Monday, September 06, 2004

Yet Another Weekend

Anyone who was near campus this weekend could easily tell that whatever advantage I may have over the students in terms of critical thinking and abstract reasoning, that they win on the issue of having a social life. While I have no interest in drinking large quantities of cheap beer (ok, to be fair, really I have no interest in drinking any quantity of any beer because to me all beer is icky), some of the other issues make me think of some parallels. Allow me to explain in a horribly extended metaphor:

If you've ever tried to help a low-level student do a somewhat non-routine math problem, you'll probably recognize the following situation.

The student will sit there, doing nothing. Maybe staring at the page. More likely doing something entirely different, having nothing whatsoever to do with math. I will ask the student how things are going with the problem, even though I already know the answer (badly, not at all, etc). The student will say, "I don't know where to start." They always say that.

I will give same vague helpful advice to get things started. I'll ask, "What are we trying to find?" or maybe, "What do we know?" They will respond, weakly, skeptical that this is in any way helpful. They will never write any of this down. Then I will move on to more specific suggestions. I have to move on to specific suggestions because the seemingly obvious suggestion of, "Well, try something," is completely ineffective. Even though I get a lot of my problems out of materials designed for use at the middle school level, they can not think of a single thing to try.

"What happens if n is 1?" I'll ask. Normally n=1 is a case you can do in your head. They'll give the answer, giving me the "are you from Neptune?" look, as so far I have done nothing helpful, as any moron knows what the problem is asking and what we already know and how to do the case with n=1 and none of that matters at all because the problem is about n=20. Or n in general.

And they do not write down anything about n=1.

Then I ask about n=2.

Often you can do n=2 in your head. Maybe a little scattered and disorganized scratchwork is needed. But still nothing gets written down. Never, never, never will they start making a list showing what the answer is for assorted small values of n. Never will they write down anything other than the final answer. (Unless I say, "Write that down.")

So I will tell them to make a chart. I will tell them how to put the values of n in one column and the answers in another. And I will ask them if they can see a pattern emerging. And usually they can, and they can get an answer. But they're not sure if it's right.

And they ask, "How was I supposed to know to do it that way?" and they'll be just as unable to do the next problem (often similar but disguised) and will have no idea where to start.

Maybe you're wondering what this has to do with cheap beer or anything else. Stay with me here, I'll explain: I view social activities much like those students view non-routine math problems.

I've lived here long enough that I probably should know more than a grand total of three people who are not in the Math Department: My two next-door neighbors (one of whom works in my school's library) and a real estate agent. What to do to meet more people? No idea. I feel exactly like I'm one of those students who don't know how to start the problem.

The last time I met someone (previous city), I used the mathematical technique of relating the problem to one that you've already solved. I was riding the bus, and I saw someone who looked like one of my friends from high school (hadn't seen him in nearly 10 years). I checked the directory of the major University in that city: yes, he was a grad student there (English). So I finally knew someone in that city. (He threw amazing parties.) Then I moved.

And when people say, "Go somewhere, anywhere!" it's like when I tell the students to try something. If we knew something to do, we would. But we have no clue. And vague suggestions are useless (I may have to hurt the next person who says, "Do something you enjoy!" or, "Volunteer!"). Do you know how many times I've driven to things on the other side of town and then turned around and came back?

Because even with a plan, the process can be overwhelming. Just like my students lose the big picture when they get tripped up by the rules of arithmetic (yes, student, for you order of multiplication does not matter), the how of the what is just as bad — if not worse. Where do I go and who should I talk to and where do I pay and who do I tip and how much and how long do I stay and how can I tell if I'm having fun and can I please go home now because this is way too stressful? (Obviously all the Normal People can tell that I'm not One Of Them.) Even with step by step directions given by someone at my side, I'm still unsure what is going on, and I certainly would never in a million years be able to do this on my own.

So I know exactly what the problem is and what I should do and what I'm doing wrong. But none of that is very helpful.