Making It Count

In today's increasingly high-tech world, it's more important than ever to have a solid grasp of the subject. Yet the nation's education efforts in this area have been inconsistent and marked by an emphasis on routine arithmetic, says a new report from the National Research Council. A more coordinated and systematic approach to math education from pre-kindergarten through eighth grade is urgently needed.

A host of assessments conducted over the past 30 years indicate that U.S. students can adequately perform straightforward computational procedures, but their comprehension of underlying mathematical ideas is limited. They also have trouble applying mathematical skills to solve simple problems. And these difficulties may further impede the academic advancement of at-risk students, the report says. In addition, studies show that many elementary and middle school teachers have only a shaky grasp of math themselves.

By the time children complete elementary school, their performance in math and reading can, to a large extent, predict their academic progress in later years. While U.S. schools have been relatively successful at improving reading instruction and developing students' reading skills, the same cannot be said about math.

The report calls on the nation to groom all students to be "mathematically proficient," comprehending more than disconnected facts and procedures. "People today are much more exposed to numbers and quantitative ideas, and they need to deal with mathematics on a higher level than they did just 20 years ago," said Jeremy Kilpatrick, chair of the committee that wrote the report and a professor of mathematics education at the University of Georgia in Athens.

The committee's definition of mathematical proficiency comprises five intertwined and equally important strands, each requiring constant attention. Foremost, all students should be able to understand and apply important concepts. For example, if students understand that the order in which two numbers are added is irrelevant to the sum, they can learn basic addition in nearly half the time. What's more, knowing how such relationships work allows students to learn new facts more easily.

To possess mathematical proficiency, students also must be able to compute with ease, formulate and solve problems, and explain their reasoning, the report says. Finally, they should have confidence in their abilities and regard mathematics as a sensible and worthwhile subject. Here, teachers also play a critical role. How they feel about the subject affects their classroom practice, which influences not only what students learn, but also how students view themselves as math learners.

Children begin to understand math well before they enroll in school, the report points out. From infancy through preschool, they develop a base of skills, concepts, and even misconceptions about math. Much of what they know is bound together with their initial understanding of counting.

Educators should use a child's rudimentary knowledge as a steppingstone toward mastery of more challenging skills and concepts in the subject. For example, teachers could use students' familiarity with the idea of fairness and getting "fair shares" as a springboard to lessons on division and proportional reasoning. Significant time also should be devoted to daily math instruction in every grade of elementary and middle school, the report says.

Teacher educators and school administrators must rethink their work, too. Colleges and universities should create programs that emphasize in-depth knowledge of mathematics and processes through which schoolchildren come to comprehend the subject, the committee said. And schools should give teachers more time as well as high-quality training to acquire a solid understanding of math.   -- Vanee Vines

Adding It Up: Helping Children Learn Mathematics. Mathematics Learning Study Committee, Division on Behavioral and Social Sciences and Education (2001, approx. 450 pp.; ISBN 0-309-06995-5; available from National Academy Press, tel. 1-800-624-6242; $29.95 plus $4.50 shipping for single copies).

The committee was chaired by Jeremy Kilpatrick, Regents Professor of Mathematics Education, department of education, University of Georgia, Athens. The study was sponsored by the U.S. Department of Education and the National Science Foundation.