I encourage you to visit and read the videopaper that the Math Forum's Bridging Research and Practice (BRAP) Group has created called "Encouraging Mathematical Thinking: Discourse around a Rich Problem." The videopaper is located at:
The videopaper includes a presentation of a stimulating mathematics problem involving cylinders as it was taught in six classrooms, video clips of students in these classrooms, and an exploration of teaching practices and discussions about how to encourage mathematical thinking.
The focus of the videopaper in particular is on discourse in the classroom; the use of questioning, listening, writing, and reflection as a means of encouraging reciprocal conversation -- the kind of teaching that enables every person to develop his or her voice in creating mathematical understanding. The video clips used in this paper help establish a grounded conversation among researchers and practitioners, allowing teachers themselves to weave together research and practice.
A mailing list (discussion) has been set up to enable readers to participate in the conversations that have started in the videopaper. You can sign up for e-mail notifications, listing the author and subject of each new post related to the topics of discussion in the videopaper, by entering your email in the following web page: