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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, Jennifer M.D . Berman, Sara Delano Moore, William L Mellman

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    • ISBN-13: 9781506362946
    • Publisher: SAGE Publications
    • Publication date: 09/30/2016
    • Series: Photos of Idaho
    • Pages: 304
    • Sales rank: 30,146
    • Product dimensions: 7.30(w) x 9.00(h) x 0.80(d)

    Dr. John Hattie has been Professor of Education and Director of the Melbourne Education Research Institute at the University of Melbourne, Australia, since March 2011. He was previously Professor of Education at the University of Auckland. His research interests are based on applying measurement models to education problems. He is president of the International Test Commission, served as advisor to various Ministers, chaired the NZ performance based research fund, and in the last Queens Birthday awards was made “Order of Merit for New Zealand” for services to education. He is a cricket umpire and coach, enjoys being a Dad to his young men, besotted with his dogs, and moved with his wife as she attained a promotion to Melbourne. Learn more about his research at www.corwin.com/visiblelearning.

    Douglas Fisher, Ph.D., is Professor of Educational Leadership at San Diego State University and a teacher leader at Health Sciences High & Middle College. He is the recipient of an IRA Celebrate Literacy Award, NCTE’s Farmer Award for Excellence in Writing, as well as a Christa McAuliffe Award for Excellence in Teacher Education. Doug can be reached at dfisher@mail.sdsu.edu.

    Nancy Frey, Ph.D., is Professor of Literacy in the Department of Educational Leadership at San Diego State University. The recipient of the 2008 Early Career Achievement Award from the National Reading Conference, she is also a teacher-leader at Health Sciences High & Middle College and a credentialed special educator, reading specialist, and administrator in California.

    Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, 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 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.

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    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 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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    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.

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