The equivalence between a statement and its contrapositive is so obvious for an expert that, usually, he does not need any explanation. In this paper, we examine the argumentations which students produce in order to justify a statement that, in their opinion, is equivalent to a given statement. We observe that the most common argumentations come out from the effort to adjust the proof of the first statement to the second one. Analysing these argumentations, it emerges that for the students the (false) equivalence between a statement and its inverse is intuitive and the (true) equivalence between a statement and its contrapositive is not intuitive
A statement, the contrapositive and the inverse: intuition and argumentation / Antonini S.. - STAMPA. - 2:(2004), pp. 47-54. (Intervento presentato al convegno 28th Conference of the International Group for the Psychology of Mathematics Education tenutosi a Bergen, Norway nel 14-18 July, 2004).
A statement, the contrapositive and the inverse: intuition and argumentation
Antonini S.
2004
Abstract
The equivalence between a statement and its contrapositive is so obvious for an expert that, usually, he does not need any explanation. In this paper, we examine the argumentations which students produce in order to justify a statement that, in their opinion, is equivalent to a given statement. We observe that the most common argumentations come out from the effort to adjust the proof of the first statement to the second one. Analysing these argumentations, it emerges that for the students the (false) equivalence between a statement and its inverse is intuitive and the (true) equivalence between a statement and its contrapositive is not intuitive
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