Tall, Dark, and Mysterious


Trying to make precalculus work

File under: Those Who Can't. Posted by Moebius Stripper at 9:23 pm.

My precalculus students wrote a quiz today. On the top of the front page I’d given the instuctions Solve the following equations for x. Show your work. If I’d instead typed Hey, kids! I’m under the impression that you know how to solve quadratic equations, but if you convince me otherwise, I’ll give you ten dollars! I would have received the exact same thirty papers.

This is the class with the crappy attendance. On Tuesdays, two thirds of my students show up. On Thursdays - quiz days - I get a full house, and then close to half of them jump ship after the break. A few weeks ago, I was willing to believe that a third of my students knew this material well enough that they didn’t need to come to class. Apparently I’m just that naive.

On a related note: a few weeks ago, I was chatting with Dr. Matt about review sheets for math tests. He was ambivalent about them, mentioning (I’m paraphrasing, and possibly misrepresenting, here) that he gives out the sheets one day, and then he goes over them the next class, and he wonders how much good that does. I was thinking about this, and also about a recent post at Learning Curves, during today’s class, when I was fielding questions about the homework. Last class, I’d assigned three word problems; this class, my students asked me to go over…three word problems.

They were difficult questions (relatively speaking), and my students have limited experience setting up word problems, so I wasn’t surprised, nor was I bothered. What did bother me was that when I prompted the students with leading questions - okay, we are given a perimeter and we need to find an area…what equations should we set up? I was met with silence. I’d realized it before, but it was only then that I fully saw just how disengaged my students were from the material. Math, for them, is a monkey-see-monkey-do affair. I may talk at length about how we need to figure out relationships among variables and translate them into equations, but my students just see how I apply those to this word problem or that one. They can’t apply a method of a problem about a rectangle to a problem about a right-angled triangle.

I started to set up some of them problems, but then realized that I’d tried this before, and it didn’t work; my students had never learned, on a large scale and to my satisfaction, how to set up word problems that differed from the few I’d shown in class. So I decided I was going to try something new. “I’ll go over these next week,” I said, “but I’ll only go over them if I get some feedback about how you tried to set up the problems. It’s okay if you don’t do it correctly; you can learn from false starts. What’s important is that you try.”

I pointed out that I don’t always know how to approach a word problem when I first see it, and that solving word problems isn’t typically something that comes to people all at once. But, I said, it never comes to anyone if they don’t try their hands at word problems first.

I know that other instructors of this course have thrown in the towel, and were satisfied with their work if their students were able to answer the same question about maximizing the area of the fence that they’d seen solved in class the week before. I personally don’t see the point in that; if the only problems my students can solve are the ones I did in class, then they can’t do math in any useful sense. From now on, I’ll do a couple of word problems in class, and then assign some that are similar in concept but slightly different in structure. And I’ll only go over those problems in class if I can see that my students have at least attempted to apply my lessons on finding relationships among unknowns. If they haven’t managed to make at least some sense of that, they’re not intellectually mature enough to learn what I’m teaching them, and there’s not much point spending more time on this material; doing word problems with students who can only mimic them isn’t any better than not doing them at all. We’ll see how this experiment goes.

Something in the air

File under: Those Who Can't. Posted by Moebius Stripper at 5:28 pm.

I give weekly quizzes in all of my classes, so I hear from my ill students more than I otherwise might: missing a class isn’t necessarily worth alerting the instructor, but a quiz worth part of the mark requires a reason, and possibly a doctor’s note.

I just got my fourth or fifth email - three weeks into the term - from my fourth or fifth student claiming that a crippling migraine was preventing them from coming to class.

Except in extreme circumstances, I tend to think that my students are honest. But I don’t think I had a single student with a migraine last term, and suddenly I have several. If these migraines are real, why the sudden prevalence? And if they’re not, why is this a more popular excuse - by far - than it was last time?

Apparently problem solving isn’t my forte

File under: Meta-Meta, Know Thyself. Posted by Moebius Stripper at 5:23 pm.

Last weekend, I took my new laptop to Vancouver, and when the two of us returned to Island Town, the sound system didn’t work. At all: I couldn’t play CDs, I couldn’t use headphones, I couldn’t get any audio on streaming videos. And this is a new computer! After several iterations of the Universal Computer Troubleshooting Procedure (shut down computer; turn it back on), I consulted the control panel for assistance. One of the questions in the help file was, “Have you checked ‘mute’ on the volume control?”

“No, you idiot,” I answered aloud to an empty room, “What do you think I am, stupid?”

Nothing worked, and after three days of computer silence, I got ready to phone the long-distance help line, when I noticed a little dial on the side of the laptop.

It was the volume dial, and it was set to minimum.

This is my excuse for not having posted anything for the last couple of days: it was out of a justified fear that the resulting entries would have been commensurate with the intellectual capacity that left me unable to turn up the volume on my computer for three straight days.

However, I do have a big post (which may turn into two or three smaller ones) about IQ, achievement, and socialization in the wings. With a graph and everything.