Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning(Corwin Mathematics Series)

In this book, John Hattie, Doug Fisher, Nancy Frey, team up with mathematics experts Linda M. Gojak, Sara Delano Moore, and William Mellman to walk teachers through the key research-based moves they should focus on in their mathematics classrooms - those with the highest effect sizes in the phases of surface, deep, and transfer learning. In accessible, every-day language, they offer their best guidance to teachers on what surface, deep, and transfer learning mean, look, and sound like in the mathematics context. How to ensure teacher clarity through setting meaningful learning intentions and success criteria that build on prior learning, and by continually checking for understanding.

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 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

About the Author :
John Hattie, PhD, is an award-winning education researcher and best-selling author with nearly thirty years of experience examining what works best in student learning and achievement. His research, better known as Visible Learning, is a culmination of nearly thirty years synthesizing more than 2,100 meta-analyses comprising more than one hundred thousand studies involving over 300 million students around the world. He has presented and keynoted in over three hundred international conferences and has received numerous recognitions for his contributions to education. His notable publications include Visible Learning, Visible Learning for Teachers, Visible Learning and the Science of How We Learn; Visible Learning for Mathematics, Grades K-12; and 10 Mindframes for Visible Learning. Douglas Fisher is professor and chair of educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. Previously, Doug was an early intervention teacher and elementary school educator. He is a credentialed English teacher and administrator in California. In 2022, he was inducted into the Reading Hall of Fame by the Literacy Research Association. He has published numerous articles on reading and literacy, leadership, and curriculum design, as well as books such as The Teacher Clarity Playbook (2nd ed.), Your Introduction to PLC+, The Illustrated Guide to Teacher Credibility, Instructional Strategies to Move Learning Forward: 50+ Tools That Support Gradual Release of Responsibility, and Welcome to Teaching! Nancy Frey is a professor in educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. She is a credentialed special educator, reading specialist, and administrator in California. She is a member of the International Literacy Association’s Literacy Research Panel. Her published titles include 50 Strategies for Activating Your PLC+, The Illustrated Guide to Visible Learning, Welcome to Teaching Multilingual Learners, Teaching Foundational Skills to Adolescent Readers, and RIGOR Unveiled: A Video-Enhanced Flipbook to Promote Teacher Expertise in Relationship Building, Instruction, Goals, Organization, and Relevance.  Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, Linda M. Gojak directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics. Sara Delano Moore is an independent mathematics education consultant at SDM Learning.  A fourth-generation educator, her work focuses on helping teachers and students understand mathematics as a coherent and connected discipline through the power of deep understanding and multiple representations for learning. Sara has worked as a classroom teacher of mathematics and science in the elementary and middle grades, a mathematics teacher educator, Director of the Center for Middle School Academic Achievement for the Commonwealth of Kentucky, and Director of Mathematics & Science at ETA hand2mind. Her journal articles appear in Mathematics Teaching in the Middle School, Teaching Children Mathematics, Science & Children, and Science Scope.