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



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

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

Mr Drew Quayle
Faculty of Health , Social Care & Education, Anglia Ruskin University
June 21, 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.

Miss Syreeta Charles-Cole
School of Education, Theology & Leadership, St Mary's University, Twickenham
June 30, 2018

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ISBN: 9781506362946
£29.99