Sunday, February 24, 2008

Overdue notices

I'm overdue to post (so saith a few faithful readers, including my mother-in-law, my wife, and two of my most diligent students). Enough, already! So here I am, I'm writing.

I've been here, I've been busy. The last few weeks have been exciting ones, and next week promises its own supply of hecticness (hecticity?).

What's new, pedagogically speaking?

Well, yesterday was the deadline for applicants to this year's REU. This afternoon I counted up the number of distinct applicants from whom I've received at least one document (application, statement of purpose, transcript, or letter of recommendation): 64. Not bad. That's about what we had last year, though I believe the ratio of men to women is higher this year than last. I've yet to break it down geographically, but I think this year's pool is more widely distributed throughout the country than last year's. I'll probably begin looking at the applications in earnest over Spring Break. No sooner: next week's going to be a bear. Tuesday brings a colleague from Davidson College to campus (hello, Twyla! thanks in advance for making it out! and sorry again for the confusion in scheduling!) for the Research Seminar. Then comes the Math Literacy Summit we've been planning for several months, highlighted by the public lecture and keynote address given by Dr. Robert P. Moses. That's Wednesday night and Thursday day. Saturday sees the start-up of Super Saturday once more (I'll see if I can enlist some student helpers...the downside is the onset of Spring Break, taking many students away from campus). By Saturday afternoon I'll be beat.

What else is new?

This past Friday my Graph Theory gurus had their first exam, an in-class ditty that represented my first attempt in almost two years at writing an in-class exam for an upper-division course. It's known far and wide that I'm not a big fan of such a format for seminar courses, and it was hard for me to write an exam that I felt made fair demands of the students' knowledge and was doable within the alloted time. The end result, I feel, was a hair (and no more!) on the long side, and a tad too easy. (I'd be interested in knowing how the students feel about both of those appraisals.) As it is, the students went down to the wire time-wise, several staying for an extra ten minutes to finish up, while the average was high, around 86%. Maybe I didn't ask for enough proofs? Maybe I was a little light in grading? I don't know. The only question that seemed regularly to ensnare the unsuspecting was the problem asking the students to compute the number of homomorphisms from the star with 3 vertices to the star with 4 vertices: there was a broad array of answers to that question.

How's the day-to-day activity in that course been? The students' presentations of solutions are getting tighter, more succinct, more precise. For the most part their diagrams are more descriptive and intuitive than they'd been during the first few weeks, and their proofs are more straightforward and understandable. Most interesting are the differences in presentation styles between the various members of the class. Some are silent until all has been written on the board; their presentations then consist of little more than "voilĂ ! Pas de lacune a remplir!" Some are so verbose they can barely put chalk to board to draw a single tittle without prefacing it with a megillah of mathematical exposition. I wonder to what extent they find others' presentations are affecting the style of their own? (This sounds like a perfect question for a mid-term evaluation!)

We've gotten to the point where the students have a grasp of the basics, I can probably branch off in whatever direction I'd like to in terms of the ground material. The most recent problem sheet (the seventh, available here), deals primarily with components, paths, and chromatic polynomials. I believe I'll make trees the focus of the next sheet, unless someone has a better plan. Lorelei mentioned the other day to me that she'd like to see more applications, so I'll do what I can to work those in (colorability has many applications, and they'll soon be ready to take off in that direction). Markus came to me on Thursday, indicating that his relatively light schedule is granting him plenty of time to take on some independent study in graph theory, so I gave him some reading on graceful labelings, maybe he can join Trixie and Sieglinde in their pursuit for new graceful trees.

Speaking of which, we'll soon have our strongest showing at an MAA Southeast Sectional meeting since my arrival at UNCA: at least five faculty members and four students have indicated interest in going to the meeting, and I'm trying to get three of these students (including Trixie) to present in the student poster session.

And speaking of Trixie, how's Calc II? They too completed their first exam this past week, and overall the grade distribution was pretty fair, with a course average of about 76% after corrections were made. Oddly enough, though, there was a profound difference between the two sections of the course: the first section's post-correction average was about 68%, the second's around 86%. I kid you not. After corrections 12 out of 16 students in the second section got either an A or a B (8 As, 4 Bs), while only 10 of 30 students in the first section earned that bragging right.

What, as they say, is up?

Could it be class size? Admittedly I find it much easier to engage the second section as a whole and as individuals, owing largely to the fact that it's got about half as many students. Moreover, the students are less intimidated by speaking up in front of one another, and by presenting on the board. They're also much less reluctant to get into groups and work on problems together. Whether any of this has anything to do with the size of the class, I don't know, but I can't help but think that class size plays at least a small role. (Incidentally, I'm happy to report that I'll be teaching two sections of Abstract Algebra I next fall, each considerably smaller than the traditional single sections that have been run in the past. Our program has been so successful in courting majors that we're having to run two sections of the upper-division courses. America gonef! [You'll have to excuse the Yiddishisms, I've been making my way through Leo Rosten's delightful Hooray for Yiddish: a book about English. I'm easily influenced].)

Could it be the time of day? But one might think that the sluggish 9:00 a.m. class would be more ideally situated in that regard than the post-lunch but usually-punchy 12:45 p.m. class. Or maybe I just think it that way because I'm a morning person. Perhaps there's something to it: the morning section's usually slow-to-rile and torpid, the afternoon section's much more get-up-and-go.

Could it be...the luck of the draw? I've got great students in both sections, but they're just more highly concentrated in that smaller second section. Maybe it's just coincidence that the second section's so much more lively.

Whatever the cause, the difference between the two sections is as that between night and day. I love both of them, but I find myself often wishing wishing wishing that the first section would wake up and stop dragging its heels!

What else?

Faculty talks have ended in the Senior Seminar, I capped them off with a presentation this past Wednesday, on open problems in graph theory. I'm proud of the fact that we had three speakers from off campus, and that we'll soon have at least two more visitors coming to speak in the Research Seminar. I truly believe that our department should attempt to cultivate a more active research environment, and I think we're well on our way towards achieving that goal.

Student talks begin in the second week after Spring Break, two-by-two they'll fill up the last six weeks of class. I'm looking forward to those talks, the topics look to interesting.

What else?

The Writing Intensive committee (well, technically it's a subcommittee, but who's keeping track?) has sprung back into life, continuing our analysis of WI applications and beginning our conversation on the assessment of the success of already-WIed courses. This is a sticky wicket of a tricky schtick: How are we to judge whether a WI course has met the goals it laid out for its students? What materials must we demand of the course instructors in order to perform a proper assessment? How many of a course's learning goals relating to writing must be met in order to call the course a success? And if a course is less than entirely successful, what consequences do we as a committee mete out? It's unrealistic to aim for the ideal right out of the gate (assuming the ideal can be articulated from the outset anyway): all but the perfect instructor is going to stumble here and there, and no course is flawless in design and execution. Therefore it's pointless to pull someone's WI away should perfection not be attained. We don't want to smite those who fail in providing this or that element of their class's purported learning experience. Instead, we wish to encourage the instructor to look carefully at her course's goals, to look at the students' products in attempting to meet those goals, and say, "this was done well. But this, when asked of the students, proved unrealistic. Better I ask that they reach for the moon with their hands at their sides!"

How many of us are so reflective? I'd like to say that I am, but who am I to say?

In the first of what will be several meetings of the writing assessment project this past week (didn't I say I've been busy?) I told my colleagues that last semester's 280 course taught me to be truly conscious of the role played by writing in my own particular discipline...indeed, I think I learned more in that class than my students did. My approach to writing as a tool for learning has changed because of that class.

Writing is playing less of a role in my Calc II class this semester than it did in either of last semester's classes, and while I've not shone a spotlight on writing in Graph Theory, it's ever present. (The work I've done in 280 over the past year is most evident in the structure of the students' proofs on the blackboard: I'm thrilled whenever I see clear statements of hypotheses, an explicit indication of proof technique, summarizing sentences that indicate when and why a proof has been concluded, and so forth. In all only two or three of that class's students didn't have 280 with me, and almost daily I see elements of my own idiosyncratic style that have rubbed off on them.) I'm going to take a few minutes during this coming week to refocus the students' attention on writing and encourage them to keep an eye on the criteria for solid mathematical writing as they put together their solutions to the problems selected for written submission.

What else? a recruitment spiel on the upcoming REU and speaking ongoing graph theory research to a wonderfully receptive and warmly inviting crowd at Morehead State University in Kentucky (y'all were great, thank you so much for having me!), writing about a dozen or so REU rec letters for current and old students, joining a couple of colleagues in a presentation to the university's Foundation Board, agreeing to help organize this coming May's Writing Intensive workshop, and shaking off a nasty cold that took me out of commission for a few days...see? There's a reason I've not been around!

If you'll now excuse me, it's Maggie's birthday (which one, I will not say, though I doubt she'd mind if I did, she's not embarrassed by her birthdays), and we've got to go celebrate it in the manner of her choosing.

As usual, all comments, questions, queries, suggestions, insinuations, epiphanies, innuendi, graffiti, scritti politti, revelations, retorts, ripostes, and recriminations are welcome on the comments page.

Until next time, live well, and try to learn something new today.

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