Where do we go?

I gotta be honest: I'm beginning to think I'm manic-depressive when it comes to this course.

At one moment, I'm on top of the world, and at the next, well...maybe I'm just blowing the little things out of proportion.

What do you think?

At the end of the problem session this last Monday night, I was practically euphoric. We had a good turnout, we had fun, as usual, we (and I'm including myself in that "we") learned a lot, we made a good deal of progress.

And in class today, when one of the applications "clicked" with someone who'd been struggling with it for a long while, well...those "clicking" moments are the moments that teachers live for.

And of the five people I've now approached about leading discussions and activities in the class, all five are excited about it and willing to rise to the challenge. You have no idea how much this encourages me.

But I know that some folks are concerned that we're not moving fast enough...

...and some folks are concerned that we're moving too fast.

Some folks are concerned that they're not getting the "formulaic" aspect of the course, laid out in theorems and proofs and computations galore by the textbook...

...and some folks are concerned that they just can't see the pictures that we use to describe the applications that come up in class.

HOW DO I MAKE EVERYONE HAPPY?!!!?!!

I know the answer.

The answer is: I can't.

And that...that weakness...that inherent and unavoidable failure...gets to me.

I just can't make sure that everyone's completely satisfied. No one can do it. It just can't be done.

I guess the best I might be able to manage is to "maximize" satisfaction.

But how on Earth can I do that?

I realized something the other day about the way I've designed this course. On the one hand, it's a good thing that I've taken the trouble to create such robust methods for communication with the class: I've had no trouble developing a rapport with the students which I think is often underrated, I've been able to quickly and (I hope) accurately assess when people are having difficulties, and I've therefore been able to remediate problems before they get too nasty. I think that I've been able to do this far more effectively than I would have had I been teaching the course in a "traditional" way. And I'm not saying that's a bad thing. But...

...I also feel like ignorance could be bliss. Bliss for me, at any rate. If I cut all these lines of communication, I would no longer know right away if something were amiss...for instance, the way things are set up now, I can tell almost immediately if someone's having difficulty with a particular concept or example, and I can take steps to fix that as soon as possible.

The "old" way, someone could fail an exam before I'd even know what was up. And in all that time, during which that poor student was struggling, maybe faking his or her way through the homework and in-class examples, managing a mediocre but not pathetic grade on the quizzes, I'd be totally unaware of that struggle, and I'd assume all was well.

Maybe that's why I might be going more slowly through this material than I should be: I've got my fingers on the pulses of every body in that class, and if even one of those pulses starts racing, I hit the emergency brakes, and we slow down.

I know I shouldn't be doing that, I know I can't expect everyone to do equally well, but how can I do otherwise? How can I let myself fail in my role as a teacher, if I know someone's not understanding?

HOW?

I don't know.

So here's my plan for the next couple of days: we'll get that quiz in on Friday (at last!), and then we'll do one more example before we call it quits for Section 2.1. Section 2.2 will take us on a short tour of notation and terminology, and then, after I've handed out the take-home exam, we'll start some really cool stuff on Monday, when we take on arbitrary vector spaces. The applications are very quickly going to become much more interesting, more realistic, more varied in nature.

What do you think? How are we doing, as a class? How are you learning, as students? And how am I helping in facilitating that learning, as the, for lack of a better term, "teacher"? I really want to know.