American students test poorly in mathematics compared to those in other developed--and in some cases, less developed--countries. While we have seen some signs of improved performance in recent years, these improvements are not yet evident among high school students. And the proportion of new college graduates who majored in math-intensive subjects has declined by nearly half over the past sixty years. Will the United States lose its edge in innovation as the math skills of our elite students atrophy? Will the average worker possess the training necessary to take advantage of technically demanding twenty-first-century job opportunities? Most important, why has the United States lost ground, and what course must we follow to gain it back? This report summarizes recent research that yields important insights into America's mathematics problem. Stated succinctly, the root of the problem is an excessive emphasis on equality in curriculum. Given the inherent variability in students' math aptitude, equity can be achieved only by delivering a suboptimal education to at least some students. A recent policy initiative undertaken by one of the nation's largest and most successful school districts, Charlotte-Mecklenburg (North Carolina), illustrates the hazards of math acceleration. In 2002, the district joined a growing number of education agencies in promoting eighth grade algebra for a larger proportion of students. The push to accelerate algebra was based on a naive interpretation of correlations between algebra timing and later success, ignoring the obvious counterargument that a propensity for future success drives early algebra taking, not the reverse. However ill-conceived the policy, though, the results are instructive: (1) In the span of two years, Charlotte-Mecklenburg students performing below average in math witnessed threefold increases in the likelihood of taking Algebra I by eighth grade; (2) Students subjected to algebra acceleration scored thirteen percentile points lower on a standardized end-of-course test than students permitted to take algebra on a regular schedule; (3) Accelerated students were less likely to pass an end-of-course test in geometry, despite receiving an extra year to do so. They were no more likely to pass an end-of-course test in algebra II. A more thorough review of curricular trends in high school mathematics over the twentieth century shows that the Charlotte-Mecklenburg experience is not a fluke. Since the beginning of the twentieth century, waves of reform, including the "new math" movement, have sought to improve the math achievement of moderate-performing students. The emphasis on the performance of lower-achieving students increased after the 1983 "A Nation At Risk" report and the 2001 passage of the No Child Left Behind Act. Recent studies have verified an obvious side effect of this focus: declining achievement among higher-performing students. The past thirty years have witnessed a 20-point increase in average math SAT scores but a 25 percent drop in the proportion of college students who major in math-intensive subjects. Altogether, the evidence suggests that America's math wounds have been self-inflicted, illustrating the hazards of a single-minded focus on relative rather than absolute performance. Closing the achievement gap by improving the performance of struggling students is hard; closing the gap by reducing the quality of education offered to high performers--for example, by eliminating tracking and promoting universal access to "rigorous" courses while reducing the definition of rigor--is easy. The thoughtless incentives often provided to close the gap make the path of least resistance even more tempting. This report concludes with a series of prescriptions for ensuring forthcoming generations of American workers will include both innovators who create jobs in technically demanding industries and workers qualified to hold them: (1) For several decades, the United States has counteracted its decline in math in part by importing highly talented immigrants. American immigration policy prioritizes family reunification over skills, in direct contrast with peer nations such as Australia and Canada. Any attempt at immigration reform should address this issue; (2) Curricular fads such as Singapore math hold promise in many circles but may not be readily adaptable to American cultural and educational settings. Experimentation is warranted, but we must be mindful that the net effect of our past curricular tinkering has been negative; and (3) Pursuing equity in curriculum must harm some students, and evidence suggests that some past reforms have managed to harm all of them. American students are heterogeneous, and a rational strategy to improve math performance must begin with that premise. (Contains 8 figures and 23 notes.)