Columbia University

With Deborah Loewenberg Ball

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. Hyman Bass' chief fields of research interest are algebraic
K-theory, number theory, geometric methods of group theory, algebraic
geometry, and mathematics education. He has been a member of the
American Academy of Arts and Sciences since 1981 and of the National
Academy of Sciences since 1982. Bass received the Cole Prize in
Algebra from the American Mathematical Society in 1975, and the Van
Amringe Prize from Columbia University for his book *Algebraic K-theory*
in 1969. In addition to being the author or co-author of over 75
publications in mathematics, Bass has written articles and given
presentations in the area of mathematics education. He is currently
Chair of the National Research Council's Mathematical Sciences
Education Board and of the American Mathematical Society's Committee
on Education. From 1998 to 2002, he will serve as the President of the
International Commission on Mathematics Instruction.