The Harvard Graduate School of Education seeks funding to establish the Mathematics Case Development Project: Converting Barriers to Bridges(MCDP) - The objective of this project is to develop teacher preparation materials in the form of teaching cases and teaching notes that will enable prospective teachers to explore important mathematical concepts in depth while encouraging the development of desirable teaching practices. The project also will offer seminars and specific dissemination activities for mathematics educators to learn about this approach. The 2 1/2 year project will produce 18 written teaching cases and accompanying teaching notes on a range of 5-12 mathematical concepts identified by researchers and practicing teachers as particularly difficult to teach -- including especially those areas where human intuition often fails the mathematics student. Teams comprised of teacher educators and mathematicians from Harvard University, the University of Massachusetts, Boston and the University of New Hampshire and practicing teachers will join to develop, pilot and revise the case materials. The (MCDP) Project will have a potential impact on novice mathematics teachers, with a possible extension to experienced mathematicians and mathematics teacher educators, and the larger teacher education community.