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Session # 1365

Technological Aids in Advanced Calculus at New Mexico State University

Ross Staffeldt New Mexico State University

Abstract

Technology in the form of the computer program Maple is proving to be an important aid to students learning advanced calculus. Availability of the program seems to help students while they learn to find and classify critical points and while they learn to set up and evaluate multiple integrals, to name two topics students find especially troublesome. For example, we have a number of goals for the course segment on the classification of critical points. In particular students should learn how to locate critical points graphically, by studying fields of gradient vectors and plots of level curves; formally, by solving explicitly for the zeroes of the gradient; and numerically, when formal solutions are infeasible. They should also learn to interpret the classification theorem verbally and graphically. The computations needed to locate the zeroes of the gradient of a function are almost always difficult, so it helps enormously to have the computer help solve equations. But a complete analysis of an example is a multi-step procedure, and, if it is all done on a computer, the procedure requires the use of many commands and thoughtful evaluation of computer output after each step.

So how does one go about making a computer program as large and sophisticated as Maple “available” to a typical group of students? We describe how the program is presented in digestible chunks, how other technology developed at NMSU helps provide adequate feedback to students, and how attaining a basic skill level contributes to the course grade. Materials created by the author are now being disseminated among other instructors of advanced calculus at NMSU. A preliminary assessment of the impact of the material on student learning is made below, and a wider study is planned.

Goals

Before any one of us would incorporate something new into teaching, each of us would consider reasons for the innovation, how familiar the innovation is to us, how we expect the innovation to affect the students, both in the short term and in the long run, and how we are going to manage Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright © 2001, American Society for Engineering Education

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Staffeldt, R. (2001, June), Technological Aids In Advanced Calculus At New Mexico State University Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--9893