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Moving Beyond Myths: Revitalizing Undergraduate Mathematics APPENDIX Challenges for College Mathematics: An Agenda for the Next Decade (Summary of Association of American Colleges-Mathematical Association of America Report) Goals and Objectives The primary goal of a mathematical sciences major should be to develop a student's capacity to undertake intellectually demanding mathematical reasoning. The undergraduate mathematics curriculum should be designed for all students with an interest in mathematics. Applications should motivate theory so that theory is seen by students as useful and enlightening. Mathematics majors should be offered extensive opportunities to read, write, listen, and speak mathematical ideas at each stage of their undergraduate study.
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics Breadth and Depth All students who major in mathematics should study some sequence of upper division courses that shows the power of study in depth. Every student who majors in mathematics should study a broad variety of advanced courses. Mathematics departments should take seriously the need to provide appropriate mathematical depth to students who wish to concentrate in mathematics without pursuing a traditional major. Mathematics majors should complete a minor in a discipline that makes significant use of mathematics. Learning and Teaching Instruction should encourage students to explore mathematical ideas on their own. Undergraduate students should not only learn the subject of mathematics, but also learn how to learn mathematics. Those who teach college mathematics should seek ways to incorporate into their own teaching styles the findings of research on teaching and learning. Mathematicians should increase their efforts to understand better how college students learn mathematics. Assessment of undergraduate majors should be aligned with broad goals of the major; tests should stress what is most important, not just what is easiest to test. Evaluation of teaching must involve robust indicators that reflect the broad purposes of mathematics education. Access and Encouragement Effective programs teach students, not just mathematics.
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics National need requires greater encouragement for students to continue their study of mathematics beyond the bachelor's degree. To provide effective opportunities for all students to learn mathematics, colleges should offer a broader spectrum of instructional practice that is better attuned to the variety of students seeking higher education. To ensure for all students equal access to higher mathematics education, mathematics departments should work with nearby two-year colleges to maintain close articulation of programs. Smooth curricular transitions improve student learning and help maintain momentum for the study of mathematics. Using Computers The mathematics curriculum should change to reflect in appropriate ways the impact of computers on the practice of mathematics. Colleges must recognize in budgets, staffing, and space the fact that undergraduate mathematics is rapidly becoming a laboratory discipline. Doing Mathematics Dealing with open-ended problem situations should be one of the highest priorities of undergraduate mathematics. All undergraduate mathematics students should undertake open-ended projects whose scope extends well beyond typical textbook problems. Undergraduate research and senior projects should be encouraged wherever there is sufficient faculty to provide appropriate supervision.
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics Students majoring in mathematics should undertake some real-world mathematical modelling project. Students Building students' well-founded self-confidence should be a major priority for all undergraduate mathematics instruction. Careful and individualized advising is crucial to students' success. All mathematics students should engage in serious study of the historical context and contemporary impact of mathematics. Mathematics departments should actively encourage extracurricular programs that enhance peer group support among mathematics majors. Renewal It is important for mathematics departments to help faculty and students recognize their own perspectives on mathematics and understand the perspectives of others. To ensure continued vitality of undergraduate mathematics programs, all mathematics faculty should engage in public professional activity, broadly defined. Regular external reviews and informal feedback are needed to assure quality in departments of mathematics. Renewal of undergraduate mathematics will require commitment, leadership, and support of graduate schools.
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics COMMITTEE ON THE MATHEMATICAL SCIENCES IN THE YEAR 2000 J. Fred Bucy (Chairman), former Chief Executive Officer of Texas Instruments, Inc. through 1989 William E. Kirwan (Chairman), President, University of Maryland at College Park Ramesh A. Gangolli (Vice Chairman), Professor of Mathematics, University of Washington Lida K. Barrett, Past President, Mathematical Association of America, Dean, College of Arts and Sciences, Mississippi State University Maria A. Berriozabal, Councilwoman, City of San Antonio, Texas Ernest L. Boyer, President, Carnegie Foundation for the Advancement of Teaching, New Jersey William Browder, Professor of Mathematics, Princeton University, New Jersey Rita R. Colwell, Director, Maryland Biotechnology Institute, Professor of Microbiology, University of Maryland John M. Deutch, Professor of Chemistry, Massachusetts Institute of Technology Ronald G. Douglas, Vice Provost for Academic Affairs, State University of New York, Stony Brook Patricia A. Dyer, Vice President for Academic Affairs, Palm Beach Community College, Florida Lloyd C. Elam, Distinguished Service Professor of Psychiatry, Meharry Medical College, Tennessee Sheldon L. Glashow, Higgins Professor of Physics, Harvard University, Massachusetts Nancy J. Kopell, Professor of Mathematics, Boston University, Massachusetts Donald W. Marquardt, Consultant Manager, E.I. du Pont de Nemours and Co., Delaware David S. Moore, Professor of Statistics, Purdue University, Indiana
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics Jaime Oaxaca, Vice Chairman, Coronado Communications, Inc., California Moshe F. Rubinstein, Professor of Engineering and Applied Science, University of California, Los Angeles Ivar Stakgold, Chairman, Department of Mathematical Sciences, University of Delaware S. Frederick Starr, President, Oberlin College, Ohio Lynn Arthur Steen, Professor of Mathematics, St. Olaf College, Minnesota Staff Bernard L. Madison, Project Director through December 1989 James A. Voytuk, Project Director Therese A. Hart, Research Associate through November 1989 Craig E. Hicks, Senior Editorial Assistant
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics BOARD ON MATHEMATICAL SCIENCES Phillip A. Griffiths (Chairman), Provost and James B. Duke Professor of Mathematics, Duke University, North Carolina Lawrence D. Brown, Professor of Mathematics, Cornell University, New York Sun-Yung A. Chang, Professor of Mathematics, University of California, Los Angeles Ronald G. Douglas, Vice Provost for Academic Affairs, State University of New York, Stony Brook David Eddy, J. Alexander McMahon Professor of Health Policy and Management, Duke University (retired) Avner Friedman, Director, Institute for Mathematics and Its Applications, University of Minnesota Frederick W. Gehring, Professor of Mathematics, University of Michigan James Glimm, Chairman, Department of Applied Mathematics and Statistics, State University of New York, Stony Brook Joseph Kadane, Professor of Statistics, Carnegie-Mellon University, Pennsylvania Diane Lambert, AT&T Bell Laboratories, Murray Hill, New Jersey Gerald J. Lieberman, Professor of Operations Research and Statistics, Stanford University, California Jerome Sacks, Head, Department of Statistics, University of Illinois Shmuel Winograd, Director, Mathematical Sciences Department, IBM Thomas J. Watson Research Center, New York William Eddy, Professor of Statistics, Carnegie-Mellon University, Pennsylvania; ex officio Staff Lawrence H. Cox, Director
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics MATHEMATICAL SCIENCES EDUCATION BOARD Alvin W. Trivelpiece (Chairman), Director, Oak Ridge National Laboratory, Tennessee Iris M. Carl (Vice Chairman), President, National Council of Teachers of Mathematics, Director of Mathematics, Houston Independent School District, Texas Lillian C. Barna, Superintendent of Schools, Tacoma Public Schools, Washington Lida K. Barrett, Past President, Mathematical Association of America, Dean, College of Arts and Sciences, Mississippi State University Maria A. Berriozabal, Councilwoman, City of San Antonio, Texas Constance Clayton, Superintendent of Schools, School District of Philadelphia, Pennsylvania Loring Coes III, Chairman, Department of Mathematics, Rocky Hill School, Rhode Island David K. Cohen, Interim Dean of Education, Professor of Education and Social Policy, Michigan State University, Liaison from Commission on Behavioral and Social Sciences and Education Nancy S. Cole, Executive Vice President, Educational Testing Service, New Jersey Rita R. Colwell, Director, Maryland Biotechnology Institute, Professor of Microbiology, College Park, Maryland David L. Crippens, Senior Vice President, KCET-TV Educational Enterprises, Inc., California Philip A. Daro, Director, California Mathematics Project, University of California, Berkeley Daniel T. Dolan, Mathematics and Computer Education Specialist, Montana Office of Public Instruction Paula B. Duckett, Elementary Mathematics Specialist, River Terrace Community School, Washington, D.C. Joan Duea, Elementary School Teacher, Price Laboratory School, Professor of Education, University of Northern Iowa
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics Joseph W. Duncan, Corporate Vice President and Chief Economist, The Dun & Bradstreet Corporation, New York Wade Ellis, Jr., Mathematics Instructor, West Valley College, California Ramanathan Gnanadesikan, Assistant Vice President, Mathematical, Communication & Computer Sciences Research Laboratory, Bell Communications Research, New Jersey Jackie Goldberg, President, Board of Education, Los Angeles Unified School District, California Norbert S. Hill, Jr., Executive Director, American Indian Science and Engineering Society, Colorado Harvey Keynes, Professor of Mathematics, Director, Minnesota Mathematics Mobilization, University of Minnesota Richard S. Lindzen, Sloan Professor of Meteorology, Massachusetts Institute of Technology Ruth McMullin, Past President, John Wiley & Sons, Westport, Connecticut Steven P. Meiring, Mathematics Specialist, Ohio State Department of Education Jose P. Mestre, Associate Professor of Physics, University of Massachusetts Calvin C. Moore, Associate Vice President, Academic Affairs, University of California, Berkeley Jo Ann Mosier, Mathematics Teacher, Fairdale High School, Kentucky Robert Nielsen, Assistant to the President for Higher Education, American Federation of Teachers, Washington, D.C. Leslie Hiles Paoletti, Chairman, Mathematics and Computer Science, Choate Rosemary Hall, Connecticut Isadore M. Singer, Institute Professor, Massachusetts Institute of Technology Lynn Arthur Steen, Professor of Mathematics, St. Olaf College, Minnesota William P. Thurston, Professor of Mathematics, Princeton University, New Jersey John S. Toll, President, Universities Research Association, Inc., Washington, D.C., Chancellor Emeritus and Professor of Physics, University of Maryland
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics P. Uri Treisman, Director, Charles A. Dana Center for Mathematics and Science Education, University of California, Berkeley Manya S. Ungar, Past President, National Parents and Teachers Association, Scotch Plains, New Jersey Zalman Usiskin, Director, School Mathematics Project, Professor of Education, University of Chicago John B. Walsh, Vice President, Research and Engineering Programs, Boeing Aerospace and Electronics, Washington Larry D. Williams, Chairman, Department of Mathematics, Eutaw High School, Alabama James J. Wynne, Manager, Biological and Molecular Science, IBM Thomas J. Watson Research Center, New York Staff Kenneth M. Hoffman, Executive Director through February 1991 Ray C. Shiflett, Executive Director Michael H. Clapp, Associate Executive Director
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Moving Beyond Myths: Revitalizing Undergraduate Mathematics ACKNOWLEDGMENTS FOR MOVING BEYOND MYTHS AMERICAN MATHEMATICAL SOCIETY Janene Winter, Composition Ralph Youngen, Composition Julie Wilczek, Composition NATIONAL ACADEMY PRESS Francesca Moghari, Cover Design Susan England, Graphic Design James Butler, Graphics Dorothy Lewis, Production Carla McCullough, Production COMMITTEE ON THE MATHEMATICAL SCIENCES IN THE YEAR 2000 James Voytuk, Project Director Craig Hicks, Senior Editorial Assistant MATHEMATICAL SCIENCES EDUCATION BOARD Michael Clapp, Associate Executive Director Linda Rosen, Associate Director for Policy Studies COMPOSITION COURTESY OF American Mathematical Society FINANCIAL SUPPORT We also wish to thank the National Science Foundation and the National Security Agency for their generous support and the Department of Education and the National Aeronautics and Space Administration for additional support.
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