Thursday, July 21, 2005

My Calculus Class

In the fall I will be teaching a standard Calc I class. I haven't given it much thought because, well, there really isn't much to think about, as calculus does have a certain "if today is Tuesday, this must be the chain rule" aspect to it. And while, yes, there is more than that, when it comes down to it (at least here), if a student who passes my class then ends up saying something like, "I don't see why when you look at the change in potential as you vary the radius that you end up with the force. How'd you get that?" then I haven't been successful.

What I have been thinking about is what sort of point-bearing (and non-point-bearing) assignments to create and how to allocate the points. Once again I am frustrated by the fact that points (and their conversion into letter grades) is the only tangible currency that I have to extrinsically motivate students. While our department web page warns students that grades in our freshman-level courses are based solely on the students' knowledge of the material (translation: don't expect a 37% to magically become a C just because your classmates did horribly on the exam, too), I'm not the only person penalizes students' papers for lack of staples, incorrect format, or lateness -- and those have nothing to do with calculus.

The real problem here is with homework. For most people, learning calculus requires doing (and by doing I mean "trying hard and thinking about the problem until you really do understand it") a significant number of calculus problems. Lots and lots and lots of calculus problems. Unfortunately, many students are unwilling to admit that this is, in fact, true. So what I need is some sort of robust incentive system to encourage my students to do their calculus homework. And while, yes, I could let them flouder and fail when they choose not to do their homework, I consider it a waste of my time if no one learns anything in my class.

So the trick is how to assign points to homework in a way that encourages students to do a good job on the homework (and not cheat) while also keeping the grading at a manageable level. A lot of people do this by giving quizzes on the homework problems (either the exact same problems or else very similar questions), but I haven't found that successful in the past. My students have judged the point pay-off of a quiz to be small relative to the work required to do the problems and have opted to punt on the quizzes and to cram before the exam.* Most don't realize that is a poor strategy until it's too late.

I've asked our sysadmin to install WeBWorK so that I won't need to grade the basic exercises. (I would still grade by hand the longer "tether-cow" type of problems.) No word yet on whether it will be ready for the fall (I asked back in December and have sent occasional reminders).

Right now I'm thinking of taking points out of the equation for the basic "exercise" types of problems -- but I'll ask the students to hand them in periodically. Instead of assigning a numeric score, I'd write a few general comments. I'd still have the longer, more involved problems count towards the grade. I haven't yet decided what to do about quizzes. What I'm hoping to find is a way to change the reason for doing calculus homework away from "because it's worth 0.2% of my grade" to "because it's what I need to do to learn calculus."

*I used a variant of this theory in a freshman-level computer science class that I took my senior year in college. Homework was worth 20% of the grade. Some of the weekly assignments were programming assignments (which took FOREVER to do) and some were "theory" assignments (easy for a senior math major). I only did one of the programming assignments -- but I did all of the theory ones and scored well on the exams -- I think I got a B in the course.