MOVING BEYOND MYTHS

Revitalizing Undergraduate Mathematics

Committee on the Mathematical Sciences in the Year 2000

Board on Mathematical Sciences

Mathematical Sciences Education Board

National Research Council

NATIONAL ACADEMY PRESS
Washington, D.C.
1991



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Moving Beyond Myths: Revitalizing Undergraduate Mathematics MOVING BEYOND MYTHS Revitalizing Undergraduate Mathematics Committee on the Mathematical Sciences in the Year 2000Board on Mathematical Sciences Mathematical Sciences Education Board National Research Council NATIONAL ACADEMY PRESS Washington, D.C. 1991

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Moving Beyond Myths: Revitalizing Undergraduate Mathematics NATIONAL ACADEMY PRESS 2101 Constitution Avenue, N.W. Washington, D.C. 20418 NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committees responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the author according to procedures approved by a report review committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. The Council functions in accordance with general policies determined by the Academy under the authority given to it in 1863 by its congressional charter, which established the Academy as a private, nonprofit, self-governing membership corporation. The Council is the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. It is administered jointly by both Academies and the Institute of Medicine. Dr. Frank Press and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council. The Mathematical Sciences Education Board was established in 1985 to provide a continuing national overview and assessment capability for mathematics education and is concerned with excellence in mathematical sciences education for all students at all levels. The board reports directly to the Governing Board of the National Research Council. The National Research Council created the Board on Mathematical Sciences in 1984. The objectives of the board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point of the Research Council for the issues connected with research in the mathematical sciences. Designed to conduct studies for federal agencies and to maintain liaison with the mathematical sciences communities, the board is part of the Commission on Physical Sciences, Mathematics, and Applications. The Committee on the Mathematical Sciences in the Year 2000, which was appointed at the beginning of 1988, is a three-year joint project of the Mathematical Sciences Education Board and the Board on Mathematical Sciences. Its purpose is to provide a national agenda for revitalizing mathematical sciences education in U.S. colleges and universities. Support for this project and for the publication and dissemination of the report was provided by grants from the National Science Foundation and the National Security Agency with additional support from the Department of Education and the National Aeronautics and Space Administration. Cover photograph reprinted courtesy of the University of Maryland and with permission from John Consoli, photographer. Copyright © 1989 by John Consoli. Copyright © 1991 by the National Academy of Sciences. Library of Congress Catalog Card No. 91-60521 International Standard Book Number 0-309-04489-8 Permission for limited reproduction of portions of this book for educational purposes but not for sale may be granted upon receipt of a written request to the Mathematical Sciences Education Board, 2101 Constitution Avenue, N.W., Harris 476, Washington, D.C. 20418 Additional copies of this report are available from: National Academy Press 2101 Constitution Avenue, N.W. Washington, D.C. 20418 S344 Summaries of this report may be obtained from the Mathematical Sciences Education Board, 2101 Constitution Avenue, N.W., Harris 476, Washington, D.C. 20418. Printed in the United States of America. First Printing, March 1991 Second Printing, May 1992

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Moving Beyond Myths: Revitalizing Undergraduate Mathematics FOREWORD Anyone who believes that educational reform is something needed only at the school level will be disabused of that notion by reading Moving Beyond Myths: Revitalizing Undergraduate Mathematics. This report, prepared by a committee of 20 distinguished citizens from academia, industry, and public policy, calls for sweeping change in mathematics education at the college-university level to parallel change underway in the nation's schools, noting that both levels play key roles in advancing science and technology and in preparing the broader work force and quantitatively literate citizenry the country needs. The publication of Moving Beyond Myths completes a decade of effort in which boards and committees of the National Research Council have analyzed the total U.S. mathematical sciences enterprise. This unique undertaking began in 1981 with the appointment of the so-called David committee, which in 1984 published its review of the status of U.S. mathematical research, along with a national plan for renewal; an update, Renewing U.S. Mathematics: A Plan for the 1990s, was published last year. In 1989, Everybody Counts—A Report to the Nation on the Future of Mathematics Education presented an overall assessment of the quality and status of mathematics education, outlining a strategy and plan for reforming school mathematics. As 1991 begins, we have the capstone, Moving Beyond Myths, which puts forth a similar plan for college-university mathematics, a plan designed to fit with those found in Everybody Counts and Renewing U.S. Mathematics. All of these three-year reviews were undertaken at the request of the U.S. mathematics and mathematics education communities, but were conducted by NRC committees representing the diverse constituencies of the mathematical sciences. The Committee on the Mathematical Sciences in the Year 2000 has been ably led by Dr. William E. Kirwan, President of the University of Maryland at College Park, since the time in 1989 when other pressing commitments drew away the first chair, Mr. J. Fred Bucy, former Chief Executive Officer of Texas Instruments, Inc.

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Moving Beyond Myths: Revitalizing Undergraduate Mathematics The MS2000 Committee's report presents a formidable challenge to higher education, especially to the nation's research universities. I urge all who read Moving Beyond Myths to reflect on it in the context of the other major reports I have mentioned and to identify their roles in implementing the action plan it contains. FRANK PRESS PRESIDENT, NATIONAL ACADEMY OF SCIENCES CHAIRMAN, NATIONAL RESEARCH COUNCIL

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Moving Beyond Myths: Revitalizing Undergraduate Mathematics PREFACE The national action plan presented in Moving Beyond Myths: Revitalizing Undergraduate Mathematics calls for dramatic change. Its implementation will tax the creativity, commitment, adaptability, and energies of mathematical sciences faculty and departments, college-university administrations and trustees, professional societies, and federal and state governments. Success will depend upon the cooperation of all these groups in a sustained effort lasting to the year 2000 and beyond. The plan challenges our institutions of higher education to bring their mathematics education efforts up to the standard set by the nation's mathematical research enterprise, which is preeminent in the world. The President and the governors of the 50 states have set just such a standard of performance by U.S. schools, colleges, and universities as a national goal for mathematics and science education. Our report states what we think it will take for undergraduate mathematics to reach this ambitious goal. The challenge is reminiscent of the one faced by the nation's universities at the middle of this century: To develop the infrastructure necessary to support scientific research of the highest quality. The response to that pressing national need was a post-World War II cooperative effort of the universities and government that produced the greatest scientific research enterprise in history, built upon a new kind of institution: the modern American research university. As we enter the last decade of the century, the country's universities, colleges, and community colleges together face an even greater challenge: To sustain the research infrastructure and also develop the climate, the support structures, the people, and the modified institutions necessary for meeting today's major national need, education of the highest quality for all students. A few comments are in order concerning how we have gone about our work. The Committee on the Mathematical Sciences in

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Moving Beyond Myths: Revitalizing Undergraduate Mathematics the Year 2000 was asked to: (i) review the status of undergraduate mathematical sciences education in the United States; (ii) develop a plan for the revitalization of mathematics education at our nation's colleges and universities; and (iii) delineate responsibilities for the implementation of the plan. Appropriately, committee membership reflects a wide variety of perspectives and experience. Over the last three years we benefited from the extensive data gathering done by Bernard Madison in preparing our earlier publication, A Challenge of Numbers, and from the advice and opinions of thousands of mathematicians, scientists, and engineers. We are grateful to them for sharing their ideas through a variety of means: (i) two large national symposia we organized: Calculus for a New Century in late 1987 and Mathematical Sciences: Servant to Other Disciplines in 1989; (ii) two national meetings of department chairs, one organized by the Joint Policy Board for Mathematics and the other by the NRC's Board on Mathematical Sciences; (iii) discussions with the science policy committees of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA) as well as the MAA Committee on the Undergraduate Program in Mathematics; (iv) dozens of presentation/discussion sessions at professional society meetings across the country, including national meetings of AMS-MAA and the American Mathematical Association of Two-Year Colleges (AMATYC); (v) two MS2000 workshops on human resources and curriculum; (vi) testimony presented at MS2000 Committee meetings; and (vii) hundreds of individual discussions conducted by committee members and staff interviews with selected department chairs and administrators. Two circumstances have combined to enable Moving Beyond Myths to be a shorter report than might be expected from a three-year project. First, our Committee presented an overview of undergraduate mathematics education as part of Everybody Counts—A Report to the Nation on the Future of Mathematics Education (NRC 1989). Second, most of the supporting data for our work were presented in our 1990 report, A Challenge of Numbers. It might properly be viewed as an appendix to this final report, just as Everybody Counts might be considered its introduction.

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Moving Beyond Myths: Revitalizing Undergraduate Mathematics We hope that the many groups to whom we have addressed our recommendations will move quickly to keep up the momentum of mathematics education change that has been building up over the last few years, and that a strong role will be played in the effort by our Committee's two NRC parent bodies: the Board on Mathematical Sciences and the Mathematical Sciences Education Board. WILLIAM E. KIRWAN CHAIRMAN, MS2000 COMMITTEE PRESIDENT UNIVERSITY OF MARYLAND AT COLLEGE PARK

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Moving Beyond Myths: Revitalizing Undergraduate Mathematics CONTENTS     THE CHALLENGE   1     THE MYTHS   9     BEHIND THE MYTHS   13     Departments Under Stress   14     Inadequacies and Deficiencies   16     FACING THE MYTHS   23     Wasted Breath   24     Missing Context   25     Casual Teaching   26     Flawed Models   28     Outmoded Values   29     Invisible Instructors   30     MOVING BEYOND MYTHS   31     Goals   33     An Action Plan   34     MATHEMATICS BEYOND MYTHS   43     EVIDENCE AND DOCUMENTATION   47     References   49     Sources   52     APPENDIX   55

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