Thoughts on Teaching

This is my second semester teaching precal recitations (what some schools call "labs"). The kids in my course attend a large lecture with their professor three days of the week, and the other two days, they have recitations, which are 50 minutes long and in small classrooms (about 35 students).

It is an interesting experience. Every Thursday I give them a quiz or an exam given to me by the professor, and on Tuesdays, and Thursdays before the quiz, I go over material with them, answering their homework questions and reviewing stuff for the upcoming quiz or exam.

Teaching (the actual teaching part) is really fun, but also weird and frustrating. When I gaze out at my class, many of them look either terminally confused or completely bored, and I can't always tell which. Many of my students totally ace all of the quizzes and exams - they probably don't need me for that. Some of my students struggle around the middle, and hopefully I help them. And some of my students are just consistently confused and their quiz answers are weird and wrong.

One thing that happens is that I don't know how to pitch my class. I know some of my students really aren't getting certain things - do I just hammer on things endlessly, trying to bring everyone along, while boring the others out of their skulls? Or do I sort of blithely move on to the newer, more exciting material, risking leaving some in the dust? There isn't one answer to this question - it is more of a feel thing, and I don't think I have the feel of it yet.

Another thing I find myself doing, and what I really want to talk about, is focusing on mistakes. There are certain persistent mistakes made by my students that sort of drive me nuts. For example, a lot of my students think (at least while taking a quiz) that the square root of (x^2 + 9) is x + 3. Or (the same error) that (x+y)^2 = x^2 + y^2. Or they add or multiply fractions completely wrong.

These are really basic mistakes that they should know better than to make, and it's easy for me to sort of become obsessed with these errors and how I can drive them out. And I'm realizing that focus is completely wrong.

I've had professors who seem more focused on mistakes than on the math they are teaching, and it's made certain classes very negative for me. It starts to feel like the point of the class is to avoid errors, to not fall into certain common traps, and so on, rather than to learn exciting new math. What's the fun of that?

I've also seen professors focus too much (I think) on their fears about students not being prepared for the next course. I don't know if this is universal, but I had a lot of middle school teachers who would say things like, "I can't let you get away with xyz, because your high school teachers will never allow that," and high school teachers who said the same thing about college professors. It never turned out to be true. And I've seen profs at my school wield calculus in the same way - "If you can't do [this particular skill], you will fail at calculus."

It's not that it's false. Your lack of ability to add fractions will increasingly be a handicap as you proceed through the calculus sequence. But I'm not sure threatening people with the upcoming courses is really the way to go. Some level of mistake-making is normal, natural, and not indicative of future failure. People get better all the time, even when they are making mistakes.

Some of them really will go on to fail calculus. Some will fail precal and not even get to calculus quite yet. But making calculus sound dire and horrible to everyone won't necessarily solve that. Calculus is one of the most beautiful inventions of the human mind. Being able to study it is a great luxury. They should look forward to it!

So despite my controlling tendencies I am going to make an effort to keep a positive focus in my teaching and not become obsessed with typical student errors and mistakes. I really don't want to be that kind of teacher.

Teacher Follies

An amusing/embarrassing thing happened to me today.

Because I write so much, I am very careful to keep paper that I've only used one side of to use as scratch paper. I have a big stack of this on my desk, and when students come to see me, I usually write with/for them on some of this paper, and then if they want, I let them take the paper with them. I figure the graduate math on the other side won't hurt them any (though it hurts me plenty, I can tell you).

Anyway, sometimes when I am working on problems, I write notes to myself in the margins. Often the notes say something like, "I suck at this type of problem :(" or "I will never get this!!!!" I try not to give papers like that to students, but I don't try very hard.

Yesterday, a guy came to my office hours and I sent him away with three sheets of my scratch paper. Today before class, he was showing it to another student, and I overheard this conversation:

Other student: Huh. It says "I am a bad ass" on this side. Did you [to the first student] write this?
First student: No, I think she wrote that. This is her work for some other stuff.

So I wandered over and sure enough, I had written "I am a bad ass" in the margin of my work. We had a good laugh over it.

It's kind of embarrassing, but I'm glad it was positive self-talk for once, and not the negative kind. One of my friends in the program pointed out that it was good that I had at least not written that I was a BAMF, which is also something I might write (either as an abbreviation or written out).

So anyway, there's that.

Takin' the Praxis II

This morning, bright and early at 7:30, I took the Praxis II Mathematics Content exam, accepted for secondary math certification in many states, including Colorado. I took it at East High School, a grand old school (built in the 20's) full of marble and hardwood, high-ceilinged, yet still with that sort of dingy quality of any urban high school. It sits just past the entrance to City Park - it is the city-hall-type building you see here:

The two pillars in the foreground are across the street from the high school. Grand, no?

While other Praxis takers (and some kids waiting to take the ACT) waited in the lobby for things to begin, I wandered the halls a bit. The classrooms all have enormously high ceilings and are more spacious than our classrooms at Metro, but also dirtier and more disheveled. (The dishevelment isn't surprising; a high school teacher's classroom is also their office.)

The test took two hours, and leaving early was forbidden. (You could go to the bathroom or whatever, but otherwise had to stay the entire two hours.) The test I took was 50 questions long (some of the other people had 120-question exams, in other subjects) and basically covered material from algebra, Calc I (possibly II), linear algebra, high school geometry, and prob/stats, with a slight sprinkling of other topics.

Like most tests by ETS, some of the questions can be solved either by brute force or in some simpler way. I probably brute forced most of them.

Although the topics I listed are broad, the questions about them were not deep. They were basically questions that you could answer if you remember the basic ideas about calculus, linear algebra, and so on. For instance, I did not have to actually differentiate or integrate anything, but I did have to do things like recognize when a graph showed the first derivative of another graph, or understand the nature of of integration as "area under the curve."

I got through the 50 questions and was able to review about 13 of them before the time was up. I did find some errors in my review, which is (a) good, because I fixed them, but also (b) bad, because it means there were probably errors throughout.

At any rate, I almost certainly passed, and nobody cares about the specifics of your scores in this area. My certainty about passing isn't based just on the fact that in general the test was extremely doable, but also on the idea that, if they wanted a better performance than I gave, there would be extremely few new high school math teachers.

So that's that.

The Next Plan

When I graduate in May, I'd like to get a job as a teacher. Yes, I finally want to really try teaching secondary (middle or high school) math. I'm ready to jump in.

The obvious way to do this would be to apply for math teaching jobs here in Denver. If I were to be hired by a principal, it would be contingent upon my enrollment in the "Teachers in Residence" alternative certification program, which I can do at my current college.

What I don't know is whether I can actually get hired. On the one hand, math and science teachers tend to be in somewhat short supply, so it's much more favorable than if I were trying to go teach, say, social studies. But on the other hand, my understanding is that Denver has a pretty tight job market for teachers. I imagine a principal would rather hire a certified teacher than an alternative certification candidate with no experience. (I have no relevant experience at all, not even tutoring.) And it's possible the sucky job market has flooded the alternative certification programs with laid-off engineers and the like as well.

I could also try to do alternative certification somewhere else, where there might be more opporunities, like Houston (which has an easier, cheaper program and higher teacher salaries) or wherever Ed moves to for his PhD. That's another level of complexity to attempt, of course.

I could also graduate as planned and then do a post-degree teacher certification program through my school. I can't quite seem to figure out how many additional hours I would have to take, but that would take at least a year if I went full time, leaving me with the problem of how to support myself for a year with either no job or some kind of a part-time job. (One semester I would be student teaching, which would make it hard if not impossible to have any other job at all, and I don't think student teaching is a paid gig.)

Even more hardcore would be trying to enroll in a Master's program for math education, which could (if properly chosen) result in both certification and a higher salary. But that would be, I think, crazily expensive and definitely require going into debt. (It would also turn out to be futile if I don't end up liking teaching.)

I estimate that, if I were crazily frugal, I could live on about $1000/month right now (net, not gross), and it's quite possible that by next Fall I'll simply have $15-20K saved up and then I could just plan to live on savings for a year while pursuing certification. That's if Ed doesn't move away.

If Ed moves away, I'd need a much cheaper apartment (and they do exist in Denver) in order to live on either my initial teaching salary, or to go to school full time without a lucrative job.

So, why teaching? I've been interested in teaching forever, which was not surprising when I was a kid since that was the one profession I got to see up close, but which has persisted since. I find that I am somewhat obsessed with schools (I especially love books set in schools, even more so if they are really about school itself). I love to read books about how to teach, too.

Can I handle being a teacher? It's a really difficult and exhausting job. Yes, you get summers off, and a lot of other holidays and things, but you also work more than 8 hour days (at least if you want to be any good at all), deal with a lot of bureaucracy, wrangle the kids who are imprisoned in your classroom each day, constantly do paperwork and grading and so on, and the pay is not nearly enough to make up for the stress. That's my understanding, anyway.

However, I have found that currently, when I am not in school, I am horribly bored in the evenings and hate my life. Being a teacher would certainly take care of that problem since I would have a lot I needed to do all the time. And I have also found (as discussed many times before) that I enjoy things in proportion to their level of difficulty assuming I can do them, so I might enjoy the difficulty itself. And reading a book is very different from having to do something, but I have to guess that the fact that I enjoy books about classroom management techniques, how to set up your paperwork, and how to deal with troublesome kids in your class is a good sign. My fantasies about teaching don't involve a class full of attentive, bright-eyed students eager to learn algebraic concepts, so...well, maybe I'm not living in a total fantasy world.

Ed thinks this is a great idea, which I find somewhat astonishing. To me it sounds like a quite evidently bad idea, taking a > 50% pay cut to do a really difficult job that requires a lot of energy and dedication.

Of course, if it turns out that I really do like teaching (or like it well enough, all things considered), it's a very convenient career in a lot of ways. The pay is less than I make now but it's not that abysmal, at least in the places I've checked (i.e., major cities). You can live on it. It's an extremely convenient schedule for raising kids, of course, though it may be that teaching completely satisfies my desire to interact with children at all, ever. It tends to have good job security, and is a job you can get anywhere in the country, and the benefits are usually generous. Unlike oil & gas, it's not likely to collapse as an industry, nor be outsourced to India or China.

And given that I'm obsessed with it, I really need to go and try it. If I find out that I hate it or can't do it, well, I have the rest of my life to pursue other goals without worrying about it any further. If I don't do it, I'll keep thinking I should do it and wondering how. So, we'll see if I can even get such a job, or get into a program, but for now, that's my plan. I'm also taking the Praxis II secondary math exam this Saturday, which I'll need for the alternative (or any other) certification, and which is accepted in many states.