then abandoned before their effectiveness has been well tested, and lessons learned from program evaluations are often lost. Although aspects of mathematics proficiency have been studied, other aspects such as productive disposition have received less attention; and no one, including the National Assessment of Educational Progress (NAEP), has studied the integrated portrait of mathematics proficiency set forth in this report. In order that efforts to improve U.S. school mathematics might be more cumulative and coordinated, we make the following recommendation:
An independent group of recognized standing should be constituted to assess the progress made in meeting the goal of mathematical proficiency for all U.S. schoolchildren.
The mathematics students need to learn today is not the same mathematics that their parents and grandparents needed to learn. Moreover, mathematics is a domain no longer limited to a select few. All students need to be mathematically proficient to the levels discussed in this report. The mathematics of grades pre-K-8 today involves much more than speed in pencil-and-paper arithmetic. Students need to understand mathematics, use it to solve problems, reason logically, compute fluently, and use it to make sense of their world. For that to happen, each student will need to develop the strands of proficiency in an integrated fashion.
No country—not even those performing highest on international surveys of mathematics achievement—has attained the goal of mathematical proficiency for all its students. It is an extremely ambitious goal, and the United States will never reach it by continuing to tinker with the controls of educational policy, pushing one button at a time. Adopting mathematics textbooks from other countries, testing teachers, holding students back a grade, putting schools under state sanctions—none of these alone will advance school mathematics very far toward mathematical proficiency for all. Instead, coordinated, systematic, and sustained modifications will need to be made in how school mathematics instruction has commonly proceeded, and support of new and different kinds will be required. Leadership and attention to the teaching of mathematics are needed in the formulation and implementation of policies at all levels of the educational system.