Wednesday, December 31, 2008

New Year's resolutions

Happy new year, folks! As I write this it's already 2009 in 11/24 of the world, with just a few hours left in 2008 for me and mine in North Carolina.

I'm not overly eager to see 2008 go, as it's been a pretty decent year for me (economic downturn notwithstanding). I am looking forward to 2009, though, as I've got a number of irons warming in the fire that should be nice and hot before the new year is up.

What's gone on this past year? What's to come in the year that begins tomorrow?

2008 Teaching Highlights (in no particular order)

1. I'm still high from my work with this past year's crop of REU students. They were smart, quick, and immensely talented. I truly felt humbled by some of the work they put out this summer.

2. I received my third nomination by my students for a university-wide teaching award. I. Am. Honored. My thanks go out to all of the wonderful students who make this job such a pleasure to perform.

3. I'm very proud of having survived my first-ever teaching of Precalculus. It presented new challenges to me, ones that I feel I met rather well. I'm incredibly grateful to my Precalc students for their seemingly limitless patience and cooperation; they taught me innumerable tricks and techniques. I've learned much from them.

4. My first full calendar year of service on the Writing Intensive Committee has taught me boatloads about the many manifestations of academic writing. In attending my first two writing-related conferences, I've learned what a welcoming and supportive bunch the composition/rhetoric community is. I look forward to developing further ties with many of that community's members.

5. I've been intrigued and excited by the possibilities I've begun to study for interplay between math and poetry. What I've seen so far, I'm sure, is little more than the tip of the iceberg. What will the coming year bring?

2009 Coming Attractions (in no particular order)

1. Spring 2009 will be my first ever semester with four preps. However, I've taught every one of these classes before, so none of them are new preps, and I've already got the structure of two of them pretty much completely worked out. Is it going to kick my ass? We'll see.

2. In the coming semester my Super Saturday class will be on-line for the first time since I've been leading it. Now that I've got a solid curriculum and a number of good resources to back it up, I'm more confident than ever as I go into my sixth semester with the program. If things go well, I'm thinking of using the course materials as the basis for a children's book on hands-on advanced mathematics.

3. I'm excited to find out how the LaTeX module is going to work out in our Foundations course. It'll be difficult to assess the overall impact of this move right away, but I hope that by introducing the students to the software early in their careers it'll make them stronger expositors of mathematics down the road.

4. I'll be submitting several non-mathematics articles this coming year, comprising a few on the scholarship of teaching and learning in various settings. I'm eager to see how these are received.

5. The third summer of the REU is fast approaching, and with six of our past two years' alumni presenting at JMM, I'm wondering how we're going to top our past successes. I hope we can come through, though, as by June 5th I'm going to have to submit my application for continued funding from the NSF.

All that and more. But I'll leave it for tomorrow. For now, it's off to the celebration!

Friday, December 26, 2008

Chapter 5. Blueprint

My first exposure to Moore method instruction came during my first year of graduate school at Vanderbilt University, back in 1998. My graduate-level topology course was taught using the Moore method, and as there were only four of us in the class, our going was painful: often every one of us would be called on to present a problem on every single day.

Of the four of us, two had seen a good deal of advanced theoretical mathematics already: I came having finished a Masters degree and having taken just about every math class offered at my undergraduate institution, and my colleague Oleg came from a European nation where his undergraduate training had been much more focused and intense. We had a decided advantage on our less-experienced colleagues. Erdrick and Tara were fresh out of American undergraduate programs and had had little more than the standard course of study one would find in such a program: both were smart, but relatively fresh.

As one might expect Oleg and I had a far easier time than our two friends: we came upon our solutions more quickly and we had an easier time presenting them. Although this advantage dwindled and then disappeared almost entirely by the time we got to algebraic topology, a topic none of us had dealt with before, for a few months Oleg and I were able to set the cruise control and drift along breezily while our friends struggled.

But about three months into the Fall 1998 semester, during one of Erdrick's more protracted proofs, I noticed something striking: his presentations were richer than mine were, they involved themselves with more details, and they provided a thicker description of the underpinning concepts and computations than my own presentations did. Moreover, they were clearer, and contained a more cohesive and coherent argument and were therefore more well composed. Even as he professed his lack of understanding of this or that topic (often one with which Oleg and I had dealt in earlier classes), it was evident that he was taking the time to dig more deeply into said topic, uprooting it and holding it up to the light to better see it and better get at its meaning. And as he held a topic up for his own examination, so he held it up for all of us to see and analyze and understand.

His relative lack of knowledge was making him a better teacher than I could ever be.

If one is able to unashamedly confront one's ignorance in front of others, one is acting in the manner of an effective educator: teaching is little more than a practiced and public examination and remediation of ignorance.

Fast-forward ten years, nearly to the day.

While I was talking on the phone with Griselda a few weeks ago, the conversation turned (surprise, surprise) to our teaching and our classes and our colleagues and our colleagues' teaching of their classes. Not shockingly, we've both had colleagues with whose methods we don't agree, and about whose teaching we've heard students say decidedly negative things.

"Isn't it funny," Griselda said, "that when students complain about a teacher not being very good or not being able to explain something at all, they take that to mean that that teacher is really smart? 'I can't understand Professor X at all...she's really smart, but I can't understand her lectures.'"

"I know!" I agreed. "The assumption is that if you can't explain something it means that you're operating at such a high level that you're unable to 'bring it down' to the level of the students."

We all know the stereotype of the absentminded mathematician whose dwelling in the realm of functions and formulas precludes any meaningful interface with the world around him. This hapless researcher wanders about the "real world" clumsily, muttering apologies to those he jostles and jabs with his elbows, even as he crunches numbers ceaselessly in his head. This professor may have difficulty in "bringing it down" to the level of his students, simply because he's often incapable of understanding just how little his students understand. (Incidentally, you'll find this type of teacher most often at research-intensive universities where the publish or perish mentality ensures faculty need not give a rat's patoot about teaching, and where even if good teaching isn't actively discouraged it's certainly neither actively encouraged.)

There's a different sort of delinquent educator, though, and one that's much more common at schools like my own: the one who has become detached from her own discipline to the point where she's no longer engaged in active research; who has ceased the active pursuit of new knowledge in her discipline and so has lost the ability to discern, to analyze, to interrogate the stuff that is the quintessence of her field; for whom academic inquiry has become static and devoid of new and novel points of view...for this one teaching will be an arduous and sometimes insurmountable task, as she will find it difficult to show her students anything more than an unchanging road map. If a new and more convenient highway is built, she may stubbornly drive on down the old routes as though unaware of the new one's existence. Who knows what sights she and her students might miss?

For this reason I believe that the highly active researcher who values teaching above all else will make the most effective educator. Let research dominate and one risks becoming an ivory tower-dwelling hermit; let research die away and one risks becoming a theorem-spewing robot stuck on autopilot.

This is an oversimplification, to be sure, and as there are exceptions to every rule so we each will be able to identify examples that defy the schema I've laid out above. Nevertheless, the rule is proved by its exceptions, and time and again I've noticed that my colleagues who excel in the classroom are generally those who excel as researchers in their respective fields.

The above observations suggest the following blueprint for teaching excellence:

An excellent teacher is one who

1. is unafraid of professing ignorance and who can confidently confront that ignorance publicly with

2. a rich skill set developed in the course of active disciplinary inquiry, and who

3. values her students' understanding above all else.

Let's see how well this blueprint poses a solution to the following question: "How can someone not trained in writing instruction provide effective writing instruction to his students?"

Following the blueprint mechanically in lockstep, were I to wish to teach my students how to write well, I would

1. admit to myself that I don't know a whole lot about teaching writing and be honest with my students about that fact,

2. take it upon myself to learn what I can about writing (in my discipline, or to learn, or to meet some other end) and the teaching of writing, engaging in the creation of new ideas on writing should the need arise to do so, and

3. keep in mind that the ultimate goal of this procedure is not to publish a paper on writing but to instill in my students a greater understanding of writing so that they may make use of the tools I've helped myself develop and so that they too can help themselves and each other to develop their own tools.

Note how process trumps product, particularly in this last point.

Does this seem a satisfactory solution to the problem I posed above?

I think so.

I have to admit that I'm really thinking out loud here, but it seems to me that the best teacher is a courageous learner, and that as each of us is fully capable of learning should we dare to, so too each of us fully capable of teaching.

To the point I'd originally meant to address, at the risk of belaboring it: any person well-trained to perform in her discipline (whatever "performance" may there mean) will be well-trained to instruct her students in that performance, so long as she keeps her own performance skills sharp. As "performance" in nearly every discipline involves the creation of a textual record of some sort, any able and active disciplinary performer will be well-trained to teach her students to write about her discipline. Indeed, who could do a better job than she could? That is, who could better teach math writing than a mathematician who is skilled in the use of writing to perform mathematics?

Put this way, the whole question of "qualifications" becomes a silly one on its face, and the idea of "writing in the disciplines" makes a hell of a lot of sense.

(As an aside I might note that perhaps the theory above could be used to prove qualifications to perform other disciplinary duties as well: who better than a sociologist to train students to use statistics as they would be used in a sociological setting? Who better than a chemist to train students in the physics that describe the commonest molecular interactions that occur in a chemical lab? How far off-base am I here?)

Perhaps one reason "qualifications" came to be questioned in the first place is that all too often we hold to very narrow and circumscribed notions of "writing" and "writing instruction" in the first place. If we demand that all academic writing take the form of five-paragraph essays whose construction is governed by a rigid set of rules, we might then consign all writing instruction to the realms ruled by composition theorists and rhetoricians.

But not all writing, not even all academic writing, takes this form. There are many more modes of writing than there are disciplines in which one can write, and we forget this at our own peril: one would never write a policy paper where a lab report is required, and a poem will generally not do for a mathematical proof.

Nevertheless, it's not always easy to remember writing's rich diversity. Even the "experts" may forget. I'll have more to say about this in this series's next chapter as I ponder the steps and missteps my colleagues and I took as we attempted to design a rubric for assessing students' mastery of writing in a particular discipline.

For now, as ever, I invite your feedback on my rambling thoughts. I came further than I'd originally hoped to in this post, and I'd really be interested in hearing others weigh in.

Tuesday, December 23, 2008

Chapter 4. How am I writing?

This essay, the fourth of an intended twelve-part series on writing instruction (and its parallels with math instruction), deals in part with an issue raised in the last essay in the series. Namely, what happens to writing instruction when first-year composition courses are done away with? Whereas the emphasis in the aforementioned essay lay on the changing roles of faculty in the event of severe shake-ups in curricula and course scheduling, the emphasis here will lie on writing instruction.

Several years ago, when its Integrative Liberal Studies (ILS) program was first implemented, our school opted to scrap half of its first-year composition program. In compensation for the lost semester of writing instruction, all first-year Liberal Studies Introductory Colloquia (LSICs), which are taught by faculty in disciplines and departments across the university, were automatically designated as Writing Intensive (WI) courses.

How good a substitute for the missing semester would these courses prove?

Some of my colleagues objected (and still object) to these courses' WI designation, claiming that faculty who are not trained to teach writing have no business in fact so doing, and that trained rhetoricians will do an incomparably better job of imparting writing skills on young college students. On the other hand proponents of writing across the curriculum and writing in the disciplines indicate that the LSICs expose students to authentically discipline-specific writing conventions, and that no one could do a better job at this than the practitioners of the respective disciplines in which the LSICs are run. (The next essay in this series will have a bit more to say about these points of view.)

Nevertheless, the sentiment among the WI folks of late has been that the LSIC instructors have as often as not been failing their students when it comes to providing meaningful writing instruction: where intentional instruction is given at all, it often focuses on the mechanics of writing (e.g., grammar and spelling) and not on substantive issues such as audience, tone, writing as a means to learning. Evidence for this failing comes not only from student/faculty scuttlebutt but from various data collected during the first year of the writing assessment study my colleague Lulabelle directed. (In particular, the rubric constructed by the participating LSIC faculty was weighted quite heavily towards mechanical issues, and the syllabi collected from these faculty showed little evidence of robust writing instruction. In fairness, the rubric constructed by the participating writing-in-the-disciplines faculty suffered from critical weaknesses of a different sort, and these faculty members' syllabi were little better, by and large, than those of their colleagues leading LSIC courses.)

Why these weaknesses? I.e., why is it that these courses' instructors are often providing what composition theorists would describe as substandard writing instruction? There are microcosmic issues at work here, as well as some broader macrocosmic ones. The former affect individuals and departments, and ultimately determine which faculty members end up leading the LSIC courses; the latter affect the nature of the LSIC courses themselves and the response that the faculty, as a body, has to them. Ultimately both of these kinds of forces stem from the structure of the ILS system as a whole.

What of the microcosmic forces? As I just said, their genesis in the structure of the Integrative Liberal Studies program itself: as it is desirable that LSICs be offered in every conceivable discipline, and as it is desirable that all of the university's faculty bear an equal share of the burden of providing the LSIC experience, every department in the university is expected to offer its fair share of LSICs.

But who in a given department is going to teach them? While there are some who will gladly volunteer to teach an LSIC, there are as many or more who will resist doing so. Given that the ideal LSICs will have minimal prerequisites (thereby making them accessible to as many first-year students as possible), offer authentic engagement of rich course content, and fulfill the university's WI requirement, they are challenging courses to teach and even more challenging ones to teach well. Moreover, the ideal LSIC instructor will show true passion for the subject matter the LSIC treats, but crafting a course about which ones feels truly passionate while remaining within the confines of the LSIC's structure can be a challenge. (For example, regular readers may recall an anecdote related by my CWPA colleague Leona back in September, as retold in the second of this series of essays, and in which she told of a fellow instructor of writing who lamented that she'd not had a chance to teach a literature course, despite her earlier assertion that she was all about first-year comp courses.)

Another, more pragmatic factor: those students enrolled in LSICs who have yet to choose an adviser are by default assigned as advisees to the instructor of their LSIC course. As a result, those faculty teaching LSICs are laden with considerably higher numbers of advisees, and in particular, more difficult-to-advise non-major advisees, than are their non-LSIC-teaching colleagues.

As a result many department chairs find themselves twisting their colleagues' arms in order to get enough LSICs on the books to satisfy the administrative powers that be. It doesn't take a learning theorist to explain that a willing instructor is going to do a much better job of teaching a course than a nonwilling instructor will do.

And what of the macrocosmic forces? Well, as I hinted at above, not everyone has bought into the ILS system in the first place. Proponents and opponents alike will agree that the ILS system is unwieldy and cumbersome: to explain it in moderate detail takes eight full pages of the latest course catalog (see pages 51-58 of the on-line version of the AY 2008-09 catalog). Not counting the required intensive courses, the student will put 47 credit-hours of work towards fulfilling the ILS goals.

In fairness, some credit-hours can be double- or even triple-counted; for instance a student might enrol in a single 3-hour course in order to satisfy simultaneously a Quantitative-Intensive requirement, a Cluster requirement, and a Lab Science requirement. However, "accounting tricks" like this make course selection seem more like a game or a strategic military move than an exercise in personal or intellectual development.

Nevertheless the ILS system is byzantine and often arbitrary; many feel it was implemented too hastily, while others bemoan the fact that it was implemented at all. The opponents of ILS are numerous and some are powerful, and I believe that some of these folks promulgate the view that the system's components and requirements are not to be taken seriously.

Note: In the interest of full disclosure, I am not an opponent of the ILS system as a whole, as one might expect knowing that I serve on the ILS Subcommittee for Writing-Intensives. I do, however, feel that the program was implemented too hastily: it was thrown together in its entirety all at once, without sufficient attention paid to its outcomes and impacts. I feel that certain of its components have proven more successful than others, and I would recommend phased elimination of some of the less successful aspects of the program, in particular the Cluster system. On the other hand, I feel that the Intensives (Diversity, Information Literacy, Quantitative, and Writing) all serve useful roles and should remain in place, although I believe much more careful management and oversight of these Intensives must go on. To put it bluntly, some of these Intensives need to get their shit together.

So what's the upshot of all of this? What havoc do these forces wreak on the writing-instruction that goes on in LSICs?

Because LSIC instructors are as often draftees as they are volunteers, and because they do not actively have to seek WI approval for their courses as instructors of any other WI course would have to do, and because they interact with often influential and powerful peers who pooh-pooh the importance of the ILS system as a whole, a good number of LSIC instructors are simply overly complacent about their duties as instructors of writing. I don't claim that this is the case of every LSIC instructor, but undeniably a fair number of our first-year students are receiving writing instruction (or, tellingly, are not receiving writing instruction) from faculty who see little reason for providing that instruction in the first place.

How widespread is this phenomenon?

I don't know.

And I don't think we're going to know any time soon.

We're a year and a half into a two-year assessment of our school's WI program, yet I don't believe we could even hope to answer that question through our study: those LSIC instructors who took part in the first year of the program (and those who are likely to take part in the final semester during Spring 2009) were highly self-selected; they're the ones who already recognize the importance of writing instruction and are therefore likely not among the ranks of the complacent.

For the time being let's assume that complacency exists, regardless of our powerlessness to measure its extent. What can be done to combat this complacency?

In May 2008 Lulabelle and I put together two day-long faculty development workshops on writing instruction; one day focused on writing in the disciplines, the other on writing instruction in LSICs. We tailored the goals and activities of each workshop to the audiences we hoped to reach. For instance, in the LSIC workshop we focused our efforts on helping participants understand the role that writing serves as a learning tool (emphasizing writing process over writing product), on guiding participants through construction of well-staged writing assignments, and on providing meaningful (not simply mechanical) feedback on students' writing.

It was a start. As one might expect, the LSIC workshop participants were noticeably less engaged than their colleagues in the disciplines workshop, but I still feel that the former get-together was a fruitful one. Similar and frequent faculty development opportunities exposing LSIC teachers to the ideals of first-year writing instruction will be crucial. My colleagues and I on the WI Subcommittee also hope to schedule meetings with interested departments in order to apprise them of resources we and the University Writing Center can offer their faculty as those faculty begin to craft WI courses, including LSICs. Moreover, through the nascent IWIn (Integrative Writing Initiative) I've been working on for a while now with several of my colleagues from across the campus we should be able to nurture further support in the form of Faculty Writing Fellows (at least, if Lulabelle has anything to say about it).

It's a tough row to hoe, but hoe that row we will.

Before I end this essay I should acknowledge that much of what I've written about here applies as much to WI courses in the disciplines as it does to LSICs; the primary difference between these courses and the LSICs is that for the former writing-intensive status must be actively sought and thus the petitioning faculty member has taken it upon herself to craft a well-structured writing experience for her students. Even if she has not taken part in any formal professional development related to writing instruction, she has submitted her plans for a WI course to a body of her peers who have been recognized as able assessors of writing instruction. Moreover, those faculty who have not themselves applied to receive writing-intensive status for the WI course they are teaching are generally apprised by their department chairs of the nature of writing instruction expected in a WI course. This circumstance arises, for example, when the instructor is one of several people who teaches a course that has received "blanket" WI approval, regardless of the course's instructor.

My next essay in this series will treat an issue that relates closely to the one dealt with here, namely, the Reluctant Instructor of Writing: how is it that someone not trained in formal composition theory can serve as an expert instructor of writing? As you may expect, my response to this question will deal primarily with writing in the discipline, the sort of writing any disciplinary expert should feel eminently confident in approaching. Moreover, I will do what I can to establish parallels between writing instruction and mathematics instruction. In so doing I will bring up a question about which I've given a lot of thought: who makes the better math teacher, the weaker mathematician or the stronger one?

Until then, as always, I invite your comments and your feedback.

Tuesday, December 16, 2008

Happy holidays

Underneath this year's Christmas tree: a three-to-seven percent budget cut campuswide.


First in line for the chopping block: adjunct salaries (and by extension ordinary faculty release time) or operating budget?

Our mission: to teach more students in bigger classes with tighter budgets and fewer resources, while we forgo our own professional development and opportunities for relaxation and disengagement from our all-consuming careers.

And by the way, happy new year.

In other news, the "just-in-time" workshop (that's actually how we billed it) on developing and implementing writing-intensive courses that Lulabelle and I ran yesterday afternoon came off very well. We had four very interested individuals take part, and I felt our conversations were elevated and meaningful. It exceeded my expectations, and I think it was worth my time.

I realized a day or two ago that I've not yet filled out my own report card for the semester, as I've done at the end of each of the past few terms. Let's remedy that.

Abstract Algebra I?: A-. This is the second time I've taught the course anywhere, and the first time at UNC Asheville. I think my relative lack of experience showed now and then: occasionally I miscalculated my students' abilities, and every now and then I fumbled a definition or a description, and as well as I I know the material (probably because of how well I know the material!) I still found myself struggling to impart intuition for it here and there.

Nevertheless, the committees functioned more or less smoothly, the students' presentations were the best I've yet seen from an upper-division class, the energy in the both sections was frequently palpable, and 12 out of 29 of the students are continuing on with me to the course's second semester. Any one of these facts indicates some sort of success.

How about...

Precalculus?: A- there, too. I didn't have a bad run of it, considering this was my first time teaching it, ever. I don't mind saying I was scared about my perfomance in the class every so often, and lost sleep over it at least once (just a couple of weeks ago I spent a whole sleepless night worried about "coverage"). Ultimately, though, I think I pulled through: the projects were well-received, the classes animated and engaging enough to distort the students' sense of time (a frequent comment was that the 50 minutes seemed to fly by), and a substantial number of of the students felt comfortable enough to perform at the board with very little cajoling by the semester's end: by then I'd managed to get a room full of relative mathematical novices to overcome their collective trepidation and lead each other to better understanding.

My greatest failing was, not surprisingly, "coverage": I could have used another week. Hell, I could have used another two weeks.

As early as three weeks in I began to suspect that I'd eventually run out of time: at that point I was only at the end of the first chapter of the text, knowing full well that I'd ought to get through the first seven chapters. By the time we'd capped off the second chapter I knew that, even though our pace had picked up substantially, there was no way we were going to make it that far.


Minimal, I think. I know 7 of the 29 students will be continuing with me to Calc I next semester, and as all of these students are quite solid and as I know how it is that I conduct the first couple of weeks of Calc I (i.e., with a good deal of review of the skills from precalculus), I don't fear for these students' learning next term.

It'll be okay.

Oh, I guess I could also rate my performance as a Senior Seminar mentor: A. That grade, however, belongs to all of the students with whom I worked, too. It was their willingness, as well as my own, to meet on their own time and go over their own and each others' talks well before they were given that helped us polish them up and make them the wonderful talks that the were. Moreover, their written work was fantastic. Thanks, y'all, for making my job such an easy one. May I ever have such intelligent, diligent, and cooperative students working with me in this course!

Okay, it's late, and tomorrow is another day. Until then, adieu.

Monday, December 15, 2008


Ten minutes to go until the end of the Precalculus final exam period...five students remain...oh...four.

Too early to tell how they did based on exit times, we'll see when I sit down to grade 'em all tomorrow.

Sunday, December 14, 2008

Chapter 3. Whither or wither?

This is the third chapter of my intended twelve-chapter series of essays on writing and writing pedagogy inspired by my colleagues at and participation in this past September's Carolina Writing Program Administrators (CWPA) conference at the beautiful Wildacres retreat center. (For the first chapters in this series, see here and here.) Since I last wrote a post in this series, much about our nation has changed, especially as regards its economy, and I believe the changes we've seen directly affect the issues I hoped here to raise.

Perusing the second link above you'll note that I closed the second essay shortly after asking the question "should a school entirely eliminate its first-year composition requirement, whither the expertise of those faculty formally trained in composition and rhetoric?" This question concerns the redundancy of comp/rhet faculty, should cost-cutting mandate a school's writing program be eviscerated.

This issue has now been magnified and universalized: our country's economic tailspin has now has left no sector unaffected, academia included. Private school endowments are drying up, state funding for public schools is disappearing, killed by a thousand cuts. Some schools now struggle to pay for things as fundamental as heat, lights, and other electrical equipment, hiring freezes are chilling the academic job market, and unfilled faculty lines are simply dying away.

In this environment nothing is certain, and nothing is safe. While the recent past has seen more courses being taught by adjunct faculty, now those adjunct faculty are being let go, and as the number of course sections being taught dwindles the number of students enrolled in each remaining course by necessity goes up. In my own department an upper-level stats course (the first upper-division course scheduled to be taught by my newest colleague, Kiri) was scrubbed due to low enrollment. The few students who had registered for it were forced into courses that, though they may impart a few useful skills, are hardly those offering them training in the skills most pertinent to their future careers.

Of course, as any above-average educator knows, the bigger the class, the lower the quality of instruction. This proposition proves as true for courses in writing and math as it does for those in any other subject. "How can I be expected to teach a writing-intensive course with 27 students in it?" my colleague Bea asked me at a party last night. "This last semester I had six in the same course, and it was wonderful. They had their own individual projects, and they all worked together on one class project. Now I'm going to have to come up with some way of putting them in teams or something."

I feel her pain: I've got 25 registered for my Foundations class right now, and I've chosen this semester to implement a new component to the writing instruction in this course.

Meanwhile the economic recession is likely to make more and more students opt for a public education over a private one. I'll bet dollars to donuts, therefore, that the next few years are going to bring yet greater pressure to grow on the nation's state schools. UNC Asheville is unlikely to be immune, though no doubt we will (and should!) continue to chant the mantra "small by choice...small by choice...small by choice" even as ou sister schools, like East Carolina, NC State, and UNC Greensboro, grow by leaps and bounds.

Fewer teachers, fewer classes, and fewer resources will all be brought to bear the burden placed on our system by a greater number of students. The question will be not "whither?" so much as "wither?"

Let's think locally: what's likely to go down in our own home departments?

This past term saw our scheduled search for a new applied mathematician get canceled (it was one of over a dozen canceled searches campuswide). Though the administration has promised that all searches suspended this year will be given a chance next year, I find it hard to believe that next year's budget will be strong enough to support the weight of both this year's leftover searches and next year's fresh ones. In all likelihood, the 2009-10 budget is going to be weaker than the 2008-09 one. A best case scenario involves us picking up our search where we left off; at worst our vacant line will simply dry up and wither away, leaving us a colleague short and with classes to cover.

What, then, goes? Do we raise enrollment caps, moving 20 to 25, 25 to 30, and 30 to 35? Or do we shift schedules so that every now and then one of us takes on 14 hours instead of 12? Or do we simply scratch a section or two of Nature of Mathematics, or Precalculus? Or do we cut Precalculus free altogether, leaving it to be ably taught by the community college on the south side of town? (Interestingly enough, the area's community colleges are not suffering through a hiring freeze right now.)

This says nothing of the upper-division courses that serve our majors. If we choose to keep covering the entry-level courses that serve the remainder of the school, the personpower we've got left over to teach the upper-level courses is diminshed. Would we be forced to keep our number of majors artificially low? At present several of my colleagues and I actively recruit majors from among the ranks of the first- and second-year students: we're an open, suppotive, and welcoming department with a "big tent" philosophy...will the coming years force us to adopt a more chilly attitude?

I don't know the answer to any one of the questions I raise above, but I'm certain the coming years will offer some response.

To return to the question I'd meant to ask originally, whither? Whither the expertise? What happens when trained rhet/comp are left out in the cold when first-year comp courses are cut? "Well, a lot of them would be assigned to writing centers," my friend Eomer (currently an adjunct in the English Department at Furman University in nearby Greenville, SC) offered when I asked him the question.

"What if their schools don't have writing centers?"

"Yeah, Furman doesn't."

What then?

At the CWPA conference someone suggested rhetoricians could find work as "facilitators" who could advise faculty in writing instruction. In such a role they could help faculty members to integrate writing into their courses, to design appropriate writing assignments and to train the faculty in providing useful and meaningful feedback on their students' written work. Thus in some way they'd be "just-in-time" writing center directors, offering some services cognate to those writing centers offer now but on a case-by-case basis.

This presupposes a demand for these services. Irrepressible optimist that I am, even I have a hard time imagining that there'd be enough call for an on-the-spot rhet/comp expert to warrant the school's employment of such a full-time member of the faculty. (The story may have a different ending at larger schools.)

Is there a parallel postulate for math and mathematica sciences? Should Precalculus be stripped from the curriculum, where might the adjuncts teaching this course be sent? The first stop would likely by the Math Lab or something like it, the mathematical equivalent, in many ways, of the Writing Center.

The same reply can be made: "what if my school lacks a math lab?"

Well, shit.

Is there then room for a rotating tutor, a one devoted to providing "just in time" assistance to students in danger of failing out of required calculus courses?

I'm not sure that these situations are cognate to one another: while on the one hand English experts may train for years to earn a specialized degree qualifying them to teach rhetoric and composition to college kids, hardly ever is it that any mathematician trains to teach entry-level college math courses, and those courses only. While Precalculus could be cut from the college curriculum, calculus courses are highly unlikely ever to feel the axe, and those who are sufficiently trained to teach Precalc are equally able to teach calculus itself, and these folks are therefore assured a modicum of job security.

I don't know. I'm having a hard time wrapping my head around all of this. As I said at length above, I believe that the current economic downturn (to put it euphemistically) has exacerbated the situation: stemming the loss of first-year comp courses is hardly the most pressing item on the typical English department's agenda.

Okay, it's a hair on the short side of eleven o'clock, and I've got an early start scheduled for tomorrow (on which my Precalckers cap off their final exam) so I'd best say good night.

The next essay in this series of twelve presupposes that your school has a writing program of some kind (WAC, WID, writing center, first-year comp...whatever form it takes), and that you're actually interested in asking the question "how am I doin'?" I'd like to turn to the area of assessment and try to understand just how it is one can tell if one's program is purring along at all perfectly.

As always, those of you who are still reading along should feel free to offer up your insights on the topic of this past post, or on that of the one to come. I.e., writing folks: I need your help!

Friday, December 12, 2008

A ream o' reading

Today I tortured our department's printer by asking it to reproduce six weeks' worth of progressively more sophisticated reports crafted by this past summer's REU students. I hope to have some time in the next few weeks to sort through this mass of data and learn a bit about the development of the research students' writing skills over the course of the program. (Having spent most of today setting up next term's classes' websites and syllabi, I'm far enough ahead of the game that I can afford a few days of textual analysis.)

The data comprise end-of-week reports for weeks 2 through 7, a weekly report from each of the the eight students. The first week's reports are highly tentative, and only three of the eight concern what would later prove to be the respective student's summer project (the others concern sample topics the students gave some thought to investigating but soon abandoned).

What variables will I be paying attention to? Most of the following should be familiar to anyone who's taken a class with me during the past couple of years.

1. Mechanics. Is the raw .tex file, when available, compilable? Has the student been able to produce a more or less error-free LaTeXed document? Has she avoided common mistakes like "dumb quotes" and misuse of the math environment? Has she used the second person, plural voice common to mathematics papers? Does her document conform to the formatting and typographical conventions of a professionally-written mathematics article? (E.g., use of section headings, figure captions, and appropriate intertextual and post-textual citations.)

2. Composition. Has the student begun by laying out the context for the problem to be studied (history, prior work in the area, etc.)? Does the student then indicate what he will show in the course of his article? Does the exposition proceed in a clear and logical fashion from this point on, culminating in one or more primary results propped up on auxiliary ones? Does the student indicate applications of his work, or directions for future study? Do the aforementioned elements interact smoothly to create a single coherent text?

3. Clarity. Does the student make effective use of notation and teminology, including appropriate use of existing terms and apt introduction of new terms? Does the student eschew jargon for jargon's sake and avoid the passive voice? Are sentences manageably short? Has the student included diagrams where needed?

4. Completeness. Has the student answered, or at least addressed, all obvious questions? Has he ensured that his proofs consider all cases?

5. Correctness. Are the student's proofs correct? On a more pedestrian note, is the student's grammar correct? (Here we speak of both standard English grammar and the "mathematical" grammar that attends to sentences formed by "expanding" mathematical notation, replacing it with the corresponding verbatim text.)

6. Audience. Does the student's writing address the appropriate level of reader? (The students were asked to write as though their work would be submitted to a mainstream math research journal. In one case the finished product, a slight modification of the seventh week's report, was submitted, and very quickly accepted, to such a journal.)

In the hour-long course of printing the articles out I noticed unmistakable development along a few of these axes; greater perspicacity will be needed to discern development along others.

I've got my work cut out for me. Between this project, my two papers on math poetry (feedback on a draft of one of which I hope to receive from Lulabelle very soon), and three ongoing math research papers, it's going to be a busy break.

Before I go, in the interest of checking as many items as I can off of my recent "to-blog" list, I thought I'd give a brief update to my long-ago note about how much online homework systems suck.

One of my students in Precalc who's put up a mighty struggle this past semester came to me and complained about how she felt the homework system had kept her from really understanding the computations that she'd had to perform. "You just don't get the sense of it that you do when you write it. When you write math, it's like you really understand it, you're forced to think about it." I couldn't agree more.

Though I've encouraged my Precalc students over and over to do their computations by hand on scratch paper or better yet in notebooks (which they can refer back to later should the software not accept their answers), for many of them it's tempting to do as little of the work as possible by hand. Some students will scribble a few scratch marks on their paper before completing the computation in their heads and transcribing the solution directly onto the computer screen. The thought process that attends to this disjointed series of events is jumbled and chaotic; it's no wonder the students who do their work in this manner come away with an incomplete understanding of the material.

Writing is a tool for learning, and online homework systems diminish the efficacy of that tool.

Moreover, as the semester's gone on, this particular system's rigidity (already discussed in the post linked to above) has become more evident. It won't accept answers in forms that I feel are entirely valid. One egregious instance arose in a section on polynomial factoring and root-finding. Of course, certain polynomials have complex roots that appear in conjugate pairs. Let's say, for instance, that 1+i and 1-i are two roots to a given polynomial p.

Educo would require you to enter the roots individually, separated by commas: "1+i,1-i." Just so. If you enter the roots as "1±i" you're assured of receiving an "Incorrect" mark, despite the fact that this section's answer palette contains a "±" button, coquettishly inviting the user to press it.

It's asinine. The rigidity of thought that this sort of functionality encourages is sure to stifle any budding mathematician's creativity and curiosity.

These technological issues aside, the text is awful: it's full of errors, unnecessarily complicated algorithms the student is encouraged to memorize, dense and unintuitive exposition, and nonstandard notation. The text is unlikely to make converts of those who don't hope to go further than Precalc in their mathematical explorations. Moreover, its often addle-pated terminology and notation is likely to prove a minor stumbling block to the students who plan to continue on to Calc I as they try to build a bridge from the math Man M. Sharma's text has mapped out for them to the math Gilbert Strang will introduce.

Yes, folks, after much hemming and hawing, our department's sticking with Strang's free textbook next semester. While most of the people who used it to teach Calc I this past term (with one notable exception) felt at best ambivalent about it, we've decided to give it another chance. I've yet to form an opinion on it. It should prove a more challenging read for the students, but I've had success with challenging texts in the past (Rotman's algebra text is certainly a tougher row to hoe than Gallian's, but I think my Abstract class has come off quite well)...besides, a good teacher can teach effectively from any text.

I'll leave you with a final thought about teaching. I truly believe that the following statement is true:

If you take the trouble to learn your students' names quickly, show that you care about their learning, and do your best to figure out their individual learning styles as soon as you can, you've mastered 75% of what it takes to be an excellent teacher. (I don't know if 75% is the right number, but it seems like a good ballpark figure.) The rest is practice and perfecting of your various pedagogical skills.

Thursday, December 11, 2008

For real this time

What a strange semester this has been.

It's almost over now. We're already two days into Finals Week, I've got half of my grades submitted, and faculty wrap parties are popping up like badgers in a Weebls video.

I told Griselda the other night that it's been one of those running-to-stand-still semesters.

Maybe it was my relative unfamiliarity with both of my classes (first time ever for Precalc, first time here for Abstract) that kept me on edge all term long.

I just don't feel like it's done yet.

Somehow I feel like it never began.

Have you ever watched a movie that, twenty minutes in, didn't even seem to have started yet?

I spent almost two hours this morning in a meeting with Casanova and Lulabelle as we attempted to hammer out the dings and dents that marred the pre- and post-surveys Lulabelle and I and several others used in last year's writing assessment project. The goal is to ready a new pair of instruments to use in various classes next term. You guessed it, my 280 students will get to be guinea pigs again.

At Lulabelle's suggestion, we cut the pre-test in half by removing discipline-specific items. "I can think of two really good reasons for doing that," I said. "First, our ultimate goal is design an instrument that is discipline-independent anyway, and second, I'd find it interesting to see what sort of general writing gains students perceive having received quality writing instruction in the disciplines."

Harrumphs of agreement.

We added a few items, changed the wording in a few others ("I hate the phrase 'that professors like,' " lamented Casanova), and tweaked the demographic questions, particularly those regarding gender, so that they became less othering and isolating. "And we don't need to know about their AP and IB experience," we agreed. Out it went.

The new survey should be about half as long and much less cumbersome. Moreover, if we run it on Moodle (the online course management software UNC Asheville uses), the data collection will be a snap.

I'm still waiting to get some of the data from last year's study. I'd really like to know how a faculty member's own field of study affected her application of the course rubric to classes in various disciplines; I conjecture that the students' scored mean is directly related and the students' scored variance inversely related to the "distance" between the discipline of the rater and that of the "ratee." That is, as a mathematician I'm more likely to judge physics papers more strictly, and to assign a broader array of scores to such papers, than would a poet.

And no, I'm not sure just how this conjecture could be quantified completely.

But does it need to be?

Tomorrow I plan on collating all of the writing products I gathered from this past summer's REU students. The primary question I'd like to answer in assessing their writing is: "can one clearly discern the student's trajectory from novice math writer to accomplished article author over the course of an eight-week program in which developing writing proficiency is a stated learning goal?"

And hey, in case you didn't know it, I've been teaching math a bit lately, too!

My colleagues and I all agree that this semester's Senior Seminar talks were of consistently high quality. Not one of the eight talks was weak (usually there'll be one or two stinkers). It's too early to tell how much of this improvement is due to the more rigid scaffolding my colleague provided the students in the form of in-class "practice" talks and writing assignments. I'll be introducing yet more structure to this writing component in next semester's installment. (I know a couple of my mentees from this past semester would have been happy with more clearly articulated guidelines for their writing.)

Shit, there I go, on about writing again. Sorry.

My Abstract Algebra students' presentations were also significantly stronger than those of most students I've had in upper-division courses in the past. Their success was a result of thorough preparation on their parts: I forced them to get their acts together early and start right away in choosing topics, finding references, and assembling thei talks. In the end I felt that only three of the 15 talks were fairly weak ones (C-quality or worse), and even these had silver linings. I was particularly impressed with the talks on point groups in chemistry, free groups and group presentations, and ordered groups.

Several days ago one of my Abstract students gave me some good constructive criticism on the committee system, about to enter its fourth semester next term. "There'd be times when I'd get my draft back from the committee and it would say 'great job!' and 'perfect!' So I'd hand it in, and I'd get it back from you and it'd have half of its points missing. That was really disheartening."

Yeah. "I understand what you mean," I said.

I told him that I'd take care to emphasize that the burden of verifying the validity of a particular proof or computation lies on the committee's members: it's their job to check the facts. That's a hefty responsibility, but one that I firmly believe they should expect to assume (how else are they to make of themselves mathematicians?). I told him that I'd take care to emphasize that I would be there as a "resident expert" should there be any dispute over the validity of a particular student's response. May my word be advice and not edict.

I'm retaining committees for both 280 and 462 (Abstract II) next term, and I'll probably introduce a modified system for projects in Calc I as well. 280 students will see a greater number of "dialogue" problems in which students are asked to construct mock expository exchanges between one another with the aim of better understanding tricky logical points or proofs: students have said consistently that these exercises are particularly effective ones.

For 480 I'll once again devote a day to abstract-writing, a day to peer-editing of students' papers, and a day to designing a multimedia presentation using PowerPoint, SliTeX, or Beamer. Tomorrow I'll take a little while to hammer out the 480 schedule, which is going to be tight: with 19 (!) students registered for the course, at least seven (!) days will be devoted to student talks alone; with the three days indicated above, we'll only have time for four or five faculty "model" talks, and students will probably have to start presenting before Spring Break, or very near to it.


The most drastic change to my m.o. next semester will be my introduction of LaTeX to the 280 students. If they're going to learn how to write mathematically, then, by gum, they're going to learn how to write mathematically.

After introducing LaTeX through the handouts and worksheets I've already developed for the REU, I'll introduce a "TeX this!" assignment like the one the REU students worked on for about an hour this past summer. Then I'll start infusing their homework with LaTeX requirements. I won't require them to TeX all of their homework: just as certain problems will be designated as committee problems, others will be designated as LaTeX problems whose solutions must be TeXed. (They'll receive a nominal amount of extra credit for TeXing the other problems.) The percentage of LaTeX problems will increase in each successive assignment, from one in four in the first few assignments to maybe two-thirds by the semester's end. I doubt the students will resist: LaTeX is easy to obtain, free to use, and damned fun once you get used to it. In my experience once students get in the habit of TeXing their work they never look back, and even the most typographically challenging documents are seen as amusing obstacles to be overcome.

Besides, I have no doubt that I'll be making my colleagues' (and my own!) grading substantially easier down the line. Imagine how jumbled and disjointed a student's non-linear mathematical thinking might appear, with a disorganized blob of exposition tacked onto the side and inserted with an arrow, and a stray sentence placed at the page's bottom beside an anchoring asterisk that leads the reader to this appendix from the main body of the text. In typesetting her work, the math student is forced to linearize her thoughts, to compose them well, to say what she wants to say in the right order, all in one place. Typing, a tool for writing, is by extension a tool for thinking.

That, and the student feels all the more accomplished fo having mastered a pretty snazzy typesetting tool.

I'm really looking foward to next semester.

I think I say that before every semester begins, don't I?

I just love what I do.

I hope it shows.

Okay, I'm off for now. More to come, more to come. Always more to come.

Until then, comments are appreciated. Take care!

Wednesday, December 10, 2008

Hey, check it out!

For the first time ever, Super Saturday's Math Discoveries class will be on-line in Spring 2009.

Today's best comment about my teaching received from a student: "You always made sure we understood how everything we'd already talked about fit together before you moved on to something else."

It helps to know what I'm doing well. I'll try to keep doing that in the future.

Thursday, December 04, 2008

To-blog list

1. The ways in which on-line homework systems suck, from a pedagogical point of view

2. Putting together a workshop on writing in the discipline of mathematics

3. Cramming a full-day writing workshop into two hours

4. Designing effective peer assessment techniques and activities for entry-level math courses

5. Overhauling the design of a senior seminar course

6. Making the most of elementary-school math enrichment programs, a.k.a. Super Saturday goes on-line

7. Writing assessment in mathematics curricula

8. Poetics as an investigative practice in the mathematical sciences

9. Ten more parts to a long-promised twelve-part series on writing instruction.

Wednesday, December 03, 2008

What's there to be said?

The cold winter months of 2005 were stressful ones.

My three-year gig in Illinois was coming to a close.

In the previous autumn I'd sent out several dozen job applications, to schools ranging from tiny Alfred University in upstate New York to the Harvard of the West, Stanford University, where maybe just maybe I could secure a second postdoc. Came December, and I started hearing tiny peeps: Cal State Chico had requested a phone interview (which I granted; I thought it went reasonably well), a colleague at Louisville had indicated that he'd seen my application and that his department might be in touch with me in the coming weeks, and a few other schools indicated they'd like to tawk. "Are you going to the Joint Meetings?"

I hadn't planned to. "Unless you're giving a talk in a special session, don't bother going," my Ph.D. adviser had told me three years before when I'd first hit the job market. "The only schools that interview there are the little ones, and you should be gunning for a postdoc." Like a good father, he wanted more for me than he'd had himself.

That was then, this was now.

Within the span of a few short days Seattle University, Carleton College, and UNC Asheville, all on my Top Ten list, contacted me and let me know they'd like to see me in Atlanta.

What the hell, why not? With only a week to go before the meeting, Maggie and I once again secured the services of Gisela, the matronly German retiree who was our regular dogsitter, packed a couple of suitcases, and with the first flurries of 2005 falling gently on the roof of our '97 Camry we began the 10-hour trip to Georgia's capital. (That it's only 10 hours from Urbana to Atlanta is somewhat surprising; it seems that it ought to take longer than that.)

I felt that my meetings with the three schools named above went well (clearly one of them went particularly well!), and although we were only there for half of the conference (I never actually registered!) we had a good time while we were there, catching a few interesting talks, seeing old friends, and putting together the first of what have now been four Annual Semiofficial Vanderbilt Mathematics Department Dinners.

I felt good about the conference, and was in good spirits during the northward drive.

Soon, though, bitterness set in.

Ned, my officemate of two years, was a highly talented number theorist who by the end of his first year at UIUC had already had an article in Inventiones and who was popping out papers at an impressive rate. I'm no slacker, but it was no secret that I put as much stock in my teaching as a I did in my research, so my publication rate couldn't compare with Ned's. Moreover, while offering fascinating and fun problems that are accessible even to talented undergraduates (thus making the field an ideal one for the focus of an REU), geometric group theory is not a particularly "sexy" subfield of mathematics, and its practitioners are not in unduly high demand. Number theory it ain't.

Hardly a day went by during January and February without our office answering machine recording a new interview request for Ned. Every day I'd trudge into campus through the snow, pull aside the heavy front door to Altgeld Hall, wind my way up the stairs to our office on the west wing overlooking the Math Library, and the first thing I'd see as I entered our office would be the blinking light on that goddamned answering machine.

"Hi, this message is for Ned Cochran...this is Joe Schmo at the University of Upper Iowa, and we were wondering if..."

Damn it.

The stress began to mount. I was a wreck. I never seriously thought that I'd be jobless, but what if I ended up having a to take a one-year appointment at a school with no research activity and a 5-5 teaching load, at $5,000 less per year than I'd been paid at Illinois? The market that year was better than the past had seen, but offered nothing close to milk and honey.

To help us kill the time our friend Kurt, an avid Trekkie, began lending us his Deep Space Nine DVDs, season by season. It took a few weeks to make it through the first set of disks, but as the pressure grew and I saw less and less of Ned (there were weeks when he had on-site interviews back-to-back-to-back and I felt like his secretary, piling sticky notes on his desk: "Prof. Gregson at Lower Quebec Superior College requests that...") Maggie and I quickened our pace. We finished Season Four in two nights.

"Can I come over and get Season Five?"

"Sure, dude. Rough week?"

Several of 'em. During which I felt impotent and useless. Somehow I managed to get a lot done: I continued to co-host our weekly radio show, I began finishing up the manuscript I'd soon be sending to my publisher, I started what would soon be two more papers of which I'm still quite proud, and I successfully put together my first (and so far only) grad-level course. How I managed all of this I'll never know, as I felt daily and nightly paralyzed by anomic and debasing stress.

As regular readers of this blog (I pity you, poor souls!) must know, this story has a happy ending. Once the clog consisting of the superstar scholars like Ned worked its way through the pipes, the second-tier folks like me (a better researcher than most "teaching" faculty and a better teacher than all but the rarest researchers, but not absolutely aces in either) had our go: the calls began to come. Within the span of two weeks at the end of February and the beginning of March I had six interview requests, from one of which grew my current position.

Happily. Ever. After.

Present contentment calms the waters of the past. Lacking the scarifying effect physical violence might leave on our bodies, psychic violence often can be forgotten. Trying times seem positively historical until those times are relived once again.

The past two months have seen me gripped with a paralytic torpor the likes of which I'd not seen in three and a half years.

I blame the economy.

And the Republican party.

And the general helter-skelter state of world affairs.

The last two months I've spent in almost biminutely refreshing sites like (who's ahead?) and (what're they saying?) and (hasn't he fucking won yet?!?), sitting zombified in front of my computer, obsessing on the electoral effect of out-of-work black Pennsylvania lesbians in the automotive industry.

And it wasn't just me. For two months just now, all was atwitter. Water cooler conversations were echoic, little more than he-said/she-said murmurs, gurgling trickles of rehashed political rhetoric. We all walked around dazedly and without conviction, as though all we did was rehearsal for the real deal, some grand pageant to be enacted a few months hence. We lacked motivation, and we were nervous. We fidgeted. Fingernails were made ragged and gnawed, eyes were rendered sleepless and puffy. We went to the edge, over it, even, and then we dangled there, gazing downward, pleading skyward, feeling our grip slacken as we sank...

Then we slept. If only for one night, we slept.

I slept for four short hours, drunk on a bottle of my lovely friends' very lovely red wine and on the excitement of a 21-hour day on which, as the Chief Election Judge for my electoral precinct, I truly feel I helped to usher in a new era.

We slept, and we're waking up now. I'm waking up.

What's gone on as I've slumbered?

The semester's nearly gone now. There are three class periods remaining in Precalc, and only two in each of my Abstract Algebra sections.

I've misjudged the amount of time I'd have for the former class, and I find myself cramming too much trig into the few hours that remain. I'm discarding all but the bare essentials, as I've got only a tiny duffel bag to serve for an oceanic passage. I feel rushed and uncomfortable.

Overall I've got mixed feelings about the way my first experience in teaching Precalculus has turned out.

As I've said in earlier posts, I'm glad I've been given the opportunity to teach the course, and I've learned boatloads from so doing. For instance, I've learned to take nothing for granted, even concepts that have become so automatic to me that I feel as though I understood them upon springing forth from my mother's womb. I've gained much more valuable practice in the art of using in-class team activities in lower-level mathematics courses. And I've had a chance to interact with students the likes of which I don't often meet in my other, higher-level, courses; namely mathphobes who really don't give a rat's ass about mathematics and who, once the semester has ended, have no intention of ever looking at another number so long as they live.

On the flip side, I've fallen in the mud a few times. I've muddled clumsily through explanations of things I've never had to explain before, I've faced attendance problems that dwarf any I've seen in classes I've taught in the past, and I've reached the semester's end feeling saddled with a slight sense of resentment. Do I resent them? I don't know. Do they resent me? I don't know. I could certainly be mistaken (I almost always have an end-of-semester freak-out about my students' perception of me as a teacher: "are my evals going to suck?"), but I feel that there's a chill, a distance, between me and them.

I've worked as hard as I've known how to in order to make this class a success...but have I done all that I could have done?

I don't know.

Maybe I just have to accept that most of the folks who took this course came in with very low expectations, and that if I've helped them to go even an inch beyond those expectations, I've succeeded.

Student presentations began in the second section of Abstract Algebra today. Derrick and Miguel started us off with a bang, giving two unintentionally interlaced talks on fundamental groups and free groups. Their talks were technical, clear, well-timed, and well-organized. I hope the next couple of days will bring more presentations of this quality.

Twelve of this semester's twenty-nine Abstract I students are continuing on to Abstract II with me in the spring. I'm looking forward to it already. (I might also mention that several of my Precalc students are on board for my Calc I class, too, and my 280 course is filled by wonderful blasts from the's going to be a great semester!)

What else has happened while I've slumbered?

Hell, what hasn't?

Just as in the winter of 2005, life's gone on even as I've numbly watched it pass. There's a lot to be said, but I'll say it later.

For now, it's late, and I've got another long day tomorrow.

Wednesday, October 22, 2008



We're all tired.

I can feel it, I can see it.

Absences are up in all of my classes (not a day goes by without a handful of students missing from Precalc, Godzilla movie marathons or no), and my students are all sick with the second major wave of colds to sweep across campus this semester. My colleagues and I wander around the department with glazed-over looks and blunder bumblingly through committee meetings.

There's more to it than a change of seasons or an onslaught of midterms. There's more to it even than the dip in the Dow and corporate profits.

I admitted to a friend the other day that I feel as though I'm suffering from an existential paralysis, and I don't think that I'm alone in that feeling. The world is holding its breath, and we're all standing here blue-faced, wondering what's going to happen next.

The moon's crawled closer to the sun each morning this week as I've made my daily trek to campus. Dawn breaks around seven or so, with blots of orange cutting through a crisp crepuscular fog. I like this time of year: the mornings are fresh, and though it's cool it's not yet cold, and I arrive at my office invigorated.

I have to admit that motivating my morning Abstract class has been a challenge for me this semester. The students are by nature quieter than those in the afternoon section, and it's often hard to rouse them. Nevertheless, they're a strong bunch, and they're quick to learn. Their committee presentations were wonderful this morning; not one of the three committees fell into the "show 'n' tell" trap of solving the problem for the rest of the class. One committee made explicit reference to the Four Cs rubric, breaking their problem down along the axes laid out by the rubric.

"Honestly, are many of you finding the Four Cs a useful tool?" I asked. "I put it out there as a tool to use, but I certainly don't want it to simply be an exercise in demagoguery. If there's anything I can do to make it better or improve upon it for future classes, let me know."

There was murmured agreement. "I use it to help critique others' work when I'm on a committee," Norbert said. "Since I'm planning on being a teacher, it really helps me to be able to grade others' work. Having some in front of me to structure my comments makes it that much easier." Others agreed, and though it sounds like no one's using the Four Cs explicitly when they're writing their own work, they're often keeping it in the backs of their minds.

The afternoon section, bigger, louder, raucous and rambunctious, offered up shorter committee reports too. They gave fewer details, and seemed a bit more timid in their responses. I wonder how much their trepidation has to do with the size of the class? I wish they'd be more bold, more descriptive. It's hard, it takes practice, but oh, how the practice is repaid!

Midway through this class the torpor returned, and I felt horribly tired. "Are you okay?" Nadia asked as class ended and people began to stow their books and take their leaves.

"I'm just really tired," I admitted.

"You don't seem tired when you're teaching," she told me. I took it as a compliment, whether it was meant that way or not. She's one of the wonderful students in our program who makes my job as pleasurable as it is.

After nearly dozing off during a frankly awful talk in the senior seminar (students: to say nothing about the poorly-organized slides and the too-detailed computations, never ever ever run over time in your talk; it's the singe worst thing you can do and while they'll forgive nearly any other sin audiences will rarely forgive you for those extra minutes), I had an a truly electrifying run home, and for the last few hours I've felt refreshed.

Just now as I was lying on the couch I gave some thought to the third chapter of my stalled series on writing pedagogy, and I promise it will come soon.

For now, bed, with a promise of less tiredness tomorrow.

Saturday, October 11, 2008

Saturdays are super

Week 1 of the Fall 2008 Super Saturday schedule!

This semester's class is a bit more balanced than last semester's. While Spring 2008's class had 10 students, all boys, this morning's class had 13 students, 6 of them girls. The better balance makes for a calmer class, as eight- and nine-year-old girls are generally a bit more staid than their masculine counterparts. They were very well-behaved today, and even though my only assistant was Zora (a high school senior who's working with me this semester in order to provide experience for her graduation project), I had no trouble at all corraling them. Moreover, the class seems like a strong one in comparison with the last couple that I've had, so I might be able to dust off the "Codemaking and Codebreaking" lesson, a fun but tough one which goes over well if the kids are up for the task and fails pretty miserably if the kids aren't quite up for the challenge.

Today it was the ever-popular "Build Your Own Fractal" lesson, in which we first play with the idea of mathematical patterns, then share in drawing some of the simplest of fractals (multiply transected triangles and squares, Sierpiński's triangle, etc.) and watch a few Mandelbrot zoom videos on YouTube before the kids go freewheeling for a half hour, designing their own self-similar patterns. We closed with twenty minutes of building pyramids, the kids (often clumsily) taping together their own three-dimensional analogues of Sierpiński's triangle.

The kids were well-behaved, attentive, shared the limited supplies (tape, glue, and scissors) responsibly, and even cleaned up after themselves at the very end without being prodded to. It was nice!

I've yet to read the final drafts of my Precalckers' poems, but I've glanced at a couple of them and noticed that some have changed significantly. Change is generally good when it comes to an iterated assignment. I'm excited to see how the students incorporated my feedback. I have a hunch there may be several very strong showings. With their permission, I'll be sure to share their work on the blog.

Okay, Maggie and I are off to a soirée at our friends' place. Au revoir!

Thursday, October 09, 2008

The promised post

So,'s about them homework committees?

They're doing well. I don't think I've been challenging them enough. For instance, members of two of the six (three per section) committees who offered up reports in yesterday's classes professed that they really didn't know what to say, as the problems they'd dealt with were so straightforward. Eventually both of these teams, who worked on the same problem in different sections, delivered some variation of "It's an if-and-only-if proof; make sure you prove both directions."

One or two of the committees slipped momentarily into "show mode," essentially solving for their classmates the problem they'd been assigned. "Please remember," I gave them a gentle reminder afterward, "that it's not necessary, nor is it even best, for you to solve the problem you've been given." While one ought to offer some feedback and direction by indicating trouble spots and possible avenues to a successful proof, one does one's fellow scholars a disservice by simply solving the problem for them.

I also reminded the class that it's not up to me to weigh in the veracity of a given mathematical proposition; it's just as much up to them. Mathematics, a passel of mutually accepted axioms and rules of logic and inference, is the the product of centuries of give and take, of argument and counterargument, of disputation of every sort. Mathematics, like any other human-made system, is a social construction, and its application is open to any who master its agreed-upon conventions.

I'm liking the committees' work, and the committee system runs more smoothly in each successive class in which I make use of it. (I'm sure this in part because I'm getting better at managing and mentoring the committees, and in part because my more recent committee classes contain veterans of my earlier committee classes, so many of the students know the drill by now.) But I've definitely got to push them harder.

No, this last round didn't offer much of a hill to climb. In order to provide a greater challenge, I'm selecting some of the harder problems from the upcoming homework set for the committee problems.

Meanwhile, at other end of the Karpen Hall basement, Precalc is oozing along. We're still several sections behind where we "should be," but I'm growing more and more comfortable with that, especially after having a brief talk with my Chair this morning about my concerns. "Not having taught the class, I'm not as sure what I should be expecting them to know, and I'm not as sure of the pace I'm taking," I admitted. "It's getting better, and I'm starting to get a sense as to their abilities, but I know I'm going more slowly than I should be." He agreed with me, though, that there are certain things they need to see, and other things they can do without. As long as they're exposed to a wide variety of functions and get the chance to apply various algebraic techniques to those functions, they'll be fine.

And that they're getting.

Today's class was a tiny one, 10 of 32 people absent. (What's up, folks? Did Fall Break start early?) Class went very smoothly, though, and I noticed today how easy it now is to coax them from their seats and get them at the board doing problems. Although there are a few showboats in the class (they know who they are) who stride to the board with alacrity, even the more wallflowerish of the bunch have grown more confident in getting up in front of the class to chalk out a few figures.

All I have to say to my fellow teachers is this: if you're going to use group work, board work, inquiry-based methods, problem-based methods...any sort of classroom technique that'll take the students out of their comfort zones for even a it early, do it often. Start 'em on the first day, and do it regularly.

Indeed, this was the advice I and several others gave to Frodo, a new high school math teacher whom I met last night at a dinner meant to bring UNC Asheville's math and science faculty together with the region's high school math and science teachers. He'd related a tale of a problem-based activity he'd done in which he'd engineered the work groups by placing a strong student, a mediocre student, and a weak student in each group. The results were all right, but not what he'd hoped for. Everyone at the table assured him he'd made the right move (while the weaker students benefit from having a peer guide them through a solution, the stronger students benefit from having to provide the guidance in the first place, thereby improving their ability to communicate mathematical ideas) and encouraged him to keep at it, and to introduce such activities to the students as early in the course as possible.

I've decided that I'm going to introduce committee work to lower-level courses beginning with next semester's Calc I class.

Oh, yeah, I promised to say a bit about the Precalckers' poetic achievements! This past weekend I spent about six or seven hours reading through the 31 rough drafts I received (all but one! y'all rock!). They range from whimsical and funny to dark and brooding (one was simply titled "Dread"). Some were humorous, some wry, some philosophical. The tendency was for the poems to be more narratively personal than the Calc I students' were, and whereas the Calc I students often chose to incorporate mathematics into the structure of their poems, the Precalc students more often chose to place math squarely within the content of the poems. (This may simply be because the Calc I students have a deeper and more sophisticated understanding of mathematics in general.)

There were very few poems that I would consider weak. In fact, I would say the "low end" was significantly higher than the corresponding low for the Calc I classes last fall. On the flip side, there weren't any that approached the caliber of the Calc I students' best offerings (I'm thinking of Farrah's "Motivation for a sweet tooth," Lisette's "Mathbeth," and the anonymously penned haikus from last year's class).

This past Monday night I held an optional "poetry reading," and sadly only three students showed up. "Don't tell me we're the only ones!"Belinda moaned when she and I arrived on the scene simultaneously, finding our classroom an empty cave. "We'll give it a few minutes." A few minutes passed, and no one else had come, so Belinda and I just talked about poetry and math for a bit longer. Then Tootsie and Omar arrived, almost at once, and we got underway in earnest. Each of the three students read their poems, and we spent about ten minutes on each, offering comments and insights. Often the conversation wandered off on poorly-lit philosophical roads (Gödel's Incompleteness Theorem, the "universality" of math, ethnomathematics, cultural scientific relativism, and so forth), but I think we all learned a lot.

I feel that these poetry exercises truly help the students to engage mathematics in an entirely different way than that they're used to, and I'm hoping they're getting something meaningful out of it. Students, feel free to chime in with a comment or two! And know that I'll soon be handing out "surveys" that'll help me to understand what you got out of this exercise, and what you put into it.

I'm looking forward to hearing more from a few students in particular. For instance, not long before handing in her rough draft at the end of last week, Gwendolyn told me that she'd had a hard time finding something to write about at first, and it sounds like she spun her wheels for the first week and a half after the assignment was handed out. But then, she informed me, she'd been inspired during class last Wednesday when I'd mentioned the ways in which math could be viewed as a metaphor. The poem came quickly then.

I'd really like to get at what it was she was thinking as she put her pen to the page!

Okay, for now I must go. Tomorrow night I hope to put together Chapter 3 in my series of CWPA-inspired essays, so please stay tuned.


I plan on writing a more substantial post later from home (I'm getting off campus early today, it's been a long last few weeks!), but I wanted to check in with the latest (G,φ)-gram, this one based on the homomorphism φ from the alphabet {A,...,Z} to the group (Z,+) of integers under addition, defined by letting φ(x)=1 if x is a vowel and -1 if x is a consonant.

This poem takes the value 0 under φ, as does its title:

A balance

O, Beauty, abound! O, Beauty, prevail!
O, Consonant, Vowel, be laid on the scale!

I'm not entirely happy with this poem, as it's a bit stilted. I admit that I wrote it largely in order to illustrate the methods of group theoretic poetics. (I'll be giving a talk on this stuff in our department's Senior Seminar next week, and I'd like to come up with a few more examples before then!) The fundamental difficulty in constructing this couplet is the prevalence of consonants in English, and I suspect writing such a balanced poem in Spanish, French, Italian, or Portuguese would be considerably easier. I believe I'll give it a try in the next few days.

Coming up in tonight's post: how are the Abstract Algebra students' committee presentations going? How are the Precalckers liking mathematical poetry, and how are they handling functions?

Monday, September 29, 2008

Chapter 2. The parallel postulate

For two years now Umberto's school has been contemplating scaling its two-semester first-year composition sequence to a single semester. His position was not an unfamiliar one to most of last week's conference-goers: many schools have made similar moves in the last so many years, including UNC Asheville, at which first-year seminars have been granted writing-intensive status in order to, in part, take away the sting of divesting ourselves of a second semester of introduction to academic writing. (Whether the sting is fully unstung will help make up a later chapter of this series.)

Having made a cursory assessment of the pros and cons, and having heard his administration hem and haw for the better part of two years now, Umberto's head was spinning. He came to the conference looking for answers.

Much of his presentation last Tuesday afternoon could be summed up in three words: "at what price?" What do the students lose in not having a second semester of focused, intentional writing instruction? Will a single semester only short-change them in terms of content? Will halving the time they spend in practicing academic writing significantly affect their proficiency? Will it do irreparable damage to eliminate one of the few courses in which students at a large comprehensive university might receive personal, one-on-one assistance with their instructors?

On the other hand, there are potential benefits to the move. Umberto's handout mentions several: "the promise of more resources," "the promise of a WAC [writing across the curriculum] program and a WAC director," and "the promise of fewer part-time dependence (staffing and space)."

What to do, y'all?

Judging from the tone of the follow-up discussion a half-hour later, the collective mind of the room had already been made up. Nearly everyone seemed to believe that the more attention students paid to writing early in their college careers, the better off they were in the long run. It was taken as gospel that more is better, that students require two full semesters of meaningful, intensive instruction in academic writing in order to gain the confidence and proficiency they need in order to succeed as writers.

After several minutes of heated exchange on the issue, Nora played a daring devil's advocate and suggested "why not get rid of first-year writing instruction altogether? What proof have we got that it works?" As an adjunct to this insinuation my own colleague Euterpe, having with me weathered the yearlong storm of assessment of our writing intensive courses, suggested that Umberto might consider designing a similar assessment for the first-year program at his own school. There was further discussion on these ideas.

After a few minutes Leona ripped a gauntlet from her hand and flung it at my face: "I don't want to put Patrick on spot," she said, placing me on the spot, "but one could make the same argument about first-year math programs! How can it be that we're sitting here talking quite seriously about cutting first-year composition programs altogether, while the same case isn't ever made about corresponding courses in other fields?"

After several more minutes of heated debate on this and related points, Euterpe, ever the mediator, stepped in to smooth down ruffled feathers and suggest adjournment for pre-dinner refreshments. As the room emptied I approached Leona.

"Touché," I said. "You're absolutely right: the same case can, and has, been made. At our own school we've watched Precalculus shrink from its onetime incarnation as a two-semester course to its current single-semester format."

I told her of the difficulty I'm facing now: I'm finding myself pressed for time as I attempt to navigate an unfamiliar content-driven course with clumsily-designed student-centered methods meant for deeper yet more leisurely engagement of the course's concepts. ("Coverage!" bellows the beast.)

Leona patiently let me unburden myself to her, though surely she hoped to sidestep me and make for the pinot grigio that was chilling in the canteen in the basement of the South Lodge, not a hundred feet away. "I'm just not familiar with the course, never having taught it before," I confessed. "I'm not sure at what pace to teach, I'm not sure of the effectiveness of the techniques I'm using, and I find myself traveling entirely too slowly. I'm already a week 'behind' where I'm 'supposed to be' by now."

(By the way, here's a tidbit for my students, any of my students, in whatever class I'm now teaching or ever have taught before: I'm a veeeeeeeeeeeery slow teacher. It's just the way I am, I like to spend much time on few concepts, discussing them more deeply and thoroughly than I would were I to whip on through without so much as a by-your-leave. Occasionally students will tell me the pace of the class seems fast. This might be because I write fast, for which I compensate by making my typewritten notes available on-line. In any case, if you think we're moving fast, my friends, you ain't never seen fast before. We're moseying, ambling, out for a collegiate constitutional. Don't worry, I'm planning on speeding up. I like the slowness. I won't let our pace worry me if you don't let it worry you. It's been working well for me for a decade now, and I don't intend to change it at any time soon.)

A two-semester Precalculus course makes much more sense to me, but there are practical reasons why this dream is not likely to come true. For one thing, we just don't have the person-power to pull it off: we're scrambling as it is to schedule all of the Nature of Mathematics sections we need, to say nothing of Calc I and Calc II. (The latest round of budget setbacks likely means we'll have another lean year or two, since it's dollars to donuts that the faculty search we'd planned to run this year isn't going to make it.)

This chorus is common to both math and writing: my fellow conference-goers intoned a long and dirge-like litany of budget cuts, over-enrollments, and staffing shortages. For instance, East Carolina University was faced with a surplus of 1500 freshpersons this past year, fodder for several dozen unplanned composition courses taught by twenty-some hastily-hired instructors. (All this and a $6 million budget cut!) North Carolina State University saw a dip in funding yet its writing program administrators have to cope with ever-rising enrollment at a school committed to growth.

Assessment aside, I suspect that every one of us present at last week's conference would agree: in math and writing both, surely two is better than one, and one better than none at claim otherwise is to stake a daring claim indeed. More than most any other topic discussed at CWPA, the trial of Two v. One made me feel close to my colleagues on the other side of our metaphorical quad.

Anyone who's read this blog for more than a month will surely know that I believe that math and writing are not so different after all. "Lost in translation: demystifying mathematical writing" is the title of one of my talks at this past May's International Writing Across the Curriculum Conference. In this talk I aimed to show that what makes good math writing good is more or less the same as that which makes good writing good in general. (Repeat after me the Four Cs: correctness, completeness, clarity, and composition!) My hope was to show writing folks that we're not so different, they and I:

1. We all work in a rich and robust linguistic medium. (Mathematics, though hardly a universal language, as many wrongly claim it is, is a language nonetheless.)

2. We all conduct our business in an economy based on metaphor and imagery.

3. We all value clear and critical argumentation, and strong composition and communication.

4. We all deal with colleagues who often have little understanding of the ways in which meaning is constructed in our disciplines.

5. We all deal with a studentry largely underprepared for the complex tasks we charge them with, and we all therefore exert Herculean efforts in remediation.

6. We all perform tremendous "service" to every other department on campus, at levels unparalleled by any of our colleagues in the college. After all, students may need to take a single course in a laboratory science, and to satisfy this requirement they might select a course in physics, or chemistry, or biology. Students may need to take a single semester, or even a full year, of a foreign language, and they will generally have several languages from which to choose (there are eight at UNC Asheville). Most liberal arts universities have "core competency" or "intensive" requirements, but the student can often meet most of these requirements by taking courses entirely within her major.

On the other hand, every student must take at least a semester of composition, and every student must take at least a semester of mathematics: writing programs and mathematics departments are thereby burdened with boatloads of "service" courses whose delivery requires that departments either retain a large number of adjuncts and lecturers or direct the efforts of its full-time ranked faculty towards teaching introductory courses.

This last point came up over and over and over at CWPA. While I am certainly not opposed to teaching the odd introductory course (I despise the term "service"; thus the ever-present quotation marks), many tenure-track faculty are opposed, and vocally so. At CWPA Leona related a story about a colleague of hers at her previous institution: predictably, this colleague had expressed great interest in teaching first-year composition courses during her interview. Once hired, her interests "changed," and she lamented that she hadn't been given a chance to teach a literature course. Clearly she felt her creative talents were being wasted.

While such an attitude is condescending and does little justice to the intelligence of first-year students and others who enroll in introductory courses, the following question is a fair one, and was asked more than once last week: should a school entirely eliminate its first-year composition requirement, whither the expertise of those faculty formally trained in composition and rhetoric? Few schools offer undergraduate degrees in these fields, and if first-year programs are scrapped, these folks' services may be rendered redundant.

This last question and its offshoots (In what way does the teaching of composition dovetail with the teaching of literature? Can one direct meaningful undergraduate research in composition theory? Are there parallel issues in mathematics or other "hard" sciences?) and possible responses will be the topic of the next essay in this series.

If any of my writing friends are still blundering through this blatherskite, I hope that they'll free to chime in by posting a comment or two. I have a feeling I'm going to need their help in understanding my own next post. Stay tuned!