Indirect proof: what is specific to this way of proving?

被引：33

作者：

Antonini, Samuele ^{[1
]}

Mariotti, Maria Alessandra ^{[2
]}

机构：

[1] Univ Pavia, Dipartimento Matemat, Via Ferrata 1, I-27100 Pavia, Italy

[2] Univ Siena, Dipartimento Sci Matemat Informat, I-53100 Siena, Italy

来源：

ZDM-MATHEMATICS EDUCATION | 2008年 / 40卷 / 03期

关键词：

Proof; Argumentation; Indirect proof; Proof by contradiction; Proof by contraposition;

D O I：

10.1007/s11858-008-0091-2

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

The study presented in this paper is part of a wide research project concerning indirect proofs. Starting from the notion of mathematical theorem as the unity of a statement, a proof and a theory, a structural analysis of indirect proofs has been carried out. Such analysis leads to the production of a model to be used in the observation, analysis and interpretation of cognitive and didactical issues related to indirect proofs and indirect argumentations. Through the analysis of exemplar protocols, the paper discusses cognitive processes, outlining cognitive and didactical aspects of students' difficulties with this way of proving.

引用

页码：401 / 412

页数：12

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