repetitive. Key ideas can be difficult to pick out from among the many incidental details. This scattered and superficial curriculum means that students learn much less than they might. They then take standardized tests that often measure low-level skills rather than the kind of problem-solving abilities needed in modern life. All too often, mathematics instruction serves to alienate students rather than to reveal to them the beauty and usefulness of mathematics.

Despite its remarkable stability, school mathematics has changed somewhat in the United States over the past decade or so. Some districts are using instructional materials that are more likely to lead to mathematical proficiency, and some states have developed tests to measure more than low-level skills. More teachers are effectively engaging students with worthwhile mathematics. However, progress has been uneven and poorly documented.

Results from national and international assessments indicate that schoolchildren in the United States are not learning mathematics well enough. During the 1990s, performance on national assessments did improve in some areas of mathematics and for some groups of students. For example, fourth and eighth graders made significant gains. Performance also improved among black and Hispanic students, although the gap between the performance of these students and that of white students remains large. Even with these gains, however, performance is still below what is needed of U.S. students.2 Many students cannot use computations to solve problems. Their understanding and use of decimals and fractions are especially weak. In international comparisons, their mathematics performance is usually no better than average and sometimes below that.

Helping all children succeed in mathematics is an imperative national goal. Yet, although there is ample research on the learning of mathematics, there is a shortage of comprehensive and reliable information gleaned from that research to guide efforts to improve school mathematics.

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