Tall, Dark, and Mysterious

8/18/2005

Is there a bike expert in the house?

File under: Know Thyself, I Like To Ride My Bicycle, What I Did On My Summer Vacation. Posted by Moebius Stripper at 2:47 pm.

Last time I asked, I received. Let’s see if this works twice…

The background: when I arrived back on the mainland last month, I decided that I was going to bike one thousand kilometers before the beginning of September. Biking here is a lot more pleasant than biking in Island Town: while the terrain is far from flat, it’s bikable, and there are enough clearly-marked bike routes that most drivers are not completely taken aback when they see someone commuting on two wheels.

Today, my odometer registered my one thousandth kilometer. In the past five weeks, I have travelled exclusively under my own power; this is the longest I’ve gone in years without setting foot in a car or bus. More amusingly, this is the longest I’ve gone in a year without setting foot on a boat - a stretch that will be broken soon, when I visit the last of the Gulf Islands.

Now that I am back in a bike-friendly city, I have become keenly aware that while my vehicle is an excellent car, it’s not such a great bike. It gets me up otherwise insurmountable hills, but it’s heavy, clunky, and awkward. So - I’m in the market for a new bike, a non-electric one.

Here’s what I am looking for:

  • I’d like to keep the cost of bike + gear under $500.
  • I live in a somewhat hilly city, so I’ll want a bike capable of handling hills.
  • I have bad knees; I’ve had a few flare-ups during which I could barely walk. Mild exercise keeps them in good shape, and biking is good for them; deep knee bends are bad for them. I’d like to get a bike for which my leg is extended completely when the pedal is at the bottom of the cycle; but setting the seat at such a position as to make that possible on most bikes I’ve ridden, doesn’t permit even my toes to rest on the ground when I stop. Do there exist bikes in which the pedals are not directly below the seat, but at an angle? Or pedals where the “up” and “down” positions are closer together than they are on most bikes?
  • In addition to having bad knees, I have a bad back. I’d like to be as close to upright as possible when biking; road bikes, therefore, are pretty much out.

Does anyone have any ideas?

8/15/2005

Adventures in Bureaucracy: An Appropriately Unwieldy Post

Or, How To (Hopefully) Get The Government Benefits You’re Entitled To In 100 Painful Steps.

First, a preamble, because reading this post will still be shorter than living it: When I was little, I was jealous of all of my friends whose parents had useful, easy-to-describe jobs, like doctor or teacher or dentist. One day in junior kindergarten, we had to draw pictures of what our mommies and daddies did at work, and our teachers then annotated the drawings as we dictated. I don’t remember what I drew for my dad (Mom, pregnant at the time, stayed at home with me) - I was four years old, so I assume that one picture of mine was more or less indistinguishable from the next - but the caption has been preserved in the family archives: “My daddy,” I explained, “plays on the computer and draws on the marker board.”

Umpteen years later, that’s still more or less the impression that I have of my father’s work, with one important modification: my daddy not only plays on the computer and draws on the marker board, he also meets with Important People in Employment Insurance. Which, at this point in my life, is a hell of a lot more useful than doctor or teacher or dentist. It means that my daddy, unlike yours, has inside dirt on the Employment Insurance department, such as “you fill everything out online but it’s all stored on paper”, “they don’t actually have a national system”, and “they tried to overhaul the system years ago, at a cost of six hundred million dollars, and it didn’t work. Now they’re trying to upgrade so they’re living somewhat less in the past.” Which, come to think of it, is not so useful, because anyone who’s ever dealt with EI could probably figure as much out themselves.

My mom, also not a doctor or a teacher or a lawyer, also has a job that has unexpectedly proven useful as of late. Mom’s job requires her to deal with disability and unemployment claims, and upon hearing that after two and a half months, I still hadn’t seen a dime, she knew exactly what I needed to do: “If you don’t get this one sorted out, call your MP,” she advised. “It’ll work. I don’t like to abuse that avenue, but it’s been long enough and you’ve tried everything else.”

I agreed to do it if it came to that, but I couldn’t imagine that being anything other than an exercise in frustration: I’d met said MP during the all-candidates debate last year, and he wowed me with his meticulously-honed ability to deflect every question directed at him by quoting irrelevancies from the Red Book. I figured a call to my MP would go something like this:

Me: Hi, I applied for EI eleven weeks ago. I haven’t seen any money yet, and my file has been frozen. Everyone I talk to tells me to talk to someone else, and as far as I can tell, there’s been no progress on my case.

The Honourable Mr. So-and-So: The Liberal Government is committed to streamlining the Employment Insurance application process. Under our initiative, the government has introduced computers to Employment Insurance offices across the country. By 2008, we will have invested $10,000,000 in hiring seven new staff who can program them to review your application instead of sending it into a black hole.

Fortunately, it didn’t come to that. What it did come to was this:

Claiming Employment Insurance Benefits: A Saga In N Parts, For N Large

April, 2005 - contract at Island U expires. Island U efficiently sends a Record of Employment to my permanent address. Permanent address is parents’ home, as I have moved ten times in as many years.

May, 2005 - I fill out massive online Employment Insurance form, putting my parents’ address as my permanent address. Upon finishing, the EI website tells me to spend the next four weeks waiting for my claim to be processed.

June, 2005 - Computer dies. Meanwhile, back East, letter from EI arrives at parents’ house, directing me to fill out my first three reports online. I fill out the first, at the local library. EI website thanks me for the report. I try to fill out the second, and this time, the EI website isn’t so happy about that state of affairs, and orders me to call their 1-800 number.

Dutifully, I call the 1-800 number, and get passed along to four different EI workers until I get someone who knows what’s going on. This EI worker is a computer-savvy one, who knows that the online report-filing system traces IPs and figured out that I was filing my reports from BC, not from out East. Bad Moebius Stripper! No benefits for you! I object, saying that I’ve been looking for work in BC for months. Helpful EI worker helpfully tells me that she will transfer my file to BC, and that I will be notified four weeks later, when the file has been successfully transferred. After receiving this notification, I should present myself to the local (BC) EI office with proof that I have been actively seeking employment in this province. “In other words,” she paraphrases, “for now you just need to hurry up and wait.”

July, 2005 - I hurry up and wait, all the while continuing to be available for suitable employment. Nothing happens. At the end of the month, I figure that even accounting for our notoriously slow postal service, it’s been too long since I’ve heard from the EI folks, so I present myself at the local office and explain my entire story to the woman at the counter, to the consternation of the half-dozen people standing behind me in line. The woman at the counter nods sympathetically, and at the end of my five-minute spiel, she takes action: she picks up a sheet of paper from the desk, highlights a 1-800 number on it, and instructs me to phone it.

August, 2005 - I phone the 1-800 number, and tell my entire story again, intending to add the part about how I stopped at the office to talk to a human being and was directed to the hotline. The operator looks up my file, putting me on hold twice in the process. “Ah,” she says finally. “There’s been a disentitlement placed on your file.”

“I beg your pardon?”

“You were listed as living out East, but our records indicated that you were actually in BC, and hence not seeking employment out East, so we’ve put a block on your file.”

“I had my file transferred,” I explain, AGAIN, “because I was never actually living out East. The reason I had my file transferred was because I have been actively seeking employment in BC all along, JUST LIKE I AM SUPPOSED TO.”

Without missing a beat, the operator says, “Well, then, in that case you’ll have to visit your local office in person, and explain that to them.”

“I did,” I reply. “They told me to phone this number.”

At which point, the stars align, or something like that, because GLORY BE, the operator says, “I’m going to put you on hold and contact a senior manager about this.”

Muzak plays. A few minutes later, the operator, invigorated, declares, “Here’s what I’m going to do. I am going to send a notice to your local office instructing them to remove the disentitlement. This will take up to two days. I will also tell them that you will be visiting them in person. Bring with you a list of job applications you’ve sent out, interviews, and so forth. They will then review that, and when they see that the disentitlement has been removed, they will be able reactivate your file.”

I thank her.

Three days later (two days to remove the block + margin of error) I arrive back at the local office, and present myself, along with my list-o-job-apps to the woman at the counter, who’s the same woman who had told me to call the 1-800 number a few days earlier. I give her the page. She takes my SIN number, and sends me on my way.

“When should I expect to see some money?” I ask.

“I can’t tell you that,” she chirps, and produces an info sheet from her desk. She highlights a 1-800 number. “You’ll have to call this number.”

“When?”

“You can call them now. There are phones by the back wall, with direct lines to the BC office.”

(Reread that part: There are phones in the local Employment Insurance office that connect you to the national Employment Insurance office. This is an institution that actively embraces its inefficiency.)

“They know stuff about my file that you don’t know, having just dealt with me in person?”

“Yes, they have that information. We just added an extra phone, for your convenience.”

I trot over to the convenient new phone, pick it up, request a human being, and tell my entire story AGAIN. The operator is confused. “I wouldn’t have that information. You’ll have to visit your local office -”

“Well, that’s convenient,” I reply. “I’m at my local office right now!”

Back to the counter, to the woman with the 1-800 fetish. “They sent me back here.”

“Okay,” she says, “I’ll put you in line to meet with someone. There’s a 20-minute wait.”

Fine.

Again the stars align, and exactly twenty minutes later I’m talking to this really patient man whom they surely hired by accident, because he’s so very good at his job that I am completely taken aback. For one, I don’t have to tell him my story, because he’s been spending the last ten minutes reading it. I ask him when I can expect to see some money.

“Well,” he says, “first we have to remove the disentitlement from your claim. From there it will be two business days.”

“The person I spoke to on the phone said that it would take two business days from the time I phoned to remove the disentitlement, and that I should hand in my list of job applications after that.”

He shakes his head. “Oh, no. We can’t remove a disentitlement until after you come in with your account of job applications. It will be two business days. Who told you otherwise?”

I provide a name.

He continues: “I see that you filed the original claim over ten weeks ago, so you’ll be wanting retroactive benefits. Did you already fill in that form? I couldn’t find it at the front desk.”

I reply that I didn’t know that there existed such a form, and that I thought that the retroactive benefits went without saying when I told Ms. 1-800 at the front desk that I’d filed the original claim ten weeks earlier.

“Hmm,” he says, “she should have given you the form to fill out. I’ll get one for you now.”

Translation: Ms. 1-800 is inept even by EI standards, and I’m grading on a VERY GENEROUS CURVE HERE, PEOPLE.

The guy returns with the form. I observe that I have half a page to explain why I haven’t filled out the biweekly reports for the last ten weeks. “Half a page?” I say. “You’ve seen my file.”

“You can use the back if you want,” he offers.

“Can I attach additional sheets?”

Five minutes later, having availed myself of the stapler on the desk, I complete the tome (”Please see my file for more details,” I conclude sadistically), and hand it to the fellow. He tells me that I should be seeing some money in two business days. I remark that I’ll believe that when I see it. I am not being rude, but I am obviously frustrated, and he responds in quiet, soothing tones - much as I do when dealing with those students of mine who are not being rude, but who are obviously frustrated. Amusingly, even though I know what he is doing, this technique works perfectly on me, and I calm down. I thank the fellow, and leave.

Two business days later, I call the 1-800 number, which I now have on speed dial. I listen to the automated service, which, disappointingly but not surprisingly, informs me that there has been no activity (none!) on my file in the past two weeks. I summon a human being, and go over my story, again, to be told that it will be three weeks before I see any money.

“I was told two business days,” I report.

“That’s incorrect. Who told you that?”

I provide a name.

The operator tells me that she’ll have someone phone me within the next two business days to discuss my situation. I reply that I’ve spent two and a half months discussing my situation, and while that’s certainly been lots of fun for all involved, at this point I’d really prefer to just get some money. She tells me they’re working on it.

Two business days pass. No one phones.

I present myself to the local EI office again, and tell an abridged version of my story to Ms. 1-800. I can tell it’s a whole new story to her, because her face registers no hint of recognition despite the fact that we have met three times before. I can’t really blame her, though; she probably meets a lot of disgruntled unemployed people with similar stories, and sooner or later they probably all blend together in one amorphous mass of disgrunt. “Hmm,” she muses sympathetically, and produces a sheet of paper. “You should call our 1-800 number. There are phones at the back…”

Because there’s no one waiting in line, I seize the opportunity to tell her the entire story, including detailed descriptions of my experiences with her, my experiences with the 1-800 number, and my experiences with her telling me to call the 1-800 number. I request an appointment with a human being. Request granted.

Twenty minutes later, I am sitting with a human being, who tells me that she doesn’t know what that other person was talking about, because it’s never two business days for the file to be processed, it’s one week. But, she tells me, it’s a good thing that I came into talk to that other person, because when you come talk to someone in person, they put your file on someone’s desk, whereas when you just drop off your materials at the front desk, they sit in someone’s outbox for two weeks before getting processed. She tells me this like it’s standard procedure. She dispatches me, telling me that it takes a week to process my file, no, really this time, and if it’s not processed then, to come back.

It’s not processed within a week. I come back and wait in line, and hear the teenaged girl directly in front of me explain that she has a Social Insurance Number, it’s just that she suspects that her mom has been using it illegally to get work. This is taking a long time, and the girl turns around at one point, sees the huge line behind her, and apologizes. I tell her that she’s not the one who should be apologizing, and that I hope she gets her stuff worked out, and that she should take as long as she needs to get this taken care of. She smiles.

When that’s done, I deal with - hallelujah - someone other than Ms. 1-800, who makes an appointment with a human being for me. The wait is short, because while the teenager was trying to get the SIN crap dealt with, the people in front of me got processed. I am called within two minutes, by a tanned woman with frizzy white-blond hair. I walk over to the desk, resolved to play the I’m going to call my MP about this card if my file doesn’t get processed right then and there.

But my resolve weakens when the blond woman gives me the most pained look I’ve ever seen from a government official. “I’ve been reading your file,” she tells me, “and reading and reading and reading it. Dear Lord. We’re going to get this resolved right now.” And then she explains that she is going to personally hunt down the person in charge of my file, and wait as he processes it. I am awestruck.

She phones the person in charge of my file. He does not answer. My heart sinks.

But, get this: the next few minutes consist of this woman, the patron saint of mismanaged EI files, running back and forth, physically hunting down this person. “He’s probably on coffee break,” she tells me. “His secretary tells me he’s in today.” She explains that this might take a few minutes, because she usually works in the call centre, not the local office, so she doesn’t know what this fellow looks like. She dashes off before I can tell her that I don’t mind waiting a few minutes to get my benefits.

Ten minutes later she announces, out of breath, that she found him, and that he’s in the process of looking at my file for the first time. I lean back in my chair and wait, because this can take awhile.

Shortly afterward he phones, and I hear one side of a conversation that goes something like Speaking…no, see, this needs to be dealt with NOW…this woman has been waiting almost three months…she’s filled in all of the relevant forms…yes, I KNOW, but this person keeps being told that it’s going to be taken care of soon, so please just take care of it now and get it over with…okay, thank you.

She hangs up. “It’s all taken care of,” she tells me. She doesn’t seem surprised that taking care of the thing that needed taking care of took all of five seconds once she got a hold of the person responsible. “You will have your money in two business days.” She then takes some information from me, and fills in the last ten weeks’ worth of reports. “Done,” she reports.

I thank her and thank her and thank her, because if she’s not sincere, then at least she’s just given an Oscar-worthy performance.

One business day later, I call the 1-800 number, and for the first time I’m told something other than the fact that there has been no activity on my file. Today, I check my account, and find that my balance has an extra digit to the left of the decimal place. It’s over.

My first purchase is going to be a bouquet of flowers for the last person from the EI office I spoke to.

8/11/2005

Moebius Stripper offers sales and marketing advice to a local entrepreneur

File under: Talking To Strangers. Posted by Moebius Stripper at 4:01 pm.

The other day, while I was unlocking my bike from outside a restaurant downtown, a scraggly-looking man with bloodshot eyes zigzagged over to me and asked me if I knew what time it was. I did, and provided it, even though the fellow didn’t look like the type who had a schedule to keep.

He thanked me, and then squinted at me. “C’Iaskyouaquesshun?” he slurred.

“Sure,” I replied. Why not.

He contorted his face and fixed his red eyes on me. There was a long pause before he took a deep breath, summonning the power to let his frantic query tumble out: “D’yousmokeweedPLEASESAYYES.” This last part was barked with an urgent clarity that almost made me feel like picking up the habit.

But, “Sorry,” I said, and I was.

His face fell. “Y’don’smokeweed?” he asked, surprised.

“No,” I repeated.

“You? Don’smoke weed?”

“Nope,” I confirmed, flattered that someone found it implausible that a square like me could possibly not smoke weed.

He shook his head, and then tilted it up at me. “No shit?”

“No shit.”

He thought for a minute. “Aw, fuck,” he said, and withdrew a crinkled baggie from his pocket. “Thisstuff’ere,” he explained, shoving it an inch from my face, “Triple A, twennybucks. Bespricentown.”

“That is a good price,” I said, because I had no reason to think otherwise.

He nodded. “AnnIdunnowhyIcange’ridovit.” He looked up, despondant.

Since I do not, as established earlier, smoke weed, I had the advantage of not being high on weed at that moment, and consequently I possessed a mental clarity that was conspicuously absent in my interlocutor and probably had been for some time. “Well,” I offered, “We’re in Chinatown. Chinatown isn’t known for its weed market. A lot of people here don’t speak English. And it’s a tightly-knit community, so people who do smoke weed probably buy it from people they already know.”

He paused. “Fuck,” he mumbled.

“But,” I said, “The Marijuana Party office is six blocks away from here, and there’s a shop nearby that sells…related merchandise.” I know this because I read the news.

He looked up. “Theresamarijuanaparty?”

“Based six blocks away.”

He thought about that. “They probably smoke weed there.”

“That’s my guess,” I replied. “Here’s what you should do. Stand about a block away from the Marijuana Party office, and offer your stuff to people who walk by. Someone in that area is going to want to pay twenty dollars for that triple-A stuff you’ve got there.”

“Yeah,” he said, his voice brightening. “Where’sissplace?”

I pulled out my map and showed him, and then I pointed him in the general direction.

“They’ll buy my weed,” he said optimistically, reenergized by this new strategy.

I hope they did.

8/8/2005

Out of the mouths of babes

File under: Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 7:04 pm.

The student I’m tutoring, explaining why he didn’t do the last five questions of the homework, each of which defined a new term, and then required students to investigate how it applied to a few given functions:

These questions seem like they should have been in the lesson, not the homework. It seems like they’re trying to teach me something new.

God forbid.

The result of this unfortunate run-in with new material in the homework, of all places: we took a half hour break from going over new mathematical content, to spend on developing the skill of reading mathematics. Teaching this is easier than it sounds, when you’re starting from zero and dealing with straightforward material: today’s lesson consisted of me asking him to read the definition, and then following up with such prompts as “ok, so now what is the question asking?”, “What should we do?”, and “How can we do that?”, all of which he answered correctly. Not bad for someone who reaches for his calculator every time he is required to add one single-digit number to another.

“You did all of that by yourself,” I pointed out when we were finished. “Why couldn’t you do it last night?”

“You were here this time,” he replied.

“Yes, and I prompted you,” I agreed, “but the questions I asked you weren’t the slightest bit leading. I just told you to read the question, and then I asked you what the question was asking, and how to go about answering it. Basically - I asked you the stuff that the question itself is asking you to do. And you did that all - correctly.”

He thought for a minute. “I guess,” he said. He then paused, and looked up as my statement registered: “So I’m supposed to be doing that whenever I see a question I don’t know how to do?”

8/7/2005

Different learning styles versus different content

File under: Those Who Can't, XX Marks the Spot, Know Thyself. Posted by Moebius Stripper at 3:32 pm.

A cognitive scientist is asked whether visual, auditory, and kinesthetic learners need to be taught according to their individual learning styles, and he responds with an unqualified no:

What cognitive science has taught us is that children do differ in their abilities with different modalities, but teaching the child in his best modality doesn’t affect his educational achievement. What does matter is whether the child is taught in the content’s best modality. All students learn more when content drives the choice of modality.

Link from Kimberly Swygert, who comments:

if a school believes in teaching students mathematics through songs and artwork, it would be nice if they backed this up with research indicating whether these are effective methods of conveying mathematical knowledge.

This is the real issue, I think. The issue isn’t that teaching a subject, say, kinesthetically doesn’t help a kinesthetic learner understand the material better; the issue is that teaching material kinesthetically may compromise the content. If you’re teaching students how to add fractions, for instance, then whichever way you do it, the student should know how to add fractions by the time you’re through. I don’t know of any tested methods of doing that through songs and artwork (though I like to present mathematics geometrically whenever suitable). The inability to convey certain content is why the songs and artwork method will probably fail. The notion that the “learning styles” philosophy is bunk, isn’t.

I’ve seen learning styles and content confounded regularly in my work. I routinely have students tell me that they’re having difficulty with the way I’m teaching, what with their learning styles not meshing with the way I conduct my course. Never has a student gone on to tell me that they process information in a more kinesthetic way than my teaching permits, or that they find my wordy notes confusing. Sometimes, “I have a different learning style” is just code for “I don’t want to do my homework“. Other times, it means “I don’t understand the material at all”, as when a unique-learning-styled individual tells me that they’d have no difficulty with the word problems I assigned, if only I provided the formulas with the text. (Hypothesis, based on personal experience: on balance, psychology majors who don’t get what you’re teaching are more likely than average to merely have different learning styles that you’re failing to recognize.)

I read of a particularly disturbing example of this confusion between differing learning styles and differing content around two years ago, in an article about a Vancouver Island junior high school. The school had recently decided to experiment with sex-segregated English and math classes. From what I gathered from the article, there were two reasons for this. The first was that boys and girls learned when they weren’t distracted by members of the opposite sex. The second was the “learning styles” argument, which submitted that girls’ brains were made of sugar and spice and everything nice, whereas boys’ were composed of frogs and snails and puppy dog tails, and so, it made sense to teach in accordance to those needs.

I’d read an article in Scientific American not long before, and it described at length and in details the difference between male and female brains. I found one observation very interesting: men and women of equal mathematical ability used different parts of their brains in solving mathematical questions.

This research played no role, however, in designing the Vancouver Island school’s sex-segregated math classes. The principal explained that boys were more adventurous, and so, the boys’ math class would be very “hands-on”: the teacher would present a new topic in limited detail, show and example or two, and then send the boys on their way to experiment with a variety of different homework problems that used the new concept in different ways. The girls, explained the principal, weren’t much for trying new things on their own, so they’d get to read about the new topic first, read dozens and examples, and then work on some homework problems that looked just like the dozens of examples they’d seen. This would build confidence, asserted the principal.

I wrote a letter to the editor, explaining math is hands-on, and that from the perspective of someone who’d taught math at the university level, the boys’ math class sounded like math, whereas the girls’ class sounded like math-lite. Reading examples before working on identical questions with the numbers changed is not “teaching to a different learning style”; it is teaching different material. In particular, this is not math; it is the mindless application of algorithms, designed to prop up mathphobic girls rather than educate them. The lucky boys, meanwhile, actually have an opportunity to apply the concepts they’ve learned and not just parrot back formulas - something that would prepare them for more difficult mathematics. If you’re using a different metric to measure whether a student has learned a subject, you’re probably not merely using a different teaching style to convey it. More likely, you’re teaching different material altogether.

More at BrightMystery, where a commenter remarks:

Perhaps it’s more important for a student to know their learning style than for a teacher to teach to it. Then the student can make whatever adjustments are needed in their classroom and study habits (as well as out of classroom time with the instructor).

Absolutely. I know that I, for instance, am a highly visual and verbal thinker. I learned how to read at the same time as I learned how to speak. From my earliest memory, during conversations, I would visualize what people were saying to me, typed out on a screen in my head. To this day, I do this whenever I need to make sense of difficult material that I encounter in spoken form: I freeze the material in my head, so that I can go back and mentally read it. It helps me, then, to take copious notes in the classroom, but I don’t expect every single teacher of mine to accommodate this preference of mine by writing everything down on the blackboard. Instead, I make sure that the notes I take in class are a proper superset of what’s on the blackboard. If anything, this is more helpful than having a teacher who writes down absolutely everything, because this way I have to be completely engaged while I’m in the classroom. Overcatering to differing learning styles, I’d wager, results in passive learning.

8/4/2005

Bookmarked for when my college students complain that my class is too hard

File under: Queen of Sciences, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 8:13 pm.

In what was to be one of many Dear God, what did my students even LEARN in the first dozen math classes they took? moments last year, I had a student come to my office for help with a linear equation he couldn’t solve. “I don’t know why I can’t get this one,” he said, and showed me one of the homework questions: Solve for x: x/4=(x-3)/3+1.

“Show me what you did,” I instructed, and he obediently went through the steps, reversing order of operations, just as he’d been taught. “And I got x=0,” he reported.

“Okay,” I said. “What’s the problem?”

“x can’t equal zero,” he explained *. Then he paused, and said, “Can it?”

“Why not?” I replied. “Zero is a number, isn’t it? And when you plug it into the original equation, it checks.”

“I guess,” he said, but I could tell he wasn’t convinced.

My student didn’t understand the concept of zero. Alex, on the other hand, understands the concept of zero:

“Alex has a zero-like concept; it’s not identical to ours, but he repeatedly showed us that he understands an absence of quantity.”

That’s Alex the African Grey parrot. And, I mean, I used to have pet parrots, and they were actually really, really smart - smarter than anyone expected - but goddamn that there are humans that age who’ve taken a dozen years’ worth of math classes who don’t seem to have attained that level mathematically.

* And now, my attempt to make sense of this absurdity, which I’ve encountered more than once: I suspect that somewhere along the way, my students were told “You can’t divide by zero in an equation”, which they processed as “blah blah CAN’T blah blah ZERO blah blah EQUATION”, like in the Far Side cartoon. Makes perfect sense now, doesn’t it? This sort of thing explains a variety of student errors, such as how an offhand mention of “you can’t use the quadratic formula to solve an equation if there’s no x2 term” got applied as “you can’t solve an equation if there’s no x2 term” by a college student who didn’t understand why her explanation of x-3=0, therefore, no solution didn’t get the full credit that IT SO CLEARLY DESERVED.

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