What's it worth to me?

19 hours, apparently.

19 hours, 7200 words in response to students' drafts, several follow-up e-mails looking for students' sources (ah, unintentional plagiarism!), countless handwritten notes (sorry for the scrawl, y'all), and, it must be said, a good number of sighs and head-shakes...but a few smiles as well.

This weekend was the perfect storm of grading. I had a look-see at the roughly 25 first drafts of Newton v. Leibniz papers my Calc I students produced, the 9 "sections" from Linear Algebra for Dummies the Linear students wrote, as well as two problems sets from the former class and one from the latter, and assorted exam revisions and older homework sets. There were times during the past 48 hours at which I cursed myself for setting a precedent for such quick turnaround, at which I thought, "is it really work it to me?"

The answer, I think, now that I've finally got a few hours of free time before things start up again tomorrow, is...yes.

That's a simple answer which masks the earnest reflection I've done over the last couple of days on a number of weighty pedagogical issues: (1) meaningful instruction of authentic disciplinary writing (or even basic academic writing at the collegiate level), (2) the role played by homework completion (and feedback received on same) in the learning process, (3) the relative uselessness of computer-generated/computer-graded homework in providing meaningful conceptual instruction, (4) the role of numerical grades, especially as they pertain to the establishment of an extrinsic rewards system that encourages students to become number-crunchers at the expense of real learning.

Et cetera.

How've these issues come up?

Newton v. Leibniz offers students an imposing and unanticipated challenge: most of my students don't expect to do much writing for a math class, and I'm quite certain that (whether they admit it or not) they don't expect their math professor to be a stickler when it comes to writing. My suspicion is that if they've ever had to write much for a math class in the past (and they likely haven't), whatever writing instruction they've gotten from their math teacher was half-assed and half-baked.

So maybe I shouldn't be surprised when I receive inchoate two- or three-page drafts in which ideas are scattered and half-formed, or reference lists peppered with websites whose authorship is unidentifiable and with textbooks which are (literally!) over a century old. Four or five of the drafts were marvelous: well-researched and well-organized, clear, correct, and easy-to-follow. Five or six others have obvious potential, and rest on a foundation of appropriately-chosen references. These might make a few slips compositionally, and they may have a few logical lacnuae here and there, but they'll be solid with a few more sources and some good ol'-fashioned elbow grease. The rest (another five or six) have a ways to go.

I've been playing this game long enough that I know almost exactly what's happened as the students put those last few together. Eight days into the nine-day period they've been given to get their shit together, the members of the group putting one of these papers together met after class (seven hours to the due date) and said, "hey, when are we going to work on this?"

By this time it's too late to make use of the fifteen-odd recent and well-reviewed books on Newton and Leibniz and their fellow-travelers I put on hold at the library, so they opt for the next-best...er...well, still a halfway-decen...um...well, at least an okay...well, all right...a pretty piss-poor stopgap solution: Google.

Pulling up the first two websites they can find when they put "Newton versus Leibniz" into the Google search field, they read.

Of course, one of those websites (this one, written by someone I can only refer to as Mr. Angelfire) is utter crap:

1. It's impossible to tell who wrote it, although it's likely a term paper written by a high school or college (I'm betting on the former) student with limited skills for selecting references:

2. the only print references it cites are at least (not kidding...wish I were!) 40 years old, including one that's over a hundred, and

3. the only relatively recent source is a website...it's a good one, but it's a website nonetheless, and unless you're familiar with that site (I am; my students are not), you wouldn't know this from the way it's cited (incorrectly).

4. It's a perfect example of that boilerplate "five-paragraph essay" nonsense they teach kids how to write (for some godawful reason) in high school these days. It takes no stance, it offers nothing real. It has no voice. I want my students to take a stand, stake a claim, and fight for it tooth-and-nail. This essay is a lousy model for this sort of behavior.

The second-most-cited website is this one. It takes a little effort, but you can find the author of this site, one Robin Jordan, Professor Emeritus of Physics at Florida Atlantic University, whose website (featuring marvelous animated .gifs written, no doubt, circa 1998) makes him seem to be a pretty decent teacher, actually. Not only is Jordan's paper much more well-written than the other, but it's richer and relies on stronger sources. I'm okay with my students drawing on Jordan's paper, but I'd still rather they use him as a stepping stone to get back to the print sources on which he himself draws.

All of that aside, what's the next step in our hypothetical students' last-minute writing process?

Reference (singular) found, they devour it, in a matter of...well, minutes...because that's all the time that's left to them during the lunch period on this last day. A few choice quotes plucked from the "paper" they've just read, they begin writing.

At this point it's too late to develop a thesis of their own, so the students opt for that old standby, "we just can't tell who it is who invented calculus, doncha know?" Asserting that there's just not enough evidence to tell which man has the greater claim (or a claim at all), the students hammer out two or three pages in which they eventually get around to saying that Newton did it first, but maybe Leibniz did it on his own anyway, who's to say?

Well, you're to say.

One thing these last-minute Larrys and Lauries don't do is say anything, at least not anything meaningful. But I so much want you to do this, my young friends! More than anything, this is what I want from you: I want to hear your voice.

Make a claim...make a bold claim. If you feel like putting it in boldface letters 18 points high, then do that. But make a claim, and make it your own. Make it your own by finding the sources that help you say what you want to say, that help to prove that, by goodness, you're right. Find the sources which lend support to your claim, and lead me through an analysis of those sources, step by step. Prove to me that you're right, sentence by sentence, page by page.

I don't want to know what Dr. Robin Jordan thinks, I sure as hell don't want to know what Mr. Angelfire thinks...I want to know what you think, and why you think it. That, my young colleagues, is the essence of academic writing (and, indeed, academic thinking of any kind): saying something intelligent, and saying it in an intelligent way as you insert it meaningfully into conversation with all of the other thinkers who have come before you.

Is it worth 6 hours of poring over drafts and 7200 words (that's 27 pages of 12-point, double-spaced text, by the way) of responding to those drafts, if it helps you all become better academic writers?

Hell, yeah. I'd do it again in a heartbeat. And I'd be delighted to look over further drafts if any of my students care to hand me some between now and the due date next Friday.

The rest, the other 13 hours? Problem sets, problem sets...yeah. The Linear problem sets were fine, and those for Calculus I...were great, actually. I put 'em through the wringer, computationally. I've no one but myself to blame if I go blind from having to puzzle through the first six or more derivatives of e^x sin(x). The extra work is worth it to me, if only so I don't have to read through thirty or forty poorly-transcribed copies of the solutions manual because I made the mistake of assigning problems from the textbook (a pedagogical practice I'll never again adopt as long as solutions manuals are readily available).

Indeed, in the end the students did really well on the two problem sets (one on the Product and Quotient Rules, the other on trig derivatives), given their relative difficulty. The only gripe I might make about them concerns, as above, evident procrastination: if you don't get going until Friday, a few hours before they're due, you're not going to do that well.

All in all, though, these problem sets too are worth the time I put into grading them: I feel strongly that feedback (frequent and full) is essential at this stage in the students' engagement of higher mathematics, and I feel strongly that graded homework is the best way to provide that feedback. (Students know this, too: almost without exception my former students remark to me how helpful graded homework is once they've gone on to a class with one of my colleagues who doesn't require it...and when given a chance to assign their own grading weights to the various activities we take part in in my classes, they always give homework a substantial boost.)

This post, which began with a gripe, now draws to a close with acceptance and contentment. I've lost a weekend, in some regards (although I did take in several really good college football games yesterday), but I've come through to the other side a better teacher, having reflected a bit more carefully on, and asked myself to remember, the reasons I do the things I do.

Before I go, here's a postscript for my Linear students (in particular, for Ino and Iris, to whom I was complaining on Friday, about having to assign numerical grades to their written projects): I plan on asking you all to assign your own grades to your Linear Algebra for Dummies sections. FYI.