‘Seldom has a book been as timely or as necessary as Productive Math Struggle is today. . . One of the remarkable accomplishments of San Giovanni, 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.
Jadual kandungan
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
Mengenai Pengarang
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.
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