Mathematicians' Perspectives on Features of a Good Pedagogical Proof

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 concludi...

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Bibliographic Details
Published in:Cognition and instruction 2012-04, Vol.30 (2), p.146-169
Main Authors: Lai, Yvonne, Weber, Keith, Mejía-Ramos, Juan Pablo
Format: Article
Language:English
Subjects:
College Faculty
College instruction
Doctoral Degrees
Educational research
Graduate Students
Higher education
Internet
Interviews
Learning
Lectures
Majors (Students)
Mathematical Formulas
Mathematical functions
Mathematical knowledge
Mathematicians
Mathematics Education
Mathematics Instruction
Mathematics teachers
Mean value theorems
Pedagogy
Qualitative Research
Reason
Sentences
Statistical Analysis
Studies
Teaching Methods
Validity
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Summary: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.
ISSN:0737-0008
1532-690X
DOI:10.1080/07370008.2012.661814