Ending week 2

The hemoraging of AP calculus students has stopped, though there may still be a trickle... One of my best and brightest told me on Friday that she's going to drop, because she doesn't want to spend her senior year working this hard. Good kid, really, and I have to appreciate her honesty... So, if she goes, that'll leave 15, of which two are going to need to either get a lot of outside help, or else drop. These two have both talked to me about dropping, one of them in tears in class, and they're both really overwhelmed and not getting it; I think that each of them, in their own way, has shut down. They're in crisis mode, and if I can get them past that, help them get some confidence, I think they've got a chance. I'll try to get ahold of their families this week, maybe visit and introduce myself, to talk about how to get them on track.

Interestingly, when I started writing this entry, I was convinced that they should both drop the class. And now, my damned undying hope is winning out... because, really, my job is not to weed out the kids who are going to struggle in this class. My job is to teach my students. (And, maybe this is close to that third epiphany I was talking about before... Not a good enough sound bite, yet, though...)


In any case, this week's exam went much better: 75% passed it, and 25% earned a B (no As, yet). And what's wild is, at the end of the second week, I was testing these kids on their ability to find the derivative formula for a polynomial-- that's right, we're doing derivatives in week two. Okay, week three we're backfilling a bit, going into more limit theory and talking about continuity, but all from the perspective of "how does this relate to the concept / computation of a derivative?"

So, that's pretty nifty. This week's exam is very lightly modified from a 2003 AP test question, which is also exciting.

Worried

I'm a bit worried about my Calculus class. I think maybe I put too much fear into them. In the first week, I've had five students drop the class. Yesterday and today, the 20 who remain have been frustrated, exhausted, and understandably upset. I think that we'll make it through this rough start, but I don't know if everyone will stick it out.

Anyway, next week, I'm diving straight in with derivation, using the velocity/acceleration idea as a hook. I want to give them something more fun to do, to keep them engaged, and I want to get straight down to finding derivatives (after all, the power rule is so simple, it'll be bound to give them some success). Also, I believe that calculus operations can be taught to students who do not have the pre-calc functions. So, here's where we find out...

Responsible risk-taking, they said back in normal school...

But what does it MEAN?

For a variety of reasons, I ended up having a student teacher observe my calculus class today.

I started the class with the following problem (ripped from the NCTM website):

A stack of oranges forms a pyramid with a rectangular base measuring 5 × 8 oranges. Each orange above level 1 rests in a pocket formed by 4 oranges on the level below it. A single row of oranges completes the stack. How many oranges are in the stack?

Before collecting papers, I asked if anyone thought they had the answer, then chose one student, and asked him to share his PROCESS, all the way through to the answer (ie, don't start with the answer, but rather, work up to the answer). He did, and I took notes on the board of what he was saying. So, EVERYONE got a chance to cheat a little, by copying down what I wrote on the board-- but they still had to finish the arithmatic, since I didn't finish out the solution.

After class, the student teacher who was observing got to talking with the other student teacher about that problem, just as a "what did you see in the class you observed." Since I was right there, I pulled out the student responses, and pointed out a few things that the student responses showed:

1. There were far more students responding with the correct response than the student teacher had expected (he figured about half, it was actually 18 of 24).
2. Of the correct responses, only about half showed evidence that convinced me that they really had a solid lock on the problem. The remainder had some sign that they had at least grasped the gist of the explanation given in class (specifically, they copied down the method, and finished the arithmatic).

What was interesting to me was the difficulty I had in relating to the student teachers that I wasn't convinced. In one case, a student had drawn the bottom (8x5) rectangle, labeled the sides thereof, added the 40 circles within it, and even drawn sketched lines of the pyramidal shape of the pile. To the side were the multiplication expressions that I had written on the board, evaluated and summed to find the correct answer. I contended that it was not clear, from that evidence, what the student was really thinking.

Since they seemed unconvinced, I changed gears a little: I contend that it is generally difficult to really understand what a student's conception is. The faculty at Northwestern really conviced me of this, particularly with the (relatively well-known) "Summer/Winter" problem (ask someone to explain why it's cold in the winter and hot in the summer; most people, regardless of education and intelligence, will first latch on to the elliptical orbit of the earth around the sun...)

So, I gave the example of one student who called me over to check his solution. "It's 97." He said. "Close, but you're a little short," I responded. He paused just a few seconds, grinned, and said, "Ah. It's 100."

The question I posed to the student teachers: What was that student thinking?

Day one

A good day.

So, early on in the summer, I was told that I'd be paired up with one of the less inspired fellow teachers in my course team (for the sophomore course). By uninspired, I mean he has a reputation among the faculty as being less enthusiastic, less engaged in his students lives, and less into using open-ended, inquiry-driven teaching methods than is the norm in our department. I've been asked to try to help push him along, which I'm happy enough to attempt.

It turns out that the upshot of this is that I have both of the honors sophomore classes. And it shows. The attitude and behavior are worlds different. So far as I can tell, the knowledge and intellect aren't worlds apart from the non-honors sophomores I have (nor from the sophomores I had last year). It begs the question-- what makes an honors student? I would argue that, in practice (as practiced at my current school, and my previous one) the metric that would most closely correlate with honors placement would be some index of "maturity", or perhaps an inverse relation to behavior complaints.

In any case, I'm pretty pleased about the situation. Four hours a day of the best and brightest, with one "hard" class (by which I mean, there are four students who appear to be poised to be discipline problems; time will tell if I'm able to handle those before they spiral out of controls, but I have plans...)