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

A Step-by-Step Guide With Activities, Games, and Lesson Planning Tools
Jennifer Knudsen - SRI International, USA
Harriette Stevens - Mathematics Education Group
Teresa Lara-Meloy - SRI International, USA
Hee-Joon Kim - SRI International, USA
Nikki Shechtman - SRI International, USA
Mathematical Argumentation in Middle School-The What, Why, and How
September 2017 | 192 pages | Corwin
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ISBN: 9781506394251
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ISBN: 9781506376691
Available from January 0001

Description

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!

Contents

Preface

Preface

Acknowledgments

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

Glossary

References

References

Index

Index

Additional materials

Description

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!

Contents

Preface

Preface

Acknowledgments

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

Glossary

References

References

Index

Index

Additional materials

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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


September 2017 | 192 pages | Corwin

Format Published Date ISBN Price
Paperback 01/02/2026 9781506376691 $37.95
Lifetime 01/02/2026 9781506394251 $35.00

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!


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

Recent Product 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, 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

Recommendations