“It is the supreme art of the teacher to awaken joy in creative expression and knowledge.”
—Albert Einstein
Whenever a new set of test results comes in, society goes through a new cycle of hand- wringing and blame-casting. The most current PISA results are no different. The best analysis I’ve seen: The Sky Is Always Falling by Bill McCallum.
Rather than join that fray, let’s step back and ask a bigger question: What do we want for our children?
Why do we school our kids? What does it mean to be “educated”? And in particular, why do we teach math? What do we hope to achieve?
We can’t think rationally about how to teach until we are clear about our goals.
What’s Your Priority?
- Do you want to produce good test-takers, children who know how to follow instructions and work efficiently?
- Or do you care less about efficiency and more about curiosity? Do you want students who enjoy wondering about concepts and are eager to learn more?
- Or maybe you want problem-solvers, students who can step into an unfamiliar situation and figure it out?
Can we choose option D, all of the above? Is it possible to work toward all these goals at once, to build solid knowledge and teach mathematical skills while at the same time encouraging curiosity and developing flexible thinking?
Like a toddler throwing a tantrum, I want it all, and I want it right now.
I don’t know how to solve the problems of classroom schooling, but here’s some advice for my fellow home schoolers.
This school year…
(1) Build Problem-Solving Skills
Whatever math curriculum you use, focus math lessons on your child’s own thinking.
Rather than telling them what to do, ask about what they know. Help children find a way to use what they’ve already learned to reason about the new topic.
Consider doing your math lessons buddy-style:
- Buddy-Style Math: Doing Homework Without Tears
In a way, it’s like Charlotte Mason-style narration applied to math.
And when your children get stuck, follow the tips in my “If Not Methods” blog series:
- If Not Methods, Then What?
As always, real math is not about the answers but the thinking.
(2) Practice for Fluency
Reinforce learning with creative practice.
Don’t just memorize facts, but use them in a variety of ways. Build mental math skills by playing math games, especially games that require strategic use of math skills.
Check out my blog for ideas:
- My Best (Free) Math Games for All Ages
Games put children in exactly the right frame of mind for learning difficult things. - Math Game Monday
Learn a new game every week, for free! - Mental Math Series
The more our children practice these structures in mental math, the better prepared they will be to recognize the same principles in algebra.
(3) Explore Non-Textbook Math
Encourage curiosity through puzzles, enrichment activities, reading good books, playing with math art, and journaling.
For example:
- Learning Math with Puzzles
As stories are to history or science, puzzles are to math. - Make Your Own Nim Games
Mathematicians enjoy studying patterns, whether they are patterns within our system of numbers or patterns of shapes or of abstract ideas. - Living Books for Math
Here are a few of my favorite books of playful, living math, both old and new. - Discover Math in Art
Art lets children experiment with lines, curves, shapes and symmetries, exploring a wide range of mathematical structures and relationships. - The Creative Way To Help Your Kids Learn Math
When you embrace this adventure of learning math through playful exploration, you’ll be surprised how much fun thinking hard can be.
“How to Teach Math” copyright © 2026 by Denise Gaskins. Image at the top of the blog copyright © Wavebreakmedia / Depositphotos.
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