Michigan University seeks funds to investigate what is involved in trying to teach mathematics for understanding in an elementary classroom, and to develop tools for inquiry into and communication about this kind of teaching. The project has three interrelated purposes: to study the kind of mathematics teaching and learning envisioned by the current reforms; to construct new approaches for teachers and teacher educators to learn about this kind of teaching; and to educate teacher educators in reforming the aims, content, and discourse of teacher education. The proposers will develop a collection of scenarios/vignettes of elementary mathematics classrooms, and will place them into a hypermedia environment for investigation and use by other mathematics educators. These materials will contribute to understanding teacher/ student dialogues and classroom interactions and will help researcher learn more about how children construct mathematics. The implications for teacher preparation include the use of materials for instruction in courses for teachers, both preservice and inservice. In addition, the instructors of the courses for teachers will learn from the materials, their interpretation, and the research results. Cost sharing amounts to over 12% of NSF funding.