Teach the field, not the exercises.

I’m increasingly coming to think that one of the big failures of required college survey courses for non-majors is that they just present the material without taking the time to explain to students what the field they’re dabbling in actually is, and what people in the field actually do. In my opinion, this should be an extensive and important unit. I know there’s often way more material than there is time to cover it all, but I think it’s much more important that students come away with an understanding of what that field actually is about than that they understand Jane Eyre or the quadratic formula.

Doing some basic freshman-level exercises in the subject doesn’t equate to understanding what the subject is actually about, at its heart, for those who do it as a career. But introductory courses, and the reason we require them, aren’t just to make sure the students pass a basic level of competency so we can feel okay about granting them a degree. Ideally they should be an introduction to the field, to help students check it out and see if they have any interest in doing it. They should also give students a basic idea of what their fellow students in other majors actually do, so that departments can understand each other, cooperate, foster mutual ideas for research, etc.

Unfortunately, this is seldom the way it actually goes. It seems like too often, English teachers just throw a bunch of analysis and essay questions at students without explaining why these questions are useful for the students to be able to answer, or why we might care about questions of that sort at all. Math teachers are often the same way. On the same day, I had to explain to one of my fellow writing tutors why math was at all useful, and to one of my fellow computer science geeks what lit majors actually do. I’m constantly being asked by science and humanities majors alike why anyone would want to study the other sort of discipline; the moment anyone hears that I have a background in both, an explanation is in order from one perspective or the other. People who are well-educated in their own fields do not always understand what other majors even do.

I remember overhearing some students complaining about a “useless” question someone had asked in their calculus class, that being why one expression did not equal another one with a superficial resemblance. The students opined that it was stupid to bother with a question like that, and that they just wanted to hear what was on the test and get out of there. I think things would be better if the whole class understood what math is about and why it is valuable. Then maybe those students would have been thinking about the underlying principles of the formulae instead of memorizing them and declaring everything else to be useless, and maybe they’d remember the test material better, too.

I think it is a big mistake that we treat it as more important that these students have extensive exposure to calculus that they’re going to forget because they’re not internalizing the important bits than that they have a unit on what higher mathematics are about and what the important things to focus on in the field might be. I wonder if it’s just that college profs don’t realise what students might need to learn about why their subjects are useful– since the profs know why the subject is useful, perhaps they consider it obvious?– and students don’t ask to the teachers’ faces; they just fake acceptance and then grumble about it when the teachers aren’t around. It isn’t being taught by default, and the students aren’t asking, so the students never really see the point, and they leave the class feeling like it’s a big useless waste of time– and I don’t think that helps their education at all. A basic survey course, which purports to introduce students to the subject, should at least explain what the subject is all about.