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Structure of deductive thinking and proving. (Struttura del ragionamento deduttivo e apprendimento della dimonstrazione.) (Italian)
Mat. Didatt., No. 4, 370-393 (1996).
Deductive thinking does not work like argumentation. However these two kinds of reasoning use very similar linguistic forms and propositional connectives. This is one of the main reasons why most of the students do not understand the requirements of mathematical proofs. In this article we present a cognitive analysis of deductive organisation versus argumentative organisation of reasoning, and the didactical applications of this analysis. We present also proofs written by young students for geometrical problems, in the frame of an experience, the goal of which was to realize dissociation between content and operative status of propositions. The analysis of proofs written by the students requires a second distinction between truth value and epistemic value of propositions: by splitting content and operative status, students discover how deductive reasoning works and, at the same time, become aware that deductive reasoning changes also the epistemic value of the proved proposition. (orig.) ‒ The original version of this article was published in: Educational Studies in Mathematics, 22, 233‒261, 1991. See also ZDM 1992 E53 0911.
Classification: E53
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