Tell Children Interesting Things

Posted on by Denise Gaskins
quote by John Conway

“You don’t educate people by telling them useful things; you educate people by telling them interesting things.”

— John Conway

If you want help educating your children with interesting things about math, check out Denise Gaskins’ Playful Math store.

We’re currently running a huge back-to-school sale on ALL of my playful math ebooks, problem-solving activities, math journaling task cards, and math art projects.

So many great ways to play with math!

The 20% discount will automatically apply when you check out. No discount code required.

Check it out:

Back to School Sale 2025

Playing to Learn

Posted on by Denise Gaskins
quotation from Dan Finkel

“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

        Musings: A Common Misconception

        Posted on by Denise Gaskins
        Father and son thinking together about a math problem

        One of my favorite podcasts to listen to is Pam Harris’s Math Is Figure-Out-Able because she puts so many of my thoughts into words.

        For example:

        “We have a misconception in math education that we think we need to teach methods so that kids can answer the craziest kind of a particular problem.

          “We would be far better served to teach kids to think about the most common kinds of questions WELL, and let the cranky ones go to ChatGPT. Because they’ll recognize the sense of the answer.

            “Let technology handle the crankiest, and REASON about the rest of them.”

            —Pam Harris,
            the Math is Figure-out-able Fractions Challenge

            Well, I do think she’s wrong about the AI chatbot, because ChatGPT comes up with the strangest bald-faced nonsense about math problems. Wolfram Alpha is a much more reliable resource.

            But Harris’s main point stands. This misconception, this math-education myth, drives much of what happens in our classrooms and home schools today.

            Continue reading Musings: A Common Misconception

            Podcast: Cultivating Math Curiosity and Reasoning in Kids

            Posted on by Denise Gaskins

            I have a new podcast interview, and I think you’ll enjoy it!

            Check out Learning Is Disruptable on your favorite podcast app, or listen on the website:

            Go to the podcast ❱

            Here’s an excerpt…

            “I think the most important thing that we need to change…we need to radically change what our idea is of what it means to learn math.

              “Our biggest failure, both in the classroom and in homeschool settings, is that we’ve given our children a totally wrong idea of what math is all about.

              Continue reading Podcast: Cultivating Math Curiosity and Reasoning in Kids

              Parents: Math Is Figure-Out-Able

              Posted on by Denise Gaskins

              I love listening to podcasts during my morning walk with the dogs. One of my favorites over the past year has been Pam Harris and Kim Montague’s Math is Figure-Out-Able podcast.

              Figure-out-able. What a great word!

              Figure-out-able sums up what I mean when I tell parents that math is “applied common sense.” Kids can use the things they know to figure out things they don’t yet know.

              And figuring things out like that is fun, like a mental game where we play with the ideas of numbers, shapes, and patterns.

              Usually, the podcast targets teachers, and the hosts try to show how they can help students learn to mathematize — to think mathematically. Over the past few weeks, however, Pam and Kim have been talking directly to parents about how to help their children learn math.

              Continue reading Parents: Math Is Figure-Out-Able

              The Principality of Mathematics

              Posted on by Denise Gaskins
              quotation from Charlotte Mason: The principality of mathematics is a mountainous land, but the air is very fine and health-giving

              Here’s the full quote:

              “The Principality of Mathematics is a mountainous land, but the air is very fine and health-giving, though some people find it too rare for their breathing. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.”

              — Charlotte Mason, Ourselves

              Charlotte Mason and Math

              Math was not one of Charlotte Mason’s primary interests. She didn’t think or write as deeply about it as she did other subjects.

              She even wrote, “It is unnecessary to exhibit mathematical work done in the P.U.S. as it is on the same lines and reaches the same standard as in other schools.”

              This leaves us modern parents and teachers having to read our own interpretations into her words. It should be no surprise when we come to different conclusions. Someday, perhaps, I’ll publish my own vision for a Charlotte Mason approach to homeschooling math.

              In the meantime, the following articles describe a method that allows even the youngest children to explore the Principality of Mathematics:

              In the years since writing those posts, Sonya and Lacy combined all their ideas into an easy-to-implement program that I think Mason herself would have enjoyed. Here’s my review:

              CREDITS: Quote background photo (top) by Kalen Emsley via Unsplash.com.

              Not Attained by Chance

              Posted on by Denise Gaskins

              I’ve been collecting quotes about life and learning. They make great discussion-starters or essay/journaling prompts.

              This is one of my favorites.

              “Learning is not attained by chance, it must be sought for with ardor and attended to with diligence.”

              —Abigail Adams

              [Aw, face it. They’re all my favorites. That’s why I collect them!]

              If you like quotes, too, you might enjoy browsing my collection:

              Math & Education Quotations

              Math as a Verb

              Posted on by Denise Gaskins

              Here’s the full quote:

              I like to play games. Almost any type of game.

              I also like to play math.

              If you’ve known enough mathematicians, you may have noticed that this isn’t unusual. I’m not sure if a love of games and puzzles among mathematicians exceeds a love of music among mathematicians, but both are strong and intersect.

              Math in play is also a way of teaching mathematics. I think that as a metaphor, it best describes how I want to teach math.

              I am constantly seeking ways to get my students thinking about math as a verb. It is about doing, not just about having right answers or the end product.

              Games help set the culture I want to develop: Teaching students that multiple approaches and strategies are valued; trying is safe; and conversations about why, how, and discovery are the goals.

              —John Golden
              Yes, Playing Around

              CREDITS: “Football outside Jakarta” photo by Robert Collins on Unsplash.

              FAQ: Playful Math for Older Students

              Posted on by Denise Gaskins

              My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

              Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

              But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

              Here are a few ideas to get your older children playing with math…

              Continue reading FAQ: Playful Math for Older Students

              The Value of Puzzles

              Posted on by Denise Gaskins

              I love puzzles. Don’t you?

              Here are several examples of river-crossing puzzles you and your kids can try. They date back at least to the time of Alcuin, the famous scholar from the court of Charlemagne.

              I wish someone would write a whole math curriculum devoted entirely to puzzles.

              W.W. Sawyer on the Value of Puzzles

              Master teacher W.W. Sawyer didn’t write a curriculum, but he often used puzzles in the classroom.

              “It is quite possible to use simultaneous equations as an introduction to algebra. Within a single lesson, pupils who previously did not know what x meant can come not merely to see what simultaneous equtions are, but to have some competence in solving them.

              “No rules need to be learnt; the work proceeds on a basis of common sense.

              “The problems the pupils solve in such a first lesson will not be of any practical value. They will be in the nature of puzzles.

              “Fortunately, nature has so arranged things that until the age of twelve years or so, children are more interested in puzzles than in realistic problems.”

              —W. W. Sawyer, Vision in Elementary Mathematics

              Then he gives this example:

              “A man has two sons. The sons are twins; they are the same height. If we add the man’s height to the height of one son, we get 10 feet. The total height of the man and the two sons is 14 feet. What are the heights of the man and his sons?”

              Try This at Home

              Not only can children solve puzzles like this, but even better — they can make up story puzzles of their own. You could spend a whole week or more making up silly height puzzles for each other to solve. By the time you were done, your kids would have a great introduction to algebra!

              Maybe I never grew up. Because I still prefer puzzles over “real world” math problems.

              What are your favorite kinds of puzzles? Please share in the comments section.

              CREDITS: “Boat puzzles” comic from xkcd.com.
              [THE FINE PRINT: I am an Amazon affiliate. If you follow the book link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]