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EDUCATION INDICATORS: An International Perspective

Curriculumincluding the types of classes offered and the material presented in these classesaffects what students learn in mathematics./2 Mathematics curricula vary significantly between the United States and other nations. In the United States, mathematical content areas tend to be divided among several grades and taught numerous times in an effort to deepen student understanding. This approach builds in repetition in successive grades. In addition, the share of time devoted to various mathematical topics is fairly equally divided in the U.S curriculum.

In contrast, France and Japan typically utilize a curricular structure in which the major piece of a content area is concentrated in a single grade and taught once. There is little room for repetition of concepts across grade levels. Further, these countries tend to place a clear emphasis on selected topics at a given point in a child's education (e.g., Japan's upper-secondary-level curriculum emphasizes calculus), and students receive indepth instruction in these topics at the time they are introduced. Although no research to date has systematically identified which content areas are best taught by each approach, an advantage of the curricular structure adopted by France and Japan is that goals and expectations for each topic are clearly defined. Because in the U.S. curriculum topics are constantly revisited, goals and expectations may have become obscured.

The following example illustrates these differing curricular styles. French students are given intensive instruction in the decimal system at the elementary level and intensive instruction in fractions at the eighth-grade level. However, U.S. students are taught fragments of each topic throughout elementary and junior high school, diminishing the overall curricular intensity and potentially obscuring the basic ideas found in each. Although Japan relies primarily on the concentration approach to teaching mathematical concepts, this reliance is not exclusive. For instance, in Japan decimals and common fractions are taught in grades 3 through 6.

This variation in a country's approach to the coverage of mathematical topic areas is reflected in the results of the Second International Mathematics Study of 1982 (SIMS). While all of the French and U.S. students participating in SIMS were taught fractions by the end of the eighth grade, 40 percent of American eighth-graders could add fractions at the beginning of the school year (fractions are introduced at the elementary level and repeated throughout junior high school in the United States), and only 5 percent of French students could do so at that time. However, by the end of the school year, 73 percent of French eighth-grade students could add fractions, while only 59 percent of U.S. eighth-graders could do so. (In France, fractions receive little attention until that year, when they are covered with a high level of intensity.)

Moreover, SIMS found that in 1982 the United States also differed from France and Japan in terms of the subjects taught to students at a given grade level. While the U.S. eighth-grade-level curriculum was largely devoted to arithmetic with some instruction in algebra, the Japanese focus was on algebra. Similarly, while the U.S. high school curriculum was focused on algebra, the Japanese one was focused on calculus.

Differences in curricular styles also are reflected in textbook formats. For example, while Japanese texts begin with a brief review of the previous year's work, they are based on the assumption that since the material has been covered, it has been learned. In contrast to U.S. textbooks, Japanese texts are short, focus only on key topics, and contain very few worked examples (it is expected that the teacher will supplement the materials with extra explanations and problems)./3

1/ Unless otherwise noted, the discussion and examples contained in this sidebar
are based upon two primary sources: (1) the results of the Second International
Mathematics Study of 1982 (SIMS) as reported in the following publication:
International Association for the Evaluation of Educational Achievement, *The
Underachieving Curriculum: Assessing U.S. School Mathematics from an
International Perspective* (Champaign, IL: 1989); and (2) Tatsuro, Miwa, "School
Mathematics in Japan and the U.S.: Focusing on Recent Trends in Elementary and
Lower Secondary School," in National Council of Teachers of Mathematics,
*Developments in School Mathematics Education Around the World: Volume 3*
(Chicago, IL: University of Chicago Press, 1992).

2/ SIMS collected information from teachers that described their students' opportunity to learn the material covered in the SIMS test.

3/ Askey, R. "Japanese Grade 7-9 Mathematics."
*College Mathematics Journal 23 *(November 1992): 445-448.

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