Happy (day after) Labor Day! While I’m guessing most of you had yesterday off, my school held classes. I’ve worked there for five or six years now so I’m used to working on Labor Day (and honestly, it’s hard to complain about working on the holiday when I just had roughly four months “off”). No one feels sorry for me.
One of my goals for the blog is to keep a running diary of thoughts and observations from my classes. After one full week, I have to admit that I’m looking forward to the semester! I have a pair of sections of Calculus I, the first class has 16 students and the second has 19 students. I appreciate having two sections with roughly the same number of students as it makes planning activities easier! My first day of theCalculus course went extremely well, but I do fear that I’ve lost a little steam and enthusiasm from the students now. I attribute that to a string of mostly lectures and problem solving in regards to limits. If there is one giant weakness to my teaching, it’s that I don’t have a steady stream of varied activities. Each semester I seem to plug in one or two new things to try (and I usually keep them for future semesters) but even so the course can get a bit monotonous.
Historically, about half of my students fail to fully grasp limits (and continuity) by the first exam. Most of the students are able to pass the exam, but limits at the Calculus I level are easy enough that I believe all the students should be able to muster at least a B on the exam. So far, my current crop of students is right on pace – most have grasped the concept but there are still four or five in each class that still don’t understand. I keep thinking that if I could come up with an activity that demonstrates the concept of the limit those students might also find themselves understanding all the course material. Unfortunately, I have yet to come across a suitable activity.
My third class is the Mathematics of Games and Gambling – a course that I am currently developing from scratch. I had ambition plans for the course but it didn’t even take a full week for me to realize that I am going to have to go quite a bit slower than I had initially planned. After a week and a day, we have covered finite probabilities and played both Chuck-a-Luck and Roulette. In the next class, we do a mathematical analysis of Roulette (other than explaining the rules, I didn’t say much about Roulette in class yesterday). My goal was for the students to experiment as they played to see if they could come up with a strategy that was either good or bad.
In terms of bad strategies, the students offered some advice like “don’t bet a dollar on black and a second dollar on red at the same time” and “don’t bet on single numbers.” The first piece of advice is perfectly valid – and quite honestly, the second was as well in the sense that I only gave each student $10 to “bet” with. Of course, we all know that betting strategies in roulette are about as helpful as a beach volleyball in the arctic circle.
All things considered, I’m moderately pleased with the first week of classes. I wish I could figure out a way to teach Calculus without resorting to as many lectures but otherwise things have gone quite well. I should have a better handle on my Gambling students’ abilities once I grade their first homework assignment (which was collected yesterday). I think I've managed to display most of the traits that my students consider important in a good mathematics teacher, though I don't think most of them find me funny*.
*When explaining the floor and ceiling functions, I like to ask my students what the floor of pi is. After getting the correct answer, I point out to them that they now know the floor of pi(e) is not actually crust but three. Each class produced three of four groans, a chuckle or two, and a lot of eyes (and heads) rolling.