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How the Brain Learns Mathematics
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How the Brain Learns Mathematics

Second Edition


December 2014 | 256 pages | Corwin

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
 
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

"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
Kagan Publishing and Professional Development, San Clemente, CA

“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
Center for Research and Reform in Education, Johns Hopkins University, Baltimore, MD

“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
James Madison University, College of Education Harrisonburg, VA

“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

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
Montana State University Bozeman

“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
Southwestern Oregon Community College

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