According to a variety of metrics (NAEP, PISA, TIMMS, college completion, etc.), the mathematics knowledge of U.S. students can be described, at best, as mediocre. In light of the growing importance of mathematics for both individual and national economic competitiveness, this weak performance has rightfully alarmed policymakers and the public. The results of decades of research on improving mathematics curricula, most notably the TIMSS, TEDS, and PROM/SE studies, points convincingly to the possibilities of more rigorous, more focused, and most of all, more coherent mathematics standards. The data clearly demonstrate that, compared with higher performing countries, the United States intended curriculum is highly fragmented and the implemented curriculum exceptionally variable across and even within local education agencies. Although the recently adopted Common Core Standards in Mathematics present a major opportunity for overcoming these defects, the weak preparation of U.S. mathematics teachers, particularly primary and early secondary teachers, poses a significant obstacle. The author concludes by calling for a major effort to strengthen the recruitment and preparation of future mathematics teachers and for more aggressively engaging the public in the task of implementing strong mathematics standards. (Contains 4 figures and 5 footnotes.)