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News from the National Academies
Date: Jan. 23, 2001
Contacts: Vanee Vines, Media Relations Associate
Mark Chesnek, Media Relations Assistant
(202) 334-2138; e-mail <>

    Overhaul of School Mathematics Needed To Boost Achievement for All
WASHINGTON -- American students' progress toward proficiency in mathematics requires major changes in instruction, curricula, and assessment in the nation's schools, says a new report from the National Research Council of the National Academies. To help schoolchildren successfully develop all aspects of mathematics learning, a coordinated and systematic approach to mathematics education from pre-kindergarten through eighth grade is critical.

"Too few students leave elementary or middle school with adequate mathematical knowledge, skill, and confidence for the nation to be satisfied with the condition of school mathematics," said Jeremy Kilpatrick, chair of the committee that wrote the report and Regents Professor of Mathematics Education at the University of Georgia, Athens. "Simply developing speed in pencil-and-paper arithmetic may have been sufficient when their parents and grandparents were in school, but today's students need a deeper understanding of mathematics to thrive in an increasingly technical economy. Improvement requires a comprehensive and sustained effort among policy-makers, administrators, teachers, university faculty, parents, and others to enhance both instruction and achievement."

Knowledge of mathematics is important for making sense of a high-tech world, yet the nation's approach to mathematics in pre-kindergarten through eighth grade has been inconsistent and marked by an emphasis on routine arithmetic -- with a heavy dose of memorization and repetition, the committee said. Furthermore, recent studies have shown that many elementary and middle school teachers have only a shaky grasp of mathematics themselves, and often are unable to clarify key concepts for students or solve problems that involve more than basic calculations.

Such failure to more fully explore mathematics limits an individual's potential and hampers national progress by insufficiently preparing future workers and citizens, the report points out. Results from state, national, and international assessments conducted over the past 30 years indicate that U.S. students can adequately perform straightforward computational procedures, but they tend to have a more limited understanding of fundamental mathematical ideas. They also have trouble applying mathematical skills to solve even simple problems. And these trends may further impede the academic advancement of at-risk students.

Paramount in the report's recommendations is the finding that the nation can and should groom all students to be "mathematically proficient," mastering much more than disconnected facts and procedures. Moreover, this target should drive school-improvement efforts, the committee emphasized after its exhaustive review and synthesis of scientific literature on mathematics education in pre-kindergarten through eighth grade.

Five intertwined and equally important strands comprise the committee's definition of mathematical proficiency. First, capable students should be able to understand and apply important concepts. They also should be able to compute with ease, formulate and solve problems, and explain their reasoning. Finally, they should have confidence in their abilities and view mathematics as a sensible and worthwhile subject. Each strand requires constant attention, the report says.

The committee concentrated on how students learn about numbers and operations. Relevant research was abundant in those areas, and debates over mathematics curricula and instruction in elementary and middle schools often center on arithmetic. Nonetheless, the goal of proficiency also applies to other important areas of mathematics, including algebra, geometry, and statistics, the report says.

Mathematical proficiency develops over time, building on a knowledge base that begins to take shape in infancy. The committee did not endorse any single approach to effective instruction, but recommended that teachers use students' informal understanding of mathematics as a steppingstone toward mastery of more challenging skills and concepts in the subject.

Beginning in preschool, educators should offer students opportunities to extend their rudimentary comprehension of numbers. In subsequent years, the curriculum should link calculation to everyday situations to help students make such connections. And it should illustrate numbers and operations in various ways, the report adds. For example, one-half could be shown as a fraction, decimal, or percentage; a point between zero and one on a number line; or as a shaded portion of a figure.

In addition, educators should teach important concepts in depth, instead of covering a multitude of topics superficially, the committee said. Significant time also should be devoted to daily mathematics instruction in every grade of elementary and middle school. Exams should test students' progress in all five strands of mathematical proficiency.

To better prepare teachers for elementary or middle school math instruction, colleges and universities should create programs or courses that emphasize thorough knowledge of mathematics and of processes through which schoolchildren come to understand the subject, the committee said. On the job, schools should give teachers more time and other resources -- such as continuous and high-quality training, as well as useful instructional materials -- to acquire a solid understanding of mathematics and improve their techniques. Teachers who have special training in the subject also should be available in all elementary schools to assist colleagues.

Proficiency is an ambitious goal, and the United States will never reach it by continuing to tinker with the controls of education policy, pushing one button at a time, the report says. In recent years, many states and school districts have raised academic standards in mathematics, introduced new assessments, and offered teachers new professional-development opportunities. But these efforts have been fragmented.

While a solid base of scientific evidence supports the committee's call for immediate action to help all students become mathematically proficient, additional research is needed to shed more light on the elements of successful mathematics teaching and learning, as well as obstacles that block progress. The fruits of such investigation, coupled with data from systematic evaluation of programs and initiatives, should routinely inform improvement efforts, the report says.

The study was sponsored by the U.S. Department of Education and the National Science Foundation. The National Research Council is the principal operating agency of the National Academy of Sciences and the National Academy of Engineering. It is a private, nonprofit institution that provides science advice under a congressional charter. A committee roster follows.

Read the full text of Adding It Up: Helping Children Learn Mathematics for free on the Web, as well as more than 1,800 other publications from the National Academies. Printed copies are available for purchase from the National Academy Press Web site or at the mailing address in the letterhead; tel. (202) 334-3313 or 1-800-624-6242. Reporters may obtain a pre-publication copy from the Office of News and Public Information at the letterhead address (contacts listed above).

Behavioral and Social Sciences and Education Division

Mathematics Learning Study Committee

Jeremy Kilpatrick (chair)
Regents Professor of Mathematics Education
University of Georgia

Deborah Loewenberg Ball
Professor of Educational Studies
School of Education
University of Michigan
Ann Arbor

Hyman Bass*
Professor of Mathematics Education, and
Roger Lyndon Collegiate Professor of Mathematics
School of Education
University of Michigan
Ann Arbor

Jere Brophy
University Distinguished Professor of Teacher Education
School of Education
Michigan State University
East Lansing

Felix Browder*
University Professor of Mathematics
Department of Mathematics, and
Vice President for Research
Rutgers University
New Brunswick, N.J.

Thomas Carpenter
Professor of Curriculum and Instruction
University of Wisconsin

Carolyn Day
Associate Director for Elementary Mathematics and Science
Dayton Public Schools
Dayton, Ohio

Karen Fuson
Professor of Education and Psychology
Institute for Learning Sciences
School of Education and Social Policy
Northwestern University
Evanston, Ill.

James Hiebert
H. Rodney Sharp Professor of Education
University of Delaware

Roger Howe*
Department of Mathematics
Yale University
New Haven, Conn.

Carolyn Kieran
Professor of Mathematics Education
Department of Curriculum and Instruction
University of Quebec

Richard Mayer
Professor of Psychology
Department of Psychology
University of California
Santa Barbara

Kevin Miller
Associate Professor
Departments of Psychology and Educational Psychology, and Beckman Institute for Advanced Science and Technology
University of Illinois

Casilda Pardo
Mathematics Resource Teacher
Valle Vista Elementary School
Albuquerque Public Schools
Albuquerque, N.M.

Edgar Robinson
Vice President and Treasurer
Exxon Corp. (retired)

Hung-Hsi Wu
Professor of Mathematics
Department of Mathematics
University of California


Jane Swafford
Study Director

* Member, National Academy of Sciences