Tall, Dark, and Mysterious


When it’s bad it’s bad, and even when it’s good it’s bad

File under: Those Who Can't. Posted by Moebius Stripper at 1:03 pm.

All hundred-odd of my students wrote tests last week, and so I spent the entire weekend grading them.

My precalculus classes, as expected, did poorly - though I was surprised by just how poorly they did. I knew that my students didn’t know how to factor, but I was surprised by the number (6) of students who thought that the graph of -2^x was a jagged line. There’s also the fact that despite my having spent three (3) weeks on the graphing arts, the preferred method seems to involve graphing functions pointwise and connecting the dots, asymptotes be damned. (One angry student told me that if I wanted a better graph, I should let him use his graphing calculator.) If I were to test my students instead on, for instance, Fermat’s Last Theorem, I think the results would be similar: pages of gibberish, followed by a dozen students whining that I never showed them how to do that question. In any case, I feel like I’ve utterly botched precalculus. Half of me wants to try it again so that I can get it right, but the other ninety percent of me never wants to teach a precalculus class again.

My discrete classes, though, surprised me: class average in the mid-seventies on what I thought was a moderately challenging test. I was happy about this, until I got into the class today, and found that a good half of them were shocked by their good marks: they’d thought they’d failed. (This didn’t stop many of them from complaining regardless that I shouldn’t have asked this question or that one.) This is making me wonder if I know anything whatsoever about setting tests. At the very least, perhaps I should rethink my generous part-marks policy.


The rejected first draft of the course catalogue

File under: Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 3:33 pm.

Rudbeckia Hirta breaks down the first-year math courses at her university. I think her descriptions are more useful than the standard “polynomial, rational, trigonometric, exponential, and logarithmic functions, their graphs, and applications”-type outlines, which give little idea of what students should expect from a psychological standpoint.


Sign of the times

File under: Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 5:32 pm.

I’ve bemoaned my students’ inability to do simple mathematics many times on these pages; I’ll spare you a rerun. Suffice it to say that by and large, my younger students - all of whom are less than a decade my junior - have been weaned on calculators, and consequently, an appalling number of them can’t multiply integers or add fractions in their heads, or even on paper.

What has surprised me is the number of students who have expressed to me that they feel cheated by their education. I’ve had a good half dozen students tell me that they wish they had not been given calculators so early. “If I hadn’t been allowed to use a calculator at such a young age, I would be able to multiply simple fractions together and add double-digit numbers,” said one student in what has become a typical conversation. “It’s ridiculous - and students today are allowed using calculators while they’re learning to add!”

But then she continued, in all seriousness: “I think that students shouldn’t be allowed to use calculators in math class until at least grade four.”


Blah blah asymptote blah blah intercept

File under: 1000 Words, Those Who Can't. Posted by Moebius Stripper at 5:20 pm.

Three of my four classes are full of students who seem to be getting at least something out of my efforts, but lately I can’t think about my early afternoon precalculus class without being reminded of this Far Side cartoon:

For whatever reason, the students who can’t solve linear equations, the students who can’t add fractions, and the students who can’t even come close to formulating an equation from a word problem, all ended up in this section. A typical Q&A session in that class goes something like this:

Student: (after I’ve graphed one function on the board) So basically, when you’re graphing a function, it goes positive-negative-positive-negative, and has two vertical asymptotes.

Me: (not knowing where to begin) Well, no, not really: in the case of the example on the board, yes, but that’s because of the factors of the two polynomials in the quotient. (expands on this a bit, explaining where the zeroes and intercepts came from, again) You need to look at the factors of the numerator and denominator, and take test points in all of the intervals that you obtain from the critical points. (does example on blackboard) Does that make sense?

Student: So basically what you’re saying is, yes, in general there’s two vertical asymptotes and the graph goes positive-negative-positive-negative.

Most of these students would benefit from a good, solid, grade nine math class, and I’m at a loss over what to do with a university precalculus class full of them.


Little Miss Math Teacher

File under: Righteous Indignation, Those Who Can't, XX Marks the Spot, Talking To Strangers. Posted by Moebius Stripper at 6:17 pm.

The following conversation wouldn’t be noteworthy, were it not for the fact that I’ve had it a good half a dozen times in the last two months:

Female Stranger: Are you a student at the college?

Me: Actually, I teach there.

FS: (eyes bulge) You do? What do you teach?

Me: I teach math.

FS: (eyes bulge, voice becomes high and squeaky) Really? GOOD FOR YOU!

I’ve gotten this from a bank teller, from the woman who sold me my cell phone, and from a good number of people on the bus. Certain details, such as the timing of the bulging eyes and the squeakiness of the voice, vary from person to person, but the “GOOD FOR YOU!” is constant. Not “I’m impressed” or “oh, interesting, I’ve never known a college math teacher,” or even the standard “I could never do math”, but “Good for you!” as though teaching college math is a milestone on par with making all gone with my brussels sprouts or graduating to big girl underpants.

Sometimes, they clarify that it’s because I’m a girl that it’s so good for me that I’m teaching math. Having stricken “I grade my students’ test papers in menstrual blood, too!” from my list of possible replies, I tend to remain silent or say something noncommittal. I think that my conversational partners are offended that I don’t beam in pride, as our chats tend to end right there. Perhaps they haven’t figured out yet that not only can girls teach math just as well as boys, we can also be just as averse to condescension and paternalism as boys. Any twentysomething male college math instructors or researchersd here had, one a regular basis, complete strangers express pride at their choice of employment? Hell, any young men here ever get verbally patted on the head for their life choices?

(My parents and older relatives are exempt from my indignation here, as they were actually there when I made all gone with my brussels sprouts and graduated to big-girl underpants and are allowed to be proud of how far I’ve come. All others, take heed.)

I know that these strangers mean well, and that they can’t help being idiots, but every single time someone focuses on the fact that I’m a female working in a male-traditional field, I find myself half wishing that I had chosen a job in which my presence were seen as a contribution to my field and not as a political statement. If I had the temperament for feminist activism, I’d get involved with that, but I don’t, which is part of why I inhabit instead the politically bland world of graphs and equations. I’m not an ambassador for womankind. I stand in front of a math classroom with the same skills and for roughly the same reasons anyone else stands in front of a math classroom, and ignoring those reasons in favour of pointing out that women are such a rarity in their field harms the cause of having women taken seriously in a myriad of fields - it doesn’t advance it. Doubly so if, in the process, you treat the woman in question in the same way you’d treat a six year old. Good for you!

Part of the problem, I think, is that it’s been my experience that the set of people interested in technical subjects (as something to study, not just as something that it’s cool that other people are studying) and the set of people interested in social activism (as something to do, rather than just as something that’s cool for other people to do) are nearly disjoint, particularly among females. Consequently, those of us , such as myself, who ally themselves with the former camp are interesting but otherwise strange and mysterious to the latter - objects of a psychological experiment conducted behind glass. The latter know all about women, but know squat about physics or math or engineering, and they talk about what they know. Okay, you’re enumerating curves on Hirzebruch surfaces via lattices of dual subdivisions, and I’m sure that’s very nice, but OMG YOU’RE A WOMAN AND YOU’RE DOING MATH and that must be like SO WEIRD, let’s discuss that.

No, I’d rather discuss enumerating curves via lattices of dual subdivisions, thankyouverymuch, but I appreciate your concern. Now go away and leave my profession to the people who are interested in it.


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?

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