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Visible Learning for Mathematics, Grades K-12
What Works Best to Optimize Student Learning

- John Hattie - The University of Melbourne, Australia
- Douglas Fisher - San Diego State University, USA
- Nancy Frey - San Diego State University, USA
- Linda M. Gojak - Mathematics Consultant, NCTM Past-President
- Sara Delano Moore - Mathematics Consultant
- William Mellman - San Diego State University, USA

Foreword by Diane J. Briars, NCTM Past-President, Corwin Official VLP Collection badge

December 2016 | 304 pages | Corwin

*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.

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

Evidence Based

Clear writing

Student response

Education Spec Ed Soc Wrk Dept, Longwood University

March 15, 2021

This gives a clear context and rationale for the 3 phase model introduced within the book. This is a valuable textbook.

Faculty of Health , Social Care & Education, Anglia Ruskin University

August 19, 2019

This book is a 'must read' for all those interested in mathematics pedagogy.

This book, and the videos available on the internet, provide the best aggregation of educational research that I have ever seen. The information provided is up to date, and draws on the work theorist such as Dweck and Boaler. The book covers all grades (year groups), and includes a sample of useful vignettes.

School of Education, Theology & Leadership, St Mary's University, Twickenham

March 22, 2019

### Sample Materials & Chapters

Chapter 1: Make Learning Visible in Mathematics

Chapter 3: Mathematical Tasks and Talk That Guide Learning