School daze, part II

My visit to my former student Maria's Discrete Math class at SILSA was a refreshing experience.

Most striking were the similarities between her class and my own: some were engaged, others were not. Some were clearly interested, others were not. Some were quick to pick up the ideas we were talking about, others were not. There was a mix of interest, apathy, passion, and torpor.

I arrived about fifteen minutes before I'd planned to, running through the rain to the entrance just below the front door of Asheville High School's gigantic main building. In the door, down the hall, past the first vestibule, and just down another corridor, I found SILSA's office and was shown to Maria's classroom, just around the corner.

Most of her students were there (15 of the 17 she'd told me to expect), milling about, working away on the laptops they'd pulled from the giant wheeled cabinet at the front of the room. "Come up with at least one question," Maria requested as she walked around the room. "Come up with at least one question and write it down. Do you have a question?"

"Yeah."

"Can you write it down please?"

"Do I have to write it?"

"Yes. Can you write it down, please?"

Some needed several requests. Meanwhile I sat and took it in. The room seemed smaller than most classrooms I teach in, and it felt more "lived-in," its walls more heavily decorated and its atmosphere homier. The comfy-looking couch at the classroom's rear was offset by the state-of-the-art Smartboard at the front of the room.

"All right, everyone, this is Dr. Patrick Bahls, who was very helpful to me when I was studying math in college. He's done a lot of research in graph theory, and written papers on it. He's very knowledgeable about it, so I hope he'll be able to answer your questions." After some obligatory applause, I assured the students that they were very likely to be able to stump me with their questions.

Just to buy a little time while I got a sense of the class's overall receptivity, I hemmed and hawed for a few minutes about graph theory and its applicability. As I warmed up, so did they, I think, and after a little while longer I segued into the topic I'd planned to speak on, channel assignment. I introduced the general ideas, using the real-life motivating example of radio station frequencies, and then passed out a worksheet which challenged the students to complete a valid channel assignment on a simple graph.

"Try to make the numbers you use as small as possible so that your choices of frequencies are as efficient as you can make them." Several students took this challenge on earnestly and bore into the task. Maria and I walked around the room watching as the students worked, much as I would in my own classes. In fact, most of the time I was there I felt very much as though I were walking the floor of my own class, stalking my own students. It was nice to know there wasn't much difference between our classes.

Ursina and her friend, sitting at the front of the class, were the first to complete what I suspected was an optimal solution, and Ursina wasted no time in acting on my invitation to share her solution on the Smartboard. We moved on to the infinite integer lattice, a graph whose span is 6 but for which the best channel choice the students could find at first had span 8. I asked another student to share her solution on the board, but she was less eager than Ursina had been, and took some cajoling.

After we'd done discussing channel assignments, we had time for me to field several general graph theory questions from the students. A few required some normalization of terminology before we could understand one another, but I think I was able to give reasonable answers to several questions on binary trees, hamiltonian cycles, and planarity. I think the students most appreciated the idea of realizing, without crossings, a complete graph on 5 vertices on the surface of a doughnut.

However I was, as I'd predicted, stumped by a question on Steiner trees.

During the Q 'n' A, with only five minutes to go before class was let out, the students got a bit restless, and several times Maria had to call for order and I had to raise my voice a bit to be heard over the steady rain of teenage titters. I finished up, and Maria's lecture to the students to take seriously their upcoming college placement exams and to treat the substitute teacher ("Who is it?" "..." "Ahhh, shit.") brought a stark reminder that this was high school and not, indeed, college. As soon as the bell rang, most of the students (all but the one who had further work to do) were out the door.

But Maria's work was not yet done; she'd be on the clock for the next hour or more, reading over students' exams, helping with exam revisions and retesting, going over lesson plans.

"I've got three preps, six sections, and since a lot of it isn't in textbooks, I'm making up a lot of the material myself," she told me afterward. She looked happy, but very, very tired. I can sympathize.

She was one of the two teaching licensure candidates our department graduated last year about whose careers I was most excited. She's smart, she's funny, she's wise, and she's good with kids. From all that I could tell of her class today, she's done a good job in earning her students' respect, and I'm sure she's a fantastic teacher.

I hope she doesn't burn out.

And she's at a good school.

It's a true dilemma, with sharply pointed, piercing horns: if they're to succeed, our nation's public schools will need nothing but the most passionate, intelligent, and dedicated teachers our colleges can provide them, yet the Herculean tasks these teachers will be asked to perform (for, frankly, shit pay and sadly little respect) are daunting to all but the most determined souls. As I've discovered recently, this makes it difficult to give career advice to students who may be thinking about teaching but who are not totally certain about the idea.

Decisions, decisions.