How to Think like a School Math Genius

Posted on by Denise Gaskins
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

      Notice, Wonder, Discover: The Foundation of Learning Well

      Posted on by Denise Gaskins
      Notebook on desk, with the words "Notice. Wonder. Discover."

      Most of us were never taught how to teach. And we certainly weren’t taught what to do when NOTHING is working.

      My friend Sonya Post is offering a free orientation course that will help you rethink how learning actually works, how you can stop second-guessing yourself and start seeing real growth.

      I’ve taken the earlier iterations of her course, and I’d recommend it to all parents.

      Truly wonderful insights!

      Find More Information

      Continue reading Notice, Wonder, Discover: The Foundation of Learning Well

      FAQ: How To Start a Homeschool Math Club

      Posted on by Denise Gaskins
      Denise Gaskins reading math with preschoolers

      The question hits my inbox whenever parents start planning for a new school year:

      “Hello! I am on the board of a homeschool co-op. We have had requests for a math club and wondered if you have any tips for starting one. We service children from K-10th and would need to try to meet the needs of as many ages as possible.”

      There are several ways you might organize a homeschool math club, depending on the students you have and on your goals. I think you would have to split the students by age groups — it is very hard to keep that wide of a range of students interested. Then decide whether you want an activity-oriented club or a more academic focus.

      When I started my first math club, I raided the math shelves in the children’s section at my library (510-519) for anything that interested me. I figured that if an activity didn’t interest me, I couldn’t make it fun for the kids. Over the years we have done a variety of games, puzzles, craft projects, and more — always looking for something that was NOT like whatever the kids would be doing in their textbooks at home.

      Let’s look at the possibilities by grade level…

      Continue reading FAQ: How To Start a Homeschool Math Club

      New Membership Tiers: One-on-One Mentorship

      Posted on by Denise Gaskins
      Two women chatting over tea

      Over the years, in my public writing and in personal correspondence, I’ve tried to help younger parents by sharing the things I wish someone would have told me forty years ago. Oftentimes, I will answer a question but never hear back what the person ended up doing or how their family got along.

      It leaves me feeling as though I could have done more to encourage them along the way.

      In the past few years, I’ve watched a professional writer I admire organize several more formal mentorships for younger indie authors to grow their writing and publishing careers. I think a similar program could be helpful for homeschooling families.

      So now I’m offering two new Patreon membership tiers that give you a direct one-on-one connection with me through email or email-plus-video.

      My goal is to help you think about math as a creative, playful investigation where you and your children explore concepts together using the math program or curriculum of your choice. This is not a tutoring arrangement. I will help you understand and teach math, but I will not do the teaching for you.

      Continue reading New Membership Tiers: One-on-One Mentorship

      Mental Math: Three Basic Principles

      Posted on by Denise Gaskins
      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

      Musings: Mental Math Is the Key to Algebra

      Posted on by Denise Gaskins
      Painting by Nikolay Bogdanov-Belsky, public domain

      “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

          Continue reading Musings: Mental Math Is the Key to Algebra

          Musings: Mathematical Beauty

          Posted on by Denise Gaskins
          photo of child making footprints on the beach

          Memories…

          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.

          Continue reading Musings: Mathematical Beauty

          Skit: The Handshake Problem

          Posted on by Denise Gaskins
          The handshake problem

          If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?

          Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned.

          I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students presented this skit.

          Download a Printable Script

          Cast

          1-3 narrators (or more, if you have a large group)
          7 friends (non-speaking parts, adjust to fit your group)

          Props

          Each friend will need a sheet of paper with a number written on it big and bold enough to be read by the audience. The numbers needed are 0, 1, 2, 3, … up to one less than the number of friends. Each friend keeps his paper in a pocket until needed.

          Continue reading Skit: The Handshake Problem

          Charlotte Mason Math: Living Books

          Posted on by Denise Gaskins
          “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