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How the Brain Learns Mathematics
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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

About the Author

David A. Sousa, EdD, an international consultant in educational neuroscience, has written 16 books for educators and parents on ways of using brain research to improve teaching and learning. He has conducted workshops for more than two hundred thousand educators in hundreds of school districts on brain research and science education at the pre-K to Grade 12 and university levels. He has presented at national conventions of educational organizations and to regional and local school districts across the United States, Canada, Europe, Australia, New Zealand, and Asia. Dr. Sousa has a bachelor of science degree in chemistry from Bridgewater (Massachusetts) State University, a master of arts degree in teaching science from Harvard University, and a doctorate from Rutgers University. His teaching experience covers all levels. He has taught high school science and has served as a K-12 director of science, a supervisor of instruction, and a district superintendent in New Jersey schools. He has been an adjunct professor of education at Seton Hall University and at Rutgers University. A past president of the National Staff Development Council (now called Learning Forward), Dr. Sousa has edited science books and published numerous articles in leading educational journals on staff development, science education, and brain research. He has received awards from professional associations, school districts, and Bridgewater State University (Distinguished Alumni Award), and several honorary doctorates for his commitment and contributions to research, staff development, and science education. He has been interviewed on the NBC Today show and on National Public Radio about his work with schools using brain research. He makes his home in south Florida.

Reviews

"Few other books discuss the scientific way the brain is mathematically wired while maintaining relevance to those interested in K-grade 12 education. Readers can expect to gain a deeper understanding of why students learn certain concepts easily and struggle with others and why the battle for successful student learning in mathematics is ever-changing. This book is not merely a collection of lesson plans and activities; it is also a deeper investigation into the science of mathematical learning and inspires readers to continue their own learning into the fascinating world of education." -- Nikki Armstrong, Mathematics Teacher From a review in NCTM's Mathematics Teaching in the Middle School: "Classroom teachers, administrators, and math coaches will appreciate the research-based explanations for why mathematics instruction that focuses on meaning making, connections, and processes is so important." -- Mary Alice Carlson "Sousa nailed it with these powerful insights on mathematics instruction. Teachers simply have to understand how students learn in order to provide top-notch instruction, and the specific teaching suggestions herein are invaluable! I love the three tier structure, emphasizing differences in teaching Pre-K and K, Pre-adolescent brains, and adolescent brains, and the emphasis on number sense at all levels is essential in the classroom today. Math teachers will apply these critical lessons immediately in their classes, and I'd urge every mathematics teacher and every elementary teacher to get this book!" -- William N. Bender, Author and Educational Consultant "David Sousa has done it again! He has produced a highly-relevant, exceptionally practically, research focused book that will build better mathematics brains in classrooms and schools." -- John T. Almarode, Assistant Professor of Education "David Sousa's How the Brain Learns Mathematics, Second Edition 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 should be a valuable text for teachers who want a deeper insight into thinking processes behind the learning and teaching of math." -- Robert E. Slavin, Director "Teaching mathematics without having read How the Brain Learns Mathematics 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

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