Thursday, December 11, 2008

For real this time

What a strange semester this has been.

It's almost over now. We're already two days into Finals Week, I've got half of my grades submitted, and faculty wrap parties are popping up like badgers in a Weebls video.

I told Griselda the other night that it's been one of those running-to-stand-still semesters.

Maybe it was my relative unfamiliarity with both of my classes (first time ever for Precalc, first time here for Abstract) that kept me on edge all term long.

I just don't feel like it's done yet.

Somehow I feel like it never began.

Have you ever watched a movie that, twenty minutes in, didn't even seem to have started yet?

I spent almost two hours this morning in a meeting with Casanova and Lulabelle as we attempted to hammer out the dings and dents that marred the pre- and post-surveys Lulabelle and I and several others used in last year's writing assessment project. The goal is to ready a new pair of instruments to use in various classes next term. You guessed it, my 280 students will get to be guinea pigs again.

At Lulabelle's suggestion, we cut the pre-test in half by removing discipline-specific items. "I can think of two really good reasons for doing that," I said. "First, our ultimate goal is design an instrument that is discipline-independent anyway, and second, I'd find it interesting to see what sort of general writing gains students perceive having received quality writing instruction in the disciplines."

Harrumphs of agreement.

We added a few items, changed the wording in a few others ("I hate the phrase 'that professors like,' " lamented Casanova), and tweaked the demographic questions, particularly those regarding gender, so that they became less othering and isolating. "And we don't need to know about their AP and IB experience," we agreed. Out it went.

The new survey should be about half as long and much less cumbersome. Moreover, if we run it on Moodle (the online course management software UNC Asheville uses), the data collection will be a snap.

I'm still waiting to get some of the data from last year's study. I'd really like to know how a faculty member's own field of study affected her application of the course rubric to classes in various disciplines; I conjecture that the students' scored mean is directly related and the students' scored variance inversely related to the "distance" between the discipline of the rater and that of the "ratee." That is, as a mathematician I'm more likely to judge physics papers more strictly, and to assign a broader array of scores to such papers, than would a poet.

And no, I'm not sure just how this conjecture could be quantified completely.

But does it need to be?

Tomorrow I plan on collating all of the writing products I gathered from this past summer's REU students. The primary question I'd like to answer in assessing their writing is: "can one clearly discern the student's trajectory from novice math writer to accomplished article author over the course of an eight-week program in which developing writing proficiency is a stated learning goal?"

And hey, in case you didn't know it, I've been teaching math a bit lately, too!

My colleagues and I all agree that this semester's Senior Seminar talks were of consistently high quality. Not one of the eight talks was weak (usually there'll be one or two stinkers). It's too early to tell how much of this improvement is due to the more rigid scaffolding my colleague provided the students in the form of in-class "practice" talks and writing assignments. I'll be introducing yet more structure to this writing component in next semester's installment. (I know a couple of my mentees from this past semester would have been happy with more clearly articulated guidelines for their writing.)

Shit, there I go, on about writing again. Sorry.

My Abstract Algebra students' presentations were also significantly stronger than those of most students I've had in upper-division courses in the past. Their success was a result of thorough preparation on their parts: I forced them to get their acts together early and start right away in choosing topics, finding references, and assembling thei talks. In the end I felt that only three of the 15 talks were fairly weak ones (C-quality or worse), and even these had silver linings. I was particularly impressed with the talks on point groups in chemistry, free groups and group presentations, and ordered groups.

Several days ago one of my Abstract students gave me some good constructive criticism on the committee system, about to enter its fourth semester next term. "There'd be times when I'd get my draft back from the committee and it would say 'great job!' and 'perfect!' So I'd hand it in, and I'd get it back from you and it'd have half of its points missing. That was really disheartening."

Yeah. "I understand what you mean," I said.

I told him that I'd take care to emphasize that the burden of verifying the validity of a particular proof or computation lies on the committee's members: it's their job to check the facts. That's a hefty responsibility, but one that I firmly believe they should expect to assume (how else are they to make of themselves mathematicians?). I told him that I'd take care to emphasize that I would be there as a "resident expert" should there be any dispute over the validity of a particular student's response. May my word be advice and not edict.

I'm retaining committees for both 280 and 462 (Abstract II) next term, and I'll probably introduce a modified system for projects in Calc I as well. 280 students will see a greater number of "dialogue" problems in which students are asked to construct mock expository exchanges between one another with the aim of better understanding tricky logical points or proofs: students have said consistently that these exercises are particularly effective ones.

For 480 I'll once again devote a day to abstract-writing, a day to peer-editing of students' papers, and a day to designing a multimedia presentation using PowerPoint, SliTeX, or Beamer. Tomorrow I'll take a little while to hammer out the 480 schedule, which is going to be tight: with 19 (!) students registered for the course, at least seven (!) days will be devoted to student talks alone; with the three days indicated above, we'll only have time for four or five faculty "model" talks, and students will probably have to start presenting before Spring Break, or very near to it.


The most drastic change to my m.o. next semester will be my introduction of LaTeX to the 280 students. If they're going to learn how to write mathematically, then, by gum, they're going to learn how to write mathematically.

After introducing LaTeX through the handouts and worksheets I've already developed for the REU, I'll introduce a "TeX this!" assignment like the one the REU students worked on for about an hour this past summer. Then I'll start infusing their homework with LaTeX requirements. I won't require them to TeX all of their homework: just as certain problems will be designated as committee problems, others will be designated as LaTeX problems whose solutions must be TeXed. (They'll receive a nominal amount of extra credit for TeXing the other problems.) The percentage of LaTeX problems will increase in each successive assignment, from one in four in the first few assignments to maybe two-thirds by the semester's end. I doubt the students will resist: LaTeX is easy to obtain, free to use, and damned fun once you get used to it. In my experience once students get in the habit of TeXing their work they never look back, and even the most typographically challenging documents are seen as amusing obstacles to be overcome.

Besides, I have no doubt that I'll be making my colleagues' (and my own!) grading substantially easier down the line. Imagine how jumbled and disjointed a student's non-linear mathematical thinking might appear, with a disorganized blob of exposition tacked onto the side and inserted with an arrow, and a stray sentence placed at the page's bottom beside an anchoring asterisk that leads the reader to this appendix from the main body of the text. In typesetting her work, the math student is forced to linearize her thoughts, to compose them well, to say what she wants to say in the right order, all in one place. Typing, a tool for writing, is by extension a tool for thinking.

That, and the student feels all the more accomplished fo having mastered a pretty snazzy typesetting tool.

I'm really looking foward to next semester.

I think I say that before every semester begins, don't I?

I just love what I do.

I hope it shows.

Okay, I'm off for now. More to come, more to come. Always more to come.

Until then, comments are appreciated. Take care!

1 comment:

Anonymous said...

Introducing Latex to 280 is a brilliant idea! That is one of the things I wish I had spent more time learning throughout the years. That's a skill that will help them in all the classes they take down the road. Good luck with that and I hope you post your handouts on your website!