This paper summarizes a number of empirical findings and theoretical conclusions about children's mathematics learning. Translating these findings and conclusions into improved instructional practices, however, will take a considerable amount of work. Stigler and Hiebert's (1998) description of the Japanese emphasis on continuous improvement in teaching points toward a process that seems essential in U.S. classrooms as well. The process that they describe involves groups of teachers working together to perfect the way in which they teach particular concepts and procedures.