Tall, Dark, and Mysterious


An equation is a relationship among quantities.

File under: Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 9:45 pm.

That’s the sentence that I utter every time I present a word problem on the blackboard in my precalculus class. Then I slowly, slowly outline what quantities we’re working with, which are known, and which are unknown, and how they’re related. Then I work through the problem, and when I’m done, I go over how - and why - we set up the equations that we did.

Today, I graded 30ish tests, and saw that I might as well have spent the above time reinforcing the prevailing view that equations are voodoo amalgamations of letters and numbers, for all the good my attempts did. (Boy, am I ever feeling Rudbeckia Hirta’s frustration today.) Answers to a “rowing with the current/rowing against the current” question revealed that while close to a quarter of my students seem to know that speed=distance/time, about as many are under the impression that speed=time/distance, and many others hold fast to the view that speed=distance*time. I’m sure there’s a bad scifi novel in here somewhere; I’m equally sure that if I asked a random student “if I drive 100 km in 2 hours, what’s my [constant] speed?” they’d reply “50 km/h”. Anyway, this may have happened because I sneakily gave the time in minutes not hours, so the time/distance formula had the advantage of giving a whole number instead of one of those tricky fractions. Another student opted to forgo multiplication and division altogether for this problem, and wrote down the formula “speed of current + 50 minutes = 10 kilometers”. The problem involved the current on the return trip being half of its original value, so some students squished all of the numbers in the original problem together in some haphazard fashion, threw in an x so they’d have something to solve for, and then multiplied the whole thing by one half.

A supply/demand problem had a number (not zero) of students finding that the equilibrium occurred when widgets were sold for negative thirty bucks a pop. No one appeared to bat an eye over this one; they just stated their conclusion and moved onto the next problem. On a question about finding the dimensions of a structure with given area and given amount of fencing, a plurality of students faithfully parrotted the formula that perimeter=2*length+2*width, apparently not noticing (or caring) that the fencing of the figure in question (I provided a diagram) did not surround a rectangle. Nor did it surround a triangle, but many students seemed eager to show off their knowledge of the Pythagorean Theorem.

The class average, despite all that, wasn’t that bad; it’s just that the poorly-done tests were really poorly done, and many of my students seem to have no idea what mathematics is. There was no point in writing comments on some of the papers; so profound is the disconnect between my weakest students and the subject matter.

I have no idea what I’m going to say when I hand these tests back tomorrow. Right now, I’m mostly angry with my students - haven’t they been listening to what I’ve been saying all term? If they were, then they clearly didn’t understand me - why didn’t they ask, in private during office hours if not in the classroom? Much of my frustration is justified - attendance in that class sucks, no one showed up to my office hours during the week before the test - but many of my students are trying. They just don’t have the background right now, and I don’t think I can provide it. But that’s not a productive way to give back the test papers. Students who bombed a test don’t need to be told that I’m disappointed in them; they’re more upset than I am as it is.

Fellow high school/college teachers: what do you say to your students when you hand back a terrible test? I don’t want to upset them, but at the same time - I ain’t scaling these test marks, and the course isn’t going to get any easier.


Any questions?

File under: No More Pencils, No More Books, Queen of Sciences. Posted by Moebius Stripper at 11:40 pm.

Suresh over at The Geomblog quotes an article about modern academic interactions. To be honest, I didn’t read the whole thing; I got stuck on Suresh’s mention of the “relative lack of questions” at theory talks, and this one part of the column:

At conferences, scholars would stand up and read their papers, one by one. Then the audience would “ask questions,” as the exercise is formally called. What that often meant, in practice, was people standing up to deliver short lectures on the papers they would have liked to have heard, instead — and presumably would have delivered, had they been invited.

…And so the implicit content of many a conference paper is not, as one might think, “Here is my research.” Rather, it is: “Here am I, qualified and capable, performing this role, which all of us here share, and none of us want to question too closely. So let’s get it over with, then go out for a drink afterwards.

Which reminded me of the list of all-purpose questions to ask at any math talk.

1. Can you produce a series of counterexamples to show that if any of the conditions of the main theorem are dropped or weakened, then the theorem no longer holds?…

4. Isn’t there a suggestion of Theorem 3 in an early paper of Gauss?

Anyway, “delivering short lectures on the papers they would have liked to have heard” sounds about right, based on the 1-2% of the average math talk that I understood. (Except for this one time the speaker was talking on my thesis topic, when my comprehension was almost up in the double-digits.) But I disagree with the article’s assessment that this may be avoided by people checking out one another’s papers ahead of time. I think the problem is far deeper: when everyone’s a specialist, it’s common for experts to lack the breadth of knowledge required to understand their colleagues’ work. And so, at a conference, the people who are specialists in almost your field understand your research just enough to segue into a question or comment about their own. My love of big-picture math, coupled with my lack of interest in any particular highfalutin subgenre of the latest hot research area of the subject in which that special case of that open problem was recently generalized, is a big part of what led me to leave grad school.

Well, that, and the fact that I was sick of being the student in Question #8.

Culling someone else’s herd

File under: Righteous Indignation, Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 8:33 pm.

The statistics class I teach is an intro course for humanities and social science students. A good half of my students are majoring in mumbleology, which I knew required its students to take statistics - but only today did I learn that it also required them to obtain B’s or better. B’s! I discovered this not from anyone employed by the Department of Mumbleology, but from a student, who came to my office after obtaining a D on the test, and - well, you know the rest. After carefully pleading her case - complete with tears, calls for mercy, the whole family of explanations (difficulties in personal life, hasn’t taken a math class in a decade, test anxiety), and a solemn oath attesting to the vast effort she’d expended on this course - she laid out her request: could she write the test again?

Ugh. Since, you know, beneath this tough exterior, yadda yadda, I hemmed and hawed out my refusal: well, I said, when I see that a student has a test that’s a real outlier (nota bene: stats terminology, indicating relevance of subject), I’ll count the other tests as well as the final exam for more. But, it’s an awful lot of work to set a test, and I have three preps, so I don’t give makeup tests, and besides, if I gave you one I’d have to give everyone one, and -

Oh, no, she said, I wouldn’t ask you to set a makeup test. Just to let me write the same test again.

I’m not going to share what I said in response, other than to mention that there’s a reason Canadians have a reputation for being polite in the face of absurdity. And, no two ways about it, the request to write the same goddamned test again is absurd.

It’s not that I don’t sympathize. I do. It must suck to have your entire future rest upon this one class that no amount of effort will get you through in a single term. And, I hate to be so fatalistic, but for this particular student it’s true: my last test was a hair too easy - the class average was a B (and, this being a stats class - standard deviation was around one letter grade) - and it’s just going to get more difficult from here. Intro stats isn’t rocket science by any stretch, but there’s no way that I can do justice to the required material in such a way that a student - no matter how hardworking - who hasn’t done math in a decade can swing a B, unless said student has some nontrivial, latent mathematical talent that I’d likely be at least vaguely acquainted with by now.

That said, I’m more than a mite peeved at the Department of Mumbleology for outsourcing its heartbreaking duties to us. A B? Required in a course that has no relevance to the student’s major as taught by Island U? And - let’s be honest, here - this is Island U, which isn’t known for being a leader in Mumbleology research. I know what I’m talking about here: I actually have a passing interest in mumbleology, to the point that I was even considering the 101 class this semester until I discovered that it conflicted with my schedule, and some knowledge of statistics is extremely useful in the field. But a substantial portion of my students, mumbleology majors all, are in their third or fourth year, and their later-year courses don’t draw upon statistics at all. When I checked out one of the second-year textbooks in the bookstore, it was filled with rousing expositions of its theories: “A groundbreaking study in 1985 revealed that over 78% of…” began one chapter, with nary a mention of the way the sample was chosen, the distribution of the data, whether the study had ever been replicated - all the stuff covered in Chapter 1 of the course I teach. It was left to the reader to trust that a certain trait and a certain childhood trauma were “strongly correlated”, something I’ll be fleshing out in my class in a few weeks. I could go on. I’m not saying that a mumbleology course should get bogged down in the statistical element of its content - to the contrary - just that there’s a clear overlap between my class and it, and there’s no reason that a class full of students who are required to get A’s or B’s in my class can’t apply their knowledge to a discipline whose integrity rests upon well-conducted and -analyzed studies.

Every college math instructor, I’m sure, can relate: we’re the gatekeepers for departments that either can’t, or won’t, offer courses challeging enough to trim their cohorts as much as they’d like. And they can’t give their students any compelling reasons for requiring such stellar performance in math classes, and that has the tendency to produce a lot of anxious, demanding and bitter students - and stressed but sympathetic teachers. I can tell my students why math is interesting, and why statistics is useful in real life; but the instructors for their majors aren’t reinforcing my lessons, and my students aren’t at school to broaden their horizons - they’re here to get degrees, and, eventually, jobs.

And so, when students come crying to my office asking if they can write the same test again, I’ll gently refuse their request. And I won’t feel guilty.

But I will feel bad.


The time, it does fly

File under: I Read The News Today, Oh Boy. Posted by Moebius Stripper at 7:32 pm.

Further to my last post: internet polls are not completely useless. For instance, I wouldn’t have realized that the Superbowl was tomorrow were it not for the most recent Globe and Mail poll.

Already, eh? Seems like only yesterday that the media were making a big deal out of Janet Jackson’s boob. Oh, wait, it was.

My kingdom for intelligent activism

I’ve mentioned before briefly that back in the Spring of ‘03, the TA union at my grad school went on strike. It was a fascinating experience, and I learned more about labour law in that one month than I learned about algebraic stacks during that entire year, which isn’t to say much, but it actually was. I stand by a statement I made back then: going on strike is an experience that everyone should have exactly once. I learned a lot from it, but the experience was emotionally draining, and it didn’t take long for me to grow weary of the continuous assumption that we stood in solidarity with every group whose members had ever joined a union. We were legislated back to work three days after the first bombs fell on Iraq; the subsequent union meeting featured some grad student flailing his arms wildly in a manic proposal that we design banners “opposing the facism of [the university’s president] and George W. Bush”. This was back in Vancouver, where a few months earlier, another group had successfully run the Women Against War And [BC Premier] Gordon Campbell Rally (because, and I quote, “Women are suffering…from Kabul to Kitsilano”), so Flailing Arm Boy was met with an enthusiastic round of applause. I argued that Vancouver already had dozens of antiwar groups, and only one TA union, so perhaps it behooved us to stay focused. I was outnumbered. For those of you wondering: Kitsilano women had to arrange alternate means of childcare (or possibly employment) in the wake of Campbell’s cuts to provincial childcare services, and Kabul women risked getting killed if they let any flesh show from beneath their burkas.

I was reminded of all of this today, when I opened my work email to read that my union is fighting for social justice where it counts - on the front lines of internet polls:

Friends: Please take the time to respond to this poll. I think the federal Liberals will take any opportunity they can to renege on their promise, Ken Dryden notwithstanding.

—–Original Message—–
Sent: Friday, February 04, 2005 9:23 AM
Subject: Support for a National Childcare program!

Hi All!

Go right now to the Globe and Mail online frontpage and vote in favour of the [national] childcare program!

So far the anti-childcare voters are winning. We are losing badly.

Vote and get the vote out. — Past it on.

Onward, cheers & solidarity

The naive, nonunionized reader may be under the impression that when membership in an organization is a condition of employment, the only political ideology that can be reasonably assumed to be shared among the organization’s members is a commitment to collecting paycheques for their work. Not so: “solidarity” means that it’s a given that every member of the Island U Faculty Union is on board with the proposed national daycare program. All that shit about critical thinking and drawing conclusions only after careful consideration of data is just something that we teach our students to do, and you know what they say about leaving work at the office!

There’s so much that I want to say in response to this email - to the person who sent it to the entire faculty of Island U - but the email is so phenomenally stultifying that I can’t for the life of me think of a way to phrase a reply that’s anything less than contemptuous in tone. There’s no way to gently point out that the federal Liberals have campaigned on the promise of a national day care program for the last twelve years, and it hasn’t happened yet. And why would it have? They’ve got a winning formula (”we promise the same stuff we didn’t make good on last time; you vote for us anyway”), and that’s a better excuse to renege on the childcare program than any damned internet poll.

Speaking of which: three weeks ago, my stats class was covering the unit on sampling and bias. Based on their performance on their most recent test, I can comfortably claim to have succeeded in driving home the lesson that self-selected surveys are, without exception, completely worthless. A few weeks ago I gave an open-ended question asking students to give an example of one, and explain why it was unlikely to be representative of a general population. Fully half of my students cited internet polls, and many gave the humourous example I’d mentioned in passing during the previous class of the Globe and Mail poll, “Do you respond to online polls?” (81% of respondants answered in the affirmative.)

My students get this, and they know that no vaguely reputable organization is going to make decisions based on internet polls. Too bad the organization that represents their instructors hasn’t figured it out yet.


Sometimes grading fifty tests isn’t so bad

File under: Those Who Can't. Posted by Moebius Stripper at 12:06 pm.

On the stats test, I gave a question about a company whose owner takes home a million dollars per year, and whose 60 employees each make $40 000 or less. I asked my students which of the measures of centre - mean, median, or mode - best described how much money the people working at the company were making.

From one test:

The median. The boss makes BIG MONEY, which screws everything up! Everyone else is making so much less, but because of the boss, the mean is really high. I mean, say you wanted to know how much money students in this class carried on them on average. Well, I carry $10 000 on me. OK not really, please don’t rob me! So anyway…does that mean that a “typical” student carries $500 on them? I DON’T THINK SO! It’s probably best to ignore me when you’re talking about how much money students have! I’m like the BIG RICH BOSS in the question!

Alas, the other tests aren’t quite as exciting, but still. Sometimes it takes only one.

« Previous PageNext Page »