Learning to Teach Mathematics: Focus on Student Thinking

great strides in developing theories and re-search-based evidence about how to teach elemen-tary school mathematics in a way that develops students ' mathematical understanding. Much of this progress has grown out of research projects that engage teachers in learning to teach mathemiatics. These projects have not only shown what is possible for teachers and students but have also provided in-sight into how to support teachers in their own leamn-ing. We use one particular research and development project, Cognitively Guided Instruction (CGI), as an illustration of how theory and research inform the teaching and learning of mathematics. The key to CGI has been an explicit, consis-tent focus on the development of children's math-ematical thinking (Carpenter, Fennema, & Franke, 1996). This focus serves as the guide for under-standing CGI's contributions as well as its evolu-tion. ' Initiated over 15 years ago by Carpenter, Fennema, and Peterson, CGI sought to bring to-gether research on the development of children's mathernatical thinking and research on teachin