Wow. It really has been too long since I posted an installment in this series. I only now have the consecutive free time to do some serious posting. Some programming notes:
- I fully planned to post an excellent proof of Morley's theorem on this blog, but I can't seem to find my notes on it, and those notes were compiled by a student of mine off of the internet, and I can't find that site. The most common proof of this (due to John Conway, I think) is not a standard high-school-geometry type of proof, and this other proof is. Until I find it, or manage to reconstruct it, I'm afraid I won't be able to post that.
- Followers of my personal life might remember that I was supposed to have news at some point in the last 8 months about the adoption of a baby from China. That is still going on, and we are supposed to receive her picture soon, but extraordinary bad luck has delayed that picture for at least a week or two past its supposed arrival date, which was like yesterday. Unbelievably frustrating.
- While I do plan to offer some observations about becoming a parent on this blog (especially as it relates to the profession and practice of teaching), I will reserve this blog more and more for notes on math and politics and teaching. My wife and I have a different blog that we are using for notes on family life, but for reasons of anonymity, I will not be linking to it or refering to it here. The vast majority of my visitors are here for math anyway—sincere apologies if you're one of the few who find my personal life interesting.
- More math in a couple of days; I so promise.
So the last few weeks of the semester had its share of frustrations. I finally figured out what works to motivate my very obstinate 7th grade class. It was not praise (always my first attempt), not appeals to maturity (usually all it takes), not appeals to despotic authority (not an enjoyable option, but I tried), and not outward expression of sincere disappointment (on the theory that if otherwise professionally detached teachers show actual emotions, they make a huge impression). It was shame. It was the decision, made only once before, to post on the board the number of days in a row that not everyone made an acceptable effort to complete the assignment—actual completion of the assignment is not required, of course, because it has to be always okay for a student to fail to understand and come back to class with questions. My most intransigent class ever (4-5 years ago) got up to like 11 or something terrible like that. This one got up to 3 before they were shamed into all completing the assignment. But now one of my students is self-destructing a bit. Doing almost no work, frequent absence, little or no attention in class. I suspect some problems at home. But now it seems unfair to hold that against the class, yet they keep asking if everyone has done the assignment. I might have to lie. I dread the prospect of handing this class over to a substitute teacher while I travel for the adoption. This teacher (recently retired from our school) is one of the best I know—she was, casually and without hyperbole, once described as one of the best calculus teachers in the country—and she doesn't deserve to have to deal with this class. I'll have to put my foot down well before I leave.
Another frustration was the feat achieved by one of my geometry students: a 49.5% on the final exam. It is not usually our practice to suggest to students that they are in a class that's too hard for them; for one thing, it opens us up to accusations of not showing confidence, railroading a student into other classes, and giving up on a kid; and for another, a student will be much more invested in that change if it is initiated by the kid him- or herself. But in this case, I might make an exception. I just hope she or her parents come up with the idea first.
This is not the girl, though, who keeps falling asleep during class. I also suspect problems at home in her case, but other kids keep noticing she's dozing and snickering, and it's starting to disrupt the class. I'm sympathetic, because she's obviously trying her absolute hardest to stay awake, but she's failing to manage it. I hate to single her out, but I told her that she only has one more freebee before I do something to keep her awake. I'll never forget what my high school phyisics teacher would do: "Dave, could you stand up, please?"...Dave stands...teacher continues class as if nothing is wrong...Dave sits...teacher repeats request...Dave stands...teacher continues class as if nothing is wrong, leaving Dave standing for the rest of the period...no one ever falls asleep in physics class again. I doubt I'll be that harsh.
On the less frustrating side, it was fun in my geometry class to teach the first theorem that I (and the students) find completely non-obvious: that if you connect the midpoints of any quadrilateral (even concave ones) in order, you always get a parallelogram. They are truly impressed that they have gone from "what's a proof, exactly?" to "wow, I totally get that proof of something I barely believe!" in just over 3 months. I'm a big fan of pointing out that kind of progress to them.
Okay...enough babbling...happy new year, everyone. Look forward to a couple of math posts before I go back to school.