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STUDYING THE MATHEMATICAL CONCEPT OF IMPLICATION THROUGH A PROBLEM ON WRITTEN PROOFS

Virginie Deloustal-Jorrand

Open publisher page 3 citations

Abstract

In this paper, we present a didactic analysis of the mathematical concept of implication under three points of view: sets, formal logic, deductive reasoning. For this study, our hypothesis is that most of the difficulties and mistakes, as well in the use of implication as in its understanding, are due to the lack of links in education between those three points of view. This article is in the continuation of one previously published in the acts of PME 26. We present here the analysis of another problem from our experimentation. We want to show how a work on written proofs can allow a work on implication. Then we conclude with some transcripts.

About this research paper

What this paper is about

In this paper, we present a didactic analysis of the mathematical concept of implication under three points of view: sets, formal logic, deductive reasoning. For this study, our hypothesis is that most of the difficulties and mistakes, as well in the use of implication as in its understanding, are due to the lack of links in education between those three points of view. This article is in the continuation of one previously published in the acts of PME 26. We present here the analysis of another problem from our experimentation. We want to show how a work on written proofs can allow a work on implication. Then we conclude with some transcripts.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we present a didactic analysis of the mathematical concept of implication under three points of view: sets, formal logic, deductive reasoning. For this study, our hypothesis is that most of the difficulties and mistakes, as well in the use of implication as in its understanding, are due to the lack of links in education between those three points of view. This article is in the continuation of one previously published in the acts of PME 26. We present here the analysis of another problem from our experimentation. We want to show how a work on written proofs can allow a work on implication. Then we conclude with some transcripts.

Key concepts: Mathematical proof, Mathematical logic, Continuation, Computer science, Mathematical practice, Mathematics education, Logical reasoning, Deductive reasoning

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