Nearly 25 percent of 15-year-olds performed below even the lowest level of competence on the Programme for International Student Assessment (PISA), a 2003 assessment of math problem solving. Even our top-performing students cannot compete with top achievers internationally. It is apparent that the approach to teaching mathematics in the United States does not work for most students.

In elementary school, we teach students efficient procedures they can use to solve arithmetic problems, but not why they work. As a result, American students make assumptions about the mathematical concepts underlying these procedures—assumptions that are often incorrect and lead to confusion as students progress through school. Meanwhile, their peers in top-performing countries are learning the underlying concepts, beginning in their early years of schooling. These students actually understand the mathematics, so they know why the procedures work. They have a mathematics foundation they can build on.

Students can do arithmetic by simply applying procedures they do not understand, but it is virtually impossible to master algebra and geometry without understanding the underlying concepts. When American students get to algebra and geometry, they have to unlearn what they already have learned before they can move on.

The problem is particularly acute in our middle and high schools, where large numbers of students enter two or more years behind. These students need Ramp-Up Mathematics, our 90-minute, full-year courses, one version for middle school and another for high school. The emphasis throughout is on providing more time and targeted, systematic instruction to accelerate student learning. We emphasize building skills, problem-solving capability, and understanding of key mathematics concepts. Teachers are provided all the help they need to understand this approach and to succeed in teaching it.

Mathematics Navigator, our intervention program, gives students who are struggling with specific mathematics concepts and skills additional time and targeted, systematic instruction outside of their regular classroom to stop the achievement gap before it starts. It addresses the root causes of common misconceptions rather than simply teaching again what has been taught before. Mathematics Navigator is broken down into discrete modules, each of which incorporates concepts, skills, and problem solving. Once students demonstrate mastery of the specific topics they need help with, they exit the program. Mathematics Navigator can be delivered during school hours, after school hours, on the weekend, or during the summer. It is intended to augment and enhance the core math program, not replace it, and can be used with any math textbook.

Well-designed student materials are included with all of our mathematics programs. Ramp-Up Mathematics and Mathematics Navigator feature pre- and post-assessments developed in partnership with the Australian Council for Educational Research, which helped develop items for the Trends in International Mathematics and Science Study (TIMSS) and created the Programme for International Student Assessments (PISA).