Monday, July 27, 2009

Who Cares If They Learn?

One of the commenters had this to say in response to my post awhile back on interactive teaching:

The "math class" approach you describe is for babies. It is the students' job to do this on their own, or have the TAs cover it in section.

With these approaches you cannot cover as much material. It is style over substance. But if you are going slowly and not trying to cover much material, I suppose it can't hurt.

Ignoring* the phrasing, the point here is one that I've heard many times - that somehow you do your students a disservice if you actually take the time to teach them the material. I believe the root of the disagreement is based in whether or not you believe that your job is to teach the material, or just present as much as possible. While I certainly don't believe it's my job to make the students to try to learn (in other words, if they don't do the homework there's only so much you can do), I do believe it's my job to actually teach the material. Yes, this involves doing examples in class. Ideally, I think it also involves doing your best to keep your students from falling asleep in your class, however early in the morning it might be. I think students learn best by interacting during class (plus it keeps them awake). And it's not just me that thinks this (see Freire, Dewey, Piaget, or generally constructivism).

I'm trying to teach in this style during the Algorithms summer term class I'm currently in the middle of. Unfortunately, I'm partially falling victim to the second argument - "but if you take the time to teach, you won't cover as much." Even though I fundamentally disagree with it (assuming that you want the students to actually learn the material, taking the time to teach it is never wasted), I can't figure out a good way to teach the vast number of algorithms that I think I'd be doing a disservice if I didn't teach, and still spend long enough on each one so that they really understand the underlying details. (This is made especially hard since the class meets every day, so there's no time for contemplation between classes.) I'm doing examples in class, having discussions about the algorithms, having them try sample instances, etc. Yet my idealist nature is somewhat unsatisfied.

On the other hand, I've assigned a half-term long programming project that does embody these values and which I'm very excited about. More on that later.

*Actually, I can't quite bring myself to ignore it altogether. While I'm glad not to be seeing a Barbie-style "math is hard," the idea that anything having to do with math class is "for babies" is rather absurd. Some things that are for babies; diapers, bottles, toys, mushed carrots. Things that are not for babies; Calculus, Algorithms, going to college, taking my classes.


Owen Astrachan said...

I don't know who said this, but it's true. It's not the teacher's task to cover material --- but rather to uncover material.

The folks who think it's important to say things in class are channeling Charlie Brown's teacher "blah blah wah wah wah"

Anonymous said...

There are advantages and disadvantages to going very quickly or very slowly, I think you need to strike a balance. It's good to take time to address immediate misunderstandings and common pitfalls in class, but I think any non-cumulative enriching material can be put into homework and/or left as an explicit reading assignment. Students who put in effort consistently thereby get to learn a lot, but you don't need to spend a ridiculous amount of time explaining absolutely everything in class.

Josh said...

Given how much we forget of what we learn in a class -- unless we actually continue to use the knowledge -- it seems to me that enrichment and excitement should actually be the *main* purpose of classes. Once a student has gotten through the basics and past the common misunderstandings (which should also be handled in class, but often only take the first couple weeks), it's much more important for them to have an active interest in the material and know where to find more of it than it is for them to have "seen all the important stuff at least once, even if cursorily."

So, at least in the long run, I say put your worries about not covering enough material behind you. On the other hand, I recognize that classes fit into curricula, so there's a certain amount of material you are essentially required to cover...but at least you're striving in the right direction.

Alex McFerron said...

nice post

Anonymous said...

I might agree with Josh's first statement, but I disagree with his conclusion. My most valuable classes have been the most challenging ones, the ones where I have had to work harder than I thought possible. Yes, there was teaching, but it was challenging teaching. The students responded by working harder and by working together to understand the material (this was encouraged). The students interacted and learned the material more on their own time than in class, lots of material was still covered, and we learned life lessons.

What approach works for you depends on your students. In the long run, I think college education would be better served if it moved away from "babying" students.

Anonymous said...

I think it depends also on the type of students and their backgrounds. Yes, the top students who already pretty much know the material will probably do fine if you try to cover a lot of stuff, but in many cases I feel that the "median" student will be left behind (particularly if the average student is already not very strong in "mathematical maturity").

Owen's point about how much we forget from class is very salient with me, I pretty much only remember the most memorable examples, plus some of the most interesting homework problems/readings from many of the more advanced classes I took. So it is probably cool to put some very challenging problems in the homework, I definitely tend to prefer the "enrichment" approach in my teaching and the students (so far) seem to like it better as well (which is not conclusive since they may not know whats good for them...)

Still, I can see the argument for "challenge them and they will grow", so I can't say this is conclusive.