Shameful self-promotion

One of my editors, Bethany, has urged me to blog more frequently. So here I am.

I understand her point: she’s legitimately concerned that I might not be doing as much as I could to promote my work. Student writing in the quantitative disciplines: A guide for college faculty (Jossey-Bass, 2012) has been out for a few months now, and though I’ve every reason to believe that sales are quite good, they could probably be better, given more ambitious self-marketing. I’m not sure I feel up to this, though.

It’s not that I feel that self-promotion would be beneath me, or would constitute “selling out.” That attitude would be intellectually elitist and unbecoming. Believe me, I’m not against garnering a little fame (and a somewhat smaller fortune) from the book. There’s nothing wrong with showing a little pride in one’s work. It’s just that I’m not sure this blog is the appropriate venue for that self-promotion. Others are doing it, why can’t I?

Bethany mentioned the blog my good friend Erdrick writes, and the one that Maryellen Weimer, who helped me tremendously as my consulting editor for the book, updates regularly. Erdrick’s a wonderful colleague and a superb teacher, and his blog is superlatively good. Maryellen’s blog, too, is a wonderful periodical piece, and a wide-open window on current best practices in teaching at the university level. But I don’t think it’s fair to compare these blogs with my own; they serve different roles. I’ve never meant this space to be an intentional documentation of best practices, or a how-to manual on pedagogy. Though I don’t doubt my own excellence as a teacher (I’ve a great deal of evidence to suggest that I am quite accomplished as an educator), I have been, and I remain, reluctant to take on the task of systematically codifying my thoughts on teaching.

Rather, I’ve always thought of Change of Basis as a safe place to unpack my own teaching activities (and not, though they may frequently coincide, best practices in teaching more generally) in real time, keeping tabs on what goes on in my classroom, in my REU, at my school, in my mind. It’s more made up of notes-to-self than it is directives-to-others. Though I may cite books on teaching, I don’t do so as a careful and intentional review of the literature, but rather as an indicator of what I happen to be reading at any given time. Though I might bring out all the buzzwords (problem-based learning, inquiry-based learning, Moore method, writing across the disciplines, writing-to-learn, etc.), I don’t treat them methodically but only as they come up in my own work. How else to put it? I try to teach by example and not rote lecture. My tone is more anecdotal and less comprehensive and directive. It’s “I tried this trick out, and it worked out well” and not “studies show that this trick will reach students most effectively.”

I mentioned to Bethany that one of the reasons I’d not updated lately was that I’d not had much time lately to write. Between near-constant travel to present at conferences, seminars, colloquia, and faculty development workshops; leadership on the Curriculum Review Task Force (a full-time job in itself lately), preparations for the REU (now done with its second day), several ongoing research projects (in both math and composition and rhetoric), assumption of the Honors Program directorship (my administration began officially a few days ago), and teaching a full load of courses, I’ve not had the time I once had to dedicate to this blog…and when I have the time, it’s often directed into other writing projects (notably, 3x30 and poetry).

Honestly, I’m too busy being a dedicated educator to write about being a dedicated educator.

It’s thus that I offer my apologies to you, Bethany. I’m sorry I’m not posting as often as I might, and that my posts aren’t as pointed or focused as they might be. Please know that I wish I had the time and energy to post once, twice, thrice a week, offering some digestible and downloadable 750-to-1000 words of wisdom each time. Please know that I’m not angry with you for asking more of me, and that I do understand, and appreciate, your concern. This just ain’t that kind of blog.

That said, please consider giving Student writing a read. I’m proud of it, and I feel that it’s a very good book. I feel very strongly that writing has much to offer to students and scholars in the quantitative disciplines, and that we do well to pay attention to writing’s potential. I will walk the Earth from end to end to say so, again and again. If you’d like to talk about it, let me know.

CRTF continues...

As the work of the Curriculum Review Task Force carries on, now well into its second year, I ask all of my colleagues, students, and friends to consider the parts they all play as citizens of the world...and the roles they all play in helping themselves and others fulfill those parts.

Someday (next summer, maybe, when the REU's direction is no longer chiefly my responsibility?) I hope to write at length about the curriculum review, for it's been a sometimes-trying, sometime-exhilarating, but ever-rich-and-rewarding experience. So much to say about it, so much to say.

And so much to say about my ever-changing perception of my part in it...and about my part in the school more broadly, and in society and humanity more broadly still. The reading I've done in the past month alone (Joseph Weizenbaum, Antonio Damasio, William McDonogh & Michael Braungart, and Martha Nussbaum, all tempered by the poetry of Marge Piercy, Ted Hughes, and Adrienne Rich) convinces me more solidly than ever before that we folks in the "hard" sciences constrain our roles too tightly: we tend to dive dangerously deeply into our disciplines. From our depths we lose sight of the stars.

More soon...

3 friends, 30 objects, etc.

For the past 10 days, my friends Libby and Mariposa (two academic writing specialists) and I have been posting daily on our blog 3 friends, 30 objects, 90 stories, our rendition of a reflective writing exercise described by composition scholars Doug Hesse, Nancy Sommers, and Kathleen Blake Yancey. This exercise (which, as the blog's title suggest, is now one-third of the way through), described more fully here, has proven to be one of the most rewarding of my recent career.

Though we'd originally meant for each of us to write for 30 minutes a day, on some days I've worked for three or more hours on what I'd like to say, drafting and redrafting, tweaking the words until they're just so. On the whole, it's making me a better writer. How could it fail to, given that I'm intentionally devoting so much time to it?

It's healthy. I've written some of the best poems I've written in a long time. I've shared openly wonderful memories from long ago I've never shared before. I've learned a great deal about two close friends. The whole experience has been calming, centering, and enlightening.

I strongly recommend this exercise to any person hoping to learn more about herself...and to any friends hoping to learn more about each other. I also recommend it to any teacher in any area, at any level, as a means of focusing students' attention.

Day of Higher Ed, part 1

My colleague Casie tipped me off that today is The Chronicle of Higher Education's Day of Higher Ed, a day on which those of us who work in higher education are supposed to raise awareness of what we do, and how much of it we're doing. Contrary to the perception of some (mostly conservative, in my experience) suit-types who view higher education with disdain and its employees as fat and fatuous sinecurists, most of us actually work quite hard.

More forcefully, most of us work our asses off.

So, what's in store for me today? (Keep in mind that I'm coming off of a weekend on which I spent roughly 12 hours grading Calc III exams...) Though I can't guarantee I'll get to it all, here's the medium-term docket:

1. Write an end-of-year project report for the National Science Foundation for my 2011 REU (estimated time to complete this: 5-6 hours)

2. Draft a welcome and informational letter to this year's crop of REU students (time to complete: 1-2 hours)

3. Send out rejection letters to the nearly 300 students who didn't get into this year's REU (time to complete: 1 hour)

4. Grade exams for my two students who are taking Abstract Algebra II as a reading course (time to complete: 1 hour)

5. Respond to final drafts of MLA students' latest written projects (time to complete: 3-4 hours)

6. Write three or four rec letters, including an incredibly urgent one for which the requesting student gave me less than a week's notice (time to complete: 2-3 hours)

7. Plan workshop materials for an upcoming writing workshop I'm leading at NC State (time to complete: 3-5 hours)

8. Review and respond to proposed Abstract Algebra curricula floated by other members of the Mathematical Association of America's Committee on Undergraduate Programs in Mathematics (time to complete: 3-5 hours)

9. Generate open problems list for this year's REU (time to complete: 2-3 hours)

10. Begin housing and payroll paperwork for this year's REU students (time to complete: 1-2 hours)

11. Draft a precis for on the latest curricular proposal by the Curriculum Review Task Force's Curricular Sustainability Subgroup (time to complete: 2-3 hours)

12. Complete drafts of research articles currently underway with three different sets of undergraduate coauthors (time to complete: 10-20 hours)

13. Oh yeah...teach!

Anyway, I'd better get to work on that list, me with my oodles of free time. More later, perhaps...

Pobject?!?

For more than five years (since this blog's inception in Summer 2006), regular readers have known me as "DocTurtle," a riff on my academic qualifications and my "totem animal," for lack of a better term. (Incidentally, I don't take pains to hide my real identity...most of you know that my DocTurtle's Bruce Wayne is a mild-manner happy-go-lucky Pollyanna of a mathematician known as Patrick Bahls.)

So why is it that my screen name has suddenly changed to "Pobject"?

At the recent 2012 Conference on College Composition and Communication, two of my wonderful friends and colleagues in rhetoric and composition studies, whose names I'll withhold here (I'm not sure how broadly they want them disseminated) took in a panel discussion led by Doug Hesse, Nancy Sommers, and Kathleen Blake Yancey, three of the leaders in the academic rhet-comp community. That discussion focused on a writing exercise they'd assigned themselves: for an hour a day on each of thirty days, these three scholars reflected in writing on a different everyday object each day. In their conference abstract, the scholars ask "What may be learned about the evocative power of objects from a sustained attention to them? How do objects reveal or conceal their origins? And what may we learn about the acts of composing from a sustained project over thirty days?" As they put it, the activity challenged the "traditional boundaries between personal and academic writing."

The three of us (my colleagues and I), all engaged in academic writing in some way, were energized by the idea of this activity and decided to try it out for ourselves. Therefore, on each day in April 2012 each of us will write (under the names "Kobject," "Lobject," and "Pobject," nods to our first initials) for at least 30 minutes on one of the 30 objects we've chosen in advance. We'll be chronicling our ongoing work on a new blog, 3 friends, 30 things, 90 stories. In that blog's first post (to appear later today), I'll say a bit more about the parameters of our exercise.

I hope you'll follow along...we're hoping this will offer us a powerful and consciousness-raising experience.

Re-visioning revision-ing

After dedicating several hours of my morning to reviewing teaching award files, I've turned my afternoon attention to the exciting task of coding drafts of past years' REU students' drafts, preparing for the panel on mathematical rhetoric I'll be presenting with my Charleston friends at this year's very-fast-approaching Conference on College Composition and Communication. While our panel will offer an overview of our earlier work on the rhetorical moves REU students make in crafting disciplinary writing, we'll also offer a sneak peak of the analysis we're doing on revision.

Regarding that analysis: this shit is hard, y'all. At least, it's time consuming. Back in December I spent a full day with my Charleston peeps Bella and Damian making qualitative observations on each of the seven drafts written by a single student author. We're taking this route because we found that existing revision coding strategies (like a classical one due to Faigley and Witte in their 1981 paper "Analyzing revision") don't adequately capture the richness of the students' rhetorical moves as they revise their drafts of authentic disciplinary writing: while Faigley and Witte applied their schema to somewhat tightly-constrained writing produced in an artificial setting with strongly-controlled revision protocols, my REU students were writing in order to elaborate on their ongoing original research projects. The complexity of the latter students' writing (both products and processes) defies easy microscopic analysis, and we quickly abandoned such analytical methods.

That's not to say that we're not getting some "quantitative" data: we're tracking measures like number of pages, number of paragraphs, number of citations and references, etc., with the hope that we can glean some interesting conclusion from this info, if nothing more than trends that roughly parallel our qualitative observations.

We'll see.

For now, back to coding...

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.

Swimming!

Two class-days into the semester, and things are going swimmingly. I'm putting the course together with a modified Moore method, cycling (roughly) through the following steps:

1. handing out problem sets,
2. giving the students time in and outside of class to work through solutions in groups,
3. asking the students to present their solutions in class,
4. asking the students to write up solutions to selected problems as homework, and
5. quizzes the students on completed problem sets.

As of now I've met with the first section of the course twice and the second section once, but every meeting has been lively and energetic, and I've needed absolutely no coaxing to get students to work in groups and to come to the board. The atmosphere in the course has been supportive and friendly. I'm delighted that this morning's class gave us an opportunity to note that, as I'd promised, no lightning bolts came down from the sky when a student made a mistake at the board.

It's been a long time since I taught course using anything close to the Moore method (my special topics course in graph theory, run in Spring 2008), and I notice that I've grown considerably as a teacher since then. I'm more confident, and that confidence has enabled me to feel less awkward taking a peripheral role. In particular, I find that I'm much more able to sit in silence than I was in the past. Silence in a crowded classroom is disconcerting, and it's all one can do to keep from saying something after ten or twelve seconds of quiet have elapsed. I've grown accustomed to such silences, though, just as I've grown accustomed to (or, more accurately, enamored of) the thrumming of three dozen voices trading tricks as the students work in groups in class.

I'm confident. It's going to be a good semester.

Day One...and WHAT a Day One!

It's been a while since I last wrote a very substantial post. I had to look back at the blog just now to see what was going on, and what state my mind was in, when I've checked recently.

Most of my last few posts have been abstruse, political, and maybe even metaphysical, dealing with everything from the affective learning goals met through inquiry-based learning to the horrors of administration-sanctioned crackdown on students' rights to peaceably assemble on their own college campus. I fear this post might continue this trend toward the abstract.

Roughly three months ago I posted about an opportunity I'd been asked to explore which, quite honestly, scares me more than a little. I feared this opportunity because I knew if I offered to take it on and if my offer were successful it would present me with an entirely new set of challenges and that I'd slip and stumble and make a mess of it every now and then as I got into the flow. But hey, no one of us is born knowing how to swim. We've all got to pick it up somehow.

Well, it's time to swim.

It's official: in Fall 2012 I will become the University of North Carolina, Asheville's new Honors Program Director.

During the next several months I'll be learning all that I can about this new responsibility. I'll be tailing the current director like a second shadow. I'll be surveying the program's current students and surveying the faculty. I'll be making new plans and making new friends. I'll be reflecting on my own ideas and I'll be reaching out for others' ideas I'd never dream up myself.

And I'll be looking for support, from the hundreds of wonderful colleagues, students, family, and friends who have helped me to get to this point in my career...and who will continue to help me as my career takes this new turn. I thank every last one of you for all that you've done for me until now. I thank my colleagues and students, for your suggestions and support and for helping me to craft the communities that have helped us all learn together. I thank my friends and family, for the time you've given me, and for the shoulders you've let me cry on and lean on. I wouldn't be where I am today if it weren't for you, all of you.

With peace and love, I thank you.

Now, let's get to work. It's dawn again, with a brand new sun shining. There's much to be done!...including getting to my first class, which begins in 12 minutes...

Blowing up the interwebs

I'm not sure this won't cause a cataclysmic loop of self-reference, but here's a link to a very nice little Chronicle write-up on this past Wednesday's JMM talk on our rhetorical analysis of the REU students' writing.

Nice.

I hope the folks that make it here from that site will take the time to poke around a little bit and read a bit more about my work with math and writing. Please think about picking up a copy of my forthcoming book, Student writing in the quantitative disciplines: A guide for college faculty, available in March from Jossey-Bass.

I hope once I'm settled back in at home tonight or tomorrow to write a run-down on my whole JMM experience (minus much of the after-hours goings-on), but for now I've got a few more talks to make.

On deck

It's a new year, and we're only a few days away from a new semester (beginning Monday, January 9th). There are big, big things in the works: my book comes out in a couple of months, the work of the Curriculum Review Task Force should be coming to a head this term (with concrete recommendations to the Faculty Senate due by April), and...well...other news items about which I'll be able to say more in a few weeks' time.

What's in store, teaching-wise? I've got three preps this term, one for two (large) sections of a course I've not taught in almost six years (Calculus III), one for a single (small) section of a course I've never taught (a Masters of Liberal Arts [MLA] course on the cognitive psychology behind mathematics), and one for my section (of two) of our senior seminar.

In the seven years I've been at UNCA we've not taught two concurrent sections of that last class, so I'm not sure exactly how we're going to manage it. I've yet to talk to my colleague Timon, who'll be teaching the other section. I imagine we might hold many activities together, splitting when it comes time for the students to present. There's simply no way we'll get through 26 student presentations in the five or six weeks we can offer them to speak. We'd have to have an unprecedented four talks per period to make it work, and that's simply unworkable. Thus splitting into separate sections for that part of the course, though not ideal, is about the best we'll be able to do.

Meanwhile, I've got plans for the other courses. Calc III, which I've not taught since Summer 2006 (the last summer I wasn't running the REU), I'll be running with a modified Moore method: one day each week will be devoted to discussion of new definitions and discoveries, a second day to small group work on the current problem set, and the third to problem presentations. Both sections of this class are big enough (roughly 30 students apiece) that I'll probably ask students to "present" simultaneously (two to four at a time) whenever feasible. This'll ensure that we make it through problem sets in a somewhat timely fashion, and that each individual student gets more opportunities to present. I've already worked with about half of the students in both sections, which familiarity will help me ease into the new term.

I can't say the same for my MLA course. It's been nearly a decade since I taught a graduate-level course (a special topics course on Coxeter groups and related groups which I led at UIUC back in Spring 2004), and this course differs dramatically from that one. We'll be exploring the learning and cognition of mathematics, and I plan to inject a good deal of philosophy and sociology into the mix as well, drawing on a number of sources to paint a picture of mathematics most people never see. We'll begin with Stanislas Dehaene's marvelous book Number sense: How the mind creates mathematics, about which I've blogged a bit before (see the "Dehaene" tag at the right), surveying the psychology of mathematical discovery, before moving onto Imre Lakatos's Proof and refutation, a philosophical treatise designed to lay bare the workings of what might be called the "mathematical method."

I'm not sure what to expect from this course. I suspect there'll be a week or two of me feeling out the students (currently there are seven students enrolled) to see where their interests and aptitudes lie. Likely none of them are straight-up mathematicians; I'll be curious to learn what they're hoping to get from the class, and I'm certain they'll help me give it more direction.

Ah, well...one week to go. Before then I'm off to Boston for this year's JMM, at which several UNCA students (and a few past REU students) are presenting. I'm particularly excited to see how far Ned's and Ino's work on nutritional data has come since their presentation at Kennesaw State in November. (They're presenting in a special session on mathematics and sustainability.)

Further bulletins as events warrant, likely soon.

Close to home

Why is it that, of all of the Occupy activities that have gone on for the past two months, the pepper-spraying of peaceful UC Davis students strikes me so much more strongly than any other?

The extremity of the incident is hard to ignore: riot-geared police officers, decked in body armor and military weaponry, approach and attack unarmed and peaceful demonstrators seated in a position of pure passivity. Whether or not you agree with the reasons for the protest (I do, but I'm certain some of my readers do not), the level of force used against the sitting students is clearly out of proportion by several orders of magnitude.

The diffidence of the university administrators (in particular, UC Davis Chancellor Linda Katehi) is as striking. Afterward she is coolly dismissive of the protestors, adopting a detached and thoroughly establishmentarian "well, that's what happens when you don't do as you're told" stance in the wake of the attack.

The immediacy (and ubiquity) of the images plays a part, too: they're arresting and unavoidable...and every video of the attack clearly shows a dozen or more others actively filming the incident, a self-replicating postmodernist pastiche of views, every one showcasing unmitigated brutality.

All of these aspects of the attack factor into its effect on me, but I think what's most striking to me is how similar the students attacked are to my own. How easily those Davis kids could be the ones who come to my classes, who hang out with me in the Math Lab, who joke with me in the hall and who ride with me to conferences! How easily my kids could have been the ones writhing in agony as they gasp for breath and when they finally find it spend several hours coughing up blood! They're interchangeable. I find myself putting my students' faces over those of the kids in the video clips, and I shudder.

I wonder: how differently would my own institution have responded to actions like those of the peaceful students at UC Davis?

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.

More big picture stuff

In regards to another recent post, it looks like we're about to beat up on the student body again. I say once more: what in the hell are we doing?

I don't usually get political here (because my pedagogy, writ small, doesn't generally intersect directly with politics outside of my own institution), but I can't help it now: if you support any leader opposed to fair taxation and rational government spending and stimulus, you support the eventual decay of our educational system. Don't re-elect these fools who are destroying our future.

Impending sense of something

Well, all my classes are prepped for a couple of days' absence from the scene. My Abstract students are hard at work on their latest problem set, and the Precalckers are plugging away at their second take-home exam.

All is calm.

Ever get that feeling that something big is about to break?

I've got that feeling right now. I can't put my finger on it. Maybe it's just that the next week and a half is frightfully busy: something's bound to happen.

We'll be ready, my friends. We'll be ready.

Big, big picture

For several years now, I've been a "big picture" kind of guy: I paint in broad strokes. I see forests and not trees. I'm more satisfied with hand-waving proofs than most of my colleagues would be. I'm more concerned that I and my students get the overall idea, the intuition, the gut-level understanding, than that we get every last detail right.

I'm not sure when I took this viewpoint on, but I think it's a relatively recent phenomenon. After all, I'm not sure you can make it through a graduate program in mathematics without punctilious attention paid to the merest minutiae of theorems and their proofs. It's come on more recently, as I've grown as a teacher and scholar, and as I've come to grips with bigger and bigger problems. It's gotten "worse" lately. I mentioned only half-jokingly to the Associate Provost for Academic Administration, with whom I've been doing a lot of work this semester for CRTF, that I'm starting to think like an administrator. For good or for ill I no longer consider curricular issues as they'll affect a single instructor or even a single department, but rather as they'll affect the school as a whole.

Perhaps the widest view one can take I took for a moment today, and it scared me: if you look at our nation's higher educational system as a whole, there are terrifying trends.

One incident: this morning I got an email from a student who's having to take a break from it all to maintain sanity. Literally. This person is going off the map for a little while and heading home to be with friends and family and to deal with mental health issues.

A second: yesterday I spent a tearful half hour with another student who's clearly dealing with stressors beyond finishing up an essay for Humanities or prepping for this week's coming Abstract Algebra exam. This is a very good student, one I know well, one whose performance this semester has declined noticeably from past semesters. There's much more going on behind the scenes.

A third: last week one student spoke of a narrow escape from dropping out and returning to military service just to make ends meet. Fortunately the financial aid office and the counseling center were able to help make an end-run around a vindictive ex-spouse whose uncooperativeness was preventing disbursement of much-needed funds.

These aren't just isolated events. Dozens of my students, in addition to managing a full load of difficult classes (often in excess of 18 hours dominated by high-level mathematics coursework) also work 20, 30, even 40 hours a week, and deal with manifold family issues (I can think of several students whose entire families depend on them for nearly everything), and still manage to keep it together...or not, as the case may be. The cracks are showing: I've had more people cry in my office than in any other semester I can remember. It ain't getting better.

These students shouldn't have to deal with all they're dealing with today. They should be free to be students, to be free from having to support themselves with back-breaking (or at least time-sucking) labor.

It hasn't always been like this. I speak from experience.

I had it far easier than these folks, barely more than a decade ago. I had student loans and a scholarship, and my family'd done well in socking some away to help me go to school, so the only work I needed to find to get me through my college years was as a work-study assistant in the Math and C&S Department's computer lab. Big. Deal. This was a sinecure. I "worked" 10, maybe 20, hours a week, passing out boot-up disks (yes, we still used those back then), trouble-shooting simple software problems (usually involving nothing harder than MS Excel), and shooting the shit with my geeky friends. Most of the time I got paid to do my homework. The rest of my time (that not devoted to hanging out, eating pizza, running, and annoying the crap out of my dorm mates by playing Pink Floyd's "One of These Days" really frickin' loudly on my monster tower speakers) was spent on schoolwork. I managed to make straight As (aside from a couple of stray minuses) and learn a lot. I was a slacker my first year of college, because I could afford to be: I quickly learned that I didn't need to put too much effort in in order to do well, so I took it easy. My second year I started taking courses that offered legitimate challenge, so I buckled down. That's also when I first realized that I could teach myself as much as anyone else could teach me, so I started studying on my own, everything from additional math and physics and computer science to philosophy, literature, languages, and history. On my free time. (Holy crap...free time! What's that, again?)

I could reminisce forever, but let me get to my point: I'd love to launch into a cliché and crotchety "kids these days" diatribe, but I can't. I had it easier than these kids. Far easier. I didn't have to work my ass off just to stay warm and well-fed, let alone well-educated, and I had time enough (and more) to do well in and learn from all of my classes.

Many of my students have no such luxury. They have to work, and often work hard, just to afford the modest cost of the education my public school provides to them. (It may be worth noting that I went to a pricey private school for college.) If they don't work (and often even if they do) they have to go into debt up to their eyeballs to pay the bills, for they cannot always rely on family to help them out (many of these students are first-generation college students and come from families who can ill-afford to give financial aid). Moreover, they face dim job prospects on graduation, with the economy lagging the way it is. There are no sure signs of long-term improvement. Thus many of my students are going to saddled with crushing student-loan debt and little opportunity to find the work they'll need to get to help pay it back.

Do you think a student with 18 hours a week of coursework and a 40-hour-a-week job who's drawing several hundred dollars per term in student loans and trying her best to hold her family together really has time to learn (or care) what a derivative is? Do you think such a student is going to be completing her homework in full, passing her exams, and finishing her oral presentation on subgroups of groups of symmetry? Even if she's meeting these superficial measures of academic achievement, do you really think she's going to be getting much meaningful out of it?

It's become cliché to put someone in "The 99%," but my students, almost every last one of them, belong there. Bless 'em all, they belong there.

And my students amaze me. Even with 18 hours of coursework and 40 hours on midnight shifts at motel desks and family foibles and student loans and squabbles with landlords over week-late rent checks, they do still learn what a derivative is. And they do still care. They don't just finish their homework, they polish it to perfection. They don't just pass their exams, they ace them. They do incredible work, and they do it without complaint. Somehow, despite having to do everything else we demand that they do, they're learning, and they're helping each other to learn. They're there for each other, even when the system's left them behind.

But this can't go on forever. A college education can't be what it used to be if we don't give these people a bit more breathing room. What in the hell are we doing to them?

The system needs to change. Otherwise, in ten or twenty years we'll look back and notice that though we've stocked our universities with the brightest scholars and the best teachers, and though we've built the shiniest classroom buildings and equipped them with the sleekest high-tech gadgetry, we've miseducated an entire generation simply because we asked too much of them while they were trying to do what we want them to be doing before they do anything else. We just wanted them to learn.

Well...I'll keep doing all that I can, and I'm sure I can count on my students and colleagues (some of the most admirable people on Earth) to do the same. It's a mountain we've got to move, and the only way we're going to move it is if we all get behind it together.

I'm new here

Parker J. Palmer's and Arthur Zajonc's The heart of higher education: A call to renewal (transforming the academy through collegial conversations) (the centerpiece of the most recent faculty Learning Circle in which I took part, and about which I've posted somewhat recently) gave me more than its fair share of things to think about. Many of its insights offered theoretical, even spiritual, enlightenment regarding teaching, but other insights were more practical and practicable.

One of the more down-to-earth suggestions offered up by one of the coauthors' colleagues (Patricia Owen-Smith, Professor of Psychology and Women's Studies in the Oxford College of Emory University) was a means of encouraging contemplative practice in the classroom simply by playing music to being each class period. Owen-Smith (pp. 157-161 in the above work) describes how several years ago she began the practice of playing 7-9 minutes of music at the outset of each class. She encouraged her students to "go within, be still, and listen to the self." While she admitted the difficulty of tying this contemplative practice to improvements in students' achievement of cognitive learning goals (as if this would be the purpose of playing the music in the first place!), she reports that

over time, I learned that the music and meditative moments had an impact on many students. Some students began to ask for guidance with their contemplation and reflection....By midsemester several students per class would mention that they looked forward to this nine-minute period of music. Some students began to bring music from their own collections that they found inspirational and important. As we neared the end of the semester, the structure of the class had changed from a group of individuals reluctantly gathered together for study to a community of friends and partners who were creating a space of introspection, quiet, and respect for the process of study and the development of self.

Once or twice a week for the past few weeks I've begun a similar practice in one of my classes. It began with my reading of an excerpt from Rilke's letters to Franz Kappus (a reading which moved one student so much she had to leave the room), and continued with a passage from Dick Leith's history of the English language. At one student's suggestion one morning we watched a scene from Harold and Maude, and the next day I read one of my own recently-written poems ("Ode to Ned Maddrell," which I penned for the last-living speaker of the Manx language). To open off on Monday (at the suggestion of another student) we'll take in one of Gil Scott-Heron's last videos.

This practice has developed naturally, in an easygoing fashion, and perhaps unsurprisingly it's happened in the most natural and easygoing section of any of my courses this semester. From Day One nearly every person in that section of Precalculus has worked well together, helping each other out and asking for help when help is needed. This natural ease with which we've worked together all term has made it hard for me to tell whether the contemplative practice has had a real effect on the esprit de corps of the class...

...but I'm not going to take any chances. The practice has definitely helped me to make connections between the intellectual and the personal, between the scientific and the humanistic. It's helped me to remain focused on what really matters, and it's helped to remind both me and my students that we do well to look for mathematics' usefulness...and to look for its beauty. Much like well-chosen low-stakes writing activities, this practice is well worth the few minutes of class time that it takes.

Beginning right away I'm going to introduce this practice in all of my classes. It can't hurt.

What effect can it have in a class like my current Abstract Algebra class, a room full of stressed-out work-wearied students representing, honestly, probably the greatest range of mathematical ability I've seen in one section since I began teaching at UNCA over six years ago? I admit here and now that I find myself frustrated at how I've managed this course. For some time now I've felt the need to slow its pace to accommodate the most modestly quick learners, but without sacrificing the true nature of the subject, a nature laden with often-abstract proofs. I don't know how much slowing the pace down has helped: several students are still struggling, and as much as I hate to leave them behind (I hate hate hate people who teach to the top ten percent), I simply must move on. Moreover, I sense that the slowness has led to frustration on the part of some of the class's quicker students, and I can feel cliquishness setting in...not a nice way to end the semester.

Maybe it'd be wise at this point to remind everyone that we all have a right to say "I'm new here": we're all free to make mistakes from time to time. After all, no one's lived this life before, and the future hits us all at the same time. But no matter how far you go, you can always turn around.

What say, folks? What are we going to make of our last five weeks or so together?

Research update

Ned and Ino are chuggin' along. Their research project, the culmination of which will be a pamphlet detailing the means of making a week's worth of healthy, affordable meals is flying forward. We just overcame a major obstacle today: we had to figure out how, once we'd found the ideally affordable combination of foods needed to obtain the right amount of each nutrient in our analysis individually, to combine this information to give us the most affordable combination of foods to give us the right amount of all nutrients at once. We made it over that hump, and I truly think it'll be the last big one before our projects reaches its end.

So proud!

Partners in crime

I know a number of people (many former and current students, a good number of colleagues, and assorted folks I've never met) read this blog, but not many often comment publicly. Quite often, though, I get comments about it on Facebook or in my in-box.

This past week I got a note from a fellow who's teaching precalculus at an inner-city high school in Boston, using inquiry-based learning. He wrote me asking about the methods I'm using in my own precalc classes right now and shared some of his own (he's asked me not to post his notes, as they're very much works in progress). I'm very impressed! His notes are clever and engaging, offering students a scaffolding students can use to climb from the barest basics up to properties of advanced functions, logs and exponents, and trigonometry. You can read about his exploits here.

By comparison, my methods that are considerably less purely inquiry-based...he's doing pretty much straight-up Moore method with high-school students! Inventive and impactful.

Dead Zone

Today I felt like every one of my classes was a bit stuck in the mud. (Oddly enough, my morning Precalc class, often my quietest, was the most lively today.) It was all we could do to keep making forward progress in a couple of the classes, and I felt like I was beating a dead horse more than once.

What to do at such times?

The classical response, at least from instructors in content-driven disciplines: "well, we've got so much to cover that we've got to keep going..."

...but this is wrongheaded. If you press on without pause, it's not like students are going to get any more engaged, and it's not like they're going to get much out of whatever you do together, anyway. In pressing on you'll be doing so only for the sake of pressing on, and any progress you make will be illusory.

This is exactly how it felt in my second section of Precalc, and in Abstract Algebra, in both of which classes we worked with (what I thought were) some pretty neat mathematical ideas: in Precalc we solved a nontrivial optimization problem involving rational functions, and in Abstract Algebra we looked at the subgroup lattices of a couple of groups and examined the asymptotic behavior of Euler's function φ. I don't feel that either class picked up on the subtle beauty in a way they would have had they been in a more receptive mood.

Don't get me wrong: I'm not blaming my classes. Both of these classes are full of wonderful students who are generally unafraid of working together to make a healthy and supportive learning environment. (I've bragged on my Precalc peeps enough this semester for you not to know how much I care about them.) Rather, I think we've just hit that point in the semester, about 50-60% of the way through, where everybody's just DEAD.

It's the Dead Zone. Wearied by exams and essays and due dates and deadlines, overburdened by homework and quizzes and lit reviews and response papers, we're tired and jaded and not having much fun. (Believe me, kiddoes, this "we" often includes me. I apologize if I'm sometimes snappy around this time of the term; it's hard to be irrepressibly chipped every hour of every day!)

On reflection, I've thought of a two-fold healthier response to these Dead Zone doldrums:

1. Play. Put down the pen or pencil, put the paper away. Let's just think of something fun we can do with whatever it is we're working at this very moment. Optimization problems? Let's come up with some kind of crazy variation on the theme, whether we have any idea how to solve it or not. Let's set it up and see if we can work it out, like Ariadne weaving a web through the labyrinth. Are we sick to death of subgroup theorems? Let's break it all down with an explicit or example, or two, or three...let's dissect the dihedral groups until there's nothing left but individual elements...let's take it apart!

2. Reflect. The next step comes as no surprise to those who know me well: once we're done playing, let's take a minute or two to write to ourselves, if only to reflect on what we've been able to discover. Did we reach an end? How? Did we run aground? Why'd we lose our way? What's our play got to do with other problems we might encounter in mathematics and beyond? Write about it, write about how we feel about it. Hell, write about how we feel in general: why are we so dead today?

Too often affective learning goals get lost when we focus too heavily on cognitive learning goals, and that goes double for content-laden quantitative sciences. Let's try not to lose sight of our humanity, and the fragility that comes with it. Let's take care of each other as we come together to learn.

By and large all of my classes this semester are doing a marvelous job at this, and I admire them for it. I never cease to be amazed at the quality of students with whom I get to interact and learn. You're terrific people, all of you!