Thinking (and Teaching) like a Mathematician

photos by fdecomite via flickr

Most people think that mathematics means working with numbers and that being “good at math” means being able to do (only slower) what any $10 calculator can do. But then, most people think all sorts of silly things, right? That’s what makes “man on the street” interviews so funny.

Numbers are definitely part of math — but only part, and not even the biggest part. And being “good at math” means much more than being able to work with numbers. It means making connections, thinking creatively, seeing familiar things in new ways, asking “Why?” and “What if?” and “Are you sure?”

It means trying something and being willing to fail, then going back and trying something else. Even if your first try succeeded — or maybe, especially if your first try succeeded. Just knowing one way to do something is not, for a mathematician, the same as understanding that something. But the more different ways you know to figure it out, the closer you are to understanding it.

Mathematics is not just memorizing and following rules. If we want to teach real mathematics, we teachers need to learn to think like mathematicians. We need to see math as a mental game, playing with ideas. James Tanton explains:

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Why Every Proof that .999… = 1 is Wrong

Vi Hart repents with an update to her last video: “Take that, mathematics!”


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What I’m Reading: Fermat’s Enigma

Homeschooling is much more than just doing school at home — it’s a lifelong lifestyle of learning. And thanks to the modern miracle of inter-library loan, even those of us who live in the middle of nowhere can get just about any book sent directly to our tiny home-town libraries.

As I mentioned in Math Teachers at Play 46, I’m trying to add more living books about math to our homeschool schedule, including my own self-education reading. So, a copy of Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem finally showed up at my library, and I am thoroughly enjoying it.

Continue reading What I’m Reading: Fermat’s Enigma

A Mathematician for President

[Image courtesy of the Images of American Political History.]

In 1876, a politician made mathematical history. James Abram Garfield, the honorable Congressman from Ohio, published a brand new proof of the Pythagorean Theorem in The New England Journal of Education. He concluded, “We think it something on which the members of both houses can unite without distinction of party.”

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Answers: Euclid’s Geometric Algebra

Alexandria JonesRemember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original post. Figure them out for yourself — and then check the answers just to prove that you got them right.

Euclid’s Geometric Algebra

Continue reading Answers: Euclid’s Geometric Algebra