math

A few weeks ago I had the opportunity to visit one of Ms. B's classes. I had been feeling frustrated with a couple of my classes, so I did what I often do when feeling frustrated: I find another teacher and go watch what they do.

Ms. B is another math teacher at my high school, and I picked her class because a) I'd heard that she was a good teacher, b) she had a class during my planning period, and c) the class she taught during that period was Pre-Calculus. This was important because the two classes I was feeling frustrated with were two of my Advanced Functions and Modeling classes. AFM is often described as "pre-calculus for kids who aren't going to be taking calculus" or "a fourth math credit for kids who are going to college but probably aren't going to be majoring in a math-intensive field." The classes are both intended for juniors and seniors, and cover much of the same material, but Pre-Calc is an honors class and AFM is a regular class, so the main difference between her classes and my classes is that she has the "honors" kids and I have the "regular" kids.

During the 25 minutes or so that I was there, Ms. B was doing a fairly standard whole-class problem review activity. The kids had completed on their own a set of five or six problems on the properties of logarithms, and Ms. B was up at the front asking different students to walk her thru the solutions, pretending like she didn't already know how to do the problems so that the students would be forced to explain their reasoning.

Here are the main things that I noticed:

The whole class appeared to be (mostly) engaged. While I'm sure there were students who weren't focusing on every problem with laserlike intensity, for the most part the kids were paying attention and even participating in the class conversation coordinated by Ms. B. This is just another way of saying that the students were working.

Ms. B would occasionally make a joke. In fact, she made lots of jokes. This seems like a fairly insignificant thing, except that Ms. B could make a joke, or respond to one of the students' jokes, without completely disrupting the lesson. She, or a student, would make some harmless comment, everyone would chuckle or groan, then they'd all get right back to the problem on logarithms. Her students, in other words, were able to play and work at the same time.

My students have a hard time with this. I often conduct similar whole-class activities with my AFM classes, and more often than not, if a joke is made it opens the door for someone to make another joke, then another joke, and pretty soon the class is off and running in the wrong direction. They seem to want so desperately to NOT have to work that they're constantly on the lookout for anything that might get the class off-task, and jokes provide great opportunities for that.

The students were willing to take turns. While Ms. B would call on a particular student to work a problem or answer a question, other students often had comments or questions, and they would ask them. It was truly a whole-class conversation, with the students taking turns, not interrupting each other, etc.

Again, my students have a hard time with this. Even when they are (mostly) engaged with the whole-class activity, the simple act of taking turns and being willing to speak one-at-a-time is a challenge for them. I often have students who are interested and want to engage in the conversation, but they are so unwilling to take turns (or speak in a normal tone of voice) that they are constantly interrupting me or other students; they essentially dominate the discussion and refuse to allow anyone else to participate. I have found that requiring my students to raise their hands before speaking sometimes helps, though again the students have trouble with this and so must constantly be reminded.

The students were willing to let Ms. B run the class. It's hard to overstate just how important this is. While there may in fact have been a number of students who were not "actively engaged" in Ms. B's lesson (thinking about lunch, for example, instead of concentrating on the math problem), there weren't any who were trying to take over the class. Her students seemed to understand that while they might prefer to be socializing with their classmates, or playing Angry Birds on their iPhones, this was math class and they were supposed to be doing math; so they rolled their eyes and got to work.

While it might seem hyperbolic to say that I often have students who want to "take over my class," that's essentially the case. They don't run up to the front of the classroom and grab the whiteboard marker out of my hand, but they frequently call out comments or questions that have nothing at all to do with what I'm talking about, initiate off-task conversations with their classmates, or otherwise try to focus the class's attention on themselves; and, there are plenty of other students happy to play along. Of course, I have class rules that address these situations, and I address them individually as needed, but the point is that in my classes I address them a lot, and Ms. B didn't have to.

I actually saw a couple of exchanges in Ms. B's class that fell into this category. One was a standard off-task conversation between two students while she was talking about the current logarithm problem with another student, which Ms. B addressed by saying, "Oh excuse me, I didn't mean to interrupt your friendship with my conversation about math." The students stopped talking, sheepishly indicated that they were sorry, and the lesson continued. Another time a young man got out of his seat and for no apparent reason walked across the room, then turned around and walked back. Again Ms. B said, "Excuse me J, I didn't mean to interrupt your random walk across the room with my conversation about math." There was some good-natured chuckling and again, the student apologized, sat back down and the lesson continued. In my classes these kinds of interruptions happen much more frequently, and they often require much more effort on my part to resolve them.

I caught up with Ms. B at some point later to ask her some questions about that class in particular and her Pre-Calc classes in general. She confirmed that yes, that particular class was a really good group of kids who were generally well-behaved and hard-working, and she genuinely enjoyed teaching them. She also noted that her other Pre-Calc class was not as well-behaved and hard-working, so there was a lot less joking around and "having fun" during that class. "If you'd visited my other Pre-Calc class, you'd have seen me be a lot stricter and less jokey," she said. "In my other class I have to spend a lot more time getting them to pay attention, stop talking, get to work, etc." I asked her how many of her Pre-Calc classes were like the one I visited and how many were like the other class, and she said it was about 50-50. About half of her Pre-Calc classes are ones where the students need a lot of "classroom management" and the other half are more like the one I visited.

For my AFM classes I'd say the proportion is more like 80-20. In general, my AFM students are either unable or unwilling to do the following things on their own:

engage with the assignment (i.e., do the work)
not talk while I'm talking
take turns asking questions
joke around without completely derailing the class activity
let me run the classroom

Which ends up having the effect that I spend more time and energy on classroom management and less time on instruction. Which is essentially the difference between honors students and regular students.

Image by jeremy.wilburn via Flickr.