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
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.
"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*
"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*
"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*
"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*
"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*
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