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:

- Cognitive Tutor Algebra

College Preparatory Mathematics (CPM)

Connected Mathematics Program (CMP)

Core-Plus Mathematics Project

Interactive Mathematics Program (IMP)

- Everyday Mathematics

MathLand

Middle-school Mathematics through Applications Project (MMAP)

Number Power

The University of Chicago School Mathematics Project (UCSMP)

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:

- Richard Askey, John Bascom Professor of Mathematics at the University of Wisconsin at Madison and a member of the National Academy of Sciences, pointed out in his paper, "

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