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Mathematical Argumentation in Middle School-The What, Why, and How
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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 | 184 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!

 
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

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