PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
Understanding Calculus Beyond Computation: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus
Page: 1-187
Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to understand calculus, many students leave their calculus course(s) with an understanding misaligned with what is needed in the follow-on discipline courses and are thus ill-prepared. By working with presumed experts (undergraduate mathematics and other discipline faculty members) to develop a small number of prototype tasks that elicit, document, and measure students’ understanding of a few calculus concepts they believe are essential to successful academic pursuits within their respective disciplines, this study documents how the faculty participants’ underlying conceptions about understanding changed and converged. Implications for calculus instruction and curriculum are mentioned.