Today the United States has the challenge and the opportunity to provide all students with the mathematical knowledge, skills, and confidence they will need in a highly technical world. There is considerable nation-wide interest in improving students’ understanding of mathematics, combined with an emerging consensus about the essential elements of mathematics instruction; in addition, research has provided valuable insights into how children learn. Together these factors are opening the way to substantial and enduring progress in school mathematics.

Greater understanding of mathematics will be essential for today’s schoolchildren. Success in tomorrow’s job market will require more than computational competence. It will require the ability to apply mathematical knowledge to solve problems. If today’s students are to compete successfully in the world of tomorrow, they must be able to learn new concepts and skills. They need to view mathematics as a tool they can use every day. They need to have the mathematical sophistication that will enable them to take full advantage of the information and communication technologies that permeate our homes and workplaces. Students with a poor understanding of mathematics will have fewer opportunities to pursue higher levels of education and to compete for good jobs.

Despite the dramatically increased role of mathematics in our society, mathematics classrooms in the United States today too often resemble their counter-parts of a century ago.¹ Many mathematics teachers still spend the bulk of their class time demonstrating procedures and supervising students while they practice those procedures. In numerous elementary and middle schools, time for learning mathematics is too brief. Textbooks are typically packed with an assortment of topics, so that the treatment of any one topic is often both shallow and