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Productive Math Struggle

Productive Math Struggle
A 6-Point Action Plan for Fostering Perseverance

Foreword by Matt Larson

April 2020 | 216 pages | Corwin

“Seldom has a book been as timely or as necessary as Productive Math Struggle is today. . . One of the remarkable accomplishments of SanGiovanni, Katt, and Dykema’s work lies in how they seamlessly connect the research on high-quality tasks, high expectations, identity, and equity to productive math struggle. This is perhaps their greatest contribution. The authors see productive math struggle as a critical feature of mathematics classrooms that support access, equity, and empowerment, specifically arguing that every student is ‘worthy of struggle.’” 

From the Foreword by Matt Larson, Ph.D.
Past President (2016-2018), National Council of Teachers of Mathematics
Associate Superintendent for Instruction, Lincoln Public Schools, Nebraska

Struggle is hard. Productive struggle is power.

All students face struggle, and they should—it is how they learn and grow. The teacher’s job is not to remove struggle, but rather to value and harness it, helping students develop good habits of productive struggle. But what’s missing for many educators is an action plan for how to achieve this, especially when it comes to math.

Persevering through difficult challenges to reach new learning is the core of Productive Math Struggle. When left unsupported, struggle can become unproductive and demoralizing, negatively influencing students’ mathematical identities. The authors guide teachers through six specific actions—including valuing, fostering, building, planning, supporting, and reflecting on struggle—to create a game plan for overcoming obstacles by sharing

  • Actionable steps, activities, and tools for implementation
  • Instructional tasks and vignettes representative of each grade level
  • Real-world examples showcasing classroom photos and student work samples

A book study guide is available under the Free Resources tab that helps math educators to learn together on how to incorporate productive math struggle in their classrooms. 

Revolving around the idea that math is a way of thinking and understanding, and not just the pursuit of answers and procedures, this book empowers students to embrace productive struggle to build essential skills for learning and living—both inside and outside the classroom.

Foreword by Matt Larson
Introduction: Why Struggle? Why Now?
Chapter 1: VALUE Productive Struggle
Why Struggle Matters

Math is more than the pursuit of answers

Math isn't a procedure

Math is about equity, access, and opportunity

Productive struggle is essential for living and learning

What Productive Struggle Is and Isn't

What struggle looks like

When schools value struggle

Teacher behaviors for productive struggle

Educating families

Productive struggle "Look-For's"

Whole school agreement about productive struggle

Struggle and growth mindset

Moving from unproductive to productive beliefs about struggle

Struggle and growth mindset

Moving from unproductive to productive beliefs about struggle

Key Takeaways About Action 1: Value Productive Struggle

Action 2: FOSTER an Identity for Productive Struggle
What Is a Math Identity?

Your mathematical identity and its effects on instructional choices

Thinking about your experiences as a math student

Knowing Your Students' Mathematical Identities

Student Identity Activity 1: My Math Autobiography

Student Identity Activity 2: My Math Timeline

Student Identity Activity 3: Journal Prompts

Student Identity Activity 4: Math Beliefs Inventory

Student Identity Activity 5: Math Role Models and Their Stories, Who Are Mathematicians?

Student Identity Activity 6: Bumper Sticker

Student Activity 7: My Math Superpower

Student Identity Activity 8: Struggle Emojis

Key Takeaways About Action 2: Foster Identity for Productive Struggle

Chapter 3: Action 3: BUILD Community for Productive Struggle
Building Classroom Community for Productive Struggle

Addressing challenges to creating community

Establishing norms for a productive community

Maintaining community throughout the year

Activities for Building and Maintaining a Productive Math Community

Community Activity 1: Math Pledge

Community Activity 2: Group Behaviors Comic Strip

Community Activity 3: Good Groups vs Bad Groups

Community Activity 4: The Number Quilt

Community Activity 5: A Picture Is Worth 1,000 Numbers

Community Activity 6: Name and Number Tents

Community Activity 7: Dimensions of Me (or Many Faces)

Activities to Promote a Community Understanding of Productive Struggle

Community of Struggle Activity 1: The Picture of Struggle

Community of Struggle Activity 2: A Time I Struggled - The Ski Jump

Community of Struggle Activity 3: Create a Class Definition of Struggle

Key Takeaways About Action 3: Build Community for Productive Struggle

Chapter 4: Action 4: PLAN for a Lesson with Productive Struggle
Planning for Struggle

Establish the mathematics goal

Select tasks that create the right amount of struggle

Selecting High-Quality Tasks for Rigor

Tasks for conceptual understanding

Tasks for procedural fluency

Tasks for application

Modify Tasks for Provoke Productive Struggle

Modification Strategy 1: Ask Students to Create Multiple Representations (Create)

Modification Strategy 2: Ask Students to Create or Connect DIfferent Representations (Connect)

Modification Strategy 3: Ask Students “Does This Always Work?” (Generalize)

Modification Strategy 4: Ask Students the Reverse (Reverse the Problem)

Modification Strategy 6: Ask Students Open Questions (Open Up)

Modification Strategy 7: Ask Students to Compare and Contrast (Similarities and Differences)

Modification Strategy 8: Ask Students to Find and Use a Pattern (Find a Pattern)

Modification Strategy 9: Ask Students to Put their Understanding in Writing (Write About It)

Modification Strategy 10: Ask Before They Are Taught (Change the Sequence)

Doing the Task and Anticipating

Anticipate representations

Anticipate language and terms

Anticipate misconceptions and flawed strategies

Planning response and reaction

Instructional Models, Routines, and Other Considerations when Planning for Struggle

Direct Instruction

Gradual Release of Responsibility

Other Instructional Choices

Key Takeaways About Action 4: Plan for Productive Struggle

Action 5: SUPPORT the Productive Struggle During the Lesson
Classifying Various Types of Struggle

Classifying Various Types of Struggle

Responding to Different Kinds of Struggle

The Problem With Rescuing Student Answers

Struggle Moves That Rescue Thinking

Struggle Move 1: Prepping the Task

Struggle Move 2: Catch and Release

Struggle Move 3: Referrals

Struggle Move 4: Metacognitive Questions

Struggle Move 5: Remove the Numbers

Tips for Navigating Struggle

Teacher Tip 1: Don’t Restate More Than They Say (Revoicing)

Teacher Tip 2: Honoring Mistakes

Teacher Tip 3: Consider When to Help and When to Hold Back

Teacher Tip 4: Be Mindful of Mnemonics and Other “Aides” or “Tricks” to Support Struggle

Teacher Tip 5: Keep It From Boiling Over

Teacher Tip 6: Be aware of early finishers

Teacher Tip 7: Adjust the time

Teacher Tip 8: Focus on a strategy

Teacher Tip 9: Celebrate it

Teacher Tip 10: Leverage accountability and participation

Key Takeaways About Action 4: Support Productive Struggle

Chapter 6: Action 6: REFLECT on Productive Struggle
Integrating Reflection on Struggle into Lesson Closure

Student Activities for Reflection on Struggle

Independent Writing and Drawing

Student Activity 1: Journaling

Student Activity 2: Struggle Doodle

Student Activity 3: Who I Learned From

Collaborative Reflections

Student Activity 4: The Picture of Struggle

Student Activity 5: One Word

Student Activity 6: Find Someone

Evaluative Reflection Activities

Student Activity 7: Got It, Tried It

Student Activity 8: Too Easy, Too Hard, Just Right: The Goldilocks Reflection

Student Activity 9: Today I, Tomorrow I Will

Teacher Reflection on Productive Struggle

Teacher Option 1: In-the-Moment Notes

Teacher Option 2: Journaling

Teacher Option 3: When Students Reflect, You Reflect

Teacher Option 4: Team Reflections or Professional Learning Cadres

Reflection Leads to Celebration

Celebration Approach 1: Notice It and Reward It with Struggle Bucks and Shout-Outs

Celebration Approach 2: Reward It Beyond Math Class with Brag Tags

Celebration Approach 3: Reward When Students Take Advantage of Tools

One caveat about celebration

Key Takeaways About Action 6: Reflect on Productive Struggle

Chapter 7: Closing Thoughts about Struggle
Productive Struggle Definition and Inventory: Where Are You Now?

One Final Note


The book provides pre-service teachers with valuable information in the area of productive struggle.

Dr Elliott Johnson
Education Dept, Luther College
January 31, 2023

John J. SanGiovanni

John J. SanGiovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is an adjunct professor and coordinator of the Elementary Mathematics Instructional Leadership graduate program at McDaniel College. In addition to this Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K-8, Answers to Your Biggest Questions about Teaching Elementary Math, the Daily Routines to Jump-Start Math series, and Productive Math Struggle: A 6-Point Action Plan for... More About Author

Susan K. Katt

Susie Katt is the K-2 Mathematics Coordinator in Lincoln, Nebraska, where she leads professional learning, assessment, and math curriculum development. She is an author of Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance and Answers to Your Biggest Questions About Teaching Elementary Math. She is also a national math curriculum consultant. Susie speaks at state, regional, and national conferences. She served the National Council of Teachers of Mathematics (NCTM) as the chair of the editorial panel for the journal Teaching Children Mathematics, as department editor for Mathematics Teacher: Learning and Teaching PK... More About Author

Kevin J. Dykema

Kevin J. Dykema is an 8th grade math teacher in Mattawan, Michigan and serves on several building and district committees. He is a professional learning consultant and is a frequent speaker at national, regional, and local conferences. Kevin is active in state and national professional organizations recently serving on the Board of Directors for the National Council of Teachers of Mathematics and as a board member and annual conference chair for the Michigan Council of Teachers of Mathematics. More About Author

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ISBN: 9781544369464