematics has led to a large variety of research in this area. We consider, generally, the demonstration as a validation procedure that characterizes Mathematics and distinguishes it from experimental sciences. We are part of a research group that develops a project together with teachers from the public and private school systems in the city of São Paulo and that, in its initial phase, discussed deductive reasoning in the process of teaching and learning Mathematics in the Middle School grades. This project provides continuing education for teachers concerned with their pedagogical practices and who would like to increment them, rethinking knowledge or even coming into contact with mathematics topics for the first time. In this work, we initially raise some theoretical questions that are related to demonstrations and that seek to better understand logical reasoning. We next present a case study, in a qualitative approach, in which we observe a teacher's difficulties in identifying the hypothesis and thesis of a mathematical affirmation in the area of geometry, especially when it does not present the famous expression "if and only if." We also discuss the issue of whether or not a proposition corresponds to a reciprocal theorem. Comprehension of the information given in the problem statement of a mathematics proposition and recognition of crucial elements such as hypothesis and thesis are fundamental to the process of constructing an acceptable demonstration.
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Submitted on : Monday, August 2, 2010 - 1:14:58 AM
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Saddo Ag Almouloud, Jean-Claude Regnier, Cristiana Abud da Silva Fusco. Resolver problemas envolvendo prova e demonstração: uma dificuldade para professores de ensino básico. 1rst International Congress of Mathematics, Engineering and Society - ICMES 2009, Dec 2009, Curitiba, Brazil. pp.ICMES2009-02. ⟨halshs-00506497⟩



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