Visible Learning for Mathematics, Grades K-12

John Hattie, PhD, is an award-winning education researcher and best-selling author with nearly thirty years of experience examining what works best in student learning and achievement. His research, better known as Visible Learning, is a culmination of nearly thirty years synthesizing more than 2,100 meta-analyses comprising more than one hundred thousand studies involving over 300 million students around the world. He has presented and keynoted in over three hundred 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 10 Mindframes for Visible Learning. Douglas Fisher is a professor and chair of educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. Previously, Fisher was an early intervention teacher and elementary school educator. In 2022, he was inducted into the Reading Hall of Fame by the Literacy Research Association. He has published numerous articles on reading and literacy, leadership, and curriculum design, as well as books such as Your Introduction to PLC+, Welcome to Teaching, How Feedback Works, Teaching Reading, and RIGOR Unveiled. Fisher loves being an educator and hopes to share that passion with others.Nancy Frey is a professor of educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. Her published titles include The Courage to Learn, The Art and Science of Coaching, How Scaffolding Works, and The Illustrated Guide to Visible Learning. Frey is a credentialed special educator, reading specialist, and administrator in California and learns from teachers and students every day.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.

Evidence BasedClear writingStudent response

• List of FiguresList of VideosAbout the Teachers Featured in the VideosForewordAbout the AuthorsAcknowledgmentsPrefaceChapter 1. Make Learning Visible in MathematicsForgetting the PastWhat Makes for Good Instruction?The Evidence BaseMeta-AnalysesEffect SizesNoticing What Does and Does Not WorkDirect and Dialogic Approaches to Teaching and LearningThe Balance of Surface, Deep, and Transfer LearningSurface LearningDeep LearningTransfer LearningSurface, Deep, and Transfer Learning Working in ConcertConclusionReflection and Discussion QuestionsChapter 2. Making Learning Visible Starts With Teacher ClarityLearning Intentions for MathematicsStudent Ownership of Learning IntentionsConnect Learning Intentions to Prior KnowledgeMake Learning Intentions Inviting and EngagingLanguage Learning Intentions and Mathematical PracticesSocial Learning Intentions and Mathematical PracticesReference the Learning Intentions Throughout a LessonSuccess Criteria for MathematicsSuccess Criteria Are Crucial for MotivationGetting Buy-In for Success CriteriaPreassessmentsConclusionReflection and Discussion QuestionsChapter 3. Mathematical Tasks and Talk That Guide LearningMaking Learning Visible Through Appropriate Mathematical TasksExercises Versus ProblemsDifficulty Versus ComplexityA Taxonomy of Tasks Based on Cognitive DemandMaking Learning Visible Through Mathematical TalkCharacteristics of Rich Classroom DiscourseConclusionReflection and Discussion QuestionsChapter 4. Surface Mathematics Learning Made VisibleThe Nature of Surface LearningSelecting Mathematical Tasks That Promote Surface LearningMathematical Talk That Guides Surface LearningWhat 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 MetacognitionStrategic Use of Vocabulary InstructionWord WallsGraphic OrganizersStrategic Use of Manipulatives for Surface LearningStrategic Use of Spaced Practice With FeedbackStrategic Use of MnemonicsConclusionReflection and Discussion QuestionsChapter 5. Deep Mathematics Learning Made VisibleThe Nature of Deep LearningSelecting Mathematical Tasks That Promote Deep LearningMathematical Talk That Guides Deep LearningAccountable TalkSupports for Accountable TalkTeach Your Students the Norms of Class DiscussionMathematical Thinking in Whole Class and Small Group DiscourseSmall Group Collaboration and Discussion StrategiesWhen Is Collaboration Appropriate?Grouping Students StrategicallyWhat Does Accountable Talk Look and Sound Like in Small Groups?Supports for Collaborative LearningSupports for Individual AccountabilityWhole Class Collaboration and Discourse StrategiesWhen Is Whole Class Discourse Appropriate?What Does Accountable Talk Look and Sound Like in Whole Class Discourse?Supports for Whole Class DiscourseUsing Multiple Representations to Promote Deep LearningStrategic Use of Manipulatives for Deep LearningConclusionReflection and Discussion QuestionsChapter 6. Making Mathematics Learning Visible Through Transfer LearningThe Nature of Transfer LearningTypes of Transfer: Near and FarThe Paths for Transfer: Low-Road Hugging and High-Road BridgingSelecting Mathematical Tasks That Promote Transfer LearningConditions Necessary for Transfer LearningMetacognition Promotes Transfer LearningSelf-QuestioningSelf-ReflectionMathematical Talk That Promotes Transfer LearningHelping Students Connect Mathematical UnderstandingsPeer Tutoring in MathematicsConnected LearningHelping Students Transform Mathematical UnderstandingsProblem-Solving TeachingReciprocal TeachingConclusionReflection and Discussion QuestionsChapter 7. Assessment, Feedback, and Meeting the Needs of All LearnersAssessing Learning and Providing FeedbackFormative Evaluation Embedded in InstructionSummative EvaluationMeeting Individual Needs Through DifferentiationClassroom Structures for DifferentiationAdjusting Instruction to DifferentiateInterventionLearning From What Doesn’t WorkGrade-Level RetentionAbility GroupingMatching Learning Styles With InstructionTest PrepHomeworkVisible Mathematics Teaching and Visible Mathematics LearningConclusionReflection 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