Change of Basis

A tale of two sections

2012-01-30T16:23:00.003-05:00

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

2012-01-28T13:34:00.003-05:00

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.

Data mining

2012-01-27T13:27:00.006-05:00

I spent a few hours this morning running the numbers on the students currently enrolled in our Honors Program, hoping to get some objective data on students' participation in the program as I move toward my new position in the fall. I made some heartening findings.

Namely, each of the school's three major disciplinary divisions (humanities, natural sciences, and social sciences) is pretty equally well-represented in the Honors Program. School-wide, 9.25% of all declared majors take part in the Honors Program, and the participation rates of the individual divisions range from 7.68% to 9.91%, quite tightly centered on the overall mean. Counting the courses these students take in Honors gives further evidence to this balanced participation: overall, a student in Honors who has declared a major has completed 3.65 Honors courses on average, and the means for the various divisions range from 3.58 courses per student to 3.81 courses per student.

There are certain departments that are particularly well-represented in Honors, including a few that are quite large (and that are therefore somewhat immune to sample-size bias). For instance, five of our seven departments with at least 100 majors can boast that more than 10% of their students take part in Honors, including one department with 122 majors, of whom 17 (13.93%) are enrolled in the Honors Program. At the other extreme, there are four departments, each home to anywhere from 26 to 31 majors, with no students in Honors. (One of these is a relatively new department, one which graduated its first majors just a couple of years ago.)

Interesting.

I don't believe these data to be "actionable" in any way...and besides, the results don't indicate dramatic action. I'll stay the course for now...though it might not be a bad idea to talk with the folks in those four departments to make sure their students are aware of the opportunity...?

We'll see.

Defragging

2012-01-26T09:29:00.003-05:00

For the past few weeks I've been hammering away at several different poems, but I've got little more than a couple of callousy handfuls of bent-nail fragments to show for it. Odd images (starry-breasted crows, fog-covered tenement-like brick blocks, concrete tunnels like birth canals), and random thoughts.

Keeping with this fashion, here are a few random thoughts on academics and academia:

1. I wonder at the extent to which we are all isolated in our disciplines, and to which we do most of our work in rooms with four walls and very often no windows.

2. I wonder at the sterility of the Platonist, universalist, formalist conception of mathematics, itself an isolating philosophy, allowing as it does a detachment from the world and from others as we engage in our mathematical work.

3. I wonder at the mechanisms we feel we must make and maintain in order to "deliver" our curricula. The more I learn about the inner workings of the Honors Program, the more I wonder if there are simpler ways to put it all together.

4. I wonder at our assessment practices, at every level, from the individual student to the institution as a whole. To what extent are they arbitrary, effective, replicable? To what extent are they doing what we need them to be doing?

5. I wonder at the effects of our educational system, both intended and unintended. How often does a student's passion for perfect grades overpower her passion for learning?

6. I wonder at things as they stand for things, and am reminded of William Carlos William's red wheelbarrow:

so much depends
upon

a red wheel
barrow

glazed with rain
water

beside the white
chickens.

Guinea pigs

2012-01-21T09:24:00.004-05:00

I have to admit some trepidation on my part going into the second meeting of my MLA course this past Thursday. Despite my strong record of teaching in mathematics, I have relatively little experience in leading wholly discussion-based courses, and this inexperience coupled with my sense that a few folks in the class are leery of mathematics in the first place made me worry that the conversation we'd have together would fall flat. Though it took a little while for the conversation to get going, my fears soon proved unfounded.

We began in small groups, where I dealt myself into a conversation with the two older gentlemen in the class, both of whom expressed some measure of skepticism about the reading. Uriah seemed appalled by Dehaene's seeming to alternate between making claims of revolutionary understanding of the brain's functioning and retreating to more palatable and defensible observations. Quinn seemed to accept some conclusions but was put off by the relative (to mathematics) lack of "rigor" and less rigid notion of "proof" in psychology literature. I found these reactions heartening, as reasoned skepticism is generally salutary, something to be expected: these two men are among the more mathematically experienced in the class (surpassed only by Bonnie, a former UNCA math major whom I taught in Abstract Algebra back in 2008!), and the insistence on rigor is a more traditionally masculine trait.

When we returned to a full-class conversation, many more ideas came out, primed by my request for each student to identify those aspects of the reading they found most intriguing, most confusing, and most well-received. It would be difficult for me to summarize all of what was said, so I'll focus on a topic we spent much of our time, dealing with the following image:

I crafted this image last spring for my Ethnomathematics course, in order to serve as a Rorschach test of sorts, testing respondents' notion of numerosity. For the longest time I've found it fascinating that as a species we tend to distinguish objects based upon contiguity and connectedness, "topological" aspects, not on color, shape, or other more "geometric" aspects. That is, most people will respond, if asked "How many objects do you see here?" that there are four, for there are four noncontiguous bodies present.

This, however, is the unskeptical answer, unaffected by the sort of "questioning bias" that doomed the Piagetian experiments Dehaene outlines in Chapter 2 of his book. Specifically, when asked to decide which of two rows of small objects is greater in number (the lesser quantity being arranged in a longer row so as to mislead), young children will often respond incorrectly simply because they suspect trickery on the part of the questioner. In our situation, the skeptical respondent, suspecting trickery, might respond (as did Quinn in my MLA class) "one," seeing a single paw, or even "two," differentiating the two objects on the basis of color and not contiguity.

For quite a long time we discussed the evolutionary advantage of enumeration based on contiguity, and various related questions came up: what would have to be true of a species whose members enumerate objects on the basis of other aspects? What could be said of their mathematics? Can a mathematics of "continuous quantity" model our "discrete" mathematics fully and effectively?

If nothing else, everyone in the class wanted to learn the likeliest response to the "how many" question above...if the question could be posed in a less leading fashion. "I've got a sample of over 60 students I can test tomorrow," I said, referring to my Calc III classes. "Why don't I get some more data?" The students loved this idea, and we debated how the Calc III students should be prompted for the purposes of this informal survey. It came down to between "What do you see?" and "Describe what you see." People seemed more satisfied with the second, as it seems to beg for a more elaborate response, increasing the likelihood of a description featuring some kind of numeric content.

Yesterday I began both sections of Calc III with the experiment, providing no context beforehand, so as to minimize bias in the students' responses. (I did inform them of my intent afterward, and gave them all the option of retrieving their responses if they'd prefer that they not be read by others. I hope that no one on our IRB is reading this...) I've not yet looked over the responses, but I'm already looking forward to the analysis we'll do this coming Thursday night. I'll be sure to post some sort of summary results here once we've had a chance to sort it out.

Anyway...I'm counting last Thursday as a success. I think this course is going to run itself. I'm not so worried anymore.

Politics

2012-01-19T15:56:00.002-05:00

Who knew there was so much of it in academic administration?

Seriously, though, I have a hunch I'm going to have to practice a good deal of diplomacy in the coming years as I inch closer to administration.

Week Two's been a blast, with Moore-method Calc III moving right along (no major hitches so far!), the second meeting of my MLA course in about two hours (one student withdrew after Week One, and I'm curious to see what the others think of Dehaene), and my first crack at putting together the Honors Program's course schedule underway. That last one's a balancing act, but I can't imagine it's nearly as hard as programming a large department's schedule. Let's just say I appreciate the work my chair's done on that task for the past several years.

One of my lovely Charleston colleagues just gave me a tip on the following book on delivery, apropos of our conversation about the role LaTeX plays in mathematical writing: Rhetorical delivery as technological discourse: A cross-historical study, by Ben McCorkle (Southern Illinois University Press, 2012). I ordered a copy. Just call me Mr. Spontaneity.

Okay, off to prepare for a meeting to discuss funding for this year's Conference on Constrained Poetry!

JaMMin' in 2012

2012-01-16T12:48:00.009-05:00

Aside from a brief post on my presentation on writing research, I've not yet had a chance to say anything about this year's Joint Mathematics Meetings (JMM), from which I returned a little over a week ago. It was a fruitful affair, marking my first ever JMM where I spent more time in meetings than I did at talks. (Avoiding administration: ur doin it wrong.)

My first full day at JMM began with a two-hour meeting of the MAA's Committee on Undergraduate Programs in Mathematics (CUPM). I was recently appointed to this body, a group charged (as you might expect from its name) with making recommendations regarding the form and content of undergraduate mathematics programs across the country. Of course, this is a very loosely-defined directive, and mission-creep inevitably sneaks in. We spent a good deal of time talking not only about the undergraduate programs themselves but also their interface with K-12 education.

What struck me most about this meeting was my sense by its end that even the most well-informed of college mathematics educators are at a loss when it comes to solving some of the biggest problems facing math education today. Why is this? It's not like the problems are new ones: for decades we've dealt with student recruitment and retention, students' transition to higher mathematics, and imperfect transfer of skills from AP coursework to college coursework. It's not that we don't have proven pedagogies and time-tested methods of math education at our disposal...and it's not that we have a shortage of talented teachers to put those pedagogies and methods into practice. Maybe it's simply that the student body we're dealing with is diverse enough to foil any attempt at applying one-size-fits-all panaceas: more than ever before we serve a population whose members differ from one another ethnically, economically, socially, spiritually, intellectually, and in every other way we can think of...to extremes heretofore unimaginable.

The next meeting I had to make was a one-on-one with one of my colleagues in the AMS. After receiving a note I'd sent a few months ago to the Project NExT list regarding my forthcoming book, Flora had expressed interest in meeting with me at the Joint Meetings to talk about it in a bit more detail. It seems that earlier in her career she'd gone down a path much like the one I've followed recently, leading WAC and WID efforts at her home campus (DePauw University) before heading over to the AMS full-time. Flora and I shared an hour or so together talking about the importance of writing (and other modes of communication) in the teaching and learning of mathematics, and before long she invited me to take part in a morning meeting of the AMS's counterpart to the CUPM a couple of days later. Though she couldn't guarantee me the floor, she mentioned that one of the members of the committee had brought up writing as a potential topic for further elaboration by the AMS's Committee on Education (CoE). Topics selected for such elaboration become the focus of discussions and workshops at the CoE's fall meetings.

So I made it to that Friday morning meeting (still bleary-eyed after a night of revelry with several of my Vanderbilt friends). Less focused than the CUPM meeting had been, this one consisted of a loosely-knit (and often heated) conversation on several topics related to undergraduate math education. We spent about twenty minutes each topic: potential certification (by the MAA, AMS, or both jointly) of undergraduate mathematics programs, facilitating students' success in calculus courses, and the necessity for upper-level "elective" coursework like point-set topology.

The first of these was the most controversial issue, on which there was much disagreement. For my part, I brought up a concern that's faced the members of the Curriculum Review Task Force this past year: those major programs which face accreditation by a professional body are among the most rigid and time-consuming, placing heavy demands on both students and faculty. In this way they are unsustainable and resource-intensive. One of the other folks present at the AMS meeting countered that the "accredited" majors at her school are the ones that receive the most attention and resources from administration, and that this alone is reason enough to pursue the adoption some sort of certification procedure.

As you might suspect, I disagree. From the point of view of a math department member, this move might make sense: why not try to carve out a bigger chunk of the pie by forcing your school to support your attainment of accreditation benchmarks? But from the point of an administrator, the move appears more questionable: the pie's only so big, and with the economy the way it is, it's likely to get any bigger. If every department's trying to carve out bigger and bigger pieces for themselves, there's not going to be much to go around. We'll starve each other out if we don't cooperate more meaningfully at higher levels than the department.

To be continued, I'm sure.

The conference wasn't just one meeting after another. I had a lovely time reconnecting with several past REU students (including Wilhelmina, from way back in 2007!), grad school friends, Project NExT buddies, and a bajillion other people I'd not seen in a long time. I spread the word everywhere I could about my book, shamelessly leaving flyers on tables all over the convention center. I made it to a dozen or so talks on graph theory and group theory...and to several posters and presentations by my students, past and present. Most outstanding was Ino's and Ned's talk on their ongoing research into nutrition, given in the MAA's session on the mathematics of sustainability. They nailed it. Several folks had great questions afterward, and they received at least three invitations for collaboration and further presentation. We'll be following up on those shortly. Well done!

Much more work to do! But it's great fun. I'm looking forward to seeing what the coming weeks and months bring. 2012's gonna be a good one.

Lesson #1

2012-01-14T08:48:00.002-05:00

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.

Back to school

2012-01-13T08:30:00.004-05:00

UNCA serves a large number of nontraditional-age students who are returning to school after taking time off for other things, and many of these folks are older than I am. Therefore I'm used to not being the oldest one in the room when I'm teaching a class; I've only been the eldest in maybe five or six of the 50-60 class sections I've led at this school.

But I'm not used to being one of the youngest in the room.

My MLA (Masters of Liberal Arts) course, Number sense: The philosophy and psychology of mathematics, met last night for the first time. I've got eight students in the class, four or five of whom are my senior in age and in life experience. It's a great bunch, and I can tell I'm going to learn more from them than they're going to learn from me.

We started off with some freewriting, through which I asked the students to probe into their own mathematical pasts. I hoped to find out what it is that makes these folks tick mathematically and to determine what they perceive to be the most basic and fundamental of mathematical operations. If we can get at the these operations, we'll be in a position to start our study of mathematical cognition where our brains begin, with approximations of enumeration.

I'm delighted to report that there's considerable diversity in the class when it comes to mathematical background. I found it interesting that the two gentlemen in the class reported more facility and familiarity with mathematics than their feminine counterparts (with one exception). Both of them described delight at working with statistics and geometry, and obsession with game-lake mathematical puzzles. The one woman with more mathematical experience is a former UNCA math major with whom I had the pleasure to work when I last taught Abstract Algebra I (in Fall 2008). This is her first semester of study in the MLA program.

The other five folks have considerably less mathematical background, but will provide perspectives from other points of view, reporting interest and expertise in psychology, history, and philosophy. I'm excited to learn from Samantha, who is taking time off from her work as a teacher for special-needs children. She mentioned how frustrated she is with mathematics education, and hopes that our class will give her the skills to help improve the way students are taught math at a young age. More power to her! Her high expectations for the course will definitely keep me on my toes.

After we probed our mathematical pasts for a bit, I presented a few exercises and experiments I hoped would whet their appetites for the material we're about to study (from Dehaene's Number sense). With no promise that this link will be evergreen, you can find Mathematica files for these exercises on the course website under the entry for January 12th.

In the first exercise I challenged students to hold in their memory progressively longer randomly generated strings of digits, demonstrating the means by which we tend to use our linguistic faculties to store such strings in short-term memory. (This use underlies linguistic differences in the ability to memorize and compute with numbers: the brevity of number words in many Asian languages allows native speakers of those tongues to outperform speakers of other languages in basic memorization and numerical manipulation.) The second exercise demonstrates how the arrangement of objects affects our sense of their number: more densely packed objects tend to appear more numerate than those that are sparsely spaced, and more orderly-arranged objects appear more numerate than those that are randomly placed. For the third activity, I asked the students to report any sort of synesthesia they've ever experienced: do they sense that numbers have specific appearance, texture, color, smell, relative spatial position, or gender? I think the students found it odd when I reported I've always had a very well-defined sense of the gender of every digit.

We wrapped up with a short discussion of formal expectations for the course, a topic I'm trying to de-emphasize as much as possible. I'm looking forward to next week's discussion. I'm curious to see if the students will find Dahaene's book as intriguing as I have.

Swimming!

2012-01-11T12:01:00.002-05:00

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:

handing out problem sets,
giving the students time in and outside of class to work through solutions in groups,
asking the students to present their solutions in class,
asking the students to write up solutions to selected problems as homework, and
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.

Day One...and WHAT a Day One!

2012-01-09T09:43:00.003-05:00

It's been a while since I last wrote a very substantial post. I had to look back at the blog just now to see what was going on, and what state my mind was in, when I've checked recently.

Most of my last few posts have been abstruse, political, and maybe even metaphysical, dealing with everything from the affective learning goals met through inquiry-based learning to the horrors of administration-sanctioned crackdown on students' rights to peaceably assemble on their own college campus. I fear this post might continue this trend toward the abstract.

Roughly three months ago I posted about an opportunity I'd been asked to explore which, quite honestly, scares me more than a little. I feared this opportunity because I knew if I offered to take it on and if my offer were successful it would present me with an entirely new set of challenges and that I'd slip and stumble and make a mess of it every now and then as I got into the flow. But hey, no one of us is born knowing how to swim. We've all got to pick it up somehow.

Well, it's time to swim.

It's official: in Fall 2012 I will become the University of North Carolina, Asheville's new Honors Program Director.

During the next several months I'll be learning all that I can about this new responsibility. I'll be tailing the current director like a second shadow. I'll be surveying the program's current students and surveying the faculty. I'll be making new plans and making new friends. I'll be reflecting on my own ideas and I'll be reaching out for others' ideas I'd never dream up myself.

And I'll be looking for support, from the hundreds of wonderful colleagues, students, family, and friends who have helped me to get to this point in my career...and who will continue to help me as my career takes this new turn. I thank every last one of you for all that you've done for me until now. I thank my colleagues and students, for your suggestions and support and for helping me to craft the communities that have helped us all learn together. I thank my friends and family, for the time you've given me, and for the shoulders you've let me cry on and lean on. I wouldn't be where I am today if it weren't for you, all of you.

With peace and love, I thank you.

Now, let's get to work. It's dawn again, with a brand new sun shining. There's much to be done!...including getting to my first class, which begins in 12 minutes...

Blowing up the interwebs

2012-01-07T09:07:00.004-05:00

I'm not sure this won't cause a cataclysmic loop of self-reference, but here's a link to a very nice little Chronicle write-up on this past Wednesday's JMM talk on our rhetorical analysis of the REU students' writing.

Nice.

I hope the folks that make it here from that site will take the time to poke around a little bit and read a bit more about my work with math and writing. Please think about picking up a copy of my forthcoming book, Student writing in the quantitative disciplines: A guide for college faculty, available in March from Jossey-Bass.

I hope once I'm settled back in at home tonight or tomorrow to write a run-down on my whole JMM experience (minus much of the after-hours goings-on), but for now I've got a few more talks to make.

On deck

2012-01-01T09:37:00.006-05:00

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.

Close to home

2011-11-20T17:59:00.006-05:00

Why is it that, of all of the Occupy activities that have gone on for the past two months, the pepper-spraying of peaceful UC Davis students strikes me so much more strongly than any other?

The extremity of the incident is hard to ignore: riot-geared police officers, decked in body armor and military weaponry, approach and attack unarmed and peaceful demonstrators seated in a position of pure passivity. Whether or not you agree with the reasons for the protest (I do, but I'm certain some of my readers do not), the level of force used against the sitting students is clearly out of proportion by several orders of magnitude.

The diffidence of the university administrators (in particular, UC Davis Chancellor Linda Katehi) is as striking. Afterward she is coolly dismissive of the protestors, adopting a detached and thoroughly establishmentarian "well, that's what happens when you don't do as you're told" stance in the wake of the attack.

The immediacy (and ubiquity) of the images plays a part, too: they're arresting and unavoidable...and every video of the attack clearly shows a dozen or more others actively filming the incident, a self-replicating postmodernist pastiche of views, every one showcasing unmitigated brutality.

All of these aspects of the attack factor into its effect on me, but I think what's most striking to me is how similar the students attacked are to my own. How easily those Davis kids could be the ones who come to my classes, who hang out with me in the Math Lab, who joke with me in the hall and who ride with me to conferences! How easily my kids could have been the ones writhing in agony as they gasp for breath and when they finally find it spend several hours coughing up blood! They're interchangeable. I find myself putting my students' faces over those of the kids in the video clips, and I shudder.

I wonder: how differently would my own institution have responded to actions like those of the peaceful students at UC Davis?

History lesson

2011-11-20T04:04:00.007-05:00

Some might say this is not a "teaching" post.

They would be wrong.

I was chagrined several weeks ago when I learned how ahistorically many of my students live their lives: one of my brightest students showed her historical ignorance by not knowing, within ten years or so, when the second world war was fought.

So it is that I worry that my students might not know what's going on around them now.

I join the chorus of academic voices expressing not disappointment, not chagrin, not tut-tutting and head-shaking sadness, but rather disgust and horror at the events taking place recently at campuses in the University of California system.

All that I might say has been said more fully and more eloquently than I can here (here, for instance, and here), so I'll say little more then to say that Chancellors Linda Katehi and Robert Birgeneau must resign...as should any other academic "leader" who condones or supports the actions (or inactions) they've taken.

I cannot say more that's not been said already. I want only for my students not to miss this moment.

To them I say: this is what history looks like.

State of mind

2011-11-09T04:36:00.002-05:00

A few months ago Zima, one of my grad school colleagues who now teaches at Kennesaw State University in Kennesaw, Georgia asked me to present at an undergraduate research conference for which she'd just received MAA funding. (Said conference is this coming weekend; it's the one Ino and Ned are presenting their findings at.) I'll be giving a run-of-the-mill plenary talk on some of the graph theory I did with a couple of REU students this past summer, and I'll be presenting in a workshop on inquiry-based learning (IBL) at the outset of the conference.

I offered Zima a title that's so generic I really could talk about anything: "Guided discovery in the mathematics classroom." I feel confined by this generality. Indeed, when I actually sat down a week or so ago to try to figure out what in the hell I needed to say about IBL, PBL (problem-based learning), Moore method, etc., I had a hard time coming up with much to say other than expressing my feeling that all too often these techniques are too "formalized." That is, I get the sense sometimes that the people who apply these techniques look on them as an all-or-nothing process: "if it ain't straight-up Moore method, it ain't anything at all" or "I use guided discovery every single day to address every one of my students' learning outcomes." So I put together a half-hour laundry list of things to say along these lines: be open to using guided discovery in moderation; it's not the be-all-end-all any more than any other pedagogical paradigm may be.

Then just now, while lying in bed unable to sleep (though admittedly probably needing to), I realized that I can say more, for I realized of a sudden why I've had such a hard time trying to come up with something practical (and original...I suspect that the folks I'll be addressing in this workshop are going to make up a choir to whom I won't really need to preach) to say about guided discovery: in my mind, guided discovery is not so much a pedagogical process as it is a state of mind.

I find more and more that in teaching it's not so much what I do with my students as how I do it that matters most. Put another, perhaps more practical way, effective teaching comprises a gestalt-like complex of actions and not a single action individually. Guided discovery is what might be called an emergent operation which cannot be broken down into its constituent parts without losing much of its energy and effectiveness. So it is that I don't necessarily engage my students in singular activities, each of which forces students to lead themselves to original, new-to-them, conclusions, so much as I try to treat them in every way, in everything I do, as co-learners, co-discoverers, seekers of authentic knowledge.

Practically, this realization makes it possible to grow opportunities for genuine discovery in the most infertile academic soil, for every simple textbook problem becomes, if viewed from the right angle (like anamorphic art) a chance for authentic "research-like" engagement. Guided discovery is an "angle" from which these problems may be viewed.

I'll try to say a bit about this on Friday when I'm leading my portion of the IBL workshop. Are these views original? Meh...perhaps not. But they're more original, and, more important, more meaningful, than whatever else I will have to say. We'll see how they're received.

More big picture stuff

2011-11-04T06:49:00.004-04:00

In regards to another recent post, it looks like we're about to beat up on the student body again. I say once more: what in the hell are we doing?

I don't usually get political here (because my pedagogy, writ small, doesn't generally intersect directly with politics outside of my own institution), but I can't help it now: if you support any leader opposed to fair taxation and rational government spending and stimulus, you support the eventual decay of our educational system. Don't re-elect these fools who are destroying our future.

Impending sense of something

2011-11-02T10:40:00.003-04:00

Well, all my classes are prepped for a couple of days' absence from the scene. My Abstract students are hard at work on their latest problem set, and the Precalckers are plugging away at their second take-home exam.

All is calm.

Ever get that feeling that something big is about to break?

I've got that feeling right now. I can't put my finger on it. Maybe it's just that the next week and a half is frightfully busy: something's bound to happen.

We'll be ready, my friends. We'll be ready.

Big, big picture

2011-11-01T14:33:00.009-04:00

For several years now, I've been a "big picture" kind of guy: I paint in broad strokes. I see forests and not trees. I'm more satisfied with hand-waving proofs than most of my colleagues would be. I'm more concerned that I and my students get the overall idea, the intuition, the gut-level understanding, than that we get every last detail right.

I'm not sure when I took this viewpoint on, but I think it's a relatively recent phenomenon. After all, I'm not sure you can make it through a graduate program in mathematics without punctilious attention paid to the merest minutiae of theorems and their proofs. It's come on more recently, as I've grown as a teacher and scholar, and as I've come to grips with bigger and bigger problems. It's gotten "worse" lately. I mentioned only half-jokingly to the Associate Provost for Academic Administration, with whom I've been doing a lot of work this semester for CRTF, that I'm starting to think like an administrator. For good or for ill I no longer consider curricular issues as they'll affect a single instructor or even a single department, but rather as they'll affect the school as a whole.

Perhaps the widest view one can take I took for a moment today, and it scared me: if you look at our nation's higher educational system as a whole, there are terrifying trends.

One incident: this morning I got an email from a student who's having to take a break from it all to maintain sanity. Literally. This person is going off the map for a little while and heading home to be with friends and family and to deal with mental health issues.

A second: yesterday I spent a tearful half hour with another student who's clearly dealing with stressors beyond finishing up an essay for Humanities or prepping for this week's coming Abstract Algebra exam. This is a very good student, one I know well, one whose performance this semester has declined noticeably from past semesters. There's much more going on behind the scenes.

A third: last week one student spoke of a narrow escape from dropping out and returning to military service just to make ends meet. Fortunately the financial aid office and the counseling center were able to help make an end-run around a vindictive ex-spouse whose uncooperativeness was preventing disbursement of much-needed funds.

These aren't just isolated events. Dozens of my students, in addition to managing a full load of difficult classes (often in excess of 18 hours dominated by high-level mathematics coursework) also work 20, 30, even 40 hours a week, and deal with manifold family issues (I can think of several students whose entire families depend on them for nearly everything), and still manage to keep it together...or not, as the case may be. The cracks are showing: I've had more people cry in my office than in any other semester I can remember. It ain't getting better.

These students shouldn't have to deal with all they're dealing with today. They should be free to be students, to be free from having to support themselves with back-breaking (or at least time-sucking) labor.

It hasn't always been like this. I speak from experience.

I had it far easier than these folks, barely more than a decade ago. I had student loans and a scholarship, and my family'd done well in socking some away to help me go to school, so the only work I needed to find to get me through my college years was as a work-study assistant in the Math and C&S Department's computer lab. Big. Deal. This was a sinecure. I "worked" 10, maybe 20, hours a week, passing out boot-up disks (yes, we still used those back then), trouble-shooting simple software problems (usually involving nothing harder than MS Excel), and shooting the shit with my geeky friends. Most of the time I got paid to do my homework. The rest of my time (that not devoted to hanging out, eating pizza, running, and annoying the crap out of my dorm mates by playing Pink Floyd's "One of These Days" really frickin' loudly on my monster tower speakers) was spent on schoolwork. I managed to make straight As (aside from a couple of stray minuses) and learn a lot. I was a slacker my first year of college, because I could afford to be: I quickly learned that I didn't need to put too much effort in in order to do well, so I took it easy. My second year I started taking courses that offered legitimate challenge, so I buckled down. That's also when I first realized that I could teach myself as much as anyone else could teach me, so I started studying on my own, everything from additional math and physics and computer science to philosophy, literature, languages, and history. On my free time. (Holy crap...free time! What's that, again?)

I could reminisce forever, but let me get to my point: I'd love to launch into a cliché and crotchety "kids these days" diatribe, but I can't. I had it easier than these kids. Far easier. I didn't have to work my ass off just to stay warm and well-fed, let alone well-educated, and I had time enough (and more) to do well in and learn from all of my classes.

Many of my students have no such luxury. They have to work, and often work hard, just to afford the modest cost of the education my public school provides to them. (It may be worth noting that I went to a pricey private school for college.) If they don't work (and often even if they do) they have to go into debt up to their eyeballs to pay the bills, for they cannot always rely on family to help them out (many of these students are first-generation college students and come from families who can ill-afford to give financial aid). Moreover, they face dim job prospects on graduation, with the economy lagging the way it is. There are no sure signs of long-term improvement. Thus many of my students are going to saddled with crushing student-loan debt and little opportunity to find the work they'll need to get to help pay it back.

Do you think a student with 18 hours a week of coursework and a 40-hour-a-week job who's drawing several hundred dollars per term in student loans and trying her best to hold her family together really has time to learn (or care) what a derivative is? Do you think such a student is going to be completing her homework in full, passing her exams, and finishing her oral presentation on subgroups of groups of symmetry? Even if she's meeting these superficial measures of academic achievement, do you really think she's going to be getting much meaningful out of it?

It's become cliché to put someone in "The 99%," but my students, almost every last one of them, belong there. Bless 'em all, they belong there.

And my students amaze me. Even with 18 hours of coursework and 40 hours on midnight shifts at motel desks and family foibles and student loans and squabbles with landlords over week-late rent checks, they do still learn what a derivative is. And they do still care. They don't just finish their homework, they polish it to perfection. They don't just pass their exams, they ace them. They do incredible work, and they do it without complaint. Somehow, despite having to do everything else we demand that they do, they're learning, and they're helping each other to learn. They're there for each other, even when the system's left them behind.

But this can't go on forever. A college education can't be what it used to be if we don't give these people a bit more breathing room. What in the hell are we doing to them?

The system needs to change. Otherwise, in ten or twenty years we'll look back and notice that though we've stocked our universities with the brightest scholars and the best teachers, and though we've built the shiniest classroom buildings and equipped them with the sleekest high-tech gadgetry, we've miseducated an entire generation simply because we asked too much of them while they were trying to do what we want them to be doing before they do anything else. We just wanted them to learn.

Well...I'll keep doing all that I can, and I'm sure I can count on my students and colleagues (some of the most admirable people on Earth) to do the same. It's a mountain we've got to move, and the only way we're going to move it is if we all get behind it together.

I'm new here

2011-10-28T21:58:00.008-04:00

Parker J. Palmer's and Arthur Zajonc's The heart of higher education: A call to renewal (transforming the academy through collegial conversations) (the centerpiece of the most recent faculty Learning Circle in which I took part, and about which I've posted somewhat recently) gave me more than its fair share of things to think about. Many of its insights offered theoretical, even spiritual, enlightenment regarding teaching, but other insights were more practical and practicable.

One of the more down-to-earth suggestions offered up by one of the coauthors' colleagues (Patricia Owen-Smith, Professor of Psychology and Women's Studies in the Oxford College of Emory University) was a means of encouraging contemplative practice in the classroom simply by playing music to being each class period. Owen-Smith (pp. 157-161 in the above work) describes how several years ago she began the practice of playing 7-9 minutes of music at the outset of each class. She encouraged her students to "go within, be still, and listen to the self." While she admitted the difficulty of tying this contemplative practice to improvements in students' achievement of cognitive learning goals (as if this would be the purpose of playing the music in the first place!), she reports that

over time, I learned that the music and meditative moments had an impact on many students. Some students began to ask for guidance with their contemplation and reflection....By midsemester several students per class would mention that they looked forward to this nine-minute period of music. Some students began to bring music from their own collections that they found inspirational and important. As we neared the end of the semester, the structure of the class had changed from a group of individuals reluctantly gathered together for study to a community of friends and partners who were creating a space of introspection, quiet, and respect for the process of study and the development of self.

Once or twice a week for the past few weeks I've begun a similar practice in one of my classes. It began with my reading of an excerpt from Rilke's letters to Franz Kappus (a reading which moved one student so much she had to leave the room), and continued with a passage from Dick Leith's history of the English language. At one student's suggestion one morning we watched a scene from Harold and Maude, and the next day I read one of my own recently-written poems ("Ode to Ned Maddrell," which I penned for the last-living speaker of the Manx language). To open off on Monday (at the suggestion of another student) we'll take in one of Gil Scott-Heron's last videos.

This practice has developed naturally, in an easygoing fashion, and perhaps unsurprisingly it's happened in the most natural and easygoing section of any of my courses this semester. From Day One nearly every person in that section of Precalculus has worked well together, helping each other out and asking for help when help is needed. This natural ease with which we've worked together all term has made it hard for me to tell whether the contemplative practice has had a real effect on the esprit de corps of the class...

...but I'm not going to take any chances. The practice has definitely helped me to make connections between the intellectual and the personal, between the scientific and the humanistic. It's helped me to remain focused on what really matters, and it's helped to remind both me and my students that we do well to look for mathematics' usefulness...and to look for its beauty. Much like well-chosen low-stakes writing activities, this practice is well worth the few minutes of class time that it takes.

Beginning right away I'm going to introduce this practice in all of my classes. It can't hurt.

What effect can it have in a class like my current Abstract Algebra class, a room full of stressed-out work-wearied students representing, honestly, probably the greatest range of mathematical ability I've seen in one section since I began teaching at UNCA over six years ago? I admit here and now that I find myself frustrated at how I've managed this course. For some time now I've felt the need to slow its pace to accommodate the most modestly quick learners, but without sacrificing the true nature of the subject, a nature laden with often-abstract proofs. I don't know how much slowing the pace down has helped: several students are still struggling, and as much as I hate to leave them behind (I hate hate hate people who teach to the top ten percent), I simply must move on. Moreover, I sense that the slowness has led to frustration on the part of some of the class's quicker students, and I can feel cliquishness setting in...not a nice way to end the semester.

Maybe it'd be wise at this point to remind everyone that we all have a right to say "I'm new here": we're all free to make mistakes from time to time. After all, no one's lived this life before, and the future hits us all at the same time. But no matter how far you go, you can always turn around.

What say, folks? What are we going to make of our last five weeks or so together?

Research update

2011-10-28T10:45:00.002-04:00

Ned and Ino are chuggin' along. Their research project, the culmination of which will be a pamphlet detailing the means of making a week's worth of healthy, affordable meals is flying forward. We just overcame a major obstacle today: we had to figure out how, once we'd found the ideally affordable combination of foods needed to obtain the right amount of each nutrient in our analysis individually, to combine this information to give us the most affordable combination of foods to give us the right amount of all nutrients at once. We made it over that hump, and I truly think it'll be the last big one before our projects reaches its end.

So proud!

Partners in crime

2011-10-26T18:57:00.005-04:00

I know a number of people (many former and current students, a good number of colleagues, and assorted folks I've never met) read this blog, but not many often comment publicly. Quite often, though, I get comments about it on Facebook or in my in-box.

This past week I got a note from a fellow who's teaching precalculus at an inner-city high school in Boston, using inquiry-based learning. He wrote me asking about the methods I'm using in my own precalc classes right now and shared some of his own (he's asked me not to post his notes, as they're very much works in progress). I'm very impressed! His notes are clever and engaging, offering students a scaffolding students can use to climb from the barest basics up to properties of advanced functions, logs and exponents, and trigonometry. You can read about his exploits here.

By comparison, my methods that are considerably less purely inquiry-based...he's doing pretty much straight-up Moore method with high-school students! Inventive and impactful.

Dead Zone

2011-10-24T15:59:00.005-04:00

Today I felt like every one of my classes was a bit stuck in the mud. (Oddly enough, my morning Precalc class, often my quietest, was the most lively today.) It was all we could do to keep making forward progress in a couple of the classes, and I felt like I was beating a dead horse more than once.

What to do at such times?

The classical response, at least from instructors in content-driven disciplines: "well, we've got so much to cover that we've got to keep going..."

...but this is wrongheaded. If you press on without pause, it's not like students are going to get any more engaged, and it's not like they're going to get much out of whatever you do together, anyway. In pressing on you'll be doing so only for the sake of pressing on, and any progress you make will be illusory.

This is exactly how it felt in my second section of Precalc, and in Abstract Algebra, in both of which classes we worked with (what I thought were) some pretty neat mathematical ideas: in Precalc we solved a nontrivial optimization problem involving rational functions, and in Abstract Algebra we looked at the subgroup lattices of a couple of groups and examined the asymptotic behavior of Euler's function φ. I don't feel that either class picked up on the subtle beauty in a way they would have had they been in a more receptive mood.

Don't get me wrong: I'm not blaming my classes. Both of these classes are full of wonderful students who are generally unafraid of working together to make a healthy and supportive learning environment. (I've bragged on my Precalc peeps enough this semester for you not to know how much I care about them.) Rather, I think we've just hit that point in the semester, about 50-60% of the way through, where everybody's just DEAD.

It's the Dead Zone. Wearied by exams and essays and due dates and deadlines, overburdened by homework and quizzes and lit reviews and response papers, we're tired and jaded and not having much fun. (Believe me, kiddoes, this "we" often includes me. I apologize if I'm sometimes snappy around this time of the term; it's hard to be irrepressibly chipped every hour of every day!)

On reflection, I've thought of a two-fold healthier response to these Dead Zone doldrums:

1. Play. Put down the pen or pencil, put the paper away. Let's just think of something fun we can do with whatever it is we're working at this very moment. Optimization problems? Let's come up with some kind of crazy variation on the theme, whether we have any idea how to solve it or not. Let's set it up and see if we can work it out, like Ariadne weaving a web through the labyrinth. Are we sick to death of subgroup theorems? Let's break it all down with an explicit or example, or two, or three...let's dissect the dihedral groups until there's nothing left but individual elements...let's take it apart!

2. Reflect. The next step comes as no surprise to those who know me well: once we're done playing, let's take a minute or two to write to ourselves, if only to reflect on what we've been able to discover. Did we reach an end? How? Did we run aground? Why'd we lose our way? What's our play got to do with other problems we might encounter in mathematics and beyond? Write about it, write about how we feel about it. Hell, write about how we feel in general: why are we so dead today?

Too often affective learning goals get lost when we focus too heavily on cognitive learning goals, and that goes double for content-laden quantitative sciences. Let's try not to lose sight of our humanity, and the fragility that comes with it. Let's take care of each other as we come together to learn.

By and large all of my classes this semester are doing a marvelous job at this, and I admire them for it. I never cease to be amazed at the quality of students with whom I get to interact and learn. You're terrific people, all of you!

A somewhat schizophrenic conversation

2011-10-22T08:02:00.006-04:00

[Note: this post includes a homework assignment for my readers, toward the very end. If you're a teacher, student, or alumna/alumnus, please take a moment to respond when you're done. Thank you!]

A few years back we graduated one of the brightest students I've yet to work with at UNC Asheville. Sedgwick was a soft-spoken and deep-thinking environmental studies major with whom I had only one chance to work, in a Calc II course he enrolled in just before he graduated. He and I shared some pleasant conversations during his studenthood here, but we've shared many more (often from afar) since his moving off to broader pastures.

He wrote a few days back indicating that he'd had some thoughts (which he'd written down) about my CRTF-related posts, and wondered if I had any interest in reading them. Knowing his perspicacity, I knew they'd be well worth the read, so I told him to send them along, by all means, asking if I might repost them here, as I've done in the past. He's granted permission.

Sedgwick's comments concern the ILS Topical Clusters in particular, which are considered by many (myself included) to be the weak point of ILS as a whole. Here's what Sedgwick has to say:

I will preface these comments by saying that I was one of the last students to graduate under the old General Education requirements, so I have no first-hand experience with ILS, despite being a recent alum.

I did take a look, however, at the clusters on offer. Currently, a cluster appears to be nothing more than an arrangement of existing courses that fit some nebulous theme. This situation seems to be the functional equivalent of forcing all students to declare a 'mini-minor,' albeit less useful because the promise of interdisciplinary depth seems hardly fulfilled, given how little time one can commit to a cluster relative to other requirements.

The main part that confuses me is the fact that there is a theme at all; it seems like a needless restriction. The structure of a student's education comes from their major, which offers the technical, career-focused classes they need. Asking the liberal arts portion of the curriculum to follow a cluster's pre-determined path is like asking a journey for directions: clusters rely on the false premise that students can (or should) connect the dots in the present.

To illustrate that last point with an example (that will no doubt become cliche): the reason that the original Macintosh debuted with multiple fonts and typefaces was because Steve Jobs took a calligraphy class at Reed College years earlier, a course that interested him but had no real-world usefulness to him at the time. My concern is that by requiring students to adhere to a theme in the 'liberal arts' part of their studies, they could be missing out on experiences that may be of use one day, in a manner that's impossible to conceive of while still in college. The way Steve put it: "you can't connect the dots looking forward; you can only connect them looking backwards." UNCA's advantage, as our state's liberal arts institution, should be in providing the broadest array of dots for students to connect in the future, as they need them. In this light, restricting the ILS experience to a small subset of available courses does not make much sense.

If all ILS wants to do (or can do at the moment) is force exposure to other departments, then get rid of clusters and just say that students should take X number of courses outside their major. However, I think UNCA's goal is to emphasize the 'integrative' part of ILS. Clusters were an important first step, but I believe the 'integration' was too high-level to have the intended effect. Ultimately, integration needs to permeate the coursework itself, which why I would suggest 'cross-up' courses instead of clusters.

A cross-up course would be a deliberate collaboration of at least two departments. What would these cross-up courses look like? It's hard to say: I trust faculty to have a better eye for how their chosen discipline can interact with another. I know the synthesis of mathematics and writing is an important part of your teaching, so that seems to be a natural fit. My own background and interests can easily see collaborations between Computer Science and Environmental Studies. I think the possibilities are only limited by the interests of faculty and their willingness to work together.

There could be a simple rule that each department must form a cross-up with at least X number of departments. With a pool of cross-up courses available, just have students take X number of them to fulfill the ILS requirement. That's it. With the Intensives requirements still in place, the curriculum would not suffer in rigor. Like custom clusters, cross-ups could also be student-initiated with proper coordination. What better way to give UNCA students an edge in cross-disciplinary work than by taking classes that are actually cross-disciplinary by design? I cannot help but imagine that this type of setup would also confer a degree of market separation from peer institutions.

In short, exposing students to several unique instances of cross-disciplinary work seems to be a more pragmatic use of the limited time students have to devote to ILS electives. Cross-ups can also align faculty more towards collaboration than rivalry, encouraging departments to think about what cross-disciplinary experiences will work for students once they leave the academy and face an unforgiving job market. Of course, given the fiscal situation up there, asking faculty across the campus to design and teach a dozen or so new courses is likely a non-starter. But doesn't it sound exciting, something that really fits with the purpose of UNCA?

My open-letter response (which is almost identical to the response I had to Sedgwick's last letter to me, linked to above): I agree...ideally. I actually think the cross-up courses are a great idea, and if implemented would lead to a much more flexible, manageable, and student-authored learning experience that would replace (and substantially improve upon) the current system of topical clusters. The primary problems I see (as does Sedgwick himself) are logistical.

Namely, cost, in person-power and faculty time, if nothing else, is a prohibitive factor. Given our current budgetary climate (if I had a dollar for every time I've typed that word in the past few months...), we quite literally can't afford to ask all faculty to take time out of their schedules to design new interlinked courses. Moreover, we lack the administrative power to begin giving faculty appropriate credit for leading the many team-taught courses the cross-up system would entail...

...But wait a minute...Even as I was typing those last two sentences I began thinking to myself..."what?!?" As Sedgwick pointed out in the post I linked to above, universities are, though many who staff them would be loathe to admit it, among the most conservative of institutions around today, and change comes very slowly to them...I often think that we often make up excuses (too expensive, too time-consuming, administratively infeasible, etc.) for doing things we, institutionally, simply don't want to do.

To the first point: how does maintenance of the admittedly flawed and unpopular ILS Topical Cluster system demand any less faculty time and resources than would implementation of a new program that would likely require considerably less oversight and administrative overhead? On reflection, the faculty claim "I just don't have time to sit down and design this course" is wholly ridiculous...faculty are designing new courses all the time. Who among us isn't thrilled and filled with pride when first given the chance (in, maybe, our second or third year on the faculty) to teach a special-topics course related to our research? And how many of us, especially those of us in our first, second, and third years of teaching, find ourselves teaching one or two new preps every year? Though these courses are often not new, they're new-to-us, and take a fair amount of time to tweak and tone as we make them our own.

The last paragraph points out an obvious "in": our newest faculty are likely to be the most willing and able to implement a new curricular component like cross-up courses. Not only do they expect to have one or two new preps any year anyway, they're also less entrenched in their disciplinary positions and are more likely to be open to cross-disciplinary fertilization. I may just have to talk to a few of my younger colleagues about these ideas...

To the second point above: the argument is often made that we don't team-teach much here because it's simply too difficult to give faculty the appropriate "credit" for teaching such courses. The system as it exists, supposedly, allows us only to give credit for teaching half of a course for such courses, and in order to meet various benchmarks for faculty activity (the infamous Delaware study among them) faculty teaching such courses would have to teach far more than an acceptable load to appear on paper as though they're being productive. I can't buy this argument; if I did, I'd be as shortsighted as the folks I've been ranting about in my recent CRTF posts.

I can't buy it because I'm just not sure I've shopped around enough yet: might it be that the problem is one of "vision"? Several of my colleagues on the Curricular Sustainability subgroup have remarked that resistance to change may be predicated on a lack of understanding of other ways we could do things than the way we're already doing them. That is, maybe we're encountering so much insistence on doing things the way we've been doing them because folks just don't know how else these things can be done. Our response on CRTF has been to try to come up with models. Just this past week I asked the folks on my subgroup to identify institutions offering "model" majors and degree programs in their respective disciplines, suspecting that these programs will likely prove more sustainable (e.g., more flexible and less prescriptive) than their cognates on our campus.

Maybe what we need is more models. This brings me to the homework I mentioned at the outset of this post:

1. For those faculty reading this post, it would delight me to no end if you could comment on this post with a paragraph or two (or more, if you wish) about the nature of team-taught interdisciplinary courses at your school. How are they organized? How are they overseen and assessed? How does the administration grant faculty credit for teaching in these courses? How are they received by the students? Are they required, recommended, or simply part of the body of electives students might opt to take? All of this information would give me ammunition I could use to make the case for these courses.

2. For those students reading this post, it would give me similar delight if you could comment on this post with a paragraph or two about how you would receive such courses. Would you be interested in taking them? Among what disciplines would you like to see more collaboration? Would you find it helpful if such courses were required...and would you take them even if they were not? For UNC Asheville students in particular: would you prefer this kind of system to the current system of ILS Topical Clusters? Why?

Obviously I can't require you to respond, but even just a few words would be of such tremendous help to me that I really hope you'll consider writing back.

I realize now that this conversation, once between Sedgwick and me and then just between two mes, has turned out slightly schizophrenic. It's really helped me to get these thoughts out of my skull, though: I'd not before now seen the untenability of the "we don't have time to..." argument. I needed to write it to see it. (It's writing-to-learn, y'all!)

My thanks for those who've read this far! I'll soon be posting on a conversation with another reader, a high school teacher in Boston who's making use of IBL methods in his precalculus course. Stay tuned!

Reflect

2011-10-21T17:16:00.002-04:00

After having started off two different meetings of my second section of Precalc with readings from reflective writing of some kind (see this post and this on e), I invited the students to join me in bringing contemplative readings into class. Several have indicated that they enjoy this start to the class, and I look forward to seeing what the others will bring in.

"Teaching"

2011-10-20T19:19:00.005-04:00

I noticed the other night, just before leaving campus, that in Abstract Algebra I'm about two weeks "behind" (about three handouts, each roughly equivalent to two days of class) the place where I was at this time in Fall 2008, the last time I taught the course.

My immediate reaction, which, fortunately, dissipated almost immediately: "Holy crap...how can I catch up?!?"

I looked over the handouts separating now from then. They were filled, for the most part, with technical lemmas and other minutiae about groups, facts like "the condition that g^-1 be a two-sided inverse is redundant" and "to check that H is a subgroup it need only be shown that gh^-1 for all g and h in H." I thought about my students, and their aims and ambitions, and I realized almost immediately that they could do without "covering" these lemmas. At best, they'd memorize them for several days, work a contrived homework problem or two meant to test them on the results, and then forget them.

Meh. We'll skip those handouts. Instead, we'll move on to the good stuff: subgroups, homomorphisms, more meaningful structural results that are powerful, intriguing, and beautiful.

Meanwhile, the homework is clearly kicking my students' butts. Even the more experienced students are struggling with it. It was only after thinking about it for a bit that I realized why this is: instead of asking them to pantomime the proof of some result that differs only slightly from something we've talked about in class or put the polish on a theorem I read out loud to them, I'm having them build from scratch most of the canonical examples; I'm having them introduce and analyze the most important definitions.

It would take me fifteen minutes to "teach" them all there is to know about the subgroups of the integers, but in doing so I'd guarantee that nine out of ten of them would smile (or scowl) and nod their heads, take careful notes, commit what I'd said to memory, and not understand a lick of it. I'd rather they take a few hours outside of class to do it for themselves, struggling with every step, pounding their heads on the Math Lab's countertops in frustration, cursing me under their breath, gaining intuition all the way. The best human computers of all time, from Napier through Gauss to Ramanujan, built their skills by living with numbers, loving them, spending their days with them cheek to jowl. It's hard work, but you'll gain so much for it, mathematically speaking. You'll gain intuition, and, ultimately, understanding.

I spent an hour or two with several of these students in the Math Lab this afternoon, and the progress they made was incredible. I'm so impressed by their intelligence and determination.

Keep it up, folks! I'm proud of you all.

Grades, schmades

2011-10-19T23:12:00.003-04:00

Tonight I talked for several hours with one of my best friends on Earth, and one of my most reflective fellow teachers of mathematics, Griselda. (Tired of this and that, and longing to move closer to friends and family in the Northeast, Griselda recently left her job teaching at a public liberal arts college in a nearby state to teach at a boarding school in Pennsylvania.) As usual, our conversation was broad and far-reaching, and dealt with issues in every corner of education.

My most meaningful self-realization of the evening: the only reason I still give grades in my courses is because I have to; the school requires them from me at the end of the term. And the only reason I give grades throughout the semester is to provide substantive justification for those end-of-term grades.

Don't get me wrong: I love responding to my students' work. My responses make up my half of a conversation with the students about the discoveries they're making. It's an ongoing dialogue, and often an exciting one. They say something to me, I say something back, and after one or two iterations we might make some sense of what it is the other is trying to convey. Eventually we'll come to a consensus regarding the meaning of whatever matter we're faced with. I love these conversations. They're where learning takes place.

But grading? Uh uh. I'm over it. I'm tired of this competitive academic economy based on artificial and extrinsic rewards.

How can I break the cycle? Maybe if I rebel and refuse to assign grades...?

Something to think about...

...Griselda always leaves me something to think about.

Thank you, my friend.

Running in reverse

2011-10-19T07:21:00.007-04:00

Recently I've had a chance to feed my undying love of linguistics. I've been reading up on the history of English and its antecedents (like Angl0-Saxon) and victims in the clash of tongues that's taken place on the British Isles since the early common era (like Cornish and Manx). The text I'm currently reading is Dick Leith's A social history of English (London: Routledge & Kegan Paul, 1983), an interesting book offering a glimpse of English's development as a social, as well as a purely linguistic, phenomenon.

More interesting than Leith's treatment of English per se are some of the observations he makes about the codification of language, and the role of "authority" in the preservation and propagation of language across time and space. A central thesis of his book is that all too often we forget that language is very much dynamic: it is ever in flux, constantly changing...and that in the end that change is not driven by grammarians or the intellectual or economic elite so much as it is by the ways in which every member of society chooses to use the language.

These are points that even the most perspicacious language-lovers among us tend to overlook. The reminders Leith offers have made me think of new (to me, at least) and "subversive" paradigms for poetry (a post on that soon, perhaps)...but they've also recalled for me the central role every member of a learning community plays in that community's advancement of knowledge, while issuing a reminder as to just how dangerous it can be to trust blindly in the authority of a textbook.

The following passage from Leith (p. 68) struck me (cf. the comments some of my precalculus students made on their last exam):

Unfortunately, many people tend to treat dictionaries with reverence: rather than being seen as a record of usage, the are often regarded as the arbiter of it, a source of enlightenment for the ignorant non-specialist. In fact, the traditional arrangement of words in dictionaries gives people a strange idea about language. The alphabetic arrangement disassociates a word from the company it keeps, presenting it as a unit isolated from context and words of similar meaning. More important, many dictionaries give the impression that words have only one meaning, to be found on the right-hand side of the page. Even the fullest dictionary, the Oxford English Dictionary (OED), which shows the whole range of meanings by citing examples of a word in use at different periods in its history, puts the meanings first, then lists the examples, thereby obscuring the process involved in deriving the meanings; for we learn the meanings of new words most efficiently by hearing them in a wide range of contexts....It is not surprising, therefore, that people often misunderstand them.

How often too we ask our math students to use their textbooks in the same way they'd use a dictionary, placing theorems and proofs before (or, more often than not, simply in lieu of) the intuition and arguments that led to those theorems and proofs in the first place? How do our textbooks obscure the many long hours of exploration and discovery that went into the derivation of the theorems that pepper the textbooks' pages? Without access to the discoverer's process of discovery, the reader is apt to feel as though a given fact or formula arises ex nihilo, and that they, the uninitiated, are not privy to its inner workings.

Food for thought. By me, it's better to let the students stumble around a bit, piecing things together for themselves as they author their own textbooks. That's just what I'll be doing when we talk about general rational functions in Precalc tomorrow...strap yourselves in!

More words of wisdom from my precalc students

2011-10-19T05:06:00.004-04:00

Yesterday afternoon I worked for an hour with the student consultants at our university's Writing Center, helping them to understand what mathematical writing might look like, preparing them to work with students in the quantitative sciences who might come in with writing assignments from their quant courses. I was happy with the conversations we had together, and delighted by the students' energy and enthusiasm.

I shared with the consultants one precalc student's response to the midterm question in which I asked the students to describe the most meaningful learning outcome they've achieved so far this semester (see here for one response, not the one I shared at the writing center), and promised that I'd share a few more.

Let me throw a few more out there, all with a common theme. Several students, including the three quoted below, indicated experiencing the realization that mastering math is more than just memorizing formulas, and that if you stop trying to memorize every last formula but rather try to break each down and understand its inner workings, you gain immeasurably through your effort. That understanding is strengthened if math is put in a contextual matrix, placed alongside other disciplines so that its relevance becomes more apparent.

Katarina had this to say about her personal revelations:

This course is unlike any other math class I've taken. We actually discuss math in English at a level that I believe everyone in the class can understand....Instead of memorizing formulas, we play them out on the board, multiple ways, so that it is almost illogical not to understand their function and there is no need to actually memorize them....We write our answers in paragraph form, truly explaining the reason for doing them and our end result....It is so unusual to me to have math and other subjects (such as writing) overlap. My initial response was to avoid it but now I'm beginning to embrace the idea. After all, isn't UNCA's liberal arts program all about integrating many subjects in order to have a broader education?

Thomasina (who took a year off from high school before coming back to college) had this to say, upping the ante by acknowledging not just understanding, but enjoyment, and even aesthetic appreciation:

When I graduated high school, I decided that school was pointless....Read, memorize, regurgitate. That is all I was ever taught. But to understand? To break something down to its very core and build it back up, seeing every piece as they’re placed together to form a whole again. It's actually beautiful. I never got what you meant when you’d say math is beautiful, but now I get it. To have the ability to look at something complex and make it simple and tangible - it's art. And it's not just with math. It applies to everything: decisions, work, other people. Everything is a complex formula waiting to be taken apart and understood, and then put back together in a way that makes sense and feels right.

Kurt reports an experience similar to that of Katarina and Thomasina:

I've found more interest and enjoyment in something that I previously found tedious and boring and have found that I actually can relate math (including calculus) to the real world and my everyday life in ways I'd not before considered or imagined....I see this insight as far more valuable to me as a person than any one mathematical concept on its own. This is the kind of insight that changes people's lives, gives the potentially brilliant scientist a view into the potential locked up inside, or even just changes a fundamental attitude or a paradigmatic shift in thinking altogether....It's a great feeling to realize suddenly 'hey, I GET this!' and even better to find 'hey, I actually LIKE this!' I truly wish there were more classes like this one which, if not persuading one to major and work in the field, to at least open one’s eyes to the possibilities.

If a precalc course can move students to wax this rhapsodically about their learning, how much can students get from still deeper and more meaningful courses? It's up to those of us who teach to make our courses as relevant as we can.

Moo...?

2011-10-15T15:04:00.003-04:00

As I mentioned in a post not long ago, I recently asked my Precalc students to draw comics in which the characters explain how to multiply two complex numbers. I'll showcase a few here and there in the next few days. Here's an almost sickeningly cute one by Thomasina and Urban:

Also soon to come: more excerpts from the students' midterm essays on their most meaningful learning experiences so far this course.

Author! Author!

2011-10-14T21:50:00.006-04:00

Every person is the author of her own adventures.

This is a point I try to make to all of the students in all of my courses, in which I downplay my own authority and up-play the students'. "I've got no more claim to the truth than you do. The only difference between you and me is that I've been doing it for a few more years."

It's a point I've tried to make to my colleagues, most recently this afternoon at yet another CRTF meeting. This one was a meeting of the "Big Picture" Subgroup, at which the leaders of the other subgroups (including yours truly) were asked to make presentations on our ongoing work. I had a bit to say about our review of department responses to our "information request," and about our intended review of various ILS components.

I hope that our review will be guided by a handful of basic principles:

1. Our curriculum will function most efficiently and effectively when ILS learning outcomes and departmental learning outcomes (and the means of achieving those outcomes) are brought into fullest alignment.

2. Our curriculum will be most sustainable when the resource demands it places on faculty, staff, and students are minimized.

3. Our curriculum will offer the most rich and most meaningful learning opportunities to our students when they are allowed to plan and pursue their own courses of study, navigating course requirements that are rigorous but flexible.

This last principle places a high value on non-prescriptive curricula, featuring both general education programs and degree programs with relatively few specific requirements...programs that ask the students to play an active role in putting their own academic houses in order. I don't feel that our current curriculum features such programs.

The other day, in a hall conversation with a colleague, I referred to our role in the current system as "helicopter professors": our requirements are structured in such a way that our students' academic careers are micromanaged stringently. Students are tended to carefully, led from year to year in flocks, protected and prepared (for graduate study or real-world employment), but rarely challenged to set out on their own. Based on analysis of student behavior over the past several years, the Research and Evaluation Subgroup of CRTF discovered that only 18.5% of the courses our students take count as "free electives," taken for no purpose beyond academic exploration (such courses satisfy neither major nor ILS requirements). All other courses, all but little more than a semester, go toward putting a check in some bureaucrat's box.

"We need to make sure that our students who want to do graduate work are at least well enough prepared to get into a decent masters program," one of my department colleagues insisted at tonight's meeting. I agree, wholeheartedly. But I disagree with the means he suggests we must use to get them there. Many of our peer institutions offer much more flexible programs, with far fewer explicit course requirements, and still manage to send higher percentages of their graduates into prestigious programs. (The fact that this friend of mine is shortsightedly using graduate school enrollment as the be-all-end-all measure of an academic program's success is a topic for another post...)

More important, students completing more self-directed courses of study gain authority over their own actions. They grow in competence and confidence as they're asked to take on more responsibility for their own lives. They mature more quickly. They learn how to ask and answer important questions concerning their coursework and their careers. Forced to connect the dots for themselves, they become more authentic experts in their own disciplines.

This isn't to say we shouldn't offer our students some kind of guidance: nothing can supplant informed academic advising. Good advising can take the place of stringent requirements. If a student should wish to pursue graduate study, she should be encouraged to take courses that will most well prepare her for that study. If she fails to follow up on the advice her professors give her, she might be sunk...but she might not. She may succeed in her ambitions, but even if she doesn't...so what? Even if she doesn't end up where she'd originally set out to be, she's had a chance to plot her own path in the meantime, learning from whatever mistakes she's made on the way. Life is what it is, and each of us is who each of us is.

In my second section of Precalc (and again in my Abstract Algebra class), I read an excerpt from Rainer Maria Rilke's 6th letter to the poet Franz Kappus (Letters To A Young Poet, translated by Joan M. Burnham, Novato, CA: New World Library, 1992, pp. 53-55):

You should not be without a greeting from me at Christmastime, when in the midst of festivities your feeling of aloneness is apt to weigh more heavily upon you. Whenever you notice that it looms large, then be glad about it. For what would aloneness be, you ask yourself, if it did not possess greatness? There exists only one aloneness, and it is great, and it is not easy to bear. To nearly everyone come those hours that we would gladly exchange for any cheap or even the most banal camaraderie, for even the slightest inclination to choose the second-best or the most unworthy thing. But perhaps it is exactly in those hours when aloneness can flourish. Its growth is painful as the growing up of a young boy and sad as the emergence of springtime....Think, dear friend, reflect on the world that you carry within yourself. And name this thinking what you wish. It might be recollections of your childhood or yearning for your own future. Just be sure that you observe carefully what wells up within you and place that above everything that you notice around you. Your innermost happening is worth all your love. You must somehow work on that.

Let us reflect, my friends. What is it you find within yourself? How can you make your life your own?

Seriously, she was not paid to say this

2011-10-13T21:56:00.004-04:00

In my last post I mentioned I'd be posting excerpts from my Precalc students' midterm exams (and a few assorted comic strips offering explanations of complex multiplication). Here's the first installment.

Tonya's always challenging me with what I believe is the best question a student can ask in a math class, a question which can be paraphrased succinctly by the words "who cares?" She's always on the lookout for relevance and applicability. "That's cool," she'll say, slightly sardonically, and then add, "but how can that be used?" I love it. Every math class should have three or four Tonyas.

Tonya's response to my midterm question asking students to indicate the most meaningful thing they've learned so far this semester was a near-perfect defense of writing-to-learn. It was a delight to read! I asked her for permission to quote her response in full, and she gave me the go-ahead.

Before letting Tonya take it home, I should note that several other students indicated the same realization (of the power of writing as a tool for discovery and for gaining understanding) as the most meaningful outcome of the course so far.

Saith Tonya:

As much as I hate to admit it I think the most beneficial thing that I have learned or rather have incorporated into my learning process during this class has been providing sort of narrative explanations for the mathematical concepts in our homework assignments. This practice really brings light to the idea that the best way to learn something is to teach it. Although laborious, time consuming, and even a bit tedious it has proven beneficial to my comprehension.

I think it may be in some way related to uniting the two sides of the brain or the two main avenues in which human beings tend to process information. It seems that people so often separate quantitative reasoning and verbal reasoning as almost dichotomic and even hierarchical in nature. The fact of the matter is however that both approaches to logic are inherent to one another. Both numbers and words are at their most fundamental level simply expressions humans use to describe the world. Thus I have found great significance in the practice of incorporating those two expressions.

In my mind (as is obvious from my questions in class) mathematics bares very little significance independent of some broader meaning or application. Being forced to go through problems step by step and constantly attend to the looming “why?” in explaining the process that leads to the solution has been instrumental in illuminating that broader meaning. Being able to explain why something was done at a certain step in the problem forces you to draw on the most rudimentary understanding of the process and ultimately universalizes the relevance of that action. I believe that this is the underlying principle behind all creative thought. It is the ability to rearrange, expound, and theorize about the world with our little tool kit of axioms if you will.

As I move forward in my professional/academic life I think it will serve me to have been denied the temptation to skip steps or overlook details in order to more readily achieve whatever end it is that I am vying for whether it be the solution to a hw problem or a policy report. It has been an exercise in demonstrating that anything whole is made up of nothing less than the sum of its parts (maybe more but definitely not less).

I love my job.

But wait, there's more...

2011-10-08T22:42:00.002-04:00

I spent most of the day responding to my Precalc students' first midterm exams and their most recent homework. It was time-consuming, but fulfilling: the trick is asking meaningful questions. The exam included a question asking students to reflect on what it is they've learned so far this semester that will most help them meet their own personal and professional goals. The homework asked them to draw a comic strip in which the characters explain how to multiply two complex numbers.

Both of these exercises were answered with truly creative responses. I'll be sharing several of each here, once I get permission from the students to do so. For now, let it suffice to say that in their reflections many of the students report new-found appreciation for mathematics, new or renewed excitement about it, and greater confidence in working with it. As many or more gave great tips on solving problems or approaching weighty matters more critically and with greater skepticism.

I expect great things from these students. I really do have the best job on Earth.

lovin' it

2011-10-07T12:29:00.003-04:00

I am so enamored of my second section of Precalc right now. They're so much fun, and so smart, and so engaged! Gush gush gush...here's a link to the first edition of their class newsletter (see this post from this past May, in which I talked about this project): To Infinity and Beyond (Issue #1). It's marvelous! I've got a full-color hardcopy on my desk right now, my own smiling face beaming up at me.

In all seriousness: I find myself very calm in that section. They're inquisitive and skeptical; they're not satisfied with pat answers or particular formulas; they think in big pictures and big ideas; they're reflective and resourceful; they're fun.

It's a good learning community, the healthiest class I've had in a long time in that regard. I like to think I've played some part in making it so.

NIMBY (academic edition)

2011-10-04T21:58:00.004-04:00

[WARNING: what follows is an administration-heavy post that will likely bore most readers to tears. Faculty, please read on only if you're masochistic. Students, please read on only if you want to learn faaaaaar more about the inner workings of your university than you ever dreamed you'd know.]

I've been serving on the Curriculum Review Task Force since its inception back in March. In the half-year since this project got off the ground, I've probably been involved in three dozen meetings (some two or more hours long), written fifty pages of position papers, policy statements, memos, information requests, findings summaries, and spreadsheets. I've read two or three hundred pages of curricular data and carefully scanned the websites of two dozen peer institutions whose programs serve in some way as a model for our own. After all of this work, I feel like we might finally be near to having something to show for our effort.

To be sure, there's more work to be done, but for the first time I feel like we might have reached the point where we'll start rolling downhill again. We've got the information on department curricula we asked for from chairs and program directors, and as we begin sifting through that info we'll be writing our responses to the departments, even while we collect a little bit more data on ILS components before writing similar responses there.

We were intentional in our move to address departments and degree-granting programs first: since several powerful people first got involved in the task force specifically because they perceived its function to be to mount an assault on ILS, we wanted to make clear early and often that we would consider just as carefully the efficiency and the sustainability of departments and programs as well. It would be unacceptable, we wanted known, simply to chuck aside ILS and retreat to the cozy confines of our disciplinary silos.

From the get-go, aside from the usual (and expected) assortment of trolls who got on board the ILS-bashing bandwagon when it first rolled into town, my impression was that folks were behind us. With times as hard as they are (and faculty as overworked), we'd look for efficiency in whatever place we could. ILS, though certainly not a sacred cow, would be considered no more carefully or critically than would the departments.

But when it comes to paying the bills, everyone seems to be busted.

Evidence showed that, expressed in terms of required courses, our degree programs are larger across the board, on average, than their corresponding programs at peer institutions. Our students, not surprisingly, take longer than their peers elsewhere take to complete these programs. Therefore we asked departments to identify ways they might move to make their programs more sustainable: might they remove unpopular concentrations? cut back on course requirements? improve opportunities for "double-dipping" courses?

What we're discovering is shocking: while the curriculum in general is in disarray, every department, on its own, is doing a fantastic job.

The story goes something like this: "our university's curriculum is clearly unsustainable. Students aren't graduating on time, and that's scaring away students, so our retention suffers. My students have a hard time figuring out how to put their schedules in order so that they can graduate in four years, and I have a hard time advising them. But...

"...my department is functioning fine. We offer a premier program, the likes of which you'll find nowhere else in this state, no matter the price." At this point the story follows one of two paths. Either (a) "our program is efficient and sustainable: the number of hours we require is well below the university average, and our students graduate on time far more often than their peers in other programs" (admittedly, this is sometimes true: there are a small number of very sustainable program on campus) or (b) "we recognize that our program makes excessive demands on our students' time, but these demands are in line with the rigors of our discipline and with the accreditation standards laid out by our discipline's professional governing body."

So where's the breakdown, folks? Who's to blame? Are we going to pick up the switch and start thrashing away at ILS, the same old whipping boy we've been beating since I got here over six years ago? (This approach is puerile, people: though ILS could be better, it's not entirely broken...and as a liberal arts institution that purports to take that mission seriously, we need some sort of ILS-like program in order to maintain our street cred.) Or are we going to waste more time pointing every finger we've got at our colleagues in other corners?

Or maybe...just maybe...we'll get the balls to ask ourselves tough questions: do we really need that extra concentration or those curiously complicated course requirements? Can we serve our students as easily through advising as we can through administrative fiat, thus making their schedules more flexible? Just what do our students gain by being forced to take these specific six courses, and not simply six from among ten or twelve, chosen according to their individual interests and aptitudes?

I can't end this post without a note of thanks to the folks in my own department. I've been at odds with many (most, perhaps?) of them on the matter of reducing our concentrations (we could easily, I feel, stand to combine our pure and applied concentrations into a single one), but I like the moves that were made today in our department meeting to make more flexible the applied concentration. I appreciate their willingness to move in that direction.

Compromise, folks, compromise. It's how shit gets done.

I apologize for the pottymouthery. I've been hard at work since 7:00 this morning (it's now nearly 11:00), and my internal filter fell off a long time ago. I'm off to bed.

(Oh, from the "it gets much more fun from here on in" department: I'm tremendously excited about the next few days in both of my classes. Applications of quadratics in Precalc...and symmetric group silliness in Abstract!)

Good can come of department meetings

2011-10-04T16:06:00.003-04:00

Propositions cut
like glass, bright obsidian
in soft poetic flesh

Welcome!

2011-10-01T20:35:00.004-04:00

Yesterday I ran into one of my Precalc students outside of class. I was on my way back to Robinson Hall after teaching my Abstract class over in Karpen; Becky was en route to the library with the rest of her LANG 120 class. There they'd be discussing the use of library resources in conducting research.

We chatted briefly, and I asked her if she was still considering a math major. (She was one of two in that section who, without prompting by me, indicated interest in the major at the outset of the semester.) "I definitely am," she said excitedly, and then a look of worry spread over her face, "do you think I still should?" I was a bit thrown off and only after a few seconds managed to reply with something like "of course!" She went her way and I went mine, but our encounter stuck with me. Why had she asked what she had?

I suspect it may be because she may not feel as confident in her math ability as she did at the start of the semester. Though she's done well on every homework set and on every quiz, like everyone else in the class she's made her share of mistakes and hasn't presented complete understanding of everything we've talked about. Might she believe that only those who can complete Precalculus with flawlessness and perfection are worthy of pursuing a degree in mathematics? (Only later did I think of an apt analogy: as I'm highly unlikely to ever run a four-minute mile, might I just as well give up on one of my favorite hobbies?)

After thinking it over, I found that I could understand Becky's belief, given the traditional structure of mathematics education, home to bell-curve-based grades, punctilious point-based assessment, and lecture-based teaching. There's an air of elitism to the way students are often ranked and ordered, made to fight with one another for a scant few As. The unsaid assumption in classrooms where deep and steep curves guarantee a normal distribution of grades is that only the best need move on, and that the others' services will not be needed. Detailed rubrics with single-percentage-point resolution signal to the student that mastery of fine detail takes priority over authentic understanding. (No wonder students clamber after every point, wondering what it is that separates a score of 8/10 from a score of 9/10!) Fast-paced lectures make sure sure the students who start off slowly get little chance to get ahead; the quickest students (who are often, but not always, the brightest) control the pace in these classes.

All of these factors discourage students who are excited or intrigued about math, but who are put off by the way in which it's often taught. We can't afford to turn these students away. The fact of the matter is we, as a society, need more mathematicians than we can possibly prepare, and we do no good in discouraging anyone who's passionate about the field from pursuing it further. We do well to let as many students through the gate as we can, and to give them all of the support and encouragement they need to develop their skills fully. We do well to eliminate curves and to downplay in-class competition between students. We do well to "coarsen" our grading scales to accommodate "big-picture" thinkers who might miss a detail or two but who grasp complex systems in their entirety. We do well to step away from our classroom's center stage and let students take our place, so that it's not to the top ten percent that we teach, but to the class as a whole.

The bad news is that these practices are not universal; the good news is that they are more popular than ever. They're in use throughout my department and many like it. The youngest math teachers (at every level) are more adept at applying them than their older peers. These teachers are daily developing new tricks and techniques to make these practices more effective, and they're not shy about sharing these tricks and techniques with their colleagues and with their students. The future is bright for math education.

Stick with it, Becky! Welcome to the team. You're in good company. You'll do wonderfully.

Coming soon to your university's bookstore...

2011-09-30T07:44:00.007-04:00

Life lurches forward in fits and starts, and all things go in cycles.

My first book (defined as something with an ISBN) was a collaborative effort with several of my fellow graduate students. From here to infinity (A foundation for calculus) (Thompson Learning, 2001) was a slender in-house volume on algebra, trig, and other precalc concepts meant for use in Vanderbilt's Calc I classes to get the students there up to speed on algebra essentials before Calc came along and kicked their butts. We worked together wonderfully well on this project, each writing a chapter, swapping chapters to review and revise during the editing stage, and sewing it together seamlessly before sending it off to the publisher. I wrote the chapter on rules for logs and exponents, a topic I feel very strongly should be taught in a certain way (it all makes total sense if you teach it this way).

I was very happy with that project.

My second book, The Isomorphism Problem in Coxeter groups (Imperial College Press/World Scientific Publishing, 2005) was a one-off, a graduate-level survey of a particular area in combinatorial and geometric group theory. I was approached by the publisher (in, admittedly, a very generic dear-author,-we-invite-you-to-publish-a-volume-in-our-new-lecture-note-series kind of way), and, having nothing better to do with a year of my time, said yes. On and off for almost a year I compiled all of my notes on rigidity problems in Coxeter groups, on automorphism structure in same, on presentation invariants, and on standard combinatorial techniques applicable to Coxeter groups, braid groups, Artin groups, and all other fellow travelers...the result was the text named above. It was something to do. It was a lot of work, and it was reviewed well. In the past six years it's sold maybe 600 or 700 copies, which honestly is more than it deserves to have sold; it's got a very niche audience. I'm proud of the book, but not excited by it; there was little passion in it.

In February 2012, my third book will appear through Jossey-Bass:

This book is a labor of love. It represents true passion, true excitement and ardor. It combines my love of teaching and my love of writing, and the sense of duty I feel toward folks in my chosen discipline. I had a blast writing it, and I'm very proud of the outcome. I hope you'll consider taking a look once it comes out!

Beaming...

2011-09-29T10:23:00.005-04:00

...with pride! My undergraduate researchers Ned and Ino are making substantial progress on their nutritional analysis project. Fresh out of a meeting with leaders of the Housing Authority of the City of Asheville (HACA), they have a better-than-ever vision of the scope of their project. They'll be working with HACA to develop affordable, nutritious, and pleasant meal plans to distribute to low-income families who rely on the federal Supplemental Nutritional Assistance Program (formerly called the Food Stamp program) for grocery purchases.

This project will be meaningful, rich, and offer technical mathematical challenges. I'm so excited for them, and immensely proud of the work they're doing. They're self-directed, focused, and quick. I have high hopes for this project, about which they're already scheduled to speak at two conferences, including the JMM in Boston in January.

Good stuff! Further bulletins as events warrant.

Where's that voice coming from...?

2011-09-28T18:12:00.003-04:00

Today I got to give only my second-ever presentation via Skype, to a small but interested (as far as I could tell) audience at LaGrange College, arrangements made by my colleague Kevin, a faculty member in LaGrange's mathematics department. (Thanks, Kevin!) Kevin and I took part in a Project NExT session at the MAA sectional meeting in Tuscaloosa last March (about which I blogged briefly here), at which time he shared some really neat online networking tools for helping increase real-time student engagement in the classroom. I shared some examples of low-stake writing activities (freewriting, doubting and believing, dialoguing, etc.), indicating their uses in disciplinary classrooms.

Today's telepresentation was an encore performance, to, as near as I can tell, an economist, a writing instructor, a reference librarian, and a couple of mathematicians. (Sounds like the set-up to a lousy joke...) They had great questions, and seemed legitimately engaged.

It's hard to tell from afar. If I learned nothing else from the presentation, I learned how awkward it is working with a group via video feed, dealing with subpar audio and video, and not being immediately present to pick up on subtle nonverbal cues from my interlocutors. In the immortal words of Marvin Gaye and Tammi Terrell, ain't nothing like the real thing, baby.

Also: I've decided to take my show on the road...tomorrow, weather permitting, I'm going to hold a couple of my office hours out on the steps of the Ramsey Library...look for me there from 2:30 to 4:00. If my current students are as excited about this idea as my former students (thanks for reading, Jack!) apparently are, I might get a few visitors. I'd love to see my colleagues out there, too. Let's mingle!

Where do you want me to be?

2011-09-27T21:03:00.006-04:00

Today was, sadly, the last of four meetings of the Learning Circle I took part in this semester, on Palmer and Zajonc's The heart of higher education (about which I've posted recently before)...even sadder was the fact that I'd only been able to attend two of the four meetings, other obligations taking me out of town and off campus. I've found this text eye-opening and enriching, and the conversations surrounding it even more enriching still.

I found myself thinking out loud in the circle today, wondering what our academic lives would look like if we took ourselves out of our offices and started doing more of our work more publicly. What if I started holding office an office hour or two on the quad, or in the student union, or in the glasshouse adjacent to the library? What if my colleagues joined me in this, sharing a table with me as we worked with our students, observing firsthand how we interact with them, witnessing the kind of learning that goes on in one anothers' disciplines?

Soon might fall the disciplinary boundaries we're all quick to dismiss but unconsciously eager to maintain. At a university so dedicated as mine purports to be to the liberal arts, we ought to be all about interdisciplinary exchange that blurs distinctions between this field and that. But when it comes down to it, as often as not we retreat inside our hard-shelled departmental silos. "I'm all for interdisciplinarity," we might say, but in practice we add "as long as it happens on someone else's time."

But if we started seeing more of each other on the quad, in the union, in the glasshouse, maybe we'd know more about each other. We'd each know more about other's passions and pursuits, and more about the way the other thinks. We'd be able, at least momentarily, to adopt the other's disciplinary perspectives, and when our students ask us why they're asked to take courses in that field or this, we'd be able to tell them why, honestly, earnestly, and confidently.

If we knew more about each other, perhaps we wouldn't find the sort of territorial entrenchment I'm witnessing right now in various departments' defenses of their current curricula to the Curricular Sustainability Subgroup of CRTF which I'm heading up. Sadly, though perhaps not surprisingly, many departments' chairs are convinced of the inestimable value of their own departments' offerings, and of the waste and profligacy that must go on elsewhere in the curriculum to result in such a burdensome mess. The written responses we've received from most chairs are for the most part meticulously-crafted hagiographies telling tales of the author's department's excellence. Without doubt there is good going on in every corner of campus, but equally doubtlessly I know we're all to blame for the unsustainable burden we've taken onto our own shoulders.

If we were to meet face-to-face more often, there'd be no need for polemic; we could engage in frank but warm discussions. It's hardly a coincidence that the considerable face-to-face work the Curricular Sustainability Subgroup has done this summer and fall has been done so smoothly and so amicably. After all, it's difficult to be defensive (or to go on the offense) when your interlocutor is sitting right in front of you. Face-to-face meetings encourage warmth, empathy, and honesty. The "rocking chair conversations" Parker J. Palmer talks about in Chapter 6 of his book with Arthur Zajonc are the perfect places for real and lasting change.

I'm ready to set out some rocking chairs. I'd like to try this, if just for a few hours each week. Maybe while the weather's nice, the steps of the library might do. When it starts getting colder and darker earlier in the day, I can move to the Pinnacle in the student union. Students, colleagues, let me know: where do you want me to be?

What have we learned?

2011-09-25T14:36:00.008-04:00

At some time in my youth I learned that I loved mathematics. Its precision and exactitude suited my budding rational empiricism (though I couldn't have thought to say this at the time). I decided that I'd be a math teacher, because what else could one do with math?

As an undergraduate math major, I learned that I'd most likely teach math at a university, and not at a high school. "Don't waste your talent," my adviser told me. In those words he said it (albeit sotto voce); being a mathematician himself, he likely lacked the social grace to say it less bluntly. I was led by him to believe the dictum that "those who can do; those who can't teach." Though I've learned that it's often the case that our future teachers struggle more mightily with advanced mathematical concepts than do some of their more pure-math-minded colleagues, that struggle is often a fruitful and maturing one, and I no longer keep stock in this saying. Besides, knowing college faculty the way I know college faculty now, and recognizing the importance of a rock-solid middle school and high school education, I'd trade a dozen run-of-the-mill university faculty for one fantastic high school math teacher.

As a grad student, I learned that I loved both teaching and research...in other words, I was born to live a life in the traditional academy. I loved the energy in my classrooms, the excitement of my students. I loved helping them to their personal epiphanies and "aha!" moments that make discovery so fulfilling. (I remember some of my experiences there with remarkable clarity, as in this old post.) As much as this, I loved holing up in my office or in the library and plugging away at the pure mathematical puzzles presented me by Coxeter groups, braid groups, and Artin groups. I loved confronting the unknown, clad only in the armor of socially-constructed axiomatic systems (though I couldn't have thought to call them this at the time), armed only with a few blunt theorems. My doctoral adviser urged me to get a postdoc, to prepare myself for a career at a top-notch research institution, where I'd surely be happiest.

As a postdoctoral scholar, I learned that I didn't want to spend the rest of my life at a research-intensive university. As much as I loved (and still love) research, I could not see myself doing it to the exclusion of almost all else. I had hearty colleagues; they were wise, intelligent, and in their own way fun. But they sacrificed virtually all for the sake of their research careers, publishing so that they might not perish and openly disdaining teaching, for it took time away from their scholarly pursuits. As I grew to be a better and better teacher and came to learn the fulfillment it gave me, and as I came to recognize how much more of an impact an exceptional teacher can have than even the best researcher in pure mathematics, my personal future in academia came more clearly into focus.

As an untenured faculty member, I learned that yes, indeed, teaching is where my passion lies. My research was (and is) fruitful and fun, but had (and has), for me, less meaning than the moments I get to spend working with my students, talking about teaching, and living as fully immersed in an authentic community of learners as I can. I learned that math wasn't all there was, and that my longstanding love of writing could play as big a part in my working life as it did in my personal one. I opened the door to poetry, composition, and rhetoric, and discovered rich new worlds I'm only just beginning to explore. (Much more about that in a forthcoming post on my personal "community of scholars.") Math was moved aside to make room.

As a tenured faculty member, I'm learning more and more each day that I can do what I want to with my career, and that I can follow my ever-changing passions. I'm learning that my most meaningful collaborations are most rarely found among people in my own discipline. I'm learning to adopt and adapt ever more reflective and integrative practices into my classes. Some of these practices are decentering and unsettling, both for the students I work with and for me...but ultimately such practices are the most rewarding. I'm learning that I stand to learn the most from those who are "supposed" to learn from me, and that only at a liberal arts institution like UNC Asheville would I have the chance that I have to engage in that learning.

I've learned enough to know that I don't know much at all, but that that's okay, because no one really does, and I know as much as anyone I'm likely to run into. We all know different things, though, and when we meet at the crossroads and shelter at the inn there for the night, we'll have wonderful stories to share with one another before we move on to make our way in the world once more. Sharing travelers' tales: that's how we learn best.

Here's a tale. This semester I'm working on an outside project with two of my favorite students, Ino and Ned, with whom I've shared several courses in the past. They've signed on as "undergraduate research" students because initially we expected that the project would involve a good deal of digging into linear programming and other linear algebraic methods of optimization, requiring us to perform original research at some point. (It's an offshoot of a miniproject Ino and Ned worked on with a couple of other students in my linear algebra course last fall, in which they performed a feasibility study of several different diets from both a nutritional and a budgetary standpoint. Wonderful stuff!)

The deeper down the rabbit hole we go, the more it becomes evident that we're unlikely to break any theoretical ground, but the more we realize the transformative potential of the work we're doing in the larger sphere. The work these bright kids (and they are among the brightest our school is privileged to serve) are doing will positively impact our region by helping community outreach organizations assist low-income families in planning healthy and affordable meals. Our off-campus partners are excited about the budding collaboration my students are forging, and I predict great things coming of our engagement with one another.

You might still call this "undergraduate research," writ large...more accurately still, you might call it "service learning." Whatever it's called, it's learning of some sort. Moreover, it's authentic, it's transformational, and it's real. It represents the sort of learning I hope to do more of as I move forward from here. It's the sort I hope to help my students and colleagues do more of as well.

Let's wait until morning and then move on, and make up more travelers' tales to tell at the next crossroads we meet.

Be afraid, but don't be afraid of your fear

2011-09-25T13:46:00.005-04:00

Today I had a very contemplative morning. I had a good run, and it couldn't have been a nicer day for it: the air has an early-autumn crispness, and the trees a golden-green that connotes an ageless seasonal change.

I gave thought this morning to an opportunity I've recently been granted, one of which I'll soon take advantage, and which I hope will bear fruit. I can't say much of it publicly yet, but I will say that I became fully determined to make a move this morning when I realized two things:

1. I'm a little afraid of taking this chance, and

2. it's that little bit of fear that's convinced me the chance is worth taking.

I know that if things work out the way I hope they will I'll be presented with entirely new challenges I've not yet faced in my career to this point. I'll be doing a lot of learning on the fly and a lot of playing it by ear. I'll be bearing a great deal of responsibility, but also relying to a greater extent than ever before on others to help me carry out the tasks I'll be responsible for. I'll be delegating, relegating, moving and shaking, and working my tail off.

It's a bit frightening. I've almost balked once or twice because I know that though I'm qualified to take this on, and though I'm as ready as I'll ever be (and as ready as anyone could be expected to be), it'll still be a rough road. I'll definitely be outside my comfort zone. It was only just this morning that I admitted to myself that I've been a little afraid of moving down this path much further.

But you know what? That's a good thing. If we don't put ourselves in that "zone of proximal development," as Vygotsky put it, we don't put ourselves in a position to do much learning or growth. If I only ever do things that I know that I can do, that I'm utterly unafraid of doing, I'm not going to get much out of them.

These twin realizations: the presence of fear and the healthfulness, the appropriateness, of that fear, have moved me forward. I feel stronger and more whole.

There's a parallel in one of my courses right now. Yesterday I spent roughly 10 hours grading (9:00 a.m. to 7:00 p.m., almost nonstop), about 7 hours on Precalculus alone. Their most recent homework sets (especially Homework 6) were challenging ones, involving complicated problems which had to be broken down into simpler subproblems. The students had mixed success in seeking solutions to these problems. Some patiently broken them down and crafted careful solutions; others were less successful, impatiently attempting to swallow the problems whole.

The problems are meant to push the students forward, to move them from a place where they feel comfortable to one where they feel challenged, and maybe just a little scared. I'm confident that the students can do what's asked of them, though, and that they have the skills needed to solve the problems I give to them if they take their time and work carefully. I'm confident that if they take time to contemplate the problems piece by piece, they'll grow in confidence and competence.

I sent the students an email just now, including a model solution to the toughest of the homework problems. Here's some of the text from that email; I hope it helps them place our work together in a healthy context:

...I also recognize that the problems I'm asking you to complete are not easy ones. Each of those on HW 6 likely took you 45 minutes apiece (maybe more) if you did them clearly, capably, carefully, and well, as many of you did. I was impressed with the neatness and precision of some of your answers!

These are not easy problems; they are challenging and probing. It's for the best: I believe that challenging problems are those most worth doing. They push us to our limits and force us to confront fully our understanding of the ideas we come up with together. I'm just relearning now (relearning from you, as much as from any other source) that those things that are most worth doing are those things that are difficult to do, that challenge us, and that, perhaps, even scare us a little.

My reflective morning's brought me other thoughts as well, about which I'll be posting throughout the week. Several stem from my ongoing reading of Parker J. Palmer's and Arthur Zajonc's The heart of higher education: A call to renewal (transforming the academy through collegial conversations) (San Francisco: Jossey-Bass, 2010), the centerpiece of the Learning Circle I've been taking part in (when possible) this semester. The book has great richness, and has led me to reflect deeply; as I wrote to myself at one point "there's poetry on every page!"

In the next few posts I'll talk about what I've learned from an ongoing project about which here I've yet said little, about resistance to curricular change on the part of even the most well-intentioned (and change-oriented) faculty, and about my own elusive "community of scholars" Palmer and Zajonc extol on page 128 of the book I mentioned above. About all of these I've thought today.

As I said, I had a very contemplative morning.

Just flew in from Little Switzerland, and...

2011-09-22T20:46:00.004-04:00

This year's CWPA was, as always, fulfilling, friendly, and enlightening in the extreme.

The focus was on grant writing and all it entails, from planning projects, to finding funding sources, and on to starting and polishing proposals. Several new ideas for medium- to long-range plans popped up, not the least of which involves finding financial support for the rhetorical analysis Bella and Damian are still performing on REU students' research writing.

Beyond the professional fulfillment the conference gave me, I benefited from the trip personally, as well. Once again the warmth and welcome of my colleagues in composition and rhetoric reinforced my belief that I've made the right decision in moving my career in this direction.

Meanwhile, back at the ranch, I'm really enjoying both courses I'm teaching this semester. As is to be expected of a course in which everyone in the room knows well ten or more of the others, my Abstract class is often rowdy, but engaged. The same can be said of the second section of Precalc. I made the mistake of calling them "squirrelly" the other day, in response to their giggliness, and this only made them giggle more. It's a good group, though, and they work hard. Their primary strength as a class, as I told them today, is their willingness to ask questions: they're completely unafraid to "look dumb" in front of one another, and this fact often makes them quick and effective learners. In contrast, my early morning section is quiet and focused, different but equally bright.

I'm going to take a few minutes at the end of class tomorrow to do a one-third-of-the-way class survey, to get the goods on the students' point of view. We'll see how much my take on our classes matches up with theirs.

Also: too early to tell what'll happen for sure, but there are some big opportunities drifting my way. More to come as time permits...

Math...who needs it?

2011-09-19T10:38:00.004-04:00

As a low-stakes exercise at the end of my first section of Precalc this morning I asked students to write down the most math-related activity in which they took part over the weekend. I got several quotidian responses ("I attempted to complete HW #5," "Chemistry HW," and the like) but I got some more exotic ones, too:

"I explained what a TI-83 was to a 6 yr old"

"The most math related thing I did this weekend was weigh the amount of almonds I wanted at Earthfare and calculate the price in my head."

"Calculated my availability for a client given all my meetings and classes that I have this week."

"I worked at the hospital all weekend, and at my job, I utilized math to calculate the number of calories and carbohydrates patients had been consuming."

"Averaging pace/mph/minutes per mile while running 1/2-marathon."

"I got kinda bored, so I figured out every time of the day where the angle of the clock hands were exactly the same as those of 4:00"

Fun times! We'll see what my second section can come up with.

On another topic, this afternoon I'm off to my fourth Carolinas Writing Program Administrators conference at the Wildacres Retreat Center just off the Blue Ridge Parkway. This year's theme is seeking external funding, and participants will spend a bit of time hammering out grant proposals as they bounce ideas off of one another. (Our current Writing Center director and I are planning some sort of regional writing-themed conference that would bring in not only university students and faculty but also K-12 educators and their students, and members of the community at large.) Of course, I'm sure I'll find time to work on my ongoing research with the College of Charleston crew (we're presenting this work at the Four Cs in March), and to cut loose with my comp-rhet buddies from all over the Carolinas.

Further bulletins as events warrant!

UPDATE!

Because I know you've all been on tenterhooks since my last post, here are some of the most interesting weekend uses of math from my second section:

"I built a table and had to measure where to cut. I also wired a dimmer switch which required me to use some math."

"The most mathematical thing that I did this weekend was to figure out how many CDs my band sold based upon how much money we had in our 'money jar' at $15 an album. Also in figuring how much we owe our bass player when paying her 22% revenue earned per gig."

"I was playing a power chord on a mandolin and my friend asked me, how do you do that? I told him it was the same as a power chord on a guitar but reflected over the origin."

"I was actually bitching last thursday about how I would probably never use the research from our homework ever, but this weekend I got into a discussion about Dow Jones & was proven wrong. I laughed and will no longer bitch. :)"

Progress! :)

Out of the wilderness

2011-09-18T15:19:00.002-04:00

This morning I finished reviewing and responding to my MATH 461 class's homework set, the one featuring several very open-ended problems related to Fibonacci sequences, Euclid's Algorithm, and greatest common divisors. Their work was fantastic, and the sense I got from most students' solutions was that they'd achieved genuine understanding, something I honestly don't see present in most responses to the cut-and-dried prove-this-theorem sorts of questions one might ask in an upper-level mathematics course.

Moreover, the students made remarkable progress in proving some nontrivial mathematical results they themselves got to formulate. Several presented solid proofs of one direction of the equivalence I mentioned in my last post, and though no one successfully proved the converse (I was only able to do it myself last night, after several false starts), a few students made earnest attempts at so doing and a few finished just shy of the mark.

Furthermore, two of the students noticed that, though I'd not intended it, the fourth problem on the homework set had close ties to the previous three (all of which were similar). This last problem asked them to characterize the numbers which caused "worst-case" performance in Euclid's Algorithm when divided into 99. A bit of thought (after examining a mess of data) will convince you that the worst case is achieved when the numbers you select give the most "Fibonacci-like" sequence of quotients when divided into 99, numbers for which most of the "q" values stemming from Euclid's Algorithm are 1, so that the corresponding remainders remain as large as possible. Thus, these two students pointed out, Euclid's Algorithm should perform most poorly when you use to divide one Fibonacci term into its successor. One student even presented several pages of numerical evidence for this worst-case behavior, building off of the generalized Fibonacci sequences we'd just worked with above. It was splendid.

Finally, one student made an observation regarding the frequencies with which each "run time" occurred when Euclid's Algorithm is applied, noting that when plotted, these frequencies traced out a very normal-looking curve. "What might happen with other values for b, besides 99?" he asked. No doubt there's some nontrivial number theory lurking just below the surface: primality plays a role, for sure, and I'm sure Euler's φ comes into play.

All in all, I get the feeling that the students got far more out of this set of exercises than most (any?) I've ever assigned in my career. I'm going to see that all of my homework sets for the rest of the semester are in a similar vein.

Into the woods

2011-09-15T16:27:00.004-04:00

It wasn't until I wrote yesterday's blog post that I realized the extent to which I'm pushing inquiry-based learning in both courses I'm teaching this term. In both Precalc and Abstract Algebra I, the majority of the homework problems students are being asked to complete are what can legitimately be called research problems, and I'm posing them as such, guiding the students through an initial "data collection" stage, leading them then to a "conjecturing" stage, and from here to a point where they should be ready to offer at least a partial proof. The questions I'm asking are very open-ended, and in a few cases already this semester I'm not even sure I know the answer.

Example: I've got the Abstract students making conjectures about the relative primeness of consecutive terms in generalized Fibonacci sequences: for what natural-number pairs (α,β) is it the case that any two consecutive terms in the sequence defined by s₀ = s₁ = 1, s_n = αs_n-1 + βs_n-2 are relatively prime? I admitted up front that I don't know the answer to this (though I have some guess as to what might be true), but I asked students to try out several cases, formulate a conjecture based on the data they gather, and try to prove their hypothesis.

What fun! I'm having fun, anyway. And what a way to learn! I have no doubt that the students are apt to become more talented mathematicians (and more generally, problem-solvers) when asked questions like this than when asked to complete cut-and-dried textbook proofs for which the answer is already told to them.

How NOT to graph a shifted function; or, The nature of mathematical research

2011-09-14T12:23:00.009-04:00

It happens to us all at some point: we're confronted with a problem to which we simply don't know the answer. It's a problem never posed to us before, one we've never seen...it may not even look much like anything in our prior experience.

It's happened to me. Many times.

For example, for the past year or so I (and, off and on, several undergraduate researchers and a couple of colleagues) have been struggling to find answer to a seemingly simple question: where on Earth does the mode of the independence polynomial of an arbitrary 2-regular caterpillar lie?

Okay, so maybe it's not that simple of a question...but it's one that's resisted analysis of every kind we've attempted for well over a year.

However, undaunted, we have tried several different means of cracking this muthah. We've tried geometric methods, combinatorial methods, algebraic methods...even analytical methods. We've tried it all, to no ava...well, to some avail: we've learned a lot about the structure of the objects we're studying, and though we don't yet know what method will work to solve the problem, we can tell you several methods that won't work. Hey, we've tried.

And that's what matters: the fact that we've tried. In the end, it's okay to not know what the answer to a particular question is. After all, none of us are born with inherent knowledge of algebra and calculus and combinatorics: we're going to be asked questions the answers to which we simply don't know.

Put another way, ignorance is inevitable; what matters most is how we confront that ignorance. Inaction gets us nowhere. Action of any organized kind is preferable, and more preferable still is action of a sort our experience suggests will give us a means of responding to the problem we're posed. This kind of confrontation with ignorance is called learning...or even research.

Yes, research: it doesn't cheapen that lofty term at all to use it to refer to the simple actions we undertake when we, for example, try to graph a simple function we're unfamiliar with.

Allow me to demonstrate.

When confronted with a truly unfamiliar function, here's what not to do:

You can't be expected to be familiar with every function ever invented...there are too many of them! But don't just sit there! Don't let ignorance get you down! If you're not sure of what to do, maybe try something that's worked in the past, like...

Ah...now we've got some traction...a few more values...

...and we're starting to see results...now let's plot some points...

Huzzah!

Ignorance dispelled! Or at least held at bay for a bit. Congratulations: you've now learned something new. Put another way, you've completed a miniature research project. Seriously, you've just done research, applying known methods to approach an unknown problem. That's how you do it.

At the risk of sounding repetitive, let me exhort you once more: please, don't just sit there. It won't simply "come to you" if you're not doing anything at all, but it might if you try something out.

P.S.: photo credits go to my former student, and awesome stats major, Karl. Thanks, Karl!

Cause 'n' effect

2011-09-13T08:16:00.006-04:00

I've already heard from several former students who are now in K-12 education that the scenario depicted by my friend Kyle is more than ever a reality. I've always known the high-stakes testing, NCLB, and all that nonsense were driving our public schools off of a cliff, but I don't think I was ever aware of just how bad it had become...and Buncombe County's schools are by no means among the nation's "worst."

What in the hell are we doing? I see two immediate and profoundly negative effects to this shortsightedness.

First, by drilling our students on "basic skills" (i.e., reading and math) to the exclusion of all else, we're ensuring that our students will grow to loathe those subjects more than they already do. Many but the most math-motivated students come out of high school hating math and reading little, and being unable to do more than solve pointless decontextualized machine-gradable math problems and extract topic sentences from unchallenging tendentious passages of "literature." This isn't an inevitable outcome: my experience in working with my department's Super Saturday "Math Discoveries" program has taught me that there are many bright 8- and 9-year-olds of all backgrounds who positively love math, and that if that love is nurtured they'll stay focused on it for a long time. Moreover, my experience in teaching Calc I, Calc II, and even Precalculus has taught me that it's not impossible to reawaken dormant affinities for math if it's presented in a way that makes it interesting, challenging, relevant, and fun. But drills and standardized tests are neither interesting nor challenging nor relevant, and they're certainly not fun.

Second, by neglecting less readily-assessable (or at least less readily-assessable-through-machine-graded-standardized-tests) subjects like social science, Earth science, literature, music, etc., we are ensuring that our students will have virtually no ability to contextualize whatever minimal understanding of reading and mathematics they're able to eke out of their loathsome experience with these latter subjects. Their knowledge of math will be disembodied, inapplicable to any other science. "Word problems" will always be "word problems," impenetrable blocks of quasi-mathematical lingo, and not opportunities to apply mathematical understanding in a meaningful setting. Worse yet, reading (and writing) will always be a soulless enterprise, undertaken in order to find a topic sentence, identify three (precisely three) salient pieces of evidence in support of that sentence, and pen a five-paragraph response containing both an introduction and a conclusion (god forbid you forget either).

I'm well aware that there are many more negative effects than these, but I've not got enough time to list them all here...nor am I the most well-trained to make this list. (I'm sure many of my recent grads who now teach in the public schools could do a better job than I could, and I hope they find their way to this post and chime in in the comments section.) I'll close by quoting a colleague/Facebook friend, who said on my link to yesterday's blog post "why is it getting so hot?...why am I in this hand basket"?

Rilly?

2011-09-12T17:09:00.006-04:00

If you didn't already know it, it might tickle you to find out that I bowl on a pretty laid-back bowling league on Monday evenings, called the S.I.N. (Service Industry Night) League. The folks I bowl with are almost to a one friendly, caring, compassionate, and often very intelligent individuals. I never cease to be amazed by the warmth and wisdom these people show to and share with others. It's fair to say that S.I.N. League helps me maintain my sanity.

One of my teammates, Kyle, recently took a job working in one of Buncombe County's public schools, as a teachers' aide. He's loving his job, and it's giving him great insight on our nation's educational system. I love that his insight is untempered by educational lingo and unfiltered by official administrative fiats. From him, you get the dirt.

Kyle keeps a blog himself, a collection of biographical blurbs tangentially related to the webcomic he and his wife (also a teammate) write about the exploits of our bowling team (I'm Parker!). While checking the comic (updated every Monday!) this afternoon, I found the following interesting comment on Kyle's blog:

One somewhat shocking thing I learned is that our teachers have been told not to teach science and social studies because they don’t have enough time, and are primarily tested on reading and math. I had noticed that every class I went to was either doing reading or math, but I thought it was simply because I was there early in the day and maybe they did other things in the afternoon, but no! There is so much pressure from the state and county governments to preform better in math and reading that they simply skip over other subjects.

Rilly? I'd be interested in learning more about this phenomenon...I mean, I know that a good deal of emphasis is being placed on certain subjects because of high-stakes testing and other accountability measures, but this seems extreme. Are teachers (at least in the 2nd/3rd grade level where Kyle helps out) being discouraged from teaching science and social studies at all, or are they simply being told to put emphasis on reading and math? And to what extent is this discouragement/recommendation official? Is it an unwritten rule that's clearly understood, or is there a paper trail somewhere?

I'm a bit shocked by this.

Thoughts?

Fishbowl

2011-09-06T21:18:00.005-04:00

Today I attended the first of several meetings of the faculty Learning Circle in which I'm taking part this semester, on Parker J. Palmer's and Arthur Zajonc's The heart of higher education: a call to renewal (transforming the academy through collegial conversation), and hot on the heels of this we held the first meeting of the Curricular Sustainability Subgroup of CRTF. The former meeting prepared me well for the latter: big talk and deep thoughts about integrative pedagogy helped inform the reflection my colleagues and I did on the general education programs at several of our peer institutions.

Most such programs differed from ours in one or two fundamental ways: either they comprised significantly fewer required courses (no more than a handful of fundamental classes scattered across the curriculum, generally a few to each major division, and maybe including a writing course or a math requirement) or they placed more stringent demands on the student but offered her a multiplicity of ways of meeting those demands (with copious menus of courses to meet requirements for history, humanities, or "world cultures" requirements).

What could go wrong? Both designs assume students (and faculty!) can pack a great deal of interdisciplinary engagement into a broad array of courses. This assumption seems like a risky one at schools like Wesleyan College (Connecticut), where students must complete only 9 general education courses, 3 from each division, all with different departmental prefixes, and hundreds of courses can count toward the gen ed requirement...wouldn't an optimal interdisciplinary experience require the instructors in all of relevant courses to work in concert to help students realize this experience? Honestly, I'm not sanguine about the ability of an entire faculty to coordinate such a widespread effort.

I wonder, though: if we were to balk at implementing a curriculum like this, would it be out of fear of handing the reins over to our students? Maybe as we contemplate changes to our own ILS program, we should consider that our students may be less risk-averse, more daring, and more willing to try new things than we are: they might not need as much help as we think they do as they muck about in their meaning-making.

In the Learning Circle several of us noted how our students can thrive on the chaos and disorder that ensues when we dare to step away from center stage. Though the exercises we plan for our students might not lead them where we expected them to, they cannot be labeled "failures," so long as they tell us something about ourselves.

I was reminded of a particular meeting of the MATH 280 course I taught a few years back (in Fall 2007, I think?). It was a small section (15 or so students), and full of bold and fearless thinkers. One day toward the end of the semester our conversation meandered from the preplanned course when one student, Quincy, asked a pointed question about modular arithmetic. Rather than finish up the exercises I'd planned for us, we wandered off (all of us, as a class, one student, and then another, and then another, suggesting steps to take) in search of patterns that would help devise solutions to very general equations. The end of class came on quickly (time flies when you're having fun), but not before every one of us in the room (including me) had a far better understanding of modular arithmetic than we'd had half an hour before.

"The Math Department should run a 'fishbowl' course," Quincy said as we walked back to Robinson Hall from our classroom in the basement of Karpen. "At the beginning of the semester, we'd fill a few dozen scraps of paper with brief notes about various topics in mathematics, and at the end of every class someone would pull a scrap at random. Whatever topic was on that scrap would be the basis for the next class discussion, a free-form exploration of that topic."

Though this sort of course would be messy, hard-to-manage, and perhaps occasionally fruitless, to this day I still think it sounds like a hell of a lot of fun.

More to come on the Learning Circle and CRTF...and not so long now before this year's CWPA meets up in the wilds of Wildacres, just yards from the Blue Ridge Parkway. Stay tuned!

[Redacted]

2011-09-01T13:27:00.003-04:00

I wrote a brief post in which I offered up more explicit complaints than ever before about the pedagogical practices in one of my school's departments before thinking better of it.

Suffice to say, I was livid this morning on hearing from some of my students about the way one of their courses is being "taught."

Livid, and impotent: what can I do? (Bitch about it on my blog, apparently...)

Another CRTF-related post, in which I begin to sound more and more like an administrator

2011-08-28T11:35:00.006-04:00

One of the issues we on the Curriculum Review Task Force are facing as we go about our business is the rather ill-defined identity of UNC Asheville as a university. We're finding it difficult to put a pin on our strengths, weaknesses, and other salient characteristics. What is it that best defines us, our commitment to undergraduate research? Our emphasis on service learning? Our small class sizes and opportunities for one-on-one teacher/student interaction? These all play a role, but it's becoming more and more evident that certain unintentional, often demographic, institutional characteristics shape our school more than these do.

Foremost among them is the predominance of transfer students at UNCA. Roughly half of those students graduated from UNC Asheville in any given year spent only half of their undergraduate careers at this school. Many transferred in after spending time at one or more regional community colleges, while others have bounced around from school to school, sometimes visiting as many as six or seven schools (in extreme cases) before coming here. These students often have more "real-world" experience than their peers who matriculated at UNCA as first-year students, and in any case they almost invariably contribute rich multifaceted perspectives to every class they attend. (In my experience many UNCA students with a community college background are "nontraditional" students, returning to school after several years in the workforce and several years of growing up. These students are mature, organized, diligent, and earnest about their learning. Even when they're not as "book smart" as some of the kids fresh out of high school, these other strengths more than make up for that shortcoming and make them fantastic students.)

Moreover, these students' presence has a profound impact on the structure of our curriculum. Consider, for instance, students' completion of the ILS requirements. A number of those students coming in from community colleges may arrive having completed the 44-hour core, an articulation agreement that suffices to knock out most ILS requirements; many other such transfer students, as well as those who've bounced around from school to school before landing at UNCA, have not completed the core and may arrive with little more than a long list of elective courses, numerous ILS core requirements outstanding. These students may therefore end up having to take three or four years at UNCA to complete their degree requirements, despite having spent two or three years elsewhere, and once done they may have taken as many 160, 170, or more credit hours, well more than the 140 beyond which tuition costs half again as much. (Every hour past 140 hours costs 150% the base tuition rate.)

Thus these students take a disproportionately long time to graduate, pay more for the privilege of enrollment, and often fail to see the point of the school's liberal arts mission in the first place. To this last point: many of these students come to UNCA because it's relatively cheap, it's convenient (Asheville's mild climate, high quality of life, and welcoming atmosphere make it a destination for many), and they believe it will provide them with the skills needed to fulfill the functions of whatever career they aspire to. Few transfer students come here specifically because of the interdisciplinary learning experience UNCA purports to offer through its liberal arts curriculum. More often, such students are annoyed by the burdensome requirements that curriculum imposes upon them. "I just want to take my major courses and get out of here."

Surely these students can't help but feel like suckers, stuck playing a game in which every hand is stacked against them. Yet, as I mentioned above, these students make up, and, indeed, for a long time have made up, a large percentage of our undergraduate population. (In each of the AYs 1995-6, 1998-9, 2004-5, and 2005-6, they accounted for a larger percentage of the graduating classes than "native" students did.) This isn't likely to change, given our status as a relatively low-cost provider of a fairly high-quality education.

How, then, can we restructure our curriculum to avoid treating these students like second-class citizens? For one thing, we should ensure that whatever core requirements we impose, they can be efficiently and effectively completed by all students, without sacrificing their goal of providing an authentic interdisciplinary learning experience. We should also take care to structure our major and degree programs flexibly, permitting students to fulfill these programs' requirements in a timely fashion and not get mired down by labyrinthine class sequences in which key courses are offered no more than once every year or every other year.

These are, in fact, among the principles which have been guiding our work on CRTF this summer. Time will tell if we succeed.

Students, what's your take? We've solicited woefully little input from students as we've begun our review, and I'm curious to know what you all see as the strengths and shortcomings of UNCA's curriculum. Feel free to comment.

Nudge

2011-08-27T12:33:00.002-04:00

I've mentioned a few times (see here) the ongoing work of UNC Asheville's relatively new Curriculum Review Task Force, on which I'm serving as "point person" for the Curricular Sustainability Subgroup. We've spent the summer reviewing the structure of our own curriculum, breaking it down into little bits and comparing those bits with the corresponding bits of other schools' curricula.

The first component we examined were the majors and degree programs, writ large. After finding data that suggest these programs are considerably more prescriptive (in terms of the specificity of courses required) and burdensome (in terms of the number of courses required), we compared several of the most prescriptive and burdensome programs with cognate programs at several peer institutions, including both a few other COPLAC schools and a few institutions which serve as "role models" in one way or another (Bates College and Davidson College, among others). Our initial findings were confirmed: with a profusion of highly-specialized concentrations whose completion requires, on average, a relatively hefty amount of coursework, our programs are byzantine beasts, looking more like miniature graduate programs in some regards than the sort of programs you'd expect to find at a liberal arts institution. Notably, these findings suggest that those who place the blame for high times-to-graduation on the ILS program (of whom there are many at UNCA, especially among the old guard) are at least in part misguided; the majors are just as much to blame as the general education program.

We've just begun to examine the ILS program, drawing on data produced over the last several years (from NSSE, from perceptions surveys conducted on our faculty, etc.) in order to understand what parts of the program are working and what parts need work. Although there's more data-digging to be done, my hunch is that we're merely going to end up corroborating all of the findings made in the past few years: the intensive programs are doing quite well, and though the Humanities program, the first-year and transfer seminars, and a few other less-controversial components of ILS may need a little tweaking, it's the ILS clusters that'll need to be overhauled.

Several weeks ago my colleague Tyrone, a member of my Curricular Sustainability Subgroup, noted in a meeting that we may do well to consider our curricular issues from the point of view of "choice architecture," the art of arranging options for people in ways that help them make decisions more easily and to greater benefit. To learn more, Tyrone recommended the book Nudge: Improving decisions about health, wealth, and happiness by Richard J. Thaler and Cass R. Sunstein (New Haven, CT: Yale University Press, 2008), which I picked up at our library a couple of days back. I'm about halfway through, and so far it's proving an interesting and enlightening read. It's full of the sort of observation that makes one think "well, duh, that's obvious" about something one likely wouldn't have thought of oneself. Example: how dumb is it to arrange the range elements in a square on a stovetop, while the knobs that control them are almost invariably organized in a row (pp. 83-4)? A better choice architecture would arrange to place both the elements and their respective knobs in similar geometric configurations.

To the matter of ILS clusters, how might close attention to choice architecture help us craft a more easily-navigable system of courses which still ensures that students enjoy a meaningfully integrative interdisciplinary learning experience? Right out of the book, we might keep in mind the following points:

We should expect students to err in their choices, and design our system so that those errors won't prove catastrophic. Example: the cluster program should be flexible enough for students to plug in a single missing course at the last minute if they've let it slip their minds until then.

We should give students feedback on the choices they've made in completing their course requirements. Example: our advising software DegPar goes a long way in this regard, letting students know what requirements remain to be completed at any given time. If we move toward a system in which students design their own interdisciplinary clusters (as we've discussed doing several times now), perhaps we can require students to craft reflective essays after each prospective cluster course is completed, ensuring that they understand the ways in which the courses interrelate.

We should help students produce "mappings" which help students translate the complex benefits of their choices into more easily understood terms. Example: in a sense, we do this already by presenting several prepackaged cluster options to our students; "complete any one of these clusters," we tell them, "and you're apt to receive a meaningful integrative learning experience." For instance, the title "The Science and Politics of Human Health and Illness" makes it clear that the contents of the cluster so named will give students a multifaceted perspective on issues related to health and wellness: though the courses may be complex and challenging, the cluster's name is an easy index that guides interested students to complete that particular cluster without having first to complete every course the cluster contains.

More to come on this matter. I do recommend Nudge; it's an easy read, but a useful one.

Back

2011-08-25T13:09:00.003-04:00

We're back. It's been a while.

While the REU seemed to eat up less of my time this summer, revisions on the book (to appear early in 2012 under the title Student writing in the quantitative disciplines: a guide for college faculty) and work on the Curriculum Review Task Force seemed to take up every last bit of whatever was left.

We're now four days into the Fall 2012 semester, and I already feel as though I've found a groove in Precalculus. I've not taught this course for three years, and I must say that I've been looking forward to teaching it again. I've thought a bit about how I would approach the course, I've come up with some new activities (like this one), and I'm coming at it with renewed energy. So far the class has been great. (It doesn't hurt that the department's choice of text is not catastrophically awful, like the text we'd adopted the last time I taught that course.)

We spent today motivating relations and functions, and I ended class with a low-stakes writing exercise (who, me?) asking the students to work in small groups to come up with several examples of relations or functions which have real-world relevance, expressed as "pairings" between sets of numbers. They came up with some fantastic ones, some of which could the basis for interesting statistical surveys. A sampling (all verbatim):

The decrease of the temperature paired with the increase of the elevation
The number of texts you send paired with the time spent on your phone
Pair the childhood obesity with each child's level of poverty
The profit of the lemonade stand paired with the amount of sugar used
The speed limit of an area paired with the number of car crashes in the area
The amount of wildlife disturbances compared to the average of the new developments
Pair the number of baseball ticket sales with the baseball team's winning record
Pair the profit made by jacket companies based on temperature

I'm stoked. Both sections of this class seem to be gelling already, and they're full of outgoing individuals. Already obvious "leaders" are emerging from among the ranks of those students who are unafraid to ask questions, suggest answers, and put solutions on the board before the whole class.

Abstract Algebra has yet to get into the same groove, but as yet we've only met twice, and yesterday's class meeting was dedicated to an intentionally chaotic consideration of a boatload of multiplication tables I'd asked them to construct. In asking them to analyze and explain the patterns these tables exhibit, I'm leading them to begin thinking about what salient features the most "well-structured" algebraic objects (sets equipped with a binary operation) might possess. We'll make that more explicit tomorrow when we define monoids, groups, and semigroups.

More to come soon, I promise! On CRTF (oy), on the QEP (oy oy), on many more things...

Butterfly effect

2011-07-04T10:44:00.004-04:00

Butterfly effect
for Lesa MacFarland, Daniel Lucas, and Kate Sweely

There was an empty desk in class today.
(At breakfast the newspaper bent back like a
bird’s broken wing) I don’t take roll,
so I had to ask “who’s not here?”
(not thick enough to hold a thing aloft,
a slate-colored sheet.)

No one said a word.

(I snapped the paper back into place.
Esther S. had died) “Who’s not here?”
I asked again, and (of age.
Just age. Sometimes people just get old.)

no one said a word.

“Someone’s brother? Sister?
Daughter? Friend?”
I waited.

“Sometimes people just get old,”
I said. “Edward Norton Lorenz
was ninety,” I said. (But Taylor R.
was seventeen, I knew, younger still than
Urysohn, Galois and Ramanujan.

Seventeen years is hardly time enough
to eat too-dry toast or get wet
while waiting in the rain for the bus to come.)

No one said a word,

and we soon moved on, as we always do,
wings cupped over the wind, wings just thick
enough to keep us off the ground.

We huddled our desks around
the empty one, (I stood and brushed away
the crumbs of too-dry toast. I looked
for my car keys.)

a hole like the eye of a storm.

***

(Note: I hope soon to post again, with updates on the QEP, CRTF, the REU, and course planning for fall...)

Rock stars

2011-06-06T17:17:00.003-04:00

So a funny thing happened to me in the UNC Asheville library today...

...Let me begin by saying that the 2011 REU officially got underway today, with a few weeks' worth of graph theory condensed into a few hours in one afternoon. (Though today was the first official day of the program, I feel like we've been at it for a few days now, as for the first time since the program's inception in 2007 every one of the students arrived on the Friday preceding the official onset. Since everyone was here by Friday night, six of them joined me in taking in a baseball game on Saturday night, and by the time the now-standard Sunday cookout rolled around I felt like everyone was fast friends.) The students are doing marvelously so far: they're quick to grasp new ideas, eager to come up with solutions and examples, and making insightful observations about a number of the tricky problems I set up for them to tackle as they begin to explore graph theory and combinatorics.

But before that...

...we spent the morning taking care of bureaucratic whatnot, first getting human resources paperwork filled out (tax forms, consent to allow background checks, etc.), and then heading over to the Onecard office to get ID cards for the students, all the while taking in a cursory tour of campus. Our third stop was the library, where the students would be entered into the system so that they will receive borrowing privileges comparable to those of UNC Asheville students. This is where things got interesting.

We entered the library, and I met up with Maryanne, our contact in the library, after being directed to the reference desk by the student working the circ desk. We discussed the students' privileges for a moment before she mentioned to me, "it's kind of quiet in here because the Governor's being interviewed over there." She indicated a spot beyond the stacks to our left, near the Writing Center. By "the Governor," she meant Gov. Bev Perdue, the Governor of the state of North Carolina. I peered around the stacks and saw Gov. Perdue talking with Anne Ponder, the university's Chancellor.

Maryanne went to begin working on the students' information, and I went to let my students know (jokingly) that we'd prepared a special welcome for them. We chatted for a few minutes about the news conference going on a hundred feet away, and then I started talking about MathSciNet and other math-specific databases, when from around the corner the Chancellor and Governor appeared and began walking our way. I expected them to walk on by and exit the library while we watched quietly, but to my surprise the Governor walked right toward us.

"And I suppose you're all students here?" she asked, putting her hand out to the first of the students, shaking it. Chancellor Ponder and I explained the purpose of the program and let her know that most of the students were from out of state, and she went around to every one of them, asking from which states they hailed, and welcomed them, one and all, to North Carolina.

She then turned to me, whom the Chancellor introduced once more, with a bit more information (tenure, teaching awards, etc.), before I had a chance to say a little bit more about the REU program. She was ecstatic that we were providing a program that encourages students to pursue careers in STEM fields, and thanked me for doing all that I could to provide that encouragement. We had a delightful conversation for several minutes before she left.

I was then accosted by several representatives from the local media, who asked me about the REU and interviewed me briefly about funding for science education (the Governor is currently considering vetoing the budget package put forth by the legislature, in part out of concern for cuts in educational spending). I think I managed halfway decent answers (one of the university's senior staff complimented me on my aplomb afterward). They also managed to get a shot of my π tattoo.

Yup, my students are rock stars. Crazy day.

Fun Times

2011-05-22T14:51:00.005-04:00

I'm smack-dab in the middle of the freest time of year for me, that three- our four-week-long end of May, during which time I'm generally "relaxing" after a successful semester, working like mad to take care of the various reports due from me in the next few weeks, and busily prepping for the REU that starts two weeks from tomorrow.

This year my wife and I were able to get away for our first "real vacation" (defined as "a trip involving neither work nor family visits") in several years, a five-day cruise to the Bahamas. Of course, being who I am I managed to make the most of it by bringing along some highly inappropriate pleasure reading, the thirtieth anniversary edition of Paulo Freire's Pedagogy of the oppressed, the central text for the summer Learning Circle I'm taking part in in June and July. (The only reading material I saw which may have vied with it for the "Most Ironical Reading on a Cruise Ship" award was one woman's copy of Orwell's 1984; I think if she'd have been reading Huxley instead, she might have had me beat.)

I'll likely have more to say in the coming weeks about Freire's philosophy as it applies to math education at the university level, but I wanted to put forward in this post an idea for a new ongoing writing project I hope to implement in at least one of the two classes I'm organizing in the fall (Precalculus and Abstract Algrebra I).

Oddly enough, I got the idea from the cruise company. Every evening around dinner time we were treated to a delightful turn-down service, featuring complimentary mints, expertly folded towel animals, viz.:

and a copy of the Fun Times, the cruise ship's guide to all of organized activities that would be going on on the ship the next day. It was little more than a newsletter, three or four pages in length, just the sort of periodical I think a class (or two) full of students, working together, could crank out at least once a week, if properly prepared to do so.

So here's the idea: ask students to put together an ongoing "newsletter" for their class, The Algebra Times, or The Precalc Picayune, if you will. Its content would be flexible, and what went into it from week to week would be left to the discretion of the students (I'd want to have as little to do with its creation as possible). Perhaps, for example, the precalculus newsletter could include

study tips,
hints for tricky homework problems,
advertising for study groups,
applications of course material to areas outside of class,
games and puzzles,
"letters to the editor,"
recommendations for class activities,
recaps of recent class activities,
personal reflections on math in general,
etc.

Whatever. It'd be up to them. I'd stay out of the day-to-day operations. Maybe I'm being overly sanguine, but I can imagine a handful of particularly eager students taking on editorial and managerial responsibilities (there are a few in every class). To ensure participation by the class as a whole I'd require every student to contribute to the newsletter at least once, twice, thrice, something like that, during the course of the semester. (Jointly-written contributions would count.) It would be difficult to "grade" contributions (I might shy away from this entirely, keeping it a low-stakes exercise), although I'd provide feedback to authors confidentially.

How's this sound? Colleagues: have you tried something like this before? Students: would this be something you'd be all upon?

Lessons learned

2011-05-04T13:00:00.002-04:00

I've just finished reading through my MATH 179 students' final exams. There I'd asked them each to write in response to three different questions; briefly: (1) how has our course challenged your assumptions about mathematics?, (2) How does UNC Asheville, as a liberal arts university, differ from traditional state schools?, and (3) how would you describe your own "writing process" as you completed one of the writing assignments required of you in our class this semester?

The students' responses to the first question were rather erratic and varied wildly in quality, ranging from unelaborated lists of concepts like meddos, abaci, or alternative bases of arithmetic to carefully crafted descriptions of personal change. Sadly, there were far more of the former than of the latter, and as often as not I suspected the students of writing what they thought I wanted to hear rather than what they truly felt. The responses to the second question were predictable, focusing on small class size, the potential for one-on-one interaction with faculty, and a curriculum emphasizing development of the student thinker as a whole.

The students' responses to the third question were the most eye-opening to me, and gave me a good deal of direction as I develop as an instructor of first-year (rather than disciplinary) writing. For instance, it's clear that in the future I'll have to be more explicit in discussing the purpose for various stages of the writing process. Several students pooh-poohed the need for revision, saying, essentially, "I don't like to write in drafts, because I'm pretty happy with how it sounds after the first draft." Others bemoaned being asked to write outlines or rough drafts; one student said, more or less, "they just get in the way of what I know I need to write about...I just want to get to the point." One of the stronger student writers explicitly questioned the validity of the writing process, indicating he felt it was a waste of time and served only to objectify what is ultimately a very subjective and personal activity. Although one could argue that this student is really a budding post-process theorist, I think it's more likely that he's simply not yet learned why we do all of the things we do when we sit down to write a piece.

I noted too that students have a very hard time viewing writing as anything but linear. Perhaps because reading (traditionally, anyway...let's not speak about the way one reads on the web) has always been seen as a linear process, something done from start to finish, from the first word to the last, students have come to think of writing as a similarly linear activity. For example, no fewer than three (out of 18) students complained about how hard it was to write the introduction to a paper. "Once I get the introduction out of the way," they seemed to be saying, "the rest of the paper comes really easily." The upshot? "You can't write anything else until you've written the first paragraph, because that's where you lay out what you're going to say." It hasn't occurred to these students (and, admittedly, I did a pretty poor job this term in helping them to see) that perhaps they're better off saying what they want to say first, even elaborating it a bit, fitting together all of the important pieces of evidence, and maybe even wrapping it up by discussing their own conclusions based on that evidence, before even thinking about writing an introduction. Most of us who write academically know well that the introduction (or abstract) to a paper is often the very last thing we write: it's so much easier to lead the reader into what you wanted to say after you've already said it.

These ideas are ones I'm not used to having to make explicit in teaching writing, as I'm not used to working with novice academic writers. I've got to keep these ideas in mind for the next time I have a chance to teach first-year students general academic writing skills.

Post 500: A note of gratitude

2011-05-02T16:07:00.004-04:00

A natural topic for my 500th post on this blog presents itself. I feel deeply humbled and honored to have been named this year's recipient of the Award for Teaching Excellence in the Natural Sciences at UNC Asheville. Honors like are not won by the recipient alone; I have many to thank.

My thanks go to my friends and family, for their ongoing love and support (and willingness to go without seeing me for long periods of time as I indulge my workaholia).

My thanks go to my colleagues, for their boundless energy and creativity, and eagerness to engage with me in scholarly programs and activities spanning several disciplines.

My thanks go to my students, nearly every one of them tireless and talented, and many of them as passionate about teaching and learning as I am; the future is bright.

Where to go from Post 500? I've not received much feedback on what folks would like to see more of, though a couple of students have asked for more anecdotes about the early days of my teaching. Certainly those are preferable to endless rants about UNCA's QEP (a topic about which I might soon have a few more words to say).

I suppose I'll do what I always do, and let it take shape from day to day.

Thank you all.

MATH 280 exams, revisited

2011-05-01T15:41:00.002-04:00

A couple of posts back, I reprinted the final question on my MATH 280 students' final exam. In asking them to reflect on the course and find something worth their whiles in all that we've done together this semester, I had hoped that the students would fulfill several beneficial purposes:

1. They would notice connections and correspondences between disparate ideas we've studied, which they didn't notice before.

2. They would take the time to generate some questions of their own about the course ideas more intriguing to them.

3. They would get a bit more experience in communicating mathematical ideas in relatively informal (and non-technical) terminology. (After all, I wasn't asking them for proofs, just conversation.)

4. They would gain a sense of accomplishment in recognizing just how much we've studied this semester.

5. They would give me guidance for designing future iterations of this course by indicating to me which topics they found most interesting, most challenging, and most relevant.

The students did all of those things, and in composing a page or two in response to each of their responses to this question, I've been able to extend our conversation about ideas mathematical well beyond the time frame of the course. The semester's now over for this class, but I have a hunch that a good number of the students will spend some time over the summer following up on some of the ideas they found most interesting about the course.

I am definitely going to include this kind of exercise on every final exam from now on.

We'll see in a couple of days how my Calc II students' final portfolios come together: will it see a similar success, or a more meager one? Stay tuned...

...incidentally, my next post on this blog will be my 500th. After nearly five years of blogging on my teaching, it's come to this. If you're a regular reader (or even just a casual one), please let me know in the comments: what would you like to see me blog about in #500? And what would you like me to make of this space in the next 500 posts? Do tell!

One more vote for confidence

2011-04-30T14:07:00.004-04:00

The second-to-last question on my MATH 280 students' final exam, designed, as was the last question, to get the students to perform a bit of reflective self-analysis, reads:

Go back over all of the proofs you've written in our class this semester, and select the single proof which you believe to be the clearest, the most complete, and most correct...that is to say, the BEST...of all of the proofs you've written this term. You may consider proofs in homework assignments, exams, or textbook chapters. Write a couple of paragraphs explaining why you selected the proof you have. Why is it that this proof represents the best you've got?

I'm currently grading this question, and I'm gratified to find that a very large number of the students are selecting the proofs that they are because those particular proofs were the ones which helped instill confidence in their abilities to do math, and to complete proofs. To me this fact underscores the importance of confidence and other affective aspects of learning. Kudos to my colleagues who work as hard at developing students' affective engagement as they do at ensuring cognitive mastery!

Lovely LaTeX

2011-04-21T12:18:00.006-04:00

Though it'll be a few days before my MATH 280 students submit their final take-home exams to me, I'm already excited about their responses to the last problem on the exam, a very open-ended one which reads as follows:

Go back over all of the topics we've talked about in our class this semester, and select one about which you'd like to know more. (Please try to make your topic a relatively narrow one..."binomial coefficients" would be a good choice, for instance, whereas "combinatorics" would be a bit broad, and "proofs" would be faaaaaaaar too general.) Would you like to see more examples of a particular topic, or further applications of it? Would you like to know more about where it's used in mathematics, or how it connects with other topics we've considered? Do you have a specific question about it, or are you simply interested in learning more about it in general?

Having chosen a topic which you find sufficiently intriguing, write a few paragraphs about that topic. (As always, please use complete, grammatically correct sentences!) Your discussion should indicate clearly why you find your topic intriguing and what about it you'd like to know more about. If you have specific questions, please feel free to raise them. If you have answers to those questions, even conjectural ones, please feel free to share those as well! My goal here is not to get you to answer questions so much as to ask them.

One of my students caught me in the hall a half hour ago and asked if "LaTeX" would be a valid topic for this question. I only hesitated a moment before responding with alacrity: "that would be awesome!" I'd really like to learn more about how students make use of LaTeX, and if they feel it helps them (a) express themselves mathematically with greater effectiveness, (b) present themselves as authentic creators of mathematics, and (c) engage mathematical ideas at a higher cognitive (or metacognitive) level.

To this last point: I hypothesize that in using LaTeX a student is forced to include an additional reflective/analytical stage in her writing process, at which stage the student more carefully than before or otherwise scrutinizes word choice, notation, and other aspects of her writing. I'd love to study this more carefully...maybe some of my Charleston posse would like to take this on with me as a side task. Any other takers?

The spider

2011-04-20T21:44:00.002-04:00

[This end-of-semester poem is dedicated to every one of us who now and then wishes to return to a simpler time...even if that time was not so long ago. That's pretty much everyone out there right now, no?]

The spider

Last autumn, when the morning
came late in low pink slats of sun
landing on the leaf-smut
that cluttered up the shrubs,
her web gleamed with
hints of early frost.

Then she went away.

I’ve searched for her
each morning for a week, in the corner
where I last saw her.
She’s not come back yet,
but I know she must.
I know she must.

Assess this!

2011-04-20T11:28:00.002-04:00

After polling my Calc II students briefly at the start of the last two class periods, I realized there was no clear consensus regarding the format of their final evaluation. I had proposed two options: (a) a more "traditional" final exam in which students would solve several more problems involving the techniques we've developed this term, or (b) a "portfolio" of prior work students would put together in order to demonstrate mastery of several different aspects of the class (techniques of integration, applications of integration, communication of mathematics, and a fourth piece of their choice). A successful portfolio would demand that the student justify her inclusion of a particular piece ("piece" being defined loosely as a single problem or an entire homework set, miniproject, quiz, or exam): why does that particular piece demonstrate the mastery being measured?

While a number of students seemed excited about the prospect of a portfolio, several balked, visibly discomfited by the idea of putting a portfolio together. I wonder if some of the less well-organized students would have trouble putting together a portfolio because they've not kept a good record of their work over the semester...? Or perhaps the reluctant students simply want to avoid the "writing" that comes with putting the portfolio in order...? I'm not sure.

As a compromise, I went ahead and made up both, and students can choose which path to take. On the one hand, I made up a four-question "traditional" exam that'll get the students solving several more problems (though one question still asks for a students to come up with their own problem to solve); on the other, I've made a prompt for a four-piece portfolio whose form mirrors the structure of the "traditional" exam. I hope this compromise will satisfy everyone's intellectual curiosities. I'm curious, for one, to see how it works out.

Wrapping up

2011-04-14T13:32:00.009-04:00

The end is near! (I realize I've been saying this a lot lately, but it's more and more true each day.) We've got just under a week of classes left, with only one more meeting of MATH 480 and three each of Calc II and 280.

My last "regular" meeting of MATH 179 was this morning. We dedicated the day to a free-wheeling discussion of the past semester, focusing on the three central purposes of the class: (1) learn how math is experienced from place to place and across time, (2) learn a bit about a liberal education in general and UNCA in particular, and (3) get some practice in writing academically in a specific discipline, and for specific purposes.

Students pointed out some of the course's strengths: it helped fine-tune their writing skills, gave them a broader view of mathematics, and offered a forum where they could talk about random school-related matters with students in similar situations without fear of looking like fools. They pointed out some rough spots, too: the first text we used (by Ascher) was awful, and the 9:25 time slot wasn't the most conducive to student excitement. A couple of students indicated that I should teach the course again, and I suspect that the next time around it'll go much more smoothly. The students' take-home final exam, due in a week or so, asks them to reflect more intentionally on the three points I mentioned above; I'm sure I'll get from it an even greater sense of the course's strengths and weaknesses.

The MATH 280 students get their last exam tomorrow, too, and like the last it'll be a collaborative one. I was tremendously gratified by the students' reception of the last exam: the learning environment the students created and cultivated as they worked on the exam was a rich and fertile one. I have no doubt that many of the students, particularly those who may struggle more mightily than their quicker peers, learned more from working with one another than they would have from any other form of assessment. (Incidentally, I've been keeping track of collaboration networks on the collaborative exams I've given over the past couple of semesters, and I hope to begin tracking the data more carefully to try to analyze correlations between indices of collaboration like number of collaborators and measures of success like initial exam scores.)

The last 280 exam asks students to provide a few more "traditional" proofs, but, like its counterpart in MATH 179, it also asks the students to reflect on the course and identify specific topics they found interesting and write at length about those. My hope is that the exam will help me to discern which areas students are most interested in, and about which they feel most "iffy." This'll help me plan the course more appropriately in the future.

Speaking of course-planning...I've already got some ideas in mind (involving multiplication tables) for first-day activities for MATH 461 (Abstract Algebra I) this coming fall. I'm excited! I know it's several months off yet, but I'm looking forward to it already.

Before I go, I have to give a shout-out, to my colleague Kelli and to our first-year junior Kamryn, for spearheading the successful founding of a UNC Asheville chapter of the Association for Women in Mathematics (AWM): wonderful first meeting! I look forward to seeing what activities the students can put together in the coming months.

P.S. -- I sent the first draft of my manuscript to the publisher today. Much happiness.

Anticlimax

2011-04-14T01:18:00.002-04:00

I'm done, but I don't feel like it.

At about 12:45 a.m. (EDT) I put the last finishing touches on Chapter 6 of the first draft of More Than Numbers. Since then I've worked up the table of contents, list of figures, title page, and a skeletal version of the acknowledgments...nothing that needs to be done immediately. Without the front matter, it weighs in at just over 200 pages.

I'm still not feeling it. I'm sure it'll hit me tomorrow. I'm sure I'm just overtired.

CCCC, Vol. 4: Putting the Paper Down?

2011-04-13T22:38:00.007-04:00

Today a couple hundred UNC Asheville students took part in a longstanding school tradition, the Spring Undergraduate Research Symposium. I took in five of my students' talks, all skilfully prepared and delivered, in topics including health care in Bolivia, foraging of endangered spiraea shrubs by beavers, and the role of the anagram in constrained poetry. Love it!

The talks I attended reminded me of a phenomenon I wanted to blog about after my first Conference on College Composition and Communication a couple of weeks back. At this wonderful conference Amherst's Joseph Berenguel delivered his talk (about which I posted here), on markers of anxiety, in a manner that offered an explicit challenge to the dominant style of delivery in humanistic disciplines. Rather than read his paper verbatim from a hard copy held in front of his nose, Berenguel instead spoke extemporaneously, delivering his presentation in a manner much more akin to that found in the natural sciences (and mathematics!). His talk was very well-organized, engaging, and clear...and its delivery was fluid and dynamic.

Berenguel was aware of the distance between the expected and the actual; he comments on my previous post (by the way, thanks for reading, Joseph! I'm sorry that I've not yet had a chance to respond to you personally): "I was quite aware of the difference between my style and the expected style. I tried to work it to my advantage. All that stuff is mostly in my head anyway." No doubt this truly was the case, for the process of writing the paper in the first place surely seared most of the thoughts (his own in the first place) into his skull...and further practice in presenting his paper further propped up the permanence of those thoughts.

Given this familiarity, why bother reading straight from the page at all? I've wondered at the divergence between the delivery styles in different disciplines for quite some time now. One of my colleagues in the Language & Literature Department here speculated (though she didn't know for sure) that the practice of word-for-word reading stems from an allegiance to the very carefully-chosen words the presenter has taken the trouble to pen in the first place: why risk a few seconds' worth of brain farting deleting the hours of careful reflection that led to the precise phrasing contained in the paper itself?

If this is the case, though, why isn't it a sauce-for-the-goose-is-sauce-for-the-gander situation? That is, aren't word choice and phrasing equally important (and equally tenuous and susceptible to on-the-spot memory lapses) in the natural sciences? Or could it be that the relatively image- and graphic-dependent nature of presentation in these fields drive down the dominance of verbal discourse?

This last argument seems unlikely to me. I'm not sure I buy the "careful choice" claim. But there ought to be a better explanation than simply calling out all humanitarians as "traditionalists" and all natural scientists as "innovators." Does anyone out there have any idea why this divergence still exists?

Whatever the reason for its being, I'm not sure the divergence has much life left in it. Several of the other talks I attended at CCCC were of the extemporaneous variety, as was one of the three talks in humanities or social sciences I attended today. (This one was a talk in an economics session; the "traditional" talks today were in film studies and poetry.) Intrigued that I'd seen so many maverick ad libbers (I'd expected few, if any, before going to CCCC), I'd asked my Charleston college Bella if she felt the traditional approach had long to live. She couldn't say definitively, though she indicated she's noticed the trend in recent years towards a more on-the-spot style of delivery.

Time will tell, I suppose.

I'm not sure I have anything more meaningful to say about this topic, so I'll let it rest. If you have insights of your own, please feel free to bring them up in the comments.

CCCC, Vol. 3: Take 2

2011-04-11T20:43:00.004-04:00

This is the third of several posts I hope to write over the next few days hitting highlights of my first Conference on College Composition and Communication, which took place a few days back in Atlanta. I want here to say a few words about the next phase of the rhetorical analysis of REU students' writing I'm currently performing with my friends at the College of Charleston.

We're moving ahead. Last Friday we met to plan our next moves, which include a session proposal for next year's CCCC in Saint Louis and a plan for our next data-gathering session, to take place during the second week of this coming summer's REU. As we did last year, we'll spend some time interviewing the student participants about their past writing instruction and their experience with writing in mathematics. We also plan on reworking the prompt for the students' weekly journaling to include more intentional language regarding writing.

Our goal? To begin to understand how students develop as disciplinary writers in mathematics by examining (1) their progress along the axes we laid out in the first phase of our research (use of sources, contextualization in the existing body of knowledge, etc.), and (2) their own reported perceptions of their growth as writers over the course of the summer program.

As of the end of the coming summer we'll have four years of data (at least four drafts, often many more, of roughly 6-8 papers per year), and analyzing these data is going to be an arduous task. To help us out with the reading we brought aboard three more Charleston-based writing folks (all former grad students at the College of Charleston). It's going to be a regular party.

Exciting stuff! Further bulletins as events warrant.

In other words

2011-04-11T20:29:00.005-04:00

Every now and then a student says something that makes me beam with pride. In my last post I asked my current students (particular those in MATH 280 and Calc II) to write and let me know what they needed to help finish out the semester strong. A large number of them responded, offering not only ideas for end-of-semester activities, but pep talks for one another and advice on helping each other across the finish line.

I wanted to pull a rather lengthy excerpt from one student's response that I thought did a better job of explaining what learning...and, in fact, doing...math is all about than anything I've ever said.

In this student's words,

Before college-level math, there was no wrong-to-be-right for a lot of students (myself included). A concept was explained and then you applied it and moved on. Right is right and wrong is wrong.

Especially before this class I would have found it very hard to believe that I could spend 6 hours on a problem, and that 5 of them would be spent barking up the wrong tree. I then would have found it near-impossible to believe that those five hours were vital to the process.

As far as the group work goes, it helped a lot when every time I found myself up a wrong tree, there seemed to be another student or two up there with me, searching for some sort of elusive coconuts. We then climbed down together and gave each other a boost up the next (for better or worse!).

The upshot: don't be afraid to be wrong; you'll almost certainly get it wrong before you get it right, and there's no consequence for going down a dead-end street. I could not have said it better myself. Literally.

I get to hang out with these people all day, every day? I'm a lucky guy!

Home stretch

2011-04-11T16:00:00.004-04:00

We've got two weeks of classes to go, including 2 meetings of MATH 480, 4 meetings of Ethnomathematics, 6 of MATH 280, and 8 of Calc II. I can't believe we're here already! This semester's gone faster than any I can recall, and it's left us all stressed and strained.

This past week's conference gave me a much-needed break, and I honestly feel much more on top of things now than I did a week ago. I felt much more relaxed going into both of my classes today, especially given that I'm feeling pretty good about where my Calc II and 280 classes are right now.

As this semester's been so dramatically abbreviated (it's almost two weeks shorter than spring semester of last year, for instance, after snow days are factored in), I've spent no small amount of time this term stressing out over how much I'd be able to "get through" in my classes. I fear MATH 280's suffered a little bit because of this, and I'm going to have to trim back on the "special topics" I like to include at the end, just to get the bare minimum in. Ditto Calc II: bye-bye differential equations, hello Taylor series; the latter I deem indispensable, the former not so much.

Despite the frustration I've felt at gettin' it done, so to speak, I'm feeling better about where we are. I think at this point I've just got an (pardon my language) "ah-fuck-it" attitude about the term. By that I don't mean that I'm cutting the students loose and letting them drift in the wind; nothing could be further from the truth. In fact, I'm relaxing my expectations for the courses and focusing on making sure every last student understands fully every last thing we work on together in these closing weeks. If that means we have to cut a quiz here or modify an assignment there, so be it. I want us all on the same page as we cross the finish line.

Students: if you're in one of my classes and you're reading this, you can help me out immensely by responding in the comments to this post. Please take five minutes to write back to me there, indicating one thing you'd like to see happen in your course before the semester's up that'll help you make the most out of our remaining time together. Tell me which class you're in (anonymously, if you'd prefer), and let me know what one thing we can do to help each other across the finish line.

CCCC, Vol. 2: The Citation Project

2011-04-09T11:11:00.006-04:00

This is the second of several posts I hope to write over the next few days hitting highlights of my first Conference on College Composition and Communication, which took place a few days ago in Atlanta. Here I'd like to focus on a comprehensive 16-school analysis of students' use of citations in first-year composition (FYC) courses, called by its investigators "The Citation Project."

For this project, Sandra Jamieson and Rebecca Moore Howard worked with faculty at over a dozen institutions to collect data on several hundred FYC students' papers, analyzing the way in which the student authors drew on the sources they cited. Four types of source use were coded and carefully tabulated. In order from least sophisticated to most, these types are as follows:

1. Direct quotation (cited or not): the student pulls a quote from the source.

2. Patchwriting: this occurs when the student "patches" together pieces of the source's text with her own. It may involve rearranging phrases here and there, or replacing some words with synonyms. Jamieson and Howard characterize patchwriting as failed paraphrasing: the student attempts to paraphrase the source author's explanations, but falls back on the original phraseology when she encounter difficult passages.

3. Paraphrase: in paraphrasing, the student expresses isolated ideas from the source in her own words. To do this requires a relatively sophisticated understanding of the source.

4. Summary: summarizing requires deeper understanding still, as the student, in her own words once more, creates a snapshot of the source as a whole, tying together disparate ideas and weaving them into a coherent piece.

Jamieson and Howard pointed out a number of significant findings, and though I hate to reduce this post to a simple series of bullet points, it's the easiest way to highlight a few of the findings I found most interesting.

1. Almost all of the students' uses of sources offered anything but summary. Over 90% of the use of sources fell into one of the other three categories.

2. Most sources students drew upon were short, unreliable, web-based sources. Although the investigators admitted they'd not looked into the matter, they agreed with the claim several audience members made that most of the sources of this type likely rank highly in a simple relevant Google search. (This was the case in my Calc I class last semester, when this source, an essay likely penned by a moderately intelligent high school student, was the most-oft cited by students working on the Newton v. Leibniz project.)

3. Students' citations peaked in the middle of their writing projects, with direct quotations dominating in this area.

4. Most text from sources students pulled from the first pages of whatever source is being used.

Jamieson and Howard raised the question of the extent to which we ourselves our guilty of the same practices in our own work...or whether we're aware of the ways in which we teach our students to make use of sources. They fear that we may have lost the forest in the trees, showing overmuch concern for proper citation and citation style while we fail to see how the sources cited are really being used.

The work of The Citation Project is purely textual analysis, with little rhetorical analysis done yet. I chatted with Jamieson for a bit after their talk, and she confirmed that it was largely the nature of the analysis that's driven the direction of their study, including their choice of source uses. I shared with her the uses for sources Damian, Bella, and Nicola came up with in our rhetorical analyses (to support the author's claims, to contextualize the author's work, to indicate results to be extended or improved, and to find other sources) of REU students' writing. She was interested in learning more, and would like to stay in touch. I would too: The Citation Project is heading in new, and surely exciting, directions.

CCCC, Vol. 1: Emotions and Authority

2011-04-09T10:58:00.006-04:00

This is the first of several posts I hope to write over the next few days hitting highlights of my first Conference on College Composition and Communication, which took place over the past days in Atlanta. The conference was absolutely fantastic. Not only did I get a chance to engage more fully with the professional composition and rhetoric community; I also got to hang out (on my birthday!) with incredible friends and colleagues. Best conference in a long, long time.

Here I'd like to focus on one of the most interesting sessions I attended, titled "Emotions and Authority in Academic Writing." Joseph Berenguel (Amherst)'s talk about writers' anxiety examined the ways in which students make certain rhetorical moves in order to cover up their anxiety. For instance, when they paraphrase (or patch-write, a move I'll talk about in the next post), they often do so not because they're lazy (as we many instructors assume), but rather in order to mask their anxiety over a lack of authentic understanding. After all, when the topic you're writing about eludes your understanding, it's difficult to "put it into your own words": sometimes the only recourse you have is paraphrasing.

I believe it would be interesting to undertake a similar study in mathematics: do students resort to purely formulaic or computational explanations not because they're lazy, or because this is what they think is expected (which many instructors would likely claim), but because they really don't possess an intuitive understanding of the ideas they're discussing? That is, whenever our students slip into purely formulaic language, might they likely do so because they cannot do otherwise, and they're anxious about letting their masks slip and showing that they don't possess a full understanding of the topics they're studying?

If this is the case, I believe it argues (yet more forcefully than even I have before) for writing-to-learn activities in mathematics classes. After all, low-stakes writing is exploratory, pressure-free, and safe. Many low-stakes techniques are designed to minimize the writer's anxiety while they help him sort through the pieces of whatever mental puzzle he's trying to put together.

Equally fascinating was Heather Robinson's talk about the rhetorical differences between the articles "a/an" and "the." She argued persuasively that in using the definite article "the," the writer is asserting a common ground with the reader. That is, when the writer says "The effects of gamma rays on man-in-the-moon marigolds are complex," in effect she hints to the reader that those effects are well-studied, and moreover that the reader ought to be aware of them before proceeding. It's a sort of hifalutin' version of "RTFM." As a simple example, she began her talk by indicating that she herself was "the authority," referring to the word "authority" appearing in the title of the session she was speaking in. It could be assumed that all present were familiar with that title, and therefore that her referent would be understood.

On the other hand, when the writer chooses to use the indefinite article, she inflects her writing with judgment, evaluation, discussion, or analysis. "A possible consequence of gamma ray exposure is the following..." says to the reader, "you may not know about this consequence, but I do, and I'm about to let you in on the action." When the writer uses an indefinite article, she asserts her own attitude an analyst or evaluator; when she uses a definite article, she instead assumes an authoritative role as member of a discourse community with a shared common body of knowledge.

In another post on this conference's goings-on I'll come back to say a bit about Berenguel's talk, as its whole style of delivery is remarkable for a few different reasons: it was delivered in unconventional (for his discipline) style, it was ironically anxiously delivered, and it was superbly well-organized.

What a difference six years make

2011-04-06T21:19:00.004-04:00

The last time I was in this hotel (The Marriott Marquis in Atlanta) was January of 2005. The Joint Meetings were in full swing. I'd crashed the party, masquerading as a registered attendee by slipping my 2002 JMM badge into a recycled badge holder and hoping no one would look too carefully at the logo on the badge's corner. No one gave me any trouble, probably because I kept a low profile and didn't try to duck into the heavily-guarded exhibit hall. After all, I'd come only for three first-round interviews (Seattle University, Carleton College, and UNCA) and a couple of dinners and lunches with Vandy friends.

The first two interviews were a bust. The third...well, you can guess how that one turned out.

Here I am again, six years later. The 2011 Conference on College Composition and Communication gets underway tomorrow. It's met since 1949, but this is my first. I'm thrilled to be here; I feel like I'm diving yet more deeply into the academic writing community, a very warm and welcoming pool of teachers and scholars.

I spent an hour or two over dinner perusing the program, planning my schedule for tomorrow. I'll never tire of the clever and insightful wordplay in which this community revels, play that goes beyond mere punnery: words like "ecopreneurship" and "hypermediacy" pepper the presentation titles, and boundaries of every variety (ethnic, national, racial, sexual, gender, etc.) are broken as presenters assert their selves unabashedly: "I write myself; this is who I am."

It makes me feel as though scholarship in my own discipline, even the scholarship of teaching and learning in math, is soft soap in comparison. A simplistic response would be to claim that considerations such as gender, ethnicity, etc., are irrelevant in the mathematics classroom. Yet this assertion is craven and evasive. Why are we (mathematicians) not so bold as to confront those issues of identity which surely affect our students' performance in our courses? Why are we afraid of letting ourselves and our students proclaim their own identity in their work? Are we afraid of losing what Scott Montgomery (in The scientific voice) calls "heroic objectivity"? Isn't hypermediacy as important in our field as it is in composition, if not more so ("hyperimmediacy")?

Anyway, I'm sure I'll head home in a few days with a boatload of new ideas to think about. For now, I'm going to head down to the hotel bar and have a drink while looking over the paper I wrote with the Charleston crew. I'm sure at some point in the next couple of days Damian and Bella and I will sit down to hash out the next stage of the project, and I want to be ready.

White screen, white text

2011-04-06T10:19:00.002-04:00

[Note: The following is a 10-minute freewrite, performed with my monitor turned off, in order to prevent me from editing. This explains the typos.]

I know what it is that's getting to me. I'm becoming, I feel, something I don't want to be, as a teacher, and I'm resisting it, but it's hard.

I have to absolutely hav ewto know where it is my students stand; I have to keep tabs on their progress, I have to know what it is they know and don't know at any time. It's why I strongly resist automatically graded homework (which I know has some advantages). It's why I teach much more slowly than most of my colleagues, many of whom fly through material without stopping to ask if everyone's on board before the boat leaves the shore.

It also means that I'm painfully aware at every step when someone doesn't understand what's going on.

Don't get me wrong, I'm glad about this: I'd rather people get it than not. But it means that I'm much more intimately invested in my students' learning than I woudl be otherwise; I feel much more connected them, much more "in the trenches." When they get frustrated, I get rustrated, and when they check out, I get more frsutrated still (you were right, yesterday, by the way...but my frsutration isn't with you, it's with me...why cCAN'T I just let go?).

This semester is the worst.I know it, I feel it: it's the worst. And not just for me. Everyone's stressed, eeveryone's tired, and everyone's angry. Everyone's taking it out on each other, with tempers short and sniping and grousing in every class.

It hasn't helped that I've not been around. I don't think my absence (freuent absence) the last few weeks...I don't know if it is itself toblame for any of the ennui, malaise, or ill will in any of my classes (I don't think so)...but I feel...I FEEL absent. I feel "not there." I don't like feeling that way.

I want you to kno wthat I haven't checked out. I'm still here.

I think I've become too much of an "administrator" this semester (something I blogged about a bit ago). Enough so that when I'm not in the classroom, there's a bit more distance than I'd like there to be. I only feel it (or at least feel it most acutely) when I'm sitting with my students in the math lab when I'm in the math lab working with them on one or another problem in Calc II or some kind of of problem for 280...that's when I feel it, because it's then that I realize that THAT'S where I need to be. Not on the road, talking about how to be a good teacher, but in the classroom, actually BEING a good teacher. In the Math Lab, helping students struggle with the most basic concepts. Not...I don't know.

I don;'t know.

I overbooked myself....I don't likw this.

What's up for next semester?

I'm off of the writing intensive committee...I'm ff of ILSOC. I'm stepping back (or at least I'll try to) from the leadership of the Sectional Project NExT. I've already shuffled off the coil of Supoer Saturday (if I'd had to deal with that this semester I'd have gone insane). I should be freer.

The book won't be coming out until early in 2012, I'm guessing, which means I won't have to do a lot of hobnobbing and hooliganism to tout that thing.

I'll have time to settle back in the center, where I belong. I've got to come home. I'm getting tired of this.

I need to be somwhere that I'm not.

I'm getting tired of this. I'm tired.

And it's not you, it's not me, it's all of us. We'rd tired.

I realize how repetitive this post must sound, given the frequent similar posts I've written in the past few weeks, but there it is. It's what some would call a thpattern.

There it is.

Here we are.

Let's try to make the best of the rest of the term.

Shall we dance?

2011-04-06T04:56:00.002-04:00

Shall we dance?
(for my Spring 2011 MATH 280 class)

We stumble, falling from step to step, counting each one
out loud like teenage boys working out their first waltz.
We are thankful that the lights are low, and that no one but the chaperone
can see us trod on our partners’ toes.

Yet not long ago we struggled just to stand. Now we’re hovering
at the gym floor’s edge, nervous fingers tugging slack into our neckties
and fretting at the seams of strapless gowns. “Omigod he’s coming over!”
Don’t just stand there! Shall we dance?

Confessions of a sometimes-mathematician

2011-04-05T11:42:00.006-04:00

Sometimes you have to let go, and let people lead their own lives.

As regular readers may know, this term's the first time I've taught a first-year colloquium at UNCA. (How I've avoided teaching one for this long is beyond me.) Therefore, before the last few weeks, I've never had to advise non-math majors. Many of the students in my MATH 179 course are "undeclared," and though many of them have some idea as to what they want to do with their lives, a few of them have almost no direction whatsoever. At the end of the day, I don't think this is necessarily a bad thing, as long as you're open to a little exploration and self-discovery. As much as it might annoy a highly-driven type-A person like me, some people just aren't sure where they're headed, and don't feel an immediate need to figure it out.

In the past two days I've met with two such students from my MATH 179 class. Both of them worked with me to hammer out tentative class schedules for next semester, but only after a good deal of discussion about possibilities ranging across the curriculum. (Oddly enough, they both might find themselves in Ancient Philosophy as they explore that route.) Neither wants much more from college right now than the experience of being in college, and right now I don't think there's much more they need to get out of it. They'll have to worry about that down the road a piece, but for the time being they'll be safe taking some core classes and getting baseline requirements out of the way. Until they reach a fork in the road, I'll help them along in whatever way I can.

Others can't afford such leisure and latitude. One of my advisees is about to graduate with a pure mathematics major, and I can't help but think she's found no more than the merest passing interest or passion in any of the math courses she's taken here. More than once in the past four years I've encouraged her to take another path if something truly striking struck her ("really, I won't take it personally"), but she's stuck with the math program, passionless as she may appear about it. I hope we've served her well.

Someday, perhaps, she'll find her path. But I've got to let go and let her do that for herself. After all, I can't help her find her way if I'm not even sure from day to day just what it is I want to do with my life. As I've confessed to some of my closest friends (and as I admit here now), I've given serious thought in the past year or so to setting math aside and diving more deeply into rhetoric and composition, areas in which I've been more keenly interested for the past couple of years. Put simply, for the past year or so rhetorical theory has gotten me far hotter than any theorem I've been able to prove.

But I love math, and I love math research, and I can't see myself setting aside the last two decades of work I've done to get me where I am. Moreover, I can do more good where I am now (as a solid math researcher with strong background in rhet/comp) than I could elsewhere (as, for instance, an ex-pat mathematician who took up rhetoric on a full-time basis). Finally, there's nothing stopping me from being a mathematician who geeks out about markers of metacognition at conferences on writing theory.

Who am I now? Who will I be tomorrow? We'll see. Sometimes you have to let go, and let your own life follow whatever course it seems bound to follow.

Whelmed

2011-04-04T18:20:00.008-04:00

The end is near. I can almost see the end of the semester from where I stand. And, unlike many of my colleagues, friends, and students, the rest of my semester should be relatively unbusy (compared to the past month or so) after this coming week. I no longer feel overwhelmed; I'm simply...whelmed. However, Webster's Free On-Line Dictionary lists "whelmed" as a synonym for "overwhelmed," so maybe that's not accurate.

The past few weeks I've felt the urge to post here, but have been at a loss for what to post about. Anything that I felt was worth saying was too trivial to mention or to comprehensive to put into a one- or two-page post.

I thought about writing on some of the Neat Teaching Ideas my colleagues offered up in the Project NExT-SE session at the MAA conference in Tuscaloosa this past weekend. My UNCA colleague Kelli talked about the "peer mentoring" program she's been using in her Calc I class here this semester, and my Project NExT colleague Kade talked about using "math moments" to expose lower-level math students to nifty ideas from higher mathematics, like the Four Color Theorem and Russell's Paradox. I've done this sort of thing in the past, but not recently, and I've never tried putting a peer mentoring program into place. I'm going to try both out in Precalc next fall.

I thought about writing on the feeling I had driving back from Alabama, a feeling of calm, serenity, and oneness, as, just for a moment, I felt like I saw with perfect clarity my role as a teacher and learner. I felt for a moment as though I understood precisely how what I do affects what my colleagues do and reciprocally, and precisely how I help my students to learn as they help me to do the same. It was a pleasant moment.

I thought earlier today about writing on a common category error my MATH 280 students tend to make...one which I didn't mention in class this morning as I was debriefing them on their latest homework sets. Namely: students frequently confuse conjunction ("and") of mathematical statements with intersection of sets, and disjunction ("or") of mathematical statements with union of sets. There's little to do but practice in order to overcome this confusion, training oneself through repetition to recognize the different between a set or a class on one hand, and a statement or a mathematical claim on the other.

Snippets, random snippets. If you've got something to say about any of them, feel free to chime in. In fact, feel free to chime in even if all you have to say is utterly non sequitur; I always love hearing from my readers, and I want to know where you are right now: puzzled and perplexed? Curious and questioning? Or simply stressed, and tired, oh so tired?

Hang in there, my friends. The end is near. Have a seat beside me and tell me a simple tale; I'd love to hear it.

Job satisfaction

2011-03-30T10:52:00.004-04:00

Every now and then you have one of those moments that makes you realize why it is you do what you do. I've had a couple of them in the past 15 hours or so.

Last night I managed to prove that the path P₅ on five vertices is Ramsey unsaturated. (Oddly, there were no ticker-tape parades this morning.) I'm pretty certain this fact has been proven before (I know it's conjectured), but it was satisfying to prove it for myself.

Just now one of the five stalwart students taking both Calc II and MATH 280 with me this term (poor souls) asked a fantastic question based on one of their take-home exam questions. "Is it possible for the center of mass of an object to lie outside the object?" Indeed it is possible, though it turns out not to be the case on the exam problem in question, and this was an astute question to ask!

We then spent about ten minutes generalizing the problem I'd asked on the exam. It turns out that by modifying the endpoints of the interval on which our object is based (and leaving alone the function giving its upper boundary, namely sec(x)), we can in fact obtain an object with center of mass lying outside of the object.

Good times.

The end is near

2011-03-29T19:59:00.006-04:00

I sure hope so, anyway. An already-short semester made nearly a week shorter by three snow days to start it off has meant that nearly every faculty member on campus has been piling on the work, making up for lost time. Everyone, faculty and students alike, is overworked this semester. The stress level is extraordinary.

This is one reason I felt bad effectively asking many of my 280 students to redo their last homework set even as they bear into the next one...and get ready for the next take home exam, to be handed out tomorrow. They took it well, though, and judging from the revisions I've seen since yesterday morning, they've made good on the opportunity: the revisions look great! I think it was the right move.

I hope this coming weekend's conference will be a welcome relief to the handful of faculty and ten or so students who are going. (Danielle, who was in my Linear class last term, jumped at the chance to go and get away from her dreaded CSCI 273 course for a little while.) This year's MAA Southeastern Sectional meeting, in Tuscaloosa, will be the second for several of the students and the first for a few others. My student Tonio is presenting on the work he did with me a year ago, we're fielding a Jeopardy! team for the second year running, and our department's faculty are presenting on everything from low-stakes writing activities (guess who?) to peer mentoring programs for Calc I courses. I'm just looking forward to the drive and a night or two to sort out some of the last revisions on the book before submitting it.

I've got one more conference coming up, at the end of next week. The annual Conference on College Composition and Communication ("Cs," as the comp/rhet people call it) takes place next week in Atlanta. It's my first. I'm looking forward to hammering out the next step on the research on REU writing Bella, Damian, and Nicola and I will be taking again this summer, and to meeting a few more folks in the composition community. (Moreover, from what I've heard, the publishers' receptions are pretty much the bomb...I've already been told about Bedford/St. Martin's shindig at Turner Field.)

Almost there...almost there...hang in there, my friends; we're almost there.

Change of plans

2011-03-27T19:53:00.006-04:00

Around four or five this afternoon I got back from a trip to Belmont University this past Friday (great trip, fun talk, good friends, etc.), and went right up to my office to pick up the MATH 280 homework that was to have been shoved under my door. 23 out of 36 students had submitted their work "on time," and two more slyly slid their work under my door while I sat there grading Calc II quizzes.

I held off on grading the 280 homework (a set dealing with set equality and properties of set operations, like commutativity and associativity of union and intersection, and so forth) until I got home. Dinner made, I then settled into my chair to start.

The first problem was rough (the proof I'd requested has a more subtle structure than do the others in the set), and I'd expected that. The second, though, was rougher, and this I'd not expected. Several people did fantastically. Several others had the right idea but their exposition was ragged and raw. Several more still, though, had only a very loose grip on the problem.

I stopped grading there, knowing that were I to keep going, I'd see more of the same. After all, these kinds of proofs (of set equality) are tricky at first, but they're also very formulaic, and once you've got one of its kind, you've got 'em all. I'm almost certain that whatever mistakes a student made on Problem 2, she'd repeat on Problem 3, and again on Problem 4, and so forth. I doubt it would make much difference were I to keep commenting.

Rather than finish off this problem set, I'm going to return the ungraded homework sets tomorrow, giving students the option of revising their work after we've had a chance to go through a variety of approaches to Problem 2 together at the outset of class.

We'll see how it goes.

Aleas being jactaed all over the place

2011-03-24T15:41:00.001-04:00

I've cast two dies in the past 24 hours.

Last night I sent my editor the first draft of the last chapter that I'd yet to finish. As of 2:18 EDT this morning, I have completed a full first draft of my book.

And...

...yesterday before leaving campus I sent an email to the Chair of our Faculty Senate indicating my willingness to serve as the "point person" for the Curricular Sustainability Subcommittee of CRTF.

We'll see if they take me up on the offer.

CRTF?!

2011-03-20T22:13:00.006-04:00

For the past two years I've served as Chair both of our university's Writing Intensive (WI) Subcommittee and of its Integrative Liberal Studies Oversight Committee (ILSOC; the body of which WI is a component). I was on WI for two years before chairing it, and during that time did a good deal of assessment and faculty development work for the body before coming to its head.

I've enjoyed all of this work: as anyone who reads this blog even casually (or anyone who's talked to me for more than a few minutes about my teaching) knows, I'm passionate about writing across the curriculum in all of its manifestations, and I consider myself duty-bound to evangelize and elegize.

I've enjoyed the work, but I'll be the first to admit that I'm tired of it. I'd estimate (if I had to pull a number or two out of a hat) that I've put an average of 5-7 hours a week towards WI during the past four years, and probably 3-5 hours a week towards ILSOC during the past two. This includes the summer months, for much of the assessment, faculty development, and reporting I've had to do for both bodies has taken place over the summer. In all this adds up to well over 1000 hours of work...and this is likely a conservative estimate.

I'll be rotating off of WI (my term is up) at the end of this academic year, and thus off of ILSOC, for it's my chairing of the former body that places me on the latter one in the first place. I've had a few good innings, and, to further that metaphor, I might say I've bowled several centuries. It's been fun.

What'll I be doing with my free time come next Fall, or even sooner? Lest you think I'll be languishing in a non-administrative lull, I might let you know that I've been placed on the "Curricular Sustainability" subcommittee of the latest chimerical beast dreamed up by our Provost and Faculty Senate Chair, the Curricular Review Task Force, or CRTF, for short.

To be clear: I volunteered to be on CRTF when the call went out a few weeks back. I even asked specifically to be placed on the subcommittee I've been placed on. (I'm delighted to find that several colleagues whom I respect deeply will be on the same subcommittee...many of whom have roughly my tenure, and many of whom I've worked with before.) I'm actually not complaining about this new assignment, as I believe it'll prove interesting, challenging, fulfilling, and (yes, I'm going to say it) fun.

But...

...there's something wrong here.

The Curricular Sustainability Subcommittee (CSS..."cascading style sheet"?) will be tasked with mapping out a proposal to make our school's curriculum deliverable by the current faculty (read: "without the adjuncts we cannot at this time afford") without driving them insane or further abrading their already red, rubbed, and raw morale. Sounds simple enough, right? During the CRTF's organizational meeting this past Friday, I began jotting down a list of related issues as they came to me. One after another they came, a few here, a few there, all interlocking and interacting, one popping up as another is squeezed down, like the flesh of a bulbous balloon.

What's involved?

Class size
Number of classes
Frequency of class meetings
Physical space available for class meetings
Student enrollment
Funding supplied by students' tuition
"Down time" (release time and sabbatical...the latter now euphemistically called "professional development leave," and before that "off-campus scholarly assignment"; heaven forbid we call it "sabbatical": that would make us sound lazy!)
Comparability with other institutions' policies
Accounting of courses (cross-listing, "double-dipping," other accounting tricks)
Meaningful co-teaching and related pedagogical practices
Relation of our mission and goals to those of the UNC system as a whole
Time to perform research
Time to perform service to the department, university, and community
Use of technology (especially regarding distance learning and hybrid course designs)
Faculty development (cost of, and targets of)
Support for curricular development efforts, for faculty development efforts...support in general
Reassessment of the roles of graders, UG teaching assistants, and other opportunities for student engagement in pedagogy
The university's identity and mission as a liberal arts institution
Et cetera

As some sample interpenetrations, working off of the unwritten (but widely stated, including over and over at this past Friday's meeting) aim of ensuring a 3-3 load:

Moving to a 3-3 load without the help of several dozen more faculty will lead to...larger class sizes, creating...greater demands for more (and more frequently unavailable) physical space, requiring...further renovations to existing physical structures, or perhaps extending hours during which regular courses are offered...unless...

...enrollment is forced downward, leading to...a decrease in the tuition monies available to fund the university's efforts across the board, raising...the school's dependence on other sources of funding...or, unless...

...a move is made to offer more and more online and hybrid online/face-to-face courses, for which...faculty will need more professional development (to better acquaint themselves with this pedagogical paradigm) and preparation time (you can teach an old dog new tricks, but not overnight), assuming we can all get over...the damage this move might do to the university's identity as a liberal arts institution, in which meaningful student-instructor engagement and student-led learning (undoubtedly harder to orchestrate from afar) are highly prized.

The astute reader will noticed that I've not yet followed up on the "something's wrong here" I threw out above.

In asking faculty to take on the job of resolving this and other equally immense issues involved with overhauling our curriculum, the administration is adding yet another duty to the already vertiginous tower of tasks it's performing (like QEP design and delivery, assessment for SACS, day-to-day operations of the Humanities, Arts and Ideas, Intensives, Clusters, and ILS Colloquia, and various and sundry other sickeningly corporatized bureaucratic functions). Faculty, most of whom are already teaching three or four increasingly large sections every semester, many of whom are facing increasingly great expectations for service and scholarship, are more and more frequently being asked to take on administrative roles.

Like it or not, we're being turned into quasi-administrators, all of us.

Halfway through Friday's CRTF meeting the question was raised: "well, once we've put all of our recommendations together, then what?" Clearly, as it stands, no single body will have the authority to make all of the changes we're likely to suggest; whatever the faculty can't do on an informal basis will have at least to go through Faculty Senate (or at least its subcommittee, the Academic Policy Committee), if not General Administration (GA) itself, far away in a semi-mythical place called Raleigh (a place where the public liberal arts university is not well-, if ever at all, understood). I imagined the scene at the end of Raiders of the Lost Ark, in which the ark is trundled off into the bowels of an immense warehouse, presumably never to be seen again...so it would be with our report, no doubt: how many months would be wasted in trying to coordinate the several separate bodies whose work it would be to try to implement whatever suggestions we could come up with?

In a delightful moment of daydream, I thought: "Rebel. Revolt. Take over. Throw the Senate out, screw GA, and rewrite the rulebook, starting with page 1. If we've got the backing of the faculty as a whole [there are some 50 or 60 of us on CRTF, by the way], who's to stop us?" It was a childish thought, to be sure, but it was nice while it lasted.

Just minutes before the meeting on Friday I'd been sitting in the Math Lab working with Didi and Belle, two of my favorite new students this semester. They were working at trying to make their submission for the Calc II Integral Insanity miniproject more fiendish (the goal is to make as difficult an integral as possible, while still making it doable). We were trying to figure out how to build a reasonably challenging integration-by-parts problem backwards, through reverse engineering. I don't think any of the three of us had had much sleep this past week, and we were all slap-happy and silly as hell. Progress was slow, but I think we eventually got there.

It's moments like these that make me remember why I do what I do. I'm a teacher (and scholar) first, and an administrator second...distantly second. As important as WI, ILSOC, CRTF, and all of the other academic acronymic entities are in the abstract, there's nothing more important in concrete terms than making sure that a future mathematician understands induction, or that a future engineer or public health official knows how to analyze a simple mathematical model, or that I keep playing an active role in the generation of new knowledge, for my own sake and for my students'.

I can't lose sight of this.

Girls and boys

2011-03-03T19:07:00.003-05:00

I know at least two web media outlets (Slate and Inside Higher Ed) commented today on a study on gender issues in STEM ("Science, Technology, Engineering, and Math," for those not in the know) fields recently done at the University of Massachusetts, and my Facebook posts on the article have led to great conversations with my (mostly female) friends. The study's results are unsurprising to those of us in STEM fields: female instructors in STEM courses lead to improved levels of engagement and confidence in female students.

At the risk of sounding dismissive, I offer a one-word response to this study: "duh."

I honestly don't mean to be dismissive. I highly value this study and others like it for reifying and drawing attention to the glaring disparities between the achievement of men and the achievement of women in math and math-related disciplines, at all levels. We need to get serious about addressing these disparities, from preschools to postdocs, and beyond.

Addressing the inequities in math education takes more than responding the Barbie's "math is hard" with "Barbie's full of shit," but telling Barbie off is a good start. Early on young women need to be told that they're as capable of doing math as their male counterparts, and that in doing so they do not sacrifice their femininity. They need to be given the same encouragement and opportunities young men are given.

I could write for hours on this topic, but I know how I feel (and I'm sure my regular readers, my colleagues, and my students both past and present know how I feel, too!)...I'm more interested in learning how those of you reading this feel. I know many of my readers are current and former students of both sexes. I'd really like to know what sort of experience you've had, and what you think your sex has had to do with it.

Has your sex made you feel at home or out of place? Have you been encouraged because of your sex, or discouraged because of it? Have you noticed your instructors treating you differently than classmates of the other sex? In what way? Let me know what you think, anonymously, of course, if you'd like.

How tweet it is

2011-03-02T19:16:00.003-05:00

My Calc II students were all atwitter again today. I knew today's tweet would treat them to a challenge: I asked them to (in 140 characters or fewer) summarize the method of partial fractions for integrating rational functions. Anyone who has more than a passing memory of Calc II likely remembers that the process is not particularly hard...but it's long as hell and therefore difficult to summarize succinctly.

Those I felt were some of the students' strongest tweets are below, complete with intentional spelling errors and sparse spacing. I think they did very well (only a couple of them seemed to miss the method altogether...if you're one of those people, please don't hesitate to come on by my office; we can go over another example or two together).

"makesuretopislowerindefreethanbottomfactorbottomdecomposethebottomintegratethatdecompositionclearthedenominatorssolveforconstantsbingo!"

"1)long divide 2)factor 3)look for decomposition 4)anti-differentiate 5)find constants"

"1.long division if degree_top>degree_bottom.2.factor denominator.3.A/linear&Bx+C/irreducable quads. cross-mult.denomxnumerators.4.solve A,B,C"

"to integrate fractions, 1st long divide, then factor separate the integral and solve if not solvable separate out each term bottom and the" [ran out of room!]

"1poly long division 2factor3decompose w/each factor in the denominator4integrate5cross multiply and solve for each constant."

"makeoriginalfunctionsumofpartialfractions.clearthedenominators.findx-valueto=0tosolveforconstants.ifcant,comparecoefficientsonlikepowers."

They're definitely growing more accustomed to writing in this highly constrained genre, one which encourages concision and carefulness, and the ability to get right to the heart of the matter.

Reboot

2011-02-24T18:28:00.006-05:00

Long day. Full day.

I got to campus by about 7:30 so I could take care of some bureaucratic matters and get ready for the "reboot" of my MATH 179 Ethnomathematics course. My intent today was to transition smoothly from the textbook by Marcia Ascher we've been using to guide the course so far to Stanislas Dehaene's (about the relative merits of these books I blogged yesterday).

That we did: we spent about half an hour talking about least common multiples, primes, and relative primeness. These concepts all come up in understanding Mayan calendar. Though some of the students were shaky with the concepts at first, they all seemed willing to engage them, and moreover the concepts are more concrete than many of those we've worked with so far this semester (like Marshall Islander stick charts and months based on Jupiter's moons). This concreteness helped students get a grip. We even dished a bit about Gauss's formula for the sum of the first n natural numbers and the conjectural infinitude of twin prime pairs.

The smooth slide into Dehaene that I'd hoped for came with an exercise I'd put together to test one of the points Dehaene makes in Chapter 4 of his text (which students are to read for next Tuesday): people who grow up with either English (13 of the 14 students present today) or French (the remaining one of the 14) as their native language have difficulty in remembering any series of more than seven or eight randomly generated digits shown to them 20 seconds previously. All 14 students were successful at remembering five, six, or seven digits, and at eight people started to falter: two students failed to get all eight, and several more failed to get nine. No one remembered ten correctly.

Incidentally, native Cantonese speakers can generally manage 10 without difficulty. If you'd like to know more, read Dehaene's book.

I felt renewed energy in class today. I'm looking forward to seeing what the students think about the reading for next week.

From Ethnomathematics I went straight to my colleague Louise's LANG 120 (our first-year composition) course, where I was guest-lecturing on the subject of writing in mathematics. Louise hoped that I could expose the students to some of the conventions of mathematical writing, partly in order to demonstrate that many of those conventions, and the criteria by means of which the quality of writing can be measured, are not all that different from those of academic writing in general. I think I succeeded in this to some extent. It was a lot of fun! It seemed like a good class, with some very outgoing and eager students.

In Calc II I (boy, that looks weird) tried out a new format for the students' quiz. Rather than offering a collaborative quiz (as the last few have been), and rather than making the quiz a fully solitary activity, I gave the students a brief "consultation period" in the middle of the exercise. The students had several minutes to get a start on solving the problem posed to them, and then I allowed them roughly two minutes to confer with one another in whatever way they wanted to, sharing ideas, checking their answers against each others', etc. This period over, they returned to solo work before submitting their quizzes. My theory was that this format would help students in much the same way "think/pair/share" exercises help them: the initial brainstorming and groundwork is done on a solo basis, but then conference with their colleagues helps to refine their initial thoughts as they take shape.

I can't tell how people felt about this, or if it had a noticeable effect on performance on the quiz. (The students did pretty well, making, for the most part, the errors I'd expect them to make. Nothing out of the ordinary.) Only one student offered feedback on the format on the quiz itself, indicating that she felt it threw her off more than it helped her.

If you're in my Calc II class, how do you think it went? If you're not in my Calc II class, how do you think you'd respond to this activity? Would it help you? Hinder you? What up? Feedback, please!

Travelers' tales

2011-02-23T20:25:00.002-05:00

It's been a much better day today.

A highlight: another meeting of the minds in my office, involving three 280 students who'd stopped by after class for a debriefing on their recently-returned homework assignments. I'd mentioned in class just an hour before how beneficial others had found such debriefings, and these three had come hoping to reap the same benefits.

The meeting was wonderful. Sibyl, Nigel, and Quark joined me in a rough circle in front of my desk, and we went through the homework together, one problem at a time. Sometimes it took no more than a minute to iron out the wrinkles they'd worked themselves into, and other times we spent ten or twelve minutes puzzling through a problem's subtleties. They fed my wisdom and of their own, which was often richer. It's good for the students to see that others often have the same struggles they do (more than once they made the same kind of mistakes on the same problems), and it's good for them to hear their peers' explanations (often more lucid than my own). We ended the meeting with my giving them a few impromptu inductive exercises for practice with the technique. (Prove: n nonparallel lines in the plane determine n(n+1)/2 + 1 regions, bounded or unbounded.)

I left our meeting invigorated. I love this aspect of my job.

A second highlight: I realized this afternoon, while rereading Stanislas Dehaene in preparation for MATH 179 tomorrow, why it is I've had such a hard time getting into the mathematical aspects of my Ethnomathematics course this semester: the book, by Marcia Ascher's Mathematics elsewhere: An exploration of ideas across cultures, is awful, at least for my course. It's a bad fit. It's boring, condescending, pedantic, preachy, and is aimed at entirely the wrong level. (It's too dry to intrigue most math majors but too mathematically sophisticated to appeal to non-mathematicians.)

By comparison, Dehaene's book, though not strictly speaking about ethnomathematics (it deals more with the psychology and neuroscience of math and math learning), is intriguing, engaging, and written in a manner that's neither condescending nor confusing. I think the students will find it much more interesting than Ascher's text. We'll start drawing from it tomorrow and next week.

It's been a good day; I'm looking forward to another one tomorrow.

A closing note: my thanks to all of you who offered me support after my day of frustration yesterday. I'm sure regular readers will recognize that blogging is a cathartic exercise for me (need evidence? Check out the "anxiety" and "bitching" tags on the right!), and I often feel tremendously better after writing.

Calm

2011-02-22T22:30:00.006-05:00

Late this morning I stopped for about a minute on the landing midway between the ground and the second floor in the stairwell at the far east end of Robinson Hall. I leaned against the wall and let the cold yellow brick rub into my back. I breathed deeply, hung my head, and closed my eyes. For a few minutes then I felt like crying. Then it passed.

I've often felt overwhelmed lately, what with four preps (i.e., teaching four different courses this term), a book draft due in dwindlingly few weeks, and an ever-growing glut of REU applications piling up in my in-box...the budget situation doesn't help, and I'm increasingly annoyed by the website migration, committee governance responsibilities, and the almost farcically bureaucratic assessment-related demands on my time brought about by the university's upcoming reaccreditation site visit. (Do I really need to write another impact statement? How long before we've simply assessed ourselves to death?)

I think perhaps what's most stressing and distressing to me lately (and may even be the root cause of the passionlessness I've lately expressed for my discipline?) is the distance I seem to have drifted from the aspect of my job I enjoy the most: hands-on, one-on-one work with my students. I don't feel like I get as much of that work as I used to, but when I do it's effect is as if godsent.

I had a few refreshing moments today. Kip, Kamryn, and Miriam all took me up on the offer I made my 280 students yesterday: I encouraged them each to come by and conference with me about the comments I made on their most recent homework assignments. Such conferences give me a chance to contextualize the issues I found in their writing, and to offer them more substantial guidance as they develop as writers and provers. The conferences also give them a chance to ask questions, to probe more deeply the problems I posed to them, and to get help on putting together new proofs that build on the old ones they've put in place before.

Every one of the conferences I had today was a helpful one, at least for me. Every one helped me normalize my expectations with those of the student I met; every one helped me better understand each student's weaknesses and strengths. (For instance, one fears being a "fraud" or an "impostor" because her strongest proof mimicked one we'd done together as a class.) I now feel as though I know each student who met with me just a little bit better than I know any of their classmates.

Moreover, as I hinted above, these conferences gave me a much-needed connection to the most meaningful aspect of my work I've too often felt missing lately. Meeting with these 280 folks, and strolling through the Math Lab and helping out with the odd trig-sub integral, really helped me get over my morning's mini-breakdown. I hope I was able to help a few other folks to wrestle down a few of their own personal demons.

We're all stressed, I can tell. But we're none of us alone. Let's all lean on each other. I'll slay your dragons if you slay mine. Together we'll make it through.

Vox populi

2011-02-22T11:29:00.004-05:00

The students have spoken. It's clear from the feedback I got at the end of class today that I've gotten a bit off-topic in MATH 179 for the past couple of weeks as we've undertaken a more in-depth analysis of the university's structure and the impact that budget cuts will have on that structure.

The students definitely want to get some more math into the course, and we'll begin doing that on Thursday when we look at the Mayan calendar more closely. I'm also thinking of bringing in some reading from Stanislas Dehaene's The number sense: How the mind creates mathematics. I found this book fascinating reading a few years back, and I think it'll start some interesting conversations. Ditto Anthony Aveni's Uncommon sense: Understanding nature's truths across time and culture.

My bad for letting us yaw of course...let's get back on track!

More about less

2011-02-18T16:04:00.005-05:00

I know very few details, but apparently the latest move is to ramp down the Dance program at UNCA, letting students finish up the courses they'll need to complete a minor before letting it drift.

UNCA readers: I don't know how effectual it'll prove, but there's a petition at the dance marathon going on outside of Phillips Hall protesting cuts to the Dance program.

I'll update if I learn more.

Recent developments

2011-02-18T07:58:00.007-05:00

Breaking news: the administration has asked that our department cut six core mathematics courses from our fall schedule (including Calc I, Precalc, and STAT 185, our introductory non-calc-based statistics course) in order that we can free up people to teach in the Humanities program and LSIC courses (like the 179 I'm teaching right now).

Leaving aside the question of the relative value of the courses in question here (how much do we as a university value the Humanities program and our ILS Colloquia?), this is pure asininity, plain and simple. It's wrongheaded.

The effects would be staggering: already-huge sections of the classes mentioned above would get larger. We're already teaching with caps of 32 in Calc I and Precalc (effectively pushing numbers up to 35 or so for these courses when flexible instructors let a few folks in over the line) and 28 in STAT 185. The classrooms we're given barely hold those numbers, if they hold them at all. Cutting even a single section of Calc I would push numbers in the remaining sections up by about 5-6 students. We're now talking 40-person sections of Calc I and Precalc, and perhaps 35-person sections of STAT 185 (computer shortage is an issue there).

It is impossible to provide the meaningful student-centered instruction expected at a liberal arts institution in a course with that many students. My suspicion is that the powers that be who are mandating this move are operating under the impression that mathematics instruction is unidirectional and purely lecture-based. They run the danger of turning mathematics instruction at UNCA into something akin to the large-lecture methods employed at our giant sister schools down the road. Despite innovations like classroom response systems, this arrangement's still got nothing on one-on-one interaction between teacher and student.

Even from a simple human resources standpoint this move is silly: it takes faculty away from courses capped at 32 to courses capped at 22, at a time when we need to make the most of every faculty member's time and energy. Of course, in most departments this would be an even trade-off, since (according to a senior colleague down the hall who ran the numbers this morning) our department teaches more 30-plus-student sections than the rest of the university combined.

That same colleague and my department chair are now at a meaning at which they hope to try to reverse this request. I'll update later.

Thoughts?

UPDATE: after further negotiations this morning, we've managed to keep Calc I and Precalc intact, compromising by scrapping one section of STAT 185 and taking on two sections of Humanities. We've also pulled one of the longtime administrators (a former regular member of our department before leaving us mortals behind) to teach one section of our Nature of Mathematics (the name for our "general education" math course). I'm actually very heartened by this gesture, for I know how busy this woman is anyway. I'm grateful to her.

This should be doable. Further bulletins as events warrant...

Brevity is the soul of wit

2011-02-17T18:17:00.003-05:00

I had the Calc II students tweeting again today, this time about the appropriate way to solve trig integrals involving sines and cosines. In 140 characters or less, how much can you say about solving such integrals? Below are some of the strongest responses. (By the way, "EFTI" means "Everyone's Favorite Trig Identity," my term for the identity sin²(θ) + cos²(θ) = 1.)

"If you see an odd # of cos(x), u=sin(x).If you see an odd # of sin(x), u=cos(x).If they are both even then throw your things and cry:("

"If there is an odd number of cos(x),letu=sin(x). If there is an odd number of sin(x) let u=cos(x).Then use trig identity if needed."

"To solve integrals with sin & cos, u=sinif ur cos is odd. u=cos if ur sin is odd. If both are even: weep. And Patrick spake it thus."

"Use EFTI!If the trigS has an odd and an even, make u=the even term.If the exponent is higher than 2,it may be easiest to seperate it first!"

"Integral with sin&cos: u sub the non-odd and sub the remainder with trig identity, then simplify. The rest should be easy."

"To solve intergral w/ sin & cos/if you see odd # of cos u=sin if you see odd # of sin u=cos/think of how to split them upsoit works out right"

"when u hav sine&cosine,ur u is the nonodd one.if both r odd u can choose either then use usub and EFTI to solve the trigintegral.its so fun!"

"In general: If the integral has an odd # of sins or cos, make the opposite one the u in the u-substitution set up.(Be careful of evens!)"

"Ifanodd#ofcos,u=sin(x)Ifanodd#ofsin,u=cos(x)Thendifferentiatetheu,andrememberthat1=sin2(x)+cos2(x).Settheintegralintermsofuandsolvewithrespecttou"

"If the powers are even/odd, use the even one as u. Iff there are extra of the odds, use EFTI. If both are odd, use the higher power as u."

I should mention that the overall quality of these tweets was stronger than that of the last set. Words were selected more carefully and fewer students felt the need to forgo spaces to say what they needed to in the room provided. I'm not sure if this improvement is a consequence of a more easily-summarized topic or a growing acquaintance with the genre. Maybe a little of both?

Everything you always wanted to know about UNCA (but were afraid to ask): Vol. 2

2011-02-17T11:10:00.003-05:00

We had another round of "Everything you always wanted to know about UNCA (but were afraid to ask)" in MATH 179 today. It came at the end of the class (after further discussion of Jupiter's moons and an overview of the Integrative Liberal Studies program at UNC Asheville), so we didn't have enough time to address every question asked, but we got a few in. We'll finish the rest on Tuesday.

I'm impressed by the students' candor and curiosity, and I'm equally impressed by the students' knowledge of campus functioning. Some of these kids are definitely up with what's going down.

Questions?

What is the cause for the recent budget cuts?
What are the advantages/disadvantages of declaring a major?
If 179 is one of the writing intensives, what are the other 2?
What all will the new health and wellness center have to offer?
Will any majors be dropped with the budget cuts?
Where do I find info on clubs?
What are the rules for the disc golf course? And how many holes is it?
How much of my tuition is going toward building the community/campus gym?
Where do you apply for a learning disability? (I write on the side WITHOUT lines, I'm such a rebel!)
How many hours are required to graduate?
When will the construction for Governors Village be finished?
If I took a Spanish at my other school and it counted as both Spanish requirements if you passed and I passed then I scored below that level on the placement test what happens?

We got around to the first four of these today. I have to admit to a little relief that some of the others have yet to come up: I'm going to have to look up the answers to a few of them!

Closer

2011-02-16T23:51:00.003-05:00

The first draft of Chapter 1 (offering an overview of WAC) is done.

Strengths: I think I did a helluva job distilling the history of the WAC/WID/WTL movements down to about 5-10 pages. I think I did a good job of motivating WAC, WID, and WTL in the first place.

Weaknesses: In moving the section on student resistance from its original location (at the end of Chapter 2, on the writing process), the inter-section transitions at this new chapter's end may be a bit awkward.

We'll see. I've just sent Libby this draft; I'll eagerly await her feedback. She promises to get some reading in en route to Tuscaloosa, home to this year's Southern Writing Center Association conference. I wish I were going! Odd that this year Bama's playing host both to SWCA and to the Southeastern Sectional MAA meeting, coming up in a little over a month.

Now...to dink around on Facebook for a little while before beddie-bye. Au revoir!

Of moons and months and mathematical manipulation

2011-02-15T14:17:00.005-05:00

This morning in Ethnomathematics we finally had a chance to spend some time trying to reconcile the "lunar" and "solar" calendars one might use were one stationed on Jupiter and decided to use the largest of the Galilean satellites, Ganymede, to reckon your "months."

A Ganymedean month (the time it takes to make one transit around Jupiter) is roughly 7.15 (Earth) days; meanwhile, Jupiter's tropical year (the time it takes the planet to make one transit around the sun) is 4331.57 (Earth days). Just as on Earth, where a tropical year doesn't contain an even number of lunar months, resulting in a "drift" between lunar-based and solar-based calendars, there are an uneven number of Ganymedean months in a Jovian year. What to do?

After a bit of numerical piddling and fiddling, we figured out two reasonably accurate ways of making the numbers jibe. Both rely on the fact that each Jovian year we have a "remainder" of 5.82 days that don't quite make up a full Ganymedean month. If we let 11 Jovian years pass, we've saved up 64.02 spare days...this figure is very close to 9 full Ganymedean months, which give us 64.35 days. Therefore, if we add 9 months every 11 years (which can be done in some systematic fashion, much as is done with the Jewish lunar calendar), we've add only 0.33 extra days. This overage is tantalizingly close to 1/3...so why not simply take away one day every three 11-year cycles? This day too can be chosen systematically, removed from the middle of the 17th year of the 33-year cycle it corresponds to, for instance.

Neat!

I'll leave it to my readers (I'm sure your curiosity is now piqued) to puzzle through the details of the other solution we arrived at, which had much the same flavor and involved slightly more frequent adjustments.

Fun stuff...now if we can only figure out how to make these systems fit nicely with the 365.24-day Earth tropical year, which some of our Jovian emigrés still insist on using...

Editing is underway

2011-02-15T14:05:00.005-05:00

As I write this the first MATH 280 "editing party" of the semester is going on in the Math Lab. Six of the class's 36 students showed up to look over one anothers' submissions for Chapter 1 of the textbook.

I'm eager to see how well the students receive this assignment this term, especially in such a large class!

UPDATE: ten people have now shown up, and the party is hoppin':

Tweet!

2011-02-14T14:38:00.004-05:00

At the end of class today I asked my Calc II students to write Twitter-style tweets in which they describe how to use the method of integration by parts. To help them stay within the 140-character limit of the genre, I provided them with graph paper on which I'd blocked out boxes containing 140 squares apiece.

The results?

They found it hard to say all that they wanted to say, so they had to focus on the issues most central to the method. (This, of course, was the point of the exercise.) Some tried to save space by eliminating spaces between words or by eliminating vowels. The former resulted in text that was still readable; the latter, I would argue, did not. Compare:

"findauvalue&differentiateit.findadvvalue&integrateit.taketheproductofuvandsubtracttheintegralofvdufromthatproduct."

versus

"Use da frmla fr ibp's. you cn chse ne prt fr u. da othr prts r dv. slve fr du and v. thn plg into frml. look a pngun <(") !!!!11one!!!"

Not only is the first easier to read; it's also correct, complete, and doesn't succumb to silly non sequitur by the end.

Some of the best were short and to the point, and even managed to get in some guidance about how to choose u and dv: "Sudv=uv-SvduumustgetsimpledvmustbeS.use formula above solve" was far terser than it needed to be; throw in a few spaces to make it more readable, and expand on what "mustbeS" surely means:

"Sudv=uv-Svdu. u must get simple. dv must be integrable. use formula above. solve."

is still well within the 140-character limit.

Clearer, but not quite as complete (it makes no mention of dv), and still pretty solid:

"pick a portion of the original integral that will get simpler when derived and set it to u, then do int(f(x))=uv-int(vdu)."

Several others were nearly as good, but used slightly awkward notation or omitted critical pieces of the formula. From what I can tell, the students get the gist of the process, but may still be a little iffy on the details.

Practice, people, practice! This gets much easier after you've done a few of them. If you want to go over a few examples together, please come on by. I'd love to work on a few with you. You'll get there, I promise.

Whaddaya mean, "liberal arts"?

2011-02-14T13:55:00.003-05:00

Last week I asked my MATH 179 students to reflect on what "liberal arts" meant to them. They were to write an ungraded page or two about what they thought it is that distinguishes a liberal arts institution from one of a different sort. Their responses to this exercise were uniformly astute. They've got a good grasp of what a liberal arts education entails already, so my goal for the next of the semester need not be so much to introduce them to this educational philosophy so much as it will be to help them investigate its subtleties and implications.

Many focused on the relatively intimate learning environment at liberal arts colleges, bolstered by their smallness: "Because of the small student-teacher ratio, students are closer to their professors and receive personal attention" and "I like the fact that it [UNCA] is a small campus, the students and teachers are very nice, and there are classes here that you probably would not find anywhere else," in contradistinction to "UNCW [UNC Wilmington, where] most of the lecture classes were very large. I had several hundred people in my Biology class and also in my Algebra class."

Some commented on the liberal arts curriculum, focusing on the curriculum's breadth as well as disciplinary depth ("Usually liberal arts colleges have more core classes than other colleges. I think this is because the college wants us to have a broader view of horizons rather than focus on the one thing that we like") and on the ways in which the curricular offerings are tied together ("Liberal arts colleges tend to look at education holistically, meaning the curriculum is usually intertwined and well-constructed relating certain areas of study") . They acknowledged that tackling this curriculum is not always easy, but should ultimately be rewarding: "Due to liberal arts requirements one must go outside of their comfort zone and take classes in topics that they are not the best at or comfortable with. Although can be cumbersome as a student at times it helps integrate all areas of study to further the student's knowledge in general."

What are the rewards? Employability, one would hope: "When I graduate I think all those requirements [clusters, writing intensives, etc.] will make me a more rounded person and make me look better to an employer" and "...a degree from a liberal arts school is better to find a job that is not specific, because it shows you have skills in many areas." There's also something to be said for the recognition of the "human" in human scholarly endeavors: "The liberal arts environment at the school has had a major impact on the way I am taught and how I learn here at the University of North Carolina Asheville. [...For example, the Newton v. Leibniz project in Calc I] seemed so absurd but it really helped me realize that the topics we were being taught and the rules that we were learning were not just things that appeared out of thin air. Every subject, every theory, and every idea has a back story, a history, a time, a place, and a brilliant mind who thought it up."

Several students expressed (sometimes extreme) satisfaction at attending a liberals university (a few have spent at least a term in a non-liberal arts environment). Some even expressed concern for their peers elsewhere: "I see a liberal arts education to be very important because I have noticed a terrifying trend that not many of my peers that attend non-liberal arts universities are very secluded and "protected" from the world and the culture in which they live."

So far they know what they're talking about.

Pet peeves, Vol. [moderately high arbitrarily-chosen number]

2011-02-12T07:26:00.006-05:00

It can be argued that the most important goal of a good university faculty member is to guide successfully her or his students through their development as scholars, specifically as practitioners of one another field and more generally as members of a greater community of rational and reasoning thinkers. (Alternative arguments, many of them cogent, are beside the point of this post.) As such, it's natural that faculty members be critical of their students' work: through careful and constructive criticism we make our and others' expectations clear, and through these means are our students led to understand how to reason and relate with others more clearly.

But as faculty, how critical are we of our own and each others' practices?

I wanted to mention a couple of indirect encounters with Colleagues (a capitalized universal subcommmunity of fellow academics) I had yesterday which really got my goat.

First. Not to harp on this (I know I bitched about it last year, too), but, Colleagues, how in the world can you sleep at night knowing how lousy are the recommendation letters you write on behalf of your students? I'm thinking in particular of a rec letter for an REU applicant I received yesterday which was roughly five lines long, clearly typed directly into the email, and sent all at once (with generic head and foot) to directors of all of the programs to which the student was applying, without even using blind carbon-copy. Never mind the utter disregard for standard email courtesy: five lines is barely long enough, in my experience, to give the merest context, including the student's name, the course(s) in which she enrolled with the writer, and her baseline performance in those courses, to say nothing of individualized evaluation including (a) day-to-day performance in class (was she outgoing, creative, clever, computationally fluent, quick, friendly, supportive, etc.?), (b) her academic work outside of class (did she take on elective projects, undergraduate research, etc.?), (c) her ability to work with others (was she a joiner, a leader, a follower, a groupie, popular with her peers and professors alike?), and (d) her writing ability (which is likely superior to your own)?

Letters like this one embarrass me on behalf of my entire profession. I pity students whose teachers show this little concern for their careers. Sending such a letter says this, and says it loudly: "you are worth roughly ten minutes of my time. I either don't remember you well enough or don't care enough for you to compose a genuine letter of support. I don't really care whether you get into these programs or not. I have better things to do." These letters usually come from faculty at schools like Princeton, Stanford, and Harvard, from faculty who like to think that they're the best in the world at what they do...they may be right, if "what they do" is taken to mean straight-up academic research. They're dead wrong if you interpret their function more broadly and take it to mean enriching the lives of their students, colleagues, and communities (academic and non).

There is a silver lining, of sorts: letters like this one make me realize why it is that my students have a strong track record of getting into graduate programs and REUs. For even the weaker students who ask letters of me I take two or more hours to write a decent letter, almost never under a page in length. Quantity is not quality, but clearly I can and do say much more in fifty lines than I could in five.

Second. On a somewhat related note, I had occasion to read a couple of a colleague's syllabi, and was deeply chagrined by their brevity and wanness. Less than a page long, they did little more than lay our the most basic mechanics of the course: professor's name and contact info, course website, texts, meeting times, grading scheme (bare-bones and anachronistic), and an obligatory statement regarding writing intensiveness and other disclaimers required by the Office of Academic Affairs and the Faculty Senate.

Missing was any kind of statement of purpose, articulation of learning goals, context, description of activities...and in the absence of this matter, the faculty member in question conveyed (as did the letter-writers above) his disdain for his students. Allow me to read (uncharacteristically pessimistically) between the lines: "I don't really care enough about this course to make it clear what we'll do together, or how what we'll do will enrich your experience at this school and provide you help as you grow as a scholar. On most days I'll likely make up class as we go along, because I consider myself too intelligent to have to do much preparation: I can do it on the fly. I'll spend most of my time working on my latest book. If you're outgoing and eager and seek out your own learning opportunities, you'll come by my office and I'll talk to you as I talk to my colleagues (silently applauding myself for empowering you by treating you as a peer and equal), while if you're not so outgoing or eager, however much you may wish to learn in our course, you'll suffer through the semester without any guidance or direction, you'll learn next to nothing, and I'll reward you with a B at the end of the term simply for not bothering me and so that you don't call on me to defend the lousy grade I've given you once the semester's done."

Sound like anyone you know? The kicker: more than once I've heard this colleague help up as a model for excellent teaching.

All right, enough mewling. On to grading. I'll check in later, after I've had another crack at Chapter 1 (a first draft of which I hope...optimistically!...to finish this weekend).

Fun with L-tiles

2011-02-11T13:54:00.003-05:00

Today was that funnest day of the semester in MATH 280, when everyone gets to take a trip back to the third grade as we play with L-tiles in order to understand the idea of induction. This day is always a fun one, but I don't think any 280 class has ever had as much fun as these folks did. They loved it!