What “Solving” Means


Image source: Steven Johnson on flickr

Sometimes, you get stuck trying to understand a math idea. It seems confusing even when you think about it.

In some cases, that’s because the idea is truly difficult.

Other times, the idea’s not so bad– but there’s a missing piece. Without that piece, the idea stays vague and confusing, no matter how hard you try to understand it. But once you “get” that piece, the whole idea clicks into place.

“Solving for” a variable is an idea that’s confusing to a lot of people. In my experience, there are two issues that come up.

One is that people try to solve for things when they shouldn’t. You can’t solve for in Fermat’s Last Theorem. Nor should you try.

The other problem is that people don’t really know what solving is. They might know how to do it, by rote practice if nothing else. But what’s really going on?

Math teacher Ben Orlin, the blogger behind Math with Bad Drawings, wrote (well, doodled) an excellent piece on the subject. In purple, stick-figured prose, Ben explained what it means to solve – it means Simplify!

Thoughts? Does this idea of solving ring true to you? Is there another explanation you like better? Let me know in the comments.