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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 R2
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
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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
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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
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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
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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
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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
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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 R9
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
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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
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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
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EVERYBODY COUNTS
A Report to the Nation
on t be
Future of Mathematics Education
OCR for page R14
