TY - JOUR

T1 - Mathematicians' perspectives on features of a good pedagogical proof

AU - Lai, Yvonne

AU - Weber, Keith

AU - Mejía-Ramos, Juan Pablo

N1 - Funding Information:
We are grateful to the editor and the anonymous reviewers for helpful comments, to Aron Samkoff for transcribing interviews in the first study, and to the mathematicians who participated in the two studies. This work was supported by grants from the National Science Foundation (#EHR-1008317, #DUE-081736, and #DRL-0643734) and by an Investigating Student Learning Grant from the Center for Research on Learning and Teaching at the University of Michigan.

PY - 2012/4

Y1 - 2012/4

N2 - In this article, we report two studies investigating what mathematicians value in a pedagogical proof. Study 1 is a qualitative study of how eight mathematicians revised two proofs that would be presented in a course for mathematics majors. These mathematicians thought that introductory and concluding sentences should be included in the proofs, main ideas should be formatted to emphasize their importance, and extraneous or redundant information should be removed to avoid distracting or confusing the reader. Study 2 is a quantitative study assessing the extent to which a larger group of mathematicians (N = 110) agreed or disagreed with the eight mathematicians interviewed in Study 1. This quantitative study confirmed the findings of Study 1 by demonstrating a high degree of agreement among mathematicians regarding how they would revise proofs for pedagogical purposes.

AB - In this article, we report two studies investigating what mathematicians value in a pedagogical proof. Study 1 is a qualitative study of how eight mathematicians revised two proofs that would be presented in a course for mathematics majors. These mathematicians thought that introductory and concluding sentences should be included in the proofs, main ideas should be formatted to emphasize their importance, and extraneous or redundant information should be removed to avoid distracting or confusing the reader. Study 2 is a quantitative study assessing the extent to which a larger group of mathematicians (N = 110) agreed or disagreed with the eight mathematicians interviewed in Study 1. This quantitative study confirmed the findings of Study 1 by demonstrating a high degree of agreement among mathematicians regarding how they would revise proofs for pedagogical purposes.

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U2 - 10.1080/07370008.2012.661814

DO - 10.1080/07370008.2012.661814

M3 - Article

AN - SCOPUS:84859651449

VL - 30

SP - 146

EP - 169

JO - Cognition and Instruction

JF - Cognition and Instruction

SN - 0737-0008

IS - 2

ER -