This morning, my assistant principal did an informal observation in my class at the end of first period. He walked in around the time I had decided the kids were not really grasping the introduction of negative exponents we'd done. They had a really hard time seeing a pattern emerging. I knew their number sense was poor, but I'd underestimated how poor when they had trouble seeing that 32, 16, 8, 4, 2, 1, 1/2, 1/4,... was a sequence of numbers divided by two from one term to the next.
We were working on whiteboards. Questions like "write x^-3 with a positive exponent" were mostly successful, but God forbid I give them x^2 • y^-5. That wasn't flying. We worked them through step by step, had students explaining their reasoning, etc. At one point, I told them to stop and erase; we needed to go back because we were lost.
So, the lesson was tanking. There was no way the students were ready to be independent and they were reaching or at their frustration point. Mercifully, we got to the end of class with a few of the easier problems. I didn't give homework knowing it would just lead to bigger problems.
You might be wondering why I called this a "happy" thought. I dismissed the class and let out a disgusted sigh when the kids were all gone. My AP asked why. I explained I'm frustrated when they need more time to get a concept than I hoped because it puts me further behind in the unit schedule that I didn't establish but must adhere to. He reminded me, "But your instruction was good." I knew this logically but I hate that I'm going to have to finish this unit in a week and I'm roughly a week behind. Still feeling bummed, I checked my mailbox 15 minutes later to find a personal note thanking me for the lesson and telling me negative exponents aren't so scary anymore. The write-up was complimentary. And when I saw my AP tonight, he told me that he was glad that's how he'd started his day.
This was a happy thought because my AP helped me feel good about my teaching in spite of the results in the moment. He pointed out that I was using good strategies. If I remember this as a "not yet" moment, I can be happy with it.
In writing this up, I've decided that tomorrow I'll have the students make additional charts on powers of 3 and 4 like we did for powers of 2. That should help them solidify the pattern. Then I'll tell my story of happy positive exponents and sad negative exponents. And I'll use this cartoon to seal the deal.
What made you happy today?