Thursday, February 19, 2009
Error and Failure
What got my attention, though, was the first comment after the story. 'Judith' wrote:
My daughter finished her freshman year at Smith with a B- average and, upon being told not to bother to major in math, took time off to do remedial math work at a community college, intending to return to Smith. One day she said to me, “I’m not going back to Smith. They think that if I’m not already good at something, I shouldn’t bother to learn it. At community college, the teacher tells us how we will use what we’re studying in the future.” She got an AS with honors and is now back in a four-year school (not Smith).Community colleges teach.
It's a simple point, but it brought back a flood of memories.
Back in my own student days, I remember getting a very clear sense in both high school and college – hell, even through grad school – that I was constantly being monitored for flaws. (This may be at the root of why so many of my cohort thought that Foucault was really onto something with the 'panopticon' idea. 'Omnipresent and internalized surveillance' described our felt reality pretty well.) The whole prestige hierarchy/pyramid model – basically an inverted funnel – is based on weeding people out. If you buy into the model early and set a goal of succeeding within it, the entire educational process becomes a game of failure avoidance.
At some level, though, failure avoidance is a horrible way to learn (not to mention a horrible way to live). It rewards the wrong traits, and inhibits some pretty important ones.
At Snooty Liberal Arts College, I remember professors constantly being frustrated as their attempts to generate class discussion fell flat. They never seemed to clue in that, having bought entirely into the failure avoidance model, we were all petrified of looking stupid. Annoyingly, in any given class there were usually enough ridiculously-gifted people that if you weren't among them, nearly anything you did offer would immediately become grist for the mill. The fear wasn't irrational; when you were being graded against the preternaturally gifted, showing weakness was just too risky.
Grad school was even worse. At that level, a self-selected bunch of failure avoiders competed for faculty approval in a pretty airless environment for years. By the end, it took an act of will just to put together a declarative sentence. The most damning insult in grad school was “naive,” which was typically applied to anyone who actually made some sort of positive claim. (“Naive realism” was the worst, since it implied the unforgivable sin of claiming to actually know something about something.) Self-doubt can be taught.
In grad school, too, I recall the faculty being perplexed as to why so many doctoral students seemed oddly hesitant and overly deferential during oral exams. At one panel of grad student papers, I recall noticing that every single grad student started her presentation with “this is a work in progress.” Translated, that means “please don't attack me.” These habits are learned. Even now, I write with far too many parentheses, which is a form of defensive self-interruption. Old habits are hard to break.
When I landed a full-time teaching gig at Proprietary U, I was immediately struck by the different way I was treated. Instead of being the object of study, constantly under scrutiny and with the burden of proving myself against unspecified and arbitrary criteria, I was suddenly assumed to be knowledgeable about my particular subject area. As the only member of the faculty in my discipline, I was suddenly the go-to guy for issues in my discipline. It took a couple of years to get past both the thrill of unaccustomed respect and the nagging sense of being an impostor. Some people never manage to integrate the two experiences, instead switching between self-abasement and self-aggrandizement in a sort of acquired narcissism.
At the end of the process, you wind up with a greater-than-average proportion of hyper-critical shrinking violets who consider any attempt to deal with the realities of the outside world to be, well, naïve.
The application of this model to the typical college Senate meeting, I'll leave to the reader.
The model of teaching at the cc, and even at Proprietary U for that matter, is entirely different. It's not about poking and prodding the students until the flaws show up, the better to exclude them from the next level up. It's based instead on the assumption that most people can handle most subjects, if the classes are structured right and the students put in the effort. Success isn't assumed to be finite. It's assumed to be there for the taking, and the goal of the institution is to help the students take it.
Underlying that model is an assumption that students are worthy of respect, even with their flaws. There's something humane, and democratic, about that. Yes, sometimes that can swing too far, and go from 'supportive' to 'vapid.' Yes, upholding standards is a sign of respect, and any college worthy of the name needs to do that.
But I'd rather teach students by example that risk-taking is a part of growth than teach them that any sign of weakness bespeaks a basic character flaw. We're all flawed. That's not the point. The point is to accomplish things anyway.
Thanks, Judith, for crystallizing so succinctly something that had brewing in my head for some time.
The SLAC where I went to school, at least, was filled with teachers that criticized failure, but they also took the time to sit down one-on-one and help us succeed. I never saw any disconnect between "high standards" and helping everyone in the class. On the other hand, my experience TAing at a Big Ten school suggests that students there do fall abandoned. I'm not comfortable lumping together big R1 universities and SLACs on this.
Second, we need a bit of perspective here. When I was teaching in a Japanese high school, students would literally consult with their neighbors before answering the question "what is your name" because they were so scared of messing up. Maybe American 4-year college teachers don't live up to the California Self-Esteem Movement, but they're a loooong way from where they could be in criticizing failure.
Finally, I've watched what your argument can do when taken too seriously. I've been involved with a charter school that implemented a policy to relentlessly avoid criticism and prohibit tracking so the class moves at the speed of the slowest in the class. So the kids think they're doing great while the school has dropped to the worst academic performance in the county. The school is failing its students.
At a broader level, you're talking about the use of shame as a tool to modify behavior--students being shaped by the shame of public failure. In US politics, liberals often say its bad, and conservatives say its good. My experiences in Japan and the US tell me that too much is bad, but too little is bad too.
I suppose I was being monitored for flaws, but the biggest flaw was not having anything worthwhile to say, or having something to say and being too afraid to say it. Ultimately, my education taught me how to take risks, and I never went to a CC.
So I suppose the point is, not all high achievers have the same experience, and not all high-level institutions have the same sort of culture. Just as not all CCs (or all regionals, in my case) have the same culture, and just as a CC might not be this awesome thing for all students. Some students would (and do) thrive at Smith (or at other comparable places). The fact that one student did better at a CC than at Smith does not mean that CCs are better than elite institutions for all students, because all elite institutions don't respect their students because that's how you felt as a student, which is what you imply in this post.
And what we learn from those experiences can make us or break us. You, Dean Dad, did not learn what a lot of people would have, which is "Do unto others...only, do it first." Good for you.
That would be what a TA at MIT could not understand, when trying to get a discussion going in their lab tutorial environment. No one explained to him/her the number 1 characteristic of their students: failure avoidance, especially in "public". I've seen some good people fail as teachers because they were afraid to fail in "public" (in front of a class) by admitting they didn't know something at that moment in time.
I think the question of Japanese style severity versus California style "gold stars for everyone" that rubashov brings up is a false dichotomy we need to get away from. I try to make clear to my students (not always successfully) that I can be hypercritical of their work, without doubting *them* or their ability to do the work. Keeping high standards need not be in conflict with holding to the belief that every student can reach those standards, with the right coaching and sufficient focused effort. I just don't buy that some students "got it" and some students "don't got it".
Of course, it's not so easy to convince students of this when all their schooling tells them otherwise - particularly when grading time comes around.
My first year I remember a faculty members frustration at the fact that we didn't slam on each other. One faculty member got tired of discussions that started "so and so has made a good point when they stated blah blah blah, however, when thinking about [something else] another way to look at it is..."
I think that person wanted us to call each other out in heated debate and deem each other naive, instead they got polite, depersonalized discussion about the pros and cons of each others take. I think this may purely be my program though.
The priority system at an R1, where I teach, is that undergraduates are socialized into seeing themselves as naturally beneath the lofty concerns of the faculty. They often don't ask for the help they deserve, and the faculty is often glad for that, because they'd rather not be bothered with it. It's a tragedy that R1's have such large concentrations of undergraduates, because I think very many of them don't get their money's worth, even at state tuition costs.
But then again, the dirty little secret of higher ed is that a good amount of time it doesn't have to do with education.
As callous as this may sound, I think the faculty at Smith have a very good point. Although I don't have any statistics at hand, I highly suspect that the probability of a student finishing a degree in mathematics given that said student started his/her college career with remedial math classes is vanishingly small. Throughout my years as a graduate student and assistant professor, I have only heard of one student who has ever done such a thing.
Certainly I didn't start out knowing that and I was definitely scared of looking stupid. Also, there were a few folks who implied they thought most of us students were pretty stupid. But overall the attitude was that the whole point of what everyone's doing---students and faculty---is to learn what's really going on with the subject at hand, and if you're not asking your questions you're probably not learning as much as you could be. And most of the time people were good about keeping the questions and criticism focused on science, not on anyone's worth as a person.
I also like getting thorough criticism of my work from colleagues...I'd rather hear it from them than from a study section or a reviewer! For that matter, some reviewers, even though they're acting as "judges", make constructive comments, too. I always appreciate that, and I try to do that when I'm reviewing.
However, I think this mental attitude requires thinking of yourself as part of a community of scholars, as opposed to a student who is being probed for flaws. As you say, it's the difference between rigorous attention to the science and being personally attacked. IMO, it takes a few years to cleanly separate the two.
The R1 where I did my undergrad work had a single "math major", but something like a thousand flowers could bloom within the scope of that program, ranging from students who took mostly grad courses in an honors program to ones who took the most minimal set of junior-level classes that were allowed. Many of the latter started in classes that would be considered "remedial" at some universities (i.e. below calc 1).
I once encountered a young woman who had dropped out of an R1 physics program after failing a calculus class, went to a CC, learned calculus from someone who could actually teach, entered a physics program at a regional university, and then ended up in a graduate physics program at an R1. Clearly talent was not the issue in her case, effective teaching was the crucial element in her early career, to fill in gaps left from her dodgy HS classes.
Regarding math majors who graduate, but start their college career in courses below the calculus sequence, the proportion of such students is certainly higher than the percentage that start with remedial courses. However, I suspect they're still in the minority; as I don't have any statistics on these matters, I'm certainly willing to be proved wrong.
Obviously its not perfect- I will say that I have felt some pressure as a woman in male dominated spaces (as Theory, with a capital T, tends to be). I happen to be outgoing, and cope really well with being the only woman participating in a conversation. It's obviously not right for everyone, but I don't think there's any reason that a high pressure environment can't co-exist with good supportive teaching.
The meaning of "math major" is quite different at Smith than at the top rated R1 I attended as an undergraduate. Smith does not offer the breadth of options (particularly at the low end, but also not at the top end that I would define as "Putnam Competitor") that the R1 does. This is a natural consequence of the numbers of students majoring in math at the respective schools.
I do question an admissions process that wasted a lot of resources at Smith on a student who did not match their model for a math major, however. Something odd going on there. You ought to be able to identify a student who needs pre-calc or trig or who has never done a proof. Maybe not.
I actually don't think that the meaning of math major differs between Smith and an R1 - at both places you have people majoring in math.
I think you might be hinting that the meaning of a math degree is different at the two institutions or that the opportunities and range of classes and teachers differs, and if I'm interpreting correctly is better at the R1.
I can say that assuming an R1 has a larger range of options in math may be a fallacy.
I majored in math (as in that was my major and I received a B.S. in the subject) from a SLAC (well SLAU, really, it does have a couple of graduate schools), which is about 1/2 hour away from a very well know R1. While the department may not have produced many Putnam competitors, it is a well know area teaching school and many of the R1 students have actually taken their math (and physics) requirement courses at our school due to the emphasis on teaching the subject (taking the requirements at the SLAU still goes on today). Of course, the pres of the AMS was in the math department of my SLAU when I was there (he was actually a great teacher who presented us when his own photocopied calc textbook that he was working on when he taught us) so it may be an outlier school.
I meant to say you seem to be hinting that the meaning of having majoring in math at the R1 or SLAC differs. In that - a major is a major, and its a pretty defined term in the U.S. But the meaning of having a degree from an R1 may be perceived differently (and may be different as well). There may be a broader rang of opportunities, harder/more rigorous coursework, etc. at an R1.
Though, to add to my previous comments conversely, at the R1 there may be more of an emphasis on research and less on teaching undergrads, so even if the opportunities are there, it may be difficult for undergrads to connect with a faculty who are primarily evaluated on their research output and for whom teaching style is an afterthought (I have heard horror stories of R1 profs lecturing to the board in math, but that was a long time ago).