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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools
Ability Grouping in Mathematics
Schmidt et al. (1999) note that 82 percent of 13-year-olds in the United States are in schools offering two or more differently titled mathematics classes for students at the same grade level, each with different expectations for student learning. These students from different middle-grade courses sometimes funnel into the same high school courses, leading to a lack of continuity in their mathematics education. Of even greater concern is that this early mathematics placement contributes to sorting students into different “pipelines,” some of which lead away from rigorous academic courses and programs. As noted below in the discussion of disparities in opportunities to pursue and succeed in advanced study, this problem is compounded for minority students and those of low socioeconomic status.
Early ability grouping at the middle school level has the most pronounced effect in mathematics because of the cumulative and sequential nature of the curriculum. Once students are placed in a mathematics sequence, it is very difficult for them to move to a more advanced sequence without doubling up (taking two mathematics courses during the same year) or attending summer school for an intensive and fast-paced version of a typical yearlong course. Summer school courses, because they are compressed, often do not provide a solid foundation of understanding for further study (see the report of the mathematics panel).
Several recent reports indicate that the process of determining which students will take advanced courses in high school begins with their placement in the first algebra course (Gamoran, 1987; Horn, Nunez, and Bobbitt, 2000; NCHSSY, 2001a).15 Once considered a ninth-grade course, algebra is becoming an eighth-grade option in increasing numbers of school districts,16 and some districts offer it to a small number of seventh graders.17
Placement in algebra is based most often on the results of standardized tests, teacher recommendations, and parental requests. It is not uncommon, however, for parental requests to take precedence over test scores. Studies have shown that, although counselors and school administrators use test scores or current mathematics placement to bar low-income students from high-level courses, they permit middle-class students with similar qualifications to enroll when parents intervene on their children’s behalf (Orfield and
Some research indicates that ability grouping begins much earlier than middle school, perhaps even as early as elementary school.
In 1998, 18 percent of U.S. eighth-graders were enrolled in Algebra 1.
This shift is beginning to place great strain on middle schools, as well as many of the teachers in those schools who may not have received appropriate preparation or professional development for teaching this subject well to younger students (NRC, 1998, 2000a).