Course Description: As the emphasis in mathematics classrooms shifts to activities in which students engage in deeper mathematical inquiries, the question arises, for both teachers and researchers: How do we describe students' mathematical ideas in ways that both respect how students experience these ideas and retain the connection of these ideas to mathematics as a discipline? Put more directly, as we push beyond a mathematics of procedures and memorization, what does it look like to do genuine mathematics in teh classroom? One it is granted that this mathematics will be different from what teachers have been traditionally tuaght, other questions also arise, such as: How does a teacher use his/her mathematics in the classroom? What mathematics do teachers need to know to understand children's mathematics?
We will consider these and related questions in this seminar. The work of the semianr will consist of close readings of a small number of critical works in mathematics education, examinaition of artifacts of practice, such as videos of classroom conversation, and smeinar discussions on the above questions built around these materials. In addition to an extended seminar paper, students will be required to submit informal writings each week to a web-based conversation in response to the course reading.
Among the works to be studied are landmark papers by authors such as Shulman, Ma, Lampert, Schifter & Fosnot, Carpenter, Fennema, & Franke., Cobb, Lehrer & Chazan, and Ball & Bass.