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.

A highly personal post

I'm demanding of my students. I push them hard. I ask them to challenge themselves on highly nontraditional projects, and on computationally and conceptually difficult assignments. I get them to work together and to present their ideas in front of one another, no matter how shy they are. I don't let up: from Day One through the Final Exam, they're hard at work, writing textbooks, critiquing each others' work, and pushing their intellectual limits.

I push my students in the same ways I push myself.

It's no secret that often try to be superhuman, and sometimes I succeed. I'm proud of the progress I've made in my teaching, of the advances my research (and that of my colleagues and students) has made, and of the work I've done in service to my department, my university, and my profession. I feel that I've achieved a lot, especially since I began this blog over three years ago.

But I've recently come to realize that I can't do it all. Even superhuman strength has its limits.

I've done such a good job of making myself ready to be "the strong one" for so many people in so many different ways that I've forgotten what it's like to lean on others when I need their strength.

This has hurt me.

I don't want to hurt.

I've decided that I'm going to relearn a lot of things I've likely forgotten.

I'm going to relearn how to let myself rest from time to time.

I'm going to relearn what it means to rely on others.

I'm going to relearn what it's like to be human, and not superhuman.

To those who may think this post may seem inappropriate for my blog, whose focus is pedagogical: anyone who's worked with me as a student or as a colleague knows that my teaching style is a very personal one. I believe it's crucial that teacher and student understand one another as persons, as human beings, before real learning can take place. I believe that for effective learning to take place, teacher and student must trust one another, and respect one another, and that teaching and learning are highly personal endeavors.

I don't know that I intend any specific exhortation by this post, except to say that if you know me and if you see me, in class or in the hall, on the quad or in my home, please know what it is that I'm trying to do: I'm trying to be a better person, and in order to be a better person I might just need your help, your support, and your understanding.

I have nothing but the deepest admiration and respect and warmth for my students, my colleagues, and my friends. Thank you for all that you've done for me, and for all that you do, and for all that you'll do in the coming days and weeks and years we spend together.

I feel more human now than I ever have before.

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.

Clusterf**k

I know I've not posted lately. I know it, I know it, I know it...things have been rather busy lately, what with a hectic Joint Mathematics Meetings in San Francisco (and thus a severely truncated first week of class), a second week of class spent trying to play catch-up, and a serious need to stick every finger I've got in the quickly-collapsing dike that is the Integrative Liberal Studies Clusters program.

I promise a more meaningful post soon.

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, part 2

One class down, one to go. The first section of Calc II went pretty well. As usual, I felt rushed, since there's just so much to be done on the first day. I left a few things unsaid, but nothing that can't be un-unsaid (would that be "said"?) tomorrow. It'll be all right.

Only fifteen minutes before I head off to the first meeting of the second section.

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?

Two calculi

A derivative is a recipe,
an integral is a poem;
the last has dreams of majesty,
the first is enchained by form.

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!