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How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on... The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this article, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for mathematics instruction and theories of epistemic cognition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Educational Psychologist Taylor & Francis

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

23 pages

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References (140)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1532-6985
eISSN
0046-1520
DOI
10.1080/00461520.2013.865527
Publisher site
See Article on Publisher Site

Abstract

The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this article, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for mathematics instruction and theories of epistemic cognition.

Journal

Educational PsychologistTaylor & Francis

Published: Jan 2, 2014

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