The Curriculum Foundations Project Voices of the Partner Disciplines Reports from a series of disciplinary workshops organized by the Curriculum Renewal Across the First Two Years (CRAFTY) subcomittee of the Committee for the Undergraduate Program in Mathematics (CUPM) Copyright ©2004 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2004100780 ISBN 0-88385-813-4 Printed in the United States of America Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 The Curriculum Foundations Project Voices of the Partner Disciplines Reports from a series of disciplinary workshops organized by the Curriculum Renewal Across the First Two Years (CRAFTY) subcomittee of the Committee for the Undergraduate Program in Mathematics (CUPM) Edited by Susan L. Ganter Clemson University William Barker Bowdoin College Published and Distributed by The Mathematical Association of America Preface Given the impact of mathematics instruction on so many other fields of study—especially instruction during the first two years—there is a need for significant input from the partner disciplines when designing the undergraduate mathematics curriculum. An unprecedented amount of information on the mathematical needs of partner disciplines has been gathered through a series of disciplinary-based workshops known as the Curriculum Foundations Project. Informed by the views expressed in these workshops, the Mathematical Association of America (MAA) has completed an extensive study of the undergraduate program in mathematics. The result is a set of rec- ommendations from the MAA Committee on the Undergraduate Program in Mathematics (CUPM)— Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004— that will assist mathematics departments as they plan their programs through the first decade of the 21st century. The CUPM subcommittee Curriculum Renewal Across the First Two Years (CRAFTY) organized and ran the Curriculum Foundations Project, gathering input from partner disciplines through a series of eleven workshops held across the country from November 1999 to February 2001. A final summary conference, attended by representatives of all the previous workshops, took place in November 2001. Each Curriculum Foundations workshop consisted of 20–35 participants, the majority chosen from the discipline under consideration, the remainder chosen from mathematics. The workshops were not intended to be discussions between mathematicians and colleagues in the partner disciplines, although this certainly happened informally. Instead, each workshop was a dialogue among the representatives from the partner discipline, with mathematicians present only to listen and serve as resources when questions arose about the mathematics curriculum. Each workshop produced a report directed to the mathematics community summarizing the workshop’s recommendations and conclusions. The reports were written by representatives of the partner disciplines, insuring accurate reporting of the workshop discussions while also adding credibility to the recommenda- tions. The Curriculum Foundations Steering Committee supplied a common set of questions to guide the discussions at each workshop. This helped achieve uniformity in structure for the reports and made it eas- ier to compare the recommendations from different disciplines. Workshop participants from the partner disciplines were extremely grateful—and surprised—to be invited by mathematicians to state their views about the mathematics curriculum. That the opinions of the partner disciplines were considered important and would be taken seriously in the development of the CUPM Guide 2004 only added to their enthusiasm for the project as well as their interest in continuing conversations with the mathematics community. At the final summary conference, held at the U. S. Military Academy at West Point in November 2001, a common set of recommendations—the Collective Vision—were distilled from the reports of the previ- ous workshops. This volume includes CRAFTY’s official report on the Collective Vision recommendations as well as the individual disciplinary reports. The disciplinary reports and Collective Vision were used extensively v vi The Curriculum Foundations Project by CUPM to inform the preparation of its CUPM Guide 2004. However, the workshop reports and Collective Vision have value independent of the CUPM Guide 2004 since they also serve as resources for multi-disciplinary discussions at individual institutions. Promoting and supporting informed interdepart- mental discussions about the undergraduate curriculum might ultimately be the most important outcome of the Curriculum Foundations Project. Contents Preface . v A Collective Vision: Voices of the Partner Disciplines . 1 Susan L. Ganter and William Barker Biology . 15 Judy Dilts and Anita Salem Business and Management . 19 Chris Lamoureux Chemistry . 27 Norman C. Craig Computer Science . 37 Charles F. Kelemen Engineering: Chemical Engineering . 51 Michael D. Graham Engineering: Civil Engineering . 57 Lynn Katz Engineering: Electrical Engineering . 65 Ben Oni Engineering: Mechanical Engineering . 79 David Bigio Health-Related Life Sciences . 91 Thomas F. Huff and William J. Terrell Interdisciplinary Core Mathematics . 97 Chris Arney and Don Small Mathematics . 109 Herbert Kasube and William McCallum Physics . 115 Karen Cummings and Guy Emery Statistics . 125 Tom Moore, Roxy Peck, and Allan Rossman Teacher Preparation: K–12 Mathematics . 145 Sharon L. Senk, Brian Keller, Joan Ferrini-Mundy Technical Mathematics: Biotechnology and Environmental Technology . 157 Elaine Johnson, John C. Peterson, and Kathy Yoshiwara vii viii The Curriculum Foundations Project Technical Mathematics: Electronics, Telecommunications, and Semiconductor Technology . 181 Bob L. Bixler, James Hyder, John C. Peterson, and Kathy Yoshiwara Technical Mathematics: Information Technology . 195 Robert D. Campbell, John C. Peterson, and Kathy Yoshiwara Technical Mathematics: Mechanical and Manufacturing Technology . 207 Al Schwabenbauer, John C. Peterson, and Kathy Yoshiwara A Collective Vision Voices of the Partner Disciplines Susan L. Ganter Clemson University William Barker Bowdoin College Introduction Mathematics can and should play an important role in the education of undergraduate students. In fact, few educators would dispute that students who can think mathematically and reason through problems are bet- ter able to face the challenges of careers in other disciplines—including those in non-scientific areas. Add to these skills the appropriate use of technology, the ability to model complex situations, and an under- standing and appreciation of the specific mathematics appropriate to their chosen fields, and students are then equipped with powerful tools for the future. Unfortunately, many mathematics courses are not successful in achieving these goals. Students do not see the connections between mathematics and their chosen disciplines; instead, they leave mathematics courses with a set of skills that they are unable to apply in non-routine settings and whose importance to their future careers is not appreciated. Indeed, the mathematics many students are taught often is not the most relevant to their chosen fields. For these reasons, faculty members outside mathematics often per- ceive the mathematics community as uninterested in the needs of non-mathematics majors, especially those in introductory courses. The mathematics community ignores this situation at its own peril since approximately 95% of the stu- dents in first-year mathematics courses go on to major in other disciplines. The challenge, therefore, is to provide mathematical experiences that are true to the spirit of mathematics yet also relevant to students’ futures in other fields. The question then is not whether they need mathematics, but what mathematics is needed and in what context. The Mathematical Association of America (MAA) is currently studying the undergraduate program in mathematics, informed by the views of a broad segment of the mathematics community and its partner dis- ciplines. The goal is a set of recommendations from the MAA Committee on the Undergraduate Program in Mathematics (CUPM)—the CUPM Curriculum Guide 2004—that will assist mathematics departments as they plan their programs through the first decade of the 21st century. The current efforts by CUPM are being informed by an unprecedented amount of information on the mathematical needs of partner disci- plines, obtained through a series of disciplinary-based workshops known as the Curriculum Foundations Project. 1 2 The Curriculum Foundations Project The Curriculum Foundations Project The CUPM subcommittee Curriculum Renewal Across the First Two Years (CRAFTY) has gathered input from partner disciplines through a series of eleven workshops held across the country from November 1999 to February 2001, followed by a final summary conference in November 2001 (see Appendix A). Each Curriculum Foundations workshop consisted of 20−35 participants, the majority chosen from the discipline under consideration, the remainder chosen from mathematics. The workshops were not intend- ed to be discussions between mathematicians and colleagues in the partner disciplines, although this cer- tainly happened informally. Instead, each workshop was a dialogue among the representatives from the partner discipline, with mathematicians present only to listen and serve as a resource when questions about the mathematics curriculum