“Play and rigor support each other.
“When students are invited to play with math, they learn more deeply, more robustly, and remember more consistently.
“Play is promoted as something that can engage kids and give them a more positive attitude about school, but it’s easy to assume that it’s not useful for learning, when in reality the opposite is true:
“The student who is playing tends to be the student who is learning most deeply.”
—Dan Finkel, Math for Love newsletter
“We know that algorithms are amazing human achievements, but they are not good teaching tools because mimicking step-by-step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.”
— Pam Harris, Math Is Figure-Out-Able Podcast
Whether you work with a math curriculum or take a less-traditional route to learning, do not be satisfied with mere pencil-and-paper competence. Instead, work on building your children’s mental math skills, because mental calculation forces a child to understand arithmetic at a much deeper level than is required by traditional pencil-and-paper methods.
Traditional algorithms (the math most of us learned in school) rely on memorizing and rigidly following the same set of rules for every problem, repeatedly applying the basic, single-digit math facts. Computers excel at this sort of step-by-step procedure, but children struggle with memory lapses and careless errors.
Mental math, on the other hand, relies on a child’s own creative mind to consider how numbers interact with each other in many ways. It teaches students the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.
The techniques that let us work with numbers in our heads reflect the fundamental properties of arithmetic. These principles are also fundamental to algebra, which explains why flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.
Your textbook may explain these properties in technical terms, but don’t be intimidated by the jargon. These are just common-sense rules for playing with numbers.
“If you stay with meaningful mental arithmetic longer, you will find that your child, if she is average, can do problems much more advanced than the level listed for her grade. You will find that she likes arithmetic more.
“And when she does get to abstractions, she will understand them better.
“She will not need two or three years of work in primary grades to learn how to write out something like a subtraction problem with two-digit numbers. She can learn that in a few moments of time, if you just wait.”
—Ruth Beechick, An Easy Start in Arithmetic
Mental math is doing calculations in your head, with perhaps the aid of scratch paper or a whiteboard to jot down notes along the way.
But you cannot simply transfer the standard pencil-and-paper calculations to a mental chalkboard. That’s far too complicated.
We were eclectic homeschoolers back in the Dark Ages before there was an internet. Our primary curriculum was the public library.
As we went along, I noticed how many of our homeschooling friends felt uncomfortable with math, and even hated or feared the subject.
Math anxiety runs rampant in Western culture. By one researcher’s estimate, more than 90% of adults experience some level of math anxiety — that is, discomfort, avoidance, and even emotional pain when faced with a math calculation.
So I became a sort of “math evangelist” in the homeschooling community, spreading the news that we can find beauty and fun even in math.
On a friend’s blog, I found this delightful letter written by Charles Lutwidge Dodgson to a young man named Wilton Cox.
The pseudonym Lewis Carroll comes from an alteration of the Latinized name Carolus (for Charles) and the replacement of Lutwidge with Lewis.
One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.
Here are a few stories to read as you sip your morning brew. . .
Download your printable Morning Coffee journal
This week’s rabbit hole started with a thought-provoking blog post by Sara Van Der Werf…
“We are all mathematicians. We all have the power to notice, describe, and generalize patterns. You have all had this ability since birth.
“If we believe this then every day we must plan lessons that allow students to act as mathematicians. We must put something in front of our students to notice. We must put something in front of our students to describe, to generalize.”
—Sara Van Der Werf
Read more about how to develop mathematical thinking in this fourth installment of professional development for homeschooling parents.
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Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my email newsletter.
This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.
“Morning Coffee: What Is Mathematics?” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.
When I was in school, math was something each person did on their own for homework, quizzes or tests.
Even when the teacher sent us to work on the chalkboard, each person did their own problem. We would never think to collaborate on math.
To look at someone else’s answer was considered cheating.
One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.
Here are a few stories to read as you sip your morning brew:
Once again, my rabbit hole started with a thought-provoking blog post from Dan Finkel…
“Not everyone can become a great artist — but a great artist can come from anywhere.”
—Ego, from Ratatouille
“Ego’s parsing of the phrase anyone can cook is not obvious, and it’s not really the primary meaning of the phrase. The truth is, there are really three meanings all wrapped up there: anyone can learn to have the joy and pleasure of cooking in their life, even if they don’t become a master chef. Some people will get serious about it. And the visionaries who change the way we think about the art can come from anywhere — lock them out of the field and we all suffer.”
—Dan Finkel
Read more about how anyone can learn math in this third installment of professional development for homeschooling parents.
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Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my email newsletter.
This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.
“Morning Coffee: Anyone Can Learn Math” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.
Mary Everest Boole, wife of English mathematician George Boole, once described algebra as “thinking logically about the fact of our own ignorance.”
This definition made me chuckle. Like any human being, I am ignorant on many things, but I usually avoid thinking about that.
So I wondered what would happen if I took Mrs. Boole’s advice and tried thinking logically about my ignorance.
How far could I go?
Perhaps you’d like to try this experiment with your children. All you need is a pen and paper or a whiteboard and markers and a bit of curiosity.
And if you enjoy this exploration, check out my Math Journaling Adventures project to discover how playful writing activities can help your students learn mathematics. Preorder your books today!
Continue reading Math Journal: Playing with My Own Ignorance
One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.
Here are a few stories to read as you sip your morning brew. . .
Download your printable Morning Coffee journal
This week’s rabbit hole started with a thought-provoking newsletter from Dan Finkel, which led me to his blog…
“Everyone who learns math is familiar with the experience of being stuck on some new idea or problem, banging their head against it, and then, when they finally understand the answer (or having someone tell them), feeling stupid. There’s something fundamental in the nature of mathematics that makes it easy once you get it, and impossible before.
“These jumps in comprehension can be thrilling, and they’re one reason math is so fun. But they do create a challenge for the student. The evidence that you learned something hard is that you feel like you’re stupid. That stupidity is essential to the process. Students need to know this feeling is the norm when it comes to learning math.”
—Dan Finkel and Katherine Cook, The centrality of stupidity in mathematics
Read more about the value of feeling stupid in this second installment of professional development for homeschooling parents.
* * *
Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my email newsletter.
This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.
“Morning Coffee: When Math Makes You Feel Stupid” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.
Denise Gaskins' Let's Play Math 