Teachers' assessment of student learning should be attuned not just to judging but to helping students learn.

of their students—especially members of traditionally underserved groups—are turning away from mathematics, dropping out either physically or mentally.2 Few students who stay with mathematics show much enthusiasm for it. It seems too abstract, too unrelated to either their present lives or their futures. Teachers are unhappy that students remember little of the mathematics they have been taught and seem incapable of using it.

Outside the classroom, politicians and school administrators, backed by the public, express dismay over low scores on mathematics achievement tests. They worry about deteriorating American competitiveness in international markets when students' mathematics skills seem to be declining.3 They want teachers to teach more mathematics to more students while maintaining or increasing test scores. At the same time, teachers are being told by their professional associations that the mathematics they teach should be more applicable to life than is now common, that their teaching should generate active learning, and that their assessment of student learning be attuned not just to judging but to helping students learn.4

On the surface, the pressures to change mathematics instruction look inconsistent, with teachers caught in the middle. Nevertheless, all the pressures reflect disappointment with the lack of interest and accomplishment so many students show. The message is the same: School mathematics is out of step with today's world and is neither well taught nor well learned.

Three pivotal forces are moving mathematics teachers toward a different approach to their teaching. These forces are changing ideas about

what should be taught,

how it should be taught, and

to whom it should be taught.

Motivating the first is a more comprehensive view of mathematics and its expanding role in society. Motivating the second is a resurgence of the view that mathematics must be made meaningful to students if it is to be learned, retained, and used. Motivating the third is the growing belief that all students can and should learn more mathematics.

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