For Tallulah...

Tallulah, one of this year's REU students mentioned that she'd gone back and read some of my old posts on this blog (props, Tallulah!), giving me one reason to post more often: it's nice to have tangible readership. (Thanks also those of you who've commented on recent posts, particularly this one and this one).

Tallulah also gave me an idea for today's post. After I channeled my inner purist and insisted on specific pronunciations of certain Greek letters, she suggested I post on the correct pronunciations of the Greek alphabet, according to modern standards. Thus...

α: alfa
β: veeta
γ: ghama (it's a guttural, with a little bit of a catch in your throat...)
δ: thelta (where the "th" is voiced, like in "there" and not "theory")
ε: ehpseelon (with a long "o"...all o's following are also long)
ζ: zeeta
η: eeta
θ: theeta (with an unvoiced "th," as in "theory")
ι: yota
κ: kapa
λ: lamvda (yes, you read that right)
μ: mee
ν: nee
ξ: ksee
ο: omikron
π: pee
ρ: rho (duh...here the "h" indicates aspiration: breathe outward slightly as you're saying it)
σ: seegma
τ: tav
υ: eepseelon
φ: fee
χ: khee (this fricative is one of the hardest sounds in Greek for American English-speakers to make)
ψ: psee
ω: omayga

Happy speakin'!

BTW: I don't pronounce β like "veeta" with my class...and I certainly don't pronounce π as "pee." So please don't write me angrily demanding consistency with these pronunciations...and don't even ask me why I didn't use standard IPA symbols. I'm trying to be accessible here, and not erudite.

Rock stars

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

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

But before that...

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

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

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

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

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

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

Yup, my students are rock stars. Crazy day.

CCCC, Vol. 3: Take 2

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

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

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

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

Exciting stuff! Further bulletins as events warrant.

On your marks, get set...

It's been a while, huh?

As you might suspect, I've had a lot going on, keeping me from posting here for the past, oh...two months? Ouch.

What's going on?

The REU's over, but the work has really just begun: the students this year were fantastic. They were smart, fun, and funny, and they worked tremendously hard, producing a ton of interesting mathematics. (We should get at least five papers out of it in the next couple of months, and maybe more beyond that in the follow-up.) And this year it was "buy eight weeks, get one free": six of the eight students ended up traveling to MathFest in Pittsburgh, PA to present on their summer research.

The REU took up much of my time, but I've had a number of other things going on, as well, among them: (1) working on student learning outcomes for both the Mathematics Department and the Writing Intensive program, (2) putting together the ILS Oversight Committee's report to the Academic Policy Committee (still not submitted, but finally almost finished), (3) planning my contribution to the short course I was helping run at MathFest, (4) working with my College of Charleston peeps on our paper on the rhetoric of mathematical writing, (5) looking ahead to my round table discussion of program assessment for this year's CWPA (coming up in a few weeks), (6) laying the groundwork for the book I'm now slated to write for Jossey-Bass (w00t), and (7) trying to get ready for my Fall classes, which start on Monday.

(1) Student learning outcomes: although I see the purpose, ultimately, of programmatic assessment, too highly institutionalized assessment tends to become bureaucratic and corporate. I don't want to say more about my role in this university-wide process this past summer other than that it was frustrating at times, had its minor joys, and though it was ultimately fulfilling in that I feel like some good will come of it, I worry about the intentions some people in administration may have for codifying the university's student learning outcomes as rigidly as is being done. 'Nuff said.

(2) The ILSOC report to the APC: this is more of the same. I see the purpose, and the writing of this document is a worthwhile activity, but one which runs the risk of being overly parliamentary and pro se. 'Nuff said.

(3) MathFest short course on Sage (an open-source computer algebra system): I actually wrote to my colleague Oscar (one of the co-organizers of the short course) in mid-July, a few weeks before the course was to take place, expressing my insecurities about putting together an hour or two of meaningful material.

"Nonsense," was the substance of his reply; "you'll do fine. Write about what you know." So I threw together several worksheets full of Sage code purporting to implement a number of higher-level graph theoretical algorithms and called it good. The worksheets actually went over really well in the short course and filled a rather comfy niche in the program. I felt good about what I'd done.

The moral of the story: just do it.

(MathFest, by the way, was a blast. Pittsburgh's a nice city with lots of pretty runs and nice architecture, the REU students were fun to hang out with, as always, and the MathFest program was replete with fun stuff to see and do. A good time had by all.)

(4) Math rhetoric: as I mentioned in my last post, oh so long ago, Bella and Damian came up from the coast to spend a couple of days with me, hammering out a plan to finish the paper we'd begun (with Nicola, who couldn't make it) on the rhetoric of the writing my REU students had produced in 2008 and 2009. They had a lovely time while here, visiting with and interviewing the REU students from this past year, working on our draft at the time, and just hanging out. I'm happy to say that as of last night we have a draft that's nearly ready to submit to the comp/rhet journal Across the Disciplines. It's the first of what we hope will be...well...at least more than one article on the rhetoric of mathematics and its learning, and the role writing plays in inducting students into the scholarly mathematical community.

(5) CWPA: I'm already looking forward to the Wildacres retreat! It's going to a be a full house this year, several dozen of us crowding into the nooks and niches of the Wildacres North Lodge to join in round table discussions of assessment with various forms and functions. I plan on presenting a brief "natural history" of the assessment that's gone on in our WI program during the past three years, exposing to public view the layers of rock comprising the "pilot" assessment Lulabelle headed up in AY 2007-8, the refinement she and I performed in the following year, the plans for assessment she and I laid out in the lead-up to the university's reaffirmation of accreditation (notice I haven't mentioned SACS yet in this post...), and the modifications those plans underwent as I limned the WI program's assessment of student learning outcomes this past summer.

It's sure to be riveting.

Actually, I'm more looking forward to hanging out with Damian and Bella, and with them planning the next phase of our study of the REU students' writing.

(6) Book: Oh yeah...I'm now under contract to write a text (working title: More Than Numbers) on the role of writing (specifically, writing to learn and writing in the disciplines) in mathematics and the mathematical sciences. Jossey-Bass received well the proposal I pitched to them several months back (in March, I think?), and after some fine-tuning of the project, I was brought on board. I'm excited, but at the same time terrified. I'm confident it'll all work out well, though. I've already done a ton of enlightening reading (if you get a chance, check out Scott L. Montgomery's The scientific voice...it's a fascinating read that, along with several other sources, has helped me put together a theory of the schizophrenic nature of undergraduate mathematical writing), and I have some great ideas. Furthermore, my consulting editor for the project is someone a few of whose books I've read and whom I respect very much; I'm sure she'll be very helpful to me.

I will say this, however: if between now and next March I start randomly babbling to you about reader response theory or the role of writing in the mathematical finance classroom, just smile and nod your head.

(7) Fall 2010: yup, we get underway in two days. Yikes. I'm actually really excited: I've got the first week mapped out in all three of my courses, and I've plotted out what I think are clear and navigable problem-centered paths for both of the lower-level courses (Calc I and Linear Algebra I) to follow.

Calc I is going to begin with a brief review, and then the students will work toward developing the skills needed to solve an optimization problem from economics. They'll need to "invent" the method of secants and tangents, the definition of a limit, and the definition of the derivative; and they'll need to learn how to compute some simple derivatives in order to solve this problem. Once all of that groundwork is laid, we'll spend some time working with the textbook and picking up some useful formulas for limits and derivatives, but everything we do is going to be application-driven and learner-centered. I hope to not have to lecture for more than 10 minutes at a time for the whole damned semester.

Linear's going to be the same: Day One features a variation on the "Markov Dance" that started the semester off the last time I taught this course, in the semi-mythical beginnings of this blog. The limiting behavior of this system is going to be the motivating problem for everything we do in the first half of the course, as we work our way through everything we'll need to do to get to the fun and useful stuff (eigenvalues, diagonalization, and Markov processes): solving linear systems, inversion of matrices, solvability criteria, and finally eigenvalues. I'm going to downplay theory and upplay (what a cool word!) functionality. I hope to get to the fun stuff by the sixth or seventh week, at which time we can spend almost all of our time on applications. It's going to be fun.

I should mention that I've modified my grading schemata somewhat, but not substantially, from last semester: students in both of the above courses will still have an opportunity to perform potentially unlimited revision on most things they hand in, but I'm tempering the grading scale so that it's no longer possible to earn full points back with each revision. I think the system I've set up is a generous and reasonable one, though, and I believe it'll still serve to motivate students to learn rather than to grub for a good grade.

Meanwhile, the Senior Seminar's speaker schedule is chocked full, with four visitors (all versed in speaking to undergraduate audiences) coming to share their knowledge and spend a little time with the students. It's going to be a good semester in that course.

Okay, that's all for now...I'm going to try to post more regularly during the coming semester, although I can't promise it'll be more than anxiety-tinged stream-of-consciousness rambling about this or that idea for the book.

Fare thee well!

Weather's great, wish you were here.

I haven't had much time to write, but I thought I'd send a postcard from this edge.

We've just finished three weeks of the 2010 REU, and things are chugging along smoothly.

Incredibly smoothly.

Wow.

The students' first presentations (yesterday) were masterful, already conference-worthy: their talk mechanics were spot-on, they displayed superb mastery of the concepts and computations they presented, and their slide designs were eminently professional. In every way their presentations were superior than many of those I've seen given at major conferences by seasoned mathematicians.

They're ready for the "minisymposium" we're playing host to next week, to which we've invited the faculty and students from two other area REUs.

I hope that I can take some of the credit for the students' success to this point: I've been yet more intentional in my design of the program's activities than I've ever been in the past, providing even more and more timely instruction on writing, presenting, use of scholarly sources, reading of math papers, etc. than in past iterations of the program.

And I've had help in this, too, that I've not had before: Bella and Damian, two of my Charleston-based partners in composition-theoretic crime, came up the mountain a little over a week ago to talk to the kids about writing and math. The visit was twofold...perhaps even threefold: (1) to give the students the rhetorician's point of view on mathematical writing, (2) to interview (though this term was never used) about their past experiences with academic writing in general and mathematical academic writing in particular, and (3) to get our shit together and make some progress on the paper we began back in February when I joined them for a working weekend down in South Carolina. (To this last point, briefly: I was tasked with coauthoring sections on the students' mastery of visual rhetoric, specifically with regard to the visual effects on the reader of white space and mathematical formulas; and on the students' use of sources. My analysis of the latter was very enlightening to me, and helped me quantify the fact that this year's students are well ahead of their predecessors when it comes to making effective use of the literature they find in the course of their investigations.)

The two-hour-long "interview" with the students was wonderful. In the discussions that arose the students revealed rich and robust histories with writing, including a good deal of relevant and highly intentional instruction I might not have expected. These students are very well-prepared (which helps to explain the success they've had so far in this summer's program!). The interview also gave us a great deal of data we can use as a foundation for our next article, in which we hope (already!) to trace the development of students as communicators of mathematics through the course of a summer research program one of whose foci is on writing in the discipline. Bella's already kicking around the idea of coming back toward the end of the program to interview the students again and see if anything's moved.

Mathematically, the students are fantastic. They're very self-directed and intrinsically motivated. They're displaying superlative creativity and originality of thought, to a greater extent than did many students in previous years of the program. They're making terrific use of the sources they find, plying them effectively to serve multiple purposes: to find other sources, to support their own propositions and theorems, and to situate their work in the context of what's come before. And every one of them has a clear sense of purpose in his or her project: no one of them is "stuck," as I've seen happen in the past.

More important, perhaps: they're getting along exceedingly well with each other. From Day One they've bonded remarkably well. They do almost everything together, not because they feel like they have to or because they're afraid to do thing alone (both of these have been moving forces in previous iterations of the program), but because they want to. They clearly like each other. A lot. It's good to see.

It comes across in simple things, too: yesterday, during the students' first round of talks, this year's group proved themselves to be the most attentive and responsive audience members we've yet had in the program. They listened with clear and unfeigned interest, they gave encouraging nonverbal feedback (nods and smiles) at appropriate moments, and they asked a number of good questions of their peers at the end of every talk. Midway through the talks Tip (my sole faculty partner in running the program this year) and I marveled at the fluency of the students' presentation skills and remarked at how though the students had all chosen to work on individual projects (something we initially bemoaned) it was evident that to a greater extent than in previous years the students are collaborating with one another behind the scenes, sharing ideas, talking about LaTeX and Beamer, and helping each other through rough spots.

Ladies and gentlemen, we have established an effective learning community.

What else is up?

I've only been to one meeting of the Learning Circle (having missed last week's to work the run-off election) I chose to take part in this summer, but I have a good feeling about the direction it seems to be taking.

I've received good feedback on the proposal I sent to Jossey-Bass for a text on writing in mathematics.

I've finally submitted a reasonable draft of an assessment plan for the university's Writing Intensive student learning outcomes to the powers that be. I doubt that's the last I'll hear of that, though.

It's been a busy summer, but a good one. I'm excited to see what the coming week will bring.

For now, I'm going to kick back and watch Ghana get the better of the U.S. soccer team.

Day Two is in the can

We've wrapped up two days of the 2010 REU, and things are running smoothly so far.

The students are gelling tremendously quickly into a friendly and supportive learning community. As early as the welcome barbecue a few nights back it was obvious these folks were going to get along really well, and the last couple of days have borne that observation out. "I was a little worried before coming here," one of the students told me at the barbecue, "but everyone's so nice that I know I'm not going to have trouble working with them. It's going to be easy to ask them for help if I need it."

Although I can't yet claim to know them all incredibly well as individuals, each is beginning to make known her or his particular strengths and weaknesses. Three of them are particularly eager to demonstrate their skills and hesitate not at all in traipsing to the board to show off their solutions. A couple of the others are more retiring, willing to whisper the answers (almost always correct) from where they sit but less enthusiastic about taking to the board. The remaining three are quieter still and it often takes a little prodding to get them to share their ideas. Notably, to an extent not seen since the first year of the program, one of the students is clearly emerging as the "social director." She's the most outgoing of the group, though a couple of her peers aren't far behind when it comes to eagerness and enthusiasm.

I should note that the students needed little convincing to complete the first day's freewriting exercise, which was designed to tease out of the students their personal goals for the overall program. I've posted the resulting list of student goals here; happily, most of the learning goals coincide very well with my own.

The students are making quick progress through the long list of graph theoretical definitions I bludgeoned them with yesterday afternoon, and we're already over halfway through the graph theory notes I hope to complete before calling it quits. We've also hit on several topics from dynamical systems and geometry, and tomorrow brings more graph theory, dynamics, LaTeX, and Mathematica. It's going to be a full day, but I think we'll get through it.

Further bulletins as events warrant. For now, bed calls. My bedtime reading? The basis for the Learning Circle in which I'm taking part this summer, Helping college students find purpose: the campus guide to meaning-making, by Robert J. Nash and Michele C. Murray (2010, San Francisco: Jossey-Bass). We'll see what comes of it.

REU ramp-up

As of 11:00 or so last night, all of the 2010 REU students are in town.

They're gelling as a group really well this year, much as they did two years ago. Last year's folks took a little while to come out of their shells, although once they did so, they got along famously and I joy in seeing their friendships continue via Facebook.

This year's crew is ready to get underway, I think. They're as excited as I am to get started tomorrow morning.

As I've mentioned before, I've made some changes, mostly minor, and all for the best, I hope, in the program this year.

What's new?

1. New focus on specific aspects of communication. As I indicated in my last post, I'll be requiring students to practice "elevator talks" and provide at least one visual in their every-other-weekly presentations. My hope is that these new requirements will lead to greater intentionality on the part of the students as they craft their talks and papers.

2. Deepening of engagement with source material. Students will now be required to perform a thorough literature search as a natural adjunct of their respective research projects, and this literature search will be accompanied by the creation of a simple annotated bibliography. This exercise should help them in developing meaningful "history" sections in their papers.

3. Alternation of presentations and papers. The students will be completing only four (not six) drafts of their papers throughout the summer, at the end of the second, fourth, sixth, and eighth weeks. They will be presenting only every other week, rather than every week, at the end of the third, fifth, seventh, and eighth weeks. We will still have a mandatory meeting on every Friday, but on alternating Fridays this time will be used for conferencing on papers, peer review, practice of elevator talks, and so forth.

4. Emphasis on collaboration. In addition to more frequent peer review (I plan to have them perform three peer reviews, as opposed to the one done in the past years), I'll be emphasizing the collaborative and communal nature of mathematical research by encouraging them to work together on their projects. As exciting as it is to have eight students working on eight different projects, the students stand to gain more by working with one another, and my attention can be much better focused if I only need to stay on top of three or four projects rather than eight.

I've got a good feeling about it. They're a bright bunch, they're getting along well already, and I think it's going to be a particularly good summer.

Sampler

During the past week I've attended, presented at, participated in, or facilitated two conferences and three faculty development workshops, on topics ranging from pure mathematics (group theory and graph theory) to the pedagogy of writing and advising first-year students who are brand new to a liberal arts university. I've written dozens of pages of notes, collected several handouts, worksheets, resource lists, and sets of slides. I've talked with, listened to, or sent e-mails to dozens of colleagues. In between doing all of the above I've been spending most of my time reading up on the history and philosophy of science and its teaching and on the role played by gender in mathematics achievement.

Below I've collected a number of quotes, factoids, observations, and questions dealing with all that I've been doing for the past week or so. Every one of these items deserves further follow-up; maybe I'll get around to addressing some of them over the summer, maybe not. I just want to get them out there for now.

1. Contextualization (and resocialization) of science. First, more from Thomas S. Kuhn's The structure of scientific revolutions (pp. 136-137), on the apparent linearity and cumulative nature of science and the related transmission of scientific knowledge:

Textbooks thus begin by truncating the scientist's sense of his [sic, here and following] discipline's history and then proceed to supply a substitute for what they have eliminated. Characteristically, textbooks of science contain just a bit of history, either in an introductory chapter or, more often, in scattered references to the great heroes of an earlier age. From such references both students and professionals come to feel like participants in a long-standing historical tradition. Yet the textbook-derived tradition in which scientists come to sense their participation is on that, in fact, never existed. For reasons that are both obvious and highly functional, science textbooks (and too many of the older histories of science) refer only to that part of the work of past scientists that can easily be viewed as contributions to the statement solution of the texts' paradigm problems. Partly by selection and partly by distortion, the scientists of earlier ages are implicitly represented as having worked upon the same set of fixed problems and in accordance with the same set of fixed canons that the most recent revolution in scientific theory and method has made seem scientific. No wonder that textbooks and the historical tradition they imply have to be rewritten after each scientific revolution. And no wonder that, as they are rewritten, science once again comes to seem largely cumulative.

My question: does it have to be this way?

My answer: no. But an elaboration of that answer will have to wait for now. I have a good deal more to say in reflecting on the social constructivist point of view of science, first (or at least first explicitly) elaborated in Kuhn's work, as in the following passage (p. 42):

Though there are obviously rules to which all practitioners of a scientific specialty adhere at a given time, those rules may not by themselves specify all that the practice of those specialists has in common. Normal science is a highly determined activity, but it need not be entirely determined by rules. That is why, at the start of this essay, I introduced shared paradigms rather than shared rules, assumptions, and points of view as the source of coherence for normal research traditions.

The nature of the rules to which specialists adhere is fluid and dynamic, susceptible to the exigencies of the day-to-day applications of those rules. Rules, as applied, evolve, and they evolve in accordance with their usefulness as judged by practitioners of the specialized discipline concerned with those rules. More than anything else reading Kuhn makes me aware of the need to be more intentional about including opportunities for my students to explore, discover, interpret, investigate, and describe the concepts we consider in any given class; they must be made, to the greatest extent possible, to feel like they as much authors of scientific discovery as I am. (Particular attention to the role of youth and neophycy in scientific "advancement" is critical as well.)

2. Invention versus discovery. I've often asked my Calc I students to think about the difference (if there is one) between invention and discovery when they take part in the Newton v. Leibniz project. Kuhn will serve as an excellent source for those students interested in learning more about the distinction between the two notions: pp. 51-53 contain a discussion of this distinction, highlighting invention as the adjustment that goes on in a paradigm's conception of science in the wake of a discovery: one may be the first to objectively observe a physical phenomenon, say, but until the significance of that phenomenon is understood and elaborated, and the discovery's relevance is described, one cannot be said to have invented a thing. In a sense invention is the recognition of the importance and relevance of a discovery via its incorporation into the normal scientific tradition that operates within a given scientific paradigm.

What might students have to say about this?

3. Revision (in writing) as revolution. The parallels between Kuhn's portrayal of scientific revolution (especially as it compares to political revolution) and revision of one's writing as a process are too great to be ignored: revision occurs concomitantly with the recognition of the inadequacy of what one's written to account fully for one's perception of the subject of the writing. That is, revision is undertaken in response to a perceived discrepancy between the author's intent and the author's ideas as communicated expressly on the page. Compare (p. 91): "In much the same way, scientific revolutions are inaugurated by a growing sense, again often restricted to a narrow subdivision of the scientific community, that an existing paradigm has ceased to function adequately in the exploration of an aspect of nature to which that paradigm itself had previously led the way."

To continue the parallel between these "revolutions" would force us ultimately to recognize what students of writing are often loath to admit (and what teachers of writing already know very well): writing is a social process, as much, if not more so, than is scientific discovery.

I should note that in the following pages in Kuhn's text (pp. 92 ff.) he most clearly articulates the role of social forces in shaping scientific revolutions. When competing paradigms come up against one another, adherents to one or the other must be prepared to argue in favor of their particular paradigm.

4. Portfolios (again). Enough about Kuhn (for now, at least). Let's get to some observations on the International Writing Across the Curriculum Conference, the first two days of which I was able to attend at the end of last week.

In talking with my colleague Nero (currently at the University of Hawai'i, Hilo) I found myself suddenly able to articulate, far more clearly than I've ever been able to before, what exactly a portfolio means of assessment might look like in a mathematics course. One or two communication outcomes would join one or two affective or metacognitive outcomes, and these would join two or three content-centered outcomes as a basis for the course's assessment. (I already generate such outcomes for all of my courses.)

Throughout the semester the students would be given a variety of assignments, successful completion of each of which would demonstrate achievement at one or more of the outcomes on the list described above. These assignments could include more traditional problem sets (though likely not sets of problems pulled from a textbook), written components of projects I already assign (like Newton v. Leibniz, Confectionary Conundrum, etc.), reflection or response papers in which students explore their personal and emotional engagement with mathematics, and so forth.

Students will have a chance to perform unlimited revision on many of these assignments, so that if a student isn't happy with a given iteration of a given assignment, she can revise her work to improve upon it. (As regular readers know, I'm still working on adjusting my revision policies.)

In the last week or so of the semester the students will be asked to select four or five assignments from among those completed during the semester to represent their mastery of as many of the course learning outcomes as possible. They will then write a brief (no more than five or six pages) paper in which they articulate explicitly the role served by each of the assignments they have chosen to include in the portfolio: why include this piece? Mastery of which outcome does it purport to demonstrate?

I'd like to recruit one or more of my colleagues to help me assess completed portfolios the first time around; there ought to be some sort of validation process.

Thoughts?

5. Intentionalize, intentionalize, intentionalize! This coming summer's REU students will receive yet more intentional instruction in writing than any previous year has received. At least two of my College of Charleston colleagues will be coming up to help impart their wisdom on rhetoric and composition. I'll be giving the students more models of professional writing than they've been exposed to in the past. And, most notably, I will obey the exhortation of the four presenters from Virginia Commonwealth University and place more emphasis on the "middle" stage of student research writing.

What do I mean by this? Much like the faculty at VCU (as described by the four presenters mentioned above), I find I've been very intentional about helping my REU students find sources at the outset of their research program, and I've been very intentional about helping them through draft after draft of their week-to-week research reports once those reports have assumed a certain level of coherence. But, like the aforementioned faculty, I've been somewhat remiss in offering the students explicit instruction in the middle stages of the process: how does one evaluate sources? How does one compare them? How does one decide on the relevance of a particular source to one's own researches?

I've decided that I'm going to require the REU students to follow their initial literature searches (which most of them do) with the construction of an annotated bibliography in which they highlight the important contributions of each source, summarize the relevance of each source to their own work, and prioritize the source, ranking it alongside the other sources they've found in terms of its strength of contribution, its clarity, and its relevance to their particular research project.

Will this make more work for the students? You bet it will. But since I'm only going to be asking the students to produce a draft of their report every other (rather than every) week, I feel it's a fair amount of work to ask of them.

It occurred to me this morning, in sitting in on a faculty development workshop focused on our LSIC courses, that the same sort of exercise should be required of students in our MATH 480 course in order that that course warrant its Information Literacy Intensive designation. Just two years ago I suggested that the department begin requiring students in MATH 480 to produce an expository paper; this suggestion met with almost no resistance. I hope this new suggestion will go over equally well.

6. Other thoughts for the REU. What else will I be asking this year's students to do? Nothing excessive, I believe. It seems to me that I should require the following of the program's participants:

History and context. Every draft (not just the last) of every student paper this summer will be required to have a section describing the history and context of the topic the student is investigating. This section, like the rest of the paper, may be rather sparse and tentative at first, but like the rest of the paper it will become more full and flourishing as the summer goes on. I believe it's important, though, that from the very onset of the program the students become accustomed to contextualizing their work and establishing its place in the field.

Visuals. One of the VCU folks mentioned above presented a metaphorical means of constructing an annotated bibliography and literature review, comparing the process of finding, evaluating, prioritizing, and applying sources to planning a conference, at which participants must be placed at various tables, grouped in various sessions, and so forth, according to interests, purposes, and points of view. The most striking aspect of this presentation to me was the insistence on a visual representation: the presenter required her students to come up with a visual means of portraying their evidence. I am going to start requiring each REU student to include at least one visual representation of her or his work in the bi-weekly presentations they'll be delivering. That visual may be the same from week to week, but if the visual remains unchanged I will ask the student to justify her or his reason for retaining the same visual. This, I hope, will encourage students to reflect upon the way in which they are representing their work through nonverbal means; this reflection could lead to further discovery and, of course, refinement of the visual rhetoric the students use in describing their work.

Elevator talks. Even the strongest undergraduate research students have trouble articulating their work clearly and concisely. I'm going to begin asking every student to open her or his presentation with a no-more-than-one-minute "elevator" version of the presentation. What is the main focus or question of your research? What method or methods are you using to try to study that focus or answer that question? How does your work fit in with others' work on the same topic? I hope this additional intentionality will help students develop the ability to communicate their work in the hurly-burly world of conferences and cocktail parties.

7. QEP. As many of my colleagues in the Southeast part of the country know, QEP stands for "Quality Enhancement Plan," and is the means by which the Southern Association of Colleges and Schools (SACS, the accreditation agency for an enormous number of institutions of higher learning in the Southeast) asks the colleges and universities it oversees to plan and implement institution-wide changes to enhance student learning.

I'll have a lot more to say about this in the coming weeks, months, and, if all goes well, years, but I'll simply say now that I am more committed than ever before to making writing the focus of UNC Asheville's QEP. I will do all that I can to lobby for this position.

8. Inkshedding. Perhaps the most delightful thing I took away from this past Wednesday's workshop on writing instruction of ESL students (ably facilitated by my colleagues Hannah and Tabitha of UNC-Chapel Hill and NC State University, respectively...thank you both so much for coming out!) is a new form of low-stakes writing to which I'd not before been exposed. "Inkshedding" is much like a collaborative form of freewriting. As they would be in a freewrite, participants (in groups of three or four) are asked to write on a given topic for a set amount of time (three minutes, say) or until they have written all they would like to on the topic at hand. When finished, each participant places his writing in the center of the circle and waits for someone else to do the same. The papers are then exchanged, and each person reads what the other has written and then responds in writing on the first writer's paper. Once done responding, the second person places the paper in the center again and takes another. And so on. In theory, the process could continue endlessly, readers writing in response to others' responses to their own responses, and so forth.

Beyond its obvious pedagogical usefulness, I think this would be a fantastic way to construct collaborative poems, or at least generate ideas and images for rich poems or other pieces of fiction. I'm eager to find a few folks who are willing to try this out. If you're game, let me know!

9. Gender matters. I'm currently reading a book that I picked up (in the simply marvelous bookstore Caveat Emptor) in Bloomington, the site of the IWAC conference last week, Mathematics and gender, edited by Elizabeth Fennema and Gilah C. Leder (1990, New York: Teachers College Press). This collection purports to analyze the different ways in which gender influences math performance, success in math coursework, and affective responses to mathematics and its study. Unsurprisingly, men and women differ with regard to their experience with math, and factors such as confidence, perception of utility, sex-role congruency (the "math is for men" stereotype), fear of success, and attribution of performance to one or another cause (effort, ability, or outside forces such as sheer luck) all strongly, and differently by gender, affect an individual's mathematical understanding and performance.

I've yet to read much in this book that's given me reason to adjust the way in which I teach math, aside, perhaps, from Lindsay A. Tartre's study (Chapter 3, "Spatial skills, gender, and mathematics") suggesting that in women there is a far stronger correlation between spatial skills and mathematical performance. Might I do well to place particular emphasis on visual representations of problems when working one-on-one with a female student? I already attempt to adapt my explanations to whatever mode it is in which I know a given student most clearly understands mathematical ideas.

It's something to think about. I may have more to say about this book as I get into the later chapters, which deal with the role of the teacher and the classroom dynamic in assisting or impeding students' mathematical understanding.

That's enough for now. I realize that this is one of the longest posts I've written in a long time. Believe me, I've tried to keep it short! I hope to be able to elaborate on one or more of the above issues in later posts, especially as I begin to implement some of the proposed changes to my REU and to my regular courses.

To be, as ever, continued!

Rocks and gravel

I've just finished reading Jonathan Kozol's Ordinary resurrections, begun just a few days back, and I feel, as I usually do on reaching the end of one of his books, an overwhelming sense of tiredness bound together with a bright and unbreakable thread of hope and strength.

It's a good book on which to end this academic year, surely the most tiring yet of my career (although, as I've noted on this blog before, not the busiest). Reading it at the close of the year gives me at once a sense of closure (which I've sorely needed) and a feeling of renewed energy. The book ends on the same note, as Kozol describes a gift of art Pineapple, one of the children of whom he speaks about most often in the book, gave to him: "an imitation stained-glass window that she made from tissue paper, brightly colored with green paint and with a wash of light-blue ink...When I asked her recently if it was supposed to be a rising sun or a setting sun, she seemed at first to not remember what I meant...'You decide,' she told me uselessly...at the risk of being sentimental about somebody whose sunny disposition brings a lot of joy into a world that has too many cloudy afternoons, I like to think it's rising" (p. 339).

Is it?

Kozol often admits in this book and others he's written since that he's getting older and feeling weaker. Although not yet as frail as he is physically (he's over seventy now, if I'm not wrong, and was sixty-four when he wrote the book I've just finished), I feel, on certain days at least, that I can empathize: each passing year steals away a little bit more of my relevance, my credibility, and my coolness.

"You may have them eating out of your hand now," my department's chair sometimes warns me, a hint of glee in his voice, "since you're not all that much older than they are. But just wait until you're my age." I'm warned that I won't be seen so much as the cool older brother but rather the stern-but-caring father. Just this past semester I encountered a student out of whom my most earnest attempts at cool cajolery could coax nothing. Magda, scarred, I suspect, by recent unpleasant experiences with mathematics, was timid in her dealing with me, reluctant to take part in any activities in class, and unresponsive to personal offerings of assistance I sent to her by e-mail. "I have to be honest that I've gotten a sense of 'defeat' from you for much of this semester," I wrote her. "I know you'd mentioned earlier this semester that you'd considered math as a major, and I hope that that's not an idea you've abandoned entirely."

I urged her to reply, but I never heard back from her.

This incident can't help but make me think of a noontime meeting several of my colleagues in the department and I shared with a pair of textbook company representatives. While my colleagues and I pored through elaborate boxed lunches bought from an off-campus catering company, the two textbook reps gushed for several minutes over the features of their company's latest Stewart-clone calculus textbook.

They tried to make their case, I'll give them that. I'd indicated that I honestly don't use whatever calculus textbook I've been assigned as much more than a source of examples and exercises (generally the exposition in such textbooks is godawful, and the organization is unmotivated, at best), supplementing the textbook substantially with descriptions, worksheets, activities, and projects of my own devising, including a number of nontraditional writing assignments. "We're very proud that [their text] contains [some unsubstantiated and moderately large number of] pre-written group projects." I nodded, unimpressed. (So does every Stewart-clone; generally these projects are as unmotivated as the integument of the text itself.)

About fifteen minutes into their demonstration, and after about ten minutes of fiddling with recalcitrant teleconferencing software, the reps got the lead textbook author himself on the line. He sounded tired, as though he'd made these dogs and ponies to dance two or three times already earlier that morning (or at least that week). He showed us a number of the features of the on-line text, most excited about the numerous Mathematica-driven animations he and his colleagues had developed for the textbook. (Such animations are not in themselves bad things; however I fear that without empowering the students to learn how to create their own animations, the animations alone do little more than provide an alternative visualization tool.)

After trotting the poor schlub of an author around the rink for a few more laps, the reps resumed their own presentation, and reached the part of their sell about which I was reminded above. "The beauty of the on-line scoring capabilities," one of them said proudly, "is that once a student has submitted her homework and the homework is graded, the computer can generate a personalized letter indicating to the student what sorts of problems she got wrong, telling her where she needs to focus her study. This can be done automatically, for a class of two hundred students. They'll think that you cared enough to write a personalized note to every one of them about their work."

I don't want to give the impression that this past year was all about weariness and defeat. To the contrary, I feel I've had some tremendous successes in the classroom.

While the textbook exercise fell on its face this past semester in Topology, it went over fantastically with the MATH 280 folks in the fall, and I can't think of many moments in my career at which I was prouder than I was when Ulrich and Uriah spoke on the project at the Elon conference (including in their presentation the phrase "writing-to-learn," and defining the phrase correctly!).

While I feel I lost the "faith" of some of my favorite students, like Magda, above, and like Tish, who became openly disillusioned about topology by the semester's end, I feel like that loss was only temporary, and that through open communication and understanding I've won that faith back.

While I feel my attempt at crafting a more meaningful system of feedback met with mixed success, the success I've earned is great enough to encourage me to recraft the system and try it again next term, rather than simply to abandon it.

While I've had my share of dealings with troubled and troubling students this past year, I've also had my share of dealings with marvelous ones. Jacobina's transformation from a hesitant and nearly math-phobic student at the outset of Calc I to one of the most outspoken, confident, and competent scholars in the stronger of my two sections of Calc II was nothing short of astounding. Words cannot describe the pride I have of her. Equally exciting is the undergraduate research Tonio and Siegfried have done, and the potential Ino and Iris have to do similar research this summer.

These small (and not-so-small) victories and many more like them are the rocks and gravel out of which, as the old blues standard goes, a solid road is built. Where's the road headed?

I've got back-to-back conferences coming up in less than a week (the International Writing Across the Curriculum Conference in Indiana and the AMS Eastern Sectional Meeting in New Jersey), then a half-week of Integrative Liberal Studies workshops in which I'm playing some role or another. A week after those come to and end the REU students start arriving. I have high hopes for this year's program; they're clearly a bright bunch with a lot of strengths. I've got a book proposal in at a good publisher, on which I'm still waiting to hear a decision. I've got great ideas for my courses next fall. It's going to be a good year.

The road is a long one, but the sun's shining yet.

I think, indeed, it is rising.

Trust me

Elon's over.

At last.

And after several months of planning, it came off all right. And the planning was worth it, as annoying as it often was: the students (particularly the younger ones!) got a lot out of it.

The drive out was a pleasant one (with only a light spray of rain), and the three-hour trip to the conference site gave the students (several of whom didn't yet know each other well) open up a bit and build bridges. As I told them then, for the first of several times during the next 48 hours or so, "you don't really know someone until you've got to a conference with them."

Obligatory alcohol-induced first-night revelry out of the way, the conference began on a high note. After an hour at the Project NExT session, I headed over to the first round of Math Jeopardy! in which our school has ever fielded a team. The Asheville team faced off against three others, and though our folks stumbled a bit at first (with a score at one point dipping into negative numbers), they quickly rebounded. Georgia Southern's team ran through the differential equations category, but with those questions depleted the UNCA team blazed through the category on "trans" words, pulling ahead, the ten or so of us in the audience exultantly pumping our fists with each right answer. A brief slump put them in second place going into Final Jeopardy, and it was only because of conservative wagering that our team came in second in the round...and ultimately ninth out of thirty-four teams. I was floored, and beaming with pride.

The conference itself began with a plenary talk on female mathematicians in the time of Euler. One of the central figures in the talk was the Italian mathematician Maria Gaetana Agnesi (of "Witch" fame), a topic I knew would be of interest to Ino, a student I've come to know as something of an Italophile. Sitting behind her, I tried to judge her level of enthusiasm during the talk. My suspicions were confirmed when I talked to her after the lecture was over, noting the excitement in her eyes. I've since suggested she might look into the possibility of translating the work of some other classical Italian mathematician as a research project straddling math and her beloved language.

The REU panel my colleague Lancelot and I put together was well-received, with nearly 100 people attending the panels and talks. I most enjoyed the student panel, on which three UNCA students, each of whom had taken part in a very different summer research experience, and one of the participants in my 2009 REU led a discussion regarding the aspects of a successful REU program. The discussion was open and frank, touching on negative aspects of summer programs as well as positive ones. As Lancelot said, our panels (both the faculty-led one and the student-led one) each could have been an hour long, and the conversations would have remained as rich at the end as at the beginning.

My new department-mate Kelli and I had a chance to catch up for a bit after the REU session ended, and after she and I and Lancelot hung out for a bit shooting the breeze I headed back to the hotel to lead our entire UNCA contingent to a Thai restaurant I happened to spy on the hotel's dining list: most of us trekked halfway across town to enjoy a surprisingly lovely dinner together in the company of twenty or so of our closest friends.

I spent most of last night putting the finishing touches on my talk for this morning, a fifteen-minute piece titled "The role of trust in teaching and learning." Here I had a few words to say about the ways in which the affective effects our learning environments as strongly as does the cognitive. More engaging to me than my talk were the conversations with my students that led up to it, in which I asked them to offer me their own views on trust in teaching. In every one of these conversations (ones similar to which I would recommend my fellow teachers to have with their own students) the students were lively and animated. I suspect that students may be so animated because they're not often asked questions like "how do you feel about the work you're doing in class?" or "how might your professors most easily earn your respect and trust?"

I think my talk was somewhat well-received, judging from comments people made to me afterward. I was a little worried that its rather unorthodox topic and methodology (highly qualitative, empirical, and anecdotal) would rub some of the more traditionalists the wrong way, but I'm not overly concerned. I feel strongly about what it is I had to say, and I can live with whatever discomfiture it may have caused a few of the gray-beards.

During the next couple of hours I had a chance to catch up with previous years' REU students (Dione from 2008 and Daria from 2009, who'd already spoken and served on a panel in the REU session the day before) and take in a couple of talks given by a few of my Asheville students: Siegfried's discussion of logarithmic concavity was breezy and easygoing, and Uriah and Ulrich's overview of last semester's textbook assignment in 280 was fantastic. Not only did they offer a full and accurate picture of the assignment's structure; they also highlighted the ways in which the assignment served as an extremal example of a writing-to-learn project and the ways in which bridges to other aspects of mathematics could be built from the abutments it offered. (Ulrich mentioned his discovery of the software package Geogebra, inspired by his need to create attractive graphics for the textbook. Reminder: the latest version of the textbook can be found by following this this link.)

The conference over, we hit the road again. I wish I'd had the van miked on the way home: Uriah, Iris, and Ino and I spent much of the drive back to Asheville talking about various things, including AP exams, life plans, Southern accents, and, yet again, trust in teaching. By the time we'd returned to the parking lot we'd left a little over two days before, several of the students were zombified from over-stimulation and lack of sleep, but everyone seemed happy and all professed to have been stimulated by the past days' goings-on. The younger students in particular, including those who may still have been on the fence regarding the pursuit of a math degree, were sold. Several are already ready for their next conference.

I'm tired. But happy. And proud. They're wonderful people.

Wha...? A new post!? (Complete with interrobang...)

Yeah, yeah. I know it's been a while.

It's been a crazy semester.

I've lost track of the number of snow days (three?) and late starts (four? or five?) we've had...there was one point at which I met with each of my classes precisely once in the span of 14 days: in the week prior to Spring Break I'd canceled Monday's Calc II classes for some reason I've since forgotten, and Tuesday and Wednesday ended up both being snow days, so I met with my Topology class and one of the Calc II sections only on Thursday, and with the other Calc II section only on Friday...and then Spring Break came.

Needless to say, this threw everyone's trains of thought off the rails, and in the subsequent weeks (the last couple) we've all been running around like mad trying to pick up the pieces.

I've made a number of mid-course adjustments in order to try to compensate for the craziness. I've scrapped several "less critical" sections from the Calc II calendar, and I've changed up the syllabus for Topology: having found from several of the most dedicated students in that class that the textbook assignments were not proving to be an effective means of learning the material, I ditched those. Many of the concepts were proving very difficult for the students to paraphrase, so that only a handful of the students were producing textbook submissions which were anything more than reiterations of my own course notes. Moreover, the homework assignments have been difficult enough to demand substantial amounts of the students' attention. In return for scrubbing the textbook project, I've asked the students to redouble their efforts at revising their homework, and so far they've kept up their end of the bargain.

I feel strongly that flexibility, both on the part of the teacher and on the part of the students, is critical in designing an effective learning environment. I've never been able to fathom faculty members who use the same rigid note sets semester after semester, or who plan precisely which exercises they'll assign to their classes for the duration of the term on the term's very first day.

Yeah, Topology could be moving a bit more smoothly, but as this is the first time I've taught the course, a few fits and starts are inevitable, I suppose. I appreciate my students' patience as I figure out what works and what doesn't.

Calc II, on the other hand, is cruising over smooth seas.

What else is new?

Um...

...I'm still waiting to hear back from Jossey-Bass regarding my book proposal. I'm hopeful that the proposal will get picked up...although I'm not sure where I'm going to find the time to finish the two chapters I'd promised by May. I've got an outline for the first chapter worked up, but little more than that right now.

There's been little movement on the rhetorical analysis of REU students' writing I began several weeks ago with the Charleston folks. Last I knew, Bella was planning on making some revisions to the initial version I posted on our Google site a few weeks back. Nothin' new there, though.

The Writing Intensive Subcommittee's knocking off new proposals left and right...moving to the Google Docs platform has made our work dramatically simpler and more streamlined. And right now ILSOC's workload has been relatively light as we've all hunkered down in our respective subcommittees to put together faculty development workshops (WI's planning one on writing instruction for ESL students, based on a workshop run at this year's Meeting in the Middle, the Carolina Writing Program Administrators' spring conference) and hammer out assessment plans. WI's assessment plan's been in the works for over a year now, and many of the materials have been collected already...it's just a matter of sitting down, establishing inter-rater reliability for the rubric (say that three times really quickly), and making our way through the students' writing samples.

What else?

Tomorrow I'm truckin' over to the 2010 MAA Southeast Sectional Meetings at Elon University with a boatload (well, a vanload, anyway) of our students. We've got 23 students attending, several of whom are giving talks or posters or serving on panels. Several first-year students are going (props, Iris, Ino! What's up, Ulysses?), and they're particularly stoked. I'm glad I put forth a strong recruiting effort...I don't mind saying that it's been a ridiculous amount of work to organize transportation, housing, special events, et cetera, but I think it'll be worth it. I'm particularly proud of my most recent research students, Siegfried and Tonio, who'll both be presenting their work in the undergraduate talk sessions; and Ulrich, Uriah, and LaDonna, whose presentation late on Saturday morning will showcase their views on the 280 textbook project.

Oh...oh...oh...OHHHHH! And after two weeks or so of intense paring and picking, my colleague Tip and I plowed through the 268 REU applications we received and came up with a list of participants for this year's program. Only three students to whom we offered positions turned us down, so we got most of our top choices. I'm excited to have them all on board. I've got a good feeling about this year.

What else?

The Tenth International Writing Across the Curriculum Conference is quickly coming closer...and plans are moving ahead for the celebration of Oulipo's 50th birthday I'm helping to put together in November. We've now got a tentative list of invited speakers, informal promises of financial support, and a rough schedule of activities. Once we've confirmed our speakers list we can begin to advertise to the campus and other communities.

I've got a few more trips coming up (two in April and two in May), but once those are over I'll be looking forward to settling in for the summer.

And I'm still waiting to find out the decision on my tenure application. Should come any day now. Fingers crossed.

That's about it, pedagogically speaking. I'll be sure to check in if anything noteworthy happens, maybe from Elon.

Fare thee well!

Shame! Shame!

I've spent 15 of the last 32 hours or so printing, sorting, collating, filing, annotating, ranking the applications submitted by this year's REU aspirants.

We ended up receiving materials from 261 different students, and 190 of those were complete enough to consider (missing at most one rec letter). I've begun the painstaking process of identifying those students I'd most like to invite to this year's installment of "Groups, Graphs, and Geometry," to begin in early June.

I'd like to share a few things that irked me about the materials submitted by the various parties to this process, both the student applicants and their faculty recommenders.

To the students: should you ever apply to an REU or to a similar program and have need to call on your professors to write a letter on your behalf, please have the courtesy to actually submit your application. If sometimes world-famous math professors have taken the time to tailor-make a two-page letter describing your talents, you can take the time to follow through on your plans to apply to the program for which you needed that two-page letter in the first place.

To the faculty: should one of your students call on your to write a letter on her behalf, please take the time to ensure that you actually know that student's name, and know how to spell it right. (Faculty from R-1 research-intensive institutions are often guilty of this oversight.) It also wouldn't hurt to bother to write more than two or three lines elegizing your student, particularly if she's a good one. (I'm making the assumption that should you have agreed to write a letter in the first place, the student likely merits the support you're offering.) There's only so much one can read into a letter whose entirety is "Cassandra was a strong student. I've had her in three classes, and she's done well in all of them. She's usually good about getting her assignments in on time. I think she'll be great in your program."

Common courtesy, folks: I'm only asking for common courtesy.

To be continued, I'm sure.

Welcome!

Not much to say at the moment (or, more accurately, not much time in which to say it), but I wanted to take a moment to welcome to UNCA our recent hire, a talented young scholar who will here be known as Kelli. She'll be joining us in Fall 2010.

Welcome, Kelli!

Kelli comes to us with experience in directing REU students, using writing-intensive methods in her courses, and designing student-centered learning activities.

Needless to say, I'm excited about her joining our department.

Now I'm off to campus. Avanti!

About last night...

Having a few spare minutes before I have to get underway with this long working weekend, and feeling guilty as hell about my long internet absence in this space, I thought I'd take a few moments to follow up on one or two of the brief comments I made in my peremptory post last night before leaving for Charleston.

Indeed, I am in Charleston. I'll be here for a couple of days, during which time I'll be working away with the three folks from The College of Charleston whom I met at the CWPA conference back in September 2009. (Nicola's already got an alias; I'll call the other two Damian and Bella.) I'm not sure how much I've said about this project: we'll be digging into the weekly written reports penned by the REU students during the 2008 and 2009 programs, analyzing them from a rhetorical point of view, using them as mileposts to help us chart the development of the students as professional writers of mathematics as the program progressed. In order to help perceive this development I've refined the list of rough criteria I developed a while back on this blog. We'll see how that goes.

I'm tremendously excited about all of this; I feel like I'm taking my scholarship of academic writing to a new level.

Speaking of which, I finished up and sent off the book proposal I've been planning for several months now, flinging it across the country on diaphanous electronic wings. Its working title is "More than numbers: writing-to-learn and writing in the disciplines in the mathematical sciences," and I've submitted the proposal to Jossey-Bass via an editor I was directed to by my wonderfully supportive grad school colleague, Erdrick (thanks, man!), who himself has a text published through Wiley (Jossey-Bass's parent company). I'll let folks know how things progress on that front.

About the allusion I made last night to advancements in IBL: I've reached that point in the term at which I'm leading the students in the tedious work of integrating rational functions via the method of partial fractions, and, just as I've done for the past few years when teaching this topic, I'm using the step-by-step worksheets I've developed to help the students guide themselves through the algebraically intense process of partial fractions.

I always enjoy myself at this point, since I'm doing next to nothing as far as lecturing goes, and it's up to the students to chart their own courses. And more than ever before, the students are having a blast.

"Are we going to be doing more work in groups today?" one of my favorite students in the class asked eagerly at the start of class on Wednesday.

"Yup," I said.

"Awesome!" They couldn't wait to get into sets of three or four and dive right in.

Yesterday I hit the pause button and said, "so let me ask this: these worksheets, this step-by-step deal, with me saying a few words before letting you all take the reins, whaddaya'll think? Are you all getting a lot out of this? Is this something that's helping you learn?" The response I got was a more eager "YES!" than I've yet gotten from them this semester. It was tremendously encouraging.

I developed these IBL guides a few years back as a means of guiding students through what I've always thought is one of the least exciting topics in Calc II, but I've never taken the time to put together similar sheets for most other topics in the term. Given the students' obvious receptivity to this method this term, I'm going to continue with this set-up for a few more sections and see how things go.

I know I've indicated somewhere in a previous post (I don't have time to find which one precisely) that I've always had an inexplicable resistance to upping the students' centrality in the first-year math courses, and I've only very slowly inched towards the edge of the cliff from which I must take that leap of faith. I'm delighted that, now that I'm standing by the canyon's rim, my students are ready to push me over.

Yes, I realize that I just wrote that my students are ready to push me over a cliff, and moreover that I'm happy about it. I made no mention of the bungee cord tied around my ankles.

I'll leave with the following bon mots from a student of mine: yesterday one of my Calc II students compared my lecturing style to the kid's show Blue's Clues. "The way you pause when you want us to respond is totally like on that show. There'll be silence, and then someone will mumble something in response." Never having seen the show, I had to check it out on YouTube. Sure enough, two minutes into a ten-minute clip in which the title character and her human companion Chris join another cartoon dog ("Magenta") in a scavenger hunt, I was treated to an example of what my student had described, almost verbatim:

"I don't know what shape this is, kids. What shape is this?"

"It's a triangle!"

I LOLed.

Though she was kind enough not to mention it, I also noticed how my classroom manner is not unlike Chris's: we both overact the hell out of almost every line we're given.

"Okay, girls and boys, today we're going to work on integrating powers of sine and cosine!"

Great. My Calc II class is like a children's show.

On that note, I'll bid adieu. My working day's about to begin.

Three great gifts

Week One has ended!

And we've not lost a one.

This afternoon's session on fractal dimension, led ably by my colleague Nostradamus (my partner in crime this summer), marked the end of the week's action for the REU. While they're still a bit reluctant to speak up in front of one another, they're definitely growing more at ease with working together, as evidenced by their professions to collaboration behind the scenes (from Nils and Ole) and the ease with which they cooperate in class (two pairs worked together to complete this morning's LaTeX exercise).

Speaking of LaTeX (and other mathematical technologies), all eight students now have installed on their computers some sort of LaTeX editor and compiler, and all eight have installed some version of Mathematica.

The students are beginning to show the first signs of focus as they near their initial selection of topics: Billie indicated specific interest in the "use it or lose it" tree construction, as did Daria. Nigel likes the look of the same algorithm, though like Daria he'd like to hear more about Cayley graphs before deciding on what to do. Several students asked more about graceful labelings and generalizations of chromatic polynomials, too.

All in all it's been a good first week. I've certainly learned from it that there's no single snapshot of a successful first week's work: while I've made no small point of this group's relative reticence, in their own way they've been no less successful in their mathematical efforts than last year's bunch, say, a band of brothers and sisters to whom I was often tempted during lectures to say, "shaddup already!"

If any of this year's REU students are reading this, please know that we're only remarking on your quietness because we find it a striking counterpoint to the previous years' groups. There's absolutely nothing wrong with your reservedness: it says nothing about your intelligence, your work ethic, or your eventual success as mathematicians. It's just very different from what we're accustomed to.

As yet I've said nothing in this post about the three gifts to which I've alluded in the post's title. It's time to remedy that.

All three of these gifts promise to expand my both my own understanding of the mathematical world and my ability to convey that understanding to others.

The first gift comes to me from Daria. When I fetched her from the airport on Sunday morning she and I got into a conversation about ethnomathematics, which readers of this blog might know is one of my less minor interests, especially given my rather unorthodox (among the research mathematical community) view that mathematics is not universal but is indeed a cultural artifact, a socially-constructed system that varies from one people to another. Somehow it came up early in one of our first conversations that Daria had recently taken a course in ethnomathematics, and in fact would soon have with her the textbooks she'd used for the course. I asked her if I could borrow them when they arrived, and yesterday she brought them to me. I have no doubt they'll prove a fascinating foundation for my own study of ethnomathematics, and a good basis for the course on the subject that I hope soon to develop for UNC Asheville students.

Both books, Ethnomathematics: a multicultural view of mathematical ideas (CRC Press: Boca Raton, 1998), and Mathematics elsewhere: an exploration of ideas across cultures (Princeton University Press: Princeton, 2002), are by Marcia Ascher of Ithaca College. In a heedless display of randomosity I began reading the second-written one first just a half-hour ago. It promises to be an interesting read. Having read little more than the introduction at this point, I already suspect I'll find a kindred epistemological spirit in Ascher.

For instance, "we now know that there is no single, universal path -- following set stages -- that cultures or mathematical ideas follow" (p. 2). Take that, proponents of mathematical universalism. As I'm fond of saying (and have said elsewhere in this blog), mathematical language is hardly more universal than the English language, and the mathematics of an alien race would likely be as indescribable and indiscernible to us as their courtship rituals.

Or take this line: "most practitioners of modern mathematics value their ideas because they believe them to be context-free; others value their ideas as inseparable from the cultural milieu that gives them meaning" (p. 4). Indeed, it's a blight on modern mathematics that so many modern mathematicians might laud math's seeming baselessness and independence from any fixed ground. This view could hardly be farther from the truth, as math is a highly predicated belief system, the truths it embodies obtaining only when certain cultural norms about truth and knowability are applied. How is it that a mathematician unwilling to state her or his hypotheses, elements necessary for the application of any reasonable theorem, would be laughed from the lecture hall, while it can be commonly supposed among mathematicians that the very science of mathematics does not rest on similar epistemological hypotheses?

I'll be sure to blog about these books as I make my way through them this summer.

A second gift, one of recognition and promise for future collaboration, comes to me from a heretofore unknown colleague in South Carolina. Lately my work on the intersections between poetry and mathematics has been getting the attention of more and more poets. Io, a poet and teacher from South Carolia, came across a copy of my paper on using poetry to teach mathematics (the one to appear in WAC Journal), and told me of her interest in the subject. She confessed that abstract algebra had been one of her favorite classes in college, and that she had great interest in understanding more fully the similarities between math and poetry.

Already, in just a short exchange of e-mails, I can tell I've found another likely friend and colleague. I hope to continue my correspondence with this woman as I further develop my own understanding of the ways poetry and math interact.

Side note: next year marks the 50th anniversary of the founding of Oulipo. Perhaps some sort of public and poetical and perimathematical celebration is in order? That's something to think about.

The third gift comes to me from an old student, Sedgwick, who graduated about a year ago with a degree in environmental studies. Sedgwick was one of the star students in the second section of my Spring 2008 Calc II course, a close-knit class that was a lot of fun to work with. He's still, a year after graduation, a regular reader of my blog (shout-out, Sedge!), and after reading a relatively recent post (this one, I believe) on the effectiveness of various components of the Integrative Liberal Studies program at UNC Asheville, and an even more recent post on Don Tapscott's Grown up digital, he wanted to offer a former student's perspective on the ILS Program, and did so extensively in an e-mail he wrote to me about a week ago.

His e-mail is, as is all of his work, thorough, well-thought out, and well-organized. This guy's always been a top-notch thinker. He makes many excellent points about various components of the ILS system. I asked Sedgwick's permission to excerpt his e-mail to me and to form a response to it in the form of an open letter consisting of a blog post here. Having been granted his leave to do that, do that I shall, in a post I hope to write this weekend.

For now, though, the dinner bell is readied to ring, and after a long, long week or work with a new crop of talented young researchers, I'd like nothing better than a few hours off. (If only I could get this damned channel assignment problem out of my head!)

To be continued...

Stand and deliver

Day Three has come and gone, and though they're still quite quiet, they've begun to strut their stuff, mathematically speaking.

Yesterday evening I presented them with the most substantial "homework assignment" I'll be giving them during these first couple of weeks of the program (the dreaded list of 34 terms and concepts from graph theory for which they were asked to find definitions and examples they would then take turns presenting to each other in seminar), and they completed it well. They'd divided the work up almost perfectly evenly, each taking about four of five of the terms for her or his own, and working together to produce a single Word document (by Friday it would be LaTeX) containing all of their findings. Impressive! They're the first group we've had who's created, unprompted, their own lexicon at the stage in the game. (Or at any stage, for that matter...)

The first few turns taken were orderly ones, each student presenting on several subjects appearing consecutively on the list.

Demeter started things off with a discussion of the many different sorts of sequences of vertices and edges one can consider: walks, paths, trails, circuits, and cycles. Her presentation was straightforward and confident. It was solid, and left little room for questioning.

Dora's presentation on cliques and blocks and related ideas raised a few more questions, which she handled smoothly. I appreciate how hard it is to think on one's feet in any setting, and I can't imagine how much harder it is when the questions you're being asked to answer (on the spot!) involve high-level math you began learning about just two days earlier.

Next it was Daria's turn, and her introduction to independence and domination led to good many more questions, which she too fielded handily.

Nigel's turn came, and he approached his presentation a bit more lightheartedly then his peers had before him. He was particularly adept at using the board and the colored chalk, and he seems very at ease working in front of his peers, providing clear and correct descriptions for each of the terms he'd been assigned. I hope he can build upon that confidence.

After a break for lunch, the rotation became more scattered. Billie's presentation on coloring and all matters chromatic stood at the center of a scattered maelstrom of turn-taking by Omer, Ole, and Nils, who traded off with one another as they discussed everything from graceful labelings to adjacency matrices.

Billie, who comes to us having taken a graph theory course (the only one of the bunch to have done so, I believe), had no trouble at all searching through her old course notes to root out a good working description of the Deletion-Contraction Algorithm. Like Demeter and Nigel before her, she was confident and clear.

To be honest, the tag-teaming trade-offs the guys made made it hard for me to get a good grip on their presentation styles. Even though they spent as much time at the board, cumulatively, as had their colleages, they weren't up before the class for a long enough chunk to get a sense as to how they'll be in sustained presentation.

Ah, but that will come later!

All around, the students did well. There were several minor slips, but that's to be expected. As I'm fond of saying, truthfully, hardly a day goes by without me making a dozen mistakes at the board. Sure, there were a few misstatements and a few definitions that might have been made clearer, but in the end it was good.

One thing I would like to see more of: the students challenging each other and asking questions that serve to further the work their colleagues have done.

And I'd like for the student who's presenting to not look at me when she or he asks "does this make sense?" or "is that right?" Who am I to say? I don't want to be thought the only expert in the room. I realized earlier this evening that in the last couple of days I've made the mistake of sitting at the center of the room's semicircular arc; tomorrow I'll decenter myself by moving to one side. (Funny: it took precisely one day for the students to fix their places in the classroom. From the near side to the far side, they sit thus: Nils, Ole, Dora, Billie, Daria, Demeter, Nigel, Omer; the last two days I've sat between Daria and Demeter.)

I find myself wondering what it is that's interesting them, mathematically...what sort of projects will they opt to undertake this summer? We've now posed maybe a score of open problems (with another score or so lying in wait), but I've no sense as to which ones they're finding appealing. I'm excited to find out.

For now, speak up, my young colleagues! Let us know what's caught your eye.

Day One, Part Deux

It's been a good day, all in all. First days are always a bit awkward, simply because (a) no one really knows everyone else yet, (b) no one's really got a full sense of what's about to go on, (c) everyone's testing each other out and figuring out what to expect from each other, and (d) there's a lot of tangentially-related bureaucratic crap to cut through before you can get to the fun stuff.

The period from 9:00 to 11:30 this morning was spent almost entirely in filling out forms, getting pictures taken, coding in identification numbers, and so forth. The upshot is that the kids now fully exist, according to most of the file systems on campus. Their existence so verified and redundicated (I know that's not a word, but I felt like using it anyway...at this point my brain is more or less tapioca, so I hope you'll cut me some slack), we were finally free to start working on some math.

We got through a couple of pages of set theory and notation (in about half an hour) and two pages of graph theory (in another hour) before it was time for lunch, after which we returned to discuss some high-level open problems in fractal geometry (yet another hour) and some more graph theory (the last hour of the day).

So far? They're a bit shy about presenting in front of one another...but who isn't at first? It's definitely too early to tell how well they'll come together as a team, but as friendly as they all are (I've had lovely conversations with them all as individuals) I can't imagine they won't coalesce into a terrific theorem-proving team.

From the "Oh, and" Department: today was also the first day of my Learning Circle for the summer, on the book Grown up digital: how the Net Generation is changing your world (McGraw Hill: New York, 2009), by Don Tapscott. I'm yet to be impressed with the book (so far, though it makes some insightful and worthwhile claims, it's a rather uncritical gathering of anecdotes, only marginally relevant data, and personal observations), I very much enjoyed the conversation I shared with my colleagues in the Circle, and I had several thoughts I might blog about later...especially regarding the construction of collaborative syllabi and other course documents. I'm looking forward to next week's discussion on the text.

So much to learn, so much to live for!

Day One

Ugh.

No sleep last night, too excited.

Much to do today, but much of it boring (sorting out housing snafus, filling out paperwork, getting folks into the library system, etc.).

We'll make it through all right.

But if I don't bowl well tonight, Wes'll kill me.

First impressions

My first impressions of this year's REU group:

1. They're a bit more timid than last summer's bunch. This isn't a good thing or a bad thing, it's just a thing. It's all good, it just might mean it'll take them a little longer to come out of their shells. (Nothing a bit of bonding over a long-ass list of graph theory definitions can't cure...)

2. They seem highly dedicated. They all talked about how much they love math, and several have mentioned how they become absorbed by problems on which they're working, and several of talked about their futures in math (grad school, teaching, etc.)

3. They strike me as talented, but modest. I already have a feeling they've got a great deal of math smarts collectively, but I don't think we've got any hotshots: almost every one of them mentioned to me within minutes after meeting me that she/he was excited to be here, and they seem to understand their participation in the program as a privilege and as a responsibility rather than as a right.

Tomorrow, we begin. Excitement!

Mission: mathematician

This summer's goal: turn eight math majors into mathematicians.