Mathematical muses

Last night I had a blast reading through my Calcsters' contribution to the world of letters. Many of their math-themed poems are positively delightful.

They run the gamut from simple, insightful haiku to epic poems in which the hero plays a pivotal role in the battle between the fractions and the decimals (one wonders what sort of heroic epithets would have to be invented to make this poem fit a classical hexametric form?). Some made math the thematic centerpiece, while others simply used it as an informant for the (as often physical as numerical) structure of their poems. Some were funny, witty, light, others were dark and brooding, still others intriguing and mysterious.

Many of them truly introspective and personal, and I thank my students for allowing me the chance to peer through this window onto their mathematical ideas.

I would like to post some of the poems, either in part or in their entirety, but I've first got to get permission from the authors. (Yes, yes, I know: I've still got to post some of the comments on Newton v. Leibniz...it's been a busy semester, all right??!)

I mentioned to Maggie the other night that I'd thought of compiling the students' poetry to produce a small bound volume they'd be able to keep as a memento. I think she liked the idea.

What say you, students? Sound like a good idea? Feel free to comment and let me know.

In other news: several students have mentioned how useful they've found 280 in improving their writing skills...the second round of 280 presentations came off rather well...I've started toying with the idea of using mathematical origami as a medium for guerrilla mathematics...and I've got two students from my Calc I classes who sound interested in looking at a little bit of graph theory over the break, just to make sure they get a head start on math research. The way I see it, the sooner they learn that math is much much much much much more than crunching numbers, the more they'll love it, and the better they'll be at it in the long run.

I am off.

I must run, quite literally.

Pre-summer reading and subsequent ruminations

My summer reading has begun with a bang.

I've been working my way through a book my colleague Tip lent to me, Radical equations: civil rights from Mississippi to the Algebra Project, by Robert P. Moses and Charles E. Cobb, Jr. (Boston: Beacon Press, 2001). Tip met up with Bob Moses, a noted civil rights leader, Harvard-trained mathematician, and founder of a grassroots math program (the aforementioned Algebra Project) targeting middle-grades mathematics students on the fringe, at the Mathematics and Social Justice Conference Tip attended in Brooklyn a month or so ago. Clearly Tip's thought deeply about the ideas in this book, especially as regards his nascent community-building math program and the NSF grant proposal he and I are soon to set about writing, and he was kind enough to lend his (signed!) copy of the book to me.

I'm about three fourths of the way through the book right now, and though I've found much of the text itself dry and unengaging (particularly when it gets bogged down in the toledoth of Moses's project's converted teachers; at some points it reads like a biblical genealogy: "and Norma Jean begat Shannon, who begat Tom, the Explainer-to-Children. Tom taught twenty years, and then begat Sylvia. From the Delta did Sylvia come, and her students were good in the eyes of the Sunflower County Board of Education..."), one or two of its ideas have really struck me. I've been won over in one respect in particular. To best describe my conversion, I ought to mention a conversation I had with a colleague at a school I recently (in January) visited.

We were talking of undergraduate math majors; I had mentioned that at UNCA we have something on the order of 80-90 majors at any given time, and my colleague was thoroughly impressed. He said that at his school (a school nearly twice as large as UNCA), there were perhaps half as many undergraduate majors. Ever wanting to be helpful, I made some comment along the lines of "I've got some ideas that might help you to bring those numbers up."

My friend's response was something like "I don't think we're looking to do that."

I was taken aback. Not only had I not scored a point on this man's scoreboard (he and I share a long history, and I've never wanted to let him down), but my view that more young people should be helped to embrace mathematics had been met with hostility. This man had no interest in bringing math to the masses; he preferred to let it stay the closely-guarded territory of the few and the proud.

Moses's book has helped me to make out this not-so-well-hidden trap many professional mathematicians fall into: too often we think of math as a religion, a cult of worship into which only a select few are to be inducted, and in which only an even smaller few are allowed to become high priests. We take pride in our weeding out of the undesirables, defined as anyone who doesn't have a natural knack for math, who comes pre-programmed with a love of abstraction and analysis.

I've seen our culling at work at several levels, more clearly at some institutions than at others, and I'm ashamed to say that I've even taken part in it, though unwittingly. Math professors have a tendency to emphasis the arcanity of their field, its abstruseness, its disconnect with reality. Many of us take pride in the difficulty of our field, and make every attempt to show off our own intellects by making math seem imponderable, impenetrable, dense. I saw this most clearly at Illinois, where research mathematicians would show open disdain for all but the brightest undergraduates in their classes ("most of them are dullards, I've got a few who might prove capable"), lending a hand to the top 5% while leaving the others to drown; "they're just not cut out for it."

For too long mathematicians (and scientists of other stripes) have tried to fill their ranks from the lists of the best and brightest of the American studentry (to borrow a wonderful turn of phrase from William Strunk), leaving the dregs to find work elsewhere when they prove themselves incapable of meeting the high standards set for practitioners of math research. This leaves the untouchables, consisting primarily, in this nation, of poorly (read: publicly) educated blacks, latinos, and poor whites, out in the cold.

Moses makes clear that there's something wrong here.

What's called for, in his mind, is a radically different paradigm: rather than drawing from the few whom opportunity and natural talent have buoyed to the top, we ought instead be working to ensure that everyone is given the chance to rise to the surface. With a system wherein all are given the tools needed to excel mathematically, everyone benefits: traditionally underrepresented groups obtain the opportunities they need to succeed academically, and academicians expand broadly the talent pool from which they will one day choose their colleagues and successors. This "bring 'em on, all of 'em," attitude is the core of the Algebra Project, a program committed to making sure that every 6th, 7th, and 8th grader is given the background needed to successfully navigate a college-prep math sequence in high school. As Moses sees it, not everyone will go to college, and while there, not everyone who goes will study mathematics, but everyone should be ready to do so.

It just makes sense.

Moses's work has definitely helped me to come around to this point of view. It's never been so clear to me that I as a mathematician have a good deal of work to do to ensure that I'm doing what I can to grant everyone the chance to experience mathematics, and to succeed at it. Work needs done at all levels, K-12, undergraduate, and higher. And the work done at each stage needs to be interwoven with work done at other stages: vertical integration is called for. I hope Tip and I will be able to capture that spirit effectively in the proposal we put together this summer.

I've also begun the book the Project NExT reading circle has chosen as its first focus of discussion, Ken Bain's What the best teachers do (Cambridge: Harvard University Press, 2004). I'm (we're) one chapter in, and so far I'm unimpressed. It strikes me as a poorly-assembled pile of truisms and platitudes, absent the concreteness and careful analysis of a seasoned student of the scholarship of teaching and learning (SoTL). Not that every SoTL text has to build up a rock-solid wall of data and facts, or deluge the reader with a statistical breakdown of every study on teaching efficacy performed since 1970...but this book just seems "lightweight" to me. So far it's a great "rah-rah" feel-good page-turner, but its place might be on the nightstand of a newbie college prof just out of grad school who needs a little cheerleading and from-the-sidelines inspiration. I wasn't a huge fan of Maryellen Weimer's book, but I found it far more useful and engaging than Bain's, at least to date.

I ought also say a word or two about preplanning I've begun for Fall's classes. Francine's agreed to help me go through the notes and homework problems we used in 280 this past semester, retooling them, getting them good. I've already written a couple new in-class exercises dealing with writing mathematics.

The one I'm happiest about was inspired by a conversation I had with my colleague Lulabelle from the Sociology Department (I'm on a team of folks helping her out with a pilot assessment program for writing across the curriculum). She indicated that as a part of the work that'd need doing for this grant we're collaborating on, I'd have to to be able to train my colleagues how to "read" mathematics. I got to thinking about how I would best do this, and realized that it's likely easiest simply to highlight the linguistic analogues mathematics shares with "natural" human languages: syntax, grammar, orthography. Not only would an exercise indicating these analogues help my colleagues; it would help my 280 students, too.

The exercise consists of a take-home portion and an in-class portion. Each part comprises three written passages of varying levels of quality; the take-home passages are in "English" and discuss the chemical element boron. Students (and my colleagues) should have no trouble in ranking these passages from worst to best, and in explaining their reasoning for the ranking. The in-class passages are in "math," each giving a "proof" of the fact that the sum of two odd numbers is even. Having given them the chance to warm up in "English," I now ask the students to rank the proofs from worst to best, and to justify their rankings. This is a more difficult task, but once it's done my students (and colleagues) should be able to see more clearly that good writing in math is only a half-step away from good writing in any other discipline.

Okay, I've prattled on long enough. I'll end this for now. As usual, feel free to check in with your comments, always appreciated!

Secret of the pyramids

As promised, here's a shot of the fractal the kids and I put together this past Saturday:


Incidentally, while visiting James Madison U. this past Monday I mentioned the Multimedia Menger Sponge Project idea to my colleague Mandi (shout out, Mandi!), whose elementary ed students were busily building Level 2 cubes out of origami paper during my visit. She seemed pretty excited about the idea, as did several of my students whom I polled yesterday.

If I can get enough "backers," I just might start this thing up.

Number nine...Number nine...Number nine...

1 More Annoying Student Habit

Come to class, people. Please?

Look, I understand that "things" come up unexpectedly: illnesses (ohhhhh...do I understand that one well), family emergencies, lottery winnings, superstardom, unexpected tickets to the Superbowl, including all-access passes to get onto the field while Prince is performing...These "things" come up, and they can come as a thief in the night.

Yet these "things" aren't the only things keeping you from coming to class. Other things, less sudden, yet more stealthy, things that don't pounce on you like a jungle cat leaping from the shadows but might rather overcome you slowly, wearing away at you as the semester gets on: excessive love of sleep, excessive love of pot, passive apathy, active antipathy, a malingering defeatist "I'm doing so poorly in this class how can hurt me more if I stop coming" attitude, fin-de-siècle ennui...any one of these things might stalk you quietly and drag you slowly down.

Please don't let these things overtake you, all right?

See, here's the thing: I like it when you come to class. I do. I like seeing you there, I like interacting with you. At the end of the day, I love what I do for a living. While in a particularly peeved mood yesternoon (brought about by, I might add, certain students exhibiting this Ninth Annoying Habit) I was musing to one of my best friends: "why didn't I take a job in industry? I'd be working nine-to-five, making twice what I make now, and I'd have none of the stress, none of the busyness." Of course, the answer came from my own lips not five seconds later: "because I'd hate that. It'd suck, and I'd hate it."

I love my job, every bit of it. I love math, I love math research, and math conferences and math committees...and above all I love teaching math. I love all of these things. I just get annoyed when you don't think it worth your time to come and share my joy. (Oh, and, by the way, your fellow students notice when you're not there, too: when only 15 people of the 23 who are registered for the course show up, your absence is distinctly palpable.)

Again, I'm not talking to those of you for whom "things" have come up. "Things" have been coming up regularly since the dawn of time, and as far as I can tell, "things" will keep coming up regularly for the rest of the foreseeable future. There's no getting around "things," but a quick phone call or e-mail to let me know about them when they do pop up might be nice.

I'm talking to those of you who've decided that it's just too much effort to come to class. Let me end this rant with this note for you.

When you miss class for an inexcusable reason, you send the following message, boldly and clearly, both to me and to your fellow students who do come regularly: "I have very little consideration for the enormous amount of time you spend in crafting learning experiences for me to take part in."

Hey, man, if that's the score, please do me a favor and don't register for the class in the first place.

Whew.

END OF RANT

So here's the deal with the Menger sponge.

While lying awake a couple of nights ago (I slept well last night, for the first time this week, thank you very much for asking!), my mind addled by codeine-laced cough syrup, I thought deeply of this fractally-formed creature. How came I to these ruminations?

Well, it began a couple of weeks ago, when we spent some time during the March 31st installment of our Super Saturday program working with fractals in the plane. At that time I had a chance to wow the kiddoes with a picture of a Menger sponge, namely this one, a shot of software engineer Jeannine Mosely, standing in front of the sponge she spent nine years building from business cards, with the help of hundreds of folks from around the country. Incidentally, there are 8000 cubes in this one, a "level-3" sponge. (By the way, The hijinx and hilarity continued this week. Just hours ago we wrapped up the today's class, spent assembling a Sierpinski pyramid out of several dozen folded pieces of recycled printer paper, affixed to one another with Scotch tape. [No pictures yet, my camera was at home. Next week! I promise.] The result is quite impressive, and the kids were proud of their achievement. Each took her or his turn holding the behemoth overhead, as though all had played an equal part in its construction. [Truly Jasmine, the lone female in the class whose time, already actively used to its full potential, was freed by not having anyone of her own sex to waste time with, contributed most of the student work on the project. I provided a goodly number of the little pyramids, while Umberto worked slowly yet diligently on his pile of triangles. The few pyramids he made he passed off to Jasmine so that she could skilfully fasten them together. Whether he was motivated by a simple crush or by a sense of pragmatism, recognizing her as the master builder, I'm not sure. In any case, it was cute.] The guts of the Menger sponge that never would be, 200 sheets of recycled printer paper with stenciled cube skeleta photocopied onto them, were left almost untouched. Too bad.) Now, I mean no insult to business cards and recycled printer paper (what better way is there for a piece of printer paper to end its practical life than to be made into a beautiful work of mathematical art?), but it must be admitted that these media are not so sexy as other materials one might choose to build fractals from. Plastic? Wood? Metal? Glass? Ceramic? Silk? The possibilities are endless.

What if, in the spirit of community projects such as Postsecret, people were asked to submit to a central source their own tiny cubes, 2 or 3 centimeters per side, made of whatever material they wished to use and decorated in any fashion desired, and these cubes were assembled lovingly by project coordinators who took care to build the structure by attaching cubes to one another in the manner specified by the contributors: "please ensure that the side bearing my name is not visible..."? Imagine a sponge stretching over 7 feet in any direction, made up of 160,000 (with all due respect, take that, Dr. Mosely!) 3x3x3 cubes of all manner of media, each cube telling a story of an individual contributor, as those submitting cubes could include stories, insights, comments on what the project means to them: "I chose to participate because..."

I'd be curious to see what people would have to say, about the project, about math in general. It's not so often that I get a chance to interact mathematically with people who know so much less about math than I do, with people whose love of math (if it's there at all) is not inherent: how do such people feel about things mathematical?

I don't know.

What do you think of this? Is it a codeine-made pipedream, or a worthwhile artistic undertaking? I'm truly tempted to try this out, but I'm not sure I'd want to start without some backing. Who's got my back? If you're out there reading this, let me know what you think, and ask your friends to check in and let me know what they think, too. Consider it an ad hoc committee on the creation of the Multimedia Menger Sponge Project. Let's get together, people!