# Improvement

Sooooooooooooooooo… in my first precalculus class today, I was trying to get kids to derive and understand the formula for combinations. I didn’t want to give it to them, but just posing the question and letting them struggle seemed like it would never turn to a productive struggle. So I came up with a different way to approach it… involving bags of scrabble tiles…

The first class was a disaster. I would be surprised if more than a quarter of the kids understood why $\frac{_{1o}P_{4}}{4!}$ is the formula for the way you could choose 4 things from 10.

In my second class, I saw some of my errors in the first class, and tried to avoid them the second time around. It wasn’t like I thought everyone came out understanding it. But I do know that I did a much better job of even setting the problem up.

• I made sure the big question we were trying to work with was clear to everyone.
• I talked about how we were looking at the problem through a different lens… we were going to work with what we do know in order to help us find out what we don’t know.
• I made sure to not introduce new terminology or notation at all. We kept our eyes on the conceptual prize.

And yes, it wasn’t a total success, I was happy to know I was able self-diagnose, make on-the-fly changes, and improve slightly.