Volume
21
Issue
1-2
Abstract
Despite plethora of research that attends to the convincing power of different types of proofs, research related to the convincing power of counterexamples is rather slim. In this paper we examine how prospective and practicing secondary school mathematics teachers respond to different types of counterexamples. The counterexamples were presented as products of students’ arguments, and the participants were asked to evaluate their correctness and comment on them. The counterexamples varied according to mathematical topic: algebra or geometry, and their explicitness. However, as we analyzed the data, we discovered that these distinctions were insufficient to explain why teachers accepted some counterexamples, but rejected others, with seemingly similar features. As we analyze the participants’ perceived transparency of different counterexamples, we employ various theoretical approaches that can advance our understanding of teachers’ conceptions of conviction with respect to counterexamples.
First Page
443
Last Page
458
Recommended Citation
Buchbinder, Orly and Zazkis, Rina
(2024)
"On Convincing Power of Counterexamples,"
The Mathematics Enthusiast: Vol. 21
:
No.
1
, Article 24.
DOI: https://doi.org/10.54870/1551-3440.1636
Available at:
https://scholarworks.umt.edu/tme/vol21/iss1/24
Digital Object Identifier (DOI)
10.54870/1551-3440.1636
Publisher
University of Montana, Maureen and Mike Mansfield Library
