About the Book
Experience the joy of answering "why" in math class like never before
Mathematics often feels like a collection of disconnected rules, but what if you could uncover their underlying story? In Math Decoded: Explaining the Why Behind the Numbers and How They Operate, author James Tanton provides educators with a compelling and accessible guide to understanding the logic, purpose, and poetry behind numbers and arithmetic.
Move away from simply teaching formulas and procedures. Instead, discover the coherent and human story of mathematics that will enliven your classroom and deepen your own mathematical knowledge.
By addressing the "why" questions students frequently ask, this book offers clarity on tricky concepts such as dividing by zero, fractions, and negative numbers through these key features
- Engaging Structure: Each chapter begins with a thought-provoking question, explores real-world scenarios, and culminates in bold insights and classroom activities.
- Grade-Banded Tasks: Includes classroom activities for elementary to high school, ensuring relevance for multiple grade levels.
- Comprehensive Resources: Accompanied by videos, supplemental essays, and practical tools to deepen the learning experience.
- Accessible Style: Written in a friendly, relatable tone to explain mathematics’ most mystifying and rigorous topics.
With this book, educators will gain a newfound appreciation for the beauty, structure, and coherence of mathematics. Math Decoded will help you inspire your students to see math not just as a subject, but as an invitation to explore, discover, and think deeply about the joy of numbers.
Table of Contents:
On the Companion Website
List of Videos
Acknowledgments
About the Author
Introduction
The Why of This Book
Who This Book Is For
The Story Behind the Story
What’s Inside
What’s Outside(!)
An Invitation
Chapter 1: Counting
Something to Mull On
Counting in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 2: Addition
Something to Mull On
Addition in the Real World
The Number Zero
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
The Solitaire Game
Some Sophisticated Jargon
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 3: Negative Numbers
Something to Mull On
Negative Numbers in the Real World
Solitaire Again
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 4: Distributing the Negative Sign
Something to Mull On
Distributing the Negative Sign in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Question on Notation
A Card Pile Mystery
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 5: Subtraction
Something to Mull On
Subtraction in the Real World
A Key Takeaway
Being Bold With the Math
Generalizing Our Thinking a Wee Bit
More Mulling and Some Classroom Tasks
Wishful Thinking Across the Curriculum
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 6: Multiplication
Something to Mull On
Multiplication in the Real World
Solitaire Yet Again!
The Number 1
A Key Takeaway
Being Bold With the Math
On the Question of What Multiplication Is
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 7: The Distributive Property
Something to Mull On
The Distributive Property in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 8: Multiplication and Zero
Something to Mull On
Multiplication and Zero in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 9: Multiplication and Negative Numbers
Something to Mull On
Multiplication and Negative Numbers in the Real World
One Way Out
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 10: Division
Something to Mull On
Division in the Real World
A Key Takeaway
Being Bold With the Math
Dividing Zero and Dividing by Zero
The Curious Case of 0 ÷ 0
More Mulling and Some Classroom Tasks
A Task for All Grades
For Extra Fun
How Some Curricula Address the Issue
Chapter 11: The Reciprocal Numbers (The Building Blocks of Fractions)
Something to Mull On
Reciprocal Numbers in the Real World
A Realistic Note
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle and High School Grades
Chapter 12: Fractions Are Answers to Division Problems
Something to Mull On
Fractions as Answers to Division Problems in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and a Classroom Task
The Definition of a Fraction
A Task for All Grades
Chapter 13: Multiplying Fractions
Something to Mull On
Multiplying Fractions in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and a Classroom Task
A Task for All Grades
Chapter 14: Equivalent Fractions
Something to Mull On
Equivalent Fractions in the Real World
Two Pieces of Language
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 15: Dividing Fractions
Something to Mull On
Dividing Fractions in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and a Classroom Task
A Task for Upper Grades
Chapter 16: Adding and Subtracting Fractions
Something to Mull On
Adding and Subtracting Fractions in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and a Classroom Task
A Task for All Grades
Chapter 17: Comparing Fractions
Something to Mull On
Comparing Fractions in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling and Some Classroom Tasks
Mixed Numbers
A Task for Elementary School Grades
A Task for Middle School Grades
A Task for High School Grades
Chapter 18: Exponents
Something to Mull On
Exponents in the Real World
A Key Takeaway
Being Bold With the Math
Understanding 212
More Mulling and Some Classroom Tasks
The Value of 00
A Task for Elementary School Grades
A Task for Upper School Grades
Chapter 19: Fractions as Decimals
Something to Mull On
Fractions as Decimals in the Real World
Leaning Into Reverse Multiplication
A Key Takeaway
Being Bold With the Math
More Mulling and a Classroom Task
On Multiplying by Ten
Understanding 0.9999 . . .
Believing 0.9999 . . . Is Meaningful
Final Conclusion
The Geometric Series
A Task for All Grades
Chapter 20: Not Every Number is a Fraction
Something to Mull On
Numbers That Are Not Fractions in the Real World
A Key Takeaway
Being Bold With the Math
More Mulling
Final Thought: Are there more Numbers
What′s Next?
But How?
Now That You Have Read This Book
Be Bold!
References
Index
About the Author :
James Tanton, born in Adelaide, Australia, earned his PhD in Mathematics from Princeton University in 1994. A passionate ambassador for mathematics, James has dedicated his career to sharing the joy, wonder, and creativity that mathematics inspires. With over 20 years of teaching experience in both university and high school classrooms, he now works globally as an independent consultant, bringing his unique perspective to learners of all ages.
James is an author, video creator, and speaker who specializes in making mathematics accessible and delightful. He collaborates with teachers, designs innovative curricula, and leads professional development sessions and demonstration classes around the world. As the co-founder of the Global Math Project, James is on a mission to transform the way people perceive mathematics. His initiative has reached over 7 million students and educators across more than 160 countries, sparking curiosity and genuine excitement about school mathematics.
James currently resides in Berkeley, California, with his wife, Lindy Elkins-Tanton.
Review :
This is an amazing resource for anyone who wonders, ‘why?’ Mathematician James Tanton takes us into an exploration of mathematical conundrums
and curiosities like dividing by zero, multiplying two negatives, and fraction division, showing us why they work and giving us creative new ideas for helping learners. It is a must-read for all math educators and the mathematically curious.
Math often feels like a play we’ve seen too many times—we know every twist and turn. Or so we thought. In Math Decoded, James Tanton takes us
backstage, revealing surprising depth in even the most familiar concepts, and shows us not only new ways to understand mathematics, but also new ways to teach it more effectively. This is a backstage tour you don’t want to miss.
James Tanton is a gift to mathematics education. There are few people who I consistently learn so much from, and Tanton is one of them. This book
is no exception. His playful and rigorous style makes important questions in K–12 math highly accessible. These are questions that are relevant whether you’re highly experienced or teaching mathematics for the first time. I dare you to read it and not be wowed!
Math Decoded is James Tanton at his brilliant best: playful, profound, and passionately human. I’m constantly inspired by how he makes the abstract
feel alive, and the complex feel inviting. This book isn’t just a masterclass in mathematical insight; it’s a love letter to the ‘why’ that fuels every curious learner.
James Tanton is a master at making complex math ideas easy to understand as readers are presented with concrete examples that
extend to deep, mathematical ideas. Following each big idea, activities are provided to engage your students in topics they (and sometimes teachers) often find confusing. This book is a worthwhile read for any educator.
This is a brilliant resource from a brilliant math educator who excels at unpacking complex mathematical concepts into simple, accessible ideas
for everybody. Tanton brings meaning, clarity, and joy to mathematics. The book masterfully addresses ‘why’ questions, providing profound
insights into numbers and their operations. A must-read for every educator!
Tanton brings to mathematics a quirky ‘what?,’ ‘why?,’ ‘how?’ approach that never fails to arouse curiosity. He’s grabbed my attention on issues
I thought I knew inside-out. For a school-aged audience, his approach can be dynamite. This book is a wonderful, inspiring resource of intriguing questions that bring ‘everyday’ math to life.
A delightful journey into the playful depths of arithmetic. Tanton makes even classic stumpers—like ‘why can’t you divide by zero?’
and ‘what is infinity?’—feel like wondrous invitations to explore. This book is perfect for anyone who finds joy in the quirks and logic of mathematics.
In classic James Tanton fashion, this book takes readers through some of mathematics’ most perplexing questions. James masterfully tackles the timeless student query—’Why do we need to do this?’—and transforms it into an invitation to wonder, discovery, and delight. With his signature joy and clarity, he helps readers make sense of the very problems that once felt out of reach. A much-needed resource that brings the beauty and purpose of mathematics to life!
As math teachers, how many times do we hear ‘Why?’ from our students? I have heard it too many times to count and have been frustrated when I didn’t have the answer. Not anymore! In Math Decoded, James Tanton takes the reader through the story of mathematics that illustrates the power and beauty behind the numbers. In this book, math transforms from stand-alone rules to intertwining concepts. I highly recommend this book to all teachers looking to deepen their own knowledge of mathematics and that of their students.
This book is a fast, fun, and inspiring journey through the big questions in learning and teaching mathematics! It sparks curiosity, joy, and deep
understanding by offering clear insights, hands-on examples, and powerful ways to make connections to big ideas we once struggled to explain. A valuable and uplifting resource for students and teachers alike!
Reading this book, I could feel Tanton’s signature joy and enthusiasm for taking big ideas and breaking them into bite-size pieces that are easy to digest, while also blowing your mind. This is an amazing resource for any teacher looking to better understand, as Tanton says, ‘the poetry of mathematics.’ The journey through the book was both incredibly validating and completely inspiring. Each idea sparks thoughts about classroom conversations my students have engaged in and how to take these conversations further with the book’s tasks.
James Tanton makes arithmetic a playground of wonder and delight, and he shows how you can too. Tanton’s insights shine as he illuminates the
creative possibilities of math when you allow numbers to take a life of their own in wider contexts. His tantalizing philosophical questions will broaden your thinking and get students talking. Math Decoded is both a satisfying read and practical resource for every teacher and parent to explain why numbers behave as they do.
What a wonderful and unique perspective James Tanton brings to this delightful book! His approach is irresistible: You’ll come away with a richer and more profound understanding of numbers and mathematical thinking.
To know James Tanton is to know that mathematics is a fully joyful and human endeavor! This book showcases his perspective perfectly through
developing critical mathematical ideas in ways that just make sense. Tanton’s innovative approach provides educators with an untangled and transformational rethinking of mathematics that is fun to read and accessible for all.
Powerful ways of thinking about numbers and operations are key to understanding and enjoying mathematics, but too often those foundations
are seen as disconnected and joyless. In Math Decoded, James Tanton weaves a delightful storyline that connects, makes sense of, and brings joy to the study of mathematics. This is a book for everyone, and along the way, you’ll have many opportunities to say to yourself ‘I never thought of it
that way, but I wish I had.’
With his Aussie wit, Tanton takes us on an almost whimsical journey to help us see a story of mathematics and think deeply about the inherent
connections that exist. Rather than giving an instruction on how to teach in the classroom, he invites us to take a look back on many intriguing parts of school mathematics.
