Objectively speaking, today was a good day. Unfortunately, I apparently have no idea how to react to good news, so my brain is melting and I’m looking around for ways to mistrust what I should be treating as evidence that I have some idea how to do my job.
My first two classes of the day are seventh graders, and they are working on volume this week. We started with cubes and rectangular solids, moved on to triangular solids, and then started working on cylinders today. Now, in some ways, all of these are fairly simple– there is a reason that “follow the formula” is literally one of my classroom rules, and I allow calculator use any time that the calculation is not the point, and in this case I don’t want an inability to multiply fluently interfering with understanding what three pieces of information you need to calculate the volume of a prism.
Cubes and rectangles and triangles went fine, but in sixteen years I’ve never had a class of math kids that didn’t struggle with cylinders. Once pi comes into the mix, and especially once not only pi is in the mix but radius squared becomes a thing, they start having trouble. They get over it, but kids always need to be monitored carefully while they’re doing cylinder volume for the first time. They screw it up. I’m used to it. It’s okay.
Nope. Both classes sailed through the assignment I gave them, and from watching the class I could tell that damn near all of them understood what they were doing. Just like they’ve sailed through basically every assignment I’ve given them this week. They just aren’t having trouble with this, in a way that I haven’t seen with my previous math classes. And how did I react, to evidence that my students have learned what I have tried to teach them, a fact that in a sane world would make a math teacher happy?
Tomorrow’s assignment is going to include a mix of shapes, because I’m paranoid that what I actually have is an age cohort that has learned to push buttons in the right order but can’t actually figure out which formula they should use if I don’t hand it directly to them. I’m still going to make sure they have access to the formulas they need; I don’t need them to have anything memorized yet– but it’s not going to be a situation where they can use the same formula every time. And we will see if they crater or if they finish this assignment with the same ease that they’ve completed everything else I’ve thrown at them this week.
“But Luther,” you may be thinking, “you used an image related to graphing equations up there! That doesn’t have anything to do with volume! Why would you choose such a misleading graphic?”
Because my 8th graders pulled the exact same shit with working on slope and graphing linear equations this week. Now, I’ve talked about teaching slope on here before— be sure to read the comments, which feature the single most entertaining fight I ever got into in my comments section in the entire history of the blog, including the utterly priceless “you’re lucky you’re Canadian” final comment– and it is something that middle school kids tend to struggle with. The whole thing is weird, really; they’re just getting used to one letter being in their math, and now there are two, and somehow there’s not one right answer but a whole bunch of right answers, and you’re telling me that this equation and this line are the same thing, somehow? Okay, boomer. Sure.
Thing is, my kids have got this this year. In a way that previous groups never have. And part of the reason is definitely that because of the way that the scope and sequence was set up this year I was able to take my time and go piece by piece with it in a way that I haven’t in previous years, but it’s still stunning how well they seem to have absorbed this particular material.
So, again, I don’t trust it a bit, and I expect to go into work tomorrow and discover that they now think you use your feet to add numbers. We shall see. One way or another, Winter Break is six teaching days away, and that means they will forget everything I’ve ever told them in six teaching days plus one minute. But for now? It’s nice to feel like I know what I’m doing.