Explanatoriness as a value in mathematics and mathematics teaching
Résumé
In this foremost philosophical paper, I propose a rather holistic idea of (re)establishing mathematical proof in school mathematics by explicating and enacting the particular merits of mathematical proof with respect to a variety of mathematical activities, e.g.: observation, systematic variation of example cases, informal argumentation, defining, hypothesising, inductive and abductive reasoning. Such activities are connected naturally to proving in practices of mathematics, with “practice” referring both to mathematics as a human endeavor in general, and to mathematics a (scientific) discipline. To this end, a concept of “mathematical value” from the philosophy of mathematical practice is employed. I focus exemplarily on the value of explanatoriness, which is both a core merit of good proof in scientific mathematical practice, and an important didactical goal of teaching proof.
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