John Almarode is a professor of education at James Madison University. He was awarded the inaugural Sarah Miller Luck Endowed Professorship in 2015 and received an Outstanding Faculty Award from the State Council for Higher Education in Virginia in 2021. John started as a mathematics and science teacher in Augusta County, Virginia. John has written multiple books, book chapters, papers, and reports. His collaborative work with colleagues on what works best in teaching and learning includes How Tutoring Works, Visible Learning in Early Childhood, and How Learning Works, all with Corwin Press.

Douglas Fisher is a professor and chair of educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. Previously, Fisher was an early intervention teacher and elementary school educator. 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 Your Introduction to PLC+, Welcome to Teaching, How Feedback Works, Teaching Reading, and RIGOR Unveiled. Fisher loves being an educator and hopes to share that passion with others.

Kateri Thunder, Ph.D., has the pleasure of collaborating with learners and educators from school divisions and early learning centers around the world to translate research into practice. She has served as an inclusive early childhood educator, an Upward Bound educator, a mathematics specialist, an assistant professor of mathematics education at James Madison University, and Site Director for the Central Virginia Writing Project. Her research, writing, and presentations focus on equity and access in early childhood and mathematics education, as well as the intersection of literacy and mathematics for teaching and learning. Kateri has collaborated with thousands of educators to catalyze change in their classrooms, centers, and schools. She is the chair of NCTM's Research Committee and co-creator of The Math Diet. Additionally, she is a best-selling author for Corwin's Teaching Mathematics in the Visible Learning Classroom Series, the Success Criteria Playbook, and Visible Learning in Early Childhood.

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.

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.

Nancy Frey is a professor of educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. Her published titles include The Courage to Learn, The Art and Science of Coaching, How Scaffolding Works, and The Illustrated Guide to Visible Learning. Frey is a credentialed special educator, reading specialist, and administrator in California and learns from teachers and students every day.

List of Videos
Acknowledgments
About the Authors
Introduction
What Works Best
What Works Best When
The Path to Assessment-Capable Visible Learners in Mathematics
How This Book Works
Chapter 1. Teaching With Clarity in Mathematics
Components of Effective Mathematics Learning
Surface, Deep, and Transfer Learning
Moving Learners Through the Phases of Learning
Differentiating Tasks for Complexity and Difficulty
Approaches to Mathematics Instruction
Checks for Understanding
Profiles of Three Teachers
Reflection
Chapter 2. Teaching for the Application of Concepts and Thinking Skills
Ms. Buchholz and the Relationship Between Multiplication and Division
Ms. Mills and Equivalent Fractions and Decimals
Ms. Campbell and the Packing Problem
Reflection
Chapter 3. Teaching for Conceptual Understanding
Ms. Buchholz and the Meaning of Multiplication
Ms. Mills and Representing Division as Fractions
Ms. Campbell and the Volume of a Rectangular Prism
Reflection
Chapter 4. Teaching for Procedural Knowledge and Fluency
Ms. Buchholz and Fluent Division Strategies
Ms. Mills and Comparing Fractions
Ms. Campbell and Computing Volume
Reflection
Chapter 5. Knowing Your Impact: Evaluating for Mastery
What Is Mastery Learning?
Ensuring Tasks Evaluate Mastery
Ensuring Tests Evaluate Mastery
Feedback for Mastery
Conclusion
Final Reflection
Appendices
A. Effect Sizes
B. Planning for Clarity Guide
C. Learning Intentions and Success Criteria Template
D. A Selection of International Mathematical Practice or Process Standards
References
Index