Before I was a math teacher, while I was still in undergrad, I was a dance teacher. It seems silly writing this now, because at the time I was going to school to become a math teacher, but I didn't take the job to learn a thing about teaching. I took the job because I wanted to keep dancing. That's all. It was very selfish.
Looking back now, I realize that I actually did learn a thing or two about teaching that can carried to the math classroom.
A lovely demonstration doesn't do the students squat if they don't get to practice. I would have gotten fired from my job if I showed up every day and put on a mini-production for my students, but never taught them how to do any of the moves I just demonstrated. I know that probably seems like a "duh" to most middle school and high school teachers, but that's honestly how I spent my first couple years as a teacher (it was at the college level, but still). I would come to class, having prepared every word I was going to say, and deliver what I felt was a pretty darn good lecture. And, then...I would cross my fingers and hope my students did the homework. Sorry to all my students those years. Truly.
A good teacher gets everyone involved. All the time. A ballet student is not going to learn a thing if she says, "I think I'll just sit in the back and take notes on this one." Ok, I didn't have any dance students want to take notes, but I did have students who were very reluctant to try new jumps or new turns, or new shoes for crying out loud. I learned that in those cases, it's important to break down every single move until you can figure out where the block in the body is. It was also important to point out what the student was doing right.
Mirrors. Mirrors are essential to a good dance lesson. Why? Because dancers have to learn what their bodies look like when they move in different ways. Eventually, a good dancer who has practiced in front of mirrors long enough can just feel what the body looks like. She knows when she royally screwed up a pirouette and she knows when she nailed a grande jete. This is what we try to foster in our math students, too. We want students who can feel when something isn't going right. When their answer isn't reasonable, when their proof is just getting messier and messier, when the calculator's window needs to be adjusted. These things don't happen, though, unless students get mirrors with which to evaluate their work on regular basis. Metacognition and all that jazz.
I tried to find some kind of picture of me as a dancer as proof that this is a real thing. But, I guess my mom must have most of that stuff. The only thing I could find on my laptop was this video. If I remember correctly, this was my last semester of college. I was practicing at the studio I taught at for a dance I was going to perform at my school's Chapel later that week.