participating in TIMSS vary in many respects—educationally, socially, economically, historically, culturally—and in each of those respects, they vary along many different dimensions. In the absence of more evidence than TIMSS can provide, one cannot select one practice and claim that if it were changed to be more like that of high-scoring countries, scores in the United States would rise.3 Studies like TIMSS can at best generate conjectures that need to be tested in the complex system of school mathematics that exists in any county. In this report, we use data from TIMSS and other international studies to help describe practice and performance in the United States— sometimes in contrast to that of other countries but never assuming a simple causal relation between a specific practice and performance.

This chapter is intended primarily to give an overall picture of U.S. mathematics education, describing the experiences and achievement of most students. But it should be emphasized that U.S. education is quite diverse, partly because of an unequal distribution of needs and resources, and partly because of the principle of local control. Thus, this chapter also attempts to describe that diversity, particularly with respect to student achievement.

In this chapter, we first take up in turn four central elements of school mathematics—learning goals, instructional programs and materials, assessment, and teaching—discussing the current status of each in the United States. We then examine the preparation and professional development of U.S. teachers of mathematics. Finally, we look at a major indicator of the health of the whole system, student achievement results, both across time and internationally.

Learning Goals

The U.S. Constitution leaves to the separate states the responsibility for public education. State and local boards of education have the authority to determine the mathematics that students learn as well as the conditions under which they learn it. Many state boards of education have created curriculum standards and frameworks, and some have specified criteria that educational materials (principally textbooks) must meet if they are to be approved. Thus, each state can, in principle, specify quite different goals for learning mathematics at each grade level, and each local district can make adjustments as long as they fall within the state guidelines.

A major effort to set comprehensive learning goals for school mathematics at the national level was undertaken in 1989 by the National Council of Teachers of Mathematics (NCTM) with the release of Curriculum and Evalu-

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