Policymakers in the U. S. have been trying to change schools and school practices for years. Though studies of such policies raise doubts about their effects, the last decade has seen an unprecedented increase in state policies designed to change instructional practice. One of the boldest and most comprehensive of these has been undertaken in California, where state policymakers have launched an ambitious effort to improve teaching and learning in schools. We offer an early report on California's reforms, focusing on mathematics. State officials have been promoting substantial changes in instruction designed to deepen students' mathematical understanding, to enhance their appreciation of mathematics and to improve their capacity to reason mathematically. If successful, these reforms would be a sharp departure from existing classroom practice, which attends chiefly to computational skills. The research reported here focuses on teachers' early responses to the state's efforts to change mathematics instruction. The case studies of five teachers highlight a key dilemma in such ambitious reforms. On the one hand, teachers are seen as the root of the problem: their instruction is mechanical, often boring, and superficial. On the other hand, teachers are cast as the key agents of improvement because students will not learn the new mathematics that policymakers intend unless teachers learn that math and teach it. But how can teachers teach a mathematics that they never learned, in ways they never experienced?That is the question explored in this special issue.