Books





Picture Books

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The Opposites, by Monique Felix 
(ages 2 to 6)
One of the earliest math skills, more basic perhaps than counting, is noticing attributes. This book has no words, and yet it tells dozens of stories, each about opposites. Noticing the one attribute that shows opposites in the detail-filled pictures is a math game your child will want to play again and again.


Quack and Count, by Keith Baker
(ages 2 to 7)
This is a board book, so it's good for the youngest child who will sit and listen to a story. And it stays good because it's so luscious. Great illustrations, fun rhythm and rhyme, cute story, and good mathematics. 7 ducklings are enjoying themselves in every combination. “Slipping, sliding, having fun, 7 ducklings, 6 plus 1.” (And then 5 plus 2, 4 plus 3, 3 plus 4, and so on.) It would be great to have a book like this for each number, showing all the number pairs that make it. If I ever get to teach math for elementary teachers again, I'd love to get my students to make books like this one.


Anno's Counting House, by Mitsumasa Anno
(ages 2 to 7)
Everything I've seen by Mitsumasa Anno is delightful. There is so much to see in his books, many of which have no words. In this book, ten people are moving from one house to another. In each two-page spread you can see one more person who's moved from the left house to the right, along with lots of furniture and other small items.

Anno's Mysterious Multiplying Jar will appeal to older readers. There is one island with two counties, which have three mountains each ..., until we get to ten jars within each box - a lovely, very visual representation of factorials. Anno's Magic Seeds does have words, and tells a fascinating story, of a plant whose seed, when baked, will keep you from being hungry for a full year. The plant grows two seeds in a year, and one needs to be used to grow a new plant... You may also enjoy Anno's Math Games. Anno has written over 40 books, most available in English.



Two of Everything, by Lily Toy Hong
(ages 3 to 7)

A poor old farming couple in China find a mysterious pot. When a hairpin drops in, they scoop two out.The math isn't discussed in the story, but it's pretty easy to add your own thoughts to this delightful tale of doubling.


 
How Hungry Are You? by Donna Jo Napoli and Richard Tchen
(ages 3 to 12)
There are lots of great of great books on sharing equally. My favorite used to be The Doorbell Rang, by Pat Hutchins, but this one is even more delightful. The picnic starts with just two friends, rabbit is bringing 12 sandwiches and frog is bringing the bug juice. Monkey wants to come, "My mom just made cookies. I could take a dozen." They figure out how much of each goody each friend will get. In the end, there are 13 of them, and the sharing becomes more complicated. One of the delights of this book is the little icons showing who’s talking. It would make a good impromptu play.



One Grain of Rice, by Demi
(ages 5 to 12)
The greedy raja is gently outsmarted by a wise village girl named Rani. This is a very sweet take on the story of grains of rice put on a chessboard. (One grain on the first square, two on the next, then 4, 8, 16, …, until the board is filled. How much rice is that, anyway?)







The Cat in Numberland, by Ivar Ekeland
(ages 5 to adult)
The story starts when Zero knocks on the door of the Hotel Infinity. He’d like a room, but they’re all full (with the number One in Room One, and so on). Turns out that’s no problem. The cat who lives in the lobby gets confused - if the hotel is full, how can the numbers make room for zero just by all moving up one room? Things get worse when the fractions come to visit. This story is charming enough to entertain young children, and deep enough to intrigue anyone. Are you ready to learn about infinity with your 5 year-old?





You Can Count on Monsters, by Richard Evan Schwartz
(any age)
Each number from 1 to 100 is a monster, and each one gets its picture on its own page. All of the numbers (except poor 1) are made up from their prime parts. The pictures are colorful, full of intriguing detail, and amusing. The pages in the front and back that explain prime factorization are unassuming, waiting for the reader to decide it’s time to find out more. This and Powers of Ten would both make great coffee table books, to peruse over and over.


I Love Math! book series, by Time-Life (age 4 to 12)
My son loves these. Each book has a wide variety of stories (fiction and non-fiction), puzzles, games, and more.


Chapter Books

The Man Who Counted, by Malba Tahan
(ages 6 to adult)
Written in Brazil, set in the Middle East, these stories follow the adventures of Beremiz, an accomplished mathematical problem-solver. He uses math to settle disputes, solve riddles and mysteries, and entertain his hosts. The series of 34 adventures, each with a math puzzle, is reminiscent of the Arabian Nights. If you read one chapter a night, your audience will be begging for more – and isn’t that the way it should be?



How to Count Like a Martian, by Glory St.John
(ages 7 to 12)
A really good way to understand place value is to work with other number bases. How to Count Like a Martian is a detective story in which the history of other number systems plays a starring role.
 “Out of the depths of the dark and starry night come the first of the faint and mysterious sounds … At your radio telescope, you are expertly tuning the dials.” You have just received a message from Mars. “You know that this is not a message in words. Martians and Earthlings would have too much trouble trying to find the same words to succeed that way. But there is another kind of language that both Martians and Earthlings understand.”
Numbers… And so you research the number systems that have been used on Earth, hoping that will help you decipher this message. The book proceeds to explain eight different counting systems, including the abacus, and computers. 

In the process, the concepts of place value (she just calls it place), base, and zero are explored. By the end of the book, you can see that the beeps and bee-beeps of the message you received are just the counting numbers, Martian style.
How to Count Like a Martian was written in 1975, when there were still dials and tape recorders. those two items may be the only evidence of its age. I wonder if young kids will like it as much as I do. Please let me know if your kid loves this book.



The Number Devil, by Hans Magnus Enzensberger
(ages 7 to adult)
The Number Devil visits Robert in his dreams, and gets him thinking about the strangest things! Rutabaga numbers and prima donnas (roots and primes) are just the beginning. Anyone who'd like a gentle introduction to lots of interesting math topics will enjoy this one.


Powers of Ten, by Philip and Phylis Morrison
(ages 6 to adult)
The first photo shows a couple having a picnic. It's shot from one meter above them. The next is from 10 meters, then 100. After we've traveled to the edge of the universe, we come back to the couple, and zoom in. Each page has one large photo, and explanatory text about what can be seen at that level. Way back when I first began teaching (in the ‘80’s), I showed a film version of this to junior high students. Now you can
watch it on Youtube.


Hannah, Divided, by Adele Griffin (age 8 to adult)
Hannah has a special gift for numbers. This sweet, simple story, set in the 30's, shows us the world from the point of view of a girl whose eccentricities aren't noticed much, until she goes to the big city to learn more math.


Carry On, Mr. Bowditch, by Jean Lee Latham (any age)
This is a fictionalized account of the life of Nathaniel Bowditch, who loved math, but had to leave school when his family needed his help. He was indentured to a ship chandlery for 9 years. Although that dashed his hopes of someday going to Harvard to study math, it was the right place to learn the mathematics behind navigation. When he finally went to sea, he invented a new way to ‘do a lunar’, and spent endless hours correcting errors in the tables used for navigation. Bowditch’s book, the American Practical Navigator, first published in 1902, is still regularly updated, and is carried on U.S. naval vessels to this day.

Math for Smarty Pants, by Marilyn Burns
The I Hate Mathematics! Book, by Marilyn Burns 
Family Math 


Older Kids & Adults

In Code, by Sarah Flannery (?)


Math Girls and Math Girls 2, by Hiroshi Yuki
The unnamed protagonist is a boy in high school who loves math. He helps Tetra with her math, and is challenged by the problems Miruka poses. In Math Girls 2, a few more girls join the gang. The math is challenging in these books, and the storyline makes it all the more fun.



Mathematics: A Human Endeavor, by Harold Jacobs
This one is a textbook, and it's delightful. The first chapter, on inductive and deductive reasoning, uses pool tables to get the reader thinking about patterns. Chapters on sequences, graphing, large numbers, symmetry, mathematical curves, counting (permutations and combinations), probability, statistics, and topology round out an introduction to a wide variety of math topics, accessible to beginners.


Who Is Fourier? by Transnational College of LEX
Fourier Series are used to describe sound. Usually an advanced college topic, they are explained in unique, easy to understand ways in this charming book, accessible to anyone who has a basic understanding of algebra.


Chances Are: Adventures in Probability, by Michael and Ellen Kaplan
History, philosophy, science, and statistics all come together in this delightful exploration of probability.


Euclid in the Rainforest, by Joseph Mazur
Logic, infinity and probability are the topics. Adventures in Venezuela, Greece, and New York furnish the background. Mazur has wide-ranging interests, and skillfully brings the math to life.


Mathsemantics, by Edward MacNeal
This book has one great chapter on estimation that’s worth getting the whole book. He talks about having a semantic web in your head that includes a few important numbers, like:  population of the earth, population of the U.S., population of your state, and radius of the earth. Then he recommends estimating often, committing to your estimate somehow, and then finding out the real value of what you estimated. For example, estimate your arrival time when you're in the car, tell the person next to you, and notice the time when you do arrive at your destination.


The Art and Craft of Problem-Solving, by Paul Zeitz
How do you go about solving challenging problems? Zeitz discusses tools, tactics, and strategies, and offers a rich storehouse of very challenging problems.


Surreal Numbers, by Donald Knuth (requires well-developed math skills)
This book requires lots of work, doing the math, and what fun work it can be! Alice and Bill are enjoying their extended vacation on an isolated tropical beach, but are getting a bit bored, when they discover a rock with two 'rules' on it. Conway has invented number through these two rules, and Alice and Bill (and the reader) are sucked in, trying to figure out how it all works. This is higher math.


The Man Who Knew Infinity: A Life of the Genius Ramanujan, by Robert Kanige
This story would be unbelievable if it were fiction or even slightly fictionalized. Ramanujan was too focused on his own mathematical work to do well in school - he was kicked out college when he failed exams in his other subjects. It took him years of working as a clerk to support himself before he managed to catch the attention of a famous mathematician in England, G.H. Hardy, whose interest in him suddenly changed his life. A year later he would sail to England to begin with Hardy the work of making his mathematical results comprehensible to others.


Uncle Petros and Goldbach’s Conjecture, by Apostolos Doxiadis
Uncle Petros is a recluse. Our hero, his nephew, is trying to discover his secrets. It seems he was close to solving Goldbach's conjecture, that every even number greater than 2 is the sum of two prime numbers. There is just a tiny bit of math in this, but lots of (slightly twisted) history of math. (Includes a few adult sexual scenes.)


 

Math Education


The Art of Problem Posing, by Stephen Brown

Math: An American Phobia, by Marilyn Burns

Out of the Labyrinth: Setting Mathematics Free, by Robert and Ellen Kaplan

Math Power: How to Help Your Child Love Math, Even If You Don't, by Patricia Kenschaft

Knowing and Teaching Elementary Mathematics, by Liping Ma

Mindstorms, by Seymour Papert

How to Enjoy Mathematics With Your Child, by Nancy Rosenberg

You can also find hundreds of suggestions at Julie Brennan's livingmath.net, and at Cindy's blog, Love to Learn Today.

 
Math Blog Directory