### Dispatches from the library

- Apparently my computer has some hard-to-diagnose computer ailment. In a sequence of events that bears striking parallels to those often experienced in my country’s health care system for humans, this has resulted in the blasted machine being discharged - thrice - from the hospital for sick computers before it was fully cured, only to be sent back for more tests and treatment. Fortunately, my computer’s health care has another important feature in common with mine: it is free. Unfortunately, I don’t know how long the waiting list is before it can see the appropriate specialist. Blissfully, this whole thing has been handled by my father, who has advocated tirelessly on its behalf. And now that I’ve praised my father, I won’t feel as guilty when I post this hilarious story involving him making a really stupid bet with my brother back when we were kids. Stay tuned!
- I had a lovely,
*lovely*week at Mathcamp. Briefly:

- I taught two classes - a squishy, very visual version of projective geometry, and Calculus Without Calculus - to the best audience of ten that anyone has ever taught. Rather than having students bitch and moan about how I gave them homework that, like, was totally unfair because it made them
*think*and shit, I had students request that I skip the routine calculations because there were only ten minutes left in class and they wanted to get to the cool stuff. I also had those same students construct a model of the real projective plane using carrots and toothpicks. - On the whole, our campers kick all kinds of ass in all kinds of ways. However, every now and again we encounter some unpleasant behaviours that need to be addressed. For instance, we often have a small but vocal contingent of campers who boast, at length, about their mathematical prowess. Last year, some of the staff had the idea of addressing these sorts of things by presenting humourous skits that parodied the unpleasant behaviour.
Fellow Mathcamp staff member A had the idea of writing a skit in which one character, played by me, would list all of the insanely difficult (”for a beginner, I suppose”) math classes she was taking. In researching for the part, we decided we needed to come up with extremely technical-sounding class names - ones that appeared to be about math, but were actually nonsense. We spent some time trying to come up with such technical sounding gibberish, until A had an idea: “Go to the ArXiv,” he suggested, “and look up quantum algebra!”

A simple permutation of preprint titles resulted in our fictitious braggart boasting about her exploits in hypercategory theory, m-difference representations, quantum affine algebroids, cohomology of semiregular twistor spectra, and quasi-coherent sheaves on Calabi-Yau manifolds, Moore Method.

I think our message got through. And if any of those topics do exist, I’m not sure I want to know.

- I taught two classes - a squishy, very visual version of projective geometry, and Calculus Without Calculus - to the best audience of ten that anyone has ever taught. Rather than having students bitch and moan about how I gave them homework that, like, was totally unfair because it made them
- And now I’m back at not-Mathcamp, still waiting the remaining two weeks for the hardworking bureaucrats at the Employment Insurance headquarters to finish transfering my file from one address to the next. Fortunately, as long as the good people at Texas Instruments have their claws in high school curricula, there will be work for unemployed math instructors willing to tutor high school math.

The kid I’m working with is in grade *n*, but I can’t for the life of me figure out what possessed any of his math teachers in grades five through *n-1* to promote him. He’s got a really good attitude about learning, and is on the whole quite pleasant to work with, though, so I shall lay off the snark. I’ll say only that if there is a Hell, I’d like to put in a suggestion to management that assign everyone who played a role in introducing calculators to the classroom to spend eternity watching eighteen year olds extract same from their backpacks, turn them on, and key in a sequence of commands in order to figure out what two times one half is.

i totally agree with your assessment of graphing calculators. My 2 experiences:

1) a quite bright 16-year-old during a test used her calculator to punch up 6*7. when i later asked her why she bothered, she said she just wanted to be sure she was right. at which point i asked her “supposing your calculator had told you that 6*7 = 46. would you think it was right, or would you think your calculator was broken?”

she broke out laughing, knowing that she would have figured her calculator was broken and that punching up 6*7 is therefore a complete waste of time.

2) on a no-calculator test about calculating with decimals, i have my 12-year-olds multiply some numbers that result in a product of, say, .0000084. then on a later test about areas, i allow them a calculator, but use the same numbers as before on one of the problems. of course, they don’t remember the problem, and use their calculator, getting a result of 8.4E-6. Invariably 3 or 4 of them come up to me to ask what that means (scientific notation doesn’t show up until later in the year). since i won’t tell them, they decide that the problem is impossible.

i don’t quite know what to do about the calculator problem: the strong students know when to use it to amplify their understanding, while the weaker students use it as a substitute for their lack of understanding. yet it’s exactly the weaker students who might need calculator skills later in life if they run across a real-world problem (oh, the horror!) that they can’t remember how to do.

most of them seem to buy the following argument: “yes, you could use a calculator here, but if you MUST use a calculator, i think you’re missing an important idea…so let’s put them away for now.” spoken at the right moment (like right after you’ve just multiplied 59*61 in your head at speeds they just can’t comprehend), a little demonstration of the idea they’re missing (a difference of squares works for numbers, not just variables!) can be quite instructive.

uhhhh also, at the risk of sounding self-aggrandizing…check out my new (2 whole posts as of right now) blog.

I’d rather like to know how you make a model of the real projective plane using carrots and toothpicks.

Actually, it would make some sort of sense to talk about quasi-coherent sheaves defined on Calabi-Yau manifolds… it’s not complete gibberish. Sheaf theory usually runs rampant in complex geometry, though, and Calabi-Yau is real, as far as I remember, so the actual utility of the concept would be low.

But you said that you weren’t sure you wanted to know…

“cohomology of semiregular twistor spectra”

Hey! I work on that! ;-)

Heh, Gorgasal, I thought something sounded familiar about quasi-coherent sheaves on CY manifolds. Probably because I took a course on them (among other things). I’d say that I don’t remember any of it, but that would be misleading, as it’s not as if I really knew any of it in the first place…

lsmsrbls - it was really just two triangles in perspective from a point - a carrot-and-toothpick version of a Zometool model I used extensively in class, and that doubled as a model of Desargues Theorem in three dimensions. Alas, the carrot model got soggy after a few hours, but it was pretty impressive while it lasted.

There is a special circle of Hell reserved for teachers who let students use their calculators to “learn” how to do operations with fractions. In that circle of Hell, these teachers are required to teach these same students how to manipulate rational expressions and do partial fraction decompositions. They are also required to grade their own exams on these topics, and made to spot all the errors and give partial credit. Whenever they overlook an error, they are whipped by demons with very nasty whips.