期刊
JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION
卷 53, 期 1, 页码 65-84出版社
NATL COUNCIL TEACHERS MATHEMATICS-NCTM
DOI: 10.5951/jresematheduc-2020-0034
关键词
Proof; Mathematical practice; Mathematical certainty; Conviction
This study investigates how advanced mathematics doctoral students obtain conviction and certainty in mathematical claims, as well as how they use proofs and empirical evidence to reduce doubts.
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.
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