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
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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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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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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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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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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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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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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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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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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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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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.