You are here

Productive Math Struggle
Share

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



May 2020 | 248 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

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

 

Preview this book

For instructors

This book is not available as an inspection copy. For more information contact your local sales representative.

Purchasing options

Please select a format:

ISBN: 9781544369464
£26.99