I'm worried that I'm getting sick. I slept nine hours or so last night, which should have been enough. But I was tired all morning, and took a two hour nap while they were gone. And I'm tired now, even though it's only a quarter till nine.
(Okay, now it's 11:09. I got sidetracked by homework, reading a couple of bedtime stories, and a little snack.)
But I thought I'd let you know how classes are going before I go to bed.
I am taking two classes, with the same professor, and you have to enroll in one if you enroll in the other, so it's effectively one class. Math 409 is "Geometry for Teachers" and Math 410 is "The History of Math."
The geometry class is sort of a rehash of 8th grade math. Or maybe it was 7th grade? Anyway, it was in the neighborhood of 25 years ago, and I found that was enough time for certain gears in my head to get a bit rusty. On the first homework I got a three out of five, which isn't as bad as it sounds, especially considering that I cut and pasted the wrong example diagram to one problem. (I received a "5" on the second homework, so I'm thinking the gears are cranking again.)
She uses a sort of gestalt system of grading. She checks the entire homework, then assigns a grade from one to five, based not on counting mistakes or correct procedures, but just a general feeling of how "right" it was. A "5" is basically 100%, "4" is 90%, "3" is 80%, and so on. She told us that research shows that this style of grading is more consistent across different teachers grading the same assignment than counting mistakes. That may be so, but it takes a huge amount of confidence to grade this way. In Korea, my test grading was as objective as I could make it. So much so that my assistants could actually do some of the marking. One reason I could do it that was was that I taught English in a very structured manner, giving students patterns that they could use to build unique sentences.
It seems a bit ironic to move from an objective style of grading conversation to a more subjective style of grading math, when I consider conversation to be an extremely subjective thing. How do you define a "great" conversation? You can list things that make it so, but they all break down to "I really liked it." Whereas math is pretty much the opposite: statements are either correct or incorrect. There is some murkiness involved in "skipping steps", but for the most part it's really subjective.
And so her grading style is giving me as much to think about as the course content itself. Fun.
It helps that these classes are actually intended for teachers, unlike the other two math classes I've taken recently. Those classes were intended for
So far, it seems that the main intent of geometry is to reinforce the idea that math is a system of ideas that builds on itself, with one step always following logically from another. Steps we covered yesterday can be abbreviated today, but the rationale must be there.
So in class we do a few things:
We follow the prof. doing proofs.
We work in groups to do proofs and constructions.
We... I guess that's pretty much it.
In the Math History class she talks more about the background, and how the ancients did what they did with such limited resources. It's not just that they didn't have calculators or computers, Pythagoras didn't even have algebra! He figured out his right triangle theorem, the one with a squared plus b squared equals c squared, without being able to use "a", "b" and "c"! I think the word "genius" is not too extreme for this guy.
We are also talking about math in different parts of the world. Our "textbook" is a CDrom with a ton of articles, showing parallels between different countries as they developed similar concepts and procedures.
And of course, she does proofs.
Enough. It's almost midnight, and I need my sleep, otherwise I may not be able to survive class tomorrow.
Oh, I almost forgot one bit of trivia: This professor is the same professor I had for a math class back when I was a student at KU the first time! I'm not sure which class, but I do remember one thing she told me, regarding getting my work done. She said, "You know what to do, and how to do it. You just need to actually do it!" A lesson with which I still wrestle today.