With honors

It seems as though in every term I hit a point at which I'm so busy taking care of what I need to do that I no longer have time to take care of those things I simply want to do (like update this here blog).

I've hit that point.

I'm busy.

I'm busy enough that by the time I've got time to tend to this site, I've got no energy. When I've energy, I've got no time.

Vicious.

Well, in a rare intersection, I've both...fleetingly.

Story: An hour and a half ago I got out of the first meeting of the faculty I've requested to teach the Honors sections of our first-year liberal studies colloquium in Fall 2012. (My thanks to my wonderfully proactive colleague Darlene for organizing and convening this meeting!) Darlene (Health and Wellness), Samuel (Literature), Noella (Computer Science), and Quentin (Psychology) will join me in offering this course to our Honors students next term.

I have to admit to a not small amount of terror at the outset of this meeting: I'm new to Honors, I'm relatively new to teaching first-year colloquia (last year's Ethnomathematics course was my first of that kind), and I'm certainly new to this quasi-administrative functionarihood with which I've found myself vested. I was worried that we'd find no agreement on form, no agreement on function, no agreement on anything.

In retrospect, of course, I must admit my foolishness: I'd underestimated the flexibility and resilience of my colleagues, who are superior to me (it must be said) in recognizing the potential we face.

In summary: we hope to design five discipline-specific-yet-common-in-purpose first-year seminars which will challenge enrollees to meet three learning outcomes common to all first-year courses, four learning outcomes peculiar to writing-intensive courses, and all expectations we hold for students taking part in the Honors program. Further, we hope to design these courses around the common theme of "Metamorphosis."

Doable?

You betcha.

Easily doable?

Not a chance.

Therein is the challenge and the excitement.

Our conversation led us through skepticism, speculation, and proposition of structure.

I'm less terrified than I was two and a half hours ago...now we have a plan, and at least the vaguest of ideas for common texts, events, and experiences.

I'm less terrified.

I'm working with four folks who, in Noella's colorful terms, "can sell swampland."

It's going to be a good term, this.

Green-eyed

While I watched several of my current and former students interacting in the Math Lab this morning, I realized how envious I am of their undergraduate experience.

Though I had good (some very good) professors, none were nearly so dedicated to my success as most of my colleagues in this department are to our students' success. I was never encouraged to do an REU, or to perform undergraduate research. I was never encouraged to attend and present at conferences. I was never given much guidance regarding grad school, and life beyond. For my students, this is all standard.

Though I had a few wonderful friends who shared my math major with me, indeed we were few, maybe ten or so the whole while I was in the program (all years included). The uppermost-level classes had three or four students, never more. My students have nearly a hundred peers in the program, and even the smallest 400-level courses claim over a dozen students...some more than two.

Though we had a satisfactory lounge and a serviceable computer lab, both of which served our needs for space, we had no "home" in the department. We were wanderers, itinerants. My students have the Math Lab, a warm and welcoming place where everybody knows everybody else, and there's never a shortage of assistance, support, and friendship.

They've got it pretty good.

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!

If they only knew

I'm pretty sure that our students would be gratified if they could see the amount of thought a good number of our faculty are giving our curriculum review. The Curricular Sustainability Subgroup alone has met at least 30 times in the past eight or nine months, and various subgroups (subsubgroups?) of this body have met many times beyond this...to say nothing of intergroup meetings with folks on the Big Picture Subgroup, meetings of the "point persons," and meetings of the Steering Committee. We've probably generated several hundred pages of data, culled from every department and program on campus, from the registrar's office and from Academic Affairs, and not least of all from the Institutional Research office.

My eyes may deceive me, but I believe I might actually see a hint of daylight: we're slowly...slowly...moving toward concrete proposals which I believe will, if we're careful, lead to a sustainable curriculum that will give our students a rich and meaningful learning experience.

Hang in there!

Salt

The world says salt
and we say six,
a number which may or may not
really exist.

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.

Georgia on my mind

I just got back from a lovely overnight trip to Kennesaw State University, where I had a chance to give a talk on the mathematics of the Incan khipu (often spelled quipu) and hang out with Zima, one of my best friends from grad school, who's on the faculty at KSU. Zima'd asked me to spend an hour with her department's faculty, talking with them about writing in the disciplines and writing-to-learn activities, which I was more than happy to do.

One of her colleagues gave me some neat teaching ideas, including the following writing exercise: take a valid mathematical statement (printed out), one with which your students are not familiar, chop it up into its individual words, and scramble it. Give it to your students and challenge them to recreate a valid mathematical statement from the scrambled words, using every word exactly once. This exercise helps students to make sense of the grammar and semantics of mathematical prose, whose density often obscures its meaning.

Later in the afternoon (after a lovely lunch playing catch-up with Zima), I delivered a presentation titled "The traditional mathematics of Peru: khipu and khipumakers" as part of KSU's Year of Peru activities. The audience was made up of faculty and students from across the KSU campus, including a good number of math-anxious folks who were more interested in the "Peru" part of the talk. Overall, I think the presentation went well, even the bit where I had all of the people in the audience making their own khipu cords. Khipu (about which you can learn much more here) offer the most salient example of Incan mathematics, as well as a touchstone of cultural determinacy: khipu demonstrate assertively that math is a cultural artifact, a product of human society. (Moreover, they're beautiful, as a peek at the gallery at the above link will show.)

I'm back home now, and am looking forward to tomorrow's attack on a new Calc III problem set, and a couple of meetings on the curriculum review (well, not really looking forward to the latter, but they'll come nonetheless...). Meanwhile, I'll savor the last sweet sips of today.

Yup, it was a good day.

Bounce

In a recent post I fretted a bit about one of my sections of Calc III, which section seemed to me a bit underprepared for class this past Monday. I worried that their apparent lackadaisicalness (if that is indeed a word) regarding Problem Set 4, on which we were working in class on Monday would lead them to be unready for today's class, in which they would be presenting their solutions.

I stand corrected. That section bounced back, showing themselves up to the challenge. Every single student called on to present did so, and did so with aplomb. I was particularly impressed by Dionne's willingness to work all of the way through the dreaded #61, which asked for a proof that two non-parallel vectors in the plane span the entire plane. Dionne, one of our promising young majors, has some exposure to linear algebra and is currently enrolled in Foundations, so she's no stranger to the proof genre. With a little help from a couple of her colleagues, she beasted that problem.

Yes, they bounced back, but not before I exhorted them to keep up with their work outside of class. Don't just come ready for the problem you think you'll be presenting (padded with the one or two preceding problems for insurance); come ready to present any one of them...and ready yourself as soon as you can so that when you're offered time in class to hash out the details, you can do so without delay.

Good work, everyone! I have to admit to a bit of nervousness at running my first Moore-method class in four or five years, but so far you're all making the most of it. Thank you for that, and for all that you do.

Feedback, as ever, is appreciated.

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...

Worth a repost

This morning I received a brief but touching comment on my most recent blog post: "I miss Patrick teaching." I responded to this anonymous post in a manner which I repost here because I think it's worth wider readership:

Please know that I'm organizing this class in a non-traditional manner not because I want to avoid "teaching" (though, believe me, I'm doing as much teaching, in a non-traditional sense, as I would in any other course), but because I truly feel that the Moore method is the best way to approach this material. By asking you all to explain your ideas to one another, it firms up your understanding of those ideas. By asking you to take responsibility for your work, you become the authors (quite literally) of the ideas you're presenting to one another. It's much more learner-centered, and ultimately (I believe, and the literature on pedagogy bears me out) more effective.

Thank you for your kind sentiment! I've not totally disappeared from the scene; as you've noticed, I hope, I'll take my turn "on stage" from time to time.

To elaborate briefly: I know I'm a good lecturer, and I know that I explain things well. But seeing something done and doing it yourself are two different things, and you stand to gain much more from actually solving the problems yourself and explaining your solutions to each other than you do listening to me do it for you. It's a bit more work on your part, to be sure, but the time you spend on that work will be time well spent. Meanwhile, please know I'm still doing a lot of work behind the scenes, arranging problems in a manner I think is effective to help you work your way through the new ideas, including the definitions and theorems I think are most critical to us in our work, and working with you in class as you develop your solutions.

This I promise you: my explanations are still here for you if you need them, and I will be delighted to help you work your way through any problem you might struggle with. All I'm asking is that you give it all you've got to come up with solutions on your own first. Believe me, you'll get much more out of it that way.

So, let's stay the course, y'all. I'm enjoying class so far, and so far you're doing a marvelous job. Keep it up!

A tale of two sections

Today it was evident that over the weekend, most folks in one of my sections of Calc III took the time to work through the problem set they'll be presenting on Wednesday. It was equally evident that most folks in the other section didn't.

We'll see how things go on Wednesday. Most of the problems are pretty straightforward, but there are a few that might give pause. If Wednesday goes as I suspect it might, a few folks might learn the hard way that though it always pays (no matter the class) to keep on top of the work, but in a course structured as ours is, it pays double.

Moore is more

Three weeks into the semester, my Moore-method Calc III class has made it through three problem sets (50 problems), treating a substantive review of topics from Calc I and II and five or six sections of the textbook. It's been a few years since I've taught a course in this fashion, so there's been a bit of adjustment as I've gotten back into it.

So far, so good. The students are getting much better at explaining their solutions in front of a large audience (one section has 27 students, and the other 35), and they're becoming more relaxed, visibly. Yesterday's second section was particularly laid back, assiduously focused on finishing their tasks but willing to joke around and have fun in order to set the solvers at ease.

I've been very impressed with students' ability to be wrong in front of each other, and similarly impressed with the audience's willingness to ask questions. They're getting better at asking each other for clarification or elaboration, and not turning to me to ask. I'm letting minor errors slide, perhaps adding a little "does everyone agree?" if the solver's slipped up somewhere. Generally this has been enough to prompt one or two to express disagreement.

How's it helping the students? Hard to say. Several have said they get a lot of the course's design, though one or two have admitted "it's not what I'm used to, and I'm having a hard time adjusting." I've reminded them a couple of times now that in this sort of course they're expected to take on a bit more responsibility than they might in a more traditional course, preparing well and keeping up without my continual exhortation for them to do so.

I'm going to poll them more formally on the course structure at the end of the coming week, after we finish off the fourth set of problems. We'll see where we are.

Meanwhile, if anyone in the class is reading this and would like to comment, please feel free to do so, anonymously if you'd like.

Data mining

I spent a few hours this morning running the numbers on the students currently enrolled in our Honors Program, hoping to get some objective data on students' participation in the program as I move toward my new position in the fall. I made some heartening findings.

Namely, each of the school's three major disciplinary divisions (humanities, natural sciences, and social sciences) is pretty equally well-represented in the Honors Program. School-wide, 9.25% of all declared majors take part in the Honors Program, and the participation rates of the individual divisions range from 7.68% to 9.91%, quite tightly centered on the overall mean. Counting the courses these students take in Honors gives further evidence to this balanced participation: overall, a student in Honors who has declared a major has completed 3.65 Honors courses on average, and the means for the various divisions range from 3.58 courses per student to 3.81 courses per student.

There are certain departments that are particularly well-represented in Honors, including a few that are quite large (and that are therefore somewhat immune to sample-size bias). For instance, five of our seven departments with at least 100 majors can boast that more than 10% of their students take part in Honors, including one department with 122 majors, of whom 17 (13.93%) are enrolled in the Honors Program. At the other extreme, there are four departments, each home to anywhere from 26 to 31 majors, with no students in Honors. (One of these is a relatively new department, one which graduated its first majors just a couple of years ago.)

Interesting.

I don't believe these data to be "actionable" in any way...and besides, the results don't indicate dramatic action. I'll stay the course for now...though it might not be a bad idea to talk with the folks in those four departments to make sure their students are aware of the opportunity...?

We'll see.

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.

Guinea pigs

I have to admit some trepidation on my part going into the second meeting of my MLA course this past Thursday. Despite my strong record of teaching in mathematics, I have relatively little experience in leading wholly discussion-based courses, and this inexperience coupled with my sense that a few folks in the class are leery of mathematics in the first place made me worry that the conversation we'd have together would fall flat. Though it took a little while for the conversation to get going, my fears soon proved unfounded.

We began in small groups, where I dealt myself into a conversation with the two older gentlemen in the class, both of whom expressed some measure of skepticism about the reading. Uriah seemed appalled by Dehaene's seeming to alternate between making claims of revolutionary understanding of the brain's functioning and retreating to more palatable and defensible observations. Quinn seemed to accept some conclusions but was put off by the relative (to mathematics) lack of "rigor" and less rigid notion of "proof" in psychology literature. I found these reactions heartening, as reasoned skepticism is generally salutary, something to be expected: these two men are among the more mathematically experienced in the class (surpassed only by Bonnie, a former UNCA math major whom I taught in Abstract Algebra back in 2008!), and the insistence on rigor is a more traditionally masculine trait.

When we returned to a full-class conversation, many more ideas came out, primed by my request for each student to identify those aspects of the reading they found most intriguing, most confusing, and most well-received. It would be difficult for me to summarize all of what was said, so I'll focus on a topic we spent much of our time, dealing with the following image:



I crafted this image last spring for my Ethnomathematics course, in order to serve as a Rorschach test of sorts, testing respondents' notion of numerosity. For the longest time I've found it fascinating that as a species we tend to distinguish objects based upon contiguity and connectedness, "topological" aspects, not on color, shape, or other more "geometric" aspects. That is, most people will respond, if asked "How many objects do you see here?" that there are four, for there are four noncontiguous bodies present.

This, however, is the unskeptical answer, unaffected by the sort of "questioning bias" that doomed the Piagetian experiments Dehaene outlines in Chapter 2 of his book. Specifically, when asked to decide which of two rows of small objects is greater in number (the lesser quantity being arranged in a longer row so as to mislead), young children will often respond incorrectly simply because they suspect trickery on the part of the questioner. In our situation, the skeptical respondent, suspecting trickery, might respond (as did Quinn in my MLA class) "one," seeing a single paw, or even "two," differentiating the two objects on the basis of color and not contiguity.

For quite a long time we discussed the evolutionary advantage of enumeration based on contiguity, and various related questions came up: what would have to be true of a species whose members enumerate objects on the basis of other aspects? What could be said of their mathematics? Can a mathematics of "continuous quantity" model our "discrete" mathematics fully and effectively?

If nothing else, everyone in the class wanted to learn the likeliest response to the "how many" question above...if the question could be posed in a less leading fashion. "I've got a sample of over 60 students I can test tomorrow," I said, referring to my Calc III classes. "Why don't I get some more data?" The students loved this idea, and we debated how the Calc III students should be prompted for the purposes of this informal survey. It came down to between "What do you see?" and "Describe what you see." People seemed more satisfied with the second, as it seems to beg for a more elaborate response, increasing the likelihood of a description featuring some kind of numeric content.

Yesterday I began both sections of Calc III with the experiment, providing no context beforehand, so as to minimize bias in the students' responses. (I did inform them of my intent afterward, and gave them all the option of retrieving their responses if they'd prefer that they not be read by others. I hope that no one on our IRB is reading this...) I've not yet looked over the responses, but I'm already looking forward to the analysis we'll do this coming Thursday night. I'll be sure to post some sort of summary results here once we've had a chance to sort it out.

Anyway...I'm counting last Thursday as a success. I think this course is going to run itself. I'm not so worried anymore.

Politics

Who knew there was so much of it in academic administration?

Seriously, though, I have a hunch I'm going to have to practice a good deal of diplomacy in the coming years as I inch closer to administration.

Week Two's been a blast, with Moore-method Calc III moving right along (no major hitches so far!), the second meeting of my MLA course in about two hours (one student withdrew after Week One, and I'm curious to see what the others think of Dehaene), and my first crack at putting together the Honors Program's course schedule underway. That last one's a balancing act, but I can't imagine it's nearly as hard as programming a large department's schedule. Let's just say I appreciate the work my chair's done on that task for the past several years.

One of my lovely Charleston colleagues just gave me a tip on the following book on delivery, apropos of our conversation about the role LaTeX plays in mathematical writing: Rhetorical delivery as technological discourse: A cross-historical study, by Ben McCorkle (Southern Illinois University Press, 2012). I ordered a copy. Just call me Mr. Spontaneity.

Okay, off to prepare for a meeting to discuss funding for this year's Conference on Constrained Poetry!

JaMMin' in 2012

Aside from a brief post on my presentation on writing research, I've not yet had a chance to say anything about this year's Joint Mathematics Meetings (JMM), from which I returned a little over a week ago. It was a fruitful affair, marking my first ever JMM where I spent more time in meetings than I did at talks. (Avoiding administration: ur doin it wrong.)

My first full day at JMM began with a two-hour meeting of the MAA's Committee on Undergraduate Programs in Mathematics (CUPM). I was recently appointed to this body, a group charged (as you might expect from its name) with making recommendations regarding the form and content of undergraduate mathematics programs across the country. Of course, this is a very loosely-defined directive, and mission-creep inevitably sneaks in. We spent a good deal of time talking not only about the undergraduate programs themselves but also their interface with K-12 education.

What struck me most about this meeting was my sense by its end that even the most well-informed of college mathematics educators are at a loss when it comes to solving some of the biggest problems facing math education today. Why is this? It's not like the problems are new ones: for decades we've dealt with student recruitment and retention, students' transition to higher mathematics, and imperfect transfer of skills from AP coursework to college coursework. It's not that we don't have proven pedagogies and time-tested methods of math education at our disposal...and it's not that we have a shortage of talented teachers to put those pedagogies and methods into practice. Maybe it's simply that the student body we're dealing with is diverse enough to foil any attempt at applying one-size-fits-all panaceas: more than ever before we serve a population whose members differ from one another ethnically, economically, socially, spiritually, intellectually, and in every other way we can think of...to extremes heretofore unimaginable.

The next meeting I had to make was a one-on-one with one of my colleagues in the AMS. After receiving a note I'd sent a few months ago to the Project NExT list regarding my forthcoming book, Flora had expressed interest in meeting with me at the Joint Meetings to talk about it in a bit more detail. It seems that earlier in her career she'd gone down a path much like the one I've followed recently, leading WAC and WID efforts at her home campus (DePauw University) before heading over to the AMS full-time. Flora and I shared an hour or so together talking about the importance of writing (and other modes of communication) in the teaching and learning of mathematics, and before long she invited me to take part in a morning meeting of the AMS's counterpart to the CUPM a couple of days later. Though she couldn't guarantee me the floor, she mentioned that one of the members of the committee had brought up writing as a potential topic for further elaboration by the AMS's Committee on Education (CoE). Topics selected for such elaboration become the focus of discussions and workshops at the CoE's fall meetings.

So I made it to that Friday morning meeting (still bleary-eyed after a night of revelry with several of my Vanderbilt friends). Less focused than the CUPM meeting had been, this one consisted of a loosely-knit (and often heated) conversation on several topics related to undergraduate math education. We spent about twenty minutes each topic: potential certification (by the MAA, AMS, or both jointly) of undergraduate mathematics programs, facilitating students' success in calculus courses, and the necessity for upper-level "elective" coursework like point-set topology.

The first of these was the most controversial issue, on which there was much disagreement. For my part, I brought up a concern that's faced the members of the Curriculum Review Task Force this past year: those major programs which face accreditation by a professional body are among the most rigid and time-consuming, placing heavy demands on both students and faculty. In this way they are unsustainable and resource-intensive. One of the other folks present at the AMS meeting countered that the "accredited" majors at her school are the ones that receive the most attention and resources from administration, and that this alone is reason enough to pursue the adoption some sort of certification procedure.

As you might suspect, I disagree. From the point of view of a math department member, this move might make sense: why not try to carve out a bigger chunk of the pie by forcing your school to support your attainment of accreditation benchmarks? But from the point of an administrator, the move appears more questionable: the pie's only so big, and with the economy the way it is, it's likely to get any bigger. If every department's trying to carve out bigger and bigger pieces for themselves, there's not going to be much to go around. We'll starve each other out if we don't cooperate more meaningfully at higher levels than the department.

To be continued, I'm sure.

The conference wasn't just one meeting after another. I had a lovely time reconnecting with several past REU students (including Wilhelmina, from way back in 2007!), grad school friends, Project NExT buddies, and a bajillion other people I'd not seen in a long time. I spread the word everywhere I could about my book, shamelessly leaving flyers on tables all over the convention center. I made it to a dozen or so talks on graph theory and group theory...and to several posters and presentations by my students, past and present. Most outstanding was Ino's and Ned's talk on their ongoing research into nutrition, given in the MAA's session on the mathematics of sustainability. They nailed it. Several folks had great questions afterward, and they received at least three invitations for collaboration and further presentation. We'll be following up on those shortly. Well done!

Much more work to do! But it's great fun. I'm looking forward to seeing what the coming weeks and months bring. 2012's gonna be a good one.

Lesson #1

One week down, a whole bunch to go. My MLA course has met just once, as have both sections of MATH 480 which I'm team-teaching with my colleague Timon this term. Calc III's had three chances to get together, and I'm very happy with how those meetings have gone.

The students have shown no hesitation whatsoever in getting together in groups and hammering out solutions to the problems posed to them, and they've shown similar eagerness in getting up to the board to strut their stuff.

What's impressed me most is the quickness with which they seem to have learned the most important lesson one learns in a Moore-method course: it's perfectly okay to be wrong.

"You know what happens when you make a mistake at the board?" I ask. "Does the sky open up, bolts of lightning raining down from above, smiting you where you stand?" Despite the inevitable one or two students who deadpan sardonic yeses, they get the point. Not only is it okay to be wrong, it's necessary, even salutary: often only in being wrong can you eventually be right, as trial and error often lead to full understanding. The process by means of which we proceed from error and ignorance to understanding is called learning.

I've got profound admiration for the several students in both Calc III sections who made mistakes at the board the past few days, every one of whom recovered almost instantly, retaining dignity and respect. My thanks go to all of my students for a wonderful first week, and especially to those who showed the others that being in error is just not that big of a deal.

Back to school

UNCA serves a large number of nontraditional-age students who are returning to school after taking time off for other things, and many of these folks are older than I am. Therefore I'm used to not being the oldest one in the room when I'm teaching a class; I've only been the eldest in maybe five or six of the 50-60 class sections I've led at this school.

But I'm not used to being one of the youngest in the room.

My MLA (Masters of Liberal Arts) course, Number sense: The philosophy and psychology of mathematics, met last night for the first time. I've got eight students in the class, four or five of whom are my senior in age and in life experience. It's a great bunch, and I can tell I'm going to learn more from them than they're going to learn from me.

We started off with some freewriting, through which I asked the students to probe into their own mathematical pasts. I hoped to find out what it is that makes these folks tick mathematically and to determine what they perceive to be the most basic and fundamental of mathematical operations. If we can get at the these operations, we'll be in a position to start our study of mathematical cognition where our brains begin, with approximations of enumeration.

I'm delighted to report that there's considerable diversity in the class when it comes to mathematical background. I found it interesting that the two gentlemen in the class reported more facility and familiarity with mathematics than their feminine counterparts (with one exception). Both of them described delight at working with statistics and geometry, and obsession with game-lake mathematical puzzles. The one woman with more mathematical experience is a former UNCA math major with whom I had the pleasure to work when I last taught Abstract Algebra I (in Fall 2008). This is her first semester of study in the MLA program.

The other five folks have considerably less mathematical background, but will provide perspectives from other points of view, reporting interest and expertise in psychology, history, and philosophy. I'm excited to learn from Samantha, who is taking time off from her work as a teacher for special-needs children. She mentioned how frustrated she is with mathematics education, and hopes that our class will give her the skills to help improve the way students are taught math at a young age. More power to her! Her high expectations for the course will definitely keep me on my toes.

After we probed our mathematical pasts for a bit, I presented a few exercises and experiments I hoped would whet their appetites for the material we're about to study (from Dehaene's Number sense). With no promise that this link will be evergreen, you can find Mathematica files for these exercises on the course website under the entry for January 12th.

In the first exercise I challenged students to hold in their memory progressively longer randomly generated strings of digits, demonstrating the means by which we tend to use our linguistic faculties to store such strings in short-term memory. (This use underlies linguistic differences in the ability to memorize and compute with numbers: the brevity of number words in many Asian languages allows native speakers of those tongues to outperform speakers of other languages in basic memorization and numerical manipulation.) The second exercise demonstrates how the arrangement of objects affects our sense of their number: more densely packed objects tend to appear more numerate than those that are sparsely spaced, and more orderly-arranged objects appear more numerate than those that are randomly placed. For the third activity, I asked the students to report any sort of synesthesia they've ever experienced: do they sense that numbers have specific appearance, texture, color, smell, relative spatial position, or gender? I think the students found it odd when I reported I've always had a very well-defined sense of the gender of every digit.

We wrapped up with a short discussion of formal expectations for the course, a topic I'm trying to de-emphasize as much as possible. I'm looking forward to next week's discussion. I'm curious to see if the students will find Dahaene's book as intriguing as I have.