Whoa...

Yeah, it's been a while.

I had no idea that I'd be so busy during the REU that I wouldn't even get around to updating this damned blog even once.

To my regular readers (I know I have a few of you dedicated souls out there, including my wonderful colleague up at Bates College), I sincerely apologize for the lack of activity on this here website. Things got a little crazy around here this summer...good crazy, not bad crazy, but crazy nonetheless.

Just this past Saturday I took our last-remaining REU student to the airport to wing her way back home in Boston (where she'd pass just a scant 10 days before heading over the sea to do a semester in Budapest, lucky devil), marking the semi-official end of our REU's first run.

Lemme tell ya, I think it went wonderfully, and I think for the most part that the students who took part in it would agree. What amazed (and warmed) me most were the strong bonds the students clearly developed for one another. No later than a week into the program it was clear that they would form a cohesive group whose members would support one another in work and play. They were a unit, and did nearly everything together. Their support for one another was evident in all that they did. And they did a lot: I think we're looking at at least five papers of the sort you might find in either an UG research or a mainstream math research journal with students' names on them. Not to mention a few other papers to be written by faculty inspired by the ideas put forth during the program. I'm tellin' ya, this place was hoppin' this summer. Not only did the program give the students the chance to work on some real math, I feel it also injected new life into the department as well.

I've nothing more specific to say about the program right now, but I'm sure that vignettes and anecdotes will trickle out of me in the coming months as I look back on the program and assess its strengths and weaknesses, especially once we start gearing up to run next summer's installment.

So what else is going on, pedagogically speaking? I've just finished writing and posting the syllabi for my Fall 2007 classes (here is the Calc I syllabus, and here is the Foundations syllabus), underway in a little less than two weeks (is it really so soon?!).

After meeting with Fiona back in May, I felt I was better able to revamp the Foundations syllabus from its Spring incarnation; I'm retaining much of the present structure of the course but am modifying the way in which students share their solutions to selected homework problems. Instead of simply soliciting for student volunteers to present these selected problems, I will be assigning committees of three students each to collect and provide summaries of all students' solutions to selected problems. Following their analysis, the committee will lead a short discussion on the solutions they encountered, indicating which they felt to be the strongest and the reasons for their choice. The details are included in the syllabus, if you have any desire to read more about it. (This sort of peer feedback exercise is a modified version of something I picked up from a session I attended at the Joint Meetings this past January.)

Fiona also helped me tinker with the homework. Many of the assignments will continue largely unchanged, but I've tweaked a few problems, deleted a couple that proved out-of-place or inappropriate, and added a few here and there. Thanks, Fiona, you rock!

As for Calc I, the biggest structural change comes in the way in which homework will be graded: since the "Homework Lottery" didn't seem to go over so well with the Calc I kiddies as it has with my last four sections of Calc II, I'm adding an additional layer of structure to encourage completion of all of the homework. (Last semester's students' primary weakness was in completing the homework.) To wit, I'll still use a lottery to select a handful of exercises to grade carefully, and for all other exercises I will merely indicate whether they are "right" or "wrong." I'm leaving it up to the individual sections' members to decide how much weight to lend to which sort of problem. In this fashion I'll be incorporating the "choose your own grading system" idea I toyed with a couple of months ago. (Incidentally, I'm not allowing a more drastic student-led grade assignment because I want to be able to maintain a high degree of consistency between the two sections; the last thing I want is some struggling student from Section 1 coming to me five weeks in with a petulant complaint that his weak homework grade wouldn't even matter in Section 3 because they chose to make HW count for 10% instead of the agreed-upon figure of 30% in his section.)

In terms of both in- and out-of-class activities, I've put together several new ones for each class. For instance, Day 1 of Calc I sees us playing with Google's pedometer feature as we puzzle through the meaning of the paths we trace on maps, and what the heck the altitude feature has to do with calculus. Day 2 of Foundations will be spent on the first of several activities focusing on the importance of clarity and correctness in written mathematical exposition: students will be asked to compare the distinctions between good and bad writing in a more "traditional" writing-intensive field with the same distinctions in the mathematical sciences.

And so on.

Much more to come in the coming weeks, on the REU, on my classes, on my students, on my random thoughts. For now, I must away and get some more work done on yet another NSF grant I'm putting together with a few of my colleagues from around the U.

Thanks for reading, take care, please come again!