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!