Abstract  Introduction  Discourse  Interventions  Decisions  Cylinder Problem  Lesson Reflections  Student Predictions  Project Reflections  Conclusion  References  Acknowledgments  Teacher Resources Authors' Biographies Table of Contents About the Project 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.		A. Abstract B. Introduction C. The Teacher's Role in Encouraging Discourse   1. Teacher Interventions   2. Making Decisions D. The Cylinder Problem: Promoting discourse   1. Elementary Level Lesson Plan    Family Math Activity   2. Middle School Lesson Plan   3. High School Lesson Plan    Constant perimeter project   4. Calculus Lesson Plan    Constant perimeter project E. Reflections on the Lesson F. Student Predictions G. Project Reflections H. Conclusion I. References J. Acknowledgments K. Lesson Plans and Resources

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