# Hands-on, Practical Guidance for Educators

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# Visible Learning for Mathematics, Grades K-12

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

Foreword by Diane J. Briars, NCTM Past-President

**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**

## Description

*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

Includes:

- 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

## Author(s)

### 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

**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

**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 Associationâ€™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

**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

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

**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 Doesnâ€™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**

### For Instructors

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### Related Resources

- Accountable Talk Moves in Mathematics [Lessons and strategies]
- Companion Website with Video [Site]
- Funneling and Focusing Questions in Mathematics [Lessons and strategies]
- Making Learning Visible Starts with Teacher Clarity [Lessons and strategies]
- Sample Language Frames for Mathematics [Lessons and strategies]