Mathematical Argumentation in Middle School-The What, Why, and How

Jennifer Knudsen has been working in mathematics education since her days as a Peace Corps volunteer in Kenya and as a teacher in in New York City Public Schools. She has focused on students' engagement in mathematics as an equity issue throughout her career, including work on numerous curriculum and professional development projects. She directs the Bridging Professional Development project as part of her role as a senior mathematics educator at SRI International. She holds a B.A. from The Evergreen State College, where she learned to love mathematical argumentation. She lives in Austin, Texas with her husband and daughter. Harriette S. Stevens attended the University of Kansas where she received her Bachelor of Arts in Applied Mathematics and Master of Arts in Education, with a concentration in Mathematics. She received her Doctorate in Education, with a focus on curriculum and instructional design, from the University of San Francisco. She was the director of a mathematics professional development program for K-12 teachers at the University of California, Berkeley's Lawrence Hall of Science. In this capacity, she worked in partnership with several urban-school districts, and designed PD and instructional materials to help improve teachers' understanding of mathematics content and their students' preparation for success in college and careers. Currently, she is a consultant with the Mathematics Education Group, San Francisco and co-director of the Bridging professional development project at SRI International, Menlo Park. Her interests include a focus on strengthening teachers' knowledge of mathematics content and the ways in which this knowledge is used to advance classroom discourse and problem solving in urban schools. Teresa Lara-Meloy is passionate about finding better ways of teaching middle school math and improving ways to support teachers. As Math Ed Researcher at SRI International, she designs technology-integrated curricular and professional development materials. She received her M.Ed. from Harvard's Graduate School of Education. She is a member of the NCSM and TODOS. She has co-authored articles on technology in education and the role of technology in supporting the participation of English Language Learners in math class. Hee-Joon Kim, Ph.D. is a mathematics education researcher at SRI International located in Menlo Park, CA. Her research focuses on understanding classroom discourse that supports mathematical argumentation in middle school. She has expertise in designing curriculum materials with dynamic tools for students in middle grades. She has been involved in research-based professional development projects that focus on improving classroom practices that support conceptual understanding and promote equity. She received a B.S. in Mathematics at Ewha Womans University in South Korea and a Ph.D. in Mathematics Education at the University of Texas at Austin. Nicole Shechtman, Ph.D., is a senior educational researcher at SRI International located in Menlo Park, CA. Her research and evaluation work explores critical issues in mathematics teaching and learning, innovative uses of educational technology, and the development of social and emotional competencies, such as effective communication, teamwork, and everyday problem-solving. She holds a PhD in psychology from Stanford University.

Preface Acknowledgments About the Authors Chapter 1. Mathematical Argumentation: Why and What Argumentation Is Important! What Argumentation Is-and Is Not A Four-Part Model of Argumentation About Truth Teaching as Disciplined Improvisation Improvisation for Argumentation and Norm Setting Sharing Mathematical Authority Getting Started With Argumentation Argumentation Lessons Versus Argumentation in Lessons Working Together Chapter 2. Generating Cases What Does It Mean to Generate Cases? An Activity Rich in Argumentation and Content Vignette: Small Groups Generate Cases Teaching Moves Establishing Norms Planning Tasks Working Together Chapter 3. Conjecturing What Does It Mean to Conjecture? Vignette: Conjecturing Together Teaching Moves Establishing Norms Planning Tasks Working Together Chapter 4. Justifying What Does It Mean to Justify? Vignette: Justifying Multiple Conjectures Teaching Moves for Eliciting Justifications Vignette: Critiquing and Connecting Arguments Teaching Moves for Critiquing and Connecting Arguments Establishing Norms Planning Tasks Working Together Chapter 5. Representations in Justifications What Are Representations? Vignette: Visual Representations Foster Participation Vignette: Gestures Enable a Unique Contribution Teaching Moves Using Dynamic Digital Tools Establishing Norms Planning Tasks Working Together Chapter 6. Levels of Justification Four Levels of Justification Level 0: No Justification Level 1: Case-Based Justifications Level 2: Partially Generalized Justifications Based on Cases Level 3: Fully Generalized Justifications A Rubric for Levels Teaching Moves for Transitions Between Levels Working Together Chapter 7. Concluding What Does It Mean to Conclude? Vignettes: Concluding Teaching Moves Establishing Norms Planning Tasks Working Together Chapter 8. Planning How Can You Plan for Students' Argumentation? Written Lesson Plans Visualizing a Lesson Vignette: Visualizing Justification Digital Tools Updating and Sharing Lesson Plans Advice on Planning Working Together Glossary References Index

If you share my belief that "construct viable arguments and critique the reasoning of others" are perhaps the nine most important words in the Common Core era, then Mathematical Argumentation in Middle School is just what you need. This powerful and practical book takes us through an accessible process of generating cases, making conjectures, and justifying that fully supports bringing SMP #3 to life in our classrooms. -- Steve Leinwand This great resource gives teachers tools to implement the four cycles of mathematical argumentation and help students develop a "variety of expertise," as described in the Standards of Mathematical Practice. As students cycle through the phases, they are guided in building "mathematical authority" as independent thinkers and creators of mathematical ideas. I recommend this book to any teacher who wants to amp up the math discussion in their classroom. -- Annette Hilts Now more than ever, we need to provide all children with opportunities to learn to think critically and participate in thoughtful, productive debate in today's society. This book translates the mathematical practice of argumentation into a four-stage process that can be applied across a wide range of mathematical content. This process utilizes an innovative, research-based approach based on improv games that opens access for all students to participate in the process of mathematical argumentation. Finally, there is a practical guide for making argumentation an everyday practice in mathematics classrooms! -- Kristen Bieda