From Greenville

My first visit to East Carolina University (ECU) has been a successful one so far, at least from my point of view. (You can ask my interlocutors in the Math Department and the university’s current WAC [Writing Across the Curriculum] Academy if they feel otherwise.) I’ve been here for a day and a half now, and it’s been pretty much nonstop action.

I got into town on Wednesday night around 7:30, having left Asheville just minutes after wrapping up my early-afternoon Calc II class. There was still enough time left on the evening to catch a late dinner at Copper & Vine with my wonderful colleagues and hosts Libby and Xavier (holla!), faculty in the ECU Writing Center.

Yesterday morning gave me some free time to finish off a couple more rec letters before the real work began. Over coffee and tea at Starbucks Libby and I went over the feedback she’d written on Chapters 3 and 6 of my book. She seemed to be apologetic about offering her comments with an eye toward reader response, but I assured her that this is exactly what I need. Besides pointing out potential points of confusion, her comments offered up several sources with which I wasn’t familiar before, and easily a dozen new ideas for low-stakes writing activities, methods of providing feedback on writing, and means of making the writing process smoother and more meaningful for student writers.

We bustled off to lunch at the Starlight Café (if nothing else when this trip is done I’ll able to tell you where to eat in Greenville) with a few more folks from the Writing Center, and shortly thereafter it was time for my first performance, a research talk in the Mathematics Department.

I was well-received and my talk was somewhat well-attended…but somehow the energy wasn’t there for me. It’s no secret to people close to me that I’ve recently found myself a little disillusioned by mathematics: there’s little sense of urgency to it, there’s little authenticity to what I do. This isn’t to say that math is pointless and purposeless; it’s simply that lately I fear I find little purpose in it for myself beyond play-like manipulation or action-under-constraint, a sort of glass-bead game or extended Oulipian exercise. I fully recognize that the mathematics I do has little, if any, immediate impact on the world and I feel that on the other hand most other aspects of my career and personal pursuits and passions (teaching, writing, and poetry) have relatively profound impact.

Couple this with the fact that mathematicians are, let’s face it, not the most outgoing or socially “ept” of individuals by and large, and I feel as though I’m alienating myself from my own discipline.

Meanwhile I’m moving closer and closer to another: right now teaching writing to me seems a much more personal, passionate, fulfilling, rich, and worthwhile activity. While one in ten thousand people might need to know what the independence polynomial of a path-like graph tells us about that graph’s connectivity, it’s impossible to know too well how best to express oneself. It doesn’t hurt that nearly every one of my colleagues in composition and rhetoric is warm and welcoming. I’m sure the discipline’s got trolls of its own; it may just be that they do a better job of hiding them.

Straight from my math talk I walked across the quad with my Quimby (another of the ECU Writing Center folks…both he and Libby attended my talk in the Math Department, brave souls!) to yesterday evening’s meeting of the WAC Academy. This six-week faculty development series challenges its participants to find more meaningful ways to involve writing in their disciplinary courses. Perhaps unsurprisingly (this is always the case in such workshops) there is a preponderance of younger faculty involved in this program, but the various disciplines are broadly represented in this semester’s group, spanning from psychology and biology at one end to drama and dance at the other.

The focus of the evening was The Writing Process, reverently rendered in capitals. Libby (who just now stopped by where I’m sitting as I write this sentence), the WAC Academy’s fearless leader, started things off by leading a “writing into the day” activity. She asked participants (and me) to illustrate the process they performed when writing their most recent substantial writing project. I portrayed my book-writing project as an Iron Chef-like jumble of too many skillets on too many stoves which gradually became more like an ever-revolving Ferris wheel, one chapter on each of several gondolas that got written on each time it spun past the spot where I stood on the ground. It was an intentionally playful exercise that definitely helped me to pinpoint where and when it is I do my best writing, and what I need to perform that writing.

Unsurprisingly, several others’ writing portraits belied decidedly different processes. One writer combined passion and intellectualization in a picture of a brain with giant red lips: a “brainkiss.” (This is the same man whose list of New Year’s resolutions included the perfection of the “cloud hug.”) A scholar in child development portrayed her writing of a grant proposal as a regular succession of polygons, signifying a step-by-step process which began with an idea and ultimately ends by branching into new ideas (represented by the same circle which symbolize the initial idea). Cyclic and circular, linear and direct, all manner of processes were represented. Surely this variety in the final product is expected, and the “discovery” of such manifold means of writing is one of the take-home points of the exercise.

My portion of the evening’s activities gave the participants a taste of the textbook writing exercise I’ve used in MATH 280 and, with less success, in Topology. (I find it interesting that as I type this sentence my 280 students are hard at work, I hope, in outlining the first chapter! I just texted Iris to see if all is well there.) I asked the participants to brainstorm ideas for the first “chapter” of a text on the ideas they’ve encountered in the first week and a half of the Academy, select five topics on which to base “sections” for the text, and then in pairs write two or three sentences on each of those topics. The emphasis through and through was on the underlying process. Though we didn’t have time to review and revise the writing they’d done, I believe the exercise was well-received and helpful.

As always, the informal and after-hours activities provided as meaningful a learning experience as the formal ones. Dinner at Wasabi 88 gave me a chance to swap traveler’s tales of disciplinary dragons, budgetary woes, and ideas for potential future collaboration. Several of my writing colleagues came, as did three of the brand new ECU faculty. Boudica, Irving, and Monica talked about the frustrations and felicitations they’ve felt during their first year at a new school. They dream big, talking about cross-listed courses they’d like to teach and plans they have for using collaborative learning and boundary-blurring pedagogies in their classes. (Think “theater of the oppressed” and “literature of the wilderness.”) The future is in good hands.

After dinner I spent a couple more hours putting together materials for my final performance at ECU, a presentation I’ll be giving in about two hours to the ECU Writing Intensive faculty. I’ll be hitting the highlights of writing-to-learn, indicating several useful types of WTL activities and letting participants play with a few of them. (I’m toying with the idea of assigning a lipogram…)

It’s been a busy, but bountiful, trip. I’ll be glad to be home, and I’ll have returned a richer man.

Rocks and gravel

I've just finished reading Jonathan Kozol's Ordinary resurrections, begun just a few days back, and I feel, as I usually do on reaching the end of one of his books, an overwhelming sense of tiredness bound together with a bright and unbreakable thread of hope and strength.

It's a good book on which to end this academic year, surely the most tiring yet of my career (although, as I've noted on this blog before, not the busiest). Reading it at the close of the year gives me at once a sense of closure (which I've sorely needed) and a feeling of renewed energy. The book ends on the same note, as Kozol describes a gift of art Pineapple, one of the children of whom he speaks about most often in the book, gave to him: "an imitation stained-glass window that she made from tissue paper, brightly colored with green paint and with a wash of light-blue ink...When I asked her recently if it was supposed to be a rising sun or a setting sun, she seemed at first to not remember what I meant...'You decide,' she told me uselessly...at the risk of being sentimental about somebody whose sunny disposition brings a lot of joy into a world that has too many cloudy afternoons, I like to think it's rising" (p. 339).

Is it?

Kozol often admits in this book and others he's written since that he's getting older and feeling weaker. Although not yet as frail as he is physically (he's over seventy now, if I'm not wrong, and was sixty-four when he wrote the book I've just finished), I feel, on certain days at least, that I can empathize: each passing year steals away a little bit more of my relevance, my credibility, and my coolness.

"You may have them eating out of your hand now," my department's chair sometimes warns me, a hint of glee in his voice, "since you're not all that much older than they are. But just wait until you're my age." I'm warned that I won't be seen so much as the cool older brother but rather the stern-but-caring father. Just this past semester I encountered a student out of whom my most earnest attempts at cool cajolery could coax nothing. Magda, scarred, I suspect, by recent unpleasant experiences with mathematics, was timid in her dealing with me, reluctant to take part in any activities in class, and unresponsive to personal offerings of assistance I sent to her by e-mail. "I have to be honest that I've gotten a sense of 'defeat' from you for much of this semester," I wrote her. "I know you'd mentioned earlier this semester that you'd considered math as a major, and I hope that that's not an idea you've abandoned entirely."

I urged her to reply, but I never heard back from her.

This incident can't help but make me think of a noontime meeting several of my colleagues in the department and I shared with a pair of textbook company representatives. While my colleagues and I pored through elaborate boxed lunches bought from an off-campus catering company, the two textbook reps gushed for several minutes over the features of their company's latest Stewart-clone calculus textbook.

They tried to make their case, I'll give them that. I'd indicated that I honestly don't use whatever calculus textbook I've been assigned as much more than a source of examples and exercises (generally the exposition in such textbooks is godawful, and the organization is unmotivated, at best), supplementing the textbook substantially with descriptions, worksheets, activities, and projects of my own devising, including a number of nontraditional writing assignments. "We're very proud that [their text] contains [some unsubstantiated and moderately large number of] pre-written group projects." I nodded, unimpressed. (So does every Stewart-clone; generally these projects are as unmotivated as the integument of the text itself.)

About fifteen minutes into their demonstration, and after about ten minutes of fiddling with recalcitrant teleconferencing software, the reps got the lead textbook author himself on the line. He sounded tired, as though he'd made these dogs and ponies to dance two or three times already earlier that morning (or at least that week). He showed us a number of the features of the on-line text, most excited about the numerous Mathematica-driven animations he and his colleagues had developed for the textbook. (Such animations are not in themselves bad things; however I fear that without empowering the students to learn how to create their own animations, the animations alone do little more than provide an alternative visualization tool.)

After trotting the poor schlub of an author around the rink for a few more laps, the reps resumed their own presentation, and reached the part of their sell about which I was reminded above. "The beauty of the on-line scoring capabilities," one of them said proudly, "is that once a student has submitted her homework and the homework is graded, the computer can generate a personalized letter indicating to the student what sorts of problems she got wrong, telling her where she needs to focus her study. This can be done automatically, for a class of two hundred students. They'll think that you cared enough to write a personalized note to every one of them about their work."

I don't want to give the impression that this past year was all about weariness and defeat. To the contrary, I feel I've had some tremendous successes in the classroom.

While the textbook exercise fell on its face this past semester in Topology, it went over fantastically with the MATH 280 folks in the fall, and I can't think of many moments in my career at which I was prouder than I was when Ulrich and Uriah spoke on the project at the Elon conference (including in their presentation the phrase "writing-to-learn," and defining the phrase correctly!).

While I feel I lost the "faith" of some of my favorite students, like Magda, above, and like Tish, who became openly disillusioned about topology by the semester's end, I feel like that loss was only temporary, and that through open communication and understanding I've won that faith back.

While I feel my attempt at crafting a more meaningful system of feedback met with mixed success, the success I've earned is great enough to encourage me to recraft the system and try it again next term, rather than simply to abandon it.

While I've had my share of dealings with troubled and troubling students this past year, I've also had my share of dealings with marvelous ones. Jacobina's transformation from a hesitant and nearly math-phobic student at the outset of Calc I to one of the most outspoken, confident, and competent scholars in the stronger of my two sections of Calc II was nothing short of astounding. Words cannot describe the pride I have of her. Equally exciting is the undergraduate research Tonio and Siegfried have done, and the potential Ino and Iris have to do similar research this summer.

These small (and not-so-small) victories and many more like them are the rocks and gravel out of which, as the old blues standard goes, a solid road is built. Where's the road headed?

I've got back-to-back conferences coming up in less than a week (the International Writing Across the Curriculum Conference in Indiana and the AMS Eastern Sectional Meeting in New Jersey), then a half-week of Integrative Liberal Studies workshops in which I'm playing some role or another. A week after those come to and end the REU students start arriving. I have high hopes for this year's program; they're clearly a bright bunch with a lot of strengths. I've got a book proposal in at a good publisher, on which I'm still waiting to hear a decision. I've got great ideas for my courses next fall. It's going to be a good year.

The road is a long one, but the sun's shining yet.

I think, indeed, it is rising.

A modest proposal (one having nothing to do with cannibalism)

Hmm.

In the past week or so I've had several really good conversations about this past semester's revisions policy with students in both Topology and Calc II. A few things are clear from these conversations:

1. A large number of students benefited from the policy of allowing unlimited revisions (on exams in Calc II and on homework in Topology). Moreover, they benefited in exactly the ways I would hope that they'd have benefited: they profess to being much more eager to look over their past mistakes, to understand what they did wrong, and to attempt (sometimes over and over again) to correct their errors.

2. A much smaller number of students played the system like a two-dollar fiddle, not taking adequate measures to prepare for the exams (or the homework), putting off studying various topics until after the exam's been given, graded, and returned (or until after time's been found to corner one of the class's brighter students and ask said student for a transcription of her or his homework).

3. Something needs to be done to counteract the inevitable effect of procrastination, so that I'm not socked with a hundred revised exams and homework sets to grade at the same time final exams come due. (I apologize if the mass of grading I had to do during the past week as more and more revisions came in made me a bit more snippy of late.)

One of my Topology students made the following suggestion (thanks, Karl!): include with each successive revision an "expiration date," which, once past, precludes further revision. For example, I might allow a student a week to complete each iteration of a revised assignment: say I hand back a graded assignment on Monday, May 10th; the next revision, should a student wish to undertake said revision, would be due on Monday, May 17th. If that date passes without revision, the student's out of luck. If the student does perform some revision and receives the paper back on Wednesday, May 19th, then he'll have until Wednesday, May 26th to effect further revision, and so on. It would be the student's responsibility to be present in class to pick up graded revisions.

This would definitely help address the third observation above. Moreover, I think it would encourage more students to take advantage of the revisions: instead of putting them off until the inevitably busy end of the semester, students would be pressed to perform revisions right away and receive the benefits thereof.

The second observation above remains unaddressed. What to do about those who play the system? I will say that to some extent the chickens came home to roost when the final exam was graded: it was clear to me from performance on the final exam which students cruised on through with little concern for actual understanding of the concepts treated in the course. However, perhaps it might be appropriate to provide some sort of system of diminishing returns, at least for the lower-level courses (like Precalc, Calc I or Calc II) in which I might allow unlimited revisions: the first round of revisions will earn 1/2 credit back, the next 1/3, and so forth, until after two or three rounds there's really no purpose, from a "credit" standpoint, to revise. I'd like to think the best students would continue to revise anyway, striving for a perfect theoretical mark and a more and more perfect understanding.

Anyway...that's where I stand right now.

FYI: I just kicked off my summer leisure-reading season by starting Jonathan Kozol's Ordinary resurrections: children in the years of hope, and although I'm only about thirty pages in (and enjoying it immensely), it's making me more and more aware of the need for "ethnographic" methods in the "hard" sciences. I suspect this coming summer will see me write a number of posts on this blog in which I discuss the humanistic side of mathematics, in which I experiment with what Laurel Richardson would call "creative analytic practices." Stay tuned!

Patrick is a patsy no more

I'm a nice guy, but I don't like to be made a fool...nor do I want people to think they can make a fool of me.

To the Calc II students who were overheard by Math Lab staff to say, while completing the homework on Taylor series after the exam featuring Taylor series questions had been given in class, "yeah, now we need to learn how to do this stuff, so we can do the revisions!": congratulations! Your flagrant display of immaturity has caused me to completely rethink the revision policy. Sufficiently many of your more mature colleagues have let me know that the revisions truly do help them learn that the opportunity for revision will remain in place, but I fear that offering full credit for unlimited revisions may simply be unfair to those who struggle to master the material in a timely fashion. Look forward to a revamped version of the policy for the Fall 2010 semester.

To the Topology students whose homework is an automatistic transcription of the work of one of your more steady peers in the same class: as I'm fond of saying, I've been in this line of work for over a decade now, and I know the score. I just want you to know that I can tell when a person's work is really that person's work. Don't think you're pulling a fast one on me.

That is all.

Please understand that I'm not angry, just tired, and, honestly, a little disappointed.

And I'm also off to class.

Wha...? A new post!? (Complete with interrobang...)

Yeah, yeah. I know it's been a while.

It's been a crazy semester.

I've lost track of the number of snow days (three?) and late starts (four? or five?) we've had...there was one point at which I met with each of my classes precisely once in the span of 14 days: in the week prior to Spring Break I'd canceled Monday's Calc II classes for some reason I've since forgotten, and Tuesday and Wednesday ended up both being snow days, so I met with my Topology class and one of the Calc II sections only on Thursday, and with the other Calc II section only on Friday...and then Spring Break came.

Needless to say, this threw everyone's trains of thought off the rails, and in the subsequent weeks (the last couple) we've all been running around like mad trying to pick up the pieces.

I've made a number of mid-course adjustments in order to try to compensate for the craziness. I've scrapped several "less critical" sections from the Calc II calendar, and I've changed up the syllabus for Topology: having found from several of the most dedicated students in that class that the textbook assignments were not proving to be an effective means of learning the material, I ditched those. Many of the concepts were proving very difficult for the students to paraphrase, so that only a handful of the students were producing textbook submissions which were anything more than reiterations of my own course notes. Moreover, the homework assignments have been difficult enough to demand substantial amounts of the students' attention. In return for scrubbing the textbook project, I've asked the students to redouble their efforts at revising their homework, and so far they've kept up their end of the bargain.

I feel strongly that flexibility, both on the part of the teacher and on the part of the students, is critical in designing an effective learning environment. I've never been able to fathom faculty members who use the same rigid note sets semester after semester, or who plan precisely which exercises they'll assign to their classes for the duration of the term on the term's very first day.

Yeah, Topology could be moving a bit more smoothly, but as this is the first time I've taught the course, a few fits and starts are inevitable, I suppose. I appreciate my students' patience as I figure out what works and what doesn't.

Calc II, on the other hand, is cruising over smooth seas.

What else is new?

Um...

...I'm still waiting to hear back from Jossey-Bass regarding my book proposal. I'm hopeful that the proposal will get picked up...although I'm not sure where I'm going to find the time to finish the two chapters I'd promised by May. I've got an outline for the first chapter worked up, but little more than that right now.

There's been little movement on the rhetorical analysis of REU students' writing I began several weeks ago with the Charleston folks. Last I knew, Bella was planning on making some revisions to the initial version I posted on our Google site a few weeks back. Nothin' new there, though.

The Writing Intensive Subcommittee's knocking off new proposals left and right...moving to the Google Docs platform has made our work dramatically simpler and more streamlined. And right now ILSOC's workload has been relatively light as we've all hunkered down in our respective subcommittees to put together faculty development workshops (WI's planning one on writing instruction for ESL students, based on a workshop run at this year's Meeting in the Middle, the Carolina Writing Program Administrators' spring conference) and hammer out assessment plans. WI's assessment plan's been in the works for over a year now, and many of the materials have been collected already...it's just a matter of sitting down, establishing inter-rater reliability for the rubric (say that three times really quickly), and making our way through the students' writing samples.

What else?

Tomorrow I'm truckin' over to the 2010 MAA Southeast Sectional Meetings at Elon University with a boatload (well, a vanload, anyway) of our students. We've got 23 students attending, several of whom are giving talks or posters or serving on panels. Several first-year students are going (props, Iris, Ino! What's up, Ulysses?), and they're particularly stoked. I'm glad I put forth a strong recruiting effort...I don't mind saying that it's been a ridiculous amount of work to organize transportation, housing, special events, et cetera, but I think it'll be worth it. I'm particularly proud of my most recent research students, Siegfried and Tonio, who'll both be presenting their work in the undergraduate talk sessions; and Ulrich, Uriah, and LaDonna, whose presentation late on Saturday morning will showcase their views on the 280 textbook project.

Oh...oh...oh...OHHHHH! And after two weeks or so of intense paring and picking, my colleague Tip and I plowed through the 268 REU applications we received and came up with a list of participants for this year's program. Only three students to whom we offered positions turned us down, so we got most of our top choices. I'm excited to have them all on board. I've got a good feeling about this year.

What else?

The Tenth International Writing Across the Curriculum Conference is quickly coming closer...and plans are moving ahead for the celebration of Oulipo's 50th birthday I'm helping to put together in November. We've now got a tentative list of invited speakers, informal promises of financial support, and a rough schedule of activities. Once we've confirmed our speakers list we can begin to advertise to the campus and other communities.

I've got a few more trips coming up (two in April and two in May), but once those are over I'll be looking forward to settling in for the summer.

And I'm still waiting to find out the decision on my tenure application. Should come any day now. Fingers crossed.

That's about it, pedagogically speaking. I'll be sure to check in if anything noteworthy happens, maybe from Elon.

Fare thee well!

Rhythmless

The semester began with a truncated week, half of the department gone to the Joint Math Meetings in San Francisco. Two weeks later I scrubbed a Friday class to make way for a writing workshop that would never be, and since then (just in the past week and a half) we've had two late starts and a full-out cancellation, the latter making academic my decision to cancel my Friday class for the second time for the non-existent workshop.

The upshot? We've yet to hit our stride.

Calculus II seems to be chugging along nicely, but I feel like Topology's full of fits and starts. Half of the students enrolled in the course are each going through one or another personal crisis, and various tricky concepts are tripping up all but the strongest among them. For instance, the definition most central to the course, namely that of topology, involves a set whose elements are sets; the same is true of basis, and the relationships between these two sets of sets are subtle and anything but clear. What's helped them most so far is to emphasize and re-emphasize that

1. nothing will help one more than knowing the definitions inside and out, and the relationships between them;

2. one is not really thinking about a problem if one is not writing about it, drawing pictures to help oneself understand it, or experimenting with various methods with which one might solve it: one must write to learn; and

3. the most important things to record in performing any proof are what you know and what you need: having written these down explicitly will often take one halfway to the end of the proof.

I've not yet heard much from the students regarding how they feel about the homework presentations, but they've been stepping up to the plate: for Homework 3 all five problems were covered.

We'll find a groove.

Meanwhile both the weather and overly complicated scheduling issues have wreaked havoc on committee schedules, and our faculty search has eaten up hour after hour in places scattered throughout my calendar. (Incidentally, the candidates who've visited us so far have given me a good deal of food for thought regarding teaching and learning, but at this time, with a week or two left in the search, I don't feel it would be right to say much about it.)

What's the next week hold in store? Two more candidate interviews, more preparations for the upcoming MAA conference at Elon University and next fall's conference on math and poetry, and work on several writing-related projects. So much going on, so little time to finish it all...let me know if you want in on the action.

Arrrrrr...avast!

The "pirate" section of Topology is on. Beginning on Tuesday, February 2nd, I'm going to try holding an intermittent "unofficial" (or "pirate," named for the manner in which we'll have to hijack a vacant classroom somewhere on campus) section of Topology, splitting the class in two in order to attempt to provide a more cozy and intimate learning environment to the students in the class. It looks like I'm going to have roughly 8 or 9 in the unofficial section and the remaining 15 or 16 in the section meeting at the official time.

We'll see how it goes.

In other Topology-related news, we've had two installments of homework presentations (operating in lieu of homework committees this semester), and the second flowed much more smoothly than the first. Students took turns explicating four of the five homework problems which were due today, and they all did a fine job. I was particularly impressed by the way in which the proofs they offered were for the most part merely sketches. It's best that the student presenters leave lacunae to be filled by their fellow scholars in their individual write-ups: to provide a complete and error-free proof would be counterproductive.

What I'd like to know at this point, from the students in Topology with whom I've worked in earlier classes (280, Abstract Algebra, etc.), is: which system do you prefer so far, homework committees or homework presentations? Obviously they both serve different purposes (one offers substantial opportunity to peer-review while the other is an instance collaborative learning in the extreme), but it might very well be asked which serves its purpose more effectively.

Which one is the most useful to you? Which one helps you learn better?

We'll see.

I'll leave by noting my frustration at Mother Nature for dumping several inches of snow all over what should have been the writing workshop I've been co-organizing, scheduled to take place in Black Mountain this afternoon. Snowpocalypse II caused my writing colleague Betty Lou and me to push the workshop back to next Friday.

Two weeks in the can

We just wrapped up Week Two here at UNC Asheville, and because of the MLK holiday I've yet to teach a full week of classes this term. In fact, I'll be skipping out on my Friday Calc II class this coming week, so it won't be until Week Four that I manage to teach a full week.

Things are...well, I think they're settling in.

I still feel unsettled, though. Missing the second half of the first week because of the Joint Meetings really threw me off. Nevertheless, the classes are starting to come together, the enrollments are stabilizing, and we're getting work done.

My Calc II students did quite well on their first miniproject. (It was the perennial favorite, "Confectionary Conundrum," in which they are asked to estimate the number of gumballs it would take to full the candy machine I keep on my office desk. They're meant to use Riemann sums, but there are always a few folks who come up with other clever ways of getting an estimate.) And I've got great attendance so far, which is somewhat troubling, since there are 36 people enrolled in one section and 37 in the other, while the room is designed to seat about 32.

Meanwhile my Topology students have weathered their first round of homework presentations. The presentations (of which there've been two so far, delivered by four students) were a bit different, as is to be expected, from the homework committee presentations in past classes. The presentations were less coy and more direct; this is unsurprising, given that in the homework presentations in this class the students are asked to sketch draft solutions for their peers, whereas the purpose of the committee presentations in past classes was not to solve the problem, but rather to highlight common errors and pitfalls, and indicate any clever methods one or more students may have discovered.

I'm hoping that as the homework sets become more difficult, the students will put more thought into their presentations, planning ways to offer their friends helpful hints without giving away the full story. Being able to sketch a proof is as important a skill as being able to write it out in detail.

I'm also hoping that students will start to take advantage of the unlimited revision and resubmission policy I've got for the course.

I think one of the things that's kept me from settling into a groove is that much of the work I've done so far this semester is administrative rather than pedagogical. We've got a lot going on in our search for a new faculty member, and I've been scrambling around putting out fires for the Writing Intensive Subcommittee (dealing with student petitions, setting a new meeting schedule, uploading course proposals, planning next week's workshop, puzzling out assessment) and the ILS Oversight Committee (another new meeting schedule, dealing with the Academic Policies Committee, and putting out a bajillion little fires regarding Clusters). And I'm trying to organize the growing list of students who are planning on going to the MAA's Southeast Sectional meeting at Elon University in March. (Twenty students have committed to going now, and I've got my sights set on nine or ten more.)

Ugh.

Okay, I just realized that I've said nothing interesting or insightful in this post, so I'll end it here and wait until I've got something more meaningful to share before I write again.

Day Two

Topology met this snowy, icy morning, although we were a few people short (due, no doubt, to the hazardous road conditions brought about by the nasty weather). Those who came were excited to be there, though, and no one seemed to have much trouble jumping right into the thick of it.

Even if we can't manage to split the class into two smaller sections (one meeting "informally," commandeering a free classroom here or there), I think the semester will go smoothly for this course: most everyone knows each other quite well, having weathered several previous courses together, and no one seems particularly shy about speaking up in front of the others or about writing on the board. I think it'll be fine.

The feedback I've gotten so far has been very positive. Generally the students respond very well to the problem-based, handout-driven class activities, and almost all of the groups that gathered this morning to work on the handouts together functioned smoothly and efficiently, with animated (and apropos!) conversation.

I should mention there was glee on the part of some regarding the disappearance of the homework committees. We'll see next week how their replacement for this course, the "homework presentations," go over.

On to Day Two of Calc II...

Topology

Sometimes our closeness cannot be
a simple reckoning of distance,
a tally of the steps from you to me;
for in a purer sense
it's in the neighborhoods we share,
and in the friends to which we're bound,
and in the circles where
we find our common ground.

Day One

It's Day One, all right, but it sure doesn't feel like it yet. There are a few quirks in my schedule this term that are going to take some getting used to:

1. I teach on every single day. Generally I teach four out of five days, and those days are typically very heavy ones, but I've usually got either Tuesday or Thursday to recuperate. Speaking of heavy days...

2. Tuesdays, the days I most frequently have off, are my heaviest days this semester: all three of my courses meet on that day.

3. I'm used to having my first class no later than 10:00 a.m. (frequently 8:00 or 9:00), but on Monday, Wednesday, and Friday of this term I don't teach until 1:45 p.m. This pushes me back to 5:25 p.m. on Mondays, the latest I've ever had class. That's going to be weird, especially for the first month or so, as it will be dark by the time class gets out. On the up-side, I've only got one class on Fridays.

4. Finally, and perhaps strangest of all, I teach two sections of Calc II, one which meets three days a week (on Mondays, Tuesdays, and Thursdays), and one which meets four days a week (on every day but Thursdays). This is going to cause my two Calc II sections to go out of sync with one another in a New York minute, making it damn near impossible for students to miss one section and show up at the other if convenient to do so, as they occasionally did last semester without any damage done.

Weird.

In other news, I spent a little while this morning walking around and scoping out potential classes for our "pirate" section of Topology. I found a couple of candidates during the 10:00 to 11:00 time slot. This could actually work.

Okay, I'm off to try to get some more bureaucratic BS done before my first class meets, at 1:45. Avanti!

First Day Jitters™

Yup.

Here they are again.

A day early, in fact. Those First Day Jitters™ have returned for another encore performance.

I've no reason for jitters, of course, but that doesn't stop 'em.

I'm prepared through next Tuesday in both of my courses (through next Thursday, likely, in Topology); I already know roughly 2/3 of my 90-odd students, and the faces of those students I don't know are now committed to memory; I'm coming off of a really good semester and looking forward to another good one.

Nope, I still don't feel quite there.

It's the newness.

It's the adventure.

It's the embarkation.

I've been doing this for almost 15 years now, but it never gets any less exciting.

God, I love my job.

Please know, my friends, that when class begins tomorrow I'll be just as nervous (probably more so) than you are.

So be gentle.

Let's make this one a semester for the ages, shall we? Let's teach one another, let's learn from one another. Let's complete compelling projects. Let's prove powerful theorems. Let's plan eye-popping conference talks. Let's give it our all. Let's get out there and make each other proud.

Let's do it, huh?

A textbook for 280

At last.

Working for about four hours this morning, La Donna and I put the finishing touches on the (pen)ultimate draft of the MATH 280 textbook, which can be accessed here.

Why "(pen)"? It would be nice to throw in a few more diagrams (there are spaces and other placeholders left for such diagrams here and there), and one of the folks in the class volunteered to come up with a cover design...but aside from relatively minor matters like that, the thing's done.

Is it perfect? No.

Is it in places sketchy and awkwardly-worded? Yes.

Is it an authentic effort, the culmination of 15 students' legitimate attempt to make sense of a number of difficult concepts drawn from high-level abstract mathematics by putting together a "textbook" which addresses those concepts? You bet yer sweet bippie.

I'm happy. I think it's gone well, and the feedback I've gotten on the project is for the most part good. With better organization on my part, the same project, assigned to my Topology students, should run even more smoothly.

Excellent work, y'all! You've all done a wonderful job both as writers and as editors.

The fun begins anew in a week.

2010

Well, it's a new year. And I've made a good start of it, I think.

This morning, after my first run of 2010, I spent a couple of hours getting a couple more days ahead in Topology (the Joint Meetings are exing out the second half of the first week of class, so I'm doing all that I can to get some traction before the semester actually gets started, since things will be getting crazy quickly once we're underway).

I've now posted the first two handouts and the first two homework sets, which should take us through the end of the second week of class.

I'm happy that this course is a "terminal" course: I'm simply not sure how "far" we'll get given the typical student-centered design of the class. I am, however, taking steps to "streamline" the flow of the course so as to maximize the material we'll be able to explore.

For instance, I'm making efforts to bring "later" concepts in early on so that students are introduced to them sooner rather than later. For instance, the second homework set already includes the definition of the Hausdorff separation condition, which Munkres doesn't address until over a hundred pages in, and I'm already weaving together treatment of continuity and closed sets, both of which come a bit later in Munkres as well.

Also, I'm taking a "just-in-time" approach to review of ideas from set theory and relations (i.e., material from MATH 280), putting off such review until it's needed. Most of that review will probably take place in the homework sets.

I'm happy about the way the course is coming together so far, and I'm eager to get underway!

Spring syllabi

At last!

The syllabi for my Spring 2010 courses have been posted on the now-up-and-openly-accessible course websites for Calc II and Topology. Supplementing these are the omnipresent links to my now-standard writing stylesheet, and for the budding topologists I've included a more-robust-than-ever introduction to LaTeX, now including a guide on inserting graphics files into LaTeX documents.

What about those syllabi? I've tried to take all of the feedback my students offered to me by e-mail (about 20 students eventually got back to me with their suggestions!) as I put them together, and I've tried to stay somewhat true to my goal of de-emphasizing grades (and thereby at least implicitly emphasizing collaboration), all while minimizing the "bureaucratic overhead" that was probably the number one complaint my 280 students had about their course this past semester, as measured by the course evaluation forms I got back a couple of weeks ago.

A few additional comments:

1. Rinse and repeat. I've backed off from explicit portfolio grading, but I've included the portfolio-esque unlimited revision-and-resubmission option in both courses: exams and projects in Calc II and everything in Topology can be revised and resubmitted as many times as the student would like to in order to craft an increasingly correct, complete, clear, and well-composed piece of mathematical writing. These systems of unlimited R 'n' R should help to cut down on the complexity of grading: if you're not happy with a grade, revise and resubmit. Again, if you'd like. And again. And again and again and again. I like this idea in theory and I'm excited to see how well it's going to work in practice.

2. Homework presentations. For the first time in two years I'll be teaching an upper-division course without homework committees, replacing the committees in Topology with "homework presentations" instead. This move too is designed to reduce "bureaucracy" by eliminating the deadlines associated with committee problem submissions and committee presentations, and it introduces a good deal of flexibility: as you can see on the syllabus, any number of students (including a single student!) may opt to join in on a particular homework problem's presentation, and there's only minimal bureaucracy involved in assessing participation in presentations. Speaking of flexibility, I believe the new syllabi offer tremendous...

3. Flexibility in assessment. Though there's no explicit mention of portfolios, in both courses I've left the exact manner of grading up to the students: in the first full week of class one of our tasks will be to decide, as a class, how each sort of assignment will be assessed, and with what weight it will affect students' grades.

4. Homework in Calc II. In Calc II, I will still be requiring homework, but at least half (probably more) of the homework will be handcrafted by yours truly, and I'll include frequent "short essay" questions demanding interpretation and explanation in addition to more traditional problems requiring no more than computation. Although I've still not made up my mind on the matter, I believe I'll grade the homework by giving each problem a number from 0 to 3:

0: no attempt, or a clearly half-assed attempt, made at solving the problem.

1: an honest attempt has been made, but the method of solution is not correct, and/or the student's work is very unclear and logically jumbled.

2: the method of solution is correct, but perhaps there are one or two minor computational errors; the writing is clear and well-composed, but insufficient explanation is given when explanation is called for.

3: solid; there are no errors (save perhaps a transcription error or a minor, minor error in computation), the student's logic is clear and straightforward, and all necessary explanations are sufficiently complete and are given in complete sentences.

It'll probably be a relatively easy matter for most students to get a 2 on a problem, but I'll warn them that getting a 3 is typically going to require careful attention to mathematical exposition as well as mathematical computation.

The syllabus for Calc II doesn't allow for unlimited revision and resubmission of homework problems, but if there's enough call for it, maybe I'll consider it.

5. The "textbook" assignment. The Topology crew is going to follow in the footsteps of this past term's 280 folks in writing a textbook for the course. As I did this past fall, I'll randomly assign topics from each "chapter" to students in the class. As in the fall, we'll meet up at "editing parties," but I'll be making these parties a bit more formal (going so far as to bring homemade goodies to them!) in order to encourage attendance. Finally, I'm taking La Donna's suggestion and writing a template the students will be asked to use in order to craft their textbook submissions; this will encourage at least basic typographical consistencies between the sections of the book.

Incidentally, La Donna and I will be meeting next week to hammer out some more edits on this past semester's textbook. I'm excited to see what we can make of it.

Before I go, I wanted to provide a link to the pedagogical Live Journal authored by my collaborator in crime, Cogswell. He and I will be sharing ideas with one another (often openly on our respective blogs) as we move forward with our courses this semester. I believe he's thinking about using the textbook assignment in his abstract algebra course, but is understandably skittish about the amount of work it might entail (he's the proud father of a brand-spankin'-new baby and has therefore clearly got other major commitments!).

More power to ya, Cogswell!

The calm at the center of the storm

It's early, early, early on Sunday morning on the weekend between the last week of class and finals week. I've had a good stack of grading to get through, but I'm about two thirds of the way through that, and tomorrow morning brings the most recent Algebra al Fresco event, a random walk through downtown Asheville.

The semester's ending well. I've been worried about how my philosophical frustrations from a few weeks back might have been adversely affecting the students in my classes (especially Calc I), as I've feared they may have been buffeted by ever-shifting winds. But signs point to students' weather the storm rather well. One Calc I student spoke of being "inspired," and one 280 student said that, despite the difficulty and relative disorderliness of the textbook project, he learned "50% of his understanding of the concepts from the project." That comment, coupled with the envy my Spring 2009 students have shown for my current ones' getting a crack at this assignment, has convinced me that the same assignment, modified to fix the weaknesses it's shown this semester, should be a part of the curriculum for next term's Topology course.

I've still not put much thought into the precise structural details of that course, but it's starting to come together. It's not going to be as tightly structured, and it's going to be highly collaborative, and all assignments will allow unlimited revision and resubmission. Beyond that, who knows?

For now, it's late, and I'm off to bed. I hope to post again tomorrow with pictures of the random walk!

Survey says...

I've heard back from about ten students so far concerning the "survey" I sent out asking for feedback on my plans for designing next semester's courses. About half are students in Calc II next term, and about half will be in Topology.

Not too shockingly, the students from whom I've heard are among the respective courses' strongest and most dedicated, so some of their views should be considered accordingly.

Nonetheless, there are patterns emerging:

1. Like it or not, even the best students are highly motivated by getting good grades. While most of the students admitted they knew they shouldn't be compelled by the desire to get high marks, most of them owned that getting high marks eggs them on and gives them what they feel is an accurate measure of their progress. It's hard to say whether these students, among my strongest, are more or less likely to be motivated by grades than their peers who have to work a bit harder to keep up.

2. Nevertheless, I'm heartened that the students who have responded are all up for something new. Though the idea of their work being assessed in some sort of "portfolio" system is an unfamiliar one to them, they seem open to the possibility.

3. Most of them are very happy with the way their current (or past) courses with me have been run, and are up for more of the same. This is also heartening to me, as ultimately I think I do a good job in most of what I do for my classes, and much of what I do now will remain in next semester's courses, largely unchanged.

More to come, as more responses come in. For now, I'm off to bed.

Good advice

I've just send e-mails to all of the students currently enrolled in my Topology class next semester, and all of the students in one of my Calc II sections who've met me before, asking them for their input on course design.

We'll see what comes of it. Even if I only get about 25% or 30% response rate, I'll be happy.

Help wanted: apply within

So here's the deal:

As regular readers know, I've been kicking around various ways of putting together next semester's courses, with ideas ranging from a simple tweaking of homework assignments all the way through out-and-out adoption of portfolio-based (and therefore virtually gradeless) assessment.

No matter what, there are certain elements of both courses I'll be teaching that will be essential.

For instance, Calculus II will involve the same sort of miniprojects it always has (we'll start things off, as usual, with A Confectionary Conundrum, and we'll keep the Funky Function Festival and various other small-scale applied projects and in-class activities involving delicious comestibles), and I'll still require that some sort of computational work be submitted each week...but much of that work will likely be ungraded, in order to engender a low-stakes atmosphere of exploration. But beyond these basics, I'm open to negotiating just about every other aspect of the class.

Topology, too will have its sine qua nons: however it's done, peer review must appear as a regular, fundamental, and well-structured aspect of the course; as in Calc II numerical grades will be de-emphasized in favor of ungraded, proficiency-based projects, and in-class discussion and discovery will form the basis of most of our class meetings. I will also be offering unlimited revision/resubmission of all coursework to be completed during the entire semester. Beyond this, I'm open to negotiations regarding the finer structure of the course.

I'd like to conduct such negotiations, in order to be sure that the courses I put together really do suit the academic needs and the learning styles of the students with whom I'll be working. Therefore what I'd like to do is ask those of my current and former students who will be joining me in one of these two courses next semester to help me put the courses together. (I'm ideally positioned to do this right now, as 27 of my current Calc I students and 4 of my Calc I students from Spring 2009 will be joining me in Calc II, and all but 4 of the 24 students enrolled in Topology have had me for at least one course in the past few years. I'll likely never have a better chance to engage so many students' opinions ahead of time.)

If you are currently enrolled in one of my courses, or if you have been a student in one of my courses in the past couple of years, and if you will find yourself in either Calc II or Topology next semester, you will soon be getting an e-mail from me asking you for your input on what our course should look like next semester.

I'm open to suggestions regarding just about everything:

1. The nature of homework (graded? ungraded? from the book? invented by me? some combination thereof?)

2. The structure of in-class activities (handout-based? note-based? suited to small groups? suited to the individual? some combination thereof?)

3. The nature of written assignments (papers? original research articles? expository articles? reflection papers? textbooks?)

4. Grading schemes (numerical? low-stakes? portfolios? how heavily is each component of the class weighted?)

5. Topics to be addressed (this applies more to the folks in Topology than those in Calc II; sadly, there's a pretty clear-cut list of topics we'll need to get through in the latter course, since it's not an elective) and the order in which we address them

As you respond to me, I'll ask you to think about what works for you: what do you need to get out of our course, and how can we put together a course which best helps you to learn?

I can't promise that I'll incorporate every suggestion, as I'm sure the range of opinions will be incredibly broad. Moreover, whatever structure results will almost certainly be guided in part by my own recent shifts in pedagogical theory, and there are a few things that will simply not fly. (For instance, I'm firmly and fundamentally opposed to the very idea of grading curves, and have been so opposed for quite some time.) Nevertheless, I'll try to take into account every word of input I receive and cobble together course plans for both of my classes next semester.

So, if you've had me for a class before and if you'll be having me again in Spring 2010, expect to get an e-mail from me soon. If you'd like to get a head start and don't want to wait for an e-mail, please feel free to respond to this post in the comments section (anonymously is fine). Let's get a discussion going.

I sincerely hope that you'll help me out here. Your education is more important to you than it is to anyone else, and I hope that you'll help me help you by taking a hand in scripting the acts of your education in which I will play a role.

Hall conversations

I spent a lot of time in the Math Lab with my students today, and in the hall outside of it.

Most of that time was spent with my Calc I students, helping them out with the volume maximization problem they're working on right now. It's a barely-unprettified problem demanding a good deal of careful computation and innovative use of derivatives for optimization. They've got to find the least costly means of constructing a collection of dumpsters designed to hold 2000 cubic meters of material, knowing that the dumpsters' shape has to fall within certain parameters. It's a tough nut to crack, whose precise solution involves techniques from Calc III. They students are either loving it or hating it, for the most part. One thing's for sure: they're spending more time on it than they'd ever spend on a set of textbook problems, and they're learning a lot. As I was leaving campus just after 5:00 p.m., two or three of the groups banded together to throw an extemporaneous "dumpster party" in the classroom in which we meet. I almost wish I could have stayed.

I also spent an hour or so talking to a couple of my 280 folks about combinatorial and topological graph theory, and just straight-up topology. I taught Uriah and La Donna how to decompose a torus into a disc with identifications, and showed how this could be used to easily find an embedding of a complete graph on 5 vertices in the torus. It was good fun.

At one point soon after that I mentioned to several current and former students who were there assembled that I'd love to put together an informal reading group (much like the RAP [Research Among Peers] groups we ran at UIUC while I was a postdoc there), and they were all game. I mentioned Herb Wilf's generatingfunctionology, a freely-available text of which I've never read more than a few chapters and into which I'd love to get deeper. I think it would be accessible to some of our stronger students, and they could help the not-so-strong ones along. It could be a fantastic learning experience for us all.

Might could be we could swing that in the Spring.

I also talked to a couple students in the hall outside the Math Lab about my plans for Topology next semester (one's registered already, and the other plans to as soon as she can tomorrow morning). They're both regular readers of this blog, so both were familiar with my portfolio plans, and I asked how they think it'd fly.

Sidney (a student in MATH 280 in Spring 2009) is all for it. "It'd definitely motivate me. What motivates me is proficiency, and you'd be measuring proficiency at achieving learning goals for the course. I'm all about that."

La Donna (a current MATH 280 student) thought it might work well, but was a bit more reserved in her acceptance of the idea. "I have to admit that I'm a little motivated by grades," she said. "A good grade is a signal to me that I'm doing well and getting it."

I suggested that perhaps, as I've posited elsewhere recently, she's motivated by grades because she's been systematically trained to be motivated by grades. She admitted this possibility.

"In any case," I told them, "whether I grade by portfolio or not, whether I hand out numerical grades or not, I know for sure I'm going to permit unlimited revisions. I'm going to let people revise and resubmit, revise and resubmit, and so on, until they're one hundred percent satisfied that they've made their work as good as it can get." Both were excited about this idea.

They're both passionate students, and a blast to have in class. En route to lunch with our speaker the other day Sidney admitted that his mind had been blown on the last day of 280 last Spring when we'd talked about the existence of infinitely many different sizes of infinity.

Crazy shit.

I'm delighted that that delighted him. It's nice to have students like him, and like La Donna. And like Cornelius and Uri and Uriah and Tedd, all of whom were there to voice strong support for the idea of an informal research reading group.

They've got my back as much as I've got theirs.

That's a comforting feeling.