Today is my first day of summer break, sort of. I spent the last six weeks working for a wonderful math camp where the teaching is so much fun.
My class is the closest that students come to school content during camp. It’s a fractions class that students get placed into based on an assessment. If the camp thinks that students could use more time working on fractions — that’s who I teach.
That said, the course content is tricky because I don’t want to simply repeat what they’ve seen in school. That would be boring for a lot of kids, and I’m aiming to approach familiar ideas in unfamiliar ways. I’m trying to work on skills, but from interesting perspectives.
Here’s a one-two-three sequence from my fractions course that I think worked particularly well.
First, I ask students to think about visuals. This was a focus of the previous lesson, but I want to make sure every students has it at the front of their minds.
I’m trying to give everyone a chance to figure out what fraction a piece is by multiplying. (“There are four pieces, this is divided into fourths, that would make sixteen in total.”)
I’m teaching this both because it’s a useful bit of visual fluency, but also because I want to use this as part of my direct instruction.
Next is the direct instruction. I’m trying to teach students a mental shortcut: if you’re dividing a fraction by an integer (e.g. 1/2 divided by 10 is 1/20) you can multiply the denominator by the integer because that’s simply making the pieces 10 times smaller. I use visuals to explain this.
I immediately give students a few chances to try out this new technique on some mental math problems. (Below is my little cheat sheet — this is what I ask students, but I don’t give them this paper.)
That’s the basics. But how are we going to practice it further? And how are we going to keep it interesting, and make sure students start using this technique in other contexts?
I then move to the third activity in this lesson, some mobile problems (designed by me on the EDC site). They’ve been carefully designed to give us a chance to use that mental shortcut we’ve just studied.
A lot of the lessons in my fractions course seem to follow something like this pattern: reminder, quick explanation, interesting practice.
What exactly is it that worked about this? I think this pattern of quick direct instruction followed by interesting practice is a useful one. Of course not every topic is amenable to quick direct instruction (some skills need to be taught in larger chunks) but some are. And after some quick “are we on the same page” questions, it was nice to follow it up with interesting practice. And what made it interesting? I think that it looked different than the direct instruction, but there was still the chance to use it frequently.
This is a way of engineering challenging classroom experiences around stuff that you want to just explicitly teach. I think a lot of people think of these things as incompatible, but they clearly aren’t. At the same time, for a lot of my groups during the year I am trying to make things more accessible — I’m not trying to make it more challenging.
Or maybe I should be? Maybe this pattern of instruction would work just fine in my school-year work. One issue during the year is that I’m much more cautious about whether the practice is actually going to help with the skill. There is a risk to practicing in a different context than instruction. It’s always possible that kids won’t make the connections, that it will be either too hard or students won’t actually practice the thing you thought they would.
So, I’m not sure whether this is something I’ve learned about teaching camp or teaching school or teaching math. Time will tell, I guess.