Saturday, April 30, 2011

One more vote for confidence

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

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

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

Thursday, April 21, 2011

Lovely LaTeX

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

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

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

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

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

Wednesday, April 20, 2011

The spider

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

The spider

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

Then she went away.

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

Assess this!

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

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

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

Thursday, April 14, 2011

Wrapping up

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

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

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

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

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

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

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

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


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

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

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

Wednesday, April 13, 2011

CCCC, Vol. 4: Putting the Paper Down?

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

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

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

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

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

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

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

Time will tell, I suppose.

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

Monday, April 11, 2011

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.

In other words

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

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

In this student's words,

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

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

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

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

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

Home stretch

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

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

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

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

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

Saturday, April 09, 2011

CCCC, Vol. 2: The Citation Project

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

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

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

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

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

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

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

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

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

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

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

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

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

CCCC, Vol. 1: Emotions and Authority

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

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

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

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

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

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

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

Wednesday, April 06, 2011

What a difference six years make

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

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

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

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

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

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

White screen, white text

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

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

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

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

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

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

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

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

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

I don;'t know.

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

What's up for next semester?

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

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

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

I need to be somwhere that I'm not.

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

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

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

There it is.

Here we are.

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

Shall we dance?

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

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

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

Tuesday, April 05, 2011

Confessions of a sometimes-mathematician

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

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

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

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

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

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

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

Monday, April 04, 2011


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

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

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

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

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

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

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