Encouraging Mathematical Thinking



 Cylinder Problem
 Lesson Reflections
 Student Predictions

 Project Reflections

 Teacher Resources


Table of Contents

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			Mathematical Thinking: Discourse and a Rich Problem

The Math 
			Forum's Bridging Research and Practice Group

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

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