tional Center for Education Statistics (NCES), TIMSS compares the performance of American students (at the end of the eighth grade) with those of other countries in five major content areas of mathematics and six content areas in science. TIMSS has been offered in 1995 and 1999 (the 2003 results are not yet available). Therefore, TIMSS provides the most reliable and comprehensive assessment of trends in student achievement from an international perspective.

The TIMMS 1999 results do not speak directly about spatial thinking as such. However, there are content areas in which performance would seem to be directly related to skill in spatial thinking. In the case of mathematics, performance in geometry is defined as understanding points, lines, planes, angles, visualization, triangles, polygons, circles, transformations, symmetry, congruence, similarity, and constructions (Mullis et al., 2000, p. 93). Although the average U.S. scale score for geometry was 473 and not statistically significantly different from the international average of 487 (range 575–335), U.S. students did rank 27 out of 38 countries. Thus, “the United States performed significantly above the international average in fractions and number sense; data representation, analysis, and probability; and algebra. In contrast, however, it performed similarly to the international average in measurement and geometry (a shift in ranking from 16th in data representation, analysis, and probability to 27th in geometry)” (Mullis et al., 2000, p. 94).

U.S. students showed a small but not statistically significant increase in achievement between 1995 and 1999. As the NCES (2000b, p. 108) report notes: “Changes in average achievement at a national level are not easy to bring about and inevitably take place over several years. Amending official curricula, producing relevant supporting resources, and changing teacher practice all take time, even under the most favorable conditions.”

In the case of science, two content areas—Earth science (includes Earth features, Earth processes, and Earth in the universe) and physics (includes physical properties and transformations, energy and physical processes, and forces and motion)—appear to have strong connections to spatial thinking. With the notable exception of physics, the average achievement of U.S. students was significantly higher than the international average. The ranking of U.S. students ranged from 13th out of 38 in the case of scientific inquiry and the nature of science to 20th for physics. U.S. students ranked 16th out of 38 in achievement in Earth science. For the four areas for which trend data are available (Earth science, life science, physics, and chemistry), there was no significant difference between 1995 and 1999.

Given the importance of science and mathematics achievement and the significant investment in those areas of education, the TIMSS results are neither impressive nor satisfactory. While it is true that changing average levels of achievement is difficult, current educational policy, as exemplified by the No Child Left Behind Act of 2001 (Public Law 107-110), is committed to fostering academic achievement in core subjects (defined as English, reading or language arts, mathematics, science, foreign languages, civics and government, economics, arts, history, and geography). For at least three of the TIMSS content areas (geometry, physics, and Earth science), achievement is related to competence in spatial thinking, and to the extent that spatial thinking is taught with adequate supports, the committee believes that achievement in mathematics and science understanding will improve. However, that improvement will come about only if the educational system focuses its attention on spatial thinking. To what extent is that happening?

5.5 SPATIAL THINKING IN THE NATIONAL EDUCATION STANDARDS

5.5.1 The Role of Spatial Thinking in the Mathematics and Science Standards

In the current educational environment one important place to look for attention to spatial thinking is in the educational standards for various disciplines. These discipline-based standards, developed in the middle to late 1990s, provide statements of what K–12 students should know,



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