Lehrer and Lesh review research in the psychology of mathematical learning and mathematics education through a genetic, developmental framework that reflects both cognitive and sociocultural perspectives on learning. The authors examine individual cognitive processes and sociocultural contexts that underscore mathematical thinking. Origins of mathematical learning are linked to the development of argument. The role of inscriptions, notations and symbolic patterns are reviewed as a distinct form of mathematical literacy. These ideas are applied to studies of geometry measurement that stress spatial visualization and to mathematical modeling. A final section presents implications for classroom learning and describes how to create a classroom culture that values mathematical explanation, thinking, and instructional design.