Title

Developing flexible procedural knowledge in undergraduate calculus

Publication Date

4-19-2016

Document Type

Article

Department

Mathematics and Statistics

Disciplines

Education | Physical Sciences and Mathematics | Science and Mathematics Education

Publication Title

Research in Mathematics Education

Volume

18

Issue

3

DOI

10.1080/14794802.2016.1148626

First Page

299

Last Page

316

Abstract

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This flexible procedural knowledge distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students’ flexible use of procedures. Two sections of the same course were randomly assigned to treatment and control conditions. Treatment students completed an assignment on which they resolved derivative-finding problems with alternative methods and compared the two resulting solutions. Control students were assigned a list of functions to differentiate. On the post-intervention test, treatment students were more likely to use a variety of solution methods without prompting than the control. Moreover, the set of treatment section solutions were closer to those of a group of mathematics experts. This study presents evidence that not only is flexible procedural knowledge a key skill in tertiary mathematics, it can be taught.

Keywords

undergraduate mathematics education, flexible procedural knowledge, calculus education

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