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Title: On Convincing Power of Counterexamples
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.  more » « less
Award ID(s):
1941720
PAR ID:
10510480
Author(s) / Creator(s):
;
Editor(s):
Sriraman, B
Publisher / Repository:
https://scholarworks.umt.edu/tme/
Date Published:
Journal Name:
The Mathematics Enthusiast
Volume:
21
Issue:
1-2
ISSN:
1551-3440
Page Range / eLocation ID:
443 to 458
Subject(s) / Keyword(s):
Counterexamples, Proof, Conviction, Secondary Teachers
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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