Prejudice and Pride

A classic 1968 study by Robert Rosenthal and Lenore Jacobsen (summarized in Pygmalion in the classroom) posited the theory that students' intellectual development is a function of the expectations placed upon them by their instructors. According to Rosenthal and Jacobsen, if teachers expect a lot from their students, and if they make these expectations clear, students will tend to rise to the occasion; if teachers' expectations are low, students will work only to leap over the low-placed bar.

Since that time various studies have called these results into question, but the power of the study still pervades a good deal of thought on pedagogy at all levels.

I must admit I've had it in mind as I compare the achievements of my two Calc II sections this semester.

Last week saw their second exam, on which the results of the first were more or less replicated: of the 19 students who received As and Bs before revisions were allowed, 10 of them were in the second section, which has only 16 students; the 29-person first section was home to under half of the overachievers. There were 10 Fs in the first section (several of them very low Fs), a section whose average score was about 68% (contrasted with the second section's 82%).

The in-class attitudes of the two sections are dramatically different: the first is torpid, laconic, nearly silent. They respond only when it's practically demanded of them, they work together in groups only reluctantly, they mutter answers almost incomprehensibly when an answer is called for. If they don't understand something, they let it slide by without question. The second section is vibrant, lively, jocose, responsive. They offer answers willingly, they ask questions unashamedly. They have fun, that much is clear.

The out-of-class attitudes are similar. The first class is lax, the second thoroughgoingly diligent. While the second section takes pride in its work, the first seems to do its work grudgingly. The second section's denizens log more hours in the Math Lab and coat their work with elbow grease; many in the first section are content to transcribe the solutions manual and call it good, assuming they bother with the homework at all. For example, with 10 weeks of homework behind us, the second section has submitted 156 out of a potential maximum of 16 x 10 = 160 assignments, a 97.5% submission rate, a mark simply unmatched by any non-upper-division course I've ever taught. I've not counted the submission rate for the first section, though I would guess that it's around 75%.

Please keep in mind that here I'm making generalizations: there are wonderful students in both classes, students who are active, proactive, interactive, attentive, and as dedicated to their studies as the finest of scholars. Keep in mind too that I have nothing personal against anyone in either section. To a one I like my students, I respect them, cheer for them, I want the best for them.

Which is why it's so damned difficult, puzzling over what it is that makes the one section so different from the other.

This brings us back to Pygmalion.

Is it something I do, or something I don't do? Is it something I can control, something I can adjust, tweak, in some way modify, so as to help the class run more smoothly, more effectively? Is it that my first section's students' development is being hampered by some set of expectations on my part? Am I, in the very act of writing this, undermining a search for a solution? By wondering aloud about the differences between my classes, am I admitting that I hold them to different standards, that I place one above the other, that I am prejudiced before I even set foot in Rhoades 105, and that that prejudice is somehow affecting, for good or for ill, the achievements of the students I meet with for an hour a day, four days each week?

It's absolutely incredible how much more tiring it is to work with a sluggish class than it is an active one. My energy is not limitless (much as I try to pretend otherwise), and more than once this calendar year I fear I've shown hints of exhaustion as my efforts to lead that first class onward peter out. Tuesday's class was a particularly rough one. "We can stop here, if y'all want," I said peevishly at one point ten minutes from the period's end, having waited for nearly half a minute for some kind of response, any kind of response, to my request for a pretty straightforward sum. "1+1/4" was all I needed to hear, yet silence was all I got. I felt like a schlemiel.

I was pissed as hell after that, not at my students, but at myself, for letting their unresponsiveness get to me as it had.

You see, I feel helpless when all that I do or try to do fails to excite, fails to entice, to allure, even to amuse (there are days when I'd be satisfied with that). I hint, I prod, I show, I cajole, I even bribe...I sit back and look on, I wheedle, needle, hint, and direct. I nudge, nurture, insinuate, and elaborate. I illustrate and animate, I offer up worlds of wonder full of mathematical mystery...what more can I do?

Or am I doing enough? Is it working? Am I getting through? Are they learning?

They must be learning, at some level. I must be getting through. There are signs, after all.

After all, as I said above, there are beautiful minds in both classes, and those minds are making progress: Section 001 is home to the author of all of my courses' most beautiful homework, a weekly technicolor fantasie of positively gorgeous (and nearly flawless) solutions. It's home to two freshmen (freshmen!) who are eagerly undertaking graph theory research under (and beyond) my direction. It's home to a quiet and unassuming young woman who made away with a perfect score on this last exam. It's home to one of my most regular Super Saturday volunteers, a brilliant young woman whose talents are remarkable, and whose career I'm sure will take her far. It's home to a couple of my brightest engineering students, one of whom willed himself most of the way from a C to an A last semester, borne on the back of his tireless efforts.

These are smart, smart people, and I'm annoyed with myself for being annoyed with their unresponsiveness.

I'm going to ask more of them in the semester's closing weeks: I'm going to crank out more worksheets, more Mathematica exercises, more interactive games. I'm going to get them up and bouncing about. I'm going to challenge their inertia and pry them from their seats. By gum, I'm going to get them moving.

Then there's Graph Theory.

Over dinner on the first night in Charleston (about which, more later) I had a delightful conversation with Sylvester and Nadia regarding the way our class has shaped up. These two, strong students both, had been too busy to submit their homework from the previous week: a paragraph or two describing their experience in our class, indicating both effective and helpful aspects of the class and what might be modified to make for a better learning environment during the waning weeks. "So, what do you two think?" I asked at the Starfish Grille. (Note to self: avoid this establishment in the future. The food is bland, the service dour, and the prices, though "Charleston cheap," still ain't "student cheap.") Egbert (auditing the class) and Trixie (nowhere near it) looked on.

Always outspoken, Nadia was happy to lend her opinion: it's all right, but she feels that fifty percent (her estimate) of the folks in the class aren't working as hard as they should be, aren't taking it seriously enough. Although she recognized that she's gotten better at presenting and communicating mathematics as the semester's gone by, I get the feeling that she felt certain people were holding the class back, and that I'd do more of the teaching. Sylvester seemed to concur.

I reminded these two that though by now they're old hands at advanced mathematics (having worked their ways through nearly two semesters of real analysis and other assorted beastliness), about a third of the class is fresh out of 280, and another third are one semester removed from 280 but have taken very little beyond that course. This course, for some, is the first course in which one encounters proofs for more than simply the sake of proofs. Thus there's a bit of trepidation on these peoples' parts: it's harder for them to take a stand on a nontrivial proof, it's harder for them to make themselves clear. Though the intuition may be there, the explanation is harder to come by.

The feedback from the rest of the class? Most of the others had primarily positive things to say. A couple regretted that the class seemed to move a bit more slowly than they'd like it to, and this comment was understandable, coming from the people who made it. Most have thoroughly enjoyed the structure of the class and have gotten a lot out of it. It seems we've come a long way from the awkward first weeks (including the awful soccer ball affair). The most concrete request was for a more real-time, group-oriented approach to the "review problems" at the end of each problem sheet. On Monday we'll try this out, picking apart the definitions, theorems, and problems in small groups and discussing the results as a class.

I'll let you know how it goes.

So, yeah, how was that MAA meeting in Charleston? (This brings us to the "Pride" in "Prejudice and Pride"...)

Every educator worth her weight in textbooks knows the feeling of pride that comes from being on site to witness her students' successes. "Them're mine!" you feel like shouting. "They're goin' home with me!" You feel a spark inside when your student boldly asks a good question at the end of a talk, you feel a glow when she defends the results of her own research.

For Charleston, Sylvester, Nadia, and Trixie all put together posters showcasing the research they've done over the past few months. (Trixie felt underprepared, yet she was the only one to finish her poster before leaving town; the other two threw theirs together at the last minute, literally. Indeed, it was five minutes into the judging period when they picked up their posters and launched themselves into the display area. The hour and a half leading up to that moment was seen through a frenzied haze of spray adhesive and hastily-scissored poster board. Trixie had watched nonchalantly from the sidelines, alternating between watching the action and fiddling with her Gameboy.)

It wasn't all work, of course. After a pleasant drive down, we had a brief break before finding dinner and taking a twilit walk on the Folly Island beach. The next morning let the kids stroll around downtown while I took part in some faculty development whatnot, and then the conference came.

Conference highlights:

• several hours' of research and relaxation with my good friend and colleague, Griselda
• warm fuzzies on hearing Sylvester and Nadia ask fantastic questions at the end of one of the conference's talks
• the elation of making a breakthrough in one's research (followed by the realization later that day, during the long and drizzly drive home, that the breakthrough was an erroneous one)
• hearing Trixie tell of an exchange between her and one of the poster judges, who had been rather critical of her design: "So, are you a junior or a senior?" "Actually, I'm a freshman..."
  
• the tired contentedness of driving a vanload of sleeping students back from their first academic conference, at which they'd made a hell of a splash

It was good.

I needn't have gone as far as the South Carolina beach to find students to be proud of this past week: Trixie's friend Blackwell has jumped on board the labeling lorry and has managed to find his own graceful labeling of a class of spiders similar to those Trixie claimed. We worked together for over an hour yesterday afternoon, hammering out a technical description of his labeling. (I even managed to sign him on as a math major! My hope is that peer pressure will finally cause Trixie to cave...) Throw his work in with Trixie's and Sieglinde's, and with the impromptu caterpillar labeling enumeration project begun the other night with Umberto and Nadia, and we've got a heckuva graph theory group coming together up here in the mountains.

And while we were away in Charleston, Tallulah led the Math Discoveries Super Saturday class. She and a few of her friends skilfully guided our troupe of elementary schoolers through the mathematical treasure hunt I'd planned for them. To hear it from Tallulah, though it poured a bit the night before and all was a bit rain-soaked, the kids had a blast. My warmest thanks go out to Belladonna, Tallulah, Sieglinde, and any others who helped them this past weekend; without wonderful students like you, these efforts wouldn't be nearly so meaningful for the kids. I really do think that we're in the business of changing lives for the better, and you're playing a big part in that venture.

I'm fixin' to wrap up this here post, but I'd like to end it on a note as high as my opening note was low. Let me be more frank than I've been since my cathartic post from December 8th, 2007.

I'm tired right now. Though overall this semester's not been as busy as last fall's, the past week or so has been a rough one on me, and I'm aware that I've not been as patient and peppy as usual. I've been short, curt, and I hope not quite rude. I've let my frustration show, and I'm frustrated by this fact.

Be patient. Remember that I'm human too, and can falter and fail as well as soar and sail, and that I need your help to make sure our classes succeed.

If you're reading this, please tell me what I can do to help you out. Let me know if you've got any hints, tips, clues, or suggestions. Post anonymously, if you'd like to, or send me an e-mail. One way or another, lemme have it. I'd love to end this semester on a high note, but I can't do that alone.