A cathartic post

It was one of those days yesterday.

One of which?

One of those.

As I write this, the dawn is creeping up in the east, grasping at the leafless trees with Homerically rosy fingers. Pink clouds are scudding on a periwinkle sea. It looks like it'll be a beautiful day, and the prettiness tempers the ugliness of the purely visceral righteous indignation I felt last night.

Yesterday at 5:00 p.m. was due my Calcsters' take-home final, their final obligation to me this semester. Their duties done, it was the last I'll see of most of them until next year.

I had some wonderful parting moments as I said my farewells for the semester. Many of these people will be back for more in Calc II, and I look forward to it. I'm very open about the fact that Calc II is my favorite class to teach. (Although now that I've got 280 down pretty pat, I'm going to miss it next semester!)

The partings were rendered bittersweet by a revelation made last night as I began grading the Calc I final exams.

Six of my students cheated off of one another.

Exams from three pairs of people (two pairs of folks from the first section, and a third pair straddling the sections) show incontrovertible signs of collaboration.

This hurts me.

It hurts me because it insults my intelligence (did they think I wouldn't notice?), and because it takes the respect I've shown them all semester (in treating them like responsible adults all semester long, in trusting them with a take-home exam in the first place when many of my colleagues would likely say "you can't trust freshmen with a take-home exam"), the respect I work ceaselessly all semester to build, and it throws it back in my face.

Did you think I wouldn't notice?

News flash, folks: I'm a pretty smart guy, and I've been playing this game for a decade now. It ain't hard to recognize when someone's worked with someone else: there'll be identical use of uncharacteristic phrases, identical idiosyncratic errors, identical stray notational boo-boos. What the cheatee writes, the cheater will often copy. If the cheater wants to try to cover her or his tracks, she or he will often modify a line or two here and there, but if said cheater has no idea what the cheatee means by a particular line or computation, the result can be a wholly incongruous modification. (I saw a couple of doozies last night, changes that rendered the corresponding sentences ungrammatical.)

Did you think I wouldn't care?

In class, I'm a nice guy.

I'm a nice guy in class mostly because I'm just a nice guy in general. I could never be a hard-ass. It's just not who I am.

But I'm also a nice guy in class because I truly believe that in showing you kindness and understanding, and in showing you respect as adults (young adults yet, to be sure, but adults nonetheless), you will return the favor.

And for the most part, you do.

Of the thousand-odd students I've had over the past ten years or so, only a very, very small handful have bobbled the trust I've placed in their hands. By and large, I receive little but respect, gratitude, and positivity from my students. Even those who don't like me so much generally agree that I treat them fairly, that I treat them like sane, rational, adult human beings capable of managing their affairs with me with all due maturity.

So, believe it or not, it really does hurt me when a few folks pull this kind of crap.

I ask again, did you think I wouldn't care?

"Do they realize how much you care?" Maggie asked last night as I was ranting and raving about the six students who'd clearly gotten a little undue help from one another. "Do they know how much work you put into their classes? How much you care about how they do?"

Yeah, they do. I know they do.

Not a semester goes by without many students remarking (to me directly and anonymously on their evals) on the effort I put into class, the consideration I show them, the amount of work that goes into making sure they'll have a quality experience in my courses.

They do know that. I still believe that.

Why, then? Why cheat?

These aren't bad people I'm talking about. I like them all. They're smart, they're funny, they're kind. They're good people.

But, at least momentarily, they're also desperate, and they're inconsiderate.

Desperate times call for desperate measures.

For the most part, these folks are first-year college students. As such, though they may be sharp as tacks and quick as whips, they're also pretty piss-poor at managing their schedules. A year from now most of them will look back at their first year and realize just how much time they were wasting simply because they hadn't yet learned how to organize themselves and get their shit together to get it all done. They feel harried and hurried. They're continually, but artificially, pressed for time. They feel they don't have enough time to finish everything they need to, mostly because they've squandered their time through mismanagement. So when time's run out and they've yet to get it done, they'll resort to desperate tactics.

A couple of disclaimers are in order here.

First, I'm not claiming that you're not working hard. In fact, I'm sure you're working your tails off, I've seen evidence of your hard work all semester in my class. I'm rather claiming that you're working inefficiently; you've not yet learned how to write effectively and efficiently, you've not yet learned how to streamline your use of your supporting resources (textbooks, internet, outside assistance), you've not yet learned how to prioritize.

These things will get easier for you. By the time you graduate, you'll get better at doing these things, mostly because you'll have to: almost without exception, every one of you will look back on your first year of college as the easiest year of your college career. Hands down. To make it from here, you're going to have to get better at managing your time.

Nidra, a student from the first class I ever taught at UNCA, stopped by my office yesterday morning. She'd just finished off her thermodynamics final, and was on her way to go study for another exam. She was in the neighborhood and thought she'd say hello. We talked for a bit, and I made some cute remark along the lines of, "ah, freshmen!" and she agreed. She's sufficiently far away from her own freshman experience to look back on herself at that time and laugh.

Note to current freshmen: you'll laugh, too. You'll have your chance. The next few years will be hard as nails, but you'll love them, and you'll sincerely wonder how you ever thought your first year of college was difficult.

My other disclaimer? There are a few of you (and I'd like to think you know who you are) who truly do have heinous, untameable schedules. Some of you work forty hours a week, and/or have small children, and/or have ridiculously long commutes to campus nearly every day of the week. Some of you have had major personal crises that have unexpectedly affected your performance in your classes this semester. Some of you can gather no more than three or four measly hours of sleep each night, night after night after night. I know who you are, and I thank you for the hard work you've given me this semester; it touches me that you value our class enough to make it such a high priority.

But you know what? Almost without exception, these are not the people who cheat. Why this is, I don't know. Perhaps respect is born of their work ethic, perhaps they simply don't enough time to orchestrate the dishonest maneuvers cheating would require. For one reason or another, these folks, who at the semester's busy end are likely the most desperate people in the class, aren't typically the ones who cheat.

As I said above, the cheaters are also being inconsiderate.

I'm using the term in its somewhat literal sense: they're simply not considering the effects their actions will have on others. I cannot believe that they would act as they have if they'd thought about how strongly it would effect me.

Or so I think.

And so it goes.

So where do we go from here?

To those of you who cheated on the final exam through undisguiseable collaboration: you will be receiving a zero on the exam. If you feel this penalty is a bit harsh, please refer to Section 2.1 of the Student Handbook, dealing with "academic honesty": I would be well within my rights if I were to fail you for the course and report you to the Student Affairs Office.

And so it goes.

So.

So yesterday wasn't all bad, in spite of those late-evening grading revelations (and no, I'm not yet done grading. I didn't want my choler to color the remainder of my job, so I've put it off until after I'll have written this cathartic post, at which time I'll set to the task once more with renewed alacrity!), and in spite of a somewhat disappointing mid-morning meeting on grant-related stuff about which it would be inappropriate to say more (actually, I lie: the meeting was a productive and pleasant one, I just wish we'd had it three months ago!), I had a good day yesterday.

I shared a group hug with Quincy, Olivia, and Davina, three of my tip-top 280 students, in the Math Lab. I have had a blast working with those three, truly with everyone in the class, this semester. I've got one more meeting with them, on Monday.

Early in the morning Sieglinde came by to drop off her Calc final. She was touched by the e-mail I'd sent her letting her know how happy it makes me that she's happy she's chosen a Math major. She'll be a great student. We met for a half hour or so on Thursday, at which time I gave her a crash course on graceful graph labelings, enough to get her started over break in thinking about the gracefulness of lobsters and other closely-related graphs.

I gave a similar problem to Trixie yesterday afternoon. On Thursday Maggie and I had lunch with five of the folks who'd helped with Super Saturday this semester, in order to show my gratitude for their efforts. Trixie was among them. Half-(but only half-)jokingly she told me she was going to miss not having any math to do over break, so I promised her I could give her something to think about. "Not calculus," I said. "Real math." She agreed to consider it, so I spent an hour or so yesterday morning typing up much of the information I'd given to Sieglinde in person the day before, indicating a related problem Trixie could work on, dealing with asterisks instead of lobsters.

As she left I put the notes in Trixie's hands. "I'm excited," she said, "I don't know why."

"Because, one, you like math," I told her, "whether you admit it or not. And two, you're good at it, whether you know it or not. And three, you, maybe not over break, maybe not by the end of this coming semester, but likely within the next year or two, if you get started now and work hard at this stuff, you, Trixie Muddleston, have a chance to discover new, original mathematical results."

"That's exciting," she said.

"I know! And that's why you're excited!"

I've got her, I hope. I've got her hooked.

After all, if I care about it, so will they.

If I'm excited, they'll be excited too.

To all beginning teachers out there: be conscious, confident, and competent, to be sure, but above all else, be passionate, and show your students that you truly care about what you do. There's no better way to do this than to get them involved in your own efforts, to give them a spot on the team. The sooner this is done, the better for them.

"But freshmen?" the traditionalists cry. "Some of them can barely add, and they butcher the Product Rule, can't expand a binomial to save their mothers' lives! What business have they got working on research?"

Here's something I've noticed: many of the students who did well at math in high school and who in their first year of college elect to pursue a Math major truly have no idea what math is really about. They're toeing up to the starting line without even knowing how to run the race.

How do they get themselves into this? Many of them believe math is little more than an extended elaboration of the almost entirely mechanical classes they went through in high school. (True quote from a first-year Math major, earlier this semester: "I'm going to be a math major. I love derivatives!") They're wholly unaware that doing math well takes more than attention to detail and carefulness in computations, that in addition it demands creativity, originality, analytical perspicacity. They're unaware that math is an art as much as it is a science, that at heart most active math researchers are no less artists than are poets, painters, and concert violinists. Though they may know that math has to do with physics and engineering, and perhaps even chemistry, they're unaware that math shares intimate bonds with biology, sociology, economics, and philosophy. They're unable to see past the numbers and plusses and minuses, to see the abstract patterns and structures that underlie it all.

Sometimes by the time they've finished off a year or two of a college mathematics curriculum (and have thereby learned a bit more about what math is about), they've discovered they're in over their heads, they don't particularly like what they're doing, they're not very good at it, but if they want to finish their degree in time, there's no time to change majors.

They've no means to see past the numbers, for the numbers are, for the most part, all they've ever known. How on Earth can you convey to a first-year college student the depth and breadth of mathematics without letting them involve themselves in its enterprise? And the sooner, the better: they'll thereby learn early on what math is about, and they'll grow stronger at it.

I'd like to put together a one-credit course titled something along the lines of "Mathematics: a Survey," whose content would comprise an overview of the mathematics discipline: what are the major branches of mathematics, how did they evolve, how do they relate to one another, how do they touch on other fields of study? It would introduce the idea of mathematics as an extended exercise in abstraction and pattern recognition, of deduction and induction. It would also showcase some of the beauty of mathematics, and so might make an effective article of propaganda. It would have no prereqs, and would be recommended to anyone majoring in or thinking about majoring in Math. "Take this course," one could tell one's students, "and it'll help you decide if math is really for you."

Anyway, I've been writing this for two and a half hours now. I'd best be getting back to grading. I'll check in later, perhaps, and follow up on some of those loose ends I keep meaning to tie up (Newton v. Leibniz, math poetry, and so forth).

For now, take care. To all of my students, even those desperate few: thank you for your work, thank you for your efforts. I look forward to working with you further.