A significant challenge in mathematics education is the explication of the development of new mathematical conceptions on the part of students. The current reform is predicated on our capacity to provide students with rich and improved opportunities to learn mathematics based on a coherent knowledge of how mathematical concepts develop in students. The PI argues that the Mathematics education community is, in general, moving forward without an adequate understanding of how learners develop new concepts and that this shortcoming is severely limiting the success of efforts to design high quality curricular materials, carry out effective mathematics teaching and improve mathematics education. To goal of this SGER proposal is to bring some redress to this situation.
