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

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

September 2017 | 192 pages | Corwin

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  

Free resources

Improv Games to Engage Students in Mathematical Discussions

Improv Games to Engage Students in Mathematical Discussions

"In our work, we help teachers support rich, inclusive mathematical discussions among all students. For these discussions to happen, a classroom culture must be developed based on what are often new norms for mathematics class: that students should listen to each other, not just the teacher; that mistakes are OK, even welcomed, as students search for mathematical truth together. New norms take time and deliberate effort to develop."

Read more from Jennifer Knudsen, author of Mathematical Argumentation in Middle School-The What, Why, and How, on Corwin Connect.

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Establishing Norms for Mathematical Argumentation

Establishing Norms for Mathematical Argumentation

"In the past, and even many classrooms today, a math class involved the teacher presenting a lesson, then students practicing the procedures therein, and the teacher correcting students along the way. But things are changing!"

Read more from Teresa Lara-Meloy, author of Mathematical Argumentation in Middle School-The What, Why, and How, on Corwin Connect.

Read Now

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
American Institutes for Research

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
Vallejo City Unified School District

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
Michigan State University

Sample Materials & Chapters

Table of Contents


Chapter 1

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