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How the Brain Learns Mathematics
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Bestseller!

How the Brain Learns Mathematics

Second Edition


© 2015 | 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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ISBN: 9781483368467
$39.95

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