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
John SanGiovanni is a mathematics supervisor in Howard County, Maryland. There he leads mathematics curriculum development, digital learning, assessment, and professional development for 41 elementary schools and more than 1,500 teachers. John is an adjunct professor and coordinator of the Elementary Mathematics Instructional Leader graduate program at McDaniel College. He is an author and national mathematics curriculum and professional learning consultant. John is a frequent speaker at national conferences and institutes. He is active in state and national professional organizations and currently serves on the Board of Directors for the National Council of Teachers of Mathematics. Susie Katt is the K-2 Mathematics Coordinator in Lincoln, Nebraska. In this role, she coordinates professional development, assessment, and curriculum development. Susie is an author for a national mathematics curriculum. She frequently speaks at state, regional, and national conferences. Susie is a special appointment lecturer for the University of Nebraska-Lincoln, a Robert Noyce Master Teaching Fellow, and a member of various state committees. She serves NCTM in a variety of ways which include chair of the Editorial Panel for the Teaching Children Mathematics journal, member of program committees for annual meetings and regional conferences, and speaker at NCTM institutes. 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.