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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
This thoroughly researched guide helps you bring well-constructed mathematical discourse to life in your classroom today! Includes activities, vignettes, sample tasks, and online tools.

Full description

Product Details
  • Grade Level: PreK-12
  • ISBN: 9781506376691
  • Published By: Corwin
  • Series: Corwin Mathematics Series
  • Year: 2017
  • Page Count: 192
  • Publication date: September 21, 2017

Price: $33.95



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!



Jennifer Knudsen photo

Jennifer Knudsen

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 photo

Harriette S. Stevens

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 photo

Teresa Lara-Meloy

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 photo

Hee-Joon Kim

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 photo

Nicole Shechtman

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 PhD in psychology from Stanford University.

Table of Contents

Table of Contents



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






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