Differences in course types
by rrusczyk, Jun 17, 2006, 3:21 PM
While teaching the Special AIME Problem Seminar, I unfortunately ran 45 minutes over in class. While I do occasionally do this just because we're in the middle of a neat problem and I really want to continue, I think this time I can point to a more general reason I chose to throw in a hard extra problem to work at what should have been the end of class.
By the end of the 3-hour class in this Special Problem Series, I felt like I simply hadn't taught as much as I should have. However, comments from the students afterwards made it clear that this probably was not the case. In retrospect, I realize that I hadn't taught as much as I'm used to teaching in that amount of time. It has been a while since I taught one of our Problem Series classes - all my teaching for the previous year has been in either the Independent Study or in our regular subject classes.
Curiously, enrollment in the Problem Series classes is always higher than in our other classes. This may be an issue of marketing, or it may be a symptom of our quick-fix society. Regardless, I've always found this peculiar because our subject classes, and especially our Independent Study, are better for the student who really wants to learn problem solving mathematics.
The Problem Series classes are a good refresher, and a good survey of some techniques. But to really learn a given area, such as counting or number theory, you have to deeply understand the tools, and you have to do more than a couple weeks of problems. When I'm teaching a subject class, I feel like I get to teach this - a deeper understanding of the tools, as well as how and when to use them. The Independent Study is an even better vehicle for this. My most satisfying ah-ha moments (when a student turns a corner and can see how to solve whole sets of problems) come in the Independent Study Office Hours, where I can zero in on a student's misunderstanding through a series of questions.
So, as for how to educate students that the problem series classes are essentially an after-dinner mint and the other courses are the main course, I confess I'm at a bit of a loss. Suggestions are welcome!
By the end of the 3-hour class in this Special Problem Series, I felt like I simply hadn't taught as much as I should have. However, comments from the students afterwards made it clear that this probably was not the case. In retrospect, I realize that I hadn't taught as much as I'm used to teaching in that amount of time. It has been a while since I taught one of our Problem Series classes - all my teaching for the previous year has been in either the Independent Study or in our regular subject classes.
Curiously, enrollment in the Problem Series classes is always higher than in our other classes. This may be an issue of marketing, or it may be a symptom of our quick-fix society. Regardless, I've always found this peculiar because our subject classes, and especially our Independent Study, are better for the student who really wants to learn problem solving mathematics.
The Problem Series classes are a good refresher, and a good survey of some techniques. But to really learn a given area, such as counting or number theory, you have to deeply understand the tools, and you have to do more than a couple weeks of problems. When I'm teaching a subject class, I feel like I get to teach this - a deeper understanding of the tools, as well as how and when to use them. The Independent Study is an even better vehicle for this. My most satisfying ah-ha moments (when a student turns a corner and can see how to solve whole sets of problems) come in the Independent Study Office Hours, where I can zero in on a student's misunderstanding through a series of questions.
So, as for how to educate students that the problem series classes are essentially an after-dinner mint and the other courses are the main course, I confess I'm at a bit of a loss. Suggestions are welcome!
February 2012
January 2012