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Morning Coffee: When Math Makes You Feel Stupid

Morning Coffee Lifelong Learning for Parents

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.

     
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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: When Math Makes You Feel Stupid” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.

    Why I Love the Math Journaling Adventures Series

    Mother and daughter doing homework outdoors

    Math Journaling Adventures series by Denise GaskinsMy Math Journaling Adventures Series is now available on Kickstarter.

    I love these books!

    Writing is one of the best ways to learn math deeply, because wrestling our thoughts into words forces us to figure out what we really believe.

    It’s the natural, no-stress way to build our children’s understanding and confidence.

    Hit the button to visit the campaign and order your books:

    Math Journaling Adventures Kickstarter ❯

    Continue reading Why I Love the Math Journaling Adventures Series

    Math Journaling Adventures Launched: Order Your Copy Today

    Math Journaling Adventures: Creative Logbooks for All Ages

    And so it begins: the Math Journaling Adventures is LIVE on Kickstarter!

    Check It Out ❯

    ⭐ Don’t delay! First-day backers get the best deals. Choose one of the Earlybird rewards:

    • Earlybird 2-Logbook Sets in Digital, Paperback, Spiral-Bound, or Hardcover
    • Earlybird Everything Bundles in Digital or Paperback

    To have a successful campaign, we need plenty of people to back the project early. The more supporters we get in these early days, the more likely the Kickstarter platform folks will help spread the news for us.

    Continue reading Math Journaling Adventures Launched: Order Your Copy Today

    Playful Math 179: Our Sweet Sixteen Carnival

    Welcome to the sweet-16 birthday edition of the Playful Math Carnival. Originally called Math Teachers at Play, our first carnival was published in February 2009.

    Each Playful Math Carnival offers a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

    There’s so much playful math to enjoy!

    By tradition, we start the carnival with a math activity in honor of our 179th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

    NOTE: Our wonderful volunteer hosts have kept the Playful Math Carnival going when so many other blog carnivals died off. If you’d like to sign up to host the carnival for a month, email Denise for information.

    Try These Prime Puzzles

    Did you know there are 179 even-numbered days this year?

    • How many even-numbered days will there be in a leap year?
    • But there are 365 days in a standard year and 366 in a leap year. Shouldn’t there be half that many even-numbered days?

    179 is a prime number, and it’s also a knockout prime. You can knock out any of the digits, and what’s left is still prime: 17, 19, or 79.

    • Can you find another knockout prime number?

    179 is a twin prime. That means that one of its odd-numbered neighbors is also prime.

    • Is the other twin 177 or 181? Can you tell without looking it up?
    • Why are twin primes limited to the odd numbers? That doesn’t seem fair!

    179 is also an emirp. That’s a special kind of prime that forms a different prime number when you write it backwards: 971 is also prime.

    • How many emirps can you find?

    “A palindrome is a word that when written in reverse results in the same word. for example, ‘racecar’ reversed is still ‘racecar’. Related to palindromes are semordnilaps. These are words that when written in reverse result in a distinct valid word. For example, ‘stressed’ written in reverse is ‘desserts’. Not all words are palindromes or semordnilaps.

      “While certainly not all numbers are palindromes, all non-palindromic numbers when written in reverse will form semordnilaps.

        “Narrowing to primes brings back the same trichotomy as with words: some numbers are emirps, some numbers are palindromic primes, but some are neither.”

        The On-Line Encyclopedia of Integer Sequences A006567

        Click here for all the mathy goodness!

        Why I Love Kickstarter

        Photo of woman thinking about books

        Math Journaling Adventures Kickstarter projectOver the several weeks, you’ll be hearing a lot about Kickstarter and my Math Journaling Adventures project. I’m proud of the books, and I want to spread the news as far and wide as possible.

        You’ll appreciate how these books make it easy to weave playful math into your family’s schedule. Just open to any page for a puzzle, activity, game, investigation, or other creative prompt.

        But I know there are many readers who don’t know much about crowdfunding. Some people even think that a campaign like this is just online begging.

        So I want to share what I totally love about Kickstarter and how much it offers you, the customer:

        (1) It’s the “New World” of publishing.

        In the old days, traditional publishing companies paid writers in advance to write the books the publisher wanted to see. In this new world, you get to choose and support the writers creating books you want to read.

        Continue reading Why I Love Kickstarter

        Coming Soon: Math Journaling Adventures

        Math Journaling Adventures Kickstarter

        Coming Soon! On March 3, I’ll be launching the first installment in my new book series, the Math Journaling Adventures.

        You’ll love these books because they make creative math investigations open-and-go for busy parents and teachers.

        And the Kickstarter prelaunch page is now live. That means you can sign up to get an email from Kickstarter as soon as the campaign launches:

        Visit the Prelaunch Page ❯

        If you back the campaign on launch day, you can catch a great deal with the Earlybird discount pledge levels.

        Continue reading Coming Soon: Math Journaling Adventures

        Morning Coffee: Professional Development for Homeschooling Parents and Other Teachers

        Morning Coffee Lifelong Learning for Parents

        Lately, I’ve spent most of my writing time thinking about the value of narration—the Charlotte Mason approach to teaching by getting kids to put ideas in their own words.

        For students, I’m writing a new series of Math Adventure Journals to get them thinking about math and putting those thoughts into words. If you’re interested, sign up to be notified when the Kickstarter goes live.

        But we parents can harness the value of narration in our own learning. After all, one of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.

        To that end, I’ve decided to relaunch my “Morning Coffee” series of professional development posts for homeschooling parents.

        Here’s How It Works

        As I read articles and follow rabbit trails around the internet, I’ll collect the posts that speak to me. Then I’ll share these in a printable format with journaling pages for your response.

        Since I’m interested in math education, many of the articles I read will be about math—but the principles of learning apply to every subject we teach.

        To kick off the series, let’s start with one of my favorite articles ever…

        Morning Coffee # 1: Learning to Ask Good Questions

        Download your printable Morning Coffee journal

        David Butler’s post Twelve matchsticks: focus or funnel presents an interesting math puzzle. But even better, it opens up a rabbit hole of thought-provoking posts about how to talk with children—or anyone:

          “The approach where you have an idea in your head of how it should be done and you try to get the student to fill in the blanks is called funnelling. It’s actually a rather unpleasant experience as a student to be funnelled by a teacher. You don’t know what the teacher is getting at, and often you feel like there is a key piece of information they are withholding from you, and when it comes, the punchline feels rather flat.”

          The printable file includes links to three more articles as I follow the rabbit around the internet. Enjoy!

           
          * * *

          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: Professional Development for Homeschooling Parents and Other Teachers” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.

          Playful Math 178: Nicomachus’s Carnival

          Playful Math Blog Carnival 178

          Welcome to the 178th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

          Bookmark this post, so you can take your time browsing.

          There’s so much playful math to enjoy!

          By tradition, we start the carnival with a puzzle/activity in honor of our 178th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

          Activity: Nicomachus’s Theorem

          Welcome to 2025, a perfectly square year — and the only one this century!

          2025 = (20 + 25)2

          • When is the next time we’ll have a perfect-square year?
          • Can you find the only perfect square less than 2025 that works by this pattern? When you split the number’s digits into two smaller numbers and square their sum, you get back to that number.

          2025 = the sum of all the numbers in the multiplication table, from 1×1 to 9×9

          2025 = the sum of the first 9 perfect cubes

          • When is the next time this will happen, that the year is the sum of the first n perfect cubes?

          And by Nicomachus’s theorem:

          2025 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93
          so it must also = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)2

          Try it for yourself with small numbers: Get some blocks, and build the first few perfect cubes. Then see if you can rearrange the block to form the sum of those numbers squared.

          Can you show that…

          • 13 = 12
          • 13 + 23 = (1 + 2)2
          • 13 + 23 + 33 = (1 + 2 + 3)2
          • 13 + 23 + 33 + 43 = (1 + 2 + 3 + 4)2
          • 13 + 23 + 33 + 43 + 53 = (1 + 2 + 3 + 4 + 5)2

          Nicomachus theorem 3D

          Older Students: Can you see that the pattern would continue as long as you want? How might you prove that?

          Here’s the formula for triangular numbers, to get you started:

          (1 + 2 + 3 + … + n) = n(n + 1)/2

          Click here for all the mathy goodness!

          FAQ: Can I Use Your Books as a Math Curriculum?

          Father helping girl with math homework

          I recently listened to you on Cindy Rollins’ podcast, and I was captivated by your perspective on math. It was exciting, freeing, and wonder-filled. I would absolutely love to be able to teach in the ways you described.

            We use early-elementary Saxon Math right now, which is thorough, but has SO MUCH to do that I’ve always struggled to do it all. Then I feel like I’m missing things, and I never know quite what is important. And yet, the actual lessons move so slowly that my kids get bored with the repetition.

              I use a published curriculum because I have no idea of an appropriate scope and sequence, or similar flow of learning. With your playful approach to math, how do I know where to start, and what to do each day?

                Do you have a suggested order to approach your books to have a full math approach? A sort of curriculum, per se, using your books.

                [For those who missed my chat with Cindy Rollins about a Charlotte Mason approach to math, you can listen to it here.]

                Continue reading FAQ: Can I Use Your Books as a Math Curriculum?