An Open Letter to Richard Riley

AN OPEN LETTER TO UNITED STATES SECRETARY OF EDUCATION, RICHARD RILEY

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:

The "promising" programs 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:

Good Intentions are not Enough

Connected Mathematics Program

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.

While we do not necessarily agree with each of the criticisms of the programs described above, given the serious nature of these criticisms by credible scholars, we believe that it is premature for the United States Government to recommend these ten mathematics programs to schools throughout the nation. We respectfully urge you to withdraw the entire list of "exemplary" and "promising" mathematics curricula, for further consideration, and to announce that withdrawal to the public. We further urge you to include well-respected mathematicians in any future evaluation of mathematics curricula conducted by the U.S. Department of Education. Until such a review has been made, we recommend that school districts not take the words "exemplary" and "promising" in their dictionary meanings, and exercise caution in choosing mathematics programs.

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