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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 and Nikki Schechtman Corwin Press
Pub Date:
Pbk 192 pages
AU$69.00 NZ$72.17
Product Status: Not Our Publication - we no longer distribute
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Get them talking: Your formula for bringing math concepts to life!


Want your middle schoolers to intelligently engage with mathematical ideas? Ready to help them construct and critique viable arguments that meet tough Standards for Mathematical Practice 3 standards? Look no further. This research-based gem will help you foster the critical reasoning and argumentation skills every student needs for intelligent discourse within our modern society. Learn how to bring mathematical argumentation alive in your classroom—all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding.


Filled with content-focused and classroom-ready games, activities, vignettes, sample tasks, and links to online tools and a rich companion website, this innovative guide will help you

    • Immediately engage students in fun, classroom-ready argumentation activities

    • Plan lessons that foster lively, content-driven, viable argumentation

    • Help students explore mathematical ideas and take ownership of their learning

    • Facilitate deep mathematical understanding

    • Promote students’ precise use of mathematical language to construct, justify, and critique mathematical ideas and mathematical statements or the arguments of others.

    • Encourage logical, clear connections between abstract ideas for enhanced 21st century skills

This guide delivers all the tools you need to get serious about mathematical argumentation and bring well-planned, well-constructed mathematical discourse to life in your classroom today!


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
Working Together
Chapter 3. Conjecturing
What Does It Mean to Conjecture?
Vignette: Conjecturing Together
Teaching Moves
Establishing Norms
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
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
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
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

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!
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 education researcher at SRI International located in Menlo Park, CA. Her research and evaluation work explores the interplay between learning disciplinary knowledge and developing the critical social and emotional competencies people need to succeed—including effective communication, teamwork, and everyday problem solving. As research director for the Bridging Project since the start, her focus through the years has been on learning deeply from the teachers. She holds a Ph.D. in psychology from Stanford University and still feels the improv course she took in grad school was one of the best experiences in her life.