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.
About the Author
Professor John Hattie is an award-winning education researcher and best-selling author with nearly 30 years of experience examining what works best in student learning and achievement. His research, better known as Visible Learning, is a culmination of nearly 30 years synthesizing more than 1,500 meta-analyses comprising more than 90,000 studies involving over 300 million students around the world. He has presented and keynoted in over 350 international conferences and has received numerous recognitions for his contributions to education. His notable publications include Visible Learning, Visible Learning for Teachers, Visible Learning and the Science of How We Learn, Visible Learning for Mathematics, Grades K-12, and, most recently, 10 Mindframes for Visible Learning. 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 leader at Health Sciences High & Middle College. He has served as a teacher, language development specialist, and administrator in public schools and non-profit organizations, including 8 years as the Director of Professional Development for the City Heights Collaborative, a time of increased student achievement in some of San Diego’s urban schools. Doug has engaged in Professional Learning Communities for several decades, building teams that design and implement systems to impact teaching and learning. He has published numerous books on teaching and learning, such as Assessment-capable Visible Learners and Engagement by Design.
Nancy Frey, Ph.D., is a Professor in Educational Leadership at San Diego State University and a leader at Health Sciences High and Middle College. She has been a special education teacher, reading specialist, and administrator in public schools. Nancy has engaged in Professional Learning Communities as a member and in designing schoolwide systems to improve teaching and learning for all students. She has published numerous books, including The Teacher Clarity Playbook and Rigorous Reading.
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.
Table of ContentsList 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