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.

Happy holidays

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

Yay.

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.

Reprecussions?

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.

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.

Ouch.

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!

Chapter 1. From either/or to both/and; from trespass to transcendence

"You're really brave to come here," was a comment I got from a few different people on a few different occasions during this past week's Carolina Writing Program Administrators conference at the Wildacres conference center just off the Blue Ridge Parkway. As a mathematician at a writing conference, I was a bit of a black sheep.

However, the camaraderie and conversations I shared with my Carolina colleagues on Monday, Tuesday, and Wednesday showed that without doubt we all face the same challenges in helping our students meet their academic goals. The further I go in my study of writing and writing pedagogy, the more similar teaching writing and teaching math begin to seem. As frequent readers of this blog can attest, I'm often struck by the parallels between the disciplines themselves.

Last week's conference was a particularly enriching one for me. I've returned more than typically energized by all that I've learned from my new-found colleagues. I'd like to share some of my insights on this conference in this forum, my blog, my personal reflective space.

This is the first of twelve posts I've planned in which I hope to lay out some of the ideas I've brought back with me from Wildacres. I make absolutely no claim about the originality of these ideas, and since I aim merely to trace outlines of some very complex notions I have no doubt that my exposition will often be skeletal and wan. I'll leave it to my readers to fill in details as they feel fit, and as always I welcome input from my colleagues and my students, my fellow-travelers in academia: please feel free to post comments!

The theme of this first post is false dichotomy and overcoming it: how does one achieve transcendence through the act of trespassing from one academic territory into another? How does one craft a "both/and" from an "either/or"? How does one efface the line between research and teaching, between control and collaboration, between "coverage" and meaningful student-centered learning? I'll address each of these apparent dichotomies in turn, and a final false dichotomy (between mathematics and writing) will lead us to the next chapter, in which I'll take a look at the parallels between first-year composition courses and entry-level mathematics courses like UNC Asheville's Nature of Mathematics or Precalculus.

Let me begin with a dichotomy that doubles itself by laying bare (one of my writing colleagues recently claimed) distinctions between academic disciplines whose modi operandi bear witness to profoundly different means of interrogating ideas.

(Incidentally, the sentence I've just written conveys a subtle such difference: just this past week I had a mildly heated discussion with Lulabelle [a sociologist, recall] over whether or not an inanimate object is capable of "witnessing" anything. In mathematics it's common to say that a computation or an instantiation of some variable "witnesses" the truth of some statement or another. Lulabelle adamantly resisted my attempt to put such language into a table she was creating for my handouts at Wildacres.)

"Research" and "teaching" generally constitute two of academe's three pillars of support (the third is "service"). One, two, or all three of these vessels into which is poured copious amounts of faculty time may be construed broadly or narrowly, depending on the whims of a particular institution's leadership. Even when granted leave to grow with utmost manifest destiny these lands, though they frequently border, don't often overlap. This is made most evident when it comes time to account for a faculty member's expenditures of effort. Even at UNC Asheville (where holism undoes parochialism on a regular basis) the faculty record, to be completed annually by every faculty member, asks faculty to categorize their achievements under the headings "Teaching," Scholarship, Creative, and Professional Activity," and "Service."

I spurred a fervent academic discussion on the way back from last week's conference when I pooh-poohed hard-and-fast distinctions between research and teaching, suggesting a dialectic between the two that synergizes my activity in both.

My teaching informs my research: in my students I find not only collaborators and future colleagues but also sources of novel insights and new perspectives. In mathematics (as in other fields) the solution to a puzzling problem may be reaped not from years of toilsome groundwork in a heretofore fallow field but rather from a few days' reworking, in some novel fashion, of a field already furrowed, sown, and freshly watered. With fresh ideas students are frequently able to do the work that's needed.

Moreover, as I've discovered again and again, my research informs my teaching: in countless classes I've been able to enliven the exposition of various topics from theoretical mathematics by bringing a particular course's techniques to bear on the research problems with which I'm grappling at the time. The Fundamental Theorem of Calculus played a crucial role in much of my recent work on random graphs, so I trot it into my Calc classes. My analysis of asymptotic connectivity required mastery of Markov processes, and I put my Linear Algebra students to work on those. Right now I'm merely waiting for my Abstract students to learn about group homomorphisms so I can challenge them to write their own (G,φ)-grams.

To me, research and teaching are inseparable, and I credit my successes in both of these areas to my willingness to let them intermingle.

I told this to a colleague who teaches here in Literature and Languages, and she responded by indicating that the situation is different in her field. There, she claims, it's more difficult to involve students in undergraduate research efforts since it's no easy matter to carve out bits of one's own research program to make fodder for undergraduate inquiry. Whereas many of my projects can be dissected into chewable chunks, the ways in which knowledge is interrogated in her corner of the humanities frequently make overseeing undergraduate research difficult for her colleagues.

I must admit my ignorance regarding undergraduate research in literature, or in composition theory, or in rhetoric. Is it so difficult? Why can it not be, as in mathematics, seamlessly grafted onto typical classroom experiences? What forms does research take in these fields? Are these forms of inquiry inaccessible to most undergraduate students? Does meaningful inquiry require the student to long immerse herself in a body of literature so deep as to preclude its plumbing by an undergraduate with a typical courseload? Are there no ways to effectively circumvent such arduous preparation?

I don't ask these questions to be obtuse or snarky, I ask because I don't know the answers.

So I drone Ben Steinianly into the blogosphere: "Anyone? Anyone?"

I cannot imagine teaching without challenging my students to engage themselves in their own original inquiry. There's no more authentic learning experience, no better means of encouraging ownership of a discipline's core concepts, than to involve students in real research. It's the ultimate form of student-centered learning.

Speaking of which brings us to another dichotomy that was addressed only occasionally at the CWPA last week: "coverage" versus student-centered classroom methods. It's understandable that this topic didn't get so much attention at this conference, as entry-level mathematics courses like Precalc are likely much more content-driven than their correspondents in the writing curriculum. In introductory writing courses, I imagine little is lost in taking time out of class to ask students to write in groups, to perform peer review, to engage in ungraded freewriting exercises: these projects all serve the course's learning goals in direct and obvious fashions.

Meanwhile, traditionalist math teachers kvetch: "I can't use group work in my class, we've got so much stuff to get through." "It'll take the students three hours to uncover this concept that I'd explain more clearly in three minutes." "If they get to Calc I without having seen the Law of Cosines, they'll be in a world of hurt, I can't slow down."

I can sympathize. I've been there. I know how it goes. Even now I catch myself about to mutter or moan a comment like one of the above, as I'm struggling to keep up with where I "should be" in my Precalculus class. On the verge of sacrificing a group project or some other active-learning exercise (one that at the very least gets them taking turns coming up to the board to jot down a number or two, a graph, or even just a point in the plane), I stop myself and say, "whooooooa, now. The hell, Patrick? What are you thinking?"

"What are millennials [students born after 1982] like?" asks Nora, one of my colleagues at CWPA, in a handout she passed around during her presentation. In partial answer Nora offers that they "gravitate toward group activity...are fascinated by new technologies." Millennials' learning styles include "teamwork, experiential activities, structure, and use of technology...collaborative style." What's to stop us from giving them every opportunity to engage in these effective practices?

The false dichotomy rears its hairy head, bellowing an eight-letter four-letter word: "coverage!"

To which I bellow back: "bullshit." Indeed, the astute reader of this blog will note that there are a few words I never use, because it pains me to do so; "cover" is one of them.

Quick quiz: I've got fifteen minutes left of class, and we're working on cleaning up some trigonometric minutiae. Are my students better served by watching me babble about the Law of Cosines or creating and solving their own problem that makes use of more fundamental computations involving sines and cosines themselves?

The former concept they'll use maybe once in each of Calc I and Calc II, and a few times Physics, assuming they go that route. And if they need the law at those times, it'll be presented to them anew and re-explained anyway. (Such "just-in-time" explanations are often the most effective, especially if the topic is one that's unintuitive or difficult to motivate: by deferring the concept's introduction until the time at which it's needed, students aren't asked to remember pointless facts and figures any longer than they have to.) Meanwhile, the latter concepts are foundational and come up continually in later coursework, and through direct engagement with them the students better understand their workings at a practical, as well as theoretical, level.

No sacrifice is made here. While I might remove a few of the ornamental baubles and bijoux that typically adorn the face of an introductory course, all that needs to be "covered" is "covered," and the face is left intact. Students then engaged the rudiments of my discipline more directly, more meaningfully, than they would have otherwise. All we need to do, as practitioners of content-rich academic fields laden with centuries and sometimes millennia of knowledge, is divorce ourselves from the rather arrogant notion that our students need to know every last fact about our fields of study.

Guess what, folks? They don't. They need to master a few core concepts, and they need to become adept problem-solvers and critical thinkers. Everything else? Icing on the cake. Accepting this fact is difficult for some of us. After several years of graduate training in highly specialized and technical fields, it's hard to remember that our students don't need to know everything there is to know about CAT(0) spaces, or about Sterne's use of the subjunctive in Tristram Shandy. We need to let go.

And we need to let go of the reins and let the students take the helm every now and then. They must be allowed to be our collaborators, not our convicts, and although guiding them in collaboration requires that our students be given a bit more control over their studies, it by no means implies a loss of control on our parts. The most meaningful learning experiences I've ever shared with my students have come at moments when everyone in the room agrees (often tacitly) on a common course of action and each person present assumes control over her or his own role in the action taking place. I can think of three such relatively recent moments off the top of my head:

1. The day, roughly two-thirds of the way through the Fall 2007 semester, on which my 280 class and I agreed to go off-script and just blundered our way about through the wilds of set theory for over a half-hour. That was the day on which Quincy suggested something along the lines of a "fishbowl seminar" in which all participants spend each day's hour discussing a topic drawn at random from a fishbowl placed at the room's center. (I'm still not sure that wouldn't work...) I blogged about that class in this post.

2. My second section of Calc I's rendition of the classic Newton v. Leibniz debate last fall. (Blog posts related to this class include this one, in which the students shared their reflections on the experience, and this one, in which I provide my own initial reflections.) It was clear that everyone had prepared carefully, and after a few minutes most people seemed to have forgotten their real identities as they let the experience take hold of them.

3. The second day of "class" during this past summer's REU, on which the students took turns presenting their findings on the roughly 40 terms and topics from graph theory I'd given them the day before. With one exception (Dione was a bit shy at first) they strode boldly to the board, one after another, and by lunchtime we'd ticked off nearly every item on the list.

In each of these experiences, every individual involved took control and directed her own actions to create a meaningful part in a collaborative project. None of these projects required abrogation of authority. None required the teacher to play the part of dictator, nor the students the part of the peasantry. Each was more than a monologue, more than a dialogue: each was a polylogue. The result in each case was what L. Dee Fink would surely call a "significant learning experience."

Control versus collaboration, coverage versus deep conceptual mastery, research versus teaching: each of these tugs-of-war is played out every day in classes across the college curriculum. With several steps forward, one combatant pulls the other across the line dividing one territory from the other...but if we're wiling to admit that the line between the two is arbitrary, then trespass becomes transcendence.

Of my new-found friends in the writing community who may be reading this, I ask: how do these false dichotomies, these plays for power between imaginary opposing forces, manifest themselves in your classrooms?

I'm curious to know the extent to which our disciplines run parallel to one another. I'm eager to learn more about the form your instruction takes, the ways in which you engage your students in your courses and programs. I'm hoping you will take the time to share your thoughts.

In my next CWPA-inspired post I'll continue by discussing parallels I've noticed between the pedagogy of writing and the pedagogy of mathematics, parallels which no doubt witness (there I go again!) more profound similarities between the disciplines themselves.

Until then, have a pleasant evening, I wish you all well.

Studies in comparative pedagogy

Today's been a bit better. I've gotten a lot done, both research-wise and teaching-wise, I've met several more of my new students, made a Math Club meeting and a meeting with the high schooler I'm mentoring as she helps me run Super Saturday this semester, and I sat in on Lulabelle's sociology class, Social and Cultural Inquiry.

To me the most beneficial aspect of my sitting in on her classes (and her sitting in on mine...tomorrow it's her turn to come to Precalc) is the chance it gives me to observe many of the same pedagogical techniques I use in my classes in an entirely different disciplinary setting. Many of the same tactics are at play: small group work, writing-to-learn, brainstorming, student discussion. And while the groundwork for Lulabelle's course is entirely different from that of my own, the ends met by the tactics she employs are ultimately very similar: both of us want our students to learn how to think critically, how to assess data and other evidence, how to solve problems and make connections between the distinct and discrete bits of information they pick up here and there.

After 75 minutes had passed, I'd punctuated my notepad with no fewer than nine ?s indicating follow-up questions I had for her when we met after class:

"How do you draw the quiet ones into the discussion? Do you?"

"Have you read The experience economy?"

"Do you like people to raise their hands [before speaking]?"

"Might this work well with small 'break-out' groups to cogitate solutions before reconvening?"

"What's your motivation for reading the daily reading out loud? Is this to achieve a multimodal pedagogical style?"

And so forth. I'm finding our exercise in comparative pedagogical practices very fruitful; it's making me much more aware of my own choices as a teacher. I hope Lulabelle's getting as much out of it as I am.

Now, I'm off, into the rain. More soon, I'm sure!

Halfway in

I've had a week now to recover from the departure of my summer's colleagues, the wonderful students that made up my REU team for the past eight weeks. The last of them took flight almost exactly a week ago this moment, winging her way back to New York last Sunday afternoon.

I miss them. They're great students, smart colleagues, and close friends. I look forward to seeing them at conferences, working with them on papers, growing up and learning by their sides.

For now they're gone, but the work continues: with two of them (those with whom I worked most closely with) I've already exchanged write-ups, graphs, ideas...yes, work continues.

But the cycle's begun anew: I arrived at my office at 7:15 this morning to find a note left on my door by two of my favorite students from last year, informing me that they're back (for RA duties, no doubt) and were surprised that they'd missed me. They were operating under the (not-all-that-erroneous) assumption that I'm never more than a hundred yards or so away from my office.

I spent this morning helping first-year students move in. For three hours I shuttled luggage carts back and forth between parents' cars and dorm rooms, schlepping all manner of stuff into Mills Hall. Fully laden one way, emptied out on return, several trips for several students. One's a budding music major, another's contemplating environmental science. A few are undecided: biology? History? "I think I want to teach."

"Math?"

"No! I'm not really good at math."

"That's what everyone says until they find out it's not true," I assured her.

It was refreshing, revitalizing. Its sense of newness and rebirth stood in contrast to the moving out my REU students did the weekend before.

My move into Johnson-MacFarlane Hall at the University of Denver 15 years (!) ago was nothing like this: my dad parked his truck in the middle of the phalanx of vehicles that lines that lined High Street for a block in either direction, and as soon as the dorm's outside doors were unlocked students and parents descended on the dorm like sharks in a frenzy. It was chaotic. There were no faculty or staff helping people to move in, there wasn't even anyone to direct activities or answer simple questions (where's the bathroom? Is the dining hall open? Where's the nearest ATM?)...that day I saw my RA cry for the first of what would be many times that year. (She was a gentle soul and didn't deserve some of the folks who lived on our floor.)

This coming week will see me getting the first few days of my two classes ready. I've read through the first few chapters of the text I'll be using for Abstract Algebra, and I've brainstormed a few opening exercises for that course, but I've yet to commit anything to paper. Tomorrow I'm meeting with one of my colleagues who's taught Precalc a number of times, and I'm hoping he can then give me a rundown on the topics I should be sure to address during the next fifteen weeks.

I've also got to get some more work done on the presentation on the writing program I'll be making at the Carolinas Writing Program Administrators conference in a month or so. Lulabelle and I met late last week to discuss that issue, but we spent most of our meeting chatting and going over the draft of my math poetry paper and syllabi.

Much work to be done, I just don't feel like doing it right now.

Time's running out, though...not long before classes start, and then where will I be?

Argh.

Okay, I'm off...I feel like I've got a lot to say, but so few words with which to say it. I've got to gather them together and compose my self before I can make any more sense.

Week Three progress report

Doin' good.

At least, I think so.

After gentle admonishment about the lengthiness of a few of the student presentations last Friday, yesterday's talks all came within a minute or so of the universal 15-minute maximum we'd prescribed in advance. ("15 minutes, MAX!") The talks were solid, with more eye-popping graphics, slick LaTeX work, and tons and TONS of data. They're beginning to come up theorems of their own, they're making conjectures, their laying out formal proofs. It's coming together. I've yet to get a look at their written work for the week yet, though I've gotten sneak peeks through reading their drafts (thanks for bringing that to me, Uwe!) and seeing their presentations. Their level of sophistication appears to be rising. I have to admit that I'm looking forward (sick scholar of scholarship that I am) to the point at the summer's end when I can lay their weekly assignments side-by-side-by-side-by-side-by-side-by-side-by-side in an attempt to track the development of their technical writing proficiency throughout the program.

One more thing I'll say about these students: they (and one or two of them in particular) ain't shy about asking for what they need from us: more ideas for things to do around town, modifications to the presentation schedule, caffeinated tea...At their behest we've scheduled a "grad school forum" in a couple of weeks, at which time we'll give them the chance to ask anything and everything they'd like to about selecting, applying to, transitioning to, and surviving grad school.

I hope that their forthrightness is indicative of a sense of belonging and collegiality, and not just out-and-out boldness. Probably a little of both.

I really wish that I'd had a chance to take part in an REU when I was a student. I know I'd have been up to the challenge. I realize now in reflecting back on my undergraduate experience that though I had solid professors who were active in their fields and who did a great job in the classroom, their mentorship didn't extend far beyond the classroom door. I fear that I was simply a student in a Ph.D.-granting department whose Ph.D. program was undergoing a period of latency, and that the faculty didn't really know how to properly mentor talented undergraduate students...I really should have been told about journals geared towards undergraduates, I should have been encouraged to go to undergraduate-appropriate conferences, I should have been pushed to apply for REUs (there weren't as many back then as there are now, but there were a good number by then, and I'm sure I would have landed a spot in one had I applied to a few).

Ah, c'est la vie. I'm pretty happy with the way my life has turned out, and now I get a chance to live the REU experience vicariously through my own program. Woo hoo!

In other pedagogical news...well...there's not much more right now. I've started to plan my syllabi for the Fall semester (two new preps! I've not taught Abstract Algebra here before, and I've never taught Precalc). I met with Lulabelle and Casanova over lunch this past Thursday, and we planned our next move in the new writing assessment study. Casanova's going to focus on analyzing the syllabi as faculty products, and I'm going to try to better articulate my hypothesis that the rubric we constructed at the conclusion of the last study was (perhaps unintentionally) skewed towards assessing more "traditional" research theses. "We might just have to report that it's not possible to create a universal rubric capable of assessing the writing of any given course," said Lulabelle.

Well, for now the waterhole calls...I must away.

I'll check in again soon...next weekend, at the latest!

Week Two progress report, v.1.0

Yowza, I'm beat.

I'm not going to write much right now, as I'm tired as hell and the needle's pegged to the far-right end of the Incoherometer.

I will say simply that the students made their first end-of-week presentations today, and they were magnificent. Aside from the so-so time management displayed by a few overeager presenters who might have taken a taaaaaaaaaad too long in singing their songs, the talks were marvelous. All eight made great use of visual aids (including Mathematica notebooks, LaTeX files, PowerPoint, good ol' fashioned boardwork), all were careful to provide their peers with history, background, and context for their respective projects, all were able to make clear some very high-level and abstract mathematics, and all held one anothers' feet to the fire through careful and clever questioning...Camilla and Thalia were particularly good at this.

To those of the students who may be reading this: I promise personalized feedback on individual presentations, no later than Monday!

There are some great projects afoot. At this point they're working on color-critical graphs, channel assignment utilities, group theory as applied to musical theory, the limiting connectivity of field automorphism graphs, the structure of growing networks of churches, statistical measures of preferential attachment models for random tree growth, variations on previous definitions of finite hyperbolic tilings, and an algebraic/geometric characterization of graceful labelings on graphs.

This last one, Thalia's pet project, has really got me intrigued right now. Thalia's taken as a starting point a "classical" observation (that a graceful labeling of a graph must place the highest- and lowest-labeled vertices next to one another, and in order to obtain the next-highest label exactly one of two configurations must obtain, and so forth), but her logic pushes her along a path I've never seen taken before, on which she's found a way to view the collection of graceful labelings on all graphs of a given size as a collection of lists of states, on which an algebraic structure can be placed. Her insight's led to some interesting ideas, and I'm eager to see where they go. We met for a couple hours this afternoon to hammer out some Mathematica code and to organize our collective thoughts on her construction. She's a fast thinker, and is a lot of fun to work with.

In other news, I met with Lulabelle and Casanova yesterday to begin our analysis of the materials submitted by our colleagues at the close of this past year's writing assessment study. The pickin's are slim, and we've decided to start our analysis by reading through those syllabi we've so far collected from our colleagues who were directing discipline-specific writing-intensive (doubly-hyphenated-adjectival-phrasedly-modified) courses last fall. Our task at this point is merely to reflect upon our critical reading of these texts: what is there in the syllabi that indicates the instructor's attention to writing pedagogy? What implicit elements might the students (or faculty) infer from a reading of the syllabi? What elements are common to the syllabi? Which are present in some but not others?

And so it goes.

Judging from the penultimate parenthetical comment in the previous paragraph (oh, the alliteration!), it's time for beddie-bye.

Until tomorrow, then, I am always yours...

Twenty-five minutes to go...

...At least that's what it feels like.

Desdemona, our REU student who's scheduled to arrive first, should be here within the next hour and a half.

Am I ready?

I've spent the last couple of weeks putting together material for this year's program, and now I've got a list of learning goals, a rough timeline, a list of about 45 possible research questions, five handouts involving set theory, graph theory, and metric geometry (and several more on the way), five handouts on Mathematica, four handouts on LaTeX and the structure of mathematical research papers, an exercise asking students to uses research databases to track down primary source material, and a map of North and Central Asheville, complete with markers indicating locations of yummy eateries and other useful establishments. (All of these are available on the REU website, here.) Not to mention a couple dozen research and survey articles on various topics of interest to me.

Still I don't feel ready.

I'm just anxious, giddy as a schoolboy on the first day of class.

I met with Lulabelle and Casanova yesterday to talk about the direction our new year-long writing assessment study is going to take. Suffice it to say we've got a mountain of data (both quantitative and qualitative), making the selection of research questions a leviathan task. For now we're focusing on collecting the final round of data from the previous year's participants, including syllabi and course assignments, as well as statements regarding these folks' experience in constructing and applying the writing rubric we all worked so hard to put together.

Lulabelle's visibly more relaxed since we've finished up with Austin. I hope she's able to get some good nights' sleep in these days.

After our meeting yesterday I stayed on to help her out with reading math papers (a scary proposition for a non-math-type person!), and then we talked about Kevin Rathunde's work on family environments that are most conducive to optimal experience in children. (I came across a reference to Rathunde's work in reading Csikszentmihalyi's Flow for our upcoming summer learning circle, and tracked down the original work, appearing as a chapter in Csikszentmihalyi and Csikszentmihalyi (ed.) Optimal experience: psychological studies of flow in consciousness (Cambridge, NY: Cambridge University Press, 1988).

Central to his study are five traits (all starting with 'C'; a fitting companion piece to my "Four Cs" rubric!): clarity (of rules and purpose, providing a stable set of experience parameters), choice (giving children the opportunity to direct their own experience within clearly defined parameters), centering (of activity in the present, making it an "autotelic" activity worthy of pursuit for its own sake), commitment (or trust, giving children a feeling of security that will enable them to boldly strike out on their activities), and challenge (ensuring that children are given tasks that are adequately interesting).

A question to ponder: in what ways are these traits best developed and nurtured in the classroom, and to what extent do they there serve the same roles as they do in a "well-flowing family" context? (I can already see how these traits mesh well with what I've always thought of as "good teaching practice.")

That's a question for later, since in the middle of my typing the above paragraph, Desdemona arrived with her family in tow. She's now safely moved into her dorm room, alone for the night but not for much longer.

I'm so excited!

And I just can't hide it!

I'll attempt to keep control.

But I'll still like it.

Until next time, ponder the following: just how long did it take Dr. Csikszentmihalyi to learn to spell his name? And how long does it take him to type it?

Back

Damn.

That was productive.

It's going to take me a while to unpack all that I've carried back from Austin.

It's been a long time since I've had a trip that fruitful; I've come away with so many ideas, insights, opportunities for collaboration, connections to new colleagues...what a wonderful crowd these WAC folks make!

It's safe to say that there's a great deal of interest in writing in the math curriculum.

Lucky me.

People were enamored with the work Lulabelle's put together, and with my piece of that project. If anything, though, the writing folks were more interested in hearing about my math poetry project from the Fall 2007 semester. I've already contacted several of the students from that Calc I class and asked if they'd like to work with me by providing me with reflections on their creative process. I'd like to know: what did they get out of the exercise? Did it help them to engage mathematics, and if so, how? I've spent the last hour or so looking over Arthur Young's Poetry Across the Curriculum and other related projects. This is such wonderful work!

As I said, it's going to be a long time before I'm done unpacking the mental baggage I've brought home from that conference. Already, though, I've begun thinking about how I can assess this summer's REU students' writing as they proceed from novice article authors to more seasoned technical mathematical writers, and I've begun puzzling through the process of assessing just how it is that a writing instructor's intentionality leads to students' gains in writing proficiency. And I'm coming up with ways I can use blogs in Abstract Algebra and wikis in Precalc this coming fall. And Lulabelle and I are meeting with Casanova on Thursday to discuss the direction(s) we'll be taking in our follow-on to the last assessment project.

And...

...and...

...and...

...too...much...to...think...about...

...and with only a week to go before the REU begins.

Until I return with a longer and more meaningful post, here's a question for all of you out there who happen upon this blog: would you rather be bored shitless or busy as hell? Discuss. You will be graded on ramblingness, incoherence, and lack of a thesis sentence.

Think 'pon it carefully. Surely your response says more about your personality than a thousand Cosmo quizzes.

Just your run-of-the-mill first-day-of-class anxiety dream

It took most of the dream I had the other night (i.e., about 5 milliseconds in real time, most likely) to put my finger on why it was I felt underprepared for the dream-class in front of which I was standing: I'd not yet pulled up my students' photos on OnePort, so I was completely unable to put names with faces. While I usually get 80% to 90% of the names right on the first day, in this dream I was shooting blanks: everyone was a stranger.

Why is it that so many of my anxiety dreams involve classroom underpreparedness?

Yes, I'm always fully clothed in these dreams...usually I'm anxious I haven't planned the activity for that particular day of class.

Ah, but class is done for the year here, commencement's come and gone, and the late-spring conference season is winding down (one to go, in Austin at the end of next week...I'm nearly prepared, and I'm very much looking forward to it!). I've got a brief lull of about two and a half weeks right now, time in which I've got to get my REU ready to go for the summer. I've got a list of about 40 problems made up for the REU. I hope that by the end of the program's first week I can throw the list to the kiddies and let them spend the weekend looking up primary source material they can then mine for their own interesting problems.

Speaking of commencement (as I did, briefly, above), I'd like to send my heartiest congratulations out to all of my wonderful students who have now passed from these hallowed halls of academia and on to bigger things. You've done wonderful work here, and I'll miss you all.

Just a few days back Fiona sent me a picture her stepmother took of Fiona, Niobe, and me, all clad in regalia (ah, pomp and circumstance). Maggie's made it the desktop image on her computer. (She's entranced by the novelty of the photo, as I'm not often seen decked out like that.)

Since returning from Nashville the other day, my time's been focused on applying the writing rubric our research team's developed to the discipline-specific writing assignments gathered by me and my colleagues. I've had the honor of reading management research papers and reflections, and response essays and creative writing assignments from a course in French composition. These works include everything from taxonomies of corporate social responsibility through original poetry pitting Baudelaire against a red balloon.

I've found it very hard to apply our rubric to the French papers, in particular to the creative writing assignments whose brevity and informality make it difficult to assess a student's mastery of items such as "be able to contextualize a thesis within the body of existing knowledge." For both assignments from the French course, and for the brief reflection papers from the management course, I've noticed certain of the items on our eleven-item rubric blending together. I wonder if my experience is similar to that of my colleagues (some of whom have the misfortune of having to slog through my 280 students' homework papers!); if so, it may be that the rubric is more difficult than we had suspected to apply universally, or it could just need some subtle tweaking. I'll be interested to hear how our conversations go on Tuesday when we all meet to compare notes before Lulabelle and I take off for Austin with the assembled data.

And speaking of assembled data, this morning Lulabelle sent me a nice thick spreadsheet full of very nice numbers showing significant gains on a number of items from the pre/post-test administered in my 280 class last Fall. I wonder how my students' responses compare with those of my colleagues' students.

Exciting!

Yes, I'm a nerd.

Anyway, I'll leave it at that for now. Maggie's likely to be home from work in a half-hour or so, and I'd like to free up my evening schedule to spend some time with her.

Arrivederci!

Déjà vu

It's raining outside, Maggie's asleep on one of our new couches, it's the perfect day for updating the blog.

I've just returned from the second of my three May conference-season journeys, this one to Nashville, and I'm spending the day recuperating before a new busy week-and-a-half that ends with me taking off to Austin, Texas for the 9th biennial International Conference on Writing Across the Curriculum. Most of the next week will be spent preparing for my presentations there, and in applying our team's newly-minted rubric to piles of papers from Management and French Literature courses taught by my colleagues participating in the study.

I could have it worse: my friends Cordelius and Lulabelle have to wade through a stack of my 280 students' papers as they try to apply the rubric to nearly a hundred pages of intermediate mathematics. I spent a few hours making up a "primer of mathematical writing" to help them begin to read math. Therein I indicated that most mathematical notation is little more than shorthand, that mathematical terminology, though daunting, has the advantage of being precise and unambiguous, and that the most unfamiliar genres of mathematical writing (namely, definition, proposition, and proof) are fairly straightforward and exhibit clear idiosyncratic qualities that make them quite accessible to someone patient enough to examine their stylistic elements.

I hope it helps.

Wednesday and Thursday of this past week were spent in faculty workshops on writing, led by me, Lulabelle, and a handful of our colleagues. Wednesday's focus was on writing for freshmen, particularly those in our "liberal studies introductory colloquium" courses in which new students are exposed to the liberal arts tradition through seminars on a variety of subjects spanning the school's academic spectrum. I felt Wednesday's session was a bit lackluster, I sensed only tepid commitment from a number of the participants, I myself was still getting over a cold that had knocked me flat the week before, and I was having a hard time granting myself the authority to speak as a "writing expert." It was the first workshop outside my discipline I've ever had to run, and I felt like something of a pretender or a charlatan, standing in front of a roomful of my colleagues and trying to convince them that I knew what in the hell I was talking about.

By Thursday I felt better, both physically and psychologically. What's more, the audience seemed a bit more receptive: I sensed much firmer conviction on the part of that day's participants than on that of their colleagues from the day before. Thursday's crew was there to talk about discipline-specific writing, the sort that (presumably) goes on in higher-level coursework. I felt good about Thursday's workshop.

Immediately after the workshop ended on Thursday I hit the road to Nashville, arriving at my hotel just before 9:00 Central Time. I called up Titania, my friend from grad school, and we met for coffee at Fido (greatest coffee shop on Earth), my home away from home much of the four years I'd lived in Nashville.

We talked for a few hours, sounding like we were a hundred years older than we were five years ago. We talked about students and committees and conferences and enrichment programs and research and course design and assessment...we talked like the real university faculty that we are.

She, like two or three others of my colleagues who graduated from Vanderbilt within a year or so of me, has just received tenure.

I'd be lying if I said I didn't wish I were in the same boat. I'm starting to feel anxious. It's not that I'm worried about dismissal; I passed this year's reappointment process with flying colors. I'm just looking forward to the symbolic stability that tenure confers. I'm looking forward to the sense of permanence that comes with it. Yet I lost three years on the tenure clock in moving from a research postdoc to a tenure-track gig at a liberal arts institution, so I've got at least another year to go (likely two). Don't get me wrong, I can understand the powers that be not wanting to credit me with three full years of time served, but I'm a little disappointed that I wasn't able to get at least a year or a year-and-a-half of credit for the teaching I did in grad school and afterward in Illinois. It would be one thing if I'd gained nothing through that experience, but in all immodesty my talents speak for themselves.

I'm sorry, I hope you'll grant me this brief bout of pridefulness.

As Fido was prepared to close, Titania and I took to the street and headed over to Vanderbilt's campus. We continued to talk as we walked, reminiscing on our time in grad school (which time both of us enjoyed immensely), updating one another on mutual friends' goings-on. After a while we found ourselves at the math building, Stevenson Center's Building #1, and happily the doors were unlocked.

Our first stop was the first subfloor, where still stand the math grad students' offices. I know three of the current grad students (one's an ex-mentee and coauthor, a second's research path has crossed my own, and I was the reviewer for a paper by the third), the rest were just a smiling sea of young mathematicians who happened currently to be squatting in the offices we'd once called our own. We wandered through the dimly-lit office suite, trying to remember who was in which office in our own time. We were able to place most of our colleagues, but one or two offices were hard to fill.

We inspected the classrooms farther down the hall. "I had semigroups in here, with Gould," I told Titania.

"I had topology," she replied.

"I defended in this room," I said in another.

"Why'd you defend down here? I was in one of the rooms upstairs."

"I don't know."

She told me about how she once broke the sliding blackboard in the larger lecture room at the end of the hall. "I grabbed it from one side only and pulled it off the track," she explained.

Not much had changed.

After a bit we went back down the hall and took the stairs to the third floor, the first one above the ground. We stopped for a moment to peruse the list of faculty, most of whom we recognized. I mused that the Fields Medalist had no office number assigned to him.

At the end of the hall on the left was the room in which I first taught a course of my own, about which I blogged back in September 2007. It's changed very little since the night on which I went to campus to prepare for class the following morning: the blackboards are the same, the desks are the same, there still superfluously hangs from the ceiling above the side board an ancient set of maps of the world. "I never figured out why those are there," Titania said.

Half of the countries depicted thereon no longer exist.

That classroom remains, though.

I don't believe I ever led a class in that room after Fall 1999, so it's been over eight years since I've taught there.

Odd.

I shudder as I think back to the first writing assignment I made up for my Calc I kiddies back in 1999. Its prompt was little more than "Write a 5-10 page paper on a mathematical topic of your choosing. This is due on November eleventy-first." Granted, I gave my students hints on how to go about picking a topic, how to get started on their research, how to vet and cite their sources, which is more than many faculty would give. (Hell, most math faculty don't even think about assigning writing projects.) But I did next to nothing to structure or stage the assignment, to allow for rough drafts, to incorporate feedback, to provide writing instruction. The completed papers I returned to the students were line-edited, as much attention paid to misplaced commas as to thematic vacuums and ill-used evidence. Small wonder the products of my students' efforts were so hit-and-miss.

Ouch.

I've come a long way as a teacher in the past ten years. I wonder what experience the next decade will bring?

For now, I'm off to fold some clothes and rearrange our bookshelves. I'll be back soon, I hope.

In the meantime, if you've got something to say, please say it.

Pre-summer reading and subsequent ruminations

My summer reading has begun with a bang.

I've been working my way through a book my colleague Tip lent to me, Radical equations: civil rights from Mississippi to the Algebra Project, by Robert P. Moses and Charles E. Cobb, Jr. (Boston: Beacon Press, 2001). Tip met up with Bob Moses, a noted civil rights leader, Harvard-trained mathematician, and founder of a grassroots math program (the aforementioned Algebra Project) targeting middle-grades mathematics students on the fringe, at the Mathematics and Social Justice Conference Tip attended in Brooklyn a month or so ago. Clearly Tip's thought deeply about the ideas in this book, especially as regards his nascent community-building math program and the NSF grant proposal he and I are soon to set about writing, and he was kind enough to lend his (signed!) copy of the book to me.

I'm about three fourths of the way through the book right now, and though I've found much of the text itself dry and unengaging (particularly when it gets bogged down in the toledoth of Moses's project's converted teachers; at some points it reads like a biblical genealogy: "and Norma Jean begat Shannon, who begat Tom, the Explainer-to-Children. Tom taught twenty years, and then begat Sylvia. From the Delta did Sylvia come, and her students were good in the eyes of the Sunflower County Board of Education..."), one or two of its ideas have really struck me. I've been won over in one respect in particular. To best describe my conversion, I ought to mention a conversation I had with a colleague at a school I recently (in January) visited.

We were talking of undergraduate math majors; I had mentioned that at UNCA we have something on the order of 80-90 majors at any given time, and my colleague was thoroughly impressed. He said that at his school (a school nearly twice as large as UNCA), there were perhaps half as many undergraduate majors. Ever wanting to be helpful, I made some comment along the lines of "I've got some ideas that might help you to bring those numbers up."

My friend's response was something like "I don't think we're looking to do that."

I was taken aback. Not only had I not scored a point on this man's scoreboard (he and I share a long history, and I've never wanted to let him down), but my view that more young people should be helped to embrace mathematics had been met with hostility. This man had no interest in bringing math to the masses; he preferred to let it stay the closely-guarded territory of the few and the proud.

Moses's book has helped me to make out this not-so-well-hidden trap many professional mathematicians fall into: too often we think of math as a religion, a cult of worship into which only a select few are to be inducted, and in which only an even smaller few are allowed to become high priests. We take pride in our weeding out of the undesirables, defined as anyone who doesn't have a natural knack for math, who comes pre-programmed with a love of abstraction and analysis.

I've seen our culling at work at several levels, more clearly at some institutions than at others, and I'm ashamed to say that I've even taken part in it, though unwittingly. Math professors have a tendency to emphasis the arcanity of their field, its abstruseness, its disconnect with reality. Many of us take pride in the difficulty of our field, and make every attempt to show off our own intellects by making math seem imponderable, impenetrable, dense. I saw this most clearly at Illinois, where research mathematicians would show open disdain for all but the brightest undergraduates in their classes ("most of them are dullards, I've got a few who might prove capable"), lending a hand to the top 5% while leaving the others to drown; "they're just not cut out for it."

For too long mathematicians (and scientists of other stripes) have tried to fill their ranks from the lists of the best and brightest of the American studentry (to borrow a wonderful turn of phrase from William Strunk), leaving the dregs to find work elsewhere when they prove themselves incapable of meeting the high standards set for practitioners of math research. This leaves the untouchables, consisting primarily, in this nation, of poorly (read: publicly) educated blacks, latinos, and poor whites, out in the cold.

Moses makes clear that there's something wrong here.

What's called for, in his mind, is a radically different paradigm: rather than drawing from the few whom opportunity and natural talent have buoyed to the top, we ought instead be working to ensure that everyone is given the chance to rise to the surface. With a system wherein all are given the tools needed to excel mathematically, everyone benefits: traditionally underrepresented groups obtain the opportunities they need to succeed academically, and academicians expand broadly the talent pool from which they will one day choose their colleagues and successors. This "bring 'em on, all of 'em," attitude is the core of the Algebra Project, a program committed to making sure that every 6th, 7th, and 8th grader is given the background needed to successfully navigate a college-prep math sequence in high school. As Moses sees it, not everyone will go to college, and while there, not everyone who goes will study mathematics, but everyone should be ready to do so.

It just makes sense.

Moses's work has definitely helped me to come around to this point of view. It's never been so clear to me that I as a mathematician have a good deal of work to do to ensure that I'm doing what I can to grant everyone the chance to experience mathematics, and to succeed at it. Work needs done at all levels, K-12, undergraduate, and higher. And the work done at each stage needs to be interwoven with work done at other stages: vertical integration is called for. I hope Tip and I will be able to capture that spirit effectively in the proposal we put together this summer.

I've also begun the book the Project NExT reading circle has chosen as its first focus of discussion, Ken Bain's What the best teachers do (Cambridge: Harvard University Press, 2004). I'm (we're) one chapter in, and so far I'm unimpressed. It strikes me as a poorly-assembled pile of truisms and platitudes, absent the concreteness and careful analysis of a seasoned student of the scholarship of teaching and learning (SoTL). Not that every SoTL text has to build up a rock-solid wall of data and facts, or deluge the reader with a statistical breakdown of every study on teaching efficacy performed since 1970...but this book just seems "lightweight" to me. So far it's a great "rah-rah" feel-good page-turner, but its place might be on the nightstand of a newbie college prof just out of grad school who needs a little cheerleading and from-the-sidelines inspiration. I wasn't a huge fan of Maryellen Weimer's book, but I found it far more useful and engaging than Bain's, at least to date.

I ought also say a word or two about preplanning I've begun for Fall's classes. Francine's agreed to help me go through the notes and homework problems we used in 280 this past semester, retooling them, getting them good. I've already written a couple new in-class exercises dealing with writing mathematics.

The one I'm happiest about was inspired by a conversation I had with my colleague Lulabelle from the Sociology Department (I'm on a team of folks helping her out with a pilot assessment program for writing across the curriculum). She indicated that as a part of the work that'd need doing for this grant we're collaborating on, I'd have to to be able to train my colleagues how to "read" mathematics. I got to thinking about how I would best do this, and realized that it's likely easiest simply to highlight the linguistic analogues mathematics shares with "natural" human languages: syntax, grammar, orthography. Not only would an exercise indicating these analogues help my colleagues; it would help my 280 students, too.

The exercise consists of a take-home portion and an in-class portion. Each part comprises three written passages of varying levels of quality; the take-home passages are in "English" and discuss the chemical element boron. Students (and my colleagues) should have no trouble in ranking these passages from worst to best, and in explaining their reasoning for the ranking. The in-class passages are in "math," each giving a "proof" of the fact that the sum of two odd numbers is even. Having given them the chance to warm up in "English," I now ask the students to rank the proofs from worst to best, and to justify their rankings. This is a more difficult task, but once it's done my students (and colleagues) should be able to see more clearly that good writing in math is only a half-step away from good writing in any other discipline.

Okay, I've prattled on long enough. I'll end this for now. As usual, feel free to check in with your comments, always appreciated!