Wednesday, April 04, 2007

Good Teacher, Bad Teacher

Sometimes they are the same teacher.

Last week we got an assignment in Geometry that has been taking everyone hours and hours. First of all, some of the algebra is taking an extremely long time. The first problem out of seven took me about 5 pages of (not very densely written) algebra to get through, though I left the vast majority of it off of my homework paper because I know he doesn't care that we show that we can do a bunch of dumb algebra. And second of all, the concepts behind the homework are a bit challenging and require thought.

The way Dr. T gives homework is that it never includes solving problems of a type we have been shown in class or anything like that - it's always an extension or a related sidebar. This is appropriate but makes the homework and tests (which are the same way) pretty challenging.

Anyway, when he asked for questions at the beginning of class, I asked if the homework due date could be pushed back because it was taking a really long time for me and, I imagined, for others people too. Instead of hanging me out to dry, the class agreed. So he agreed to move the due date to Tuesday. Good teacher!

Then he told us we shouldn't be doing all this algebra by hand, but should be using Mathematica. I was already planning to do this, but a lot of the class was astonished to find out that it would be OK and not cheating. My take on it (having known for a few weeks that it was OK) is that using Mathematica to do algebra in this class is like using a calculator for arithmetic in a Calculus class - kind of a no-brainer. (It's assumed that we know algebra.)

You could, of course, program Mathematica to solve the whole problem, rather than just using it for fill-in algebra, but you'd be demonstrating total mastery of the problem in so doing, so it ought to be fine.

Anyway, then it came up that most of us don't know how to use Mathematica. So he actually spent about 10 minutes showing us how (writing the commands on the board). That was neat since I had just taught myself the same stuff earlier in the day.

This led to more questions about the homework, and I got into a little argument with Dr. T over a point I had misunderstood, and some other folks argued over different things, and he eventually said, "The concepts in this course are not difficult. If you think they are, you might be barking up the wrong tree."

Well, fuck you too. (Bad teacher!)

There are times when it's appropriate to suggest that having unusual difficulty with the material of a course might suggest an ill-chosen field of study, but this wasn't one of them. For one thing, every student in this class besides me is a secondary math education major. You need to know a lot of math to pass the tests to get certified, and of course you should know a lot of math to teach high school math, but (a) none of the material for this course is needed for teaching, and (b) you don't need to be a math genius for it either.

And for another thing, even a person good enough to potentially pursue a Math PhD will probably occasionally have conceptual difficulty with a math topic, and it's impossible for someone very familiar with the math to judge how hard it is. I'm not a math genius, but I'm not unfit for advanced study either, and I find this material pretty challenging at times.

Anyway, I got Mathematica in the mail yesterday (joy!) and I've decided to do my entire homework in it - write-up, graphs, drawings, and all. I've been working on that all day (I took the day off work) and it's going to take me hours and hours but be incredibly fun and result in a beautiful paper to turn in. What could be better?

My wall now sports a banner-shaped poster that proclaims "MATHEMATICA SPOKEN HERE" and I hope that will soon be true.


Sally said...

Another question he doesn't address with his "barking up the wrong tree" comment, in addition to the fact that being able to master this material is irrelevant to a person's ability to pass certification exams and excel at teaching high school math, is whether you guys are having any more difficulty with it than students in other sections of this same class that he has taught before. Obviously, he thinks the concepts are not difficult; he has been doing this for years and perhaps he truly is a math genius (at least by comparison to you guys). But the obvious comparison set is other students preparing for careers as high school math teachers, not college geometry professors.

I mean, it's not like he's teaching the future Fields Medal candidates of the world in this class. Has he not considered that it is his own expectations, and not your (the students in the class) performance, that is out of line?

And there's just something nasty and insulting about the idea of telling you guys that it's not enough for you to eventually master this material, but that it must come easily for you or you are wasting your time in this field. It's another example of emphasizing inherent talent over effort that is so wrong-headed.

In the end, how much does it matter if a person is a mathematical quick study or a mathematical plodder? In a math teacher, having a little bit of the plodder in you is probably a good thing. This means that when your students inevitably don't find the concepts immediately obvious, you can at least relate to the idea of having to work to understand something.

Ed said...

"and it's going to take me hours and hours but be incredibly fun and result in a beautiful paper to turn in. What could be better?"

I have so BEEN THERE. And I have turned in projects so many days late because of it......