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Session 3565

Calculus Reform, Differential Equations and Engineering

Michael Ruane Electrical & Computer Engineering, Boston University

Abstract

Through much of the 1990’s, the National Science Foundation supported the development of new pedagogical methods, textbooks, and teaching materials, including software, for calculus. This was done in response to concerns from mathematicians, and from scientists and engineers in client disciplines who believed students were not being well prepared for further study with calculus applications. The ’calculus reform’ movement has significantly changed the teaching and learning of calculus where it is implemented and has been a constant topic of discussion in the mathematics community. Calculus reform is often unknown among engineering faculty.

Three Boston University mathematics faculty developed a ’reform’ differential equations course, textbook, and computer labs, incorporating an unusual degree of engineering applications, modeling and jargon. Their systems approach was later disseminated in workshops to the math community. In those workshops, a common theme from the math professors was ’we don’t talk with the engineers--they don’t even know that we’re teaching differently!’

Calculus reform, including the NSF differential equations project at Boston University, emphasizes using graphical solutions, numerical solutions, and symbolic solutions, as well as writing about mathematics, discovery learning, and team-based learning. This talk will describe these elements and discuss the possibilities for closer collaboration between mathematics and engineering around reform of the curriculum.

Introduction

The early 1980’s saw growing discussions in the mathematics community about the role and effectiveness of calculus instruction, particularly in the freshman year. Concerns were diverse. Some argued that discrete mathematics should become the core undergraduate mathematics course. Others felt the calculus sequence had lost sight of essentials under the burden of covering an increasing list of topics demanded by client disciplines and publishers. Changing instructional technology and new appreciation for student learning models seemed to require new curricular approaches.1,2

In January, 1986, a Tulane University Conference produced a report “Toward a Lean and Lively Calculus”3 which attempted to start a complete redesign of single variable calculus pedagogy and content. Almost immediately a strong case was made for computer-based algebra and plotting tools to help students overcome widespread weaknesses in numerical and symbolic Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright © 2001, American Society for Engineering Education

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Ruane, M. (2001, June), Calculus Reform, Differential Equations And Engineering Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--8976