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 Fostering Perseverance. John is a national mathematics curriculum and professional learning consultant who also speaks frequently at national conferences and institutes. He is active in state and national professional organizations, recently serving on the board of directors for the National Council of Teachers of Mathematics (NCTM) and currently on the board of directors for the National Council of Supervisors of Mathematics (NCSM).

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