Many people have worked very hard in recent years to change the ways in which mathematics is taught and learned. However, the problem requires greater and different efforts than those made so far. Complex systems like school mathematics are what social scientists call overdetermined. A large number of pressures exert forces on these systems, making them remarkably stable and resistant to change. Altering such a system requires the coordinated efforts of everyone involved.

Mathematical proficiency for all is an ambitious objective. In fact, in no country—not even those that have performed better than the United States on international comparisons of mathematics achievement—do all students display mathematical proficiency as defined in this book. Reaching this goal will require fundamental changes in many areas of school mathematics.

The only way to achieve long-term improvement is through a coherent and systematic approach. This will require that all aspects of the system be reformed simultaneously. We therefore conclude with a list of actions that the individuals and groups to whom this book is addressed must take to achieve the goal of mathematical proficiency for all. By pursuing these actions in a coordinated and resolute fashion, those people involved in mathematics education in the United States can drive changes that will have substantial and lasting benefits for all students and for the nation as a whole.