Mathematical Argumentation in Middle School-The What, Why, and How: A Step-by-Step Guide With Activities, Games, and Lesson Planning Tools

by Jennifer Knudsen, Harriette Stevens, Teresa Lara-Meloy, Hee-Joon Kim, Nikki Shechtman

Overview

Get them talking: Your formula for bringing math concepts to life!

Want your middle schoolers to intelligently engage with mathematical ideas? Look no further. This research-based gem brings tough Standards for Mathematical Practice 3 standards for mathematical argumentation and critical reasoning alive—all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding.

• Immediately engage students in fun, classroom-ready argumentation activities
• Help students explore—and take ownership of—mathematical ideas and concepts
• Promote precise use of mathematical language

Includes games, vignettes, a rich companion website, sample tasks, and links to online tools. Bring well-planned, well-constructed mathematical discourse to life in your classroom today!

Product Details

ISBN-13:	9781506376691
Publisher:	SAGE Publications
Publication date:	10/05/2017
Series:	Corwin Mathematics Series
Pages:	192
Product dimensions:	8.50(w) x 11.00(h) x 0.50(d)

About the Author

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 Ph D in psychology from Stanford University.

Table of Contents

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

Editorial Reviews

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

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

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