The Relationship Between Proof and Certainty in Mathematical Practice

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Keith Weber Rutgers University, New Brunswick, NJ

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Juan Pablo Mejía-Ramos Rutgers University, New Brunswick, NJ

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Tyler Volpe Somerville High School, Somerville, NJ

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Many mathematics educators believe a goal of instruction is for students to obtain conviction and certainty in mathematical statements using the same types of evidence that mathematicians do. However, few empirical studies have examined how mathematicians use proofs to obtain conviction and certainty. We report on a study in which 16 advanced mathematics doctoral students were given a task-based interview in which they were presented with various sources of evidence in support of a specific mathematical claim and were asked how convinced they were that the claim was true after reviewing this evidence. In particular, we explore why our participants retained doubts about our claim after reading its proof and how they used empirical evidence to reduce those doubts.

Footnotes

We would like to thank Eric Knuth for helpful comments on an earlier draft of this manuscript. The JRME review process was especially helpful for improving this manuscript, and we would like to express our gratitude to all the reviewers and the JRME Editorial Team for their constructive feedback. In particular, we would like to thank Alan Schoenfeld, who—acting in his capacity as a reviewer—showed us the right way to frame our manuscript, and Reviewer 2, who offered a great deal of careful critiques that were critical, fair, and constructive.

Contributor Notes

Keith Weber, Graduate School of Education, Rutgers University, 10 Seminary Place, New Brunswick, NJ 08901; keith.weber@gse.rutgers.edu

Juan Pablo Mejía-Ramos, Graduate School of Education and Department of Mathematics, Rutgers University, 10 Seminary Place, New Brunswick, NJ 08901; pablo.mejia@gse.rutgers.edu

Tyler Volpe, Somerville High School, 222 Davenport Street, Somerville, NJ 08876; tvolpe96@gmail.com

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