Catching Your Glitches

We all make mistakes. Ideally, we learn from the mistake and don't make it again. Realistically, there's a certain type of mistake that we make over and over again. I'll refer to that as a glitch.

Some glitches we're aware of. I have plenty of students who see "three squared" and automatically think the answer's six. But they know they have that tendency, so they catch themselves and say nine before I say anything.

Other glitches sneak around, leaving us oblivious until someone else points them out. Sometimes they turn into the first kind after they've been pointed out. But sometimes they stay rooted, refusing to be corrected.

Students who continue to combine unlike terms no matter how often it's marked wrong. Or who say X plus X is X-squared.

It's not just in math, I'm sure. We fail to shift from second to third gear properly with our manual transmission. We mix up "lay" and "lie" or "affect" and "effect."

With the math, at least, I suspect part of why the glitches keep happening is because the student doesn't understand the foundation of why it's a mistake. Attempting to memorize arbitrary rules without understanding their basis is rarely effective.

Unfortunately, students are often so used to thinking of math as a matter of memorizing arbitrary rules, they don't shift into looking for meaning. At least, not easily. All I can do is try to open their eyes to the hows and whys behind the what-to-dos.