Visible Learning for Mathematics, Grades K-12

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 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