# Math Teachers Don’t Know What They’re Doing

Yes, the title may seem rude, weird, or even like fighting words. But give me some latitude and you’ll agree.

It’s not that math teachers don’t know what they’re doing in *teaching* (or driving, eating birthday cake, picking a lock or changing the oil).

It’s that math teachers don’t know what they’re doing *when they first open the textbook*.

I have never opened a math textbook and knew exactly what was going on. Never. *Ever*.

People say math is a language. And that like any language, you have to learn the terminology.

This is partially true. Math has a language. But unlike languages like French or Russian, every math textbook has a *different* language. Yes — every *textbook*’s language is different.

Or can be.

When you open a math textbook, you’re never ever really sure if the word that you’re reading is meant the way you understand it. Or some slight variation of your understanding. Or some totally different meaning altogether!

I’ve experienced hundreds, maybe even thousands, of math textbooks. Even if you go from one textbook to another in the same series, there’s a chance of slightly different definitions.

And clear definitions are essential in math.

#### What’s “Normal”?

Open a new tab and google “normal math.” You’ll find more than a dozen different definitions.

In a math textbook you’d have to look back a few pages, or a few chapters, to see what definition *this textbook* is using.

#### Is 1 Prime?

Back in the day (before the internet), some textbooks included 1 as a prime number. And some didn’t.

Again, you’d have to check in the earlier part of the text to see.

(Note: since the internet, we’ve become more consistent. But you still have to be careful.)

#### How About Crazy Aunt Sally?

And then there’s the Order of Operations: the mathematician’s version of the Trojan War. (Without the handsome Helen.)

Try this problem: 6 ÷ 2 (1 + 2)

Now google it.

Your answer depends on your decision to do multiplication *before* division or multiplication and division *at the same time*.

Again, the textbook, or the group’s decision, dictates if you’re to **Please Excuse My Dear Aunt Sally**. Or **Please Excuse Mydear Auntsally**.

#### It’s All Greek to Me!

Of course the English words are less frightening than things like *f(x), *ϴ or ξ.

Consider this formula: *sin (π + φ) = sin π cos φ + sin φ cos π*

If it freaks you out, look a little deeper. Some of the things are familiar:

You may recognize π. It’s 3.14.

And clearly *sin* is what you do on Saturday nights.

And you do those things *cos* they’re fun, right?

Now take a deep breath and flip back a couple of pages. That’s what a math teacher would do.

Because…

#### Math Teachers Don’t Know What They’re Doing, Either.

You may open a math book and think, “I don’t know what I’m doing.”

Well, math teachers do that too.

We just **also** think, “But I know I can figure it out.”