New Results in Research on Undergraduate Mathematics Majors' Understanding of the Role of Definitions in Mathematics

Document Type

Presentation Abstract

Presentation Date

4-17-2003

Abstract

Undergraduate mathematics majors enrolled in their first Real Analysis course can have understandings about the role of mathematical definitions that affect their understandings of the content of the course and their abilities to construct and understand formal mathematical proofs. One might think that this is not so surprising since many of the concepts (and even their formal definitions) may have been encountered in the students' previous calculus courses, and since students' understandings of elementary calculus concepts can often be imperfect, these students might 'unconsciously' misuse the related definitions. My recent research (with Michael Ward at Western Oregon University) involving students in an introductory Abstract Algebra course has led to similar conclusions, however, even though many of the concepts in introductory abstract algebra may be completely new to the students. (Thus, theoretically, there should be no interference by previous incomplete understandings of the concepts.) I have also discovered that misconceptions about the role of mathematical definition are much harder to uproot than previously thought. I will also discuss a revised and refined theoretical framework for studying student's use of definitions in mathematics.

Additional Details

Thursday, 17 April 2003
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (Lounge)

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