Through more than three decades of homeschooling five kids, my family lived by two rules:
Do math. Do reading.
As long as we hit those two topics each day, I knew the kids would be fine. Do some sort of mathematical game or activity. Read something from that big stack of books we collected at the library.
Conquer the basics of math and reading, then everything else will fall into place.
Learning math is an adventure into the unknown. The ideas we adults take for granted are a wild, unexplored country to our children. Like any traveler in a strange land, they will stumble over rocky places and meet with unexpected detours.
Many parents long to find a perfect math curriculum that will smooth over those rocky places. There is no such thing. Stumbles and detours are a necessary part of learning.
But you can help your children along the journey.
Here are my top five tips for navigating the mathematical wilderness:
- Start with Play.
- Read Books Together.
- Consider Your Own Perspective.
- Listen to Your Children.
- Focus on Making Sense.
I’ll expand on each of these tips below, including links to a variety of ideas and resources to help you and your kids explore the world of math.
Do you want to get started right away? Download a free copy of my Sampler ebook featuring ten family-favorite math games you can enjoy with your children today.
 Start with Play
For children, learning always begins with play. This is how they wrap their minds around new ideas and make them their own.
“There should be no element of slavery in learning. Enforced exercise does no harm to the body, but enforced learning will not stay in the mind. So avoid compulsion, and let your children’s lessons take the form of play.”
—Plato, The Republic
If we want our children to learn math, our first job is to establish an attitude of playfulness.
This is especially important for anyone working with a discouraged child or a child who is afraid of math. The best way to help a discouraged child is to put away the workbook. Try something different, fun, and challenging.
Play Math Games
Games meet children each at their own level, helping them understand that hard mental effort can be fun.
- My Best (Free) Math Games: All the games here on my Let’s Play Math blog, sorted by age/grade levels.
- Math Game Monday: A new math game every week, available for one week only.
- Math for Love Games: Collected by the creator of Tiny Polka Dot and Prime Climb.
- Games for Young Minds: Kent Haines’s posts teach not only how to play the games, but also how to help your children think about the math.
- Acing Math: A huge collection of topical worksheet-replacement games to play with a deck of cards.
- Math Hombre Games: The motherlode of math games for all ages. It’s easy to get lost on this page, so bookmark it and explore a bit at a time.
- For older students: Games and Math at Math Munch blog.
Play Math Art
Math art lets children experiment with geometric shapes and symmetries. Through art, students can explore a wide range of mathematical structures and relationships.
- Dot Grid Doodling: Several ways to explore mathematical concepts on a page of dot-grid paper.
- Spirolateral Math Doodles from Anna Weltman’s delightful This Is Not a Math Book.
- Math Art Projects for Kids from Erica at What Do We Do All Day? blog.
- Mathematical Art Lessons from Clarissa Grandi’s Artful Maths blog.
- Math Art Project Blog Tour to celebrate the release of Karyn Tripp’s book.
- For older students: Art and Math at Math Munch blog.
- Or the Math Hombre Math x Art page.
- And Annie Perkins’s amazing #MathArtChallenge with links to 100 creative ideas for playful math art!
 Read Books Together
Do you want to enrich your mind with the great ideas of mathematics? Are you looking for a good book to whet your child’s appetite?
Then you need to explore the wonderful world of living math books.
What Are Living Books?
The British education reformer (and homeschooling proponent) Charlotte Mason defined “living” books as those which bring children into direct contact with the great ideas of life:
“I know you may bring a horse to the water, but you cannot make him drink. What I complain of is that we do not bring our horse to the water. We give him miserable little textbooks, mere compendiums of facts, which he is to learn off and say and produce at an examination … And all the time we have books, books teeming with ideas fresh from the minds of thinkers upon every subject to which we can wish to introduce children.”
— Charlotte Mason, Schoolbooks and How They Make for Education
“Our business is to give [our students] mind-stuff, and both quality and quantity are essential. Naturally, each of us possesses this mind-stuff only in limited measure, but we know where to procure it; for the best thought the world possesses is stored in books; we must open books to children.”
— Charlotte Mason, Toward A Philosophy of Education
“A child’s intercourse must always be with good books, the best that we can find. For the mind is capable of dealing with only one kind of food; it lives, grows and is nourished upon ideas only; mere information is to it as a meal of sawdust to the body.“
— Charlotte Mason, Toward A Philosophy of Education
Browse and Enjoy
Below I’ve collected several lists of living math books that I enjoyed over the years, either for my own reading or with my children and my homeschool co-op students:
- Books for Parents and Other Teachers
A bookshelf full of math activities for your family, classroom, or math club.
- Picture Books and Early Readers
From counting books to math history, picture books offer a gentle introduction to a variety of topics. Elementary and middle school students will also enjoy many of these.
- Elementary and Middle School
Patterns, puzzles, games, and activities — here are plenty of ideas to get your children playing around with math.
- Problem Solving and Math Circles
From the elementary puzzles to Olympiad-level stumpers, the problems in these books will intrigue and challenge your students.
- High School and Beyond
These histories, biographies, and explanations of mathematical concepts are written for an adult general audience, so most of them assume no mathematical knowledge beyond a vague memory of high school.
Within each subcategory, books are listed alphabetically by author. If you click on a book cover, the links take you to Amazon.com, where you can read reviews and other details (and where I earn a few cents of affiliate commission if you actually buy the book), but most of these books should be available through your public library or via inter-library loan.
Ask a librarian to find you a copy — they love to help!
Note: These book pages are a work in progress. Over the next several months, I will continue to add favorites from my own overflowing bookshelves and books I have enjoyed from my local library (and a few that I’ve only coveted online). If you know of a book I missed, please let me know. I would love to add it to my library loan reading list.
Other Lists of Living Math Books
My bookshelves are limited to what I’ve read myself or seen online, but there are so many books in the world that I can’t possibly list them all. Round out your math education with:
- Math Readers
The motherlode living math books, organized by topic and grade level. From the Living Math! website by Julie Brennan.
- Math Books for Kids
From one of my favorite older blogs. Browse her archives for plenty of great love-to-learn ideas.
- Kelly Darke’s Math Book Magic
If you have young children, follow this blog! Reviews and tips for sharing magical math books with your kids.
 Consider Your Own Perspective
All parents and teachers have one thing in common: we want our children to understand and be able to use math. Counting, multiplication, fractions, geometry — these topics are older than the pyramids.
So why is mathematical mastery so elusive?
The culture we grew up in, with all of its strengths and faults, shaped our experience and understanding of math, as we in turn shape the experience of our children.
“The root problem is that we’re all graduates of the same system. The vast majority of us, including those with the power to shape reform, believe that if we can compute the answer, then we understand the concept; and if we can solve routine problems, then we have developed problem-solving skills.”
— Burt Furuta, Understanding Is Overrated
What Does It Mean to “Understand Math”?
Math education fads come and go, but our underlying problem remains consistent. Even before they reach the schoolhouse door, students are convinced that math is all about memorizing and following arbitrary rules.
Understanding math, according to popular culture — according to movie actors, TV comedians, politicians pushing “accountability,” and the aunt who quizzes you on your times tables at a family gathering — means knowing which procedures to apply so you can get the correct answers.
But when mathematicians talk about understanding math, they have something different in mind. To them, mathematics is all about ideas and the relationships between them, and understanding math means seeing the patterns in these relationships: how things are connected, how they work together, and how a single change can send ripples through the system.
“Mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination. Theories emerge as patterns of patterns, and significance is measured by the degree to which patterns in one area link to patterns in other areas.”
— Lynn Arthur Steen, The Science of Patterns
If you’d like to know more about how your mathematical worldview affects homeschooling — and what you can do about it — read my Understanding Math blog post series. Start here: What Is Your Worldview?
 Listen to Your Children
The most important thing for our children, especially when they are young, is for them to enjoy learning. The joy of learning is a child’s natural state. As parents, our primary job is to keep ourselves from stomping it out.
But our parental fears can push us into joy-trampling before we realize it.
And our own experience of school makes it hard for us to see how much of our children’s play really is learning. We are afraid they’re falling “behind” because we expect education to look like schoolwork. But natural learning looks nothing like that.
“The lesson here is that children are brilliant. They build math out of their everyday experiences, and when you offer them opportunities they apply the math they know to make further sense of their worlds.”
— Christopher Danielson, Counting in downtown Saint Paul
How to Talk Math with Your Kids
A friend shared this video, and I loved it! From Kent Haines, a father who happens to also be a math teacher…
More Tips for Talking Math
Check out this wonderful poster of rules for parents, from Haines’ Family Math Event.
And if you enjoyed the video, I think you’ll love Christopher Danielson’s book and blog.
They’re a wealth of great stories, advice, and conversation-starters for anyone who wants to help children notice and think about math in daily life.
“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds … The dialogues in this book are intended to open your eyes to these opportunities in your own family’s life.”
— Christopher Danielson, Talking Math with Your Kids
 Focus on Making Sense
Would you like to know the one, simple thing you can do right now to transform your child’s experience of math? Listen to this wise advice from Annie Fetter:
Fetter is talking to classroom teachers, but her message is just as important for homeschoolers. Math is all about making sense. Let’s help our kids see it that way.
Here’s another video that may resonate — especially if you think of yourself as “not a math person.”
“Sense-making is the first mathematical practice for a reason. If we don’t do this one, the rest of them don’t matter. If we’re not doing this, our children are not going to learn mathematics.”
— Annie Fetter, Sense Making: It Isn’t Just for Literacy Anymore
You can download the notes for Fetter’s longer session on sense-making and find several links to wonderful, thought-provoking posts on her blog:
How Can We Encourage Sense-Making?
Here are some ideas from Fetter’s updated notes, which expand on her comments in the video above:
- Get rid of the question. Literally. See what the students notice.
- Get rid of the question and the numbers. What do the students wonder?
- Give the answer. Ask students “What could the question be?”
- Or give several answers. What questions might have led to each answer?
- Ask about ideas, not answers.
- Ask “Why?”
- Or “How did you know?”
- Or “How did you decide that?”
- Or “Tell me more about that.”
- Use active reading strategies. Clarify, summarize, react, predict, connect, visualize…
A Few Resources to Practice Sense-Making
In no particular order…
- Play math games!
- Numberless Word Problems
- Numberless Word Problems for Older Kids
- Which One Doesn’t Belong?
- Visual Patterns
- Estimation 180
- Would You Rather? Math
- 3-Act Math
- Clothesline Math
- Fraction Talks
- Math Talks
- Graphing Stories
“I implore you, stop ‘cracking the math code.’ Make sense-making the focus of every single thing you do in your math classroom.”
— Annie Fetter, Sense Making: It Isn’t Just for Literacy Anymore
Whew! Feeling Overwhelmed Yet?
I’m so glad we don’t have to do everything all at once. Aren’t you?
Homeschooling is a marathon, so we can pace ourselves for the long stretch. Today, all we have to get done is to play a little math, do a little reading.
And if you read this far, I’d love to hear from you!
- What are your most pressing questions about helping your children with math?
- Or what tips would you share with other parents?
You can add your ideas in the Comments section below or send me a private message using the form on my About /Contact page.
And if you’d like to receive my email series “8 Weeks of Playful Math for Families” plus regular math activity ideas and other updates, click here to join my Math Reader’s Group.