28 minutes to go!

28 minutes to my first class of the semester!

I feel ready to face today (it's a beautiful day, by the way), having had the help and support of many wonderful colleagues and friends. In particular, many thanks go to my colleagues Fyodor and Ignatz for helping me to get on the ball with the Educo software for MATH 167, to Lulabelle and Thalia for their perpetual moral support, and to Maggie for everything!

Now, to get set for the first (and smaller) section of MATH 461...

...further bulletins as events warrant!

Jitters

Yup, it's that time of year again...Fall's nearly here, classes begin in less than a week, and I'm freaking out that I'm nowhere nearly as well-prepared as I ought to be.

Likely that's not true, but hey.

What's eating at me most this time around is my preparation for Precalc. I've never taught Precalc before (not here, not anywhere...the closest thing I've ever taught was Vandy's one-semester "Survey of Calculus" that took the highlights from a two-semester course of calculus and condensed it into a single semester for the benefit of folks like business majors who didn't want to bother with proofs), for one thing, and for another the course as we teach it involves a substantial on-line homework system with which I have next to no familiarity. It's easy enough to learn, but I'm still puzzling through the details myself and I know it's going to be a few weeks before I'm proficient enough to help guide my students through it.

I'm definitely feeling underprepared. With a week to go, I've got the first couple of days of both of my classes ready: Precalc will start off with a review of the structure of the real numbers, before vaulting into absolute values. Abstract begins with an examination of the Division Algorithm and related results. I'd like to be a week further ahead than this...I've still got next Monday and Tuesday to prepare, though, and with classes starting on Tuesday the hum and thrum of surrounding activity should invigorate me.

Just a couple of days back I was chatting with one of the REU students, and we talked about how we both feed off of the energy of the semester, we get high off of our work and the work that's demanded of us. I'm looking forward to getting that high again.

On a positive note, I've come up with several good ideas for relevant, meaningful Precalc projects that should not only prove challenging and enlightening to the students, but should also give them a leg up when they get to certain cognate problems in their future calculus classes.

For instance, a standard optimization problem in first-year calculus courses is to maximize the volume of a box that can be built from a piece of material of fixed dimensions, according to fixed parameters. The only step that actually involves calculus is the differentiation of the formula the students obtain for volume as a function of one of the linear metrics for the box; deriving that formula in the first place, plotting it and interpreting the graph, and determining maxima and minima visually are all actions that require the skills taught in Precalculus, and students who accomplish such tasks now will be more ready to handle the cognate problems when they recur in the calculus curriculum.

Another plus: while running into campus this morning I finally figured out the general form for the function that governs the work Thalia and I have both kept working on since parting a little over a week ago. I don't know why I didn't see it before, but now with the general equation in mind we might be able to make real progress on actual proofs.

Ah, research.

Here's hoping this semester goes well! Once things get underway, I'm sure I'll slip into the right frame of mind. I always have, for nearly three decades now. I'll be fine. Besides, I've already got pledges of moral support from two dear friends should Precalc prove to be the back-breaking straw.

Much as I know I need to prepare a bit more, I'm having difficulty focusing. I'm feeling very sluggish today. And why should I not be? The weather took a much-needed turn for the rainy overnight, so the sky is a shroud of white. Campus (where I sit as I type this) is dead: my department's a tomb, the building's air is still and warm (the cooler's on the fritz...again), all is quiet.

All right, I'm going to head home...no sense in cocooning myself in this scholarly sarcophagus any longer today. I'm sorry this post has been so scattered and erratic.

To be continued...

Halfway in

I've had a week now to recover from the departure of my summer's colleagues, the wonderful students that made up my REU team for the past eight weeks. The last of them took flight almost exactly a week ago this moment, winging her way back to New York last Sunday afternoon.

I miss them. They're great students, smart colleagues, and close friends. I look forward to seeing them at conferences, working with them on papers, growing up and learning by their sides.

For now they're gone, but the work continues: with two of them (those with whom I worked most closely with) I've already exchanged write-ups, graphs, ideas...yes, work continues.

But the cycle's begun anew: I arrived at my office at 7:15 this morning to find a note left on my door by two of my favorite students from last year, informing me that they're back (for RA duties, no doubt) and were surprised that they'd missed me. They were operating under the (not-all-that-erroneous) assumption that I'm never more than a hundred yards or so away from my office.

I spent this morning helping first-year students move in. For three hours I shuttled luggage carts back and forth between parents' cars and dorm rooms, schlepping all manner of stuff into Mills Hall. Fully laden one way, emptied out on return, several trips for several students. One's a budding music major, another's contemplating environmental science. A few are undecided: biology? History? "I think I want to teach."

"Math?"

"No! I'm not really good at math."

"That's what everyone says until they find out it's not true," I assured her.

It was refreshing, revitalizing. Its sense of newness and rebirth stood in contrast to the moving out my REU students did the weekend before.

My move into Johnson-MacFarlane Hall at the University of Denver 15 years (!) ago was nothing like this: my dad parked his truck in the middle of the phalanx of vehicles that lines that lined High Street for a block in either direction, and as soon as the dorm's outside doors were unlocked students and parents descended on the dorm like sharks in a frenzy. It was chaotic. There were no faculty or staff helping people to move in, there wasn't even anyone to direct activities or answer simple questions (where's the bathroom? Is the dining hall open? Where's the nearest ATM?)...that day I saw my RA cry for the first of what would be many times that year. (She was a gentle soul and didn't deserve some of the folks who lived on our floor.)

This coming week will see me getting the first few days of my two classes ready. I've read through the first few chapters of the text I'll be using for Abstract Algebra, and I've brainstormed a few opening exercises for that course, but I've yet to commit anything to paper. Tomorrow I'm meeting with one of my colleagues who's taught Precalc a number of times, and I'm hoping he can then give me a rundown on the topics I should be sure to address during the next fifteen weeks.

I've also got to get some more work done on the presentation on the writing program I'll be making at the Carolinas Writing Program Administrators conference in a month or so. Lulabelle and I met late last week to discuss that issue, but we spent most of our meeting chatting and going over the draft of my math poetry paper and syllabi.

Much work to be done, I just don't feel like doing it right now.

Time's running out, though...not long before classes start, and then where will I be?

Argh.

Okay, I'm off...I feel like I've got a lot to say, but so few words with which to say it. I've got to gather them together and compose my self before I can make any more sense.

Halfway gone

As you may surmise from my four-week blogospheric absence (an absence that has elicited chagrin from at least a small handful of dedicated readers...most of them connected to the primary reason for my absence in the first place), things have been a mite busy in my neck of the woods.

The program's nearly complete: four have now left, four remain.

Yesterday was the last "official" day of the 2008 REU, on which the students gave their final presentations and partook of a summative ceremonial repast at the West Asheville Asiana Grand Buffet on Smoky Park Highway.

Huzzah.

The presentations were wonderful, truly of a quality greater than that of most faculty conference talks. Although a few of the kids were obviously nervous, they did marvelously.

I'm stunned by the caliber of research they've produced, as well. The new knowledge they've brought into the world should make fodder for at least four or five papers, and all of the projects they've begun are worth following up. Some have barely started! I'll probably spend a good deal of time in the next few weeks beginning my share of the papers that should come from the program.

The better part of my time, however, will be dedicated to getting ready to teach this coming term's courses: Precalc and Abstract Algebra. I've not taught Abstract here before (I did a semester in Illinois), so that'll be something new...and I've never taught Precalc...nowhere, no how. I'm looking forward to that experience. I've already met a few of my students (they're friends of past students), and they seem a good lot. It's going to be a departure for me content-wise, but a worthy challenge pedagogically.

Elsewhere in my professional career, I've now written about four or five pages of my paper on math poetry. I've yet to really pick apart many of my students' responses to the experience of writing math-themed poetry, aside from identifying a "sense-making" trend in their poems (about which I believe I may have blogged before). My reflections on the students' reflections should form a core part of the paper, and I hope to get to that soon.

I've also got two papers to referee and one to review...reading material for the beach when Maggie and I head down to Savannah for a few days at the end of the week after next.

Ah, well.

I'm going to go now and have a bite of breakfast. I plan to return more soon than four weeks hence, so stay tuned.

Let the world wait

Last night
a weary worldly friend
crept in and sat down by my bed.

"What's happening?"

"What's not?"

She settled in.
I sighed.

Staring at the ceiling fan,
I told her of a summer long before,
of when sixth grade had ended
and for the last time until September
I'd bounded home from school.

"My pack slid from my shoulders,
my shoes fell on the floor.
Down the stairs I flew, twelve of them in seven steps,
my brother a blur behind me.
On the concrete floor we crouched,
a pair of academic acolytes.
Gleefully we lit a fire:
in the wood stove went
papers,
notes,
diagrams.
More still:
maps I'd drawn,
games I'd made,
worksheets,
outlines,
quizzes,
tests,
an unsent love letter or two?
page after page after page after page after page after page of
all that made
a year of school
vanished,
a pile of learned lifeless ash."

Over.
So easily ended.
As though a heavy blade had sliced the summer from the spring,
I was cut free
to waste those sunny days in whatever way I could.

The ceiling fan spun on.

"And now?"

"And now it's hard to extricate
tomorrow from today.
So much undone
makes what is done
remain unsung.
I can't rest on my laurels
if my laurels aren't yet won!
If I flew westward fast enough,
might I outrace the sun?"

"Now it's time to get some sleep,"
she said.

Nodding, I agreed.
I let her close my eyes.

"Close the door.
Shut me in.
Make me a cup of chamomile tea.
As I sit sipping,
let the world wait.
For a day,
let the world wait."

Week Four progress report

Halfway.

Damn.

This summer has been flying by.

Our program evaluator, Ophelia, is currently in town (she's been down in Jacksonville, FL, preparing for her upcoming year of teaching there). She arranged for the mass comm people to videotape yesterday's student presentations, which she herself attended as well. (Not to mention one student's mother and another student I'm doing research with who is not taking part in the program...) The talks are improving steadily: they're all getting better at pacing themselves to say what they need to in fifteen minutes and no more, and they're getting better at making use of board space and multimedia tools. I was particularly impressed with Ethelred(not the Unready!)'s presentation, in which (I only noticed in reflecting on it, while composing a feedback e-mail to him) he didn't write a single alphanumeric character on the board. His fifteen minutes were focused on a series of well-chosen diagrams that illustrated his technique, a complicated generalization of a method I developed last year for navigating internally disjoint edge paths in a certain kind of graph. His method seems to work, but he's yet to make it one hundred percent rigorous. I eagerly await the finished algorithm.

Others made solid presentations, too: Desdemona seemed hurried, but she too made great use of appropriate pictures in explaining how to find homomorphisms between graphs; Camilla and Dione worked together to weave a multimedia presentation on growing networks that was bursting with differential equations; Norton couldn't resist replaying his PowerPoint presentation illustrating Bach's unintentional use of the theory of cyclic subgroups in his Violin Concerto, BWV 1041; Uwe gave the first public presentation of his algorithm for finding optimal L(2,1)-labelings of internally three-regular trees; Hector talked about his progress through the research program that should allow him to show that all algebraically realizable finite hyperbolic tilings are indeed constructible; and Thalia put forth her new technique for hunting down gracefully labeled paths...her work this past week has been really interesting stuff for me, and I've had a blast trying to tell Mathematica how to help us out in our search.

From a pedagogical point of view, it's clear that the students are helping each other out as much as we (the faculty) are helping them. Though we see four or five of them regularly during our common morning office hours, and we see a few more somewhat regularly in the afternoons, in between those sessions they're all progressing in great loping strides. That progress is often attributable to one another: "yeah, Ethelred helped me code this in Mathematica...", "Thalia can help me with the differential equations...", "Uwe figured out how to do that..."

The quality of their written work is improving substantially, too: several of them are already producing work that's beginning to look publication-ready, and we've got four weeks to go yet!

Craziness.

I really need to start thinking about my courses for the Fall semester. Ouch.

Not to mention the two grants that I promised myself I'd be working on for the fall.

And the review I've got to be writing.

And the papers I'd like to finish off and send on in.

Why is it that the summer is busier than the school year?

Anyone who says academics get a three-month paid vacation is full of shit.

Pardon my French.

Of course, I've been spending my free time reading up on the pedagogical uses of poetry as I start to write my paper on poetry in mathematics, so I can't complain overmuch about not having time to complete the above tasks. I've got a stack of papers, mostly from educational theory journals, some from general qualitative research publications, dealing with the roles poetry can play in research and education. The literature is somewhat sparse, judging from what I've found, but I have found some relevant material. Not surprisingly I've seen nothing about poetry in the "hard" sciences apart from the offshoots of Clemson's Art Young's Poetry Across the Curriculum movement.

I have managed to get some great responses from my student poets from last Fall. I'm going to send out a reminder to those from whom I've yet to hear, and maybe include a couple more students in the process before I begin writing.

For now, I've got to go and clean up a bit for the company we've got coming over for our inaugural Thanksgiving in July party.

Arrivederci!

"So they remember you when you're gone"

Life seems shorter after dark:
you can barely see your fingertips.

The concrete path ahead ends
in the umbra of the streetlight's edge.

What's out there?
No one knows.

Acre after acre
of unplowed, unfurrowed, virgin land.

Mortality is closer
when the sun has gone to bed.

The stubborn say "I'll beat this,"
while the tired say "I'm dead."

Week Three progress report

Doin' good.

At least, I think so.

After gentle admonishment about the lengthiness of a few of the student presentations last Friday, yesterday's talks all came within a minute or so of the universal 15-minute maximum we'd prescribed in advance. ("15 minutes, MAX!") The talks were solid, with more eye-popping graphics, slick LaTeX work, and tons and TONS of data. They're beginning to come up theorems of their own, they're making conjectures, their laying out formal proofs. It's coming together. I've yet to get a look at their written work for the week yet, though I've gotten sneak peeks through reading their drafts (thanks for bringing that to me, Uwe!) and seeing their presentations. Their level of sophistication appears to be rising. I have to admit that I'm looking forward (sick scholar of scholarship that I am) to the point at the summer's end when I can lay their weekly assignments side-by-side-by-side-by-side-by-side-by-side-by-side in an attempt to track the development of their technical writing proficiency throughout the program.

One more thing I'll say about these students: they (and one or two of them in particular) ain't shy about asking for what they need from us: more ideas for things to do around town, modifications to the presentation schedule, caffeinated tea...At their behest we've scheduled a "grad school forum" in a couple of weeks, at which time we'll give them the chance to ask anything and everything they'd like to about selecting, applying to, transitioning to, and surviving grad school.

I hope that their forthrightness is indicative of a sense of belonging and collegiality, and not just out-and-out boldness. Probably a little of both.

I really wish that I'd had a chance to take part in an REU when I was a student. I know I'd have been up to the challenge. I realize now in reflecting back on my undergraduate experience that though I had solid professors who were active in their fields and who did a great job in the classroom, their mentorship didn't extend far beyond the classroom door. I fear that I was simply a student in a Ph.D.-granting department whose Ph.D. program was undergoing a period of latency, and that the faculty didn't really know how to properly mentor talented undergraduate students...I really should have been told about journals geared towards undergraduates, I should have been encouraged to go to undergraduate-appropriate conferences, I should have been pushed to apply for REUs (there weren't as many back then as there are now, but there were a good number by then, and I'm sure I would have landed a spot in one had I applied to a few).

Ah, c'est la vie. I'm pretty happy with the way my life has turned out, and now I get a chance to live the REU experience vicariously through my own program. Woo hoo!

In other pedagogical news...well...there's not much more right now. I've started to plan my syllabi for the Fall semester (two new preps! I've not taught Abstract Algebra here before, and I've never taught Precalc). I met with Lulabelle and Casanova over lunch this past Thursday, and we planned our next move in the new writing assessment study. Casanova's going to focus on analyzing the syllabi as faculty products, and I'm going to try to better articulate my hypothesis that the rubric we constructed at the conclusion of the last study was (perhaps unintentionally) skewed towards assessing more "traditional" research theses. "We might just have to report that it's not possible to create a universal rubric capable of assessing the writing of any given course," said Lulabelle.

Well, for now the waterhole calls...I must away.

I'll check in again soon...next weekend, at the latest!

Week Two progress report, v.1.0

Yowza, I'm beat.

I'm not going to write much right now, as I'm tired as hell and the needle's pegged to the far-right end of the Incoherometer.

I will say simply that the students made their first end-of-week presentations today, and they were magnificent. Aside from the so-so time management displayed by a few overeager presenters who might have taken a taaaaaaaaaad too long in singing their songs, the talks were marvelous. All eight made great use of visual aids (including Mathematica notebooks, LaTeX files, PowerPoint, good ol' fashioned boardwork), all were careful to provide their peers with history, background, and context for their respective projects, all were able to make clear some very high-level and abstract mathematics, and all held one anothers' feet to the fire through careful and clever questioning...Camilla and Thalia were particularly good at this.

To those of the students who may be reading this: I promise personalized feedback on individual presentations, no later than Monday!

There are some great projects afoot. At this point they're working on color-critical graphs, channel assignment utilities, group theory as applied to musical theory, the limiting connectivity of field automorphism graphs, the structure of growing networks of churches, statistical measures of preferential attachment models for random tree growth, variations on previous definitions of finite hyperbolic tilings, and an algebraic/geometric characterization of graceful labelings on graphs.

This last one, Thalia's pet project, has really got me intrigued right now. Thalia's taken as a starting point a "classical" observation (that a graceful labeling of a graph must place the highest- and lowest-labeled vertices next to one another, and in order to obtain the next-highest label exactly one of two configurations must obtain, and so forth), but her logic pushes her along a path I've never seen taken before, on which she's found a way to view the collection of graceful labelings on all graphs of a given size as a collection of lists of states, on which an algebraic structure can be placed. Her insight's led to some interesting ideas, and I'm eager to see where they go. We met for a couple hours this afternoon to hammer out some Mathematica code and to organize our collective thoughts on her construction. She's a fast thinker, and is a lot of fun to work with.

In other news, I met with Lulabelle and Casanova yesterday to begin our analysis of the materials submitted by our colleagues at the close of this past year's writing assessment study. The pickin's are slim, and we've decided to start our analysis by reading through those syllabi we've so far collected from our colleagues who were directing discipline-specific writing-intensive (doubly-hyphenated-adjectival-phrasedly-modified) courses last fall. Our task at this point is merely to reflect upon our critical reading of these texts: what is there in the syllabi that indicates the instructor's attention to writing pedagogy? What implicit elements might the students (or faculty) infer from a reading of the syllabi? What elements are common to the syllabi? Which are present in some but not others?

And so it goes.

Judging from the penultimate parenthetical comment in the previous paragraph (oh, the alliteration!), it's time for beddie-bye.

Until tomorrow, then, I am always yours...

Week One progress report

How we doin'?

If I had to say off the bat, I'd have to come back with a "not too shabby."

The students are fast, sharp, and diligent. They excel not only at the formal mathematics but at the auxiliary activities: LaTeX, Mathematica, you name it. They're kickin' butt and takin' reservations. I've already begun to think of them as able colleagues, and I and my fellow faculty have encouraged them to adopt the same viewpoint. Hell, no doubt in less than a month they'll be slowing down to let us catch up to them.

I don't know how much of their apparent progress this past week can be chalked up to the design of our program (a design which I feel is much tighter, clearer, more well organized...well, just so darned much more effective than last year's) and how much to the strengths of the students themselves. I'll be eager to know their take on the matter.

Meanwhile, I'd like to take a moment to look back over the first week and hold it up against the learning goals I'd put forth for the program's participants...how well do they match up?

1. Have a grasp on the fundamental concepts of graph theory, group theory, metric geometry, and dynamical systems; and understand cutting-edge open problems in these fields. We're there. I figure that in the first week we've given them the equivalent of one half to two thirds of a semester each of graph theory, abstract algebra, and dynamical systems. (Not to mention a year's worth of seminars, as Tip has said.) They've soaked it up, and they've been far more than passive note-takers. We've given them some pretty challenging exercises, all of which they've navigated with aplomb. Their mastery shows best in the brilliant questions some of them have asked (Norton's got a thing for topology, judging by his constant queries about that area) and in the frequent and astute observations they've made (late yesterday afternoon Thalia noted an omission in a project Tip and I have been working on for over a year; it was easily fixed, but her insight led us to find and fill the gap in our method...summer research has begun in earnest!). I think they've got the "fundamental concepts" down and are ready to hammer away at the open problems. A couple have already started to apply the concepts we've covered to original ideas. Uwe's application of graph theory to analyze the efficiency of saxophone fingerings is absolutely delightful!

2. Be able to make effective use of research databases, including MathSciNet and arXiv. We spent an hour or so on Wednesday talking about these databases. Our conversation, directed largely by Camilla's questions about how one becomes a referee, how one becomes an editor, how much publication is expected of faculty, and so forth, took us, on this third day of the program, deeper into the issues surrounding professional development than we ventured all summer last year. I don't think the conversation's tangents were distracting; the students did admirably on their first research assignment. On Friday each submitted the results of at least two literature searches, each including at least three academically rigorous references. The annotated search results proved the students' comfort in working with the relevant databases. I think they're ready to ply their skills to authentic searches.

3. Feel comfortable in generating new questions and topics for research, either by modifying and generalizing existing statements, or by branching off into uncharted territory. The verdict's still out on this hard-to-assess issue, but judging from the number of questions several of the students have put forth during the past week, I don't think we're going to have to worry about this one. A few of the students are more reticent than the others, and it's hard to say whether this is out of shyness or lack of skepticism. Time only will tell.

4. Appreciate the qualities that make for a friendly and effective research community. Progress towards this cognitive goal will be exceedingly hard to measure without hearing from the students themselves. We've got our first meeting (by conference call) with Ophelia (our evaluator) on Monday, and by then I hope she's had a chance to glean some feedback from the students.

5. Understand how to make high-level use of a computer algebra system such as Mathematica. On Thursday morning we spent about two hours plowing through several Mathematica notebooks put together by my currently-honeymooning colleague Nostradamus. About half of the students have had previous experience with Mathematica, and a couple others had worked with its main rival among computer algebra systems, Maple. As far as I could tell, there were no major snags. The most heartening indicators of student success are the applications the students have already found for the software. Uwe's made extensive use of its high-level functioning as he's undertaken his analysis of saxophone key structures. During the last few days he's developed incredible proficiency in using Mathematica's Combinatorica package. Meanwhile a few of the others put the software to work in crafting a T-shirt design featuring a complete graph on 11 vertices, each of which holds the name of a program participant. (Ain't they sweet?)

6. Have facility in working within the LaTeX typesetting environment. They made mincemeat of yesterday morning's typesetting exercise, in which I asked them to mimic as closely as they could a one-page sample document I gave them. Though I could have made it substantially harder, that one page featured a number of minor obstacles (double quotation marks, positive horizontal spaces, etc.) as well as some tricky mathematical typesetting conundra (arrays, commutative diagrams, variably-sized delimiters). Three or four of the students have used LaTeX before, and they made short work of the exercise (Norton finished in about 50 minutes, over a half hour faster than the final finisher). Even the least experienced of the bunch managed to put together a beautiful document, and in a totally reasonable amount of time. Just a week in, and they've all got text editors and compilers installed, ready to be pressed into service. I'm eager to see how their first "papers" turn out; they're due on Monday.

And speaking of Monday's assignment...

7. Be familiar with the structure of a mathematical research paper, and be able to construct such a paper. Monday's assignment calls for them to produce a brief report mimicking the structure of a formal mathematical research paper. At this point the content is unimportant; I merely asked them to write on a topic we've talked about at some time during the first week. What's important is that they begin to understand how a mathematics paper is structured. Though I'm by no means expecting perfection from the students on Monday, I've already come to expect excellence.

8. Have confidence when communicating mathematics orally, to an audience of peers or to an audience consisting of research professionals. At this point we've had no structured oral presentations, but all three of us faculty facilitating the program have asked the students to perform impromptu exercises at the board. To a one they've performed with skill and grace. As I mentioned in Tuesday's post, on that day the students ran the show for roughly four and a half hours, during which time only infrequently were I and my colleagues at the board. Surely their first oral progress reports, to be given next Friday morning, will be strong.

9. Understand the dynamics of, and feel comfortable working in, a collegial research group. As somewhat of an outsider, it's difficult for me to say how the students are functioning as a unit outside of the seminar setting. However, it seems to me that the students have already formed a tight-knit social group. They're supportive, they stick up for one another, they're good at reading and meeting one anothers' needs. Camilla's fantastic at sensing the mood of her friends and conveying it to the faculty if there's any doubt we don't grok what's going on. With her confidence, intelligence, and outspoken character, she's a natural leader. Meanwhile, as I'm sure you can judge from the comments to the above learning goals, the students' interactions with faculty bespeak a high level of comfort in working with us. I think we've already made good progress towards meeting this particular goal.

10. Possess a healthy skepticism and authority to challenge as yet unproven results. This is a tough one to measure as yet. Once the students have begun to put together coherent research agendas, I'll be able to say more about the strength of their skepticism. Nevertheless, if confident questioning is any indicator of the students' sense of authority (and I believe it is), these students are well on their way to developing the ownership of mathematical knowledge it will take to make them exceptional scholars.

11. Be ready to present their findings to an appropriate audience at a regional or national conference. This one too is difficult to assess, and might remain difficult for some time yet. The students have hardly begun to present to one another, so it's understandable that they might be nowhere near ready to present to a broader and perhaps (though as likely perhaps not!) more sophisticated audience. I expect great strides will be made in this direction before August 1st comes around.

12. Have a sense as to the structure of the mathematical community at large, and understand their own place in it. This goal too is a bit nebulous, and evidence of its achievement will really only become evident by the end of the program, at which point it might be witnessed by maturity, poise, and overall mastery of the tasks demanded of a professional research mathematician. However, as I said above, we've already had a number of serious conversations about what it means to be an academic mathematicians, and I delightfully anticipate many more before the summer's through.

Keep it up, my friends! You're doing wonderfully, and you've made the first week a joy. I look forward to the next seven weeks, and beyond, in which time many of you will no doubt become my colleagues, coauthors, and coworkers in the mathematical community. What a wonderful time it will be!

Well, by Wednesday we'll be done with our intensive "seminars," at which point the students will be cut loose to seek out research problems and begin their work in earnest.

Before I close this entry out, I'd like to mention that I've now heard back from one of the Calc I students whom I approached regarding her poetry. I'm happy to say that her responses to my "interview" questions showed honesty and depth of thought, and they showed that she really did give a good deal of consideration to the exercise last Fall semester. I also heard from Magdalena, another of those students I contacted: she indicated that she's "still working on" her responses, implying that she's taking time to compose robust and meaningful replies. I can't wait to read what she's written.

I'll check in again in a few days. Until then, your homework: think back on the most meaningful academic experience you've ever had, and explain in 250 words or less why it left its mark on you. Spelling counts.

Leaps and bounds

Two days in, and going strong.

We've now wrapped up two days of intensive seminar-style introductions to graph theory and group theory (to say nothing of mountains of paperwork, campus tours, and bureaucratic snafus of various orders of magnitude), and the students seem to be taking it just fine.

Example: after three and a half hours in which we plowed through four weeks' worth of graph theory (we worked off of modified versions of my Moore-method notes for last semester's 473 course...the out-of-class homework problems adapted well to their new niche of in-class exercises), their "homework" was to strike out on their own and track down definitions, examples, and applications pertaining to 30 different graph theoretical concepts. The kids came through in spades, spending the first four and a half hours of our working time together in taking turns presenting the material they'd come up with. Although I suspect there was a good deal of division of labor (certain students "claimed" certain problems and broke up the workload along clearly demarcated lines) it was just as clear that many of the topics had been multiply-researched, and thoroughly, at that.

They kept each other honest, too: they weren't shy about comparing divergent definitions, asking questions to reconcile apparent contradictions, demanding clarification on points that weren't so obvious at first. One of the students is particularly bold about asking for elaboration, it's marvelous to have her there since her boldness and the elaboration it requires are no doubt leading to greater understanding on everyone's part, including my own. My thanks to you, I hope you know who you are!

Indeed, few of the students are shy about taking part. Two or three are ever eager to strut their stuff on the board, and a few more are just as comfortable in directing the action from the cozy quarters of their desks. A couple are quieter than the others and are therefore harder to read, but I have a hunch they're all following along pretty well. (Two of the students have yet to take an abstract algebra course and today's dessert course included and introduction to geometric group theory, so those two folks might have felt a bit pinched at the end. I hope they roll with the punches and persevere, I know they're both highly intelligent and will weather this first week's storm if they stay the course.)

I've got very high hopes for this group of young mathematicians. They're already top-notch scholars, and I hope we can effectively take them to the next level.

In other news, I've just received the copy of Oulipo: a primer of potential literature (Warren Motte, trans. and ed., Dalkey Archive Press: Champaign, IL & London, 2007) I ordered. Oulipo is a French acronym, standing for Ouvroir de Littérature Potentielle, a consortium of artists (most French) who in 1960 began a movement dedicated to the production of rule-based works of literature. The generative rules that govern the poems they create are highly mathematical in nature, and any serious study of math and poetry demands that Oulipo's work be considered.

Meanwhile I just this morning sent "interview" questions to seven of my students from last Fall's Calc I classes, asking them to reflect not only on the poems they created for that course, but also on the process that led to the poems, and on the thoughts and feelings that governed that process.

I have to admit I'm not entirely sure what I'm going to do with the data I glean from these interviews. I think I'll only be able to find that out once I've got the student responses in front of me.

For now, I'll put down my pen and away myself to bed. It's late, and I've got another long day that begins early tomorrow (at 8:45 in the OneCard office, where I must meet with our Excellent Eight to sort out a minor matter involving their inability to check out library materials on their cards).

Feel free to let me know if you're out there!

All in

We're set.

In ten and a half hours we'll begin officially the 2008 installment of our REU.

I'm excited.

And nervous.

These are some smart people I'll be working with; it's evident in their conversations, their interests, in the way they carry themselves and express themselves. They're sharp.

What'll they be like as colleagues, tomorrow and beyond? As I was telling Thalia last night, I hope that this summer we can succeed in forming a community of learners in which no one is deemed as The Expert™, in which we all feel free to question and learn from one another as equals. The only difference between me and her is that I've been doing it for a few more years than has she; time will erase that advantage too, and if she keeps at it ten years down the line we'll be sitting in a side room at some conference, yammering away and remembering our conversation ten years back.

Last year's group: where are they now?

I've been in fairly close contact with five of last year's eight.

A couple of days ago I invited Kieran to come down at some point in the next eight weeks and give a talk about his current research program. He may be able to make it, he's not sure. He's got a lot to get ready for in the fall, when he begins graduate work at the University of Kentucky. He's got his name on a paper with me and my next-door neighbor in the department, on one that's been submitted to Complex Systems.

As I mentioned a few days back, I've been spending some time during the last couple of days retooling a draft of a paper I'll be submitting with my name alongside Wilhelmina's and Mirabel's. I may shoot for Communications in Algebra again; we'll see. Mirabel will be headed southward in the fall; she begins grad work at Wake Forest in August. I hope I'll get a chance to do some more work with her.

I'll be incorporating work by Nestor into the sequel to my paper that will soon appear in Discrete Mathematics; I don't think this sequel will sit for long before getting snapped up by a pretty decent journal.

And twice this past half-year I've seen Opal at conferences. I don't know if she intends to keep on keepin' on once she finishes her undergraduate degree, but I'm sure she's bound to do good things.

Where will this year's eight find themselves in the coming years?

Six of the eight are rising seniors (three last year), one is a rising junior (five last year), and one a rising sophomore (none last year), so this year's crowd is slightly older on average. As a whole they seem a little more sure about themselves and their mathematical futures than last year's group did. Grad school's a likely feature in all of these kid's futures.

I'm sure I'm setting myself up for a heavy round of rec-letter-writing in the fall.

That thought in mind, I'm off to bed; tomorrow promises an early start and a long, long day, crowned by (havah nagilah!) bowling night. I'll so be ready for that by the time 9:00 p.m. rolls around.

Who's who

Six in, two to go, both of whom will arrive in the next seven hours or so.

Loads of meetin' 'n' greetin' and gettin' to know one another goin' on. Everyone seems to be getting along so far (some more well than others...I'm going to have to separate certain people during the introductory seminars), I don't foresee any obstacles to this crowd's forming a hard-core tight-knit learning community within the first few days!

Further bulletins as events warrant; for now, everything appears to be copacetic.

Twenty-five minutes to go...

...At least that's what it feels like.

Desdemona, our REU student who's scheduled to arrive first, should be here within the next hour and a half.

Am I ready?

I've spent the last couple of weeks putting together material for this year's program, and now I've got a list of learning goals, a rough timeline, a list of about 45 possible research questions, five handouts involving set theory, graph theory, and metric geometry (and several more on the way), five handouts on Mathematica, four handouts on LaTeX and the structure of mathematical research papers, an exercise asking students to uses research databases to track down primary source material, and a map of North and Central Asheville, complete with markers indicating locations of yummy eateries and other useful establishments. (All of these are available on the REU website, here.) Not to mention a couple dozen research and survey articles on various topics of interest to me.

Still I don't feel ready.

I'm just anxious, giddy as a schoolboy on the first day of class.

I met with Lulabelle and Casanova yesterday to talk about the direction our new year-long writing assessment study is going to take. Suffice it to say we've got a mountain of data (both quantitative and qualitative), making the selection of research questions a leviathan task. For now we're focusing on collecting the final round of data from the previous year's participants, including syllabi and course assignments, as well as statements regarding these folks' experience in constructing and applying the writing rubric we all worked so hard to put together.

Lulabelle's visibly more relaxed since we've finished up with Austin. I hope she's able to get some good nights' sleep in these days.

After our meeting yesterday I stayed on to help her out with reading math papers (a scary proposition for a non-math-type person!), and then we talked about Kevin Rathunde's work on family environments that are most conducive to optimal experience in children. (I came across a reference to Rathunde's work in reading Csikszentmihalyi's Flow for our upcoming summer learning circle, and tracked down the original work, appearing as a chapter in Csikszentmihalyi and Csikszentmihalyi (ed.) Optimal experience: psychological studies of flow in consciousness (Cambridge, NY: Cambridge University Press, 1988).

Central to his study are five traits (all starting with 'C'; a fitting companion piece to my "Four Cs" rubric!): clarity (of rules and purpose, providing a stable set of experience parameters), choice (giving children the opportunity to direct their own experience within clearly defined parameters), centering (of activity in the present, making it an "autotelic" activity worthy of pursuit for its own sake), commitment (or trust, giving children a feeling of security that will enable them to boldly strike out on their activities), and challenge (ensuring that children are given tasks that are adequately interesting).

A question to ponder: in what ways are these traits best developed and nurtured in the classroom, and to what extent do they there serve the same roles as they do in a "well-flowing family" context? (I can already see how these traits mesh well with what I've always thought of as "good teaching practice.")

That's a question for later, since in the middle of my typing the above paragraph, Desdemona arrived with her family in tow. She's now safely moved into her dorm room, alone for the night but not for much longer.

I'm so excited!

And I just can't hide it!

I'll attempt to keep control.

But I'll still like it.

Until next time, ponder the following: just how long did it take Dr. Csikszentmihalyi to learn to spell his name? And how long does it take him to type it?

Channel assignment

Channel assignment

Were you a step away from me,
and I a step from you,
then you could hear
were I to speak.
Yet another step between us
would make two,
and to speak would mean to scream.
Beyond two steps
no sound could penetrate:
we’d sit alone
on silent isles
until some friends between us stood
to mediate,
one a step from you, one a step from me,
with a single step between them, too.

Sleepless in SoTL

One of the questions that arose during yesterday's midmorning meeting with my colleagues Ophelia (official evaluator for my REU) and Fidelis (world-renowned expert in science education assessment who just happens to have retired to the Asheville area) is: "How does student technical writing improve over the course of a summer REU, given that this learning goal is given attention?" Fidelis assures us that next to nothing is known about process when it comes to REUs, especially regarding the attainment of specific learning goals surrounding professional development: writing proficiency, oral presentation, acculturation to the career of a professional academician. Any one of these would make an excellent target towards which to aim the arrows of study.

I wonder why it is that I had writing on my mind?

This summer's REU will feature much more intentional instruction in writing, the use of research databases, and the use of Mathematica. Fortunately I've got access to a good store of material relating to the second two activities: I can recycle a lot of the handouts on research I used in Fall 2006 for the now-infamous MATH 365 course, and I can borrow liberally from (or just simply reuse) the Mathematica files my colleague Nostradamus made up for the REU last summer.

As far as writing is concerned, it's always a pleasure to make up some new material. I've already got a few handouts that I gave to the students in Week 6 last summer, introducing them to the rudiments of LaTeX. Instead of holding off for six weeks, they'll be given those handouts right away, and they'll get the ball rolling in Week 1:

Week 1, Wednesday: students will be asked to download freeware LaTeX compilers and text editors (OSTeX, MiKTeX, TexnicCenter, WinEdT, etc.).

Week 1, Friday: by the end of the day, students will be asked to submit their first assignment in LaTeX, a rudimentary paperlet discussing one concept with which we've dealt during the first week's seminars. The paperlet will have the form of a research paper in miniature, structured roughly as follows:

1. Introduction:what exactly is the concept you've chosen to write about? (Give a simple definition.) What is its history? What is known about it?
2. Elaboration and examples: say a bit more about the concept by elaborating on your definition from above. In what context does your concept live? What concepts are related to it, and how? Give a few examples of your concept.
3. Conclusion and discussion of future work: Bring your work together, summarizing the findings, and indicate open questions surrounding the concept you've chosen to talk about.

I hope that by asking them to so structure their work right away they'll grow accustomed to this genre.

Week 2, Friday: students will be asked to submit a research prospectus indicating at least three topics into which they would like to look during the coming weeks, including an abbreviated (and unannotated) literature review for at least one of them.

Weeks 3 through 7, Friday: students will be asked to submit "progress reports" taking the form of mini-research papers. These reports will be structured much as the paperlets described above and will continually update the reader on the students' active research. A student may choose to report on only one week at a time, or to maintain an ever-up-to-date comprehensive report summarizing all work performed until the present.

Week 8, Friday: the "final version" of a paper will be submitted. If all goes well, this paper should be a fairly close approximation to something publishworthy.

Last year only Wilhelmina's and Mirabel's paper approached publication quality by the end of the summer (speaking of which, I've got Wilhelmina's most up-to-date version sitting in my in-box, I hope to get to that today...), though with the intentional iteration highlighted above, I have hopes that many more of the students will leave with a strong piece of work in hand.

In other writing news, I'll be meeting with Lulabelle and our colleague Casanova on Thursday to discuss the directions our new writing study might take. We've got a ton of data to sift through, and any number of ways we could conceivably slice it. Between faculty journals and conversations, student pre- and post-tests, student assignments, the faculty-developed rubric and the results of its application to the students' work, there's a lot to work off of.

As I indicated towards the end of this previous assessment project, I have a hunch that this study is going to say more about faculty writing practice than it is student writing practice; this is why I'm interested in tracking the elusive "instructional intentionality": how is it that faculty's attention to writing instruction manifests itself in the classroom, and to what extent does that attention pay off in (at least perceived) significant student proficiency gains?

Beh. Mumbo jumbo mumbo jumbo...

...finally, I should say that I've already heard back from most of the former Calc I students I'd written regarding their poetry from last Fall semester. I need to make up an "interview" form to send them so that I can help them reflect on their writing process.

Well, I'm going to get going and take a look at my graph theory notes from this past semester's seminar course; I have a hunch I'll be able to modify the problem sheets to serve as a basis for next week's graph theory instruction. We may end up playing a lot of it by ear and making it up as we go along.

Avanti!

Back

Damn.

That was productive.

It's going to take me a while to unpack all that I've carried back from Austin.

It's been a long time since I've had a trip that fruitful; I've come away with so many ideas, insights, opportunities for collaboration, connections to new colleagues...what a wonderful crowd these WAC folks make!

It's safe to say that there's a great deal of interest in writing in the math curriculum.

Lucky me.

People were enamored with the work Lulabelle's put together, and with my piece of that project. If anything, though, the writing folks were more interested in hearing about my math poetry project from the Fall 2007 semester. I've already contacted several of the students from that Calc I class and asked if they'd like to work with me by providing me with reflections on their creative process. I'd like to know: what did they get out of the exercise? Did it help them to engage mathematics, and if so, how? I've spent the last hour or so looking over Arthur Young's Poetry Across the Curriculum and other related projects. This is such wonderful work!

As I said, it's going to be a long time before I'm done unpacking the mental baggage I've brought home from that conference. Already, though, I've begun thinking about how I can assess this summer's REU students' writing as they proceed from novice article authors to more seasoned technical mathematical writers, and I've begun puzzling through the process of assessing just how it is that a writing instructor's intentionality leads to students' gains in writing proficiency. And I'm coming up with ways I can use blogs in Abstract Algebra and wikis in Precalc this coming fall. And Lulabelle and I are meeting with Casanova on Thursday to discuss the direction(s) we'll be taking in our follow-on to the last assessment project.

And...

...and...

...and...

...too...much...to...think...about...

...and with only a week to go before the REU begins.

Until I return with a longer and more meaningful post, here's a question for all of you out there who happen upon this blog: would you rather be bored shitless or busy as hell? Discuss. You will be graded on ramblingness, incoherence, and lack of a thesis sentence.

Think 'pon it carefully. Surely your response says more about your personality than a thousand Cosmo quizzes.

Jump

Tomorrow has me jetting off to Austin (from what I'm to understand just about the only livable place in Texas, and just about the only place in that state I've never been) to take part in the Ninth Biennial International Writing Across the Curriculum Conference.

That's a mouthful.

It's also mildly frightening, since it'll be the first time I've ever presented at a decidedly non-math conference before. Frightening but exhilarating at once. The feeling I've got going into this shindig is not unlike the one I had when I made my first research presentation at a non-group theory conference a little more than two years ago now. (As a group theorist by formal training, I felt a bit of a dilettante in dabbling with graph theory, so I felt it a pivotal moment when I started going to/presenting at graph theory conferences.) It's a jump.

It's fitting that I've started reading Mihaly Csikszentmihalyi's Flow: the psychology of optimal experience (Harper: New York, 1991), the centerpiece for the summer Learning Circle in which I'm participating.

A relevant passage, read just last night (p. 61):

What people enjoy is not the sense of being in control, but the sense of exercising control in difficult situations. It is not possible to experience a feeling of control unless one is willing to give up the safety of protective routines. Only when a doubtful outcome is at stake, and one is able to influence that outcome, can a person really know whether she is in control.

This conference should be fun.

Just your run-of-the-mill first-day-of-class anxiety dream

It took most of the dream I had the other night (i.e., about 5 milliseconds in real time, most likely) to put my finger on why it was I felt underprepared for the dream-class in front of which I was standing: I'd not yet pulled up my students' photos on OnePort, so I was completely unable to put names with faces. While I usually get 80% to 90% of the names right on the first day, in this dream I was shooting blanks: everyone was a stranger.

Why is it that so many of my anxiety dreams involve classroom underpreparedness?

Yes, I'm always fully clothed in these dreams...usually I'm anxious I haven't planned the activity for that particular day of class.

Ah, but class is done for the year here, commencement's come and gone, and the late-spring conference season is winding down (one to go, in Austin at the end of next week...I'm nearly prepared, and I'm very much looking forward to it!). I've got a brief lull of about two and a half weeks right now, time in which I've got to get my REU ready to go for the summer. I've got a list of about 40 problems made up for the REU. I hope that by the end of the program's first week I can throw the list to the kiddies and let them spend the weekend looking up primary source material they can then mine for their own interesting problems.

Speaking of commencement (as I did, briefly, above), I'd like to send my heartiest congratulations out to all of my wonderful students who have now passed from these hallowed halls of academia and on to bigger things. You've done wonderful work here, and I'll miss you all.

Just a few days back Fiona sent me a picture her stepmother took of Fiona, Niobe, and me, all clad in regalia (ah, pomp and circumstance). Maggie's made it the desktop image on her computer. (She's entranced by the novelty of the photo, as I'm not often seen decked out like that.)

Since returning from Nashville the other day, my time's been focused on applying the writing rubric our research team's developed to the discipline-specific writing assignments gathered by me and my colleagues. I've had the honor of reading management research papers and reflections, and response essays and creative writing assignments from a course in French composition. These works include everything from taxonomies of corporate social responsibility through original poetry pitting Baudelaire against a red balloon.

I've found it very hard to apply our rubric to the French papers, in particular to the creative writing assignments whose brevity and informality make it difficult to assess a student's mastery of items such as "be able to contextualize a thesis within the body of existing knowledge." For both assignments from the French course, and for the brief reflection papers from the management course, I've noticed certain of the items on our eleven-item rubric blending together. I wonder if my experience is similar to that of my colleagues (some of whom have the misfortune of having to slog through my 280 students' homework papers!); if so, it may be that the rubric is more difficult than we had suspected to apply universally, or it could just need some subtle tweaking. I'll be interested to hear how our conversations go on Tuesday when we all meet to compare notes before Lulabelle and I take off for Austin with the assembled data.

And speaking of assembled data, this morning Lulabelle sent me a nice thick spreadsheet full of very nice numbers showing significant gains on a number of items from the pre/post-test administered in my 280 class last Fall. I wonder how my students' responses compare with those of my colleagues' students.

Exciting!

Yes, I'm a nerd.

Anyway, I'll leave it at that for now. Maggie's likely to be home from work in a half-hour or so, and I'd like to free up my evening schedule to spend some time with her.

Arrivederci!

Déjà vu

It's raining outside, Maggie's asleep on one of our new couches, it's the perfect day for updating the blog.

I've just returned from the second of my three May conference-season journeys, this one to Nashville, and I'm spending the day recuperating before a new busy week-and-a-half that ends with me taking off to Austin, Texas for the 9th biennial International Conference on Writing Across the Curriculum. Most of the next week will be spent preparing for my presentations there, and in applying our team's newly-minted rubric to piles of papers from Management and French Literature courses taught by my colleagues participating in the study.

I could have it worse: my friends Cordelius and Lulabelle have to wade through a stack of my 280 students' papers as they try to apply the rubric to nearly a hundred pages of intermediate mathematics. I spent a few hours making up a "primer of mathematical writing" to help them begin to read math. Therein I indicated that most mathematical notation is little more than shorthand, that mathematical terminology, though daunting, has the advantage of being precise and unambiguous, and that the most unfamiliar genres of mathematical writing (namely, definition, proposition, and proof) are fairly straightforward and exhibit clear idiosyncratic qualities that make them quite accessible to someone patient enough to examine their stylistic elements.

I hope it helps.

Wednesday and Thursday of this past week were spent in faculty workshops on writing, led by me, Lulabelle, and a handful of our colleagues. Wednesday's focus was on writing for freshmen, particularly those in our "liberal studies introductory colloquium" courses in which new students are exposed to the liberal arts tradition through seminars on a variety of subjects spanning the school's academic spectrum. I felt Wednesday's session was a bit lackluster, I sensed only tepid commitment from a number of the participants, I myself was still getting over a cold that had knocked me flat the week before, and I was having a hard time granting myself the authority to speak as a "writing expert." It was the first workshop outside my discipline I've ever had to run, and I felt like something of a pretender or a charlatan, standing in front of a roomful of my colleagues and trying to convince them that I knew what in the hell I was talking about.

By Thursday I felt better, both physically and psychologically. What's more, the audience seemed a bit more receptive: I sensed much firmer conviction on the part of that day's participants than on that of their colleagues from the day before. Thursday's crew was there to talk about discipline-specific writing, the sort that (presumably) goes on in higher-level coursework. I felt good about Thursday's workshop.

Immediately after the workshop ended on Thursday I hit the road to Nashville, arriving at my hotel just before 9:00 Central Time. I called up Titania, my friend from grad school, and we met for coffee at Fido (greatest coffee shop on Earth), my home away from home much of the four years I'd lived in Nashville.

We talked for a few hours, sounding like we were a hundred years older than we were five years ago. We talked about students and committees and conferences and enrichment programs and research and course design and assessment...we talked like the real university faculty that we are.

She, like two or three others of my colleagues who graduated from Vanderbilt within a year or so of me, has just received tenure.

I'd be lying if I said I didn't wish I were in the same boat. I'm starting to feel anxious. It's not that I'm worried about dismissal; I passed this year's reappointment process with flying colors. I'm just looking forward to the symbolic stability that tenure confers. I'm looking forward to the sense of permanence that comes with it. Yet I lost three years on the tenure clock in moving from a research postdoc to a tenure-track gig at a liberal arts institution, so I've got at least another year to go (likely two). Don't get me wrong, I can understand the powers that be not wanting to credit me with three full years of time served, but I'm a little disappointed that I wasn't able to get at least a year or a year-and-a-half of credit for the teaching I did in grad school and afterward in Illinois. It would be one thing if I'd gained nothing through that experience, but in all immodesty my talents speak for themselves.

I'm sorry, I hope you'll grant me this brief bout of pridefulness.

As Fido was prepared to close, Titania and I took to the street and headed over to Vanderbilt's campus. We continued to talk as we walked, reminiscing on our time in grad school (which time both of us enjoyed immensely), updating one another on mutual friends' goings-on. After a while we found ourselves at the math building, Stevenson Center's Building #1, and happily the doors were unlocked.

Our first stop was the first subfloor, where still stand the math grad students' offices. I know three of the current grad students (one's an ex-mentee and coauthor, a second's research path has crossed my own, and I was the reviewer for a paper by the third), the rest were just a smiling sea of young mathematicians who happened currently to be squatting in the offices we'd once called our own. We wandered through the dimly-lit office suite, trying to remember who was in which office in our own time. We were able to place most of our colleagues, but one or two offices were hard to fill.

We inspected the classrooms farther down the hall. "I had semigroups in here, with Gould," I told Titania.

"I had topology," she replied.

"I defended in this room," I said in another.

"Why'd you defend down here? I was in one of the rooms upstairs."

"I don't know."

She told me about how she once broke the sliding blackboard in the larger lecture room at the end of the hall. "I grabbed it from one side only and pulled it off the track," she explained.

Not much had changed.

After a bit we went back down the hall and took the stairs to the third floor, the first one above the ground. We stopped for a moment to peruse the list of faculty, most of whom we recognized. I mused that the Fields Medalist had no office number assigned to him.

At the end of the hall on the left was the room in which I first taught a course of my own, about which I blogged back in September 2007. It's changed very little since the night on which I went to campus to prepare for class the following morning: the blackboards are the same, the desks are the same, there still superfluously hangs from the ceiling above the side board an ancient set of maps of the world. "I never figured out why those are there," Titania said.

Half of the countries depicted thereon no longer exist.

That classroom remains, though.

I don't believe I ever led a class in that room after Fall 1999, so it's been over eight years since I've taught there.

Odd.

I shudder as I think back to the first writing assignment I made up for my Calc I kiddies back in 1999. Its prompt was little more than "Write a 5-10 page paper on a mathematical topic of your choosing. This is due on November eleventy-first." Granted, I gave my students hints on how to go about picking a topic, how to get started on their research, how to vet and cite their sources, which is more than many faculty would give. (Hell, most math faculty don't even think about assigning writing projects.) But I did next to nothing to structure or stage the assignment, to allow for rough drafts, to incorporate feedback, to provide writing instruction. The completed papers I returned to the students were line-edited, as much attention paid to misplaced commas as to thematic vacuums and ill-used evidence. Small wonder the products of my students' efforts were so hit-and-miss.

Ouch.

I've come a long way as a teacher in the past ten years. I wonder what experience the next decade will bring?

For now, I'm off to fold some clothes and rearrange our bookshelves. I'll be back soon, I hope.

In the meantime, if you've got something to say, please say it.