Dear Secretary Riley:
In early October of 1999, the United States Department of Education endorsed ten K-12 mathematics programs by describing them as "exemplary" or "promising." There are five programs in each category. The "exemplary" programs announced by the Department of Education are:
These mathematics programs are listed and described on the government web site: http://www.enc.org/ed/exemplary/
The Expert Panel that made the final decisions did not include active research mathematicians. Expert Panel members originally included former NSF Assistant Director, Luther Williams, and former President of the National Council of Teachers of Mathematics, Jack Price. A list of current Expert Panel members is given at: http://www.ed.gov/offices/OERI/ORAD/KAD/expert_panel/mathmemb.html
It is not likely that the mainstream views of practicing mathematicians and scientists were shared by those who designed the criteria for selection of "exemplary" and "promising" mathematics curricula. For example, the strong views about arithmetic algorithms expressed by one of the Expert Panel members, Steven Leinwand, are not widely held within the mathematics and scientific communities. In an article entitled, "It's Time To Abandon Computational Algorithms," published February 9, 1994, in Education Week on the Web, he wrote:
"It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous." (http://www.edweek.org/ew/1994/20lein.h13)
In sharp contrast, a committee of the American Mathematical Society (AMS), formed for the purpose of representing the views of the AMS to the National Council of Teachers of Mathematics, published a report which stressed the mathematical significance of the arithmetic algorithms, as well as addressing other mathematical issues. This report, published in the February 1998 issue of the Notices of the American Mathematical Society, includes the statement:
"We would like to emphasize that the standard algorithms of arithmetic are more than just 'ways to get the answer' -- that is, they have theoretical as well as practical significance. For one thing, all the algorithms of arithmetic are preparatory for algebra, since there are (again, not by accident, but by virtue of the construction of the decimal system) strong analogies between arithmetic of ordinary numbers and arithmetic of polynomials."
Even before the endorsements by the Department of Education were announced, mathematicians and scientists from leading universities had already expressed opposition to several of the programs listed above and had pointed out serious mathematical shortcomings in them. The following criticisms, while not exhaustive, illustrate the level of opposition to the Department of Education's recommended mathematics programs by respected scholars:
R. James Milgram, professor of mathematics at Stanford University, is the author of "An Evaluation of CMP," "A Preliminary Analysis of SAT-I Mathematics Data for IMP Schools in California," and "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later." This latter paper is based on a statistical survey undertaken by Gregory Bachelis, professor of mathematics at Wayne State University. Each of these papers identifies serious shortcomings in the mathematics programs: CMP, Core-Plus, and IMP. Professor Milgram's papers are posted at: ftp://math.stanford.edu/pub/papers/milgram/
Martin Scharlemann, while chairman of the Department of Mathematics at the University of California at Santa Barbara, wrote an open letter deeply critical of the K-6 curriculum MathLand, identified as "promising" by the U. S. Department of Education. In his letter, Professor Scharlemann explains that the standard multiplication algorithm for numbers is not explained in MathLand. Specifically he states, "Astonishing but true -- MathLand does not even mention to its students the standard method of doing multiplication." The letter is posted at: http://mathematicallycorrect.com/ml1.htm
Betty Tsang, research physicist at Michigan State University, has posted detailed criticisms of the Connected Mathematics Project on her web site at: http://www.nscl.msu.edu/~tsang/CMP/cmp.html
Hung-Hsi Wu, professor of mathematics at the University of California at Berkeley, has written a general critique of these recent curricula ("The mathematics education reform: Why you should be concerned and what you can do", American Mathematical Monthly 104(1997), 946-954) and a detailed review of one of the "exemplary" curricula, IMP ("Review of Interactive Mathematics Program (IMP) at Berkeley High School", http://www.math.berkeley.edu/~wu). He is concerned about the general lack of careful attention to mathematical substance in the newer offerings.
Sincerely,
David Klein
Professor of Mathematics
California State University, Northridge
Richard Askey
John Bascom Professor of Mathematics
University of Wisconsin at Madison
R. James Milgram
Professor of Mathematics
Stanford University
Hung-Hsi Wu
Professor of Mathematics
University of California, Berkeley
Martin Scharlemann
Professor of Mathematics
University of California, Santa Barbara
Professor Betty Tsang
National Superconducting Cyclotron Laboratory
Michigan State University
The following endorsements are listed in alphabetical order.
William W. Adams
Professor of Mathematics
University of Maryland, College Park
Alejandro Adem
Professor & Chair
Department of Mathematics
University of Wisconsin-Madison
Max K. Agoston
Associate Professor
Department of Mathematics and Computer Science
San Jose State University
Henry L. Alder
Professor of Mathematics
University of California, Davis
Former member of the California Board of Education
Former President of the Mathematical Association of America
Kenneth Alexander
Professor of Mathematics
University of Southern California
Frank B. Allen
Professor of Mathematics Emeritus, Elmhurst College
Former President, National Council of Teachers of Mathematics
George E. Andrews
Evan Pugh Professor of Mathematics
Pennsylvania State University
Gregory F. Bachelis
Professor of Mathematics
Wayne State University
Michael Beeson
Professor of Mathematics and Computer Science
San Jose State University
George Biriuk
Professor of Mathmatics
California State University, Northridge
Wayne Bishop
Professor of Mathematics
California State University, Los Angeles
Gary J. Blanchard
Professor of Chemistry
Michigan State University
Charles C. Blatchley, Chair
Department of Physics
Pittsburg State University
Michael N. Bleicher
Professor Emeritus,
University of Wisconsin - Madison
Chair, Department of Mathematical Sciences
Clark Atlanta University
John C. Bowman
Vice-President
National Association of Professional Educators
Khristo N. Boyadzhiev
Professor of Mathematics
Ohio Northern University
Bart Braden
Professor of Mathematics
Northern Kentucky University
Stephen Breen
Associate Professor
Department of Mathematics
California State University, Northridge
David A. Buchsbaum
Professor of Mathematics, Emeritus
Brandeis University
Frank Burk
Professor of Mathematics
California State University, Chico
Ana Cristina Cadavid
Professor of Physics
California State University, Northridge
Gunnar Carlsson
Professor of Mathematics
Stanford University
Douglas Carnine
Professor of Education
University of Oregon
Director of the National Center to Improve the Tools of Educators
Mei-Chu Chang
Professor of Mathematics
University of California, Riverside
Sun-Yung Alice Chang
Professor of Mathematics
Princeton University and UCLA
Jeff Cheeger
Professor of Mathematics
Courant Institute, NYU
Orin Chein
Professor of Mathematics
Temple University
Steven Chu
Theodore and Francis Geballe Professor of Physics and Applied Physics
Chair of Physics
Stanford University
1997 Nobel Prize for Physics
Fredrick Cohen
Professor of Mathematics
University of Rochester
Marshall M. Cohen
Professor, Mathematics
Cornell University
Paul Cohen
Professor of Mathematics
Stanford University
Ralph Cohen
Professor of Mathematics
Stanford University
Peter Collas
Professor of Physics
California State University, Northridge
Bruce Conrad
Associate Dean College of Science and Technology
Temple University
Daryl Cooper
Professor of Mathematics
University of California, Santa Barbara
Robert M. Costrell
Director of Research and Development
Executive Office for Administration and Finance
Commonwealth of Massachusetts
Professor of Economics
University of Massachusetts at Amherst
George K. Cunningham, Professor
Department of Educational and Counseling Psychology
University of Louisville
Jerome Dancis
Associate Professor of Mathematics
University of Maryland
Pawel Danielewicz
Professor, Department of Physics and Astronomy
Michigan State University
Ernest Davis
Associate Professor of Computer Science
New York University
Martin Davis
Professor Emeritus of Mathematics and Computer Science
Courant Institute
New York University
Jane M. Day
Professor of Mathematics and Computer Science
San Jose State University
Carl de Boor
Professor of Mathematics and Computer Sciences
University of Wisconsin-Madison
Percy Deift
Professor of Mathematics
Courant Institute
New York University
John de Pillis
Professor of Mathematics
University of California, Riverside
Robert Dewar
Professor of Computer Science
Courant Institute of Mathematical Sciences
Former Chair of Computer Science
Former Associate Director of the Courant Institute
New York University
Jim Dole
Professor and Chair of Biology
California State University, Northridge
Josef Dorfmeister
Professor of Mathematics
University of Kansas
Bruce T. Draine
Professor of Astrophysical Sciences
Princeton University
Bruce K. Driver
Professor of Mathematics
University of California, San Diego
Vladimir Drobot
Professor
Department of Mathematics and Computer Science
San Jose State University
William Duke
Professor of Mathematics
Rutgers University
John R. Durbin
Professor of Mathematics
Secretary of the General Faculty
The University of Texas at Austin
Peter Duren
Professor of Mathematics
University of Michigan
Mark Dykman
Professor of Physics
Michigan State University
Allan L. Edelson
Professor of Mathematics and
Vice Chair for Graduate Affairs
Department of Mathematics
University of California, Davis
Yakov Eliashberg
Professor of Mathematics
Stanford University
Richard H. Escobales, Jr.
Professor of Mathematics
Canisius College, Buffalo, NY
Lawrence C. Evans
Professor of Mathematics
University of California, Berkeley
Bill Evers
Research Fellow
Hoover Institution
Stanford University
California State Academic Standards Commission
Barry Fagin
Professor of Computer Science
US Air Force Academy
George Farkas
Professor of Psychology
Director, Center for Education and Social Policy
University of Texas at Dallas
Editor, Rose Monograph Series of the American Sociological Association
Robert Fefferman
Louis Block Professor of Mathematics
Chairman, Mathematics Department
University of Chicago
Chester E. Finn, Jr.
John M. Olin Fellow
Manhattan Institute
Former U.S. Assistant Secretary of Education
Ronald Fintushel
University Distinguished Professor of Mathematics
Michigan State University
Michael E. Fisher
Distinguished Univeristy Professor & USM Regents Professor
Insitute of Physical Sciences and Technology
University of Maryland
Wolf Prize in Physics, 1980
Patrick M. Fitzpatrick
Professor and Chair
Department of Mathematics
University of Maryland
Yuval Flicker
Professor of Mathematics
The Ohio State University
Gerald Folland
Professor of Mathematics
University of Washington, Seattle
Daniel S. Freed
Professor of Mathematics
University of Texas at Austin
Dmitry Fuchs
Professor
Department of Mathematics
University of California, Davis
David C. Geary
Professor of Psychology
University of Missouri
Samuel Gitler
Professor of Mathematics
University of Rochester
Sheldon Lee Glashow
Higgins Professor of Physics
Harvard University
1979 Nobel Prize in Physics
Simon M. Goberstein
Professor of Mathematics
California State University, Chico
Steve Gonek
Professor of Mathematics
University of Rochester
Jeremy Goodman
Department of Astrophysical Sciences
Princeton University
Co-founder, Princeton Charter School
Jonathan Goodman
Professor of Mathematics
Courant Institute of Mathematical Sciences
New York University
David Goss
Professor of Mathematics
The Ohio State University
Steven R. Goss
Chairman of the Board
Arizona Scholarship Fund
Mechanical Engineer - Raytheon Systems
Christopher M. Gould
Professor of Physics
Department of Physics and Astronomy
University of Southern California
Mark L. Green
Professor of Mathematics
University of California at Los Angeles
Benedict H. Gross
Leverett Professor of Mathematics
Harvard University
Leonard Gross
Professor of Mathematics
Cornell University
Paul R. Gross
University Professor of Life Sciences (emeritus)
University of Virginia
Dina Gutkowicz-Krusin
Principal Scientist
Electro-Optical Sciences, Inc.
Irvington, New York
Kamel Haddad
Associate Professor of Mathematics
California State University, Bakersfield
Deborah Tepper Haimo
Visiting Scholar
University of California, San Diego
Trustee of Association of Members of the Institute for Advanced Study
at Princeton
Former President of the Mathematical Association of America
Joel Hass
Professor of Mathematics
University of California, Davis
David F. Hayes
Professor of Mathematics and Computer Science
San Jose State University
Dr. Adrian D. Herzog
Chairman, Deprtment of Physics and Astronomy
California State University, Northridge
Member Content Review Panel for California Science Materials
Richard O. Hill
Professor of Mathematics
Michigan State University
E. D. Hirsch, Jr.
University Professor of Education and Humanities
University of Virginia
Dr. Hanna J. Hoffman
Senior Laser Scientist
IRVision, Inc.
San Jose, California
Douglas L. Inman
Research Professor of Oceanography
Scripps Institution of Oceanography
University of California, San Diego
George Jennings
Professor of Mathematics
California State University, Dominguez Hills
Svetlana Jitomirskaya
Associate Professor of Mathematics
University of California, Irvine
Peter W. Jones
Professor and Chair of Mathematics
Yale University
Vaughan Jones
Professor of Mathematics
Mathematics Department
UC Berkeley
Peter J. Kahn
Professor of Mathematics and
Senior Associate Dean
College of Arts and Sciences
Cornell University
Sheldon Kamienny
Professor of Mathematics
University of Southern California
Ilya Kapovich
Assistant Professor of Mathematics
Rutgers, The State University of New Jersey
Hidefumi Katsuura
Professor of Mathematics
San Jose State University
Jerry Kazdan
Professor of Mathematics
Univerity of Pennsylvania
David Kazhdan
Professor of Mathematics
Harvard University
Lisa Graham Keegan
Superintendent of Public Education
State of Arizona
Sharad Keny
Professor of Mathematics
Department of Mathematics
Whittier College
Steve Kerckhoff
Professor of Mathematics
Stanford University
Robion C. Kirby
Professor of Mathematics
University of California at Berkeley
Steven G. Krantz
Chairman and Professor
Department of Mathematics
Washington University in St. Louis
St. Louis, Missouri
Sergiu Klainerman
Professor of Mathematics
Princeton University
Abel Klein
Professor of Mathematics
University of California, Irvine
Kurt Kreith
Professor Emeritus of Mathematics
University of California at Davis
Boris A. Kushner
Professor of Mathematics
University of Pittsburgh at Johnstown
Tsit-Yuen Lam
Professor of Mathematics
University of California at Berkeley
Serge Lang
Professor of Mathematics
Yale University
Benedict Leimkuhler
Associate Professor of Mathematics
University of Kansas
and Fellow, Kansas Center for Advanced Scientific Computing
Norman Levitt
Professor of Mathematics
Rutgers University, New Brunswick
Jun Li
Associate Professor of Mathematics
Stanford University
Peter Li
Professor and Chair of Mathematics
University of California, Irvine
Alexander Lichtman
Professor of Mathematics
University of Wisconsin-Parkside
Seymour Lipschutz
Professor of Mathematics
Temple University
Mei-Ling Liu
Professor of Computer Science
California Polytechnic State University
Darren Long
Professor of Mathematics
University of California, Santa Barbara
John Lott
Professor of Mathematics
University of Michigan - Ann Arbor
Tom Loveless
Director, Brown Center on Education Policy
The Brookings Institution
Washington, DC
Steve P. Lund
Professor of Geophysics
Department of Earth Sciences
University of Southern California
William G. Lynch
Professor, Department of Physics
Michigan State University
Michael G. Lyons
Consulting Assoc. Prof
Management Science and Engineering
Stanford University
Saunders Mac Lane
Max Mason Distinguished Service Professor, Emeritus
University of Chicago
National Medal of Science, 1989
Former Vice President, National Academy of Sciences, 1973-1981
Former Member, National Science Board, 1973-1979
Michael Maller
Associate Professor of Mathematics
Queens College of CUNY
Igor Malyshev
Professor of Mathematics
San Jose State University
Edward Matzdorff
Professor of Mathematics
California State University, Chico
Michael May
Co-Director, Center for International Security and Arms Control
(Research) Professor
Department of Engineering-Economic Systems and Operations Research
Stanford University
Rafe Mazzeo
Professor of Mathematics
Stanford University
John McCarthy
Professor of Computer Science
Stanford University
John D. McCarthy
Professor of Mathematics
Michigan State University
John E. McCarthy
Professor of Mathematics
Washington University
Henry P. McKean
Professor of Mathematics
Courant Institute
New York University
Michael McKeown
Professor of Medical Science
Program in Molecular Biology, Cell Biology and Biochemistry
Brown University
Former Member - San Diego Unified Math Standards Committee
Former Member - Superintendent's Math Advisory Committee, San Diego
Co-Founder Mathematically Correct
Marc Mehlman
Associate Professor of Mathematics
University of Pittsburgh, Johnstown
Adrian L. Melott
Professor of Physics and Astronomy
University of Kansas
Aida Metzenberg
Assistant Professor of Biology
California State University, Northridge
Stan Metzenberg
Assistant Professor of Biology
California State University, Northridge
M. Eugene Meyer
Professor of Mathematics
California State University, Chico
James E. Midgley
Professor of Physics, Emeritus
University of Texas at Dallas
Dragan Milicic
Professor of Mathematics
University of Utah
Henri Moscovici
Professor of Mathematics
The Ohio State University
Clay Mathematics Institute Scholar
Govind S. Mudholkar
Professor of Statistics and Biostatistics
University of Rochester
Gregory Naber
Professor of Mathematics
California State University, Chico
Bruno Nachtergaele
Associate Professor of Mathematics
University of California, Davis
Chiara R. Nappi
Visiting Professor of Physics
University of Southern California
On leave from the
Institute for Advanced Study at Princeton
Anil Nerode
Goldwin Smith Professor of Mathematics
Cornell University
Charles M. Newman
Professor and Chair of Mathematics
Courant Institute of Mathematical Sciences
New York University
Louis Nirenberg
Professor of Mathematics
Courant Institute, New York University
Maria Helena Noronha
Professor of Mathematics
California State University, Northridge
Robert H. O'Bannon, Ph.D.
Professor, Department of Natural Sciences and Mathematics
Lee University
Cleveland, TN
Richard Palais
Professor of Mathematics, Emeritus
Brandeis University
Dimitri A. Papanastassiou
Faculty Associate in Geochemistry
Caltech
Thomas H. Parker
Professor of Mathematics
Michigan State University
Donald S. Passman
Professor of Mathematics
University of Wisconsin at Madison
Peter Petersen
Undergraduate Vice Chair and Professor of Mathematics
Department of Mathematics
UCLA
Steven Pinker
Professor of Psychology
Department of Brain and Cognitive Sciences
Massachusetts Institute of Technology
Author of How the Mind Works
Jacek Polewczak
Professor of Mathematics
California State University, Northridge
Dr. Ned Price
Mathematics Department
Framingham State College
Framingham,Ma.
David Protas
Professor of Mathematics
California State University, Northridge
Ralph A. Raimi
Professor Emeritus of Mathematics
University of Rochester, Rochester, New York
Douglas C. Ravenel
Professor and Chair of Mathematics
University of Rochester
Marc A. Rieffel
Professor of Mathematics
University of California, Berkeley
Tom Roby
Assistant Professor of Mathematics
California State University, Hayward
Cris T. Roosenraad
Professor of Mathematics
Carleton College
Jerry Rosen
Professor of Mathematics
California State University, Northridge
Mary Rosen
Professor of Mathematics
California State University, Northridge
Yoram Sagher
Prof. of Mathematics
University of Illinois at Chicago
Charles G. Sammis
Professor of Geophysics
University of Southern California
Mark Sapir
Professor of Mathematics
Vanderbilt University
Peter Sarnak
Professor of Mathematics
Princeton University
Stephen Scheinberg, Ph.D., M.D.
Professor of Mathematics
Clinical Assistant Professor of Dermatology
University of California, Irvine
Wilfried Schmid
Dwight Parker Robinson Professor of Mathematics
Harvard University
Dr. Martha Schwartz
Geophysicist
California Mathematics Framework Committee
Co-founder of Mathematically Correct
Albert Schwarz
Professor of Mathematics
University of California, Davis
Roger Shouse
Asst. Professor of Education Policy Studies
The Pennsylvania State University
Barry Simon
I.B.M. Professor of Mathematics and Theoretical Physics
Chair, Department of Mathematics
Caltech
Leon Simon
Professor of Mathematics and Chairman
Department of Mathematics
Stanford University
David Singer
Professor of Mathematics
Case Western Reserve University
William T. Sledd
Professor of Mathematics
Michigan State University
Alan Sokal
Professor of Physics
New York University
M.C. Stanley
Professor of Mathematics
San Jose State University
Dennis Stanton
Professor of Mathematics
University of Minnesota
Professor James D. Stein Jr.
Department of Mathematics
California State University, Long Beach
Sherman Stein
Professor Emeritus of Mathematics
University of California at Davis
Harold Stevenson
Professor of Psychology
University of Michigan, Ann Arbor
J. E. Stone
Professor of Human Development & Learning
College of Education
East Tennessee State University
Sandra Stotsky
Deputy Commissioner for Academic Affairs and Planning
Massachusetts Department of Education
Research Associate
Harvard Graduate School of Education
Robert S. Strichartz
Professor of Mathematics
Cornell University
Daniel W. Stroock
Professor of Mathematics
MIT
Justine Su
Professor of Education
Director, The China Institute
California State University, Northridge
P. K. Subramanian
Professor of Mathematics & Computer Sciences
California State University, Los Angeles
Howard Swann
Professor of Mathematics and Computer Science
San Jose State University
Daniel B. Szyld
Professor of Mathematics
Temple University, Philadelphia
Professor Sara G. Tarver, Ph.D.
Department of Rehabilitation Psychology and
Special Education
University of Wisconsin-Madison
Clifford H. Taubes
Department of Mathematics
Harvard University
Abigail Thompson
Professor of Mathematics
University of California, Davis
John B. Wagoner
Professor of Mathematics
University of California at Berkeley
Bertram Walsh
Professor of Mathematics
Rutgers University--New Brunswick
Steven Weinberg
Josey Regental Professor of Science
University of Texas at Austin
1979 Nobel Prize in Physics
Steven H. Weintraub
Professor of Mathematics
Louisiana State University
James E. West
Professor of Mathematics
Cornell University
Brian White
Professor of Mathematics
Stanford University
Professor Olof B. Widlund
Courant Institute of Mathematical Sciences
New York University
Herbert S. Wilf
Thomas A. Scott Professor of Mathematics
University of Pennsylvania
Robert F. Williams
Professor of Mathematics, Emeritus
University of Texas at Austin
W. Stephen Wilson
Professor of Mathematics
Johns Hopkins University
Jet Wimp
Professor of Mathematics
Drexel University
Charles N. Winton, Professor
Department of Computer and Information Sciences
University of North Florida
Edward Witten
Professor of Physics
Institute for Advanced Study at Princeton
Jon Wolfson
Professor of Mathematics
Michigan State University
Wei-Shih Yang
Professor of Mathematics
Temple University
Shing-Tung Yau
Professor of Mathematics
Harvard University