Reading day

One course down, two to go.

Abstract Algebra II is now wrapped up, all grades successfully submitted by noon today. Overall the students did very well, which is hardly a surprise since the class had a number of our best and brightest and most senior students, five of whom are leaving us after commencement in a few weeks.

So far the questions from students in the other two courses (both sets of students are dealing with take-home exams) have come in a steady trickle.

Yup, two take-home exams.

I was a bit reluctant to make the Calc I exam a take-home exam, after the debacle from Fall 2007, but I decided that what I perceive to be the benefits of granting the students a take-home far outweigh the negative aspects, including the risk that one or more students might again decide to cheat.

1. By affording the students time for meaningful reflection on the concepts learned in class, take-home exams offer a further formative learning opportunity rather than simply a summative assessment of a student's ultimate performance.

2. By eliminating the largely artificial "high-pressure, high-stakes" environment of an in-class test, take-home exams are more apt to measure more clearly students' understanding of (or at least ability to recover and synthesize deep ideas involving) the course's subject matter than simply aptitude in test-taking.

3. As hinted in the previous point, take-home exams more closely approximate "real-world" settings in which students will eventually find their skills tested, in which they will generally have access to resources (books, notes, mentors, and, yes, the outlawed-even-on-take-home-exams colleagues!) in order to better to meet the challenges with which they're faced.

We'll see how it turns out. I did give a little bit of a lecture when I distributed the exam sheets a few days ago, an uncharacteristically stern admonition at the outset, hoping to instill in the students the gravity of the trust I'm placing in them.

I've received one student's exam so far, but I've not had a chance to look over it. We'll see.

For now, I'm working away, one day at a time.

Tomorrow: donuts and derivatives, and a meeting about writing assessment. Oh boy!

Not ones to disappoint

The 462 presentations were solid.

Though they too have yet to get so far in their careers as to overcome the butterflies that bubble up when one's at the front of a darkened room, all six students whose task it was to speak today did very well. One of the presentations was the tiniest bit rigid, another could have stood slightly stronger preparation, and another seemed a little hurried as the speakers tried to fit in all that they had to say, but the slips were only of the slightest kind, and overall the talks were of the quality you'd expect from this set of mostly seniors. It'll probably be a bunch of As, all around.

For my part, I feel I did better in providing the students (both those in 280 and those in Abstract) with the scaffolding they needed to construct their talks this time around. Next semester I hope to be more intentional still in preparing my students for sharing their ideas with one another orally, both in the formal structured setting of end-of-semester presentations and in relatively informal day-to-day chit-chat sessions (both fora have their merits).

As another day draws to a close, I'll say farewell for now.

It's come to this, has it?

Three days of class remain.

A handful of homework sets, a few exams (most of them take-home), a couple dozen presentations.

There's not much left to do, not much left to say.

We're here now.

It seems like only now some of the lessons I've tried to teach all semester have begun to sink in.

"If you write what you know and what you need, you're halfway...if not further...to a full and valid proof."

I don't just say that to hear it be said. I say it because it's true.

And I think they're finally starting to believe me.

What else? Open my mouth, what other jewels fall out?

"You get out of a class more or less what you put into it."

"The folks who do well on the homework sets are the ones who get started on it right away."

Do I sound a million years old, or what? Who am I to speak?

Was there ever a time when I didn't know how to do a derivative, let alone compute a Galois group? And it's hard to remember that induction isn't a naturally occurring process, that we have to train our brains to mold themselves around its artificial angles and uncomfortable corners.

"...By inductive hypothesis we know that Γ(n+1)=n!..."

By now, nothing could be clearer.

I wonder if those same students who nodded casual assent as we plowed through today's inductive proof would recognize the confusion they themselves faced just two months back when first confronted with that arcane mathematical method. The way's been long and sinuous, and even knowing where it twists and turns it's easy to fall off to its side.

Who knows what takes us to where we are now in our lives?

I used to like to exercise my mind in what I called the "Causality Game": think about a major life event you've undergone, and trace it back, step by step, to its earliest observable genesis: n-1 begat n, n-2 begat n-1, n-3 begat n-2, and so forth and so on and so forth...at a certain point the exercise is absurd, a diagnosis of butterfly burps and other unanalyzable initial conditions.

In the middle of a panel discussion at the WAC/CAC Symposium at UNC Greensboro a week and a half ago I caught myself playing the Causality Game, if only for a minute or so. "What in the world has brought me here?" I asked myself. I was sitting in the center of a room filled mostly with rhetoricians and composition specialists, the people in front of me backed by a graceful arc of windows filled with bright blue sky and overlooking a lush and verdant campusscape. It was a gorgeous day outside.

I took mental stock.

"I'm 34 years old," I thought, "and I'm a mathematician. I feel strongly about more than math: writing matters, too. I care enough about writing to be here, to be in this room. In fact I'm surrounded by teachers of writing, and they're talking about writing. They're talking about assessing writing. Someone's just asked a question. What did she ask?"

It wasn't a question, it was a comment. It was a divisive comment, meant to be divisive. For an hour or more (before lunch, at which time the combatants no doubt held parley) it was Duke and Wake and Davidson versus all the rest of the room. Old habits die hard.

"What brought me here? What right have I?" I smiled to myself, I almost laughed out loud.

For a minute or so I clumsily fumbled with the knot that tied today to yesterday, trying to make sense of the tangled mess of words and numbers that sat upon my lap, and after a bit I said "ah fuck it" and let it drop.

Oughtn't I be happy enough knowing that I'm happy enough, and leave it at that? Who cares how I got here?

I watched the first episode of Carl Sagan's Cosmos yesterday on Hulu. It's been years since I've seen that, and seeing it again reminded me of just how strong an influence it had on me when I was a child. Sagan was a boyhood hero, and I can safely say that few individuals more strongly than he made me want to be a scientist of some kind. (My dad's about the only one that's got him beat.)

I just looked it up: Carl Sagan's been dead for over 12 years now. I'm glad that I had a chance to see him speak before he passed away.

Just that once.

He was as witty and wise as I knew he'd be.

And now he's gone. And now I'm here. And I've got now what I'd wanted then.

As I'm fond of saying, I'm blessed (there, I said it!) in that I get paid to do something I'm damned good at and that I love doing, so much so that I'd do it even if I didn't get paid. (This is good, because as of today I'm getting paid 0.5% less than last year to do what I do.)

What more could I want?

The wants are never-ending.

I want a roomful of peers and pupils who are in love with learning and who aren't afraid to share that love with each other.

I want unlimited time with which to elaborate every beautiful idea those folks can come up with.

I want unfettered, unfeigned, unrestricted, unlimited inquiry.

I want every who what when where why and how to be asked and answered.

I want to not be so goddamned tired when there's so much more to do, and I want the same for everyone around me.

I want...

...I want...

...I want this semester to be over.

Summer's nearly here, and as my wonderful friend Bedelia hinted on her Facebook page a few days back, next semester's already calling on us to atone for this term's teacherly sins with a drawn-out dunk in the salvific waters of early classroom preparation.

Hallelujah.

One and a half more weeks. It's been a hell of a ride, folks.

Take one last deep breath, we're almost there.

It's come to this, has it? Ever wonder what got you here?

Wonder away.

Field extensions photo

Here's a shot of the Venn diagram we made for yesterday's exercise (my apologies for the crappy quality of my cell phone's camera):



As we decided in class, the sets of pure, radical, finite/algebraic, and arbitrary extensions make up a rough map of the inner solar system, while the normal field extensions act as a short-period comet orbiting the rational sun on an elliptical orbit pointing to the upper left corner of the picture. (The field of complex numbers, clearly visible in the upper left, marks the comet's aphelion.)

It's such a perfect day

Well...perfect might be a stretch, but it was a good one, capping off a great week. The jewel in the crown of today's classroom antics shone brightly in the afternoon sun.

As soon as I reached campus at 8:30 I began fielding questions regarding the second of two homework problems I'd assigned to my Abstract II students for today; Quincy caught me as I walked in the door to the department with a couple of questions. A few hours later he was at it again in the Math Lab, and Derrick, Nadia, Hermann, Opal, and Katya all had difficulties too. Clearly the question (to which I openly admitted I knew not all the answers) was proving rougher than I'd thought it would.

The problem is simple to state: starting with the field of rationals, describe the various intercontainments of the following sorts of extensions that field: all extensions, finite extensions, algebraic extensions, normal extensions, pure extensions, and radical extensions. (Each containment or failure of containment had to be justified by proof or example.)

Between five or six of us, by 2:30 (class begins at 2:45) we'd catalogued examples and proofs verifying all but a couple of the containments/noncontainments we needed to show, but it was clear that the best course of action was to bring it up together in class.

That we did, and our team solution was an exciting one.

Several of the containments were easy and indisputable: pure extensions are radical, radical extensions are finite, finite extensions and algebraic extensions are one and the same. What wasn't clear was how normal extensions fit into the picture. It took us about half an hour of field wrangling before we'd found all of the examples we'd needed, constructing a convoluted splitting field here, a two-step radical tower there.

We were done.

Or so most of us thought.

Miguel had the temerity to ask about the exact location of the complex numbers in the scheme we'd laid out.

After a Moonlightingesque (kids, ask your parents) three minutes of high-level mathematical crosstalk, we remembered that the equivalence of two characterizations of normal extensions only holds for finite extensions (of which the complex numbers are not one), and therefore we were definitely allowed to call the complex numbers a normal extension of the rationals.

I realize that much of the above discussion will be over the heads of uninitiated, but I wanted to provide something close to a blow-by-blow account in order to highlight the phenomenal work of several of my students. Derrick, Nadia, Quincy, Miguel, Hermann, and Bertrand all contributed substantially to the conversation. The result was a true work of social mathematics, a finely-crafted piece of collaborative art.

Moreover, through our class today the students and I all gained a better understanding of the interrelationships of the manifold definitions we've encountered over the past few weeks; I can think of few fifty-minute periods this past semester that have been more mathematically or pedagogically satisfying. Though the exercise was definitely more challenging than I had intended it to be, it proved to be not insurmountably challenging, and the result of the solution was to solidify our fundamental understanding of several tricky concepts. This exercise is definitely a keeper, and I may just use it as a classroom activity that next time I teach this course (however long from now that will be).

I wonder if I might find similar exercises for my upcoming classes next fall? Or for the REU students this summer as they undertake a brutal and bruising survey of graph theory in the second week of June...?

Good day, sunshine

It's been a great week. Now that I'm over the semester's hump (for me the period of complete and utter insane busyness ended about a week ago), I'm relaxed enough to enjoy the day-to-day interaction with my students.

There's nothing like a Thursday for that kind of deal, and today was a wonderful one: I had several awesome meetings with students. A few just wanted me to vet homework solutions (way to go, Karlie! Your answer was spot on! Gorgeous!), others had meetings with me to talk about their upcoming presentations in 280 or 462 (Pascal's fractal and Ramsey numbers! This stuff is awesome, and your presentations are gonna rock!), and another met with me so we could talk turkey about undergraduate research into poset representation of graph coloring games. (Tish, you are so going to clean up on this one...)

I've been in a good mood all week. It doesn't hurt that we're doing awesome stuff in all three of my classes: Riemann sums in Calc I, sizes of infinity in 280, and Galois groups in 462...what's not to like?

It's cheesed me off a little bit that it's taken me roughly 13 weeks to really get into the groove with this semester...and now it's almost over.

Well, I've nearly managed to survive yet another term, and I don't mind saying this one's been brutal. The four-prep schedule (one new, one a rerun but with a new text, and a third, also a rerun, but with a substantial new component) has been a bear: in some weeks it took all that I had just to take care of the bare essentials for each of my classes. I hope my weariness has not shown itself too starkly.

Ah, well. Water under the bridge, I trust.

For now, let's enjoy the sunshine and the last week or so we've got together. This goes especially to my graduating seniors, with some of whom I've enjoyed as many as six classes over the past four years. Nadia and Sylvester top that list...I'm going to miss you guys! It won't be the same department without either of you around.

Two out of three ain't bad

I felt good about yesterday, for the most part. It's always a bit awkward getting back to work after a long weekend (like the one handed us by the Spring Undergraduate Research Symposium last Friday), but neither of my first two classes missed a beat.

As I said before and I'll say again, Newton v. Leibniz came off without a major hitch, and all participants were lively and engaged. Moreover, the 280 folks bounced back from their Homework Set 5 debacle and made real headway into the jungle of equivalence relations. I had a really good time in that class, and I feel a lot was learned.

But Abstract II felt a bit...forced?...flummoxed?...flat?...some other suitable and non-scatological f-word?

Maybe you're all tired, which I can definitely understand. Maybe you're all a bit overwhelmed by the notation and the terminology associated with quotients of polynomial rings and with finite fields, which is admittedly dense. Or maybe, as I suggested in class, it's a combination of spring fever and senioritis (if I'm counting right, 5 of the 13 are graduating in May, with three or four more to follow in December).

Whatever the reason, y'all looked yesterday as though someone had cranked gravity up by a factor of two.

Is there something I can do to get you guys unstuck from this rut?

I tried to slow things down a bit yesterday to make sure we were all on the same page with the current proof, but maybe that's not what's needed.

Maybe we need rather to gun the engine and red-line it down the highway for a class or two, to burn off some of the junk that's cluttered up the engine valves?

Or maybe we just need to have a stock-taking class where we look back over everything we've done and fit it all together?

Maybe we just need another day off, like the one this coming Friday offers while I'm out of town.

Or maybe I just need to bring in donuts again.

Unlike my "younger" classes, I know most of you MATH 462 people read this blog regularly, so I encourage you to comment: what can I do for you right now? Help me lead us out of this quotient-ring quagmire!

Ouch burn!

Jeez Louise.

In rereading my post from last night, I realize how embittered and cold I must have sounded to my students who've happened to peruse the post.

The note I'd hoped to strike was more akin to the one I sang in class today (well, yesterday, technically, but who's counting?)...more of a "please, please, on bended knees" sort of deal: please help me to help you, Jerry Maguire style.

I want you all to know that I'm frustrated, but it's not with you, it's with the inherent difficulty of the problems with which we're all dealing together, and with the frustration you're all feeling in meeting that difficulty head-on.

I guess what I'm trying to say is this: y'all are awesome people who are a genuine joy to work with, and I want to make the most of our time together. Whatever you need from me to make that "most" happen, let me know; I hope I've just done a good deal to let you know what I need from you.

Meanwhile, I have to say that I had a wonderful day this past day: all four classes offered up cool mathematical ideas, from optimization problems in Calc I to cool combinatorial trickery in 280, and from 480's highly successful peer review (folks, chime in in the comments section if you'd like to say something about how things went for you today) to philosophical meanderings and ethnomathematical thought experiments in Abstract II. For homework, try to think about what sort of intelligent alien creature it might be who would have no understanding of discrete quantities.

It was a magnificent day, and I thoroughly enjoyed spending it with all of you.

I hope tomorrow brings as much fun and fulfillment as the past 24 hours have.

With that note of confidence (and with the bulk of this damned NSF report finally behind me), I'm off to a belated beddie-bye. Avanti!

Right wrong turns

Sometimes it just all comes together, y'know? It helps having a class full of kids (and a few older folks) who are willing and able to put the responsibility for their learning on their own shoulders and run off with it, leaving me in the dust.

Several times during the past week I've found myself extemporizing in Abstract II as the students have asked questions the answers to which I had no idea. That's the satisfying/scary thing about teaching these high-end courses: on the one hand, the students are smart and savvy enough enough to ask really deep and interesting questions on the fly; on the other hand, the students are smart and savvy enough to ask really deep and interesting questions on the fly. It ain't Calc I in there: although I will never tire of the thrill of teaching calculus (Calc I folks: I'm not kidding when I say that I never get over the beauty of the definition of the derivative. That's not feigned excitement: I really am in awe of the limit definition, after all of these years, and I'll never get tired of seeing the hs magically disappear!), and though those first-year courses are often jam-packed with smart students, it's no more than once every few semesters that I find myself perplexed by a student's question in Calc I: there's just not enough that's unfamiliar, and the concepts are second nature to me by now.

But Abstract II? Wow. That class is a kaleidoscope, and whatever view we find on a given day seems to depend as much on the mood of the class as it does on the phase of the moon.

A couple of the questions that have come up lately in that course are pretty routine and standard ones I was able to respond to without skipping a beat: "If f(x) is irreducible in k₁[x] and k₂ is a subfield of k₁, then is f(x) irreducible in k₂[x]?" "What would an irreducible cubic polynomial in ℚ[x] look like?" (This last was in response to the proposition showing that the irreducible quadratic and cubic polynomials over any field k are precisely those with no roots in k.)

The really interesting stuff happened when I was momentarily fertumult.

"Why would you want to represent f(x) in 'base' b(x)?" asked Bertrand in class on Wednesday. He's always good for a truly probing question or two.

"Um..." For a moment I rethought my policy of encouraging students to ask good questions like why?

"Um...well...if we know that k is finite..." I hemmed and hawed for a few minutes and waved my arms around in an unconvincing fashion. A few muttered words seemed to make some sense, and reason returned, and I felt better as my mental wheels gained a bit of purchase. "...then if we've got a homomorphism φ:k[x] → k[x], φ is completely determined by its action on the finitely many polynomials of degree less than deg(b) and its action on b itself."

Whew!

I've not done so much tiptoeing as I've done with these kids since my first semester at the University of Illinois when they gave me a section of Accelerated Honors Calc III for engineers to teach...those kids were smart. It hadn't helped me that at the time I hadn't done vector integration since my second year of undergrad.

This past Monday's class was the funnest so far this week, and it came about because I'd been sloppy in setting up an example in my worksheet for that day. The exercise asked the students to come up with two quadratic polynomials in ℤ₈[x] which each exhibit more than one nontrivial factorization, thus demonstrating twice over that ℤ₈[x] is not a unique factorization domain.

One of my preplanned examples worked, the other was verkochte (I'd forgotten that in ℤ₈, -3 and 5 are identical, so the "distinct" factorizations I'd expected were one and the same). Did the students give up? No, no, no! Instead, after a few minutes of floundering about trying to fix the failed example I'd started with, we just set up the equation that would have to hold in order to yield two nontrivially distinct factorizations, and solved away. We soon had a whole passel (not a half of a passel, or even two-thirds of one) of examples.

That's a great class.

While I'm bragging on them for their self-directed successes, I should give props to Uri for coming up with the basis for a fantastic question for the first exam. Though several of the students, when asked last week as part of their homework to posit potential exam questions (with accompanying solution sketches), came up with appropriately difficult and interesting posers, it was Uri's question involving the advanced ring theoretic properties of the powerset ring that proved the most amenable to inclusion on the exam. It was just right.

Okay, off to read a few Project NExT-Southeast Fellow applications before I hit the hay.

Au revoir!

Breakthrough

Today's the day I'm going to want to remember in the waning weeks of the semester: in the closing classes of the term I nearly always find myself thinking "what could I have done better? Did I really reach them? Did they ever find that spark?"

This morning my Calc I class lit up like a powder keg. Though it's taken a little longer than I would have liked it to, I genuinely feel that at last I've got a sort of simpatico with these students: I get them, they get me, and we're both willing to work our asses off for each other.

(Incidentally, I apologize for the uncharacteristic potty-mouthery in the past couple of posts. It's just been that kind of week.)

What happened this morning? Things just clicked.

I think the restructuring of the homework, basing it on problems of my own devising instead of on the arcane and ethereal exercises offered by the textbook, has helped a lot. It's a no-brainer, really: only I can create the sort of exercises that challenge the students to grapple with the topics as we see them come up in class. Moreover, while the book's exercises are interesting and thoughtful ones, the lessons the exercises purport to teach are wasted if the density of the problem precludes the student's understanding of the lesson's import. For example, the problem that purports to show that the derivative of a quotient is not the quotient of the derivatives (the now-infamous #36 from Section 2.3) would do well to simply say that that's bloody well what it's trying to show, rather than coyly trying to trick students into that understanding. "That's what it's trying to show us?" said several students, one after another, after I'd shown them the point behind the problem. "Why didn't they just say so?" Understatement's all well and good for French cinema, but with first-year mathematics exercises you're often better off being as subtle as an atomic bomb.

Yes, the few extra minutes it takes me in preparing for each day's class are a small price to pay for the benefits that accrue. Several students have indicated that though the exercises I've made up are still challenging and enlightening, they make a hell of a lot more sense than the ones the book had dealt them.

Today's in-class activities also proved exciting. We went on a limit hunt along the lines of an exciting game of Battleships: Having shown that the ratio (a^h - 1)/h tends to roughly 0.693 when a = 2 as h tends to 0, and to something slightly more than 1.098 when a = 3, the students set about trying to find the value that would make the limiting value 1 on the dot, asking Mathematica to graph the ratio for increasingly precise values of a. Several times Hera literally jumped from her seat in excitement as the race to estimate e tightened (granted, she's an exciteable soul in the first place, but still...). The excitement was hardly hers alone: several others were visibly intrigued, and by the time it was revealed that the number we were seeking could never be numerically known, there were warm smiles of understanding on faces scattered throughout the room.

To the Calc I folks who may be reading this: thank you. Thank you for your feedback in leading me to the change in course on the homework, and thank you for the warm and supportive reception of the change once we made it. Thank you, too, for the willingness to work with me in class and to take an active role on in-class exercises. I got more out of class today than I have from any class in a long time, and that success is based largely on the cooperation you've shown in creating a healthy learning environment.

Meanwhile the students were a bit more subdued in Foundations, a class that mercilessly meets just after the lunch hour, in the valley of biorhythmic cycles that tend to pull people bedward. "I'm sorry I was so quiet in class today," Trixie told me later. "I'm quiet in all my classes, but I feel bad that you were getting mad at us for being so quiet."

"I wasn't mad," I said, "I was just trying to wake people up!"

I will credit 280's Nighthawk with the line that brought me the greatest joy today, though: "it's [this course's emphasis on clarity in writing is] bleeding over into my other courses." It would shock me not if Nighthawk's colleagues found him guilty of felonious brownnosery and bullshitting in the first degree, but the fact remains I was tickled by the comment.

Meanwhile, my twelve-member Abstract II class was cozy and familiar. Indeed, I remarked at one point, as I paused to find my place on our worksheet, on how they chatted with one another warmly like old friends. "You are old friends," I said. "You've been in many classes together by this point, and most of you know each other really well." Then I waxed a bit pre-nostalgic. "I've had many of you in several classes, too, and for some of you this will be the last class I'll ever see you in! Many of you will be graduating in a few months, and it's going to be a very different school without you."

"Oh no, I'm going to cry!" Nadia said, hiding her face behind her notebook.

Fortunately Euclid's Algorithm intervened and saved her from her tears.

All told, it was a good day. A mite busy (two hours of unceasing student deluge after Abstract II...can y'all make an effort to finish the homework with a liiiiiittle bit more of a margin than a few minutes before five?) as the day neared dusk, but a good day in the end.

And now it's time to end this day (14 minutes to go!). Tomorrow brings a batch of grading and a little bit more class prep for which I won't have time as I'm winging it to Washington next week...and I hope too tomorrow brings a happy Valentine's Day to one and all.

From a hopeless romantic to his faithful readers, my thanks for your words of wisdom, your help, and your support!

Committee report report

I've just picked a perilous path through the eye of the perfect storm of grading, fourteen and a half hours of toiling and troubling over computational exercises and low-stakes writing on derivatives from my Calc I kids, first-order logic problems and truth tables (not to mention first-time LaTeX exercises!) from my Foundations students, and a passel of problems on ring theory from my Abstract II class.

Fortunately the cold I came down with at the end of this last week made sure I didn't want to be anywhere else but home this weekend.

I've been meaning for some time now to say a bit about how the homework committees are going this semester, since so far I've been proud of their smooth functioning. (For the people reading this on my first-ever cross-post on the Young Mathematicians' Network, you can read a number of my older posts about using homework committees here. Briefly, it's a peer-review technique I use to encourage students to (1) begin their homework more promptly, (2) engage in self-authorship, (3) grow accustomed with the frequent multiplicity of correct solutions, and (4) develop their teamwork skills. Students volunteer to serve on committees tasked with reviewing and offering feedback on their peers' drafts of solutions to particular homework problems. After reviewing all submitted drafts they lead a brief class discussion on the problem they considered and return the drafts to their respective authors, who then have time to revise their work before submitting a final draft one class period later.)

There have been four reports in each of Foundations and Abstract II, and despite their relative inexperience with the genre, the former students' committee reports have been stronger than those of their Abstract II counterparts: they've skillfully avoided simply answering the problem placed before them (this was a major problem the first semester I asked students to serve on homework committees), they've intentionally made use of the course's writing stylesheet (the now-infamous Four Cs), and they've done a marvelous job of indicating common pitfalls, clever solutions, and helpful hints.

When the first homework set was handed in there was a little misunderstanding concerning exactly who received which draft of which problem, and as a consequence I was given a glimpse of the feedback the students were offering to one another on the drafts submitted to the committees. It was heartening: the few comments I saw were meaningful, respectful, and helpful without being too much so.

The quality of these students' committee work greatly exceeds that of the students in the first Foundations course in which I assigned committee problems. Back in "the day" the kids'd frequently just get up in front of the class and solve the given problem for their friends, resulting in a couple dozen nearly identical eventual submissions in which the students would faithfully render every jot and tittle (whether correct or not) of their colleagues' proffered solution. During the past couple of semesters I've very deliberately pointed out that it is not the job of the committee to perform this disservice.

Word's gotten out.

So, props.

In other news, I'm happy to see that I've received a few (not even anonymous!) replies from my students regarding Gil Strang's free text, Calculus. I might be misreading the message here, but it seems that though people are not yet ready to chuck the text through the nearest open window, it might not hurt to mix a few of my own exercises in with the relatively recondite ones offered at the end of Strang's sections?

I believe this is exactly what I shall begin doing.

Thank you all for your feedback, I appreciate your attention to improving our classroom environment! Together we'll make it to the semester's end.

More face time

"I don't know if you knew this," said one of my Abstract II students to me just moments ago, "but I'm planning on being a teacher."

"Excellent!"

"Yeah, so...the more face time as we can get in front of class, the better."

"Excellent!"

"I know I griped a lot about the way graph theory was taught, but that was right around the time I was beginning to think about teaching."

I hope more students appreciate Moore's method!

Day One, vol. 2

Ach, what a long day it's been.

I'd fully intended (honest!) to check in in between each of my classes, but that proved impossible. The only chance I might have had came between Calc I and 280 around noonish, but even then I was swamped with various course-related nonesuches.

Here it is, though, near the day's end, and I've come through alive. More than that: I feel that almost all of my classes came off splendidly.

Calc I, a colossal class with 35 students now enrolled, went particularly swimmingly. After Quentin did his spiel on the precalc review test on the Educo software he helped put together, I took over and led the students through the syllabus. After this we had twenty minutes or so during which the students brainstormed terms, concepts, and ideas from algebra, trig, and other areas of precalc, taking turns writing their brainchildren on the board. By the class's end I think even the more timorous students were beginning to feel at ease.

Two hours passed before I had to run to my abbreviated 280 class. I love teaching this course, but the first day is a difficult one: even with the full complement of 50 minutes, I generally feel overly rushed. With only 40 minutes it was a hopeless battle to try to get through the first day's activities. While the students typically finish crafting rough proofs of "even + odd = odd" with mere minutes to spare, there was no way in heaven, hell, or Earth they'd finish at all today; I made it part of their homework for Friday (along with responding to the "history exam responses") to put together some rudimentary verifications of E + O = O.

Sadly, I also felt as though I had nowhere near enough time to give the necessary details on LaTeX and the committee system. Bleh.

An hour passed, and then it was off to Abstract II. "I feel great walking into this classroom," I told them on my arrival, "this is the first class I've had all day where I don't have any new names or faces to remember, where I don't have to introduce myself, and where I can just feel free to be who I am, since you all already know I'm crazy." These folks know the drill: committees, playing cards, presentations, the whole nine yards. It took no more than three minutes to make it through the syllabus, and that left us with the better part of an hour in which to help each other recall the highlights of Abstract I. Much as in Calc I, we spent a bit of time brainstorming the concepts that underlie that first semester of algebra. That done, the students took turns building a concept map of the first course on the board. Their homework asks each of them to investigate a topic from Abstract I in greater detail and be ready to present their findings to the class on Friday.

Finally, it was time for 480.

That class is huge! We've got 20 people enrolled as of this morning, making it far and away the largest crop of Senior Seminar students we've had since I came here almost four years ago. After the introductory song and dance, I had these folks too do a bit of brainstorming, creating a table with two columns, one filled with properties of a good talk, the other with properties of a bad talk. It's a fun activity, and the students easily filled a page with good advice for presenters. Loopy as a broken loom at this point, I had a fun time acting out some of the "bad advice."

The bell couldn't have rung too soon, and 5:30 found me done for the day and tired as hell.

A refreshing run and a little over two hours later, I'm home, my belly full of homemade split pea soup over rice, the next few hours stretched lazily before me.

What shall I do?

Tomorrow, tomorrow, I love ya, tomorrow!

19 hours until my first class of the Spring 2009 semester begins.

At 9:00 it's 75 minutes of Calc I.

At 12:45 MATH 280 takes over.

At 2:45, Abstract Algebra II.

And at 4:10 we'll convene the semester's first meeting of MATH 480.

One of the myriad things I somehow managed to get done in Washington was arrange for the first guest speaker of the semester in MATH 480: my new colleague from Clemson, Nikos, offered to speak on the semester's third Wednesday, two weeks hence. Much appreciated, Nikos!

What else went on at this year's JMM?

Six of our sixteen REU students from the past two years were present, and all were presenting research in some form or another. Two of them, Nestor and Norton, won prizes for their contributions to the undergraduate poster session (Nestor's poster dealt with work he completed at his second REU this past summer). Most of us got together for a lovely dinner on Tuesday night of the conference.

The Fifth Annual Semi-Official Vanderbilt Mathematics Department Reunion Dinner had five attendees this year, the smallest it's been since its inception. Timing the dinner was a pain in the patoot: there were three other mathematicians and assorted hangers-on present at the meetings, but they were unable to reconcile their schedules with everyone else's. Bummer.

I managed to make a few new contacts in the math/poetry community, including a number of other readers in the Wednesday night poetry reading (good to meet you, Kaz, if you're reading this, and thank you for all of your organizational ability, Katarina!) and a fellow faculty member who, like me, is using poetry in her classrooms in order to instill confidence in struggling students (props, Lorena!). Incidentally, if you're at all intrigued (as a poet, as a mathematician, or as both) by math poetry, you should do yourself a favor and find a copy of Strange Attractors (available from A.K. Peters Press, edited by Sarah Glaz and JoAnne Growney), from which a number of last week's readings came.

Tip and I and Klaus, our colleague from Chemistry (hereinafte known as "The Shepherd"), made it over the river to Virginia to hold a highly productive meeting with one of the nabobs of the NSF. We got a number of practical suggestions regarding our still-in-progress vertically-integrated U/K-12 community outreach program proposal. Progress! Ah, elusive thing...

...and somehow I managed to make it to twenty-odd talks ranging from combinatorics to mathematical biology. That's "twenty-odd" with a hyphen. Although it must be admitted that some of them were odd indeed.

Finally, I should say that shout-outs go to some of my best friends whom I don't see nearly often enough, including the Vandy folks and the stalwart sterling dots who still manage to make it to most of the JMMs no matter where they're held.

So...

...tomorrow, huh?

I think I'm ready.

I'm starting MATH 280 off in the same manner I've started it off the last two times I've taught it: the first activities (both in-class and take-home) are highly intentional writing exercises designed to get students thinking about just what it means to write in mathematics, and it gets them doing peer review right away. Moreover, the exercises always prove immensely fun and popular.

Both Calc I and Abstract II get underway with review exercises. After doing a bit of brainstorming together on the first day of class, Friday will give the students a chance to strut their stuff as I'll be asking them to pair up between tomorrow and Friday and develop brief presentations on various topics from the relevant course material (Precalc and Abstract I, respectively).

And Senior Seminar? I'll figure that out when I get there. I think by 4:10 everyone (including me) is going to be so zombified that I'd be amazed if we get anything fruitful finished. I'll probably just make sure everyone's on board with the format, and maybe lead a discussion on what elements make up a good math talk. My hope is that in the first couple of weeks we can come up with a commonly-created rubric for oral presentations.

What else? Hmmmm...

...I'm going to go for now, and try to enjoy my last hours of relative boredom.

Tomorrow: class-by-class updates, as per custom.