What sorts of activities do you do with kids to help them avoid common mistakes?
There's obviously no easy fix for common mathematical mistakes. They're common for a reason. Helping kids avoid common math mistakes is synonymous with effective math teaching, and there's no recipe for teaching good.
OK, fine. But here's a move that I often make when I know that there's an especially nasty math mistake coming up.
Example: cos(a+b) = cos(a) + cos(b)
1. I ask kids what they think cos(a + b) is.
2. We get the wrong answer on the table, and we give it a name. In this case, I name it "The Distributive Property for Cosine."
3. I get kids to argue about the wrong answer until it's been disproved.
4. We give language to the truth: "The Distributive Property Isn't True for Cosine," and "Cosine Isn't Linear."
5. We practice the true thing a bunch in the next few days.
Trying to provoke interesting conversations amongst the childrens is a pretty big part of what I try to do. I also think it's important not to tip kids to the fact that you're setting a trap for them, so I try to hide my hand. (In this case, cos(a+b) = cos(a) + cos(b) was included in a long list of Always, Sometimes, Never problems.) I think that giving kids language to talk about this debate is absolutely crucial to them remembering it, so it needs to happen.
This is a go-to pedagogical format for me.
(New Blogging Rule? I only blog if it'll take less than 10 minutes or more than 2 hours to write the post?)