Signed Numbers

Highlight of the Day: Context: AP Calc class, talking through some multiple choice (no calculator) problems from a practice test. Problem: what is  ; Me (typical first question): So....what should we do? Student: Substitute the 2 in for t to find the answer Me: Why would we want to do that? Student: Well, f(x) is the integral there, which means it's really the anti-derivative of the function. We want the derivative of that anti-derivative, which basically means we want the stuff inside the integral. So if you just substitute 2 in, you'll get the answer. Me: You basically just explained the first part of the Fundamental Theorem of Calculus that you struggled with when we first talked about it. Woohoo! Granted, I know his explanation skips the step where t in the integrand becomes x after you take the derivative, but the conceptual understanding of the relationship between derivatives and integrals is there. Made my day.

Last Monday I was feeling overwhelmed. I go through these phases when I plan ahead, get a few days worth of lessons/notes put together, and then I get through one day and realize I'm not really ready for the next day at all because things didn't go the way I planned. These phases often leave me frustrated and irritated that I spent time up front that seems to be wasted. In the long run the time spent is not wasted, but it's still frustrating to *think* you're ahead and then *realize* that you're just as far behind as you normally are, despite the extra time you put in. Anyway, that's how I was feeling Monday. And Tuesday I was supposed to get observed for the first time this school year. "Great," I was thinking, "just great." I had a less-than-stellar lesson planned, introducing graphing one-variable inequalities and solving one-step inqualities. Not something normally covered in Alg1 (it's a middle school concept), but that's what ...