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.