Cover Image

PAPERBACK
$8.95



View/Hide Left Panel
Click for next page ( R2


The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page R1
EVERYBODY COUNTS A Report to the Nation on the Future of Mathematics Education Mathematical Sciences Education Board Boarc! on Mathematical Sciences Committee on the Mathematical Sciences in the Year 2000 National Research Council NATIONAL ACADEMY PRESS Washington, D.C. 1989

OCR for page R1
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 Research 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 Research 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 ofthe board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point in the Research Council for 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 Resources. The Committee on the \iathematical 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. Publication and dissemination of this book were supported by grants from Exxon Education Foundation, National Aeronautics and Space Administration, National Institutes of Health, National Research Council, National Science Foundation (Directorates for Biological and Behavioral and Social Sciences; Computer and Information Science and Engineering; Engineering; Geosciences; Math- ematical and Physical Sciences; and Science and Engineer- ing Education), Shell Oil Company Foundation, The Teagle Foundation, U.S. Department of Defense (Air Force Office of Scientific Research; Army Research Office; National Security Agency; Office of Naval Research), and U.S. Department of Energy. The observations made herein do not necessarily reflect the views of the grantors. Library of Congress Cataloging-in-Publication Data Everybody Counts: A Report to the Nation on the Future of Mathematics Education / Board on Mathematical Sci- ences (and] Mathematical Sciences Education Board, National Research Council. p. cm. Bibliography: p. ISBN 0-309-03977-0 1. Mathematics-Study and teaching-United States. I. National Research Council (U.S.~. Board on Mathe- matical Sciences. II. National Research Council (U.S.~. Mathematical Sciences Education Board. QA13.E94 1989 510'.7'1073-dcl9 Copyright ~ 1989 by the National Academy of Sciences 88-37684 CIP 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 National Academy Press, 2101 Constitution Avenue, N.W., Washington, D.C. 20418. Summaries of this report may be obtained from the Mathe- matical Sciences Education Board, 818 Connecticut Avenue, N.W., Washington, D.C.20006. Printed in the United States of America First Printing, January 1989 Second Printing. March 1989 Third Printing. June 1989 Fourth Printing. October 1989 Fifth Printing, December 1989 Sixth Printing, March 1990 Seventh Printing, March 1991 Eighth Printing, July 1992 Ninth Printing. April 1995

OCR for page R1
FOREWORD In response to the urgent national need to revitalize mathematics and science education, the National Research Council (NRC) has undertaken an examination of U.S. mathematics education from kinder- garten through graduate study. Major studies being conducted for the NRC by the Mathematical Sciences Education Board, the Board on Mathematical Sciences, and their joint Committee on the Mathematical Sciences in the Year 2000 have the goals of identifying weaknesses in the present system as well as strengths to build on for the future. Everybody Counts is a public preface to the work of these three NRC units and other national organi- zations with which the NRC is cooperating in the revitalization of mathematics education. It outlines in stark terms the seriousness of the situation facing our country emphasizing how crucial it is for science , . . . . ~ ~ .. . . . ~ ~ . . . . . . tecnno~ogy, and the economy ot the nation that all students receive h~gh-quality education in mathematics. Yet, it goes well beyond this. Numerous reports have appeared in recent years analyzing the problems of American education. Every- bod~y Counts could easily be just one more report, pointing to problems and recommending that somebody, somewhere, should do something. Several features distinguish this report from others: It examines mathematics education as all one system, from kindergarten through graduate school. It treats all the major components of the system, from curricula, teaching, and assessment to human resources and national needs. It does not merely identify problems, but also charts a general course for the future, outlining a national strategy for pursuing that course. . It is not the final report of a commission, but the beginning of a process through which teachers, state and local authorities, and the varied constituencies of mathematics education can draw together in a sustained revitalization effort. This report reflects the thinking of 70 leading Americans, among them classroom teachers; college and university faculty and administrators; research mathematicians and statisticians; scientists and engineers; mathematics supervisors; school principals; school superintendents; chief state school officers; school board members; members of state and local governments; and leaders of parent groups, business, and industry. It also signals to the nation that acting through the National Research Council the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine are prepared to participate actively in the long-term work of rebuilding mathematics education in the United States. Few other tasks are more important to our children and to our nation. Cams Frank Press President, National Academy of Sciences Chairman, National Research Council

OCR for page R1
MATHEMATICAL SCIENCES EDUCATION BOARD Shirley Ae Hill (Chairman), Curators' Professor of Mathematics and Education, University of Missouri, Kansas City J. Myron Atkin, Professor, School of Education, Stanford University Lillian Barna, Superintendent of Schools, Tacoma Public Schools, Washington C. Diane Bishop, Superintendent of Public Instruction, State of Arizona Iris M. Carl, Elementary Mathematics Instructional Supervisor, Houston Independent School District, 1 exas Constance Clayton, Superintendent of Schools, School District of Philadelphia John A. Dossey, Professor of Mathematics, Illinois State University Joan Duea, Elementary School Teacher, Price Laboratory School, and Professor of Education, University of Northern Iowa Wade Ellis, Or., Mathematics Instructor, West Valley College Shirley M. Frye, Director of Curriculum and Instruction, Scottsdale School District, Arizona Andrew M. Gleason, Hollis Professor of Mathematicks and Natural Philosophy, Harvard University David R. Johnson, Chairman, Department of Mathematics, Nicolet High School, Glendale, Wisconsin Donald L. Kreider, Vice Chairman, Mathematics and Computer Science Department, Dartmouth College Martin D. Kruskal, Professor of Mathematics and of Astrophysical Sciences, Princeton University Katherine P. Layton, Mathematics Teacher, Beverly Hills High School, California Steven J. Leinwand, Mathematics Consultant, Connecticut State Department of Education Richard S. Lindzen, Sloan Professor of Meteorology, Massachusetts Institute of Technology Gail Lowe, Principal, Acacia Elementary School, Thousand Oaks, California Steven P. Meiring, Mathematics Specialist, Ohio State Department of Education Jose P. Mestre, Associate Professor of Physics, University of Massachusetts Leslie Paoletti, Chairman, Department of Mathematics and Computer Science, Choate Rosemary Hall, Connecticut Henry O. Pollak, Assistant Vice President, Mathematical, Communications and Computer Sciences Re- search Laboratory, Bell Communications Research, New Jersey (retired) Anthony Ralston, Professor of Computer Science and Mathematics, State University of New York, Buffalo Lauren B. Resnick, Director, Learning Research and Development Center, University of Pittsburgh; liaison with the Commission on Behavioral and Social Sciences and Education, National Research Council Yolanda Rodriguez, Middle School Teacher, Martin Luther King School, Cambridge, Massachusetts Frederick A. Roesch, Senior Vice President, Global Electronic Marketing, Citibank, N.A., New York Thomas A. Romberg, Professor, Department of Curriculum and Instruction, University of Wisconsin, Madison 1V

OCR for page R1
Ted Sanders, Superintendent of Education, State of Illinois Isadore M. Singer, Institute Professor, Department of Mathematics, Massachusetts Institute of Technology Lynn Arthur Steen, Professor of Mathematics, St. Olaf College Manya S. Ungar, President, National Congress of Parents and Teachers Zalman Usiskin, Professor of Education, University of Chicago Nellie C. Well, Past President, National School Boards Association Guido L. Weiss, Elinor Anheuser Professor of Mathematics, Washington University; liaison with the Commission on Physical Sciences, Mathematics, and Resources, National Research Council Staff Marcia P. Sward, Executive Director John R. B.-Clement, Senior Program Officer Audrey Pendergast, Program Officer/Editor Linda P. Rosen, Program Officer Julie Kraman, Administrative Specialist Susan Adams, Administrative Secretary Grace Kulnarong, Administrative Secretary Joan Rood, Administrative Secretary Claudette Brown, Senior Secretary Consultants Kenneth M. Hoffman, Senior Adviser Beverly J. Anderson, Minority Affairs Jane Heckler, Dissemination Kathleen Holmay, Public Information Ann P. Kahn, Public Affairs Bernice Kastner, Education Research John H. Lawson, Education Agencies v

OCR for page R1
BOARD ON MATHEMATICAL SCIENCES Phillip A. Griffiths (Chairman), Provost and James B. Duke Professor of Mathematics, Duke University Peter Bickel, Professor of Statistics, University of California, Berkeley Herman Chernoff, Professor of Statistics, Harvard University Ronald G. Douglas, Dean, College of Physical Sciences and Mathematics, State University of New York, Stony Brook David Eddy, Professor of Health Policy and Management, Duke University Frederick W. Gehring, Professor of Mathematics, University of Michigan James Glimm, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University William Jaco, Executive Director, American Mathematical Society Joseph Kadane, Professor of Statistics, Carnegie-Mellon University Gerald J. Lieberman, Professor of Operations Research and Statistics, Stanford University Cathleen Se Morawetz, Director, Courant Institute of Mathematical Sciences, New York University Alan Newell, Chairman, Department of Mathematics, University of Arizona Guido L. Weiss, Elinor Anheuser Professor of Mathematics, Washington University Shmuel Winograd, Director, Mathematical Sciences Department, IBM Thomas J. Watson Research Center Morris DeGroot, Professor of Statistics, Carnegie-Mellon University; ex officio Staff Lawrence H. Cox, Director Seymour Selig, Staff Officer Ruth O'Brien, Staff Associate Deborah Reischman, Administrative Secretary Consultants William Rosen, Government Programs Robert Smythe, Statistical Science V1

OCR for page R1
COMMITTEE ON THE MATHEMATICAL SCIENCES IN THE YEAR 2000 J. Fred Bucy (Chairman), Chief Executive Officer, Texas Instruments Incorporated (retired) Lida K. Barrett, Dean, College of Arts and Sciences, Mississippi State University Maria Antonietta Berriozabal, Councilwoman, City of San Antonio Ernest L. Boyer, President, Carnegie Foundation for the Advancement of Teaching William Browder, Professor of Mathematics, Princeton University Rita R. Colwell, Director, Maryland Biotechnology Institute, University of Maryland John M. Deutch, Provost, Massachusetts Institute of Technology Ronald G. Douglas, Dean, College of Physical Sciences and Mathematics, State University of New York, Stony Brook Patricia A. Dyer, Vice President for Academic Affairs, Palm Beach Junior College Lloyd C. Elam, Professor of Psychiatry, Meharry Medical College Ramesh A. Gangolli, Professor of Mathematics, University of Washington William E. Kirwan, Vice Chancellor for Academic Affairs and Provost, University of Maryland Nancy J. Kopell, Professor of Mathematics, Boston University Donald W. Marquardt, Consultant Manager, E. I. du Pont de Nemours and Company David S. Moore, Professor of Statistics, Purdue University Jaime Oaxaca, Vice President, Northrop Corporation 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 Lynn Arthur Steen, Professor of Mathematics, St. Olaf College David R. Johnson, Chairman, Department of Mathematics, Nicolet High School, Glendale, Wisconsin; liaison with the Mathematical Sciences Education Board Staff James A. Voytuk, Project Director Bernard L. Madison, Project Director (through August 1988) Therese A. Hart, Research Associate . . V11

OCR for page R1
PREFA CE As science and technology have come to influence all aspects of life, from health and environment to financial affairs and national defense, so mathematics has come to be of vital importance to the educational agenda of our nation. Mathematics is the foundation of science and technology. Increasingly, it plays a major role in determining the strength of the nation's work force. Yet, evidence all around us shows that American students are not fulfilling their potential in mathematics education. Three of every four Americans stop studying mathematics before completing career or job prerequisites. Most students leave school without sufficient preparation in mathematics to cope with either on-thejob demands for problem-solving or college expectations for mathematical literacy. Industry, universities, and the armed forces are thus burdened by extensive and costly demands for remedial education. Our country cannot afford continuing generations of students limited by lack of mathematical power to second-class status in the society in which they live. It cannot afford to weaken its preeminent position in science and technology. The three units which we chair at the National Research Council have committed themselves to reme- dying this situation. As a first step, we commissioned Lynn Arthur Steen, professor of mathematics at St. Olaf College, to write a synthesis of the thinking developed through three years of analysis by the Math- ematical Sciences Education Board, two years of involvement by the Board on Mathematical Sciences (which deals with research), and the first year of work by the Committee on the Mathematical Sciences in the Year 2000, which is concerned with college and university mathematics. Everybody Counts describes various forces that impinge on mathematics and on education computers, research, demography, competitiveness and explains how each is a major force for change, and yet interactions among these forces produce a system that is peculiarly resistant to change. The problems are complex. While the facts are indisputable, there is not complete unanimity on interpretations, priorities, or proposed solutions, even within the scientific community. Nevertheless, change must come. When one compares the potential return on investment in education with the consequences of inaction, it becomes clear that we as a nation have no choice: we must improve the ways our children learn mathematics. Not merely a cry for reform, Everybocly Counts points to specific transitions which our nation's schools and colleges must make in their mathematics programs over the next two decades if they are to meet the needs of students and the country as well as the accelerating momentum of a grass-roots reform effort already well under way. It argues for development of a national support structure to undergird that effort and describes major pieces of such a structure to be put in place over the next year. Its intent is to seek a broad consensus on a national strategy for getting the job done. Throughout, it reflects our prime concern that, whatever any of us do as individuals or through organizations to improve education, we see our role as supporting the efforts of the central person who can bring about meaningful and lasting change: the teacher. . . . vail

OCR for page R1
We take this opportunity to express our gratitude to Lynn Steen for applying his considerable writing talents to the task of creating Everybody Counts. He has described in eloquent language the complex issues of mathematics education with which we shall be grappling for years to come. of/ Shirley A. Hill Chairman, Mathematical Sciences Education Board Curators' Professor of Mathematics and Education University of Missouri, Kansas City Yet A, ~ Phillip A. Griffiths Chairman, Board on Mathematical Sciences Provost and James B. Duke Professor of Mathematics Duke University J. Fred Bucy Chairman, Committee on the Mathematical Sciences in the Year 2000 Chief Executive Officer Texas Instruments Incorporated (retired) 1X

OCR for page R1
CONTENTS OPPORTUNITY . . . tapping the power of mathematics Context for Change 2 Mathematics for Tomorrow 4 A Pump, Not a Filter 6 Numeracy 7 Attitudes 9 Goals 1 1 Students at Risk 12 HUMAN RESOURCES Demographic Trends 18 Minorities 20 Women 21 Disabled Persons 23 Graduate Students 24 Supply and Demand 26 Equity and Excellence 28 1 . . investing in intellectual capital ~ 7 MATHEMATICS . . . searching for patterns 31 Our Invisible Culture 32 From Abstraction to Application 33 Computers 36 The Mathematical Community 37 Undergraduate Mathematics 39 CURRICULUM . . . developing mathematical power 43 Philosophy 43 Standards 45 Elementary Education 46 Secondary Education 48 Higher Education 51 x

OCR for page R1
TEACHING . . . learning through involvement Understanding Mathematics 57 Learning Mathematics 58 Engaging Students 59 Impact of Computers 61 Education of Teachers 63 Resources 66 Assessment 67 CHANGE . . . mobilizing for curricular reform Challenges 73 Counterproductive Beliefs 75 The American Way 77 Modern Mathematics 78 Lessons from the Past 79 Transitions 81 ACTION . . . moving into the 21st census National Goals 88 Reaching Consensus 89 National Strategy 90 Support Structures 91 Leadership 93 Taking Action 95 REFERENCES . . . documenting the challenge Notes 99 Sources 102 Bibliography 104 57 73 87 99 X1

OCR for page R1

OCR for page R1
EVERYBODY COUNTS A Report to the Nation on t be Future of Mathematics Education

OCR for page R1