Archived Information

All students can and must learn mathematics, which should serve as a "pump," not a "filter."

Reality: Only in the United States do people believe that learning mathematics depends on special ability. In other countries, students, parents, and teachers all expect that most students can master mathematics if only they work hard enough. The record of accomplishment in these countries--and in some intervention programs in the United States--shows that most students can learn much more mathematics than is commonly assumed in this country.

                     (Mathematical Sciences Education Board 1989, p. 10)

In the past it was assumed that problem-solving ability was tied to the ability to perform paper-and-pencil calculations. Years of teachers' and students' time were spent trying to remediate children who lacked this ability. The emphasis on remediation was based on the premise that mathematics is linear and hierarchical and must be taught in a prescribed order--rote skills first, problem solving later. But research shows that repeating the same uninteresting tasks in the same unimaginative way is not effective. Students learn best when they are intellectually challenged so that they are motivated to fill in mathematical gaps when necessary. The teacher's role is to provide stimulating problems and environment to motivate mathematical learning. In fact, research points out that certain teaching strategies can help all students develop "mathematical power." Providing students with real-life problems to investigate is just one strategy for helping them develop an understanding of the mathematical concepts that underlie a variety of problems.

Tracking, on the other hand, when it is used to filter students out of mathematics, is antithetical to the development of mathematical power: little learning is expected of students in lower tracks and, as a result, they produce little and lose the opportunity to work in mathematics-related occupations; teachers of these tracks often feel like second-class citizens too and lose their enthusiasm and creativity over the years; tracking fosters an elitism that contributes to the underrepresentation of women and non-Asian minorities in mathematics fields and careers that rely on a solid mathematics background; and tracking is a poor substitute for implementing a wide variety of the enrichment activities at the pre-high school level and of mathematics courses at the high school level, including advanced placement courses, that can stimulate the quickest students to greater achievement.

All school mathematics courses should be of high quality and challenge all students to high achievement. Parents and students must be shown that achievement in mathematics does not depend on an accident of birth such as innate talent, but that it is attainable through hard work--the same way all skills are successfully accessed.

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[Background]

[Teachers need to listen to students and to incorporate into their instruction what they learn from listening.]

This page was last updated January 4, 2002 (jca)