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Mathematics Equals Opportunity (White Paper -- October 20, 1997)

Mathematics in the U.S. Today

International Comparisons of Middle School Mathematics and Science Proficiency

U.S. Performance on TIMSS, Relative to International Average Recent findings from the Third International Mathematics and Science Study (TIMSS), indicate that the mathematics curriculum from grades five through eight may be a weak link in the U. S. educational system. Newly available data from TIMSS (the most comprehensive international comparison of schools and students ever undertaken) reveal that U.S. 4th graders scored above the international average in both mathematics and science. Among 25 other participating nations, only Korea performed better than the U.S. in 4th grade science, and only 7 of the 25 other countries did better than the U.S. in 4th grade mathematics. These findings are in contrast to earlier findings from TIMSS that indicate that U.S. 8th graders perform slightly below the international average in mathematics, and only slightly above the international average in science. In fact, only one country--the U.S. in mathematics--falls from above the international average at 4th grade to below the international average at 8th grade.

The U.S. expects less of its middle school students compared to high performing nations. TIMSS data suggest that one reason U.S. students do less well at 8th grade is that the middle school mathematics curriculum in the U.S. is significantly less challenging than curricula in other countries. In Germany and Japan, virtually all students in grades 5 through 8 move beyond arithmetic to the foundations of algebra and geometry. By 8th grade, mathematics courses in virtually all other countries participating in TIMSS include significant algebra and geometry, while in the U.S., only students in college-preparatory classes receive significant exposure to algebra, and very few students study geometry. As a result, the content taught in U.S. 8th grade mathematics classrooms is usually at a 7th-grade level compared to the 40 other nations in the TIMSS study.

TIMSS also found that U.S. mathematics classes require students to engage in less high-level mathematical thought and solve fewer multi-step problems than classes in Germany and Japan. A U.S. mathematics teacher's typical goal is to teach students the mechanics of solving a problem versus understanding the concepts behind it, while a Japanese teacher's goal is to help them learn the basics as well as understand the relevant mathematical concepts. In a typical U.S. classroom, students follow the teacher as he or she leads them through solutions to mathematics problems. In Japan, students are asked to solve problems, present them to the class, and describe how they approached the problem to increase their own understanding.

How Does Our Curriculum Compare Internationally?

The 8th grade mathematics curricula in both Germany and Japan are more advanced than in the United States. The TIMSS analysis of U.S. curricula examined both the content of textbooks and how it is implemented in classrooms.

  • An analysis of curricula in the U.S. and other countries found that algebra and geometry occupy more space (Footnote: Space is defined in terms of the percentage of a textbook or guidebook that is devoted to particular topics/blocks. Topics include such items as formulas, geometry, numbers, and estimation. Blocks are sub-units of topics that are parts of a textbook and which might include individual pedagogical suggestions, individual examples, individual testing, narrative blocks, graphic blocks, suggested activities, and mathematical problems.) in German and Japanese textbooks than they do in the textbooks used by a majority of U.S. 8th graders (Figure 6 -- 4,963 bytes).

  • Analyses of curriculum implementation make clear that in the middle school years, the U.S. still focuses on arithmetic. For example, 40 percent of U.S. 8th grade mathematics lessons included arithmetic topics, whereas only 13 percent of Germany's and none of Japan's lessons at the 8th grade level included these topics. The major focus of curriculum taught in these countries is on algebra and geometry.


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Last Updated -- October 20, 1997, (pjk)