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Research in Mathematics Education Volume 12, 2010 - Issue 1
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Research papers

Can a proof and a counterexample coexist? Students' conceptions about the relationship between proof and refutation

Andreas J. Stylianides Faculty of Education, University of Cambridge, Cambridge, UKCorrespondence[email protected]
&
Thabit Al-Murani Department of Education, University of Oxford, Oxford, UK
Pages 21-36 | Published online: 12 Feb 2010

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Read on this site (5)

Yusuke Shinno & Taro Fujita. (2022) Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach. International Journal of Mathematical Education in Science and Technology 53:12, pages 3326-3351.
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Tye G. Campbell, Shande King & Jeremy Zelkowski. (2021) Comparing middle grade students’ oral and written arguments. Research in Mathematics Education 23:1, pages 21-38.
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Keith Weber, Kristen Lew & Juan Pablo Mejía-Ramos. (2020) Using Expectancy Value Theory to Account for Individuals’ Mathematical Justifications. Cognition and Instruction 38:1, pages 27-56.
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Gabriel J. Stylianides & Andreas J. Stylianides. (2014) The Role of Instructional Engineering in Reducing the Uncertainties of Ambitious Teaching. Cognition and Instruction 32:4, pages 374-415.
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Barbara A. Shipman & Patrick D. Shipman. (2013) Simple yet Hidden Counterexamples in Undergraduate Real Analysis. PRIMUS 23:2, pages 111-120.
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Articles from other publishers (12)

Lara Alcock & Nina Attridge. (2023) Refutations and Reasoning in Undergraduate Mathematics. International Journal of Research in Undergraduate Mathematics Education.
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Mervenur Belin & Gülseren Karagöz Akar. (2020) The effect of quantitative reasoning on prospective mathematics teachers’ proof comprehension: The case of real numbers. The Journal of Mathematical Behavior 57, pages 100757.
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David A. Yopp, Rob Ely, Anne E. Adams, Annelise W. Nielsen & Erin C. Corwine. (2020) Eliminating counterexamples: A case study intervention for improving adolescents’ ability to critique direct arguments. The Journal of Mathematical Behavior 57, pages 100751.
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Orly Buchbinder & Orit Zaslavsky. (2019) Strengths and inconsistencies in students’ understanding of the roles of examples in proving. The Journal of Mathematical Behavior 53, pages 129-147.
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Dragana Martinovic. 2019. Interdisciplinary Perspectives on Math Cognition. Interdisciplinary Perspectives on Math Cognition 303 313 .
Erik Jacobson, Joanne Lobato & Chandra H. Orrill. (2017) Middle School Teachers’ Use of Mathematics to Make Sense of Student Solutions to Proportional Reasoning Problems. International Journal of Science and Mathematics Education 16:8, pages 1541-1559.
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Orly Buchbinder. 2018. Scripting Approaches in Mathematics Education. Scripting Approaches in Mathematics Education 89 113 .
Emma Enström & Viggo Kann. (2017) Iteratively Intervening with the “Most Difficult” Topics of an Algorithms and Complexity Course. ACM Transactions on Computing Education 17:1, pages 1-38.
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David A. Yopp. (2017) Eliminating counterexamples: A Grade 8 student’s learning trajectory for contrapositive proving. The Journal of Mathematical Behavior 45, pages 150-166.
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David A. Yopp. (2015) Prospective elementary teachers’ claiming in responses to false generalizations. The Journal of Mathematical Behavior 39, pages 79-99.
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Taro Fujita & Keith Jones. (2014) Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research 64, pages 81-91.
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Andreas J. Stylianides. (2011) Towards a comprehensive knowledge package for teaching proof: A focus on the misconception that empirical arguments are proofs. Pythagoras 32:1.
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