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Session 1265

Using an Integrated Engineering Curriculum to Improve Freshman Calculus David L. Barrow, Stephen A. Fulling Department of Mathematics Texas A&M University College Station, Texas 77843-3368

ABSTRACT This paper addresses the following question: What are some of the ways that the beginning calculus course for engineers can be improved, if it is part of an integrated curriculum that also includes physics, engineering, and chemistry courses? The authors have had the opportunity to participate in such an integrated curriculum at Texas A&M for the past two to four years. Several major changes were made in the first-year calculus sequence in order to present various topics at the times they were applied in other courses. We have found that these changes not only serve the needs of the partner disciplines, but also provide a more unified and coherent treatment of some topics from the point of view of mathematics itself. Vectors, parametric curves, line integrals, and especially centers of mass and moments of inertia are topics that students traditionally find difficult, unmotivated, or confusing because of inconsistent notation or terminology in different courses; covering them “early” actually improves their presentation. Other topics, such as multiple integrals, orthonormal bases, ordinary differential equations, and numerical approximation of derivatives and integrals, can be introduced in a motivated way in preparation for their more in-depth treatment in later years. Following “learning cycle” and “learning style” ideas, we have made an effort to provide more motivation and practice within the mathematics course; but the most effective and efficient motivators and practice fields are coordinated courses in other disciplines where the mathematics is actually used.

INTRODUCTION We were recently presented with the challenge of rethinking how to teach calculus to freshman engineering students as part of an integrated curriculum. We immediately saw this as an opportunity to motivate calculus concepts by linking them to topics being covered in other courses. What educator wouldn't jump at the opportunity to use other courses to provide motivation, reinforcement, and credibility for one's own course? Upon closer examination of the idea, however, it became obvious that compromises were required by all of the disciplines involved, primarily in the order and depth in which topics are covered. Since presumably there are very good, time-tested reasons for the existing, traditional course syllabi, we wanted to make only changes that were, from the viewpoint of the overall curriculum, clearly improvements.

The purpose of this paper is to describe some of the major changes that were made to the freshman calculus courses, and our experiences using them in a pilot program (the Foundation Coalition) at Texas A&M over the past four years. The thrusts of this program are curriculum integration, classroom technology, active and team learning, and continuous assessment. We hope that the assessment efforts will soon provide validation of the conclusions we argue for here.

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Fulling, S. A., & Barrow, D. L. (1998, June), Using An Integrated Engineering Curriculum To Improve Freshman Calculus Paper presented at 1998 Annual Conference, Seattle, Washington. 10.18260/1-2--7499