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.
Archive for November, 2004
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
Nov 22
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.”
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
Nov 17
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.
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 na