So far, so good

Halfway through the second day, and the semester's chugging along nicely.

The first meeting of my Complex Variables class came off without a hitch yesterday. I've got a relatively small group (15 students), comprising math, physics, and engineering majors. We had a lively first class, in which, after a brief review of operations on and properties of real numbers, we encountered the basic definition of a complex number. Tomorrow will tell if the structure I've designed for this course will work out well. I'm doing a sort of "flipped Moore method," wherein the students will be presenting only certain of the problems they're assigned, while they'll be submitting written solutions to them all. From the second problem set on, they'll be required to submit their solutions in LaTeX, and I'll be giving them all the option of taking part in the study my colleague Beatrice and I have put together for this coming year's Conference on College Composition and Communication (viva, Las Vegas!). Our goal will be to understand the effect that using LaTeX has on students' composition processes.

Meanwhile, I'm busy settling into the Honors office and meeting with Honors students as they drop in. I'm beginning to realize that much of this job entails putting out the dozens of little range fires that pop up on an almost hourly basis. (Welcome to administration, I suppose...?) It's not often the same thing twice, so far, so there's enough variety to make the job interesting. Moreover, the students are fantastic. I'm particularly enjoying meeting majors from departments very far removed from my own (Accounting, Health and Wellness Promotion, etc.).

It's going smoothly. Things are settling quickly enough that I'm already starting to look ahead to my next round of trips. First I'm off to Texas A&M International University in Laredo, where I'll be leading a day and a half of faculty development workshops centering on writing in the disciplines. Next, it's up the mountain to the Wildacres Retreat Center for my fifth Carolinas Writing Program Administrators fall conference (love those people!). Finally, a week later I'm off to my first North Carolina English Teachers Association conference (featuring my first official book signing!). I've got a couple more weeks to get ready, but need to get on it, especially for that first trip.

Speaking of which, let me get back to it...

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.

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.

Coming soon to your university's bookstore...

Life lurches forward in fits and starts, and all things go in cycles.

My first book (defined as something with an ISBN) was a collaborative effort with several of my fellow graduate students. From here to infinity (A foundation for calculus) (Thompson Learning, 2001) was a slender in-house volume on algebra, trig, and other precalc concepts meant for use in Vanderbilt's Calc I classes to get the students there up to speed on algebra essentials before Calc came along and kicked their butts. We worked together wonderfully well on this project, each writing a chapter, swapping chapters to review and revise during the editing stage, and sewing it together seamlessly before sending it off to the publisher. I wrote the chapter on rules for logs and exponents, a topic I feel very strongly should be taught in a certain way (it all makes total sense if you teach it this way).

I was very happy with that project.

My second book, The Isomorphism Problem in Coxeter groups (Imperial College Press/World Scientific Publishing, 2005) was a one-off, a graduate-level survey of a particular area in combinatorial and geometric group theory. I was approached by the publisher (in, admittedly, a very generic dear-author,-we-invite-you-to-publish-a-volume-in-our-new-lecture-note-series kind of way), and, having nothing better to do with a year of my time, said yes. On and off for almost a year I compiled all of my notes on rigidity problems in Coxeter groups, on automorphism structure in same, on presentation invariants, and on standard combinatorial techniques applicable to Coxeter groups, braid groups, Artin groups, and all other fellow travelers...the result was the text named above. It was something to do. It was a lot of work, and it was reviewed well. In the past six years it's sold maybe 600 or 700 copies, which honestly is more than it deserves to have sold; it's got a very niche audience. I'm proud of the book, but not excited by it; there was little passion in it.

In February 2012, my third book will appear through Jossey-Bass:


This book is a labor of love. It represents true passion, true excitement and ardor. It combines my love of teaching and my love of writing, and the sense of duty I feel toward folks in my chosen discipline. I had a blast writing it, and I'm very proud of the outcome. I hope you'll consider taking a look once it comes out!

Back

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

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

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

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

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

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

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

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

Anticlimax

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

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

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

Aleas being jactaed all over the place

I've cast two dies in the past 24 hours.

Last night I sent my editor the first draft of the last chapter that I'd yet to finish. As of 2:18 EDT this morning, I have completed a full first draft of my book.

And...

...yesterday before leaving campus I sent an email to the Chair of our Faculty Senate indicating my willingness to serve as the "point person" for the Curricular Sustainability Subcommittee of CRTF.

We'll see if they take me up on the offer.

Closer

The first draft of Chapter 1 (offering an overview of WAC) is done.

Strengths: I think I did a helluva job distilling the history of the WAC/WID/WTL movements down to about 5-10 pages. I think I did a good job of motivating WAC, WID, and WTL in the first place.

Weaknesses: In moving the section on student resistance from its original location (at the end of Chapter 2, on the writing process), the inter-section transitions at this new chapter's end may be a bit awkward.

We'll see. I've just sent Libby this draft; I'll eagerly await her feedback. She promises to get some reading in en route to Tuscaloosa, home to this year's Southern Writing Center Association conference. I wish I were going! Odd that this year Bama's playing host both to SWCA and to the Southeastern Sectional MAA meeting, coming up in a little over a month.

Now...to dink around on Facebook for a little while before beddie-bye. Au revoir!

Status report

Almost daily now I find myself explaining just what it is I'm working on, to Facebook friends and students who've caught an oblique comment or passing mention of my book, making me realize I've not been nearly so forthcoming as I ought to be. Regular readers of this blog will likely know, but newbies may as likely not, that I'm under contract with Jossey-Bass to complete a text on teaching writing and using writing as a learning tool in math-based fields. The working title is More than number: writing in the disciplines and writing-to-learn in the quantitative sciences.

As of this moment I've written somewhere on the order of 42,000 or 43,000 words of the book, comprising nearly four finished chapters, a halfway-decent outline for a fifth, and the very beginnings of a sixth. (My original outline called for seven chapters, but I suspect the first two will be folded into one.) As it becomes more and more fully formed, I'm becoming increasingly aware of the things that it will do well, and the things it will not do so well. Fortunately, I believe that the things it won't do well are things that are done well elsewhere, and which I never intended to do well in the first place.

Namely, it will not offer extensive treatment of more "traditional" discipline-specific genres like research papers, technical reports, and literature reviews. Those forms of writing are addressed at length by authors who have come before, and who are most definitely more qualified than I am to speak on those forms. It will not offer a ready-made blueprint for making writing work in this course or the other: the reader cannot expect to be able to read the book and become an expert overnight, capable of guiding her students through numerous complex writing activities on the first day of the new semester. As important as knowledge is practice, and this I cannot offer.

It will (and, in fact, does) give a great deal of direction in teaching writing in the quantitative classroom, offering advice on sequencing and structuring writing activities, assessing student writing, delivering feedback on writing, and helping students use writing to help them think, learn, and explore, rather than simply to communicate. It will (and does) involve new contributions to writing instruction from me, my colleagues, and my students. I'm particularly proud of the exemplary samples of student writing I'll be able to include.

I'm quite happy with the book so far, despite occasional nighttime anxiety that drives me out of bed to work on the damned thing at two in the morning. I'm sure it'll only get better as I get more and more feedback from my friends and editors.

I've got two more months before the first draft is due in completed form, at which time it'll get shipped off to various reviewers. Between now and then if I look sleepless and haggard, if I stumble past you in the hall or mumble something to myself before scribbling something frantically on the back of a campus mail envelope, forgive me: I'm likely lost in a literary world hovering somewhere several feet off of the ground.

Tired? Yeah. Nervous? Hell, yeah. But excited.

Confuzzled

At the end of class yesterday I asked each of my Calc II students to write down two things: the single topic (of all those we've addressed so far) about which she feels most confused, and the single topic about which she feels most confident.

The results?

Ambiguous.

What are you confused about?

1. Antiderivatives: 3
2. Riemann sums and finding area: 6
3. Basics from Calc I: 7
4. Trigonometry: 7
5. u-substitution: 10

What do you feel good about?

1. Setting up problems: 1
2. Riemann sums: 1
3. Derivatives: 2
4. Antiderivatives: 8
5. Finding area: 10
6. u-substitution: 10

I find it funny that equally many people find u-substitution confusing as find it fine. More people are okay with both antidifferentiation and area-finding than aren't, and there seems to be more uncertainty about carry-over from Calc I than there is about anything else.

Bottom line? I don't think any adjustments are necessary at this point. I'll just keep in mind that people are going to want reminders about tricksy twists in trig and algebra as those twists appear (as they did today in the form of 30-60-90 right triangles).

Having identified several students in this class who are accomplished writers, I'm including in this course a greater-than-even-I-generally-include number of writing-to-learn exercises. Today we ended class with a two-minute reflection on the process of finding volumes using integrals; I hope it helped.

In other news, I've now finished three of the tentatively-six chapters of my book. This weekend I hope to make a dent in Chapter 4, which deals with assessing and responding to student writing. The current draft's largely complete but is still rather ellipsis-ridden...

Day One...finally

Well, yesterday was our first day of classes. I knew we'd get there eventually, but Snowpocalypse 2011 gave us three days of canceled classes before we finally got things underway with a two-hour delay.

My "first class" therefore turned out to be the first meeting of my first-ever first-year seminar, on ethnomathematics. Although we were a bit rushed (trying to take care of two days' worth of business in a single day), I think things went well. At 14 students, the class is the smallest I've taught in years (not counting, perhaps, one or two sessions of the senior seminar); this is going to offer me a welcome relief. It'll also make my student-centered teaching techniques more effective.

After introductions and bureaucratic whatnot, we got started with a "Think/Three/Share" on campus services, offices, et cetera. (One of the purposes of the course is to introduce students to the university and to academic life, and to help students understand the purpose of a liberal arts institution.) Unprompted, the students came up with a substantial list of university offerings, including everything from the Health and Wellness Center to the many offices lining the student union. In a few weeks I'll be asking them to go around to each of these points of interest, interviewing employees there, and designing brochures to advertise those offices' services to prospective students.

After this exercise, we got the mathematical ball rolling with an activity I thought might help the students to identify certain mathematical "conceits" we hold. I showed a clip from the movie Contact (1997), in which Jodie Foster (as Carl Sagan's Eleanor Arroway) and friends are first contacted by an alien intelligence. The alien transmits a series of radio pulses their way, consisting of 2 bursts, then a pause; 3 bursts, then a pause; 5 bursts, then a pause...the first few dozen primes are pulsed out, and from this nonrandom behavior the scientists infer that whatever's sending the message must be a smart cookie.

Of course, there are several assumptions here that are arrogant and "humanocentric." Ranging from the most specific to the most broad:

1. The pulses are sent assuming knowledge about (and concern for) divisibility, the conceptual underpinning of prime numbers),
2. the pulses are meant to be interpreted in base-10 arithmetic, and
3. the pulses are broadcast with the assumption that we use a discrete number system in the first place.

The students didn't catch the first of these, but they caught the second two. I was impressed! We didn't have a whole lot of time to follow up on this exercise before we had to go. I only had a small bit of time to explain their first writing assignment, an "ethnomathematical autobiography," which, besides having the most Greek I've ever fit into a single assignment title, will challenge them to speculate on the ways in which one's upbringing might affect one's perception of mathematics, in the context of their own lives. We'll do some writing exercises on Tuesday (peer review and metacognitive writing), and Thursday will see us begin talking about math in other cultures.

My second class was the first meeting of my Calc II kiddoes. This class is packed! The room's designed to max out around 30 students; I've got 34 in the class now, and one or two more who'd like to get in. It was almost standing-room-only: once the desks ran out we had just enough chairs (and a single stool) to accommodate every last tush in the room. Moreover, the room itself is rather small and cramped. Fortunately we meet in a different room on Mondays, Wednesdays, and Fridays; I hope this other room is larger.

However, this begs a pedagogical point: what effect does it have on learning, moving the class from room to room on different days of the week? It can't help but have a noticeable impact, I would think. I've got to be open about this: I'm becoming increasingly ticked about the lack of respect the administration has shown the Mathematics Department here, in the form of allocation of space and resources. Every single semester we teach with too few rooms and too few seats. Despite serving more students (as measured by face-time equivalents) than any other department except perhaps Literature and Language, we always get the short end of the stick when it comes to classroom space.

It's verging on the absurd now. I teach in four different buildings this semester. Four. There's one day of the week (Wednesday) on which I'll teach in three different buildings in one day. I understand if occasionally one might need to be sent out into some far-flung corner of campus for one class or another, but considering most departments teach courses which meet almost exclusively in that department's faculty's home building, I can't help but feel we're being slighted. (I just did a quick survey of our course offerings; at a glance most departments teach either one or no sections outside of their home buildings.)

At the risk of sounding crass, that shit ain't right. Can you imagine the holy hell that would be raised if the chemists were asked to teach their small upper-level courses in the basement of New Hall, where all of the foreign language people dwell?

Anyway....

Aside from being cramped, the first day of Calc II came off rather well. No major kinks. We spent much of the class time building a rough concept map of Calc I, which I hope to include in my book.

Speaking of which: I finished off about 26,000 words over break, and am now about 80% done with a first draft. Draft versions of Chapters 3, 4, 5, and 6 are nearly done, and 7's coming along as well. Chapters 1 and 2 might end up getting merged into one, and I'll likely get a start on those/that this weekend.

For now, I'm off...in twenty minutes I've got the first meeting of this semester's 280 course. 34 students! The last time I taught it (Fall 2009), I had 15. Crikey.

Wish me luck.

In the interest of full disclosure

It's been a busy break.

Winter Break started, effectively, just under three weeks ago. In that time I've been almost completely submerged in writing theory and pedagogy, hard at work on my book. I've written about 17,000 words in the past two and a half weeks, so that I'm now roughly 60% done with a first draft of the damned thing.

I say "damned thing," but of course you know I'm loving every minute of it. Some paragraphs are slow going and take me an hour or more to kill, and others just fly from my fingers. It's all fun, though, and I'm excited about how the book's developing. I'm working away at several chapters simultaneously (I've started every chapter but the second and the seventh), and they're starting to grow and to grow together. By the end of next week I hope to have completed first drafts of Chapters 3, 4, 5, and 6. (That'll leave 1, 2, and 7 to go.)

While I'm at it, I'd like to give a massive shout-out to my writing colleague Libby of East Carolina University, who gave me fantastic feedback on my introduction, and excellent ideas for later chapters. She's the first of my colleagues in composition and rhetoric to read any substantive portion of the book, and her reading, and her response to it, has encouraged me greatly. Peace!

Unsurprisingly, in working so closely on the book I've begun to think about ways I can model to my students good writing and good writing process to an even greater extent than I already do. I'd like to offer them a window on my own writing process in whatever way I can. I'd like them to see rough drafts, wrong turns, dead-end ideas, reviewers' feedback, and revision, revision, revision.

Obviously they're not going to give a day-old donut about every single version I write of one or another dry math paper. But it can't hurt to show them some of my first-draft research notes that are little more than mathematical freewriting (see below), or the copious comments and suggested emendations my editor offers me on draft chapters of my textbook. If it accomplishes nothing else, at least showing these things to my students will show them that I too am human, that I too make (often very stupid) mistakes, and that I too am continually growing as a writer and a thinker.

Without further ado...here's a sample. Below are the first five out of nine pages of notes I scribbled out the other day as I was working on a paper dealing with the combinatorics of complex polynomials. In these notes, if you look closely (I don't recommend it) you'll see everything I indicated above: wrong turns, dead ends, and idiotic mistakes. (My Facebook friends may even be able to notice on one of these pages the (-1)(-1) = -1 mistake that was the focus of my Facebook status for several hours earlier this week.)

After all, I'm only human.












Coming soon: my thoughts on putting together my first-ever first-year seminar, on Ethnomathematics! This course begins in a little over a week, and I plan on writing my syllabus this weekend. Stay tuned...

Clarification

As I was falling asleep at faaaaaaaaar too late an hour last night (technically this morning...aaaaah, bowling night!), I felt a twinge of anxiety over something I'd written in my blog yesterday. I want to speak briefly to that something.

I realized that both in class yesterday (twice!) and then in my last post here I really gave it to that one response: the "0, 1" answer to the homework question on last week's problem sets. True, the answer is a pretty awful one, but what I should have made clear is that though the answer is awful, that says nothing about the talent or intelligence of its author.

I realize that most of you (my Calc I kiddoes) have probably never been asked to write in complete sentences in mathematics before, and most of you are trained to think of "writing" and "math" as two ends of an academic spectrum. (I'm addressing these issues in Chapter 2 of my book.) Therefore I understand that there's a good deal of inertia you're trying to overcome as you're moving toward writing more robust responses to my homework questions.

I appreciate all that you're doing to get things moving in the right direction. All of you, from the most experienced "math writers" to the least, are intelligent people, and I want to make sure you all know that there's a difference between a lousy answer and a lousy mathematician. We all give the former from time to time, but that doesn't mean that any one of us is the latter.

See you in class!

Humbled

It's always humbling to get good (read: "thorough" and "direct") constructive feedback.

Like the feedback I just got back on my first draft of More Than Numbers's intro from my consulting editor.

I plan on using my experience in getting this feedback as a teaching tool for all of my classes: "you think you've got work to do?"

Warming

I had a good time with my Calc I kiddies today, mostly because they did the lion's share of the work. (We spent the day working through several archetypal examples of tangent slope computations, observing patterns along the way.)

So far (six class periods in) several students have expressed mild apprehension regarding the structure of the course. It's noteworthy, though, that they're all enjoying the class and are clearly willing to ride it out and let themselves grow more comfortable as the semester goes on.

Most unsettling to them, I think, is the decentering of formulas that's gone on. There's no call to memorize formulas...in fact, there have been almost no formulas needing memorization. Central, instead, is concept: rather than hand them ready-made formulas for computing slopes of tangent lines to the graphs of various families of functions, I've asked them to derive those formulas from scratch from a single formula, emphasizing constantly why that formula works and where it comes from.

Most of the students are used to being told to memorize; they're used to "theorem proof theorem proof formula formula formula definition example example theorem proof" math courses.

Most of the students are not used to being told to understand; they're not used to "why is that what are we looking for how can we find it how does that formula work how can we use it to our gain" math courses.

I give them tremendous credit: they're patient, they're hard-working, and they're doing great.

They're also fun to talk to, in class and out of class. We jawed a bit today about the following pretty well-documented pedagogical fact: though it's painful (for both the professor and the pupils) to sit in a silent classroom in which everyone's staring at everyone else, when a greater lag time is allowed for between a teacher's question and a student's response, the response that comes is generally richer, more complete, and more meaningful than the one that will come from continual once-every-few-seconds prodding on the part of the professor.

As a part of that same conversation, I mused out loud about why it is that students seem more eager to write a solution on the board when I'm out of the room than when I'm sitting right there in front of them. "Is it because you feel safer making mistakes in front of each other than you do making them in front of me?" I asked.

"No," someone said. "I think it's just because we feel bad if you come back in and we haven't written anything."

There could be something to that.

In any case, I'm looking forward to following up tomorrow (limits!), and to continuing our discussion of matrix algebra in Linear.

For now, I've got to finish a few more paragraphs of my book (tonight: the unique challenges faced by writers in quantitative disciplines) before calling it a night.

It takes two, baby

(Caveat: I've got writing process on the brain, as I just started work on Chapter 3 this afternoon, in which I hope to discuss writing as process, and how to effectively stage that process, in the quantitative disciplines.)

For future reference: when asked to write a dialogue in which you're to help a hapless friend who's hopelessly lost regarding one or another mathematical concept, it helps to involve two people in the conversation.

The second interlocutor plays a crucial role: with this person in play you, playing the role of The Expert, need not anticipate every difficulty that might arise to trouble your poor partner in conversation. This partner is the one who need only act naturally in order to bring to light the most subtle and sophisticated aspects of the problem you've been posed. That is, this partner is your foil, the dunce whom you can task with asking every question that might conceivably come up when learning a tricky technique.

With two people talking it through, what might otherwise be a boring monologue or lecture (in which posing trivial questions and then immediately dispatching them would seem stilted at worst or pedantic at best) is now a dynamic dialogue, where nearly real-world interaction is possible.

Talk with your dialogue partner as though you would talk with a real-life friend; help him as you would help a real-life friend, let his ignorance and your expertise take turns driving the conversation forward as you uncover the truth together.

Could there be a better low-stakes writing-to-learn activity?

Week One: done!

Ugh.

In Linear Algebra today I used rampant tidal locking as an explanation for the fact that this past week has easily been the longest one ever.

It's been a long week, but a good one, and I've gotten a lot done. More importantly, I feel I've set the appropriate mood in all of my classes. The Calc I kids are slowly starting to come to life, and Linear's just getting better and better.

I've now had "get to know ya" meet 'n' greets with about 20 or 25 of my new students, and these have been uniformly fun. As always my students very in every conceivable way: age, prior education, academic background, major, motivations for study. I've got young, old, quiet, bold, math-minded, math-shy, self-directed, and diffuse. A couple share my love of poetry, one my fascination with early human evolution. Some are sarcastic, like Dwight, the student in my second Calc I section who showed both bravado and cojones by merely modifying the work I'd done on the board to solve an earlier problem, instead of transcribing his own solution from scratch. Others are retiring, like Bertie, whose description of greatest common factors was practically unintelligible owing to the quiet of his voice.

So far, aside from a little bit of hesitation on the part of a couple of the more outspoken students, all of the feedback I've gotten on the structure of the courses (both highly student-centered, Calc I to an extent I've not taught it in the past) has been positive. A couple of the Calc I students have even commented appreciatively on the use of writing. One thanked me for asking them to write in order to more deeply understand the difference between two oft-confused rules for exponents (when do you add 'em, when do you multiply 'em?): "I didn't do so well the last time around in calculus, but I feel like I'm going to do a lot better this time."

One of my nontraditional students (I'm always happy to have them in my classes: they're generally so much less shy about speaking up) expressed some concern in my meeting with her on Tuesday morning. "Am I going to be prepared for Calc II by the end of this semester?" I assured her that we'll do all of the computations we'd do in a theorem-driven calculus course, and we'll learn all of the concepts we'd learn in that setting...we'll just approach them all from a much more useful angle.

"Don't worry," I said. "We'll get there."

In fact, freed from having to put together a punctilious list of soon-forgotten limit laws, we're making good time: just a week in and we've already computed the slopes of several tangent lines, having figured out that that's what we need to do in order to solve the problem posed to us on Wednesday morning.

Yup, classes are going well.

In other news, I've finished the first draft of an introduction to my book. I'm quite satisfied with it. It charts my personal history with writing in the discipline of mathematics, highlighting the ways in which I've grown as a writing instructor as I've progressed in my career and indicating the empty spaces in the writing literature which need to be filled. Tomorrow I hope to start work on either the first or the fifth chapter (these are the two whose structure I can most clearly envision right now).

Now, bed calls. Students: please let me know what you thought of this first week. Where do we go from here?

Oh, and: 400th post!

Dialectical driver's ed

How's it going?

Three days into Calc I, and it 's difficult to say which way the class is going to break this term: the students are still strongly engaged in class and contributing well to the problem-centered classes, but I think a few are hesitant about the rather non-traditional format of the class. As yet we've not done a great deal of computation, haven't derived or delved into any formulas, haven't stated any theorems. A number of the students are used to doing all of these things within the first couple of days of a math class and so they've got a sort of deer-in-headlights, "WTF?" sort of look in their eyes.

The formulas will come soon, I'm certain, and I hope that with them a sense of familiarity and comfort: we're about to enter into a discussion of tangent lines and secant lines and their slopes, a discussion will include a great deal of computation and review (and practice) with algebra.

I'm not sure quite how quickly we'll get there: it really all depends on the pace at which the students end up driving the course. As I mentioned to my first section this morning, they're sitting in the driver's seat, working the pedals, holding the wheel. Every now and then, as instructor, I'll reach over and grab the wheel with one hand to steady it or add a few degrees to a particularly too-tight turn.

So far the structure of the course is "dialectical," an exercise in turn-taking: I've proposed an initial course heading, and now we've walked for a while. Now, at the end of the first day of hardcore hiking, having surveyed the site at which we've made camp, I've worked out an itinerary for our next day's travel together. We'll see where that takes us. We'll make camp again, make some next-day plans, and set out again in the morning. I know the stops we need to make, and we'll make them all, but it's up to the students to figure out which we hit when, and in what order.

We'll figure it out.

Meanwhile, I am loving Linear. The class is huge (the largest I've yet taught at UNCA), but has great cohesion. The students are eager to work and are making great progress, and I feel that I'm doing a much better job of structuring the discovery process than I did the last time I taught the class. I've put a lot more thought into precisely which skills are needed to solve which problems, and we're making a (long) beeline toward our first major goal: analyzing the long-term behavior of a simple Markov process (like the game we played on the first day).

Today we figured out how row operations mirror the operations needed to solve a system of linear equations. Next, after posing and solving a couple of realistic problems requiring the solution of a linear system, we'll motivate and move toward matrix multiplication. From there, it's on to matrix inverses, invertibility, determinants, eigenvalues, and, at last, an analysis of Markov processes like those we began with. At every stop we'll solve another real-world problem or two, get some practice with computation, and write a bit about what each concept really means.

I figure it should take us something like 5-7 weeks to get where we're going. After that, we'll talk about linear transformations, vector spaces, changes of basis, etc.

Exciting!

Meanwhile, I'm reading some fascinating works on writing and rhetoric in preparation for various parts of my book. Most recently I've begun Deirdre McCloskey's The rhetoric of economics (2nd edition, 1998, Madison: The University of Wisconsin Press), a delightful rhetorical analysis of economic discourse in which she dissects the ways in which economists convince one another and others of the truth of their assertions. According to McCloskey, much of what many economists consider unassailable scientific truth is really rhetorical "smoke and mirrors."

Not that there's anything wrong with "rhetoric," a word which McCloskey takes pains to save from those who would use it only in a pejorative sense: rhetoric is ubiquitous and unavoidable, and McCloskey merely asks that we be intentional with the rhetoric we use. We all use metaphors and other rhetorical devices; it's simply important that we be aware of the devices we employ. As one might put it, extending the tried-and-true "lens" metaphor, it's no crime to have poor eyesight, as long as you can admit that you need to put your glasses on in order to see properly.

Her opening chapter, which begins with a close reading of passages from canonical articles in economics, has made me think about the way in which I begin some of my own mathematical papers: what sense of authority am I conveying though my choice of words? What world am I building? What agent is acting? What am I asserting about the truth? I'd like to look into my own writing to do a careful reflective analysis.

But with all that I've got on my plate right now, such an analysis has got to wait for a little while. I hope to finish off the first draft of the introduction to More Than Numbers tomorrow, and set to work on the slightly slanted history of WAC, WID, and WTL which will make up much of Chapter 1.

Much to do, much to do, and so little time...but so much fun!

On your marks, get set...

It's been a while, huh?

As you might suspect, I've had a lot going on, keeping me from posting here for the past, oh...two months? Ouch.

What's going on?

The REU's over, but the work has really just begun: the students this year were fantastic. They were smart, fun, and funny, and they worked tremendously hard, producing a ton of interesting mathematics. (We should get at least five papers out of it in the next couple of months, and maybe more beyond that in the follow-up.) And this year it was "buy eight weeks, get one free": six of the eight students ended up traveling to MathFest in Pittsburgh, PA to present on their summer research.

The REU took up much of my time, but I've had a number of other things going on, as well, among them: (1) working on student learning outcomes for both the Mathematics Department and the Writing Intensive program, (2) putting together the ILS Oversight Committee's report to the Academic Policy Committee (still not submitted, but finally almost finished), (3) planning my contribution to the short course I was helping run at MathFest, (4) working with my College of Charleston peeps on our paper on the rhetoric of mathematical writing, (5) looking ahead to my round table discussion of program assessment for this year's CWPA (coming up in a few weeks), (6) laying the groundwork for the book I'm now slated to write for Jossey-Bass (w00t), and (7) trying to get ready for my Fall classes, which start on Monday.

(1) Student learning outcomes: although I see the purpose, ultimately, of programmatic assessment, too highly institutionalized assessment tends to become bureaucratic and corporate. I don't want to say more about my role in this university-wide process this past summer other than that it was frustrating at times, had its minor joys, and though it was ultimately fulfilling in that I feel like some good will come of it, I worry about the intentions some people in administration may have for codifying the university's student learning outcomes as rigidly as is being done. 'Nuff said.

(2) The ILSOC report to the APC: this is more of the same. I see the purpose, and the writing of this document is a worthwhile activity, but one which runs the risk of being overly parliamentary and pro se. 'Nuff said.

(3) MathFest short course on Sage (an open-source computer algebra system): I actually wrote to my colleague Oscar (one of the co-organizers of the short course) in mid-July, a few weeks before the course was to take place, expressing my insecurities about putting together an hour or two of meaningful material.

"Nonsense," was the substance of his reply; "you'll do fine. Write about what you know." So I threw together several worksheets full of Sage code purporting to implement a number of higher-level graph theoretical algorithms and called it good. The worksheets actually went over really well in the short course and filled a rather comfy niche in the program. I felt good about what I'd done.

The moral of the story: just do it.

(MathFest, by the way, was a blast. Pittsburgh's a nice city with lots of pretty runs and nice architecture, the REU students were fun to hang out with, as always, and the MathFest program was replete with fun stuff to see and do. A good time had by all.)

(4) Math rhetoric: as I mentioned in my last post, oh so long ago, Bella and Damian came up from the coast to spend a couple of days with me, hammering out a plan to finish the paper we'd begun (with Nicola, who couldn't make it) on the rhetoric of the writing my REU students had produced in 2008 and 2009. They had a lovely time while here, visiting with and interviewing the REU students from this past year, working on our draft at the time, and just hanging out. I'm happy to say that as of last night we have a draft that's nearly ready to submit to the comp/rhet journal Across the Disciplines. It's the first of what we hope will be...well...at least more than one article on the rhetoric of mathematics and its learning, and the role writing plays in inducting students into the scholarly mathematical community.

(5) CWPA: I'm already looking forward to the Wildacres retreat! It's going to a be a full house this year, several dozen of us crowding into the nooks and niches of the Wildacres North Lodge to join in round table discussions of assessment with various forms and functions. I plan on presenting a brief "natural history" of the assessment that's gone on in our WI program during the past three years, exposing to public view the layers of rock comprising the "pilot" assessment Lulabelle headed up in AY 2007-8, the refinement she and I performed in the following year, the plans for assessment she and I laid out in the lead-up to the university's reaffirmation of accreditation (notice I haven't mentioned SACS yet in this post...), and the modifications those plans underwent as I limned the WI program's assessment of student learning outcomes this past summer.

It's sure to be riveting.

Actually, I'm more looking forward to hanging out with Damian and Bella, and with them planning the next phase of our study of the REU students' writing.

(6) Book: Oh yeah...I'm now under contract to write a text (working title: More Than Numbers) on the role of writing (specifically, writing to learn and writing in the disciplines) in mathematics and the mathematical sciences. Jossey-Bass received well the proposal I pitched to them several months back (in March, I think?), and after some fine-tuning of the project, I was brought on board. I'm excited, but at the same time terrified. I'm confident it'll all work out well, though. I've already done a ton of enlightening reading (if you get a chance, check out Scott L. Montgomery's The scientific voice...it's a fascinating read that, along with several other sources, has helped me put together a theory of the schizophrenic nature of undergraduate mathematical writing), and I have some great ideas. Furthermore, my consulting editor for the project is someone a few of whose books I've read and whom I respect very much; I'm sure she'll be very helpful to me.

I will say this, however: if between now and next March I start randomly babbling to you about reader response theory or the role of writing in the mathematical finance classroom, just smile and nod your head.

(7) Fall 2010: yup, we get underway in two days. Yikes. I'm actually really excited: I've got the first week mapped out in all three of my courses, and I've plotted out what I think are clear and navigable problem-centered paths for both of the lower-level courses (Calc I and Linear Algebra I) to follow.

Calc I is going to begin with a brief review, and then the students will work toward developing the skills needed to solve an optimization problem from economics. They'll need to "invent" the method of secants and tangents, the definition of a limit, and the definition of the derivative; and they'll need to learn how to compute some simple derivatives in order to solve this problem. Once all of that groundwork is laid, we'll spend some time working with the textbook and picking up some useful formulas for limits and derivatives, but everything we do is going to be application-driven and learner-centered. I hope to not have to lecture for more than 10 minutes at a time for the whole damned semester.

Linear's going to be the same: Day One features a variation on the "Markov Dance" that started the semester off the last time I taught this course, in the semi-mythical beginnings of this blog. The limiting behavior of this system is going to be the motivating problem for everything we do in the first half of the course, as we work our way through everything we'll need to do to get to the fun and useful stuff (eigenvalues, diagonalization, and Markov processes): solving linear systems, inversion of matrices, solvability criteria, and finally eigenvalues. I'm going to downplay theory and upplay (what a cool word!) functionality. I hope to get to the fun stuff by the sixth or seventh week, at which time we can spend almost all of our time on applications. It's going to be fun.

I should mention that I've modified my grading schemata somewhat, but not substantially, from last semester: students in both of the above courses will still have an opportunity to perform potentially unlimited revision on most things they hand in, but I'm tempering the grading scale so that it's no longer possible to earn full points back with each revision. I think the system I've set up is a generous and reasonable one, though, and I believe it'll still serve to motivate students to learn rather than to grub for a good grade.

Meanwhile, the Senior Seminar's speaker schedule is chocked full, with four visitors (all versed in speaking to undergraduate audiences) coming to share their knowledge and spend a little time with the students. It's going to be a good semester in that course.

Okay, that's all for now...I'm going to try to post more regularly during the coming semester, although I can't promise it'll be more than anxiety-tinged stream-of-consciousness rambling about this or that idea for the book.

Fare thee well!