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

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

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

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

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

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

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

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

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

Nudge

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

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

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

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

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

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

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

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

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

Back

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

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

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

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

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

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

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

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

Butterfly effect

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

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

No one said a word.

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

no one said a word.

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

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

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

No one said a word,

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

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

a hole like the eye of a storm.

***

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

Rock stars

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

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

But before that...

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

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

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

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

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

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

Yup, my students are rock stars. Crazy day.

Fun Times

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

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

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

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


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

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

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

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

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

Lessons learned

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

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

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

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

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

Post 500: A note of gratitude

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

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

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

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

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

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

Thank you all.

MATH 280 exams, revisited

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

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

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

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

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

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

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

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

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

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

One more vote for confidence

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

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

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

Lovely LaTeX

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

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

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

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

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

The spider

[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.

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.

Anticlimax

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

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

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

CCCC, Vol. 4: Putting the Paper Down?

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

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

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

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

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

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

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

Time will tell, I suppose.

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

CCCC, Vol. 3: Take 2

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.

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.