Skip to main content
Location: United States |  Change Location
Male flipping through Corwin book

Hands-on, Practical Guidance for Educators

From math, literacy, equity, multilingual learners, and SEL, to assessment, school counseling, and education leadership, our books are research-based and authored by experts on topics most relevant to what educators are facing today.


Visible Learning for Mathematics, Grades K-12 - Book Cover Look Inside

Visible Learning for Mathematics, Grades K-12

What Works Best to Optimize Student Learning

By: John Allan Hattie, Douglas Fisher, Nancy Frey, Linda M. Gojak, Sara Delano Moore, William Buckley Mellman

Discover the right mathematics strategy to use at each learning phase so all students demonstrate more than a year’s worth of learning per school year.
Product Details
  • Grade Level: PreK-12
  • ISBN: 9781506362946
  • Published By: Corwin
  • Series: Corwin Mathematics Series
  • Year: 2016
  • Page Count: 304
  • Publication date: September 16, 2016

Price: $41.95

Price: $41.95
Volume Discounts applied in Shopping Cart

For Instructors

Request Exam Copy

By selecting the request for exam copy above, you will be redirected to our parent site, Sage Publishing, to process your inspection copy request.  Thank you.



Selected as the Michigan Council of Teachers of Mathematics winter book club book!

Rich tasks, collaborative work, number talks, problem-based learning, direct instruction…with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school.

That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in “visible” learning because the 
effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students

Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: 

Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings.

Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency.

Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. 

To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Key features


  • Vignettes, teaching takeaways, and key vocabulary terms
  • 140 minutes of video clips from real classrooms
  • End-of-chapter discussion questions
  • Companion website with reproducibles from the book


John Allan Hattie photo

John Allan Hattie

John Hattie, Ph.D., is an award-winning education researcher and best-selling author with nearly 30 years of experience examining what works best in student learning and achievement. His research, better known as Visible Learning, is a culmination of nearly 30 years synthesizing more than 1,700 meta-analyses comprising more than 100,000 studies involving over 300 million students around the world. He has presented and keynoted in over 350 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 photo

Douglas Fisher

Douglas Fisher, Ph.D., 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 the recipient of an International Reading Association William S. Grey citation of merit and an Exemplary Leader award from the Conference on English Leadership of NCTE. He has published numerous articles on teaching and learning as well as books such as The Teacher Clarity Playbook, PLC+, Visible Learning for Literacy, Comprehension: The Skill, Will, and Thrill of Reading, How Tutoring Works, and How Learning Works. Doug loves being an educator and hopes to share that passion with others.

Nancy Frey photo

Nancy Frey

Nancy Frey, Ph.D., is a Professor in Educational Leadership at San Diego State and a teacher leader at Health Sciences High and Middle College. She is a member of the International Literacy Association’s Literacy Research Panel. Her published titles include Visible Learning in Literacy, This Is Balanced Literacy, Removing Labels, and Rebound. Nancy is a credentialed special educator, reading specialist, and administrator in California and learns from teachers and students every day.
Linda M. Gojak photo

Linda M. Gojak

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 photo

Sara Delano Moore

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.

Table of Contents

Table of Contents

List of Figures

List of Videos

About the Teachers Featured in the Videos


About the Authors



Chapter 1. Make Learning Visible in Mathematics

     Forgetting the Past

     What Makes for Good Instruction?

     The Evidence Base


     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


     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



     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


     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


     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


     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



     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


     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


     Learning From What Doesn’t Work

     Grade-Level Retention

     Ability Grouping

     Matching Learning Styles With Instruction

     Test Prep


     Visible Mathematics Teaching and Visible Mathematics Learning


     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