Problematizing Honors, or, Thirteen questions

I’m finding it harder and harder to defend what I do. I want to be an agent of change, and not simply a caretaker of the status quo.

What is the Honors Program now? Is it now just a vehicle for perpetuating inequity, reinforcing hegemony, keeping the academic elite (those students who have best learned how to play the “school” game) ensconced in existential safety? Or is it now an opportunity to offer a way out of inequity and hegemony, a place where doctrinaire views can be dissected, interrogated, and challenged?

What can the Honors Program be? How can I do the work to further make it a place where the privileged students who find themselves there encounter a place where their safety and surety, their privileged positions, are challenged?

Is this the best that can come from it? Can it be more still?

While walking together the other day a close friend of mine suggested that I should use my position to dismantle the program from within, to work to replace it with a more equitable support structure, one which offers resources and opportunities to those students who are more marginalized, more vulnerable, less acquainted with the patriarchalist assumptions of a mainstream university education. Such an institution would be something more than a learning resources center, more than an agglomeration of math labs and writing centers. It would be an institution devoted to advocacy for change and not simply to helping students cope with the status quo.

What would I even call such a structure? Where would it be housed? How would the university react to it? What would its charge be? Its day-to-day functions? Is there a precedent for such an entity?

To be continued, no doubt...

Day One, revisited, or, Patrick very quickly gets off into pedagogical theory

Back to the grind. Today hardly felt like a school day at all, as my only MWF class is an 8:00-to-8:50 section of Linear Algebra I that was over nearly as soon as it started. (At least on Tuesdays and Thursdays I won't be done in the classroom until noon-thirty.) As first-days-of-class go, it was a good one, though. I've had better, but I've had far worse.

Plus ça change, plus c'est la même chose. Both other times I've taught this course (including the first time, the iteration of the course that occasioned the founding of this blog) I've started with some variation of the same game, a simulation of a Markov process in which the students shuttle some sort of token back and forth at each iteration of the game. The first run (Fall 2006), the students themselves were the tokens as the class participated in a great big single instance of the game; I switched to pennies (and smaller groups) the next time I taught the course (Fall 2010), and I stuck with that latter version today, though leaving a bit more room than I did before for students to discover and speculate upon the patterns their own damned selves. This time around I also asked the students to take bolder and more unassisted steps toward the next conceptual mile marker, solution of the linear systems that arise from the Markov process we investigate together: not only must the students experiment and then speculate on the outcome of their experiment, they must then find the appropriate mathematical model (a simple linear system in two unknowns) and then back-solve the "run the model in reverse." All in 45 minutes' time!

All in all, it went remarkably well. No one seemed lost ("one in a row!" as my colleague Tip would say), and everyone participated actively. I'm aided this semester by the fact that I've only got 23 student in the class (yay), though they're packt like sardines in a crushd tin box (boo), sitting at single-person-sized tables (yay) bolted together and arrayed in orderly rows (boo) in such a fashion as to discourage all but the most anachronistic teaching techniques (boo hiss).

Interesting facts (yes, there is a train of thought that took me from the previous paragraph to this one): recently, while reviewing the literature on the effect of class size on learning, I discovered that (1) said literature says almost nothing about college-level instruction, most research having been done at the K-12 level, and (2) a number of studies do not, strangely enough, suggest small class size improves student learning in mathematics. It was only after a bit of reflection that I realized why this might be: such studies, while controlling for class size, do not (and, methodologically, cannot) control for instructional method. Thus what I suspect is happening in these studies is large-section lectures are being pitted against small-section lectures, lecture being, until recently, about the only viable instructional paradigm for large-section classes. Of course, it is pedagogically retarded (in the literal...well...until recently literal...sense) to assume that one's instructional method remain the same when smaller class size permits more effective application of student-centered learning strategies: pit large-section lectures against small-section IBL and you're sure to see a difference.

Maybe more about that in a post soon to come (why on Earth was Patrick researching this topic? Edge-of-your-seat action!). For now, I've got reading to do for my first meeting of HON 479 tomorrow!

An astronomer, a physicist, and a mathematician...

...are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "how odd. Scottish sheep are black."

"No, no, no!" says the physicist. "Only some Scottish sheep are black."

The mathematician rolls his eyes at his companions' muddled thinking and says, "in Scotland, there is at least one sheep, at least one side of which appears to be black from here."

There is danger in inductive thinking, as even Hume acknowledged.

I've been reading up on epistemology for my MLA class's initial foray into the philosophy of mathematics: Bacon, Hume, Descartes, Kant, and Popper...and of course Lakatos! We're going to get in pretty deep. For good measure we'll prove Euler's formula for polyhedra and try to understand what's so unsettling about the Law of Excluded Middle, the Axiom of Choice, and the proof of the Four Color Theorem.

You know you want to join us!

I oughta know better...

I'm about 30 pages into Michael Gurian and Kathy Stevens's The minds of boys: Saving our sons from falling behind in school and life (San Francisco: Jossey Bass, 2005), and I have no earthly idea how much more I'll be able to read. It's tendentious, fatuous, and overwritten, relying primarily on anecdotal evidence to prove its points, and when more critical evidence is given it's given second-hand, safely filtered through reference to other texts and not to the studies those texts rely upon.

Bluntly, it's pap.

Why read it? I thought I'd try to get a grip on views contrasting with that of Cordelia Fine (see this post), who holds that the biological bases for gender differences are blown entirely out of proportion, and that acculturation more than anything else is responsible for differentiation of gender, including differentiation in intelligence and academic performance. Gurian's name shows up an awful lot as one of the giants of biological determinism, and he's written stacks of books on gender difference, so I thought I'd check him out.

His website's not particularly promising, listing scant credentials relevant to the books he writes and boasting membership in three professional organizations, one which doesn't exist, one whose website hasn't been updated in seven years, and another which appears somewhat reputable. I'm not sure I'm one to lobby the former objection, having just finished a book in an area I'm not "credentialed" to write, but I would think that one of the foremost "authorities" in gender difference, its ramifications, and its ameliorations, should have some sort of post-graduate degree in psychology, neuroscience, or at least counseling or social work. Gurian's most advanced degree is an M.F.A., and before that he holds a B.A. in philosophy. In fact, his most promising claim to authority is his unwavering insistence that he has authority: his website is a fantasia of self-promotion, and he mentions his own institute on just about every other page of the book I've begun.

About that book...its primary thesis is that our schools are in crisis (his words, not mine): boys are falling behind and failing in disproportionate numbers...and it's because our educational system does not take into account crucial differences between the ways boys and girls learn. Truly this is a crisis, Gurian insists: "Yes, we're sorry to say, there really is a crisis" (p. 20...did I mention the text is nothing if not inflammatory?). The extremist language he uses to introduce numerous "statistics" (none properly cited and all treated uncritically) "proving" boys' educational crisis is particularly chauvinistic: for all his righteous indignation you'd think that it's men and not women who for the last several centuries have been underserved by Westernized educational systems. Once or twice he throws us a bone and insists that he has equity in mind: "Calling attention to the college problem for males is not to decry an individual's particular qualities, nor to lament women's successes in increasing their college attendance, wages, and financial independence from males" (pp. 27-28). Such mots ring hollow, however, and I can't help but come away feeling that a hundred years ago Gurian would have been a phrenologist, palpating female skulls in order to point out their "obvious" mental deficiencies.

Ugh.

I'll read on, but I can't see this getting any better...

UPDATE: I'm on page 39 now, and can't help sharing this bit of nonsense: "Research in the 1990s clarified ways in which our schools fail our girls, especially in areas of math and science, the dynamics of self-esteem in the classrooms, and computer design instruction. Because our culture recognized a girls' crisis, it has addressed those problems and to a great extent has changed things for the better as far as teaching girls is concerned."

Yay, according to Michael Gurian sexism in educational practice is now over! It's a thing of the past, a problem we're no longer wrestling with. I'm so happy to live in a post-sexist, post-racial America, where we're all colorblind, a black man can be president, and the mathematical sciences are roundly dominated by women.

Random thought #564

Why is it that we fight so hard for students to major in our academic disciplines? (I'm no angel: as a constant salesperson for our department, I'm as guilty as anyone else.) I suspect it's because we feel we need "our own students" to justify our departments' existences. No matter how many students from other areas count on us to teach them skills they need in their disciplines, if don't have a few majors of our own, we become "no more than" a "service" department, a group of contingent faculty, our positions conditioned on the whim of curricular programs elsewhere on campus.

Old habits die hard.

What would our schools look like if we did away with disciplinary and departmental divisions, did away with traditional majors, and did all we could to foster interdisciplinarity and academic interactivity across campus? Not only would our students live a richer and more robust learning experience, with realistic integration of ideas at every turn...but we'd all be a lot less territorial and hoggish about our limited resources.

Just a thought.

Breadcrumbs

I feel like Hansel and Gretel (being both at once would be an apt ontology for this post), following a trail of breadcrumbs as I wind my way through a forest.

In each of the three meetings we've had so far, the students in my MLA course have raised some interesting (and as yet unanswerable) questions. Many of these concern the classic "nature vs. nurture" matter that infects every conversation involving human abilities and achievements. For instance, is it nature or nurture that leads to mathematical (and otherwise) savantism? That is, do "human calculators" owe their skills to some advantageous neural network structure in their brains...or do they develop those skills through hard work and constant application of ordinary neurological machinery?

Opinions were definitely divided on this matter during our last meeting: some accepted Dehaene's explanation that practice makes perfect, and that those who have plenty of time to practice are liable to more closely approach perfection; others weren't convinced. "Maybe none of us are born geniuses," one student said, "but some of us are born with better propensity to achieve genius than others are. Just like most of us will never be professional basketball players, as we lack the physique it would require."

This analogy might remind us that after all the brain is as much a piece of our anatomy as are our arms and legs, and our interpersonal differences in overall anatomy carry over to interpersonal differences in our brains as well. No doubt some of those differences predispose us well to certain kinds of genius inaccessible to others? It's up to each individual to nurture latent talent in the most efficacious way from that point on.

The risk we run in arguing like this is making dangerous generalizations along the following lines: "brain difference X translates into ability difference Y" and so forth. As I quipped mysteriously on Facebook the other day, brain does not equal mind anymore than map equals territory, and if we pretend that we can extrapolate everything we need to know about a person from the structure of their braincase, we anachronize and become phrenologists, feeling for bumps, risking claims about racial or sexual superiority. Remember that it was held for a long, long time that women were less bright than men because their brains were less massive...and that when this point of view was assailed from all sides, its adherents did all they could to rescue it, falling back on more and more convoluted sophistry to save their theory: "well, it's not brain volume per se, but volume of gray matter...or at least the ratio of gray to white matter...well, maybe the degree to which it's all convoluted..." (See Stephen Jay Gould's marvelous The mismeasure of man for a blow-by-blow debunking of such arguments.)

About sexual superiority (and getting back to our trail of breadcrumbs): one of my students turned me onto Cordelia Fine's Delusions of gender: How our minds, society, and neurosexism create difference (New York: W.W. Norton & Company, Inc, 2010), a thorough discussion of modern attempts to pin gender differences in intellect on neurochemistry. Phrenology's not dead, it just looks a lot different than it did 150 years ago: now we don't look for protrusions in the skull, just higher-than-normal levels of fetal testosterone, and we don't come right out and suggest that women aren't as smart as men, we just say they have a greater propensity to empathize than they do to systematize. Fine spends much of her time pointing out flaws in modern phrenologists' methodologies, though not as many she might; I've noted a few flaws she could have mentioned but didn't.

It's a stimulating read, and I plan on sharing a few chapters with the MLA students. It's also leading me to other sources. Some of these are general in scope, like Jan Morris's Conundrum (New York: Harcourt Brace Jovanovich, Inc., 1974), a first-person account of the author's transition from male to female and the worlds she lost and gained in the process. Others are more specific, like Nash and Grossi's analysis ("Picking Barbie's brain: Inherent sex differences in scientific ability?" Journal of Interdisciplinary Feminist Thought 2(1), Article 5) of Simon Baron-Cohen's methodologies...which analysis might doom some of the infant studies which Dehaene cites, as well (O, circularity!).

I also plan on offering up a few excerpts from Richard E. Cytowic's The man who tasted shapes (Cambridge: MIT Press, 2003), an odd novel/memoir/neuropsychology text dealing with the phenomenon of synesthesia. Though not directly related to our course, I think certain passages bear tangentially on our discussions of brain function and will lead to interesting discussions.

More fun to come! Exciting. I hope the students are getting as much out of the class as I am. I may have to offer this course again soon in the Honors Program. Something to think about for next year...

Defragging

For the past few weeks I've been hammering away at several different poems, but I've got little more than a couple of callousy handfuls of bent-nail fragments to show for it. Odd images (starry-breasted crows, fog-covered tenement-like brick blocks, concrete tunnels like birth canals), and random thoughts.

Keeping with this fashion, here are a few random thoughts on academics and academia:

1. I wonder at the extent to which we are all isolated in our disciplines, and to which we do most of our work in rooms with four walls and very often no windows.

2. I wonder at the sterility of the Platonist, universalist, formalist conception of mathematics, itself an isolating philosophy, allowing as it does a detachment from the world and from others as we engage in our mathematical work.

3. I wonder at the mechanisms we feel we must make and maintain in order to "deliver" our curricula. The more I learn about the inner workings of the Honors Program, the more I wonder if there are simpler ways to put it all together.

4. I wonder at our assessment practices, at every level, from the individual student to the institution as a whole. To what extent are they arbitrary, effective, replicable? To what extent are they doing what we need them to be doing?

5. I wonder at the effects of our educational system, both intended and unintended. How often does a student's passion for perfect grades overpower her passion for learning?

6. I wonder at things as they stand for things, and am reminded of William Carlos William's red wheelbarrow:

so much depends
upon

a red wheel
barrow

glazed with rain
water

beside the white
chickens.

History lesson

Some might say this is not a "teaching" post.

They would be wrong.

I was chagrined several weeks ago when I learned how ahistorically many of my students live their lives: one of my brightest students showed her historical ignorance by not knowing, within ten years or so, when the second world war was fought.

So it is that I worry that my students might not know what's going on around them now.

I join the chorus of academic voices expressing not disappointment, not chagrin, not tut-tutting and head-shaking sadness, but rather disgust and horror at the events taking place recently at campuses in the University of California system.

All that I might say has been said more fully and more eloquently than I can here (here, for instance, and here), so I'll say little more then to say that Chancellors Linda Katehi and Robert Birgeneau must resign...as should any other academic "leader" who condones or supports the actions (or inactions) they've taken.

I cannot say more that's not been said already. I want only for my students not to miss this moment.

To them I say: this is what history looks like.

State of mind

A few months ago Zima, one of my grad school colleagues who now teaches at Kennesaw State University in Kennesaw, Georgia asked me to present at an undergraduate research conference for which she'd just received MAA funding. (Said conference is this coming weekend; it's the one Ino and Ned are presenting their findings at.) I'll be giving a run-of-the-mill plenary talk on some of the graph theory I did with a couple of REU students this past summer, and I'll be presenting in a workshop on inquiry-based learning (IBL) at the outset of the conference.

I offered Zima a title that's so generic I really could talk about anything: "Guided discovery in the mathematics classroom." I feel confined by this generality. Indeed, when I actually sat down a week or so ago to try to figure out what in the hell I needed to say about IBL, PBL (problem-based learning), Moore method, etc., I had a hard time coming up with much to say other than expressing my feeling that all too often these techniques are too "formalized." That is, I get the sense sometimes that the people who apply these techniques look on them as an all-or-nothing process: "if it ain't straight-up Moore method, it ain't anything at all" or "I use guided discovery every single day to address every one of my students' learning outcomes." So I put together a half-hour laundry list of things to say along these lines: be open to using guided discovery in moderation; it's not the be-all-end-all any more than any other pedagogical paradigm may be.

Then just now, while lying in bed unable to sleep (though admittedly probably needing to), I realized that I can say more, for I realized of a sudden why I've had such a hard time trying to come up with something practical (and original...I suspect that the folks I'll be addressing in this workshop are going to make up a choir to whom I won't really need to preach) to say about guided discovery: in my mind, guided discovery is not so much a pedagogical process as it is a state of mind.

I find more and more that in teaching it's not so much what I do with my students as how I do it that matters most. Put another, perhaps more practical way, effective teaching comprises a gestalt-like complex of actions and not a single action individually. Guided discovery is what might be called an emergent operation which cannot be broken down into its constituent parts without losing much of its energy and effectiveness. So it is that I don't necessarily engage my students in singular activities, each of which forces students to lead themselves to original, new-to-them, conclusions, so much as I try to treat them in every way, in everything I do, as co-learners, co-discoverers, seekers of authentic knowledge.

Practically, this realization makes it possible to grow opportunities for genuine discovery in the most infertile academic soil, for every simple textbook problem becomes, if viewed from the right angle (like anamorphic art) a chance for authentic "research-like" engagement. Guided discovery is an "angle" from which these problems may be viewed.

I'll try to say a bit about this on Friday when I'm leading my portion of the IBL workshop. Are these views original? Meh...perhaps not. But they're more original, and, more important, more meaningful, than whatever else I will have to say. We'll see how they're received.

Running in reverse

Recently I've had a chance to feed my undying love of linguistics. I've been reading up on the history of English and its antecedents (like Angl0-Saxon) and victims in the clash of tongues that's taken place on the British Isles since the early common era (like Cornish and Manx). The text I'm currently reading is Dick Leith's A social history of English (London: Routledge & Kegan Paul, 1983), an interesting book offering a glimpse of English's development as a social, as well as a purely linguistic, phenomenon.

More interesting than Leith's treatment of English per se are some of the observations he makes about the codification of language, and the role of "authority" in the preservation and propagation of language across time and space. A central thesis of his book is that all too often we forget that language is very much dynamic: it is ever in flux, constantly changing...and that in the end that change is not driven by grammarians or the intellectual or economic elite so much as it is by the ways in which every member of society chooses to use the language.

These are points that even the most perspicacious language-lovers among us tend to overlook. The reminders Leith offers have made me think of new (to me, at least) and "subversive" paradigms for poetry (a post on that soon, perhaps)...but they've also recalled for me the central role every member of a learning community plays in that community's advancement of knowledge, while issuing a reminder as to just how dangerous it can be to trust blindly in the authority of a textbook.

The following passage from Leith (p. 68) struck me (cf. the comments some of my precalculus students made on their last exam):

Unfortunately, many people tend to treat dictionaries with reverence: rather than being seen as a record of usage, the are often regarded as the arbiter of it, a source of enlightenment for the ignorant non-specialist. In fact, the traditional arrangement of words in dictionaries gives people a strange idea about language. The alphabetic arrangement disassociates a word from the company it keeps, presenting it as a unit isolated from context and words of similar meaning. More important, many dictionaries give the impression that words have only one meaning, to be found on the right-hand side of the page. Even the fullest dictionary, the Oxford English Dictionary (OED), which shows the whole range of meanings by citing examples of a word in use at different periods in its history, puts the meanings first, then lists the examples, thereby obscuring the process involved in deriving the meanings; for we learn the meanings of new words most efficiently by hearing them in a wide range of contexts....It is not surprising, therefore, that people often misunderstand them.

How often too we ask our math students to use their textbooks in the same way they'd use a dictionary, placing theorems and proofs before (or, more often than not, simply in lieu of) the intuition and arguments that led to those theorems and proofs in the first place? How do our textbooks obscure the many long hours of exploration and discovery that went into the derivation of the theorems that pepper the textbooks' pages? Without access to the discoverer's process of discovery, the reader is apt to feel as though a given fact or formula arises ex nihilo, and that they, the uninitiated, are not privy to its inner workings.

Food for thought. By me, it's better to let the students stumble around a bit, piecing things together for themselves as they author their own textbooks. That's just what I'll be doing when we talk about general rational functions in Precalc tomorrow...strap yourselves in!

Welcome!

Yesterday I ran into one of my Precalc students outside of class. I was on my way back to Robinson Hall after teaching my Abstract class over in Karpen; Becky was en route to the library with the rest of her LANG 120 class. There they'd be discussing the use of library resources in conducting research.

We chatted briefly, and I asked her if she was still considering a math major. (She was one of two in that section who, without prompting by me, indicated interest in the major at the outset of the semester.) "I definitely am," she said excitedly, and then a look of worry spread over her face, "do you think I still should?" I was a bit thrown off and only after a few seconds managed to reply with something like "of course!" She went her way and I went mine, but our encounter stuck with me. Why had she asked what she had?

I suspect it may be because she may not feel as confident in her math ability as she did at the start of the semester. Though she's done well on every homework set and on every quiz, like everyone else in the class she's made her share of mistakes and hasn't presented complete understanding of everything we've talked about. Might she believe that only those who can complete Precalculus with flawlessness and perfection are worthy of pursuing a degree in mathematics? (Only later did I think of an apt analogy: as I'm highly unlikely to ever run a four-minute mile, might I just as well give up on one of my favorite hobbies?)

After thinking it over, I found that I could understand Becky's belief, given the traditional structure of mathematics education, home to bell-curve-based grades, punctilious point-based assessment, and lecture-based teaching. There's an air of elitism to the way students are often ranked and ordered, made to fight with one another for a scant few As. The unsaid assumption in classrooms where deep and steep curves guarantee a normal distribution of grades is that only the best need move on, and that the others' services will not be needed. Detailed rubrics with single-percentage-point resolution signal to the student that mastery of fine detail takes priority over authentic understanding. (No wonder students clamber after every point, wondering what it is that separates a score of 8/10 from a score of 9/10!) Fast-paced lectures make sure sure the students who start off slowly get little chance to get ahead; the quickest students (who are often, but not always, the brightest) control the pace in these classes.

All of these factors discourage students who are excited or intrigued about math, but who are put off by the way in which it's often taught. We can't afford to turn these students away. The fact of the matter is we, as a society, need more mathematicians than we can possibly prepare, and we do no good in discouraging anyone who's passionate about the field from pursuing it further. We do well to let as many students through the gate as we can, and to give them all of the support and encouragement they need to develop their skills fully. We do well to eliminate curves and to downplay in-class competition between students. We do well to "coarsen" our grading scales to accommodate "big-picture" thinkers who might miss a detail or two but who grasp complex systems in their entirety. We do well to step away from our classroom's center stage and let students take our place, so that it's not to the top ten percent that we teach, but to the class as a whole.

The bad news is that these practices are not universal; the good news is that they are more popular than ever. They're in use throughout my department and many like it. The youngest math teachers (at every level) are more adept at applying them than their older peers. These teachers are daily developing new tricks and techniques to make these practices more effective, and they're not shy about sharing these tricks and techniques with their colleagues and with their students. The future is bright for math education.

Stick with it, Becky! Welcome to the team. You're in good company. You'll do wonderfully.

Where do you want me to be?

Today was, sadly, the last of four meetings of the Learning Circle I took part in this semester, on Palmer and Zajonc's The heart of higher education (about which I've posted recently before)...even sadder was the fact that I'd only been able to attend two of the four meetings, other obligations taking me out of town and off campus. I've found this text eye-opening and enriching, and the conversations surrounding it even more enriching still.

I found myself thinking out loud in the circle today, wondering what our academic lives would look like if we took ourselves out of our offices and started doing more of our work more publicly. What if I started holding office an office hour or two on the quad, or in the student union, or in the glasshouse adjacent to the library? What if my colleagues joined me in this, sharing a table with me as we worked with our students, observing firsthand how we interact with them, witnessing the kind of learning that goes on in one anothers' disciplines?

Soon might fall the disciplinary boundaries we're all quick to dismiss but unconsciously eager to maintain. At a university so dedicated as mine purports to be to the liberal arts, we ought to be all about interdisciplinary exchange that blurs distinctions between this field and that. But when it comes down to it, as often as not we retreat inside our hard-shelled departmental silos. "I'm all for interdisciplinarity," we might say, but in practice we add "as long as it happens on someone else's time."

But if we started seeing more of each other on the quad, in the union, in the glasshouse, maybe we'd know more about each other. We'd each know more about other's passions and pursuits, and more about the way the other thinks. We'd be able, at least momentarily, to adopt the other's disciplinary perspectives, and when our students ask us why they're asked to take courses in that field or this, we'd be able to tell them why, honestly, earnestly, and confidently.

If we knew more about each other, perhaps we wouldn't find the sort of territorial entrenchment I'm witnessing right now in various departments' defenses of their current curricula to the Curricular Sustainability Subgroup of CRTF which I'm heading up. Sadly, though perhaps not surprisingly, many departments' chairs are convinced of the inestimable value of their own departments' offerings, and of the waste and profligacy that must go on elsewhere in the curriculum to result in such a burdensome mess. The written responses we've received from most chairs are for the most part meticulously-crafted hagiographies telling tales of the author's department's excellence. Without doubt there is good going on in every corner of campus, but equally doubtlessly I know we're all to blame for the unsustainable burden we've taken onto our own shoulders.

If we were to meet face-to-face more often, there'd be no need for polemic; we could engage in frank but warm discussions. It's hardly a coincidence that the considerable face-to-face work the Curricular Sustainability Subgroup has done this summer and fall has been done so smoothly and so amicably. After all, it's difficult to be defensive (or to go on the offense) when your interlocutor is sitting right in front of you. Face-to-face meetings encourage warmth, empathy, and honesty. The "rocking chair conversations" Parker J. Palmer talks about in Chapter 6 of his book with Arthur Zajonc are the perfect places for real and lasting change.

I'm ready to set out some rocking chairs. I'd like to try this, if just for a few hours each week. Maybe while the weather's nice, the steps of the library might do. When it starts getting colder and darker earlier in the day, I can move to the Pinnacle in the student union. Students, colleagues, let me know: where do you want me to be?

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.

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?

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.

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.

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.