Sunday, May 20, 2007

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!


Anonymous said...

I hope you keep reading Bain's book. I've read ahead and found it very engaging. True, there's not much depth in Chapter 1 (the introduction), but throughout the book he expands greatly on the ideas touched upon in Chapter 1. I think what's most compelling about the book is the way Bain connects theory with practice. For instance, in Chapter 2 he summarizes some important research-based results on how students learn (from the cognitive science book How People Learn) and then illustrates those points with stories about the teachers he interviewed for this book. I'm a big fan of research-based educational theory, but I also know that when helping faculty and TAs make sense of that theory, "real-world" applications of that theory--contextualized examples of how instructors have put that theory into practice--can be a big help. I think Bain does a good job with this task. So while I do find the book inspirational, it's also a useful way to better understand a wide range of educational research.

I'm not sure if I would consider Bain's book SoTL, at least using the definition of that term that I typically use. I see SoTL as asking and attempting to answer questions about student learning (what they're learning, how they're learning) by a systematic, appropriate analysis of evidence of student learning. Bain isn't investigating evidence of student learning directly--he's observing, interviewing, analyzing teachers, not students. This isn't to de-value his work in any way. Rather, I wanted to point out that he decided to study teachers, not students, which is an important distinction.

DocTurtle said...

derek: I will definitely keep reading Bain, never fear! I don't typically put down a book unless it actively disinterests me, which this one most definitely is not doing.

I agree with your definition of SoTL, but I would also expand it to include more "survey" literature, including some of the authors I mentioned in my recent contribution to the NExTBook listserv, and perhaps Bain as well. Whenever suggestions for practice and operational dicta are created from conclusions based upon research into the mechanics of teaching and learning, you've got SoTL at some level. While you're absolutely right in that ultimately SoTL rests on a bedrock of careful investigation and application of the scientific method, so too ought SoTL to include "practical" literature as well; perhaps a good analogy might be the distinction between articles in theoretical and experimental physics?

Anonymous said...

You should read Alexander and the terrible, horrible, no good very bad day. A much quicker read than the above book choices and the pictures are funny too.

Anonymous said...

DocTurtle, Why did you take my reflection off?