id: 06664509
dt: j
an: 2016f.00800
au: Jourdan, Nicolas; Yevdokimov, Oleksiy
ti: On the analysis of indirect proofs: contradiction and contraposition.
so: Aust. Sr. Math. J. 30, No. 1, 55-64 (2016).
py: 2016
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: E50
ut: indirect proofs; contradiction; contraposition; proving
ci:
li:
ab: Summary: 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 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. (ERIC)
rv: