Musings: Mental Math Is the Key to Algebra

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

      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

      Playful Math Carnival 180 via Math Hombre

      carnival party banner

      If you’re into math education — or just curious about how learning math could possibly be fun — you’ll definitely want to check out the latest edition of the Playful Math Carnival.

      It’s a collection of awesome blog posts curated by John Golden and published on the Math Hombre website:

      The whole point of the carnival is to show that math doesn’t have to be tedious or repetitive. Through a bunch of fun and engaging posts, we celebrate math that’s playful, creative, and totally relevant to everyday life.

      Because what could be more relevant than having fun while we learn?

      In this edition, you’ll find everything from math puzzles and games to humor and much more — even an interesting math art game.

      So if you want to mix up your math teaching and make it more enjoyable for your students (and for yourself), definitely check out the Playful Math Carnival. Happy reading!

      Go Visit the Carnival

      Continue reading Playful Math Carnival 180 via Math Hombre

      Skit: The Handshake Problem

      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

      “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