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Home » Books » Nonfiction » Education » Teaching Methods » Mathematics

Visible Learning for Mathematics, Grades K-12

What Works Best to Optimize Student Learning

By John A. Hattie, Douglas B. Fisher, Nancy Frey

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Format: Paperback, 304 pages
Published In: United States, 14 January 2017
In this book, John Hattie, Doug Fisher, Nancy Frey, team up with mathematics experts Linda M. Gojak, Sara Delano Moore, and William Mellman to walk teachers through the key research-based moves they should focus on in their mathematics classrooms - those with the highest effect sizes in the phases of surface, deep, and transfer learning. In accessible, every-day language, they offer their best guidance to teachers on what surface, deep, and transfer learning mean, look, and sound like in the mathematics context. How to ensure teacher clarity through setting meaningful learning intentions and success criteria that build on prior learning, and by continually checking for understanding.

Table of Contents

List of FiguresList of VideosAbout the Teachers Featured in the VideosForewordAbout the AuthorsAcknowledgmentsPrefaceChapter 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 QuestionsChapter 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 QuestionsChapter 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 QuestionsChapter 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 QuestionsChapter 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 QuestionsChapter 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 QuestionsChapter 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 QuestionsAppendix A. Effect SizesAppendix B. Standards for Mathematical PracticeAppendix C. A Selection of International Mathematical Practice or Process StandardsAppendix D- Eight Effective Mathematics Teaching PracticesAppendix E. Websites to Help Make Mathematics Learning VisibleReferencesIndex

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EAN: 9781506362946
ISBN: 150636294X
Publisher: Corwin Publishers
Dimensions: 22.86 x 18.54 x 2.03 centimetres (0.54 kg)
Age Range: 15+ years

About the Author

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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