Abstract  Introduction  Discourse  Interventions  Decisions  Cylinder Problem  Lesson Reflections  Student Predictions  Project Reflections  Conclusion  References  Acknowledgments  Teacher Resources Authors' Biographies Table of Contents VIDEO CLIPS: Internet access via modem may mean very long download times for video clips. If you are not on a fast line, you may want to read this paper without viewing the clips. share your thoughts, ideas, questions, and experiences; read what others have to say.		This videopaper opens a conversation about the use of discourse as the basis for encouraging students' mathematical thinking in classrooms and for supporting professional growth. A collaboration of teacher practitioners and Math Forum staff, it reflects an attempt to integrate practice and research, reporting on findings culled from discussions of research articles and chapters, classroom practice, and videotapes of classroom teaching. Each of the teacher participants worked with his or her students on the cylinder problem, a non-routine challenge problem providing the opportunity for rich discourse and for reflection on its use. Links between these findings and the research on student learning and instruction are noted. Discussion focuses on the specific strategies that are used to help students become engaged in inquiry and take more responsibility and initiative in their learning. Video clips from the teacher's classrooms illustrate the interventions discussed. The challenge problem and lessons for the elementary, middle school, and high school classroom are detailed, and a corresponding set of student predictions is presented. Finally, authors' reflections on their participation in this project are summarized. 1 The Math Forum's Bridging Research and Practice Group: Jon Basden, Susan Boone, Annie Fetter, Judith Koenig, Cynthia Lanius, Art Mabbott, John McKinstry, K. Ann Renninger, Roya Salehi, Susan Stein, Jody Underwood, Stephen Weimar PLEASE READ: You will need to have QuickTime 4 or 5 in order to view the video clips that are included in this article. Go to the Download QuickTime page. Scroll down to the "Tell us who you are" section, tell them who you are, and then click on Download QuickTime.

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