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ERIC Number: EJ1106788
Record Type: Journal
Publication Date: 2016
Pages: 10
Abstractor: ERIC
ISSN: ISSN-0819-4564
On the Analysis of Indirect Proofs: Contradiction and Contraposition
Jourdan, Nicolas; Yevdokimov, Oleksiy
Australian Senior Mathematics Journal, v30 n1 p55-64 2016
The paper explores and clarifies the similarities and differences that exist between proof by contradiction and proof by contraposition. The paper also focuses on the concept of contradiction, and a general model for this method of proof is offered. The introduction of mathematical proof in the classroom remains a formidable challenge to students given that, at this stage of their schooling, they are used to manipulating symbols through sequential steps. There is a consensus that learners do find indirect types of proof quite difficult and do struggle with the conceptual and technical aspects of indirect proofs. As Epp (1998, p. 711) states, "Students find proof by contradiction considerably harder to master than direct proof". Indeed, learners may struggle with understanding the concept of indirect proofs in general and of proof by contradiction in particular. To address this issue further, and for learning purposes, proof by contradiction may be considered in conjunction with other methods and didactic tools, e.g., counterexamples or the pigeon-hole principle. But, that is a topic for another investigation.
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A