Tall, Dark, and Mysterious


…stay for the job security and benefits.

File under: Home And Native Land, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 7:52 pm.

I predict a sudden spike in the number of listless, ambitionless teenage boys who suddenly know exactly what they they want to be when they grow up. (Particularly what with the shortage.)


Learn only what I teach you, and teach me not.

File under: Righteous Indignation, This One Time, At Mathcamp, Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 5:34 pm.

One of my favourite classes to teach at Mathcamp is a bit of performance art I call “Calculus Without Calculus”. I cribbed the curriculum from a high school calculus textbook - take your pick - and from a class I took as a camper eight years ago, under the instruction of the inimitable Loren Larson. In my class, we solve a handful of calculus problems without defining a single function, evaluating a single limit, or taking a single derivative. My campers have eaten up the alternative methods, and often they return to camp the following year to tell me of the many calculus test questions they solved, for instance, by reflecting a line in the x-axis and doing three lines of simple calculations rather than setting a derivative equal to zero and doing a page or two of computation.

“I got a zero on the test for that question,” one camper reported, “because I didn’t use calculus.”

Another camper, who had two weeks of projective geometry but no calculus under his belt, used the former to find a tangent to a parabola. “I got it right,” he told me, “but my teacher didn’t know what I was doing and wouldn’t give me any credit for it.”

I can count on the fingers of one hand the number of times a university student of mine used anything but the method I’d taught them to correctly solve a problem. And I remember my reaction each of those times: I was ecstatic. I am pleased when students are able to apply what I have taught them, but I am delighted when they are able to think beyond my lessons and use prior knowledge to attack the problems I assign them. A handful of times at Mathcamp, a student will show me a solution that I’d never have thought of myself. It’s amazing to watch them assimilate my lessons and expose them to branches of mathematics about which they know more than I do.

Anyone who feels differently shouldn’t be teaching math.



I think about the lessons that some of my campers’ teachers, who scrawl big X’s through their students’ perfectly correct work, are teaching their students, and they appal me:

  1. Mathematics isn’t about logic, or reasoning, or thinking creatively. It is about following instructions.
  2. If the teacher has never before seen what you’re doing, then it’s not worth any credit.

My campers know math, and love it, and they know that they’re good at it. Other students could learn to like it if they were encouraged sufficiently. And I can guarantee that these lessons about what is and is not acceptable in a math class will stay with those students far longer than the lessons about factoring quadratics or computing derivatives or plotting ellipses.

So often I hear adults dismiss their high school math education with the comment that what they learned wasn’t useful, that it was irrelevant to their lives and their work. And in a way, they’re right: there is not a single job in the world which a person will be asked to optimize a solution by defining a real-valued function and setting its first derivative equal to zero, which, if their teachers are anything like the ones my campers describe, is what comprised their high school math education. There are, however, plenty of jobs, and plenty of everyday tasks, in which a person will be asked to figure something out from some numerical data. The method won’t be given - part of that person’s job is to figure out which method or methods should be applied. If you’re insisting that your students use the method that you taught them last week, and ONLY the method you taught them last week, to solve Question #5 on Test #3, then how on earth do you expect them to react when they encounter a mathematical problem that’s not quite like anything they’ve seen before, a year after they took your course? And if you dismiss a solution that doesn’t look like anything you’ve seen before, rather than ask your student for insight and clarification, what message does that send them? I’ll tell you what message it sends them: it sends them the message that they must work within the static confines of what you know. It tells them that in mathematics, the teacher, rather than the subject matter, decides what is legitimate. It discourages them from experimenting.

What a sorry way to do math. What a sorry way to do anything.

Working with tremendously talented students, I am aware that it’s not easy to stay on top of the workings of all of one’s pupils’ minds. By allowing students to give solutions other than the ones that I have in mind, I relinquish some measure of control over my curriculum, and that’s difficult. Often I’ll ask a question in class, and get a response that’s wildly different from the one I had thought of. Sometimes it’s tempting to nod and quietly dismiss the student’s answer, and give mine - the correct one - as an alternative. But I make a point of not doing that; instead, I’ll work through my student’s reasoning, on the blackboard if necessary, and after class if the complexity of the response demands it. Sometimes my student is wrong. But often, very often, they’re right, if in a roundabout way. Other times, they’ve come up with an explanation of a proof or a justification of a theorem that’s better than the one I had, but one that I had to think about. And I’m awed.

If I ever stop feeling that way, I hope that someone has the guts to tell me that I have outlived my usefulness as a math teacher.


Oh the possibilities:

File under: This One Time, At Mathcamp. Posted by Moebius Stripper at 5:09 pm.

One of our campers has diplomatic immunity.


With apologies in advance to all notaries public reading this

File under: This One Time, At Mathcamp, Home And Native Land. Posted by Moebius Stripper at 7:29 pm.

Last October, during the (Canadian) Thanksgiving long weekend when I was away, my apartment was broken into. My old neighbourhood is close to a forest, a beach, the university, and a bevy of amenities, and so it is populated primarily by rich people, and students living in rich people’s basements. A member of the latter demographic, I lacked many of the usual black market staples - computer, TV, DVD player - but was able to provide my visitors with a stereo, a discman, and a digital camera, the acquisition of which apparently required every single drawer in my small apartment to be emptied on my carpet. In the process of this, they managed to find, and snag, my (Canadian) passport. As though this weren’t enough, they celebrated by eating my soy ice cream, and then carted my belongings away in one of my suitcases.

The stereo, the discman, and the digital camera, I could live with, or without, as it were: none had any sentimental value, and they could be relatively easily replaced. The suitcase was insulting, but I had to respect the theives’ efficiency - why bring what you could just as easily acquire on the spot? The ice cream offended me mightily. The mess was a pain in the ass, but I dealt with it in much the same way that I deal with most messes that have afflicted my various apartments from 1997 to present, many of which have been only slightly less monumental than this one: I ignored it.

The passport was another story. I made a point of mentioning it when I filed the police report, and then I made a point of mentioning it again when I called for an update on the status of the police report, and then I made a point of mentioning it to the Passport Office.

This, apparently, was not enough; four months later, I went to apply for a new passport, which is now more of an ordeal than it used to be, because if the next terrorist attack on US soil was the fault of people with Canadian passports, the US will never reopen its borders to Canadian beef. Replacing a lost or stolen passport is even harder, thanks to the antics of the Khadrs, and so anyone who finds themselves in that unfortunate situation has to fill out PPT 203 (Statutory Declaration concerning a lost, stolen, damaged, destroyed, or otherwise inaccessible Canadian passport or travel document). This form requires one to complete sentences such as “I have made the following efforts to locate this document:” In that space, I wrote “I cleaned my apartment,” which was true, albeit after a week of stalling on the matter, but I doubt the Canadian government fully appreciated the effort this took.

Halfway through filling out this form, I read the actual instructions, which began:

This form must be completed before, and signed by, a qualified official who has the authority to administer an oath or a solemn declaration (e.g. a commissioner of oaths, notary public, lawyer, etc.)

Commissioners of oaths sounded intimidating, and lawyers sounded expensive. I phoned the phone and dialed the passport office. “Where do I find a notary public?” I asked.

“Where do you live?”


“Check the Yellow Pages. There should be several listed.”

And several there were. I couldn’t fathom how one perfect stranger to watch me fill out a form and scribble a signature could be particularly better or worse than the next, so I narrowed my choices down to notaries public that were within a twenty minute walk of my house. There were ten of them. I phoned them all.

“Harold isn’t in right now,” answered one secretary, in a conversation that would become frustratingly predictable over the course of the next ten minutes. “He’s gone home for the day.”

It was three o’clock pm.

Finally I settled upon Jim, who was a bus ride away, but on the way to the passport office. So that you may fully appreciate the service provided by this individual, I have reproduced in full our meeting below:

Me: Hi, I’m the one who called you about witnessing and signing my PPT 203 form.
Jim the Notary Public: Oh yes. Just fill it out and step into my office.
Me: Here you go.
JtNP: (scans form) Do you swear that this is true?
Me: Yes.
JtNP: Can I see some ID?
Me: (producing a driver’s licence) Here’s my driver’s licence.
JtNP: (glances at licence, stamps form, scribbles name) That’ll be $35.

This explains why notaries public, at least judging from my small sample, leave their offices before 3 pm.

Sometime later, I told this story to L, who saw opportunity where I saw a conspiracy between the Canadian government and the Society of Notaries Public. “$35? To sign your name and stamp a form? How hard could it be to get certified to do that?”

She started doing some research. Not hard at all, she found out. It varied from state to state. Here in Maine, you have to be a resident of the state to get certified, but that seemed to be the principal limiting factor. She started to look up the information for her home state of Minnesota. It’s right here: You have to be 18 or over. You have to live in a state that shares a border with Minnesota. You have to fill out some forms and shell out $40, which you can make back in your first ten minutes of being a notary public. But your responsibilities don’t end there: you then have to pay $25 to your court administrator, and purchase a seal. L tells me there’s some other thing you have to pay $100 for. And your responsibilities do end there. Done.

In British Columbia, the requirements are a bit sketchier:

To become a notary public, a person must be a Canadian citizen or permanent resident of Canada and apply to the BC Supreme Court for enrollment as a member. Applicants are screened as to their personal, financial, educational and business background, as well as their character, reputation and integrity

and if they pass, they have to take an exam after two years of education. Nevertheless, this is still an attractive enough career path than supply needs to be curbed:

The Schedule to the Notaries Public Act sets out the maximum number of notaries which can be enrolled in each district, ranging from, for example, one in the Town of Hope or Village of MacBride to 107 in Vancouver and 20 in Victoria. If the Court is satisfied there is a need, the Court can also order the enrollment of an applicant in an area outside a notarial district.

L is excited about this. There’s a folder on the camp computers titled “Notary”. Becoming a notary public became L’s goal. She told everyone of her plan. One day, at the cafeteria, she mentioned this, and a camper of ours remarked, “I’m a notary public.” His father was a lawyer, and figured that it didn’t take much to get his kid certified, so what the hell.

Somehow, though, she managed to forget who this camper was. “You forgot which of our campers is a notary public?” I exclaimed.

She shrugged. “We can ask around. We can ask them at sign-in tonight - ‘Are you a notary public?’ Maybe there’s more than one of them.”

We asked some campers wandering around. “No,” said S, “but my mom is. Why do you ask?”

Behind us, A overheard and asked what we were talking about. “Are you a notary public?” I asked him.

“No,” he responded, “but my dad is. Why do you ask?”

Yet another career option to file under my canned answers to “what are you going to be able to do with just a Master’s degree in math?”


Wow, all of my conversational pet peeves have names!

File under: Know Thyself. Posted by Moebius Stripper at 3:41 pm.

A pretty comprehensive list of conversational cheap shots, and more conversational cheap shots. I can’t think of a way to elaborate on these without sounding either a) passive-aggressive, b) arrogant, c) self-deprecating, or d) some combination of above, so I won’t try.

Okay, maybe a bit - some of these, such as the “Knee Jerk”:

“I would like to answer your question directly, but considering your past reactions / ability to cope with the truth / emotional instability, I feel that to do so would be a disservice to you at this time.” [Other person gets (justifiably) upset.] “See, what did I tell you. You are flying off the handle already!”

might be perfectly understandable, if not terribly sensitive or productive, responses to other tactics, such as the “Pretend Ad Hominem”:

make it seem as if the other person is attacking you rather than making a simple point or correction, especially if you suspect that the other party is correct. Rather than staying on the subject, begin to act hurt–as if you have been viciously attacked as a human being–rather than admit you are wrong, or could do better, etc.

“I can’t do anything right…”

“I suppose in your eyes I am just a total failure.”

[”I think the reason people are honking and gesticulating at you is that the sign says MERGE, not STOP.”] “Well, if you think me such a terrible, horrible person….”

Manipulativeness and emotional instability, alas, are far from mutually exclusive; if I were the betting type, I’d wager that they’re positively correlated. Which is part of why I deal with rudeness and overt hostility a lot better than I deal with insecurity.

Okay, maybe a little passive-aggression.


Lest there be any confusion as to whether or not I am a math geek

File under: This One Time, At Mathcamp. Posted by Moebius Stripper at 2:12 pm.

Here’s the joke circulating at camp right now:

Q: What did the natural log of the 16th primitive root of unity say after the pie was gone?
A: I overate.

Because the sixteenth primitive root of unity is e^(pi*i/8), and its natural log is pi*i/8, and when the pi is gone, that’s i/8…I overate…get it?

Well, we think it’s funny.

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