On Convincing Power of Counterexamples

IF 0.3 Q4 MATHEMATICS
Orly Buchbinder, Rina Zazkis
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引用次数: 0

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.
论反例的说服力
尽管有大量的研究关注不同类型证明的说服力,但与反例的说服力相关的研究却相当少。本文考察了中学数学教师对不同类型反例的反应。反例作为学生论点的产物呈现,参与者被要求评估其正确性并对其进行评论。反例根据数学主题的不同而不同:代数或几何,以及它们的明确性。然而,当我们分析数据时,我们发现这些区别不足以解释为什么教师接受一些反例,而拒绝其他看似相似的反例。当我们分析参与者对不同反例的感知透明度时,我们采用了各种理论方法,可以促进我们对教师关于反例的信念概念的理解。
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来源期刊
Mathematics Enthusiast
Mathematics Enthusiast MATHEMATICS-
CiteScore
1.40
自引率
0.00%
发文量
43
期刊介绍: The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. The electronic version is hosted by the Department of Mathematical Sciences- University of Montana. The journal is NOT affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education- North America] through special issues on various research topics. TME strives to promote equity internationally by adopting an open access policy, as well as allowing authors to retain full copyright of their scholarship contingent on the journals’ publication ethics guidelines. Authors do not need to be affiliated with the University of Montana in order to publish in this journal. Journal articles cover a wide spectrum of topics such as mathematics content (including advanced mathematics), educational studies related to mathematics, and reports of innovative pedagogical practices with the hope of stimulating dialogue between pre-service and practicing teachers, university educators and mathematicians. The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning. The journal also includes a monograph series on special topics of interest to the community of readers.
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