Midsemester musings

We're about halfway through the semester now, and I have to say I'm enjoying teaching more than I have for a few years now. I love both of my classes and am having tremendous amounts of fun with both of them. The Calc III class is the most engaged math class I've had in several semesters: the students are eager, active, and awesome. And Oulipo...I don't know how we can fit so much fun into three fifty-minute periods each week. I wish we met for longer...

In Calc III I've been starting each Wednesday (the dreaded "hump day") with a contemplative exercise of some sort, much like the first, about which I wrote a few weeks back. The purpose of each exercise is to ask students to put themselves in a positive frame of mind, to reflect on something that's lifting them up and to cast aside something that's holding them down. Today I asked them each to write a simple haiku (no season indicators or "turns," just a simple 5-7-5 syllabic scheme) about their current state of mind. Though I saw a lot of counting on fingers, I also saw a lot of earnest scribbling. Though I don't collect a single word the students write in response to these simple prompts, I have no doubt most (if not all) of the students are taking the assignments seriously, and I hope that they're having salutary effects.

In Oulipo the most recent out-of-class assignment was to write a "lofty" poem elegizing a quotidian object. Each of us selected an everyday object that was then randomly selected by one of the others in the class. We were then each tasked with writing verse that we deemed "lofty" in some fashion, extolling the virtues of the object we'd been assigned. For many people "lofty" meant "classical," and several student wrote poems in a romantic style, with rime and meter appropriate to an 18th-century-or-earlier bard.

After we'd workshopped our poems and read a number of them out loud, we talked briefly about conventional devices we might make use of to "loftyize" a piece of non-lofty writing and as a group came up with the following:

1. Germanic capitalizing: selectively or systematically capitalize nouns throughout the piece.
2. Inverting: selectively or systematically invert the standard modern subject-verb order throughout the piece.
3. Theethouizing: selectively or systematically turn "you"s into "thee"s and "thou"s throughout the piece.
4. Oloizing: selectively or systematically insert "o!"s and "lo!"s throughout the piece.
5. Adjectival inflating (a nod to n + 7): selectively or systematically replace each adjective with its longest synonym appearing in an agreed-upon thesaurus throughout the piece.

I'm going to try these out on a piece of non-lofty writing, maybe something from Jon Rogawski's Calculus...? Results posted soon...

Obligatory whatnots

I've been posting somewhat regularly lately, and though today's not given me considerable fodder for a brand-spankin' new post (cross products in Calc III and an introductory discussion of Italo Calvino's If on a winter's night a traveler in Oulipo), I thought I might mention a few ongoing whatnots.

Whatnot #1, CRTF...WTF? I've begun drafting a "contextualizing" document that might help folks who haven't been intimately involved in the process of crafting the current proposal understand exactly what in the hell those of us who have been intimately involved in the process of crafting the current proposal are thinking. Of course, I've come out semi-publicly (here and elsewhere) as having serious reservations about the proposal as it stands, so it's ironic that it falls to me to explain our reasoning.

I think at this point, the powers that be are concerned that given some of the language of the Strategic Plan (about more below) we're better off streamlining and "standardizing" our curriculum before someone else (*cough* GA? *cough cough*) does it for us.

Whatnot #2, This post by Teacherken of education-related blogging fame. (He's been a fixture in various places, including The Daily Kos.) The writing's on the wall, and it ain't pretty. As if I needed more reason to loathe AP exams. Students, parents, everyone: the AP system is fundamentally fraught with error of every kind. It's a wrongheaded hydra. We need to slay the damned thing. Of course, we're going to have to fight through ETS and friends to even get to it.

Whatnot #1 and Whatnot #2 bring me to...

...Whatnot #3, The Strategic Plan. I'm about 1/6 of the way through reading this sucker. I regaled (read: "bored/annoyed the crap out of") my Facebook friends with a line-by-line response to this damned thing a few days ago when I started reading it, alcoholic beverage in hand. It's awful, folks. It adopts the rhetoric of the corporate community, eyes intently focused on the bottom line, offering one way to the university system, and one way only: make us money or die. It's all about measurable production benchmarks (graduates are "produced," donchano?) and accountability to stakeholders. It's all about uniformity and portability and seamless transfer. It's all about standards. It's NCLB on steroids, repackaged for the 'teens. It's a godawful mess.

But it's the UNC system's lodestone for the next several years. It's our way through the woods. It's the house we have to beat, the inside straight we've got to draw into. It's our future.

I plan on finishing reading it this week sometime, provided I can find enough liquor. I'll post my thoughts about it here as I read it.

Constraint and contemplation

I thought I might mention a couple of the activities I asked my students to take part in today.

The first was a simple freewrite, with an even simpler summative exercise at the end. I asked my Oulipo students to freewrite for five minutes on the ways in which they've noticed their writing to be affected by constraint. Once they'd completed this freewrite I asked them each to identify three words which gave some indication of their freewrite's content and tone. They then shared these words on the board:

I joined the students in this exercise. I was intrigued that my three words ended up being "pattern," "unknown," and "death." The first was unsurprising but the last two were unexpected. I reasoned (if one can call analysis through freewriting "reason") roughly as follows: "we seek patterns in everything we see, including heavily constrained literature, because patterns have predictive power and allow us to extrapolate from the known present and past to the unknown future; perhaps the most compelling unknown is death...can the patterns we find in constrained poetry help us understand even this ultimate unknown?"

We'll have a chance on Friday to discuss the words above more thoroughly. So far we've only talked briefly in pairs about our ideas. I'm looking forward to these upcoming conversations.

The other activity I wanted to mention is a contemplative exercise I asked students in both classes to complete. Knowing full well that Wednesday is the longest and most stressful day for many folks in academia (students, faculty, and staff alike), I wanted to do something to help alleviate the stress. Yesterday, while sitting in the first session of my first faculty/staff learning circle since Fall 2011 (it's been too long!), I thought up the following activity, though I'm sure it's not original to me:

1. Take out two scraps of paper.
2. On one of them, write something that's stressing you out or bringing you down.
3. On the other, write something that's bringing you joy or making you smile.
4. Ball the first scrap up into a tiny origami boulder and chuck it into the recycling bin lovingly provided in the middle of the room.
5. Fold the second scrap neatly and tuck it into your pocket, where you're likely to find it once, twice, thrice, throughout the rest of the day, a gentle reminder of something you should be happy about.

It's a simple exercise, but in both classes it elicited a great response. People in both classes gleefully threw their stressors into the recycling bin in a hail of discarded worry. ("This feels really therapeutic," said one of my Oulipo students.) I noticed smiles and nods from many folks as they put their happy thoughts away. The activity took three minutes out of class time, but I believe it went a long way to establishing a sense of community and a more relaxed state of mind in which we would all be a bit more receptive to new ideas. I might have to make this, or something like it, a regular Wednesday occurrence.

I have a Beau-présent for you!

I'm sitting in my Oulipo class at the moment, updating as my students take part in their first peer review activity of the semester, reading over one another's beaux-présents, poems written using only the letters appearing in the name of the poem's dedicatee (in this case, the author herself or himself). For shits and grins, here's Mathematica's representation of my beau-présent, as a finite-state automaton:

I'm curious to see how these turn out! Perhaps I'll ask permission to share one or two of the resulting poems once they're done.

It's been a bit since I mentioned my other course this term, Calc III. Please know this omission does not indicate dissatisfaction; on the contrary, this section of the course is by far the most engaged and engaging section I've ever taught. (I think the presence of several really eager nontraditional-aged students helps!) I'm just a bit more outspoken regarding the Oulipo class owing to its newness.

More soon!

Day Three

Calc III's now met thrice (love that word!), and Oulipo twice. I've learned a lot in both, already.

The second meeting of the latter offered a great discussion on the many ways we can construe "constraint," and how constraint affects us. "What kinds of constraints do we see in our lives?" I asked. One student spoke of the way her anxiety constrains her actions: she must choose to do or not do certain things for fear her anxiety will overwhelm her. Another student talked about physical constraints, explaining how the perspectives we take on, constrained by the routes we take when we travel and the modes of transportation we use, affect our engagement with the world. While much of our discussion focused on the negative aspects of constraint and the ways in which removal of constraints liberates us, I asked the students to indicate some positive effects, too.

Regarding constrained literature, one student brought up a point an Oulipian might make: by constraining the words you're allowed to use or the way you're allowed to use them, though you you may find yourself with an impoverished list, you can nevertheless focus your attention on this list and make more astute, intentional choices as you write. Indeed, much the same can be said in other forms of art: as one of the Honors Program's star musicians pointed out, once free jazz hit the scene and all bets were off, one could argue that music became meaningless and it was only with the reinstitution of constraint that meaning was restored. Though we find pleasure in flouting constraint, as another student pointed out, that pleasure is unobtainable if constraint does not exist: how can we break the rules if there are no rules to break?

This class is going to be a good one, I think. The only complaint I have is that the classroom stinks, as I explained in a previous post.

More on my Calc III class, and curriculum-review goings-on, Honors Program whatnot, etc., soon. For now, I've got to get to dinner.

Day One, Spring 2013

My first class of 2013 went well! I've got 31 folks enrolled in Calc III, and one more itchin' to get in.

We met today for the first time and began with a brief low-stakes writing activity, a brief version of the now-common object-ive writing activity elaborated in the blog 3 friends, 30 things, 90 stories which I wrote with my colleagues Libby and Mariposa (and yes, we're doing it again this coming April!). This broke the ice, got people talking, and got everyone up to the board to jot a few words down. After that, we had just enough time to go over the syllabus before breaking for the day.

A minor rant: I hate hate HATE the configuration of Rhoades 213, the windowless pit in which I teach both of my courses this term. The "desks" consist of modular table-lets which each accommodate a single chair. They're small and mobile and ideal for gathering together in small groups to form a place for collaborative learning...if only they weren't bolted together, side-to-side, in phalanges of three or four per row. This static and stultifying configuration is nothing short of asinine. Only a pedagogical peewee would think that this structure of classroom is helpful. I am appalled.

How will it work out? Stay tuned...I've got the first meeting of my Honors seminar on Oulipo in that same classroom in about 30 minutes...

Day of Higher Ed, part 1

My colleague Casie tipped me off that today is The Chronicle of Higher Education's Day of Higher Ed, a day on which those of us who work in higher education are supposed to raise awareness of what we do, and how much of it we're doing. Contrary to the perception of some (mostly conservative, in my experience) suit-types who view higher education with disdain and its employees as fat and fatuous sinecurists, most of us actually work quite hard.

More forcefully, most of us work our asses off.

So, what's in store for me today? (Keep in mind that I'm coming off of a weekend on which I spent roughly 12 hours grading Calc III exams...) Though I can't guarantee I'll get to it all, here's the medium-term docket:

1. Write an end-of-year project report for the National Science Foundation for my 2011 REU (estimated time to complete this: 5-6 hours)

2. Draft a welcome and informational letter to this year's crop of REU students (time to complete: 1-2 hours)

3. Send out rejection letters to the nearly 300 students who didn't get into this year's REU (time to complete: 1 hour)

4. Grade exams for my two students who are taking Abstract Algebra II as a reading course (time to complete: 1 hour)

5. Respond to final drafts of MLA students' latest written projects (time to complete: 3-4 hours)

6. Write three or four rec letters, including an incredibly urgent one for which the requesting student gave me less than a week's notice (time to complete: 2-3 hours)

7. Plan workshop materials for an upcoming writing workshop I'm leading at NC State (time to complete: 3-5 hours)

8. Review and respond to proposed Abstract Algebra curricula floated by other members of the Mathematical Association of America's Committee on Undergraduate Programs in Mathematics (time to complete: 3-5 hours)

9. Generate open problems list for this year's REU (time to complete: 2-3 hours)

10. Begin housing and payroll paperwork for this year's REU students (time to complete: 1-2 hours)

11. Draft a precis for on the latest curricular proposal by the Curriculum Review Task Force's Curricular Sustainability Subgroup (time to complete: 2-3 hours)

12. Complete drafts of research articles currently underway with three different sets of undergraduate coauthors (time to complete: 10-20 hours)

13. Oh yeah...teach!

Anyway, I'd better get to work on that list, me with my oodles of free time. More later, perhaps...

Bounce

In a recent post I fretted a bit about one of my sections of Calc III, which section seemed to me a bit underprepared for class this past Monday. I worried that their apparent lackadaisicalness (if that is indeed a word) regarding Problem Set 4, on which we were working in class on Monday would lead them to be unready for today's class, in which they would be presenting their solutions.

I stand corrected. That section bounced back, showing themselves up to the challenge. Every single student called on to present did so, and did so with aplomb. I was particularly impressed by Dionne's willingness to work all of the way through the dreaded #61, which asked for a proof that two non-parallel vectors in the plane span the entire plane. Dionne, one of our promising young majors, has some exposure to linear algebra and is currently enrolled in Foundations, so she's no stranger to the proof genre. With a little help from a couple of her colleagues, she beasted that problem.

Yes, they bounced back, but not before I exhorted them to keep up with their work outside of class. Don't just come ready for the problem you think you'll be presenting (padded with the one or two preceding problems for insurance); come ready to present any one of them...and ready yourself as soon as you can so that when you're offered time in class to hash out the details, you can do so without delay.

Good work, everyone! I have to admit to a bit of nervousness at running my first Moore-method class in four or five years, but so far you're all making the most of it. Thank you for that, and for all that you do.

Feedback, as ever, is appreciated.

Worth a repost

This morning I received a brief but touching comment on my most recent blog post: "I miss Patrick teaching." I responded to this anonymous post in a manner which I repost here because I think it's worth wider readership:

Please know that I'm organizing this class in a non-traditional manner not because I want to avoid "teaching" (though, believe me, I'm doing as much teaching, in a non-traditional sense, as I would in any other course), but because I truly feel that the Moore method is the best way to approach this material. By asking you all to explain your ideas to one another, it firms up your understanding of those ideas. By asking you to take responsibility for your work, you become the authors (quite literally) of the ideas you're presenting to one another. It's much more learner-centered, and ultimately (I believe, and the literature on pedagogy bears me out) more effective.

Thank you for your kind sentiment! I've not totally disappeared from the scene; as you've noticed, I hope, I'll take my turn "on stage" from time to time.

To elaborate briefly: I know I'm a good lecturer, and I know that I explain things well. But seeing something done and doing it yourself are two different things, and you stand to gain much more from actually solving the problems yourself and explaining your solutions to each other than you do listening to me do it for you. It's a bit more work on your part, to be sure, but the time you spend on that work will be time well spent. Meanwhile, please know I'm still doing a lot of work behind the scenes, arranging problems in a manner I think is effective to help you work your way through the new ideas, including the definitions and theorems I think are most critical to us in our work, and working with you in class as you develop your solutions.

This I promise you: my explanations are still here for you if you need them, and I will be delighted to help you work your way through any problem you might struggle with. All I'm asking is that you give it all you've got to come up with solutions on your own first. Believe me, you'll get much more out of it that way.

So, let's stay the course, y'all. I'm enjoying class so far, and so far you're doing a marvelous job. Keep it up!

A tale of two sections

Today it was evident that over the weekend, most folks in one of my sections of Calc III took the time to work through the problem set they'll be presenting on Wednesday. It was equally evident that most folks in the other section didn't.

We'll see how things go on Wednesday. Most of the problems are pretty straightforward, but there are a few that might give pause. If Wednesday goes as I suspect it might, a few folks might learn the hard way that though it always pays (no matter the class) to keep on top of the work, but in a course structured as ours is, it pays double.

Moore is more

Three weeks into the semester, my Moore-method Calc III class has made it through three problem sets (50 problems), treating a substantive review of topics from Calc I and II and five or six sections of the textbook. It's been a few years since I've taught a course in this fashion, so there's been a bit of adjustment as I've gotten back into it.

So far, so good. The students are getting much better at explaining their solutions in front of a large audience (one section has 27 students, and the other 35), and they're becoming more relaxed, visibly. Yesterday's second section was particularly laid back, assiduously focused on finishing their tasks but willing to joke around and have fun in order to set the solvers at ease.

I've been very impressed with students' ability to be wrong in front of each other, and similarly impressed with the audience's willingness to ask questions. They're getting better at asking each other for clarification or elaboration, and not turning to me to ask. I'm letting minor errors slide, perhaps adding a little "does everyone agree?" if the solver's slipped up somewhere. Generally this has been enough to prompt one or two to express disagreement.

How's it helping the students? Hard to say. Several have said they get a lot of the course's design, though one or two have admitted "it's not what I'm used to, and I'm having a hard time adjusting." I've reminded them a couple of times now that in this sort of course they're expected to take on a bit more responsibility than they might in a more traditional course, preparing well and keeping up without my continual exhortation for them to do so.

I'm going to poll them more formally on the course structure at the end of the coming week, after we finish off the fourth set of problems. We'll see where we are.

Meanwhile, if anyone in the class is reading this and would like to comment, please feel free to do so, anonymously if you'd like.

Lesson #1

One week down, a whole bunch to go. My MLA course has met just once, as have both sections of MATH 480 which I'm team-teaching with my colleague Timon this term. Calc III's had three chances to get together, and I'm very happy with how those meetings have gone.

The students have shown no hesitation whatsoever in getting together in groups and hammering out solutions to the problems posed to them, and they've shown similar eagerness in getting up to the board to strut their stuff.

What's impressed me most is the quickness with which they seem to have learned the most important lesson one learns in a Moore-method course: it's perfectly okay to be wrong.

"You know what happens when you make a mistake at the board?" I ask. "Does the sky open up, bolts of lightning raining down from above, smiting you where you stand?" Despite the inevitable one or two students who deadpan sardonic yeses, they get the point. Not only is it okay to be wrong, it's necessary, even salutary: often only in being wrong can you eventually be right, as trial and error often lead to full understanding. The process by means of which we proceed from error and ignorance to understanding is called learning.

I've got profound admiration for the several students in both Calc III sections who made mistakes at the board the past few days, every one of whom recovered almost instantly, retaining dignity and respect. My thanks go to all of my students for a wonderful first week, and especially to those who showed the others that being in error is just not that big of a deal.

Swimming!

Two class-days into the semester, and things are going swimmingly. I'm putting the course together with a modified Moore method, cycling (roughly) through the following steps:

1. handing out problem sets,
2. giving the students time in and outside of class to work through solutions in groups,
3. asking the students to present their solutions in class,
4. asking the students to write up solutions to selected problems as homework, and
5. quizzes the students on completed problem sets.

As of now I've met with the first section of the course twice and the second section once, but every meeting has been lively and energetic, and I've needed absolutely no coaxing to get students to work in groups and to come to the board. The atmosphere in the course has been supportive and friendly. I'm delighted that this morning's class gave us an opportunity to note that, as I'd promised, no lightning bolts came down from the sky when a student made a mistake at the board.

It's been a long time since I taught course using anything close to the Moore method (my special topics course in graph theory, run in Spring 2008), and I notice that I've grown considerably as a teacher since then. I'm more confident, and that confidence has enabled me to feel less awkward taking a peripheral role. In particular, I find that I'm much more able to sit in silence than I was in the past. Silence in a crowded classroom is disconcerting, and it's all one can do to keep from saying something after ten or twelve seconds of quiet have elapsed. I've grown accustomed to such silences, though, just as I've grown accustomed to (or, more accurately, enamored of) the thrumming of three dozen voices trading tricks as the students work in groups in class.

I'm confident. It's going to be a good semester.

On deck

It's a new year, and we're only a few days away from a new semester (beginning Monday, January 9th). There are big, big things in the works: my book comes out in a couple of months, the work of the Curriculum Review Task Force should be coming to a head this term (with concrete recommendations to the Faculty Senate due by April), and...well...other news items about which I'll be able to say more in a few weeks' time.

What's in store, teaching-wise? I've got three preps this term, one for two (large) sections of a course I've not taught in almost six years (Calculus III), one for a single (small) section of a course I've never taught (a Masters of Liberal Arts [MLA] course on the cognitive psychology behind mathematics), and one for my section (of two) of our senior seminar.

In the seven years I've been at UNCA we've not taught two concurrent sections of that last class, so I'm not sure exactly how we're going to manage it. I've yet to talk to my colleague Timon, who'll be teaching the other section. I imagine we might hold many activities together, splitting when it comes time for the students to present. There's simply no way we'll get through 26 student presentations in the five or six weeks we can offer them to speak. We'd have to have an unprecedented four talks per period to make it work, and that's simply unworkable. Thus splitting into separate sections for that part of the course, though not ideal, is about the best we'll be able to do.

Meanwhile, I've got plans for the other courses. Calc III, which I've not taught since Summer 2006 (the last summer I wasn't running the REU), I'll be running with a modified Moore method: one day each week will be devoted to discussion of new definitions and discoveries, a second day to small group work on the current problem set, and the third to problem presentations. Both sections of this class are big enough (roughly 30 students apiece) that I'll probably ask students to "present" simultaneously (two to four at a time) whenever feasible. This'll ensure that we make it through problem sets in a somewhat timely fashion, and that each individual student gets more opportunities to present. I've already worked with about half of the students in both sections, which familiarity will help me ease into the new term.

I can't say the same for my MLA course. It's been nearly a decade since I taught a graduate-level course (a special topics course on Coxeter groups and related groups which I led at UIUC back in Spring 2004), and this course differs dramatically from that one. We'll be exploring the learning and cognition of mathematics, and I plan to inject a good deal of philosophy and sociology into the mix as well, drawing on a number of sources to paint a picture of mathematics most people never see. We'll begin with Stanislas Dehaene's marvelous book Number sense: How the mind creates mathematics, about which I've blogged a bit before (see the "Dehaene" tag at the right), surveying the psychology of mathematical discovery, before moving onto Imre Lakatos's Proof and refutation, a philosophical treatise designed to lay bare the workings of what might be called the "mathematical method."

I'm not sure what to expect from this course. I suspect there'll be a week or two of me feeling out the students (currently there are seven students enrolled) to see where their interests and aptitudes lie. Likely none of them are straight-up mathematicians; I'll be curious to learn what they're hoping to get from the class, and I'm certain they'll help me give it more direction.

Ah, well...one week to go. Before then I'm off to Boston for this year's JMM, at which several UNCA students (and a few past REU students) are presenting. I'm particularly excited to see how far Ned's and Ino's work on nutritional data has come since their presentation at Kennesaw State in November. (They're presenting in a special session on mathematics and sustainability.)

Further bulletins as events warrant, likely soon.