Mathematically Correct
Mathematics Program Reviews

Concluding Remarks

In conducting these reviews, we established criteria at each of three grade levels that represented significant progress in mathematics achievement. It is our belief that an effective school mathematics program can pilot students through these objectives and produce a competent population of American eight-graders that are ready for a rigorous algebra program.

It is with some relief that we note that materials do exist today that are reasonably well on target to achieve this level of mathematics development. On the other hand, it is with much regret that we see other programs that are not even close to these objectives. As we might have expected, the majority of programs reviewed fall in the middle of this range. They provide some support for modest levels of achievement, but would need supplementation to varying degrees to approximate the level of achievement we hope to see.

The programs reviewed also vary considerably in style and in the demands they place on teachers. In some cases, the achievements even to the levels indicated would require considerable expertise and professional judgment on the part of the teacher. Put another way, we can envision many of these programs being implemented ineffectively, and this may well be an important factor when considering curriculum materials.

Finally, we hope that the process that characterizes these reviews will encourage others to think critically about the detailed requirements for mathematics curricula designed to support high achievement levels. To support the completion of mathematics through all of the material required for a solid pre-algebra curriculum by the end of seventh grade means that high expectations and efficient programs must characterize K-7 mathematics education. On the one hand, concepts must be introduced earlier than has often been the case. On the other, we do not want to sacrifice mastery to early topic introduction.

A high level of achievement in mathematics is within the realm of possibility and well within the raw ability level of American students. As this review clearly suggests, curriculum material selection will play a critical part in providing an effective mathematics education. With deficient materials, our students will have lost before they begin. While materials must be selected to meet the needs of students in the local setting, it is our hope that we have encouraged the adoption of materials that can indeed support higher levels of mathematics achievement.