**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 Doesnâ€™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

**Appendix A. Effect Sizes**

**Appendix B. Standards for Mathematical Practice**

**Appendix C. A Selection of International Mathematical Practice or Process Standards**

**Appendix D- Eight Effective Mathematics Teaching Practices**

**Appendix E. Websites to Help Make Mathematics Learning Visible**

**References**

**Index**