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:

1. a brief overview of past work on teachers' mathematical knowledge;
2. the design of our current work on the mathematical entailments of teaching (including why we frame the problem this way);
3. 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;
4. what we are learning about the effort to collaborate across the substantial gulf that traditionally divides mathematics and education.