Continued!

Lunch went well!

I need to stop hanging around with Quimby, he keeps making more work for me.

Short version: I'm now in dialogue with some folks over in psychology regarding work they're doing to put together a grant to get support for a lab they'd like to put together. There'd be a substantial human element to their program, involving, for instance, student researchers. Quimby thought that my experience with the REU would come in handy to them, and that their need for researchers might dovetail nicely into the ongoing STEM-related NSF grant we're all busily working away at over here...it's all good.

After lunch I got waylaid in the Math Lab by student after student...Calc I folks cleaning up their exams (good job on those so far!), 280 students making good progress on the homework and the take-home exam...a good group.

Topic for a future post: how in the hell do you manage blips and burps in group dynamics when students are working together? This is a cause for much consternation. When personalities clash, well...

...to be continued, again...

A few days late: what's up?

I promised another entry last Saturday, now that Saturday's come and gone, and beyond it another week, come and gone. Promises, promises...

Last Saturday brought my first Super Saturday of the season, in which I and three of my stalwart students spent an hour and a half (thanks Deidre, Belladonna, Sieglinde!) with seven little 9ish-year-old munchkins, teaching them the ins and outs of binary arithmetic, and how it can be used to make hard-to-break codes.

This lesson I used last semester with the Spring installment of Super Saturday. The kids then were on average a year or two older and a bit quicker out of the chute: I remember that it took only a few minutes to run through binary arithmetic, almost all of them had seen it before and knew all about it already. In this new group only one of the seven had seen it before, and he was willing enough to let the others catch up. We spent about a half hour learning to count by twos, and then another forty minutes or so running through an example of the code. Time ran out while they were working through their own examples, but I think most of them were getting the hang of it in the end.

Later that day...I finished grading for the weekend sometime in the middle of Saturday afternoon, and left teaching alone until Sunday night, when Griselda and I talked on the phone for about four hours, the bulk of our conversation, as usual, about our respective classes, colleagues, and institutions. She gave me an encouraging word regarding my plans for a Moore-method graph theory course next semester (verbatim: "Do it! Do it!"), as I'd asked her to do several times by e-mail.

Then came Monday, ushering in a hellish week of work, work, work. I was able to get ahead in my class prep on Monday morning, whipping together several note sets, worksheets, and handouts for both of my courses. I got everything set through to this coming Monday in 280 and through Wednesday in Calc I, freeing me to work on other things, like grading 280 homework sets and papers (oh, by the way, here's a link to a compilation I made of what I felt were the most insightful comments in their Professional Proof Analysis papers), helping out with Who Wants to be a Math Major?, putting on Part II of my Research Seminar talk, meeting with several advisees, putting some finishing touches on the grant proposal I'd be bringing with me to Fayetteville for the NSF Day held there on Friday, getting exams ready for my Calc kids' Thursday thrill, touching base with all three of my independent study students, and hauling ass eastward for a less-than-24-hour whirlwind tour of the drizzly and depressingly drab city of Fayetteville. Tons of ideas took shape there, and on the way my highly experienced colleague Quimby giving me plenty of food for thought. On the road there and back, he was able to help me sort out and solidify several promising ideas for future initiatives in both teaching and research. I was also able to meet up with folks at nearby colleges whom I'd not met before. Here's a big fat CoB shout out to Winslow and Queshia, and to Bonnie!

Last night I staggered, overdressed, into Robinson Hall at the ungodly hour of 10:00 p.m., having spent little more than 24 hours away and not having been home since the morning before. Strangely enough, the third floor hall lights were on, the Math Lab door was open. My 280 students Quincy and Olivia were there, working away on their homework from my class. (It's no wonder they're doing so well...) After calling Maggie to bring the chariot round and pick me up, I unlocked the installation blocker on one of the Math Lab computers and downloaded a workable LaTeX editor for Olivia, something I'd promised to do for her long ago. She was, to understate the matter, happy.

Super Saturday returned this morning, six kids, four student helpers, all from the second section of my Calc class. For an hour and a half we worked away on fractals. After an easy definition and a few simple examples, I brought out the by-now-beloved L-tiles. The elementary-school kids were ecstatic when they beat the college kids in creating the L₂ from four L₁s, and it took little more time before both teams worked together to build first several separate L₄s, and from these an L₈. Next came a music video built upon the Mandelbrot set and a round of free-form fractal building, finished off with a level-2 Sierpinski pyramid. I think we all had fun this morning, but I was most heartened by the turnaround shown by the class's youngest child: Boudica began the morning too terrified to even sit next to the class's other young girl, and she spent much of the period working by herself. While working on her own fractal, she sat next to my Calc I student Henrietta, a warm and friendly young woman (whom I've been lobbying heavily regarding a math major...she's clearly passionate about the subject) who was able to put Boudica at ease. By the time her parents came to pick her up, she was hell-bent on putting together a few more components for our communal pyramid, and Boudica didn't want to leave. "I want to come back next week," she said. "This is awesome!"

I spent the next hour doing a bit of grading, and after lunch with Maggie at Noi's Thai Kitchen (mmmmm...spring rolls...), I got a couple more hours in. And (you'll be amazed by this!) after dinner came...more grading! I'm finally done grading all of the Calc kids' exams, and about a third of the way through the homework.

Whew.

Damn.

I'm tired.

The last couple weeks have both been 90-hour weeks.

And you know what?

I'm pissed.

Weeeeeeell...not pissed. Just disappointed.

Why's that? Let me answer with a question.

What's up, Calcsters? What happened?

Let's just look at the numbers: the course average (both sections) on Thursday's exam was just a hair under 68%. While 9 out of 54 people taking the exam got As (including a 99 and, yes, a single 100) and another 8 got Bs, there were also nearly as many Fs. There weren't many low Fs, but a few too many Fs overall to let me sleep easily tonight. The performance was perceptibly bad: on Thursday afternoon, Neville, easily one of my first section's best students, offered me a humble apology as he handed in his homework. I nearly melted.

"I wanted to apologize for my performance on this morning's test."

"Neville, it's okay. We all have our off days."

"I just know I did really bad. I've never done that bad on a math test before."

"Did you feel that it was too hard of an exam?"

"No! That's the thing! I knew how to do all of the problems, I just looked at it and went blank."

"Even so, there's no need to apologize."

"I just didn't want you to think any less of me."

"If there's one thing a good teacher can't afford to do, it's let his students' performance affect the way he feels about them personally."

So I ask again, what happened? I agree with Neville: I don't think the exam was too hard. It was hard, to be sure, but not too hard. Moreover, it was very similar to the practice exam, and some of the exam problems people did worst on are ones dealing with topics through which we spent a great deal of time working (like related rates).

As I started grading the homework just a few hours ago, I got a clue as to what might have gone wrong: it's clear that nearly none of the students did any of this most recent homework set before taking the exam. Though I assigned the related rates problem set early last week, early enough so that I was able to offer those who wanted it the opportunity to turn in the homework a week early and get feedback on it for study purposes, most of the students didn't get started on it and the two accompanying homework sets (exponential and logarithmic models, and linear density) until the wee hours in the lead-up to the exam, or later still, after the exam was over.

I really hate to use this word this term, y'all, but there's one word for that sort of academic behavior, and that word is stupid.

Settle down, settle down: I'm not calling you stupid, I'm just saying you made a stupid move. There's just no other way to put it.

You simply cannot expect to well on a difficult exam if you've not done the homework for the sections with which the exam deals by the time you've taken the exam. (One or two of the brighter students might be able to get away with this kind of crap, but they're living on the edge. Don't follow their reckless example.)

I'm feeling disappointed right now. I'm feeling disappointed, helpless, and, to be frank, a little hurt.

Disappointed: you're smart kids. You wouldn't be here if you weren't. UNCA's a tough school to get in to. You're the cream of the crop, in many ways. You're smart cookies. Every last one of you has the potential to do well in my class, and I'm disappointed that many of you are clearly not doing what's needed to wrestle down and master some of the concepts we're dealing with in this class. You can do it, that's what frustrates me: you can do it, but you're choosing not to.

Helpless: what else can I do? I sometimes feel like I've done all that I can. I work my rear end off each week, forcing me to ask myself whether I need to invoke the tired old aphorism and work smarter, not harder...but how so? I pride myself in my ability to blend traditional teaching methods with more innovative ones; what better way to make most effective use of the time given to me? I troll the Math Lab, helping out any students I come across in my travels. I offer up nearly endless office hours, my open-door policy allows students to drop in and chat just about whenever they want to. I put together practice exams and solutions, similar, as I always say, to the actual exams in length, content, and format. I give review sessions, in some of which are solved problems that will appear verbatim on the next day's test. I do a lot, and moreover, a bit immodestly, I must say that I think I do it well. Some might say very well.

Mother of Claude, what more can I do?

Thus, helpless.

Hurt: why? As I told Neville, it's unwise for a teacher to let his students' performance affect the way he feels about them personally...moreover, I shouldn't let my students' performance affect the way I feel about myself. But I do, if only a little bit. I feel hurt because I fear a disheartening answer to the question, "do they just not care?" And I want so much for you to care. I want you to care, as much or more than I want you to succeed. I don't feel that I've succeeded in guiding you through my course unless you not only understand, but you also share at least some of the excitement that I feel for what I do. See, I very truly believe that mathematics is a beautiful thing, I care deeply about it, and I bring my enthusiasm about it with me to the classroom. My excitement isn't an act, it's genuine, and I hope that excitement rubs off on you, if only a little.

Where's that leave me? Where's that leave us?

Look, y'all: I know the score. As a rule, you're young, you're full of life. You're free, many of you for the first time in your lives. Most of you are being pulled in a zillion and a half different directions, and you're trying to figure your lives out. I understand that it's hard to manage your time, your space, your resources, in some fashion that allows you to finish everything you need to do in your day in time for you to plop your head restfully down on your pillow before the next morning comes.

Yeah, you've got a long list of things to do.

And guess what? My class, and the work it comes with, are on that list.

You signed up for it, you've fought through the semester this far, we've got about five weeks left. Let's stick with it, all right?

So where do we go from here? Here's a short to-do list:

1. Do the exam revisions. Seriously. Do them. Even for those of you who scored in the 40s, it shouldn't take you more than a couple of hours. Sit down, get out your book, find yourself a quiet hour or two in the library or your dorm room or your apartment, and do the revisions. Do them neatly, fully, correctly. If you all can manage half credit back, you can bring the class average on the exam back up to a more-than-respectable-in-fact-pretty-damned-good 84%. As you do the revisions, try to understand how you messed up when you did. Keep in mind that I allow revisions not because I want you to get a high score on the exam (that's a happy bonus), but because I feel that your understanding of the ideas we've talked about comes before everything else. That being the case, I want you to take this chance to grapple with the concepts that may have eluded you before.

2. I've said it before, I'll now say it again, and I hope that maybe with those pretty sad-lookin' exam grades standing right behind me, you'll all take me seriously this time: do the homework. Seriously. Do it. Get started on it early. "Early" does not mean "on the evening before the homework is due." Rather, "early" means "right when the homework is assigned." That night. Set aside a half hour or an hour to get started. Don't feel the need to do it all at once, unless you find yourself having fun and cruising right through it. Do a few problems, enough to get the hang of what you're doing. If you get stuck, get as far as you can, write down whatever ideas you've got for solving the problem, and move on. Make a note of your difficulties so you can catch me after class with them, or bring them to me or to the Math Lab folks later on. Work on the homework a little at a time. Don't get frustrated. If it's just no fun anymore, put it down for a few hours and come back to it later. I don't assign all that much of it; almost without exception the work I give you in any week should be doable within three or four hours all told, and if you spread that out over the week you shouldn't have more than a half hour or an hour a day.

Hey, if you want to be where the action is, go to the Math Lab, hang out there, do your work there. You'll find a lot of your friends in the Math Lab: a lot of you already come and spend a good deal of time there, so you won't be alone. There's absolutely no stigma attached to hanging out there. It's a free service, they've got cheap coffee, cheap tea, and often a ready supply of free food. Smart people roam the Math Lab. They're paid to help you. It's a good place to be.

All that I ask is that if you make use of some of the Math Lab's resources, like the solutions manuals, don't abuse them. That is, don't allow yourself to become fully reliant on them, don't use them as crutches. A few of you, I can tell, "complete" your homework by copying the solutions from this book. You might not mean to, you may have every intention of doing the work yourself. But you come on in, you camp out in front of the manual, and you start to work. Here's how it might go:

"Okay, let's get started! Problem number 17...all right, here we go. Okay, I know how to get this started...there's f(x)=sin(x)...okay, now let's see...hmmm...what's next?...[15 seconds later]...I'm stuck...let me just peek real quick here...oh, yeah! Duh! Okay...now...yeah. Hmmm...I know this...[10 seconds later]...just another peek. Zomg! I knew that! I'm almost done now, I can do this in my head...write it down...and...there! Okay, let me just check my answer...[peeks]...wait, how'd they get that?...oh, yeah, I see...[erases]...that's what I meant. Duh. Okay, next one, number 22..."

How can you effectively make use of the manual? Use it only to check your final answer. If you didn't get the right answer, walk away from the manual and see if you can find your mistake yourself: look back over your work. Does the problem present itself? It might. Many errors are easy to catch yourself. If you can't find anything wrong, flag down the Math Lab assistant, elbow your friend working next to you, or come across the hall to my office. Ask someone else to take a look; generally another set of eyes, even if it belongs to someone less mathematically adept than you are, will do a good job of spotting something amiss. If you find a mistake, revise. Give it another go. Only go back to the solutions manual once you've got a revised answer.

By the way, I can tell if you're relying too heavily on the solutions manual when you complete your homework. (I'm not a fool, however well I play one in the classroom.) If you're addicted to the manual, you're only hurting yourself, since it'll nearly always kick you in the pants come exam-time. Here's a tip: a high percentage (over half) of the people who are nailing the exams to the wall ("nailing" being defined as "getting As"), including the one person who's received the highest scores on both of the exams so far, are doing sub-optimally on the homework. They're not doing horribly, but they're not doing perfectly either.

You wanna know why that is? Because they're actually doing the work. They're actually (horrors!) making mistakes. Because even though they're really smart, they're also really human. They're making honest mistakes, and they're giving themselves the chance to learn from their mistakes. Their homework isn't perfect because they're legitimately trying, and not just copying the answers from a book, however innocently that act of copying might be.

And by the way, if I sound cliché in offering up all of this tired old advice, I apologize. I'm only shoveling all of this shit because it happens to be true. Believe me, I don't wanna sound like an old-fart fogey, any more than you want to hear me sitting here lecturing you. I wouldn't say any of this if it weren't true, and if I didn't care.

3. Come and see me if you're having difficulties. I'm not a scary guy, I'm probably one of the most approachable professors on campus. (I'm a bit of a nerd, but I can't really help that. At least I recognize that fact, and I revel in my nerdiness.) Don't worry, I don't hate you because you're doing poorly. I don't hate you at all. As I'm fond of saying, I've had two students out of the thousand or so I've taught over the past decade whom I really just couldn't stand. And you are neither of them.

I don't hate you, I'm not mad at you. I might feel bad for you, that you've gotten a rough start, that you've slipped so far behind. Whatever position you're in, whether you're one of the best students in the class who's having a momentary lapse of reason or one of the weakest students in the class who's struggling mightily to just keep up, I'm ready, willing, and I hope able to help you. It's my job. It's what I get paid to do. More than that, it's what I'm most passionate about in life. Funny, isn't it? It's funny that you've got someone sitting there nearly 60 hours a week who gets all fired up about the possibility that you'll traipse into his office and ask him for help? Funny.

4. In class, take notes (please don't think I don't notice you when you're not doing so, and don't think I don't see the correlation between not taking notes and doing poorly on the exams...as I said before, I'm not a fool, and I'm probably one of the most observant people you've ever met), ask questions, and if I ask you to take part in a group activity, please take part in that activity. Some of the group activities seem corny, I know. (Just wait for the Mean Value Theorem exercises coming up this week!) I'm a bit of a cornball, it comes with the nerdiness. But cornballery can be fun if you just let yourself be taken away by the cornballitude. What's more: I've spent thousands of hours designing my classroom activities, and I don't do anything in the classroom unless I think it serves a useful purpose, so nothing's ever corny for the sake of corniness. Please keep in mind that my primary goal is to help you understand what we're talking about on any given day, and I'll do anything I damned well can to meet that goal. I'd really appreciate your cooperation in this endeavor.

You know what? I'm feeling less disappointed than I was, less hurt, and less helpless. I feel like I've actually done something, I've managed to unburden myself. Writing this entry, though it's cost me another three hours, has really helped me work through this issue.

I'll finish grading your homework tomorrow, folks, and I promise that I'll be in a better mood. I'm there already, in fact, as the end of this leviathan post draws into sight.

We've got four or five weeks left in the class, and a fair chunk of hard work ahead of us. I won't promise that it'll be easy, but if you stay with me and you keep on top of the work, I promise you'll make it through alive.

So how 'bout it, huh? Are you ready?

I'm ready.

Let's do it.

Pre-summer reading and subsequent ruminations

My summer reading has begun with a bang.

I've been working my way through a book my colleague Tip lent to me, Radical equations: civil rights from Mississippi to the Algebra Project, by Robert P. Moses and Charles E. Cobb, Jr. (Boston: Beacon Press, 2001). Tip met up with Bob Moses, a noted civil rights leader, Harvard-trained mathematician, and founder of a grassroots math program (the aforementioned Algebra Project) targeting middle-grades mathematics students on the fringe, at the Mathematics and Social Justice Conference Tip attended in Brooklyn a month or so ago. Clearly Tip's thought deeply about the ideas in this book, especially as regards his nascent community-building math program and the NSF grant proposal he and I are soon to set about writing, and he was kind enough to lend his (signed!) copy of the book to me.

I'm about three fourths of the way through the book right now, and though I've found much of the text itself dry and unengaging (particularly when it gets bogged down in the toledoth of Moses's project's converted teachers; at some points it reads like a biblical genealogy: "and Norma Jean begat Shannon, who begat Tom, the Explainer-to-Children. Tom taught twenty years, and then begat Sylvia. From the Delta did Sylvia come, and her students were good in the eyes of the Sunflower County Board of Education..."), one or two of its ideas have really struck me. I've been won over in one respect in particular. To best describe my conversion, I ought to mention a conversation I had with a colleague at a school I recently (in January) visited.

We were talking of undergraduate math majors; I had mentioned that at UNCA we have something on the order of 80-90 majors at any given time, and my colleague was thoroughly impressed. He said that at his school (a school nearly twice as large as UNCA), there were perhaps half as many undergraduate majors. Ever wanting to be helpful, I made some comment along the lines of "I've got some ideas that might help you to bring those numbers up."

My friend's response was something like "I don't think we're looking to do that."

I was taken aback. Not only had I not scored a point on this man's scoreboard (he and I share a long history, and I've never wanted to let him down), but my view that more young people should be helped to embrace mathematics had been met with hostility. This man had no interest in bringing math to the masses; he preferred to let it stay the closely-guarded territory of the few and the proud.

Moses's book has helped me to make out this not-so-well-hidden trap many professional mathematicians fall into: too often we think of math as a religion, a cult of worship into which only a select few are to be inducted, and in which only an even smaller few are allowed to become high priests. We take pride in our weeding out of the undesirables, defined as anyone who doesn't have a natural knack for math, who comes pre-programmed with a love of abstraction and analysis.

I've seen our culling at work at several levels, more clearly at some institutions than at others, and I'm ashamed to say that I've even taken part in it, though unwittingly. Math professors have a tendency to emphasis the arcanity of their field, its abstruseness, its disconnect with reality. Many of us take pride in the difficulty of our field, and make every attempt to show off our own intellects by making math seem imponderable, impenetrable, dense. I saw this most clearly at Illinois, where research mathematicians would show open disdain for all but the brightest undergraduates in their classes ("most of them are dullards, I've got a few who might prove capable"), lending a hand to the top 5% while leaving the others to drown; "they're just not cut out for it."

For too long mathematicians (and scientists of other stripes) have tried to fill their ranks from the lists of the best and brightest of the American studentry (to borrow a wonderful turn of phrase from William Strunk), leaving the dregs to find work elsewhere when they prove themselves incapable of meeting the high standards set for practitioners of math research. This leaves the untouchables, consisting primarily, in this nation, of poorly (read: publicly) educated blacks, latinos, and poor whites, out in the cold.

Moses makes clear that there's something wrong here.

What's called for, in his mind, is a radically different paradigm: rather than drawing from the few whom opportunity and natural talent have buoyed to the top, we ought instead be working to ensure that everyone is given the chance to rise to the surface. With a system wherein all are given the tools needed to excel mathematically, everyone benefits: traditionally underrepresented groups obtain the opportunities they need to succeed academically, and academicians expand broadly the talent pool from which they will one day choose their colleagues and successors. This "bring 'em on, all of 'em," attitude is the core of the Algebra Project, a program committed to making sure that every 6th, 7th, and 8th grader is given the background needed to successfully navigate a college-prep math sequence in high school. As Moses sees it, not everyone will go to college, and while there, not everyone who goes will study mathematics, but everyone should be ready to do so.

It just makes sense.

Moses's work has definitely helped me to come around to this point of view. It's never been so clear to me that I as a mathematician have a good deal of work to do to ensure that I'm doing what I can to grant everyone the chance to experience mathematics, and to succeed at it. Work needs done at all levels, K-12, undergraduate, and higher. And the work done at each stage needs to be interwoven with work done at other stages: vertical integration is called for. I hope Tip and I will be able to capture that spirit effectively in the proposal we put together this summer.

I've also begun the book the Project NExT reading circle has chosen as its first focus of discussion, Ken Bain's What the best teachers do (Cambridge: Harvard University Press, 2004). I'm (we're) one chapter in, and so far I'm unimpressed. It strikes me as a poorly-assembled pile of truisms and platitudes, absent the concreteness and careful analysis of a seasoned student of the scholarship of teaching and learning (SoTL). Not that every SoTL text has to build up a rock-solid wall of data and facts, or deluge the reader with a statistical breakdown of every study on teaching efficacy performed since 1970...but this book just seems "lightweight" to me. So far it's a great "rah-rah" feel-good page-turner, but its place might be on the nightstand of a newbie college prof just out of grad school who needs a little cheerleading and from-the-sidelines inspiration. I wasn't a huge fan of Maryellen Weimer's book, but I found it far more useful and engaging than Bain's, at least to date.

I ought also say a word or two about preplanning I've begun for Fall's classes. Francine's agreed to help me go through the notes and homework problems we used in 280 this past semester, retooling them, getting them good. I've already written a couple new in-class exercises dealing with writing mathematics.

The one I'm happiest about was inspired by a conversation I had with my colleague Lulabelle from the Sociology Department (I'm on a team of folks helping her out with a pilot assessment program for writing across the curriculum). She indicated that as a part of the work that'd need doing for this grant we're collaborating on, I'd have to to be able to train my colleagues how to "read" mathematics. I got to thinking about how I would best do this, and realized that it's likely easiest simply to highlight the linguistic analogues mathematics shares with "natural" human languages: syntax, grammar, orthography. Not only would an exercise indicating these analogues help my colleagues; it would help my 280 students, too.

The exercise consists of a take-home portion and an in-class portion. Each part comprises three written passages of varying levels of quality; the take-home passages are in "English" and discuss the chemical element boron. Students (and my colleagues) should have no trouble in ranking these passages from worst to best, and in explaining their reasoning for the ranking. The in-class passages are in "math," each giving a "proof" of the fact that the sum of two odd numbers is even. Having given them the chance to warm up in "English," I now ask the students to rank the proofs from worst to best, and to justify their rankings. This is a more difficult task, but once it's done my students (and colleagues) should be able to see more clearly that good writing in math is only a half-step away from good writing in any other discipline.

Okay, I've prattled on long enough. I'll end this for now. As usual, feel free to check in with your comments, always appreciated!