students for mathematics tests. Each country provides a unique setting for school mathematics, one that very much determines how students are taught, what they learn, how successful they are, and how satisfied society is with the products of the system.

Education in the United States is marked by a diverse, mobile population of students and teachers, a variety of organizational structures, and minimal centralized control over policies and practices. The U.S. system of school mathematics has evolved over several centuries in accordance with these characteristics. Not only do the components of the U.S. system differ from those of other countries, but they are organized and operate differently. To understand the possibilities for improving children’s learning of mathematics, one needs a sense of how the elements of U.S. school mathematics currently function.

To understand the possibilities for improving children’s learning of mathematics, one needs a sense of how the elements of U.S. school mathematics currently function.

In the past half century, a number of research studies have examined differences in the mathematics learned by students in various educational systems. Some of these studies have also looked at various features of the systems that might help researchers understand and interpret the pattern of results. To date, the most comprehensive study to be analyzed in detail has been the Third International Mathematics and Science Study (TIMSS), which was conducted in the mid-1990s. Over 40 countries participated in TIMSS. Tests in science and mathematics, as well as questionnaires about their studies and their beliefs, were given to students midway through elementary school (grade 4 in the United States), midway through lower secondary school (U.S. grade 8), and at the end of upper secondary school (U.S. grade 12). Questionnaires about beliefs, practices, and policies were also given to these students’ teachers and school administrators. Unique features of TIMSS included an extensive examination of textbooks and curriculum guides from many of the participating countries, a video study of eighth-grade mathematics classes in three countries, and case studies of educational policies in those three countries.

The results from TIMSS have been widely reported in the media, catching the attention of politicians, policy makers, and the general public. Many people have compared various practices, programs, and policies in the United States with those of high-achieving countries. Such comparisons are interesting but at best can only be suggestive of the sources of achievement differences. TIMSS provides no evidence that a single practice—say, the amount of homework assigned, the particular textbook used, or how periods of mathematics instruction are arranged during the school day—is responsible for higher mathematics test scores in one country than in another. The countries



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