I don’t really have the energy to give a true update, and I don’t want to complain. I just feel like in the past few days, I’ve been struck with a sense of lingering ennui, and I’m hoping that Spring Break rejuvinates me. It appears that students are really stressed out this week, and it’s being reflected in the way they’re acting. And honestly, it’s a bit of a cycle, because the way the students are feeling is affecting the way I’m feeling, which is affecting the way that students react to me, and so on and so forth.
For short updates on my three preps, read on.
1. In Multivariable Calculus, we’ve been working very slowly on our current chapter. I thought we’d be able to finish it before the quarter ends, but now I’m skeptical. We’re going to have to work pretty darn hard. The current problem set that I’ve given them is pretty tough, but we’re doing this one even more collaboratively than the others, so I’m glad about that. Recently, in class, we had to solve and I forgot how to even go about it. We found a nice, but convoluted solution, because we were working with nice limits of integration. But I have to tell you… I forgot how to do a lot of these less straightforward integrals. The good news is that we came up with ideas and found the solution using symmetry arguments and trig identities. Awesome. At first I feared this was a waste a time, but then I realized: this is what this course is about. Problem solving. You have something you don’t know, and you don’t have a formula for it. Work it out.
2. In Algebra II, I’m a bit behind the other teacher. We’re teaching function transformations, after a pretty arduous — but I’d say successful — unit on inequalities and quadratics. I don’t have a great way to introduce function translations, other than students doing some graphing by hand and noticing some patterns. (“Oh! The graph is the same as the other graph, but moved up one unit!” or “Oh, why is the graph the same as the other one, but moved to the left?”) I’m repressing the name now, but some math blogger posted a Logarithm Bingo game. I think that once I finish the functions transformations unit, I’m going to design and play Function Transformation Bingo!
3. In Calculus, we’ve been working more on the anti-derivative. It’s funny how different my students are. Some have the intuition like *that* while others are struggling to figure out what’s going on. But honestly the only way to do these problems is to really struggle through them. My favorite problem from last night’s homework was to find the antiderivative of . Almost all students got it wrong, because they didn’t see that if you expand everything out, the problem reduces to something much easier: finding the antiderivative of . Well, them not seeing that it is easily expanded causes me less chagrin than a student saying, “so you must first multiply the by each term in the expression, and then square it?” YEARGH!
That’s all folks.
For the cos^4(x) problem, try integration by parts (along with sin^2(x) = 1 – cos^2(x) ) to reduce it to finding the integral of cos^2(x). Another application of integration by parts will solve the problem.
@Adam: Thanks! (We did something similar.)