On Friday, last period, I was giving a test in my calculus class. This week has been really l — o — o — oooooo — ong because we had to write and proof narrative comments on our kids. It’s consumed me for last weekend, and this whole week. So it felt good, on Friday, to be done.
I was antsy. Right before the last period, I saw another math teacher, and I told her I wish I were doing something other than proctoring a test. She said “we should switch! you should teach my geometry class!” At first, I was all like nooooooooo and that’s crazy but then I said “what’s the downside?” (I told her I could only do it for about 30 minutes because I wanted to field any questions my kids had.)
So I went. I taught geometry. I was teaching sectors and arc length. It was weird being in a new classroom, with kids I didn’t know. But it was that weirdness that was fun. I’d point to a kid in a blue shirt and say “hey you, blue shirt, what’s the …”
What was great was that I wasn’t really following a script. So I first showed them how to get the area of a circle if you know the circumference… this little trick:
Then I threw up three circles on the board, and I shaded in a 90 degree sector, a 120 degree sector, and a 212 degree sector. I asked them to find the areas of these pieces in partners. I told them I wasn’t giving them any help — so they have to use their brains.
They did that fine. A few struggled with the last one, but their partners helped. I then asked them to come up with a formula for the area of a sector with radius r and angle 
Then I did the same with the arc length for the three circles. They used their knowledge (use the proportion of the whole circle!). Some partners came up with the formula first and then applied it to the circles, and some solved for the arc length of the circles and generalized it to the formula and saw the connection.
Finally, we re-wrote the general formula for both, and I said they should NOT memorize them. They should think about the logic we used to come up with them, and use that logic to come up with the formula.
It was fun to do this sort of impromptu teacher exchange. I think if we did this every so often (planned or unplanned) and the new teacher could just do a little strange song and dance, it could liven up a class. I’m pretty sure my kids would LOVE to get a new teacher for a day. It’s like an alternate reality for a day!
P.S. The math teachers had planned on switching classes on April Fools day, and start teaching without acknowledging any students’ comments or mentioning anything about it, but April 1st fell during Spring Break.
Continuous Everywhere but Differentiable Nowhere 
“The math teachers had planned on switching classes on April Fools day, and start teaching without acknowledging any students’ comments or mentioning anything about it.”
Oh, I am soooooooooo going to steal that idea for next year, Sam! And switching classes is an intriguing idea as well: the most we come to that is covering for someone’s class when they’re unexpectedly out without a sub who can teach math.
Paul Hawking
Blog:
The Challenge of Teaching Math
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Creating a culture of double-checking your work
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Sam, switching classes is a great idea. I think it is good for teachers to see the contexts in which their colleagues work. When I was department head, one day at lunch I suggested we draw from a hat for classes to teach after lunch. The suggestion was vetoed. Too crazy an idea, I suppose. They said, “What if a remedial math teacher ended up in a senior IB class?” (I think that would have been pretty neat, for all involved)
The drawback to changing classes like that, though, is that you don’t get to see what someone else does with your class. It’s almost better to give up a preparation period to teach in another class, so that the classroom teacher can hang around and see how you approach a concept.
Did this exchange fill you with Geometry-love? :) I gotta tell you, Algebra 2 was my LOVE till I taught Geometry for the second year in a row this year. Now I think Geometry is my love!
OMG, this was super-brave of both of you! I love that you were not totally weirded out by going in with zero preparation — not even names (I also loved “Yo, you — blue shirt”).
It sounds like it shook up that semi-spring rut we all get into. Both classes must have enjoyed it. Thanks for writing about it!
– Elizabeth (aka @cheesemonkeysf on Twitter)