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Visible Learning for Mathematics, Grades K-12
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Bestseller!

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

Foreword by Diane J. Briars, NCTM Past-President



© 2017 | 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

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ISBN: 9781506362946
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