Tall, Dark, and Mysterious


Standardization, freedom to teach, and the university marketplace

File under: Righteous Indignation, Those Who Can't, Queen of Sciences, Know Thyself. Posted by Moebius Stripper at 12:56 pm.

I have a question for the university instructors, particularly the math instructors, who read this:

How does your university reconcile a commitment to high standards with a desire to create a good work environment for its instructors who wish to teach freely? For that matter, how does it reconcile both with the fact that so many students are overwhelmingly ill-prepared for university?

(I’m assuming a simplified model in which universities actually care about such matters, and have devoted some thought to the issues thereto appertaining. This is not naïvete on my part; it’s a just a mathematician’s smoothing of data in order to create a solvable problem.)

(If you have an answer, feel free to skip the rest and just post in the comments. This entry’s really all over the place.)

My old university, where I did my Master’s degree, took the position that we have high standards, dammit, and so if half of our students fail their first year math courses, then so be it. It was something of an open secret that the first year calc courses were designed with the express purpose of culling the commerce herd: the head of the commerce department had explicitly asked that we fail a third of our students, because his department didn’t have room for all of its applicants. And so we did, appealing more than once to the defence that “the department made us do it.” Our curriculum was designed accordingly; follow the textbook, cover all of the examples, and don’t digress. We were not permitted to see the final exam; that way, we would not be tempted to teach to it. The instructors were just textbook appendages, and useless ones at that; the deparment head pretty much said as much back when the TAs went on strike. To wit: we were not to adjust the final exam despite the fact that we’d been away for a third of the term - after all, the students could just read the text and learn the material on their own.

Somehow my old university managed to micromanage us while giving us just enough freedom to completely screw our students, which is pretty remarkable, when I think back on it. If we wanted to prepare our students for the exam and for the next course, we had to do everything by the book, example by example, question by question; on the other hand, we designed our own midterms, so if we didn’t give a crap about our students, we could just babble about the easiest aspects of the course, and leave our pupils to flounder on the final exam. But don’t worry: the students in the latter type of classes would just fail the final, and term marks would be adjusted in order to be in line with exam grades, so at least the students would have their university careers ruined.

My current university takes the opposite position, handing us textbooks, telling us to cover chapters n through m, and then letting us go play. I loved the freedom, and entered the classroom with the optimism of a first-time full-timer: I would not just teach my students how to factor quadratics and graph polynomials and solve systems of equations; I would teach them to think! They would learn how to check their work! To estimate ballpark figures for the values they were computing! By God, they would LEARN!

I anticipated that that radical philosophy would encounter some opposition (see also, “you make us do DIFFERENT problems on the test!”) , and I chalked much of that up to the fact that some students fresh out of high school take a while to realize that, well, we’re not in Kansas anymore. But recently, I’ve begun to seriously question - and somewhat regret - my approach. My students are doing fine - average in the mid 60’s, which is where it ought to be - but some of them are failing despite what I believe are their best efforts. I went in to this course deciding that I wouldn’t teach them to memorize formulas; I’d teach them to think mathematically. But so many of them simply aren’t at that level. As a result, not only are they not learning to think mathematically, they’re not even learning to memorize formulas. I now know what the secretary meant.

And my students are angry. And they’re not just angry because I make them do problems they haven’t seen before on tests, whereas their high school teachers didn’t; they’re angry because the Nice Teacher who teaches section 104 doesn’t make his students solve new problems on tests, either.

Nice Teacher is another temporary instructor here, one who has complained at length to me and to others about what lazy-asses his students are. Some of my students are lazy, too, but I wouldn’t describe them as lazy en masse; and if they were, I’d remedy their laziness by making them work. Given the option between being lazy and failing, or working hard and passing, prudent students - even lazy ones - tend toward the latter.

Nice Teacher chose a different approach. If the students are lazy, then the path of least resistance is to challenge them so little that even their lazy asses can pull B’s without effort. Nice Teacher spends half a class or so on applications - two or three of them per section - and then assures his students that they won’t see any applications that deviate even slightly from the ones he did in class. His tests are shorter than mine, and the front page of them contains a list of all of the formulas that any first-year math student could possibly want. As though that weren’t enough, the test problems - which are pretty easy, as far as the subject goes - are annotated with hints. An example: “Use Formula #3.”

For the benefit of those students who are so weak and so lazy that even that’s not enough, Nice Teacher gives what he calls “pretests”, which are word-for-word identical to the tests themselves, with only a few numbers changed.

I know this because I supervised Nice Teacher’s students during a test last week, and saw most them leave halfway into the allocated time they had to write, and fielded questions such as “It says to use Formula #3 - so do I plug in a=10, p=5, or the other way around?” I replied that I couldn’t answer that question, and the student pouted: “Nice Teacher would have told me.”

Anyway, Nice Teacher’s class full of lazy students has an average of 80%. Some of my students are acquainted with some of his, and have asked me why I can’t give pretests, why I can’t give formulas on the test, and why I can’t overall not require them to do any work in order to get B’s. I’m hard-pressed to give an answer that isn’t of the form “Because I’m actually teaching you how to do math, not how to be a slacker.”

Most of my students would rather learn nothing and get A’s than learn something and get B’s (or even C’s), and so there’s been a migration of my students into the other sections. The department head tells me that he often gets students complaining that they paid for this course, so they deserved to pass. Department Head is of the dry British persuasion, and treats these claims with the irreverence they deserve. Once I had a student complain about same to me, and I remarked that a university education was a poor investment for them, as a diploma mill could provide them with higher marks for less money. But my students have an even better option now: transfer sections for the high marks, and get the same university degree. If you’re unhappy with a product, switch brands. This is what happens in an environment with few standards.

I have no data on the subject (Kimberly? Do you?), but I would wager that the most zealous faction of the anti-standardized-testing crew barely overlaps with the set of mathematics instructors. By and large, math instructors would be delighted to have a classroomful of students who have mastered some set of basics, the content of which we could for the most part agree upon. When a student arrives in university unable to add fractions, unable to deal with negative numbers, unable to set up a simple equation from a paragraph of information - it’s not because that student’s teachers were spending so much time preparing for a test that they couldn’t teach creatively; witness the disaster that was the New Math. Often, in grading a test, I wonder what on earth some of my students were doing in math class for the last decade, because it obviously wasn’t math.

Department Head was unaware of my situation until I brought it to his attention, of necessity telling on Nice Teacher in the process. What should I do about the gulf in standards, I asked? We arrived at a compromise: scale the grades after the final exam, so that no one would be penalized for being in my class. It’s not an ideal situation, as I strongly believe that my students who are getting 40’s in my class do not deserve to pass, but it’s a decent balance between achieving fairness across sections and maintaining my standards.

Nice Teacher’s students get punished by not actually learning anything; alternatively, depending on your perspective, my students get punished by only possibly learning anything and getting bad marks in the process. At my old university, poorly-taught students would be punished by failing the common final exam, and hence the course. In both universities - one superstandardized, the other giving full freedom to the instructors - the only quality assurance was the sort that would (in some form) punish the poorly-taught students. Has your university come up with anything better?

Or maybe they just studied really hard.

File under: Those Who Can't. Posted by Moebius Stripper at 11:43 am.

My early afternoon precaclulus class has always been a shade weaker than my late afternoon precalculus class; class averages tend to differ by around 5% from one class to the next.

Until this week. Class average on the early afternoon test: 58%. I found this bewildering, as I thought that this test was considerably easier than the previous two. My late afternoon class agreed with me: their class average was 78%.

I don’t like to assume the worst of my students, but no mathematician can look at the data I’m looking at, without incorporatinng their knowledge of standard deviations and variance and accuracy within such and such percent so many times out of twenty and concluding that in all likelihood, something is awry. Since my two classes are one right after the other, with only the ten minute break to get between buildings, I’d naively assumed that it would be okay to give the same test to both sections. Curiously, my early afternoon class - the ones who bombed the test - tended to leave the classroom early. Most were gone an hour into the sixty eighty (thanks, rohan!) minute test, which left them with half an hour to talk to the late afternoon students. By contrast, I had to pry the test out of half of my late afternoon students’ fingers.

Next week, I’ll write two tests. This shouldn’t be much extra work, as many of my students are so weak that “find the maximum possible product of two numbers that sum to 50″ is a completely different question from “find the maximum possible product of two numbers that sum to 60″. But this still leaves the question of what to do this time. I hope that at the very least, the early afternoon informants were being paid well for their sacrifice.