Wednesday, April 8, 2015

Top Picks: Living Math

This may look a bit different than our traditional "Top Picks" lists. Math is NOT a verbal subject and so books are more removed from the learning process than any other subject. We believe however, that living math books can help supplement the teaching of mathematics; papers like this one are being written that emphasize that learning in as many different forms as possible increases math fluency. We also believe that is entirely possible, maybe even preferable to forego a traditional math textbook or curriculum for elementary math instruction. Whoa. Yes, you did just read that right. And it terrified us just as much when we first entertained the idea. But with three childrens' experience behind us, we do see the benefits--a much deeper understanding of what numbers mean and do than their three older, traditionally taught siblings.

But don't just take our word for it. Read about Louis Benezet and his practical implementation of this concept. That doesn't mean you don't teach math at all in elementary years, but it is hands-on with lots of practical use of numbers, and no textbook (!). This firm foundation pays off in later years of study.

What does a teacher use then? Do they have to be a mathematical genius themselves? Absolutely not. Here are some resources that will help guide you as you give your children a slow and steady exposure to numbers and reasoning, moving from concrete to abstract thinking and progressing from simple to more complex ideas.

"An Easy Start in Arithmetic" from Ruth Beechick's The Three R's provides a "scope and sequence" for math to be learned in grades K-3; what's even better are her suggestions on how to teach these principles and concepts in everyday life, with games and hands-on activities, without a "math curriculum."

This volume picks up where The Three R's left off, explaining concepts and skills that should be learned in grades 4-8.

A distinctly Charlotte Mason resource. In this book the author distills all of Mason's teaching on mathematics and lays it out systematically to give the teacher an understanding of the philosophy underlying math instruction as 

The amazing gift of Julie Brennan is a treasure trove of math help. From math readers by concept to activity suggestions for teaching everything from addition to algebra, this page will help guide your steps.

So which particular titles are some of LBL's favorites? Since humans are created to respond to story, the history of mathematics and the stories of men who used it throughout history are great books to weave throughout your children's education:

A good overview of the use of math throughout history. Each section focuses on one geographic/historic area and examines the exploration and application of math that each developed. From Ancient Egypt to Babylon & Assyria, the Phoencicians, Greeks, Muslims and into the modern era, plentiful illustrations help describe the contributions each culture made to mathematics. Appropriate for upper-elementary students on up.

This book gave me a passion for math that I never received from my years of formal study. Unfortunately, I didn't read it until I was 25. This lovely book traces the development of geometry from ancient times through the Golden Age of Greece. I consider it a "not-to-be-missed" book!

Another great way to introduce your students to the possibilities of mathematics is to acquaint them with great mathematicians of the past. This helps them see how men of the past sought to answer questions and solve problems using numbers.

Some good picture-biographies for the youngest students are:

For older elementary students:

And for middle and high school students:


Here are some of our favorite practical math books:

Arithmetic Can be Fun by Munro Leaf (J.B. Lippincott, 1949)
This book is a good introduction to basic arithmetic concepts from individual numbers through measurement, all ideas pictured in Leaf's fun line drawings.

Domino Addition by Lynette Long (Charlesbridge, 1996)
Using dominoes for the illustrations, this book shows how to add/subtract figures to make all the number combinations from 0-12. It is fun to follow along with one's own dominoes as well.

Sea Squares by Joy Hulme (Hyperion, 1991)
This book looks specifically at square numbers as various marine flora/fauna are pictured to demonstrate the numbers. (Three clownfish with three stripes each equals nine stripes)

The M & M's Counting Book and More M & M's Math by Barbara McGrath (Charlesbridge)
What math manipulative can be more fun than chocolate candies?! Pick up a bag of candy and follow along with these books to work out basic math concepts.

Another set of books using chocolate as the concrete example for multiplication and fractions. Mmmm.

Apple Fractions by Jerry Pallotta (Carthwheel, 2003)
If you'd prefer your kids to have a more healthy food manipulative, try Apple Fractions. 

The Sir Cumference Series by Cindy Neuschwander (Charlesbridge)
These are fun "Math Adventures" that are mostly geometric topics. Kids in our library love them and check them out over and over.

The Young Math Series by various authors (Crowell)
This is our favorite series, though sadly out-of-print, dealing with all kinds of math topics. Each is presented using pictures and often manipulative activities that you can follow along with. Though topics include algebra and probability as well as very basic measuring and numbers, the books themselves are approachable for young elementary students, and can help introduce or reinforce concepts for older students. You can find a list of  all the titles in the series here.

I hope these suggestions help you and your children explore and love the beauties of mathematics!

Happy reading,



  1. Excellent list, Emily! And I agree that delaying formal textbook math is scary...but preferable.

  2. Emily, I really enjoyed your thoughts on living math! May I share a link to your post with readers of my blog?

    ~ Dani

    1. Dani,

      I'm so glad this was a helpful resource for you! I'd love you to share it with other readers.


  3. This is a very good list. Would you include Pascal ? Any titles for him? Do you know the book: Mathematics , Is God Silent?

  4. I've been investigating math through literature lately, not to replace figures and practical application but to enliven it & help create more excitement around it. (I am not a math fan myself and see the same attitude in some of my children, but I want us to be enthralled by math because it was created by God!) I have read the first Life of Fred book with my eldest and we really liked it and I have worked through the first M&M book with my second child, but I'm hungry for more. :) So I checked out a few books from our local library that piqued my interest in a general search. I'm curious if you've heard of any of them & would love your opinion!
    1. Missing Math: A Number Mystery, by Loreen Leedy
    -I liked this picture book for young kids. All the numbers in this cartoon animal town start vanishing and they discover how little they can do without them.
    2. The Adventures of Penrose--The Mathematical Cat, by Theoni Pappas
    3. The Number Devil: A Mathematical Adventure, by Hans Magnus Enzensberger
    -This one intrigues me because it is a European author and looks to me like it reads as one big story problem.

    So what do you think?

    1. Bethany,

      Reading about mathematicians, math concepts, and math problems is a great supplement to math. Our children need mastery of function, but a deeper understanding of the principles. It sounds like you're doing a good job. We have a quantity of similar titles in our library, many older and out of print, but many children are helped by hearing and
      seeing math talked about in many contexts.