* Little Kids – Powerful Problem Solvers: Math Stories from a Kindergarten Classroom*, by Angela Andrews and Paul Trafton

One story for each of the ten months of the school year, from a kindergarten classroom. Here’s some of the deep mathematical thinking that young children can do.

* The Art of Problem Posing*, by Stephen Brown

This is a helpful book for rethinking how to approach learning math. The math is at about high-school level.

* Math: Facing An American Phobia*, by Marilyn Burns

I have recommended this book for math-anxious students. What I remember best is her conversation on an airplane with an engineer who adamantly opposed kids using calculators in school. She explained to him how they can be used to explore topics the kids wouldn’t be ready for otherwise.

* Talking Mathematics: Supporting Children’s Voices*, by Rebecca Corwin

It takes some real skill to get students talking about their mathematical thinking. Watching experts lead the process has helped me move along this path. I think maybe I should read this book every few years, even though I teach college and this is about elementary math classrooms.

* Show and Tell*, by Linda Dacy and Rebeka Eston

Another good book about communicating mathematical thinking in the classroom, this one is focused on Kindergarten to second grade.

* Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It*, by Denise Gaskins

This is currently a Kindle-only edition. I hope her paper edition comes out soon – I don’t know how to highlight e-books, and I want to be able to highlight so many things in this great book. Denise tells stories from her years of homeschooling, debunks the many destructive myths about math, helps you learn more about what math really is, and shows you how to do it. She includes problems invented by kids, problems she made up, and classics from mathematical history.

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

This is the book that started it all for me. I learned about math circles, fell in love with the Kaplans’ sensibilities, and found out how to get involved – participating in math circles, then leading them. They describe circles with young kids. They dispel the myth of talent, convincingly arguing that math is for everyone. And they tell wonderful stories of many people doing lots of challenging mathematics.

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

Recommended for homeschoolers (and other parents) who want to get a better feel for what their children’s paths through elementary math education might look like.

* Knowing and Teaching Elementary Mathematics*, by Liping Ma

Ma changed how we discuss the math needed to teach elementary students. She coined the phrase “profound understanding of fundamental mathematics.” In this book she compares the preparation and knowledge of Chinese and U.S. teachers. The Chinese teachers start out with a better grounding in the basics, and then are able to use daily time to work together deepening their understanding even more.

* Moebius Noodles: Adventurous Math for the Playground Crowd*, by Yelena McManaman, Maria Droujkova, and Ever Salazar

I love this book. It came out after my son was past the best age for it, but I hope to share it with friends with babies for a long time to come. Full of playful math activities for babies, toddlers, and big kids, it helps you to provide a rich math environment for your children. [Disclaimer: We share publisher, illustrator, and one author. Lucky us.]

* Mindstorms: Children, Computers, and Powerful Ideas*, by Seymour Papert

Children can learn to use computers in a masterful way, and learning to use computers can change the way they learn everything else.

* How to Enjoy Mathematics With Your Child*, by Nancy Rosenberg

The chapters include The Shapes of Numbers, Number Bases and the Game of Nim, Flexagons, Probability and Pascal’s Triangle, and A New Approach to Geometry.

* Vision in Elementary Mathematics*, by W.W. Sawyer

Written in 1964, this book is a delightful reminder that wisdom about how to teach math with meaning is not new. Sawyer suggests starting algebra with problems that involve two variables. These can show the power of algebra, while still being simple problems. This is just one example of his clarity about pedagogy. I may end up reading this book every year before starting classes. Also worth reading are his books Mathematician’s Delight and Prelude to Mathematics.

*Volumes one and two, by Deborah Schifter*

**What’s Happening in Math Class?**These books introduced me to good questioning as a method of teaching mathematics. Almost every one of the teacher chapters in these books includes lots of dialogue, both between students and between teacher and students. Between the two volumes, twenty-two teachers tell their stories of working to change their classrooms, and of lessons that engaged their students. Reading these books, like reading teacher blogs, reminds me that the teacher is always learning in a good classroom, right alongside the students. Volume one focuses on what a good mathematics classroom might look like, and volume two focuses more on the struggle the teachers went through as they attempted to change the way they taught.

* The Book of Learning and Forgetting*, by Frank Smith

Although this book is not about math, the author’s insights about learning are very useful for anyone trying to re-conceptualize education, including those of us who would like to help others learn math. Easy to read and thought-provoking.

* Math From Three to Seven: The Story of a Mathematical Circle for Preschoolers*, by Alexander Zvonkin

Zvonkin conducted a math circle for his pre-school-age kids and some of their friends, and documents his successes and failures with them. He had lots of great ideas for getting very young children to think about deep math. This book is part of the Math Circles Library series, published by the American Mathematical Society in conjunction with the Mathematical Sciences Research Institute.