Observations

Having taught MATH 280 four times now (counting this current semester's installment) in the past four years, I've begun to notice trends in my teaching of it.

I noticed a few weeks ago that so far I've had two "on" sections of the course (Fall 2007 and the current section, Fall 2009), and two "off" sections (Spring 2007 and Spring 2009).

To say that a section is "off" isn't to say that it's full of bad students, or that the course itself isn't a pleasure to teach (it's still, along with Calc II, my favorite course to teach); it's merely to say that it doesn't run quite as smoothly as it would were it "on": certain handouts give the students more difficulty than they give students in "on" sections, committee reports don't have quite the snap that they would in "on" sections, and the general atmosphere isn't quite as jazzed.

I've also noticed trends that might one day help me predict whether a section will be "on" or "off." In descending order of influence on the "onness/offness" of the course, I've noticed that

1. both "on" sections are/were smaller (sometimes significantly so) than were the "off" ones (15 and 20 versus 24 and 27...I went from 27 down to 15 from last semester to this one). Obviously students in smaller classes will receive significantly more one-on-one attention than students in larger classes, and their in-class experience will be more meaningful and student-centered.

2. Both "on" sections are/were taught in semesters immediately following my having taught the course in the previous term. This "recency" allows me to be more aware of the difficulties students face with certain concepts than I would be were there a year or year an a half intervening between my teaching the course once and then once again. For instance, having just taught 280 last Spring, I remember how damned difficult students find the very idea of induction. This memory helps me more patiently coach them through their inevitable struggles with this concept than I would had I a year to forget just how hard they found induction. Whether it's fair or not, I find myself being more understanding of students' conceptual miscues and misfires this semester than I was last semester.

3. Both "on" sections mark/marked the occasion of a brand new major curricular component: in Fall 2007 I unveiled homework committees for the first time, and this semester I'm asking students to write a "textbook" for the first time. These overhauls may carry with them a sharpening of focus: since I'm making significant changes in the way the course is laid out, I pay more attention to the nuts and bolts of the course's functioning, and this greater attention leads to a more carefully crafted experience for the students.

Speculation, speculation: all speculation.

For now, I'm off to lead the first Super Saturday of the Fall 2009 term, my seventh term at the class's helm. Today's topic: fractal fun!