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
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 leader at Health Sciences High and Middle College.
Previously, Doug was an early intervention teacher and elementary
school educator. He is a credentialed teacher and leader in
California. In 2022, he was inducted into the Reading Hall of
Fame by the Literacy Research Association. He has published widely
on literacy, quality instruction, and assessment, as well as books
such as Welcome to Teaching, PLC+, Teaching Students to Drive their
Learning, and Student Assessment: Better Evidence, Better
Decisions, Better Learning.
Nancy Frey is professor of educational leadership at San Diego
State University and a leader at Health Sciences High and Middle
College. Previously, Nancy was a teacher, academic coach, and
central office resource coordinator in Florida. 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. She
has published widely on literacy, quality instruction, and
assessment, as well as books such as The Artificial Intelligences
Playbook, How Scaffolding Works, How Teams Work, and The Vocabulary
Playbook.
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.
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