Table of Contents

List of Figures

List of Videos

About the Teachers Featured in the Videos

Foreword

About the Authors

Acknowledgments

Preface

Chapter 1. Make Learning Visible in Mathematics

• Forgetting the Past
• What Makes for Good Instruction?
• The Evidence Base
• Meta-Analyses
• Effect Sizes
• Noticing What Does and Does Not Work
• Direct and Dialogic Approaches to Teaching and Learning
• The Balance of Surface, Deep, and Transfer Learning
• Surface Learning
• Deep Learning
• Transfer Learning
• Surface, Deep, and Transfer Learning Working in Concert
• Conclusion
• Reflection and Discussion Questions

Chapter 2. Making Learning Visible Starts With Teacher Clarity

• Learning Intentions for Mathematics
• Student Ownership of Learning Intentions
• Connect Learning Intentions to Prior Knowledge
• Make Learning Intentions Inviting and Engaging
• Language Learning Intentions and Mathematical Practices
• Social Learning Intentions and Mathematical Practices
• Reference the Learning Intentions Throughout a Lesson
• Success Criteria for Mathematics
• Success Criteria Are Crucial for Motivation
• Getting Buy-In for Success Criteria
• Preassessments
• Conclusion
• Reflection and Discussion Questions

Chapter 3. Mathematical Tasks and Talk That Guide Learning

• Making Learning Visible Through Appropriate Mathematical Tasks
• Exercises Versus Problems
• Difficulty Versus Complexity
• A Taxonomy of Tasks Based on Cognitive Demand
• Making Learning Visible Through Mathematical Talk
• Characteristics of Rich Classroom Discourse
• Conclusion
• Reflection and Discussion Questions

Chapter 4. Surface Mathematics Learning Made Visible

• The Nature of Surface Learning
• Selecting Mathematical Tasks That Promote Surface Learning
• Mathematical Talk That Guides Surface Learning
• What Are Number Talks, and When Are They Appropriate?
• What Is Guided Questioning, and When Is It Appropriate?
• What Are Worked Examples, and When Are They Appropriate?
• What Is Direct Instruction, and When Is It Appropriate?
• Mathematical Talk and Metacognition
• Strategic Use of Vocabulary Instruction
• Word Walls
• Graphic Organizers
• Strategic Use of Manipulatives for Surface Learning
• Strategic Use of Spaced Practice With Feedback
• Strategic Use of Mnemonics
• Conclusion
• Reflection and Discussion Questions

Chapter 5. Deep Mathematics Learning Made Visible

• The Nature of Deep Learning
• Selecting Mathematical Tasks That Promote Deep Learning
• Mathematical Talk That Guides Deep Learning
• Accountable Talk
• Supports for Accountable Talk
• Teach Your Students the Norms of Class Discussion
• Mathematical Thinking in Whole Class and Small Group Discourse
• Small Group Collaboration and Discussion Strategies
• When Is Collaboration Appropriate?
• Grouping Students Strategically
• What Does Accountable Talk Look and Sound Like in Small Groups?
• Supports for Collaborative Learning
• Supports for Individual Accountability
• Whole Class Collaboration and Discourse Strategies
• When Is Whole Class Discourse Appropriate?
• What Does Accountable Talk Look and Sound Like in Whole Class Discourse?
• Supports for Whole Class Discourse
• Using Multiple Representations to Promote Deep Learning
• Strategic Use of Manipulatives for Deep Learning
• Conclusion
• Reflection and Discussion Questions

Chapter 6. Making Mathematics Learning Visible Through Transfer Learning

• The Nature of Transfer Learning
• Types of Transfer: Near and Far
• The Paths for Transfer: Low-Road Hugging and High-Road Bridging
• Selecting Mathematical Tasks That Promote Transfer Learning
• Conditions Necessary for Transfer Learning
• Metacognition Promotes Transfer Learning
• Self-Questioning
• Self-Reflection
• Mathematical Talk That Promotes Transfer Learning
• Helping Students Connect Mathematical Understandings
• Peer Tutoring in Mathematics
• Connected Learning
• Helping Students Transform Mathematical Understandings
• Problem-Solving Teaching
• Reciprocal Teaching
• Conclusion
• Reflection and Discussion Questions

Chapter 7. Assessment, Feedback, and Meeting the Needs of All Learners

• Assessing Learning and Providing Feedback
• Formative Evaluation Embedded in Instruction
• Summative Evaluation
• Meeting Individual Needs Through Differentiation
• Classroom Structures for Differentiation
• Adjusting Instruction to Differentiate
• Intervention
• Learning From What Doesn’t Work
• Grade-Level Retention
• Ability Grouping
• Matching Learning Styles With Instruction
• Test Prep
• Homework
• Visible Mathematics Teaching and Visible Mathematics Learning
• Conclusion
• Reflection and Discussion Questions

Appendices

• A. Effect Sizes
• B. Standards for Mathematical Practice
• C. A Selection of International Mathematical Practice or Process Standards
• D. Eight Effective Mathematics Teaching Practices
• E. Websites to Help Make Mathematics Learning Visible

References

Index