At the beginning of the term, I was unhappy with my teaching schedule: sixteen hours per week, thirteen of which are spread over two days, and the other three of which are spread over another two days. I didn’t anticipate one huge benefit of that until the term began: my light teaching days don’t leave me ready to collapse at the end of the day, and that makes them good days to bike to school.”I put 100 km on my bicycle last week, and when I get back home today, it’ll have travelled another 20 km. I used to hate exercising, because I have an unusual mix of preferences and abilities: I’m woefully uncoordinated (which rules out team sports and dancing), I have bad knees (running would be the death of them), I hate being indoors (nix aerobics and the gym track), and I like being able to keep track of my progress (making things like hiking less than ideal). A bicycle equipped with a speedometer/odometer is tailor-made for people like me.”One of these days I should write about the dozen more conversations I’ve had that began with, say – is that an electric bike? It’s made me the most popular kid on the Island.
Archive for January, 2005
Last week, Rudbeckia Hirta at Learning Curves posted a handful of definitions of the Pigeonhole Principle, as given by her students. Go read them if you haven’t already: they’re not only spectacularly incorrect, they’re also bizarre, incoherent, and could rival the output of The Random Sentence Generator. I was jealous. My students’ incorrect answers just make me cry, not laugh. I said as much in the comments, and RH replied, You would get equally comic answers if you were able to ask this sort of question. Maybe you could try, “What is a function?”"I have no qualms about designing quizzes with the singular purpose of acquiring fodder for entertaining blog posts, so The opportunity presented itself this week, when I decided to check if my students really knew what the standard deviation measured, and not just how to evaluate it. “What characteristic of a data set does the standard deviation measure? Explain in a sentence or two,” I instructed, and tingled with anticipation as I collected the papers.”I sat down to grade them later that day, and “I got nothin’ for you, folks. Apparently my students actually know what characteristic of a data set the standard deviation measures.”Hunh. I guess that’s okay, too.”* * *”One aspect of my job that never fails to surprise me: the strange and many ways in which my students don’t understand the subject. I’m still caught off guard by these, even after tutoring and teaching math for years. And I’m not referring to the sort of dear God, why can’t they add fractions already frustration that I experience on occasion and have chronicled in detail, but rather the very frequent oh, they’re confused by THAT. I didn’t even realize that that could be confusing realizations.”For instance: on the stats quiz, I asked students to write down the formula for the standard deviation, and also to specify what each of the variables represented. The question was, for the most part, quite well done: most got the formula right or close to right, and most were able to tell me that x-bar was the mean, the xi’s were the data values, and n was the number of values.” and then, half a dozen or so of them also went on to explain that the capital sigma meant to add stuff up, and that the symbol that looked like a checkmark with a horizontal tail meant to take the square root.”They don’t know the difference between variables and functions. I had no idea.
Last week, I gave my stats students an assignment: to figure out how to use the statistical functions on their calculators. The distribution of times at which twenty or so of them came to my office for assistance with [above] was heavily skewed to the left, with five or so of my pupils asking for help before the quiz day, and around fifteen coming in between forty five minutes and three hours before they would be called upon to find the standard deviation of a month’s worth of daily snowfalls in Edmonton.”I am not a calculator expert, and took pride in my nonownership of one from the time I ditched my physics minor until the beginning of this term. But I have a decent intuition for these things – most of the time. Half of my students, God bless
My precalculus students wrote a quiz today. On the top of the front page I’d given the instuctions Solve the following equations for x. Show your work. If I’d instead typed Hey, kids! I’m under the impression that you know how to solve quadratic equations, but if you convince me otherwise, I’ll give you ten dollars! I would have received the exact same thirty papers.”This is the class with the crappy attendance. On Tuesdays, two thirds of my students show up. On Thursdays – quiz days – I get a full house, and then close to half of them jump ship after the break. A few weeks ago, I was willing to believe that a third of my students knew this material well enough that they didn’t need to come to class. Apparently I’m just that naive.”On a related note: a few weeks ago, I was chatting with Dr. Matt about review sheets for math tests. He was ambivalent about them, mentioning (I’m paraphrasing, and possibly misrepresenting, here) that he gives out the sheets one day, and then he goes over them the next class, and he wonders how much good that does. I was thinking about this, and also about a recent post at Learning Curves, during today’s class, when I was fielding questions about the homework. Last class, I’d assigned three word problems; this class, my students asked me to go over three word problems.”They were difficult questions (relatively speaking), and my students have limited experience setting up word problems, so I wasn’t surprised, nor was I bothered. What did bother me was that when I prompted the students with leading questions – okay, we are given a perimeter and we need to find an area what equations should we set up? I was met with silence. I’d realized it before, but it was only then that I fully saw just how disengaged my students were from the material. Math, for them, is a monkey-see-monkey-do affair. I may talk at length about how we need to figure out relationships among variables and translate them into equations, but my students just see how I apply those to this word problem or that one. They can’t apply a method of a problem about a rectangle to a problem about a right-angled triangle.”I started to set up some of them problems, but then realized that I’d tried this before, and it didn’t work; my students had never learned, on a large scale and to my satisfaction, how to set up word problems that differed from the few I’d shown in class. So I decided I was going to try something new. “I’ll go over these next week,” I said, “but I’ll only go over them if I get some feedback about how you tried to set up the problems. It’s okay if you don’t do it correctly; you can learn from false starts. What’s important is that you try.”"I pointed out that I don’t always know how to approach a word problem when I first see it, and that solving word problems isn’t typically something that comes to people all at once. But, I said, it never comes to anyone if they don’t try their hands at word problems first.”I know that other instructors of this course have thrown in the towel, and were satisfied with their work if their students were able to answer the same question about maximizing the area of the fence that they’d seen solved in class the week before. I personally don’t see the point in that; if the only problems my students can solve are the ones I did in class, then they can’t do math in any useful sense. From now on, I’ll do a couple of word problems in class, and then assign some that are similar in concept but slightly different in structure. And I’ll only go over those problems in class if I can see that my students have at least attempted to apply my lessons on finding relationships among unknowns. If they haven’t managed to make at least some sense of that, they’re not intellectually mature enough to learn what I’m teaching them, and there’s not much point spending more time on this material; doing word problems with students who can only mimic them isn’t any better than not doing them at all. We’ll see how this experiment goes.”Something in the air” Those Who Can’t. “I give weekly quizzes in all of my classes, so I hear from my ill students more than I otherwise might: missing a class isn’t necessarily worth alerting the instructor, but a quiz worth part of the mark requires a reason, and possibly a doctor’s note.”I just got my fourth or fifth email – three weeks into the term – from my fourth or fifth student claiming that a crippling migraine was preventing them from coming to class.”Except in extreme circumstances, I tend to think that my students are honest. But I don’t think I had a single student with a migraine last term, and suddenly I have several. If these migraines are real, why the sudden prevalence? And if they’re not, why is this a more popular excuse – by far – than it was last time?”Apparently problem solving isn’t my forte”" Meta-Meta, Know Thyself.”Last weekend, I took my new laptop to Vancouver, and when the two of us returned to Island Town, the sound system didn’t work. At all: I couldn’t play CDs, I couldn’t use headphones, I couldn’t get any audio on streaming videos. And this is a new computer! After several iterations of the Universal Computer Troubleshooting Procedure (shut down computer; turn it back on), I consulted the control panel for assistance. One of the questions in the help file was, “Have you checked
It took three comments for my post about students’ excuses to devolve into a conversation about boobs (thanks, Daniel Lemire and TonyB), so here’s my story about students and cleavage:
One day, back at my grad school, I was subbing for another teacher’s calculus class. At the end of the lesson, one girl approached me after class to ask me a question. I didn’t hear her question the first time, because I was too busy staring at her chest.
She was wearing a tight shirt across which was written – right on the breasts – “DON’T LOOK…TOUCH!”
Swear to God.
“Do you want me to touch your breasts?” I asked her.
She stared at me, stunned.
“Your shirt,” I explained. “It’s instructing me to stop looking – which is odd, given that when one sees text, one is inclined to look at it to read it, and how else am I supposed to see what it’s saying? – and touch your chest.”
“No,” said the girl. She backed away slowly.
“Then perhaps you should wear a different shirt,” I suggested, “because the one you’re wearing explicitly instructs everyone who reads it to touch your breasts.”
At this point she was getting visibly uncomfortable, and explained that she hadn’t said that she wanted me to touch her, and that if I did, then that would be sexual harrassment. “No means no,” she explained.
“But your shirt says YES,” I responded.
She seemed seriously confused about this.
Eventually I gave up and she asked me her original question pertaining to the concavity of some function, but I was having trouble concentrating. And I’m not the type that often gets distracted by breasts.
Anyway, I guess this is one reason it’s good to have more women in math: if I were a man, she’d have interpreted my comments as sexual harrassment. I’d still have been in the right to make them, but it’d’ve been a pain in the ass to go through the rigamarole to prove that.