How the Brain Learns Mathematics

by David A. Sousa

Overview

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

Product Details

ISBN-13:	9781483368474
Publisher:	SAGE Publications
Publication date:	11/13/2014
Sold by:	Barnes & Noble
Format:	eBook
Pages:	256
File size:	4 MB

About the Author

DR. David A. Sousa is an international consultant in educational neuroscience and author of more than twenty books that suggest ways educators and parents can translate current brain research into strategies for improving learning. A member of the Cognitive Neuroscience Society, he has conducted workshops in hundreds of school districts on brain research, instructional skills, and science education at the preK–12 and university levels. He has made presentations to more than two hundred thousand educators 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’s degree in chemistry from Bridgewater State University in Massachusetts, a master of arts in teaching degree in science from Harvard University, and a doctorate from Rutgers University. His teaching experience covers all levels. He has taught senior high school science and served as a K–12 director of science, supervisor of instruction, and district superintendent in New Jersey schools. He was an adjunct professor of education at Seton Hall University for ten years and a visiting lecturer at Rutgers University.

Prior to his career in New Jersey, Dr. Sousa taught at the American School of Paris (France) and served for five years as a foreign service officer and science advisor at the US diplomatic missions in Geneva (Switzerland) and Vienna (Austria).

Dr. Sousa has edited science books and published dozens of articles in leading journals on professional development, science education, and educational research. His most popular books for educators include How the Brain Learns, now in its sixth edition; How the Special Needs Brain Learns, second edition; How the Gifted Brain Learns; How the Brain Learns to Read, second edition; How the Brain Influences Behavior; How the ELL Brain Learns; Differentiation and the Brain, second edition (with Carol Tomlinson); and How the Brain Learns Mathematics, second edition, which was selected by the Independent Book Publishers Association as one of the best professional development books. The Leadership Brain suggests ways for educators to lead today’s schools more effectively. Dr. Sousa’s books have been published in French, Spanish, Chinese, Arabic, Korean, Russian, and several other languages. His book Brainwork: The Neuroscience Behind How We Lead Others is written for business and organizational leaders.

Dr. Sousa is past president of the National Staff Development Council (now called Learning Forward). He has received numerous awards from professional associations, school districts, and educational foundations for his commitment to research, staff development, and science education. He received the Distinguished Alumni Award and an honorary doctorate from Bridgewater State University and an honorary doctorate in humane letters from Gratz College in Philadelphia.

Dr. Sousa has been interviewed on the NBC Today show, by other television programs, and by National Public Radio about his work with schools using brain research. He makes his home in south Florida.

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

Editorial Reviews

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

"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.

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

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

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

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

"This book has actually changed the way I think now of teaching math in particular and learning in general, and I’ve been teaching math for over 25 years. "

Jim Barta

"Teachers of all grade levels will be intrigued by Sousa’s explanation of the brain processes involved in learning math concepts and why so many people find them difficult to understand. Developmentally appropriate math strategies and lessons for pre K-12 students that focus on both memory and meaning are offered, along with a section on diagnosing and addressing difficulties in students. "

Curriculum Connections

"I am so impressed with this book that I believe it should be required reading for all teachers who teach math at any level. "

Mary Thoreen

"The cognitive findings of this book are powerful and affirming and add support to my current work and practice. I took away powerful concepts that have enormous implications for teaching and learning mathematics. "

Daniel Raguse

"Totally absorbing. I found myself discussing different aspects of it with my colleagues and reading passages out loud to my husband. Any teacher who teaches math should have this on his or her book list. "

Carol Amos

"This text is written the way we should be teaching—making you eagerly anticipate what is coming next. "

Renee Ponce-Nealon

"The very bottom line is that this book is about what is best for helping students learn mathematics and helping teachers teach it in a way that is purposeful and meaningful for their students. "

Deborah Gordon

"Comes from a respected author and researcher who explores the latest neuroscientific findings in learning and math cognition. Pairs research with lesson plans specific to elementary and secondary school teachers. "

California Bookwatch

"The book’s unique contribution to the field is the connection of research to educational practice, providing a common language for researchers and practitioners to begin dialogues about learning mathematics. "

Janice Bradley

"An excellent, well-organized, well-written book—practical advice grounded in solid research and presented in compelling language. "

Robert Sylwester