How the Brain Learns Mathematics

To reach all your math students, use your brain—and theirs, too! The bestselling and award-winning first edition of How the Brain Learns Mathematics quickly revolutionized math teaching and learning. The second edition takes readers to the next level with new brain-friendly strategies backed by the latest research from education and neuroscience and even more ways to seamlessly incorporate what you learn about your students’ developing minds into your math classroom. In this essential resource, you’ll discover the cognitive mechanisms involved in processing mathematical operations, while exploring the environmental and developmental factors that create learning difficulties. How the Brain Learns Mathematics also presents a unique and simplified four-step teaching model that relates students’ classroom experience to concrete, real-world applications. Features of the new edition include More strategies for motivating adolescents Integration of the arts into mathematics instruction New information on how technology affects attention and memory Expanded sections on number sense and ELL instruction More than 160 new references and a greatly expanded index for readers’ convenience No matter what grade you teach, your students are growing and changing. Understanding how their brains work is the key to reaching every one of them—and making math a positive part of their lives for years to come. "David Sousa’s book is a wonderfully readable presentation of how neuroscience and cognitive psychology can inform the teaching of mathematics in elementary and secondary schools. Sousa engages his readers intellectually with recent research on the brain and mathematics learning, and avoids pat answers where the evidence is suggestive rather than conclusive. The book is a valuable text for teachers who want a deeper insight into thinking processes behind the learning and teaching of math." —Robert E. Slavin, Director, Center for Research and Reform in Education Johns Hopkins University "Teaching mathematics without having read this book is like trying to master tennis without a coach. Sousa's book is a tour de force: It builds a solid bridge from cognitive neuroscience to daily classroom practice. Every teacher of mathematics will benefit from this well-researched, well-organized, thoughtful, and practical approach to making math instruction align with how brains learn." —Spencer Kagan, Publisher/Professional Developer Kagan Publishing and Professional Development

Table of Contents:
About the Author Introduction Everyone Can Do Mathematics Why is Learning Mathematics So Hard? Response From Mathematics Educators About This Book Questions This Book Will Answer Chapter Contents Other Helpful Tools Assessing Your Current Knowledge of How We Learn Mathematics What′s Coming? 1. Developing Number Sense Babies Can Count What Is Number Sense? Animals Also Have Number Sense Why Do We Have Number Sense? Piaget and Number Sense Learning to Count Subitizing Counting How Language Affects Counting The Mental Number Line Expanded Notions of Number Sense Can We Teach Number Sense? Quantities to Words to Symbols Gardner’s Logical/Mathematical Intelligence What’s Coming? Reflections on Chapter 1 2. Learning to Calculate Development of Conceptual Structures Structures in Four-Year-Olds Structures in Six-Year-Olds Structures in Eight-Year-Olds Structures in Ten-Year-Olds Dealing With Multiplication Why Are Multiplication Tables Difficult to Learn? Multiplication and Memory Is the Way We Teach the Multiplication Tables Intuitive? The Impact of Language on Learning Multiplication Do the Multiplication Tables Help or Hinder? What’s Coming? Reflections on Chapter 2 3. Reviewing the Elements of Learning Learning and Remembering Memory Systems Rehearsal Enhances Memory The Importance of Meaning How Will the Learning Be Stored? When Should New Learning Be Presented in a Lesson? Does Practice Make Perfect? Include Writing Activities Gender Differences in Mathematics Consider Learning Styles Consider Teaching Styles How Do You Think About Mathematics? What’s Coming? Reflections on Chapter 3 4. Teaching Mathematics to the Preschool and Kindergarten Brain Should Preschoolers Learn Mathematics at All? Assessing Students’ Number Sense Preschoolers’ Social and Emotional Behavior What Mathematics Should Preschoolers Learn? Preschool and Kindergarten Instructional Suggestions General Guidelines Suggestions for Teaching Subitizing Learning to Count An Easier Counting System Teacher Talk Improves Number Knowledge Questioning Developing Sorting and Classifying Skills What’s Coming? Reflections on Chapter 4 5. Teaching Mathematics to the Preadolescent Brain What Is the Preadolescent Brain? How Nature Influences the Growing Brain Environment Influences on the Young Brain Teaching for Meaning Using Cognitive Closure to Remember Meaning What Content Should We Be Teaching? Teaching Process Skills Does the Lesson Enhance Number Sense? Does the Lesson Deal With Estimation? From Memorization to Understanding Multiplication With Understanding Does the Lesson Develop Mathematical Reasoning? Using Practice Effectively With Young Students Graphic Organizers Don’t Forget the Technology What’s Coming? Reflections on Chapter 5 6. Teaching Mathematics to the Adolescent Brain What Is the Adolescent Brain? Overworking the Frontal Lobes The Search for Novelty Learning Styles and Mathematics Curriculum Qualitative Versus Quantitative Learning Styles Developing Mathematical Reasoning Instructional Choices in Mathematics Graphic Organizers Interpreting Word Problems Making Mathematics Meaningful to Teenagers What’s Coming? Reflections on Chapter 6 7. Recognizing and Addressing Mathematics Difficulties Detecting Mathematics Difficulties Determining the Nature of the Problem Diagnostic Tools Environmental Factors Student Attitudes About Mathematics Fear of Mathematics (Math Anxiety) Neurological and Other Factors Dyscalculia Addressing Mathematics Difficulties Research Findings The Concrete-Pictorial-Abstract Approach Using Process Mnemonics Numeracy Intervention Process Students With Nonverbal Learning Disability Students With Both Mathematics and Reading Difficulties Other Considerations What’s Coming? Reflections on Chapter 7 8. Putting It All Together: Planning Lessons in PreK–12 Mathematics What Is Mathematics? Questions to Ask When Planning Lessons Is the Lesson Memory-Compatible? Does the Lesson Include Cognitive Closure? Will the Primacy-Recency Effect Be Taken Into Account? What About Practice? What Writing Will Be Involved? Are Multiple Intelligences Being Addressed? Does the Lesson Provide for Differentiation? Simplified Instructional Model Conclusion Reflections on Chapter 8 Glossary References Resources Index