Contents

1. List of Figures
2. List of Videos
3. About the Teachers Featured in the Videos
4. Foreword
5. About the Authors
6. Acknowledgments
7. Preface
8. Chapter 1. Make Learning Visible in Mathematics
   1. Forgetting the Past
   2. What Makes for Good Instruction?
   3. The Evidence Base
      1. Meta-Analyses
      2. Effect Sizes
   4. Noticing What Does and Does Not Work
   5. Direct and Dialogic Approaches to Teaching and Learning
   6. The Balance of Surface, Deep, and Transfer Learning
      1. Surface Learning
      2. Deep Learning
      3. Transfer Learning
   7. Surface, Deep, and Transfer Learning Working in Concert
   8. Conclusion
   9. Reflection and Discussion Questions
9. Chapter 2. Making Learning Visible Starts With Teacher Clarity
   1. Learning Intentions for Mathematics
      1. Student Ownership of Learning Intentions
      2. Connect Learning Intentions to Prior Knowledge
      3. Make Learning Intentions Inviting and Engaging
      4. Language Learning Intentions and Mathematical Practices
      5. Social Learning Intentions and Mathematical Practices
      6. Reference the Learning Intentions Throughout a Lesson
   2. Success Criteria for Mathematics
      1. Success Criteria Are Crucial for Motivation
      2. Getting Buy-In for Success Criteria
   3. Preassessments
   4. Conclusion
   5. Reflection and Discussion Questions
10. Chapter 3. Mathematical Tasks and Talk That Guide Learning
    1. Making Learning Visible Through Appropriate Mathematical Tasks
       1. Exercises Versus Problems
       2. Difficulty Versus Complexity
       3. A Taxonomy of Tasks Based on Cognitive Demand
    2. Making Learning Visible Through Mathematical Talk
       1. Characteristics of Rich Classroom Discourse
    3. Conclusion
    4. Reflection and Discussion Questions
11. Chapter 4. Surface Mathematics Learning Made Visible
    1. The Nature of Surface Learning
    2. Selecting Mathematical Tasks That Promote Surface Learning
    3. Mathematical Talk That Guides Surface Learning
       1. What Are Number Talks, and When Are They Appropriate?
       2. What Is Guided Questioning, and When Is It Appropriate?
       3. What Are Worked Examples, and When Are They Appropriate?
       4. What Is Direct Instruction, and When Is It Appropriate?
    4. Mathematical Talk and Metacognition
    5. Strategic Use of Vocabulary Instruction
       1. Word Walls
       2. Graphic Organizers
    6. Strategic Use of Manipulatives for Surface Learning
    7. Strategic Use of Spaced Practice With Feedback
    8. Strategic Use of Mnemonics
    9. Conclusion
    10. Reflection and Discussion Questions
12. Chapter 5. Deep Mathematics Learning Made Visible
    1. The Nature of Deep Learning
    2. Selecting Mathematical Tasks That Promote Deep Learning
    3. Mathematical Talk That Guides Deep Learning
       1. Accountable Talk
       2. Supports for Accountable Talk
       3. Teach Your Students the Norms of Class Discussion
    4. Mathematical Thinking in Whole Class and Small Group Discourse
    5. Small Group Collaboration and Discussion Strategies
       1. When Is Collaboration Appropriate?
       2. Grouping Students Strategically
       3. What Does Accountable Talk Look and Sound Like in Small Groups?
       4. Supports for Collaborative Learning
       5. Supports for Individual Accountability
    6. Whole Class Collaboration and Discourse Strategies
       1. When Is Whole Class Discourse Appropriate?
       2. What Does Accountable Talk Look and Sound Like in Whole Class Discourse?
       3. Supports for Whole Class Discourse
    7. Using Multiple Representations to Promote Deep Learning
    8. Strategic Use of Manipulatives for Deep Learning
    9. Conclusion
    10. Reflection and Discussion Questions
13. Chapter 6. Making Mathematics Learning Visible Through Transfer Learning
    1. The Nature of Transfer Learning
       1. Types of Transfer: Near and Far
    2. The Paths for Transfer: Low-Road Hugging and High-Road Bridging
    3. Selecting Mathematical Tasks That Promote Transfer Learning
    4. Conditions Necessary for Transfer Learning
    5. Metacognition Promotes Transfer Learning
       1. Self-Questioning
       2. Self-Reflection
    6. Mathematical Talk That Promotes Transfer Learning
    7. Helping Students Connect Mathematical Understandings
       1. Peer Tutoring in Mathematics
       2. Connected Learning
    8. Helping Students Transform Mathematical Understandings
       1. Problem-Solving Teaching
       2. Reciprocal Teaching
    9. Conclusion
    10. Reflection and Discussion Questions
14. Chapter 7. Assessment, Feedback, and Meeting the Needs of All Learners
    1. Assessing Learning and Providing Feedback
       1. Formative Evaluation Embedded in Instruction
       2. Summative Evaluation
    2. Meeting Individual Needs Through Differentiation
       1. Classroom Structures for Differentiation
       2. Adjusting Instruction to Differentiate
       3. Intervention
    3. Learning From What Doesn’t Work
       1. Grade-Level Retention
       2. Ability Grouping
       3. Matching Learning Styles With Instruction
       4. Test Prep
       5. Homework
    4. Visible Mathematics Teaching and Visible Mathematics Learning
    5. Conclusion
    6. Reflection and Discussion Questions
15. Appendix A. Effect Sizes
16. Appendix B. Standards for Mathematical Practice
17. Appendix C. A Selection of International Mathematical Practice or Process Standards
18. Appendix D. Eight Effective Mathematics Teaching Practices
19. Appendix E. Websites to Help Make Mathematics Learning Visible
20. References
21. Index