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

by John Hattie, Douglas Fisher, Nancy Frey, Linda Gojak, Sara Moore and William Mellman Corwin Press
Pub Date:
10/2016
ISBN:
9781506362946
Format:
Pbk 304 pages
Price:
AU$71.00 NZ$73.91
Product Status: In Stock Now
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Available as eBook
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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 Math, 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
Foreword by Diane Briars
Preface
Acknowledgments
About the Authors
Chapter 1. Make Learning Visible in Mathematics
Forgetting the Past
What Makes for Good Instruction?
The Evidence Base
Noticing What Does and Does Not Work
Direct and Dialogic Approaches to Teaching and Learning
The Balance of Surface, Deep, and 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
Success Criteria for Mathematics
Preassessments
Conclusion
Reflection and Discussion Questions
Chapter 3. Mathematical Tasks and Talk That Guide Learning
Making Learning Visible Through Appropriate Mathematical Tasks
Making Learning Visible Through Mathematical Talk
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
Mathematical Talk and Metacognition
Strategic Use of Vocabulary Instruction
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
Mathematical Thinking in Whole Class and Small Group Discourse
Small Group Collaboration and Discussion Strategies
Whole Class Collaboration and Discourse Strategies
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
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
Helping Students Transform Mathematical Understandings
Conclusion
Reflection and Discussion Questions
Chapter 7. Assessment, Feedback, and Meeting the Needs of All Learners
Assessing Learning and Providing Feedback
Meeting Individual Needs Through Differentiation
Learning From What Doesn’t Work
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

John Hattie - The University of Melbourne, Australia


Douglas Fisher - San Diego State University, USA


Nancy Frey - San Diego State University, USA


Linda M. Gojak - Center for Mathematics and Science Education, Teaching, and Technology, Director


Sara Delano Moore - ETA Hand2Mind


William Mellman