Against my better judgment, I have actually volunteered to teach Calculus II this semester. Sure, part of the reason is that one particularly annoying student from Calculus I did far too well last semester, and I want to make sure her ego and her spirit, is crushed this semester. But beyond that, I have decided to embrace this freshman class.
Why is that? Well, second semester calculus has a bit of a reputation among students as being the hardest math class in the calculus sequence, if not the curriculum. I suspect this is partly to do with the fact that many of the students taking this class are in the less technical BS degree programs, possibly even education, where most of the bottom of the barrel will have committed their lives. These poor souls will never know, or even probably have the ability to comprehend, the beauty in boundary value problems, measure theory, or the structure of rings and varieties.
Beyond the intrinsic mental and curriculum finality of this course, I know there are portions of it that, to the students, seem out of place among all the mechanical computation and memorization of the rest of the sequence. I speak, of course, of sequences and series. The understanding of sequences and series is absolutely essential to the entire subject of analysis, especially the underpinnings of calculus itself. Yet I know the students do their best to resist paying attention during the section on Riemann sums. I know they'll probably leave this class still trying to pretend that a capital sigma can be treated as a letter "E." But I will enjoy the look of suffering on their faces as they come to terms with the fact that they will face at least one exam consisting almost entirely of sequences and series, with almost nothing coming out to a solid, concrete answer.
Well, maybe I'll throw them a bone and give them a geometric series. Maybe even a Taylor polynomial. One with varying parameters and odd boundary behavior.
Saturday, January 26, 2013
Friday, January 4, 2013
A Beacon of Inspiration
Clearly I have been busy and distracted lately. The transition between semesters will always do that. But this is not what I'm here to talk about today. No, today I want to share a story I heard recently. A story of a person who may be the most wonderful math teacher ever. Many people will fail to see it that way, so I will make sure to keep everything as anonymous as possible, even though this happened years ago.
There was this university. It was a small university, with an even smaller math department. Many students there majored in engineering, but few majored in mathematics. There wasn't even a masters degree available in math. As a result, the math classes were plagued by students who were determined to waste their time insisting on practical applications to every problem. The faculty in the department, naturally, were not terribly sympathetic toward these creatures.
This department did something very interesting. When they posted their courses for an upcoming semester, they didn't list professor names with any of the classes. Why? Well, there was this one particular professor who had a bit of a reputation. How bad of a reputation?
Imagine you have signed up for a vector calculus class. There are about forty people signed up for the class at the outset. The professor walks in, and he has a very distinct look to him. He walks to the front of the class and looks out over the room. Half the class stands up, gathers their things, and walks out the room. This professor then turns and writes his name on the board. Half the class again gets up and walks out, leaving about ten or so to sit through the lecture. The next time the class meets, the attendance will have halved yet again, leaving about five students left who had no choice but to take this section of this class. By the end of the semester, perhaps one or two of the remaining students will have passed the class. All told, a successful semester.
And what was his big crime? Proof-based tests that allow no partial credit and no homework. Cry me a river. Those engineering students don't deserve their degrees if they can't think logically for a few hours a week.
I must admit, this is the sort of reputation that most teachers can only dream of having. The reputation of instilling such fear and hate in the student body that the entire department will adjust how they list courses to try to dupe students into taking your classes.
My only criticism is that this technique is a bit too harsh. If you chase off all your students in the first day, then that leaves altogether too few to torment over the course of the semester. The best suffering is that held until after the drop date has passed.
There was this university. It was a small university, with an even smaller math department. Many students there majored in engineering, but few majored in mathematics. There wasn't even a masters degree available in math. As a result, the math classes were plagued by students who were determined to waste their time insisting on practical applications to every problem. The faculty in the department, naturally, were not terribly sympathetic toward these creatures.
This department did something very interesting. When they posted their courses for an upcoming semester, they didn't list professor names with any of the classes. Why? Well, there was this one particular professor who had a bit of a reputation. How bad of a reputation?
Imagine you have signed up for a vector calculus class. There are about forty people signed up for the class at the outset. The professor walks in, and he has a very distinct look to him. He walks to the front of the class and looks out over the room. Half the class stands up, gathers their things, and walks out the room. This professor then turns and writes his name on the board. Half the class again gets up and walks out, leaving about ten or so to sit through the lecture. The next time the class meets, the attendance will have halved yet again, leaving about five students left who had no choice but to take this section of this class. By the end of the semester, perhaps one or two of the remaining students will have passed the class. All told, a successful semester.
And what was his big crime? Proof-based tests that allow no partial credit and no homework. Cry me a river. Those engineering students don't deserve their degrees if they can't think logically for a few hours a week.
I must admit, this is the sort of reputation that most teachers can only dream of having. The reputation of instilling such fear and hate in the student body that the entire department will adjust how they list courses to try to dupe students into taking your classes.
My only criticism is that this technique is a bit too harsh. If you chase off all your students in the first day, then that leaves altogether too few to torment over the course of the semester. The best suffering is that held until after the drop date has passed.
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