Wednesday, March 28, 2007

My Geometry Test

Don't worry, this post is not about math. Honest. (Alternately: don't get excited, this post is not about math.)

Three weeks ago, we were given a take-home test in my Foundations of Geometry course. We had one week to complete the test, and were allowed to use any sources available to us, including friends and classmates, as long as we cited them, and as long as the work we submitted was in our own handwriting and based on our own understanding. (In other words, you could have someone explain to you how to work the problem, but then you should work it.) If the professor was in doubt about your understanding of what you submitted, he might ask you to solve it in front of him with no sources, for instance.

I got this test on a Thursday. It had 6 problems, some with two parts, and I worked on it all weekend. (By "all weekend" I mean I spent about 10 hours on it over the weekend.) I had been to every class session and felt I understood the material as well as anyone in the class, but the test asked us to do things we had never been shown. By Sunday night, I had completed 3.5 of the 6 questions, or 58%. That's an F.

I was feeling pretty bad about my chances, but forced myself to work on the test consistently during the week. I had known already that some of the questions would likely take a lot of "brain processing time," so I was sure to attempt every question over the weekend, just so my brain would have the material to work on while I wasn't doing anything.

Over the week, as a result of my work and thinking, ways of solving these problems eventually came to me. Wednesday night, I had finished 5.5 out of 6 problems, correctly I thought, and had an idea about how to approach the last 1/2 problem. I figured this would be enough to get me an A, even if I didn't quite correctly solve the last 1/2 problem. I ended up taking what I thought was a good stab at that problem though I wasn't at all sure my answer was correct.

I ended up with a 97 on the test, which was higher than I'd hoped for, and obviously a very pleasing grade. I have no idea how the class as a whole did. (I felt a bit pessimistic because some people were saying things like "That test took me 8 hours!" and I was like "8 hours?? You did that all that in 8 hours?!")

This story is pretty boring, perhaps even self-aggrandizing, until you consider that this type of experience - consistent applied effort towards something originally impossible-seeming leading to success - is very rare for me. Usually I either succeed at something pretty easily or I give up. Usually I put off assignments until the last minute, which in this case would have resulted in an F (considering that the entire weekend was only enough to get me 58% finished).

I didn't really enjoy the anxiety I had to go through with this test, but I'm really pleased that this course - which I chose for my degree plan partly because I thought it would force me to work hard to think through problems - is providing an experience where effort correlates to results so closely. It should help me move away from the model where I am either smart or stupid at something, and towards a belief that I can succeed at even difficult things if I keep working at them.

I reserve the right to change my mind if I end up with a C in the course.


Sally said...

I like it that the professor gave you all such a nice long time to work on the exam, rather than making this a "how close can you get to the right approach on your first attempt under extreme time deadline" kind of thing. Given the nature of the questions, having time to continue the siege against the test was really helpful and a better measure of your ability.

I contrast this to the terrible math-stat midterm I took, in which you had like 2 hours in the test room to develop from the ground up about 6 statistical models. (The whole class was predicated on the idea that it's more interesting to the professor if we do everything from scratch, as though nobody else had already figured any of this out.) I have no idea if I had the chops to actually succeed at that test, but it wasn't going to happen in 2 hours for damn sure.

Tam said...

I totally agree that having a week to do this test was great; I can't see how anyone wouldn't have bombed it otherwise.

One thing that giving the test over the course of a week allowed was for the test to include questions of a type we had never been shown how to solve. It could end up being a test of using the taught concepts to invent new methods and process new ideas, instead of just a test of applying taught processes to new problems.

Of course, as Sally saw at Rice, you can do that in a timed test too. But the results are not always very encouraging.