Two Weeks / One Post

Yeah, I've been neglecting the blog for a couple of weeks now. I'd feel worse about it if I weren't so busy! Then again, I will now have a difficult time trying to reflect on my initial teaching forays, since I'm doing it after the fact. Most of my writing takes place on the job these days: I try to jot down observations from each class period into a sectioned spiral notebook that I keep at my desk.

I have lead taught several lessons by now, and done so for each class in my schedule. Some of those sessions were planned out in advance, but a few were spur-of-the-moment appointments. On the Thursday before last, Ms. Cranford had to rush home to care for one of her sick children. She called in a sub, of course, but she left three of her classes in my hands that day with naught but her notes as preparation -- and I had never lead taught for any of those students before. As nerve-wracking as it may sound, I actually rather enjoyed that experience. When given time to prepare a lesson I tend to over-analyze my approach, just as I tend to over-analyze many things. (It's a common occupational hazard for mathematicians.) While I do not plan to make a habit of going up cold and improvising, it does generate a healthy surge of stage adrenaline (I got over stage fright long ago) which loosens me up a bit. I don't how smooth my delivery was for my students -- you would have to ask them yourselves -- but I must not have screwed up too badly as Ms Cranford was able to pick up right where I left off when she returned the next day.

Whether I get to plan my lesson in advance or not, I'm learning firsthand about the role schema play for students. I'm often surprised by what they do and do not know coming into a classroom. Just today, when I was grading an assignment about scientific notation, I noticed that several students did not seem to know how many zeroes are found in millions, billions, and trillions. Naturally they had trouble with word problems in which quantities were expressed using those words instead of just numbers. Oh well, teach and learn. Sometime in the future, expect a post from me about the mathematical concepts I think every student needs to know. Some of them may surprise you.

So far in my lessons, I have stuck to the basic format espoused by Ms Cranford: spend 10-15 minutes answering questions about yesterday's topic, demonstrate the concept of the day through lecture and whiteboard, and then leave the students with time to start working on the corresponding assignment. It's very traditional -- some critics may even call it obsolete -- but Ms Cranford carries it off very well. I'm not sure that I want to go down that road myself -- I'm not sure that I can travel that road with any degree of success once I'm teaching solo -- but I haven't yet figured out how I want to break from this model. Maybe our upcoming Methods courses will shed some light on the topic. I've heard about different approaches for running a math class during our summer MAT courses, but I've watched math teachers implement the classic approach for many years now. A certain amount of internalization has taken place, I fear. I get the feeling that any serious experimentation will have to wait until I have secured my own teaching position: Ms Cranford's students seem comfortable with her style of teaching, and there is something to be said for having a student know what to expect in class. I don't want to mess up her system just to satisfy my own curiosity, especially when she's getting such good results from it overall.

No doubt some of you are wondering why I'm not fully comfortable with the review/lecture/assignment routine. I have my reasons, but the exploration of those reasons will have to wait for my next post -- whenever I can take time out for another round of blogging. Sleep beckons.