First of all, if you somehow read my blog, but not Andrew Stadel’s, stop here and subscribe to his blog. He’s been doing awesome work with 3 Act videos, his estimation site, and recently analyzing math mistakes. Then, as Mr. Stadel said in a recent blog, you gotta check out Michael Pershan’s Math Mistakes page as well.
Ok, so here’s my contribution to the mistakes conversation. I had students do this activity (it’s a functions matching activity) that I got from Mrs Reilly’s blog. It went pretty well and I was pleased with the results in general. Then, as an extension I gave each group a whiteboard with a quadratic equation on it.
That’s it. No real instructions.
They naturally decided to make a table, a graph, and a sentence for their equation. This ability to go right to work creating different representations is something that we’ve been working hard on in physics and algebra, and I was pretty proud of them for just doing it without explicit instructions.
The results in one of my classes were not so great though. Their boards were riddled with mistakes and we ran out of time in class to do any real work on fixing them.
But the next day (different classes), I had a spur of the moment idea. I had a hunch that this class was going to do a little better on them in general, so I thought “Why don’t I give them the same problems and then have them compare their boards to the boards with the mistakes?” And then that turned into the students writing notes to the other class to help them out. Here’s the boards with mistakes and the notes (some are more helpful than others):
I love the idea, but it didn’t work exactly as planned. The students were not really thinking about the specific mistakes made by their peers. They were mostly just pointing out that something was wrong.
I like that the mistakes weren’t obvious necessarily, but that did make it harder for students to spot them. I think I can build up to this activity by using the mistakes game more frequently in class (basically, they insert a mistake on purpose and the rest of the class tries to find it). By getting good at finding these purposeful mistakes (which should be easier to spot), they should be better prepared to spot accidental mistakes and even misconceptions.