How to Think like a School Math Genius

Teen student thinking

“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

    “There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

      “Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

      —James Tanton

      James Tanton has a new website. It looks cool, and it’s a great place to discover the things he’s working on these days.

      But his wonderful, old-fashioned site full of great insights and interesting problems is gone.

      😞 I hate it when some part of the internet that I love disappears. So here’s my attempt to recover one tiny bit of the old site, five tips for creative problem solving through intellectual play.

      Continue reading How to Think like a School Math Genius

      Tell Children Interesting Things

      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

      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

            Mental Math: Three Basic Principles

            Doing mental math on the couch

            “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.

            Continue reading Mental Math: Three Basic Principles

            Charlotte Mason Math: Living Books

            “The Reading Lesson” painting by Jonathan Pratt, public domain

            [An addendum to my earlier Charlotte Mason Math series.]

            “Our business is to give [children] 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, the best books; our own concern is abundant provision and orderly serving.”

            — Charlotte Mason, Toward A Philosophy of Education

            Most homeschool teachers, whatever our curriculum or schooling approach, understand the importance of teaching with living books. We read aloud biographies, historical fiction, or the classics of literature. We scour library shelves for the most creative presentations of scientific topics that interest our children, and encourage our high school students to go back to the original documents whenever possible.

            And we teach math with a textbook.

            Not that textbooks are inherently bad, because math is an abstract science. We need to meet the ideas  — the “mind-stuff” — of math on their own terms, and textbooks can help with that.

            But it’s not enough.

            Continue reading Charlotte Mason Math: Living Books

            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

            Continue reading Morning Coffee: When Math Makes You Feel Stupid