Memorizing the Math Facts

Central City Times Tables[Photo by dsb nola via flickr.]

The most effective and powerful way I’ve found to commit math facts to memory is to try to understand why they’re true in as many ways as possible. It’s a very slow process, but the fact becomes permanently lodged, and I usually learn a lot of surrounding information as well that helps me use it more effectively.

Actually, a close friend of mine describes this same experience: he couldn’t learn his times tables in elementary school and used to think he was dumb. Meanwhile, he was forced to rely on actually thinking about number relationships and properties of operations in order to do his schoolwork. (E.g. I can’t remember 9×5, but I know 8×5 is half of 8×10, which is 80, so 8×5 must be 40, and 9×5 is one more 5, so 45. This is how he got through school.) Later, he figured out that all this hard work had actually given him a leg up because he understood numbers better than other folks. He majored in math in college and is now a cancer researcher who deals with a lot of statistics.

Ben Blum-Smith
Comment on Math Mama’s post What must be memorized?

The entire discussion (article and comments) is well worth reading:

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Quotable: On Teaching

classroom scene

[Photo by City of Boston Archives via Flickr (CC BY 2.0).]

I’ve started collecting quotes about teaching math for the chapter pages in my next Math You Can Play book. Here are a couple snippets that don’t fit the theme of “Multiplication & Fractions,” but they struck my fancy anyway:

If teachers would only encourage guessing. I remember so many of my math teachers telling me that if you guess, it shows that you don’t know. But in fact there is no way to really proceed in mathematics without guessing. You have to guess! You have to have intuitive judgment as to the way it might go. But then you must be willing to check your guess. You have to know that simply thinking it may be right doesn’t make it right.

teaching

[Photo by Nathan Russell via Flickr (CC BY 2.0).]

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics.

Leon Henkin
from “Round and Round at the Round Table”
Teaching Teachers, Teaching Students: Reflections on Mathematical Education

What Are Your Favorite Quotes?

Do you have some favorite quotes on math and teaching? I’d love to hear them! Please share in the Comments section below.


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Active Math Game: Rock

Gordon Hamilton of Math Pickle posted Rock, a new active math game for grades K–2. If you have a set of kids and a few minutes to spare, give it a try!

How to Play Rock

  • Everyone makes a rock shape with eyes closed.
  • Everyone chooses a number: 0, 1, 2, 3, 4, 5, 6, 7, 8 …
  • Teacher calls out numbers consecutively, starting at 0.
  • When a student hears their number being called they immediately raise a hand. When the teacher tags the hand, they stand up.
  • If more than one hand was raised, those students lose. They become your helpers, tagging raised hands.
  • If only one hand was raised, that child wins the round.

Rock-game

“Each game takes about 45 seconds,” Hamilton says. “This is part of the key to its success. Children who have not learned the art of losing are quickly thrown into another game before they have a chance to get sad.”

The experience of mathematics should be profound and beautiful. Too much of the regular K-12 mathematics experience is trite and true. Children deserve tough, beautiful puzzles.

Gordon Hamilton

What Happens When Grownups Play Rock

What are the best numbers to pick? Patrick Vennebush hosted on online version of the game at his Math Jokes 4 Mathy Folks blog a few years back, though we didn’t have to bend over into rocks‌—‌which is a good thing for some of us older folks.

Vennebush also posted a finger-game version suitable for small groups of all ages, called Low-Sham-Bo:

  • On the count of 1-2-3, each person “throws” out a hand showing any number of fingers from zero to five.
  • The winner is the person who throws the smallest unique number.

You may want to count “Ready, set, go!” for throwing out fingers, so the numbers in the count don’t influence the play.

The official name for this sort of game is Lowest Unique Bid Auction.


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Learning to Think is Hard Work

Learning-to-Think

“Learning to think a problem through can be hard work‌—‌and that is exactly what makes it fun.”

—Denise Gaskins

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from my book Let’s Play Math: How Families Can Learn Math Together‌‌—‌And Enjoy It. Background photo courtesy of Chris_Parfitt (CC BY 2.0) via Flickr.


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Unending Digits… Why Not Keep It Simple?

Unending-digits

Unending digits …
Why not keep it simple, like
Twenty-two sevenths?

—Luke Anderson

Math Poetry Activity

Encourage your students to make their own Pi Day haiku with these tips from Mr. L’s Math:

And remember, Pi Day is also Albert Einstein’s birthday! Check out this series of short videos about his life and work: Happy Birthday, Einstein.

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from Luke Anderson, via TeachPi.org. Background photo courtesy of Robert Couse-Baker (CC BY 2.0) via Flickr.


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Quote: Living Mathematics

Only-dead-mathematics

Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession.

— Mary Everest Boole

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from Mary Everest Boole. Background photo courtesy of State Library of Queensland, Australia (no known copyright) via Flickr.


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Get in the Math Car

Math-car

Get in the math car with a list of destinations and no map. Take whatever route you want, and marvel at the things you discover along the way.

— Nick Harris

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from @Mr_Harris_Math, via Twitter. Background photo courtesy of Forrest Cavale (CC0 1.0) via Unsplash.


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