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Counterexamples and refutations in undergraduate mathematics

How do undergraduate mathematics students interpret refutations? We investigated this question by asking participants to 1) decide whether statements are true or false and provide refutations, 2) evaluate counterexamples and ‘correct versions’ of the statements as valid or invalid refutations, and 3...

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Main Authors: Lara Alcock, Nina Attridge
Format: Default Conference proceeding
Published: 2022
Subjects:
Online Access:https://hdl.handle.net/2134/19273676.v1
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author Lara Alcock
Nina Attridge
author_facet Lara Alcock
Nina Attridge
author_sort Lara Alcock (1384308)
collection Figshare
description How do undergraduate mathematics students interpret refutations? We investigated this question by asking participants to 1) decide whether statements are true or false and provide refutations, 2) evaluate counterexamples and ‘correct versions’ of the statements as valid or invalid refutations, and 3) judge which potential refutations are better, explaining why. We report a study in which 173 undergraduate mathematics students completed this task. Results reveal that participants did largely understand the logic of counterexamples but did not reliably understand the broader logic of refutations.
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institution Loughborough University
publishDate 2022
record_format Figshare
spelling rr-article-192736762022-07-01T00:00:00Z Counterexamples and refutations in undergraduate mathematics Lara Alcock (1384308) Nina Attridge (433622) Counterexample Refutation Conditional Statement Logic Undergraduate How do undergraduate mathematics students interpret refutations? We investigated this question by asking participants to 1) decide whether statements are true or false and provide refutations, 2) evaluate counterexamples and ‘correct versions’ of the statements as valid or invalid refutations, and 3) judge which potential refutations are better, explaining why. We report a study in which 173 undergraduate mathematics students completed this task. Results reveal that participants did largely understand the logic of counterexamples but did not reliably understand the broader logic of refutations. 2022-07-01T00:00:00Z Text Conference contribution 2134/19273676.v1 https://figshare.com/articles/conference_contribution/Counterexamples_and_refutations_in_undergraduate_mathematics/19273676 CC BY-NC-ND 4.0
spellingShingle Counterexample
Refutation
Conditional Statement
Logic
Undergraduate
Lara Alcock
Nina Attridge
Counterexamples and refutations in undergraduate mathematics
title Counterexamples and refutations in undergraduate mathematics
title_full Counterexamples and refutations in undergraduate mathematics
title_fullStr Counterexamples and refutations in undergraduate mathematics
title_full_unstemmed Counterexamples and refutations in undergraduate mathematics
title_short Counterexamples and refutations in undergraduate mathematics
title_sort counterexamples and refutations in undergraduate mathematics
topic Counterexample
Refutation
Conditional Statement
Logic
Undergraduate
url https://hdl.handle.net/2134/19273676.v1