Good day, folks, it's been a good day.

I spent most of my free time today beating my brains senseless (a misleading phrase which seems to suggest that there was some sense in there in the first place) on a couple of twisted research problems I'm working on with my colleague Tip: after a month or so of work we've managed to get a handle on the expected degree, at time *t*, of the *n*th vertex constructed through applying any one of an infinite family of random tree construction algorithms. At this point we're trying to recover the same statistic for a broader class (or other related classes) of algorithms, and to no avail.

Hey, and every now and then I took a break and taught a couple of classes!

I felt much more comfortable in Section 1 of my Calc I class this morning. (I made damned sure that the classroom door was open before traipsing up to my office so that I wouldn't be greeted by a hulking phalanx of students waiting outside the locked door.) After going over a few bureaucratic points I'd intentionally let slide on Monday, we spent about twenty minutes figuring out what sort of grading system we wanted for the HW: as planned, I split everyone into groups of four and asked them to consider, if they would, the weight the wanted to assign to each of the sets of HW problems graded in a certain fashion. (Details are on the syllabus; roughly, a fraction of the problems, selected randomly as I've done in the past, will be graded "carefully," lots o' juicy feedback and whatnot, while the remainder will be graded "quickly," based solely on whether or not the correct answer was obtained. All told, 20% of the overall grade will come from HW graded in one way or another.) After reaching a consensus within each group, we reconvened and briefly discussed the pros and cons of each grading system. Each group then reported the figures arrived at, and we agreed to go with the straight average of the resulting weights. In Section 1, we ended up with something like 65/7% for the "careful" method and 75/7% for the "quick" method, and everyone seemed pretty satisfied. The same exercise, run by the second section, yielded a more arcane division that we decided to round off to 5% "careful," 15% "quick." Though there wasn't out-and-out rebellion, I sensed a little bit more resistance to this decision. I asked anyone who was unhappy with the result to let me know confidentially, in case they didn't want to be put on the spot in front of 30 of their peers.

Once all of those parliamentary matters were out of the way, it was time for...MATH! Oh boy! We actually ran short of time in the second section, having spent a few more minutes still on discussing what it is that students and teachers can do to work together in bringing about a classroom atmosphere conducive to effective learning. (This discussion yielded a wealth of good ideas, and everyone seemed to agree that the best environment involves an active classroom in which a variety of learning styles were addressed and in which both teacher and student come prepared to play their respective parts. Duh.) Even in the first section we only got to scratch the surface of our discussion on functions and models. We'll pick it up there tomorrow. These "environmental exercises" are fairly new to my teaching repertoire, and I'm really glad I included them in this semester's proceedings, I think they'll make for a healthy place to study.

Meanwhile, 280 went *very* well. Folks came prepared (some folks came *very* prepared) to discuss the writing samples on chemistry I'd given them to think about (this one here), and we had an active conversation on the relative strengths and weaknesses of these samples. Although everyone agreed that the second fragment was the strongest, there was a healthy debate as to whether the first or the third came in second. Ultimately I think we were all willing to admit that the though the third fragment was the most informative, concise, and precise, it was simply inappropriate in terms of its format (given that the assignment was to construct a *formal paper*).

From this we went into the mathematical version of the exercise (here), on which there was greater unanimity: the third fragment was the clear winner, followed by the first, with the second coming in last: the second one simply isn't a proof, and while the first provides very little context and lacks clarity (and a bit of correctness), at least the basic idea of the proof is sound.

I have to tell ya, I had a blast in all three of my classes today, and I hope they all continue along the lines we've established so far. I'm totally digging all of my students, and so far they're all really engaged.

It's all good. Tomorrow's calc sections will dig more deeply into some interesting mathematical models. We'll see what they have to say about Jane Austen's *Northanger Abbey*. And of course my 280 folks get the day off! Yay!

Ladies, gentlemen: have a nice night. I'll catch you on the dayside.

## Wednesday, August 22, 2007

### Hmmm...

Posted by DocTurtle at 8:34 PM

Labels: Calculus I, course prep, Foundations, MATH 191, MATH 280, research

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