University of Michigan

With Hyman Bass

The mathematical knowledge that it takes to teach has been a topic of recurrent interest, concern, and debate. Most policy and development in this area has produced lists of topics teachers should know; at the same time, a host of studies have documented how much of this teachers do not know. Our research turns this problem on its head and starts with the practice of teaching, analyzing primary records of practice (videotapes of classroom lessons, children's work, teacher notes) to examine what mathematics is entailed in teaching children. This seminar will have four parts:

- a brief overview of past work on teachers' mathematical knowledge;
- the design of our current work on the mathematical entailments of teaching (including why we frame the problem this way);
- a close investigation of a small segment of videotape, with a look at the embedded mathematics, including what the mathematics is, where and how it seems to play a role;
- what we are learning about the effort to collaborate across the substantial gulf that traditionally divides mathematics and education.

Dr. Deborah Loewenberg Ball's work as a researcher and teacher
educator is rooted in practice, drawing directly and indirectly on her
experience as a classroom teacher. With elementary school mathematics
as the main context, Ball studies the practice of teaching and the
processes of learning to teach, with a current focus on learning in
and from practice itself. Ball's publications include articles on
teacher learning and teacher education; the role of subject matter
knowledge in teaching and learning to teach; endemic challenges of
teaching; and the relations of policy and practice in instructional
reform. She is Associate Editor of the *Journal for Research in
Mathematics Teacher Education*, and is a member of the Mathematical
Sciences Education Board, and of the Commission on Behavioral and
Social Science Education. She was a lead author for the Professional
Standards for Teaching Mathematics. In 1997, Ball received the Raymond
B. Cattell Early Career Award for Programmatic Research from the
American Educational Research Association.