Faculty Publications

Mathematicians' Views on Transition-to-Proof and Advanced Mathematics Courses

Document Type

Article

Publication Date

2014

Abstract

This study explores mathematicians’ views on 1) knowledge and skills students need in order to succeed in subsequent mathematics courses, 2) content courses as transition-to-proof courses, and 3) differences in the proving process across mathematical content areas. Seven mathematicians from three different universities (varying in geographic location and department size), were interviewed. Precision, sense-making, flexibility, definition use, reading and validating proofs, and proof techniques are skills that the mathematicians stated were necessary to be successful in advanced mathematics courses. The participants agreed unanimously that a content course could be used as a transition-to-proof course under certain conditions. They also noted differences in the proving processes between abstract algebra and real analysis. Results from this study will be used to frame a larger study investigating students’ proof processes in their subsequent mathematics content courses and investigating how these skills can be incorporated into a transition-to-proof course.

Journal Title

Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education

First Page

1009

Last Page

1013

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