Tall, Dark, and Mysterious

4/21/2005

Exam notes: qualitative

File under: 1000 Words, Those Who Can't. Posted by Moebius Stripper at 3:46 pm.
  1. Despite the fact that marks-wise, I was most disappointed by the statistics students (several of them can’t plug numbers into their calculators! I gave them a formula sheet! They copied the correct formula down correctly! Wrote down the correct numbers for the variables! And got the wrong result!), their papers were the most enjoyable to grade, because the statistics students tended far moreso than the students in my other classes to leave me little notes about how they felt about the material. For instance, I had a probability question about a die-rolling game, which one girl opted to inform me was the “stupidest game EVER.” Another student (correctly) subjected a manufacturer’s claim about its products to statistical analysis before stating her conclusion, as instructed, “in [her] own words”: “It’s TOTAL BS!” Also, my attempt to make mathematics relevant to the lives of my students succeeded in the mind of one student: I included a question in which students were to test a hypothethesis that women generally underreport their weights, which prompted one pupil to write sic, “OMG THIS IS SO TRUE, I DO THIS ALL THE TIME.” (She did the question incorrectly.)

  2. Aside to all students reading this: if you are ever asked to define a term on a test, and you don’t remember what that term means in the subject - for instance, math - that the test is about, try analyzing the language in the term. I mention this because hardly any of my students were able to tell me what mutually exclusive events were (most gave me the definition of independent events), even though realizing that “exclusive” and “exclude” contain the same root just might be enough to jog the memory. The only student to attempt a linguistic desconstruction was an Asian girl whose English is shaky. “Mutually exclusive events,” she wrote, “are events which are very special…”

  3. Back to the die-rolling game: when my contract expires at the end of the month and I am without regular income, would it be unethical to engage some of my former students in various games for money? I have certain students in mind, such as the guy who wrote that if you play one hundred rounds of the game that costs you $4 per round and that pays you the dollar value of the number appearing on the top face of the die, then you can expect to make $2000.

  4. The college where I work prides itself as being “student-centred”. Part of what this means is that the many, many student lounges are located “centrally”, like right outside classrooms and adjacent to them. I submit that if there was ever a good reason to revoke an architecture degree, then surely this design is it. Precalculus was held in a lounge-adjacent room, as was the statistics exam. During both, students were in the lounge, chatting at perfectly normal volumes, which was enough to create a distraction for me and my students. On approximately fifty occasions this term, I had to enter the lounge to request quiet, because a dozen students talking quietly results in a din that is not quiet. On forty-eight of these occasions, students were apologetic and lowered their voices accordingly, which helped things for the next twenty minutes until either a) they got excited about something else, or b) they were replaced by an uninitiated group of students. (Large signs in the lounge requesting quiet do not help.)

    The other two times, I had the pleasure of dealing with one girl who asserted her rights to sit at the lounge and talk because “this is the only place where we can do this”, where (judging from the lack of books or anything else on the table where she and her friends were sitting) “this” consisted of sitting and talking with two friends in the lounge outside my classroom. She told me that this was “total bullshit” and that “maybe I should use a different classroom”, as though it was my decision to teach and hold exams in a room that is a ten minute walk from my office and is located right next to a student meeting hub that has the acoustics of a cathedral. When I quietly explained that although perhaps the lounge was the only place where she could do “this”, it was even more certain that the adjacent classroom was actually the only place where my students could write their exam for the next twenty-five minutes, she declared that this was TOTAL BULLSHIT. WE ARE TALKING AT A NORMAL VOLUME, which at that point was no longer true. Grasping for common ground, I started to tell her that I was in agreement with the bullshit assessment, and reached into my pocket to call campus security on my cell phone when her friend - bless his heart - said, “Come on, we can go somewhere else for the next half hour…there’s an exam, she’s asking us nicely.” And that, apart from an evil eye directed my way (me without my camera, I tell you), was the end of that.

  5. Often I get teaching advice from my readers. I should do dimensional analysis! I should make math relevant to their lives! I should relate the difficult concepts they’re studying now to the easy concepts they’re familiar with!

    Generally I smile and nod, because I think that few of my readers know what I’m dealing with. Allow me, then, to present an example of what I am dealing with:

    The question, which is a bit unclear in the image, reads “Solve for x: 4x+2(1/2)-2x = 8x+2.” The student’s work, which follows, resembles the sort of thing junkies might hallucinate if LSD induced images of equations. Notice how the variable x goes missing in the very first line of this “solution”, leaving an equation that reduces to 0=0, which is then tortured until it finally gives up the ghost - though not before confessing, in its dying breath, that x (remember x? it’s back!) equals 50. Note also how the declaration that we “can’t have negative numbers” (surely a surprise to those of us who have endured frigid Canadian winters during which the temperature dipped to…oh, CRAP) apparently allows us to do away with them altogether, on our own terms, and at our leisure. (Ernie has taken the time to transcribe this work of art, in toto.)

    No, this corruption of reason is not representative of a typical paper in my precalculus class. However, it is representative of a typical page of this student’s exam (she got a 3% on it, and this was with me assigning marks to everything that even vaguely resembled mathematics - by the way, she sat in the exam room for an hour and a bloody HALF tormenting her paper; I left out the question in which she concluded that a $1000 principal invested at 4.8% per year compounded continuously yields $240,000 after five years, and I also left out around ten others that I could easily have posted instead of the one above), and I have had, on average, two students like her in every class I have taught in the past five years. I guess I could have spent more time on dimensional analysis and such, but somehow I don’t think it would have helped that much.

    (ETA: By popular request (okay, one person asked, but apparently he speaks for all), here’s more of the exam.)

  6. One of my students missed an exam because of a dire family situation, which now requires me to navigate that murky territory between being sympathetic and being a sucker. I don’t want to get into too much detail, but suffice it to say that Distressed Student is both suffering a terrible crisis, and attempting to play the system like it’s going out of style. I’ve had to outline explicitly what I am and am not willing to do to accommodate her. For example: I am willing to allow her to write the exam a month from now, but I am not willing to just assign her a final grade that assumes that her exam grade would have surpassed the class average by nearly 10% when her term test grades consistently fell far short of it. As evidence that this student’s family crisis is not the only thing standing between her and such success on the final exam, I present the email she sent me the other day, which read, in part, Since I am going thru such difficulties would you be able to just make my term mark my final grade? Right now I have 41/65 on the quizzes and tests. I have been meeting with a math tutor for the past few weeks and he told me that this is a 63%, which is the mark I need in this course.

Exam notes: quantitative

File under: Those Who Can't. Posted by Moebius Stripper at 1:26 pm.
  1. Number of pages of exams graded in the past six (6) days: 1344

    • For precalculus: 392
    • For calculus: 280
    • For statistics: 644
  2. Average number of unclaimed tests/quizzes sitting in my office, per student, in
    • Precalculus: 2.7
    • Statistics: 1.1
    • Calculus: 0.5
  3. Number of students enrolled who didn’t show up for the final exam: 5
    • Of those, number who have dealt with situation quickly and painlessly: 2
    • Number who are being ongoing big pains in the ass to deal with: 1
    • Number who have said nothing and who, judging from their term marks, can safely be assumed to have dropped the course, in spirit if not in writing: 2
  4. (Inspired by Becky) Pearson’s correlation coefficient relating position of statistics student’s surname in alphabet (46 students wrote the exam) with student’s exam grade: 0.466.
    • Probability that the correlation in a simple random sample of size 46 would be so strong if there were, in general, no correlation between surname and exam grade: less than 1%
    • Regression equation relating student’s grade y to first initial of student’s surname x: y=52+0.94x
      • Predicted grade for Aaron Aaronson: 53%
      • Predicted grade for Ziggy Zuckerman: 76%
    • First initial of Needs-a-B’s surname: B
    • Actual exam grade of Needs-a-B: Less than 50%
    • Number of mistakes on Needs-a-B’s exam that were identical to ones she’d made several times before, on quizzes or tests, and that I’d addressed explicitly with her during my office hours: 4

4/16/2005

But in a way, everyone loses.

File under: Those Who Can't. Posted by Moebius Stripper at 4:17 pm.

That was painful, but now it’s over and we never have to think of it again.

In first place is Dr. Matt, with a whopping twenty squares. The squares he didn’t get, were largely for reasons such as “students all have fraction-doing calculators anyway and even if they can’t add them it’s possible that such a thing won’t come up”, and “I gave them the axes so they didn’t have to draw any, let alone label them.”

In a distant second is Meep, who also made bingo with thirteen squares. Meep had a lot of close matches: for instance, none of my students “forgot to add both sides when completing the square” so much as they just plain “forgot to complete the square.” And although none of my students derived a fractional answer for area, which they claimed couldn’t be possible, around half claimed that the polynomial f(x)=x^3+5x^2+x-2 had no zeroes in the interval (-5,1), just because they were able to figure out that it had no rational ones. It’s almost as though we didn’t spend two weeks on approximating irrational zeroes of polynomials. (Seven students claimed that it had one zero - the one halfway between -1 and 1. For this insight I added an additional zero to their papers.)

In close third is Moses, with eleven squares. Moses, alas, overestimated my students with predictions such as “Student derives trivial equation, gets confused “. Moses, my naïve friend - the half-dozen-odd students of mine who derived the trivial equation didn’t get confused in the least. They just concluded that x=0 or somesuch, and moved right along.

Bringing up the rear is James, with a measly four squares. I must say, though, I’m surprised that none of my students asked me how to do the exam questions during the exam period. I have trained them well.

* * *

Despite this, the exam wasn’t quite the bloodbath I’d anticipated: average was a pass, failure rate was only 40% for the exam, and a bit over 20% for the course after I applied a small linear scaling that bumped up three high F’s to D’s. Almost half the class got B-’s and above. But the bad papers…Lord Almighty, were they bad. I don’t have a scanner handy, but later I’m going to see if I can get some decent quality photgraphs of one exam that earned a grade of three (3) percent. It wasn’t mostly blank, either.

4/15/2005

Let the games begin.

File under: Those Who Can't. Posted by Moebius Stripper at 2:52 pm.

I don’t know exactly what combination of amused and disturbed I should be at the knowledge that some of my readers are apparently marking their calendars with my students’ exam dates, but in any case, yes, it’s true, my precalculus students wrote their exams yesterday. And that means that I’ll be spending much of this weekend grading them. And that means…it’s bingo time!

The First Annual TD&M Precalculus Bingo Contest drew four entries, all from people I know personally, which means that if I stiff the winner on their prize then they’ll probably forgive me, because being my friend is reward enough. Let’s meet our contestants, shall we?

Meep is a former mathematics graduate student, currently employed as an actuary in New York City. She’s taught plenty of intro-level mathematics classes, and has seen more than her share of exam wackiness such as “Copies full text of question in the answer”!

Dr. Matt, who works as a discrete math professor south of the 49th parallel, was a few years ahead of me at our alma mater. He edited the math faculty humour magazine for some time, so he knows math funny! When I pointed out that my class didn’t cover complex numbers, he told me that he wasn’t going to change his prediction that my students’ exams would contain “Misguided adventures in imaginary numbers”. Matt knows that precalculus students don’t have to know what imaginary numbers are to take square roots of negative quantities!

Also teaching discrete math in the United States is Moses, who predicts that a student of mine will “ask for exam average within 24 hours of writing exam”. If we can count an email that a student sent four days before writing the exam, requesting that her grade be computed even before she’d be finished writing it, then Moses is well on his way to precalculus bingo victory!

Finally, James goes for broke with predictions such as “Bomb threat called in during exam”. Fortunately, that didn’t happen, but James isn’t out of the running yet!

Who will win? Stay tuned for breaking updates of Precalculus Bingo!

4/13/2005

In Which Our Protagonist Learns The Importance Of The Base Case

File under: When We Were Young, Queen of Sciences. Posted by Moebius Stripper at 6:35 pm.

Mike, by way of Michele, shares 25 of his favourite memories from Sesame Street, which reminds me of the time Big Bird made me cry.

I was three years old. By this point in my life, the residents of Sesame Street had educated me about as well as any community of puppets could reasonably be expected to educate any small child. Family legend has my father holding me, age fifteen months, as he selected an ice cream treat from the Dickie Dee vendor outside our Virginia home. I don’t know if I recognized the varieties of snacks, but apparently I could make some sense of their names. “I,” I enunciated, pointing. “C. E. C…”

Incredulous, my father informed my mother, “She knows letters.” Since neither of them had thought to teach me the alphabet by that point, Cookie Monster and his friends were quickly credited with this development. I soon learned the rest of the alphabet with the aid of refrigerator magnets and blocks. A few months later, I was reading.

With the alphabet under my belt, I turned my attention to the Count’s endless enumeration of everything under the sun, and within less than a year I could rattle off the integers from one to two hundred in sequence. Two hundred exactly, by the way, and no further. Why I knew that one hundred and one came right after one hundred but was unable to extrapolate any further I have no idea, but my parents had good reason for not furnishing that connection: so proud was I of my ability to count to two hundred that I would count to two hundred on the telephone, to my grandparents, every single time they called. Long distance. And this was back in the olden days when long distance cost an arm and a leg, so when it became clear that I was not to tire of my long distance counts to two hundred, my mother gently pointed out that maybe my grandparents didn’t want to hear me count to two hundred over the phone anymore. I threw a fit; didn’t they love me? By the way, Mom and Dad, I stand by that tantrum, because what the hell is the point of grandparents if not to have someone to listen to - and enjoy listening to - some two-and-a-half-year-old kid count to two hundred over the phone, even if it’s costing them fifty cents a minute to hear it?

Anyway, my point here is, by the time I was three I already knew how to read and how to count, so I guess I was old enough to learn computer science - specifically, recursion - and fortunately, Big Bird was on hand to teach me.

Big Bird was painting a bench. He’d just finished applying the last coat of paint, and his friends were admiring his handiwork. As he replaced the paint brush, he explained - concerned citizen that he was - that it was necessary to warn any passers-by that this was a freshly-painted bench. This made sense to me, because I remembered a previous episode in which whatshisface, the mime, sat down on a freshly-painted bench and got white stripes all over his black suit. Big Bird would have none of that, so he produced a blank piece of paper and wrote WET PAINT on it, and hung it by the bench. His only writing implements, however, were the paint and paintbrush he’d brought with him, so after creating the WET PAINT sign he realized that the sign itself contained wet paint, and so he needed to create another WET PAINT sign, to warn people about the first sign. So he created the second sign, and - apparently having learned nothing from his experience with the first sign - realized that he’d need a new one.

I watched this intently, and suddenly it dawned on me: every WET PAINT sign demanded another. I got it, but Big Bird didn’t. I got worried; would he be doing this forever? Or would someone give him a crayon and tell him to use it for the next sign?

Soon the scene ended, and I distractedly watched for the next few minutes as the mime explained the WALK/DON’T WALK signs, and as the Count showed that it doesn’t matter how you arrange the blocks because you still have the same number of them, and as someone didn’t want to share his cookie with Cookie Monster until Kermit came by to teach a lesson about sharing. Whatever. I didn’t care, because I was concerned that Big Bird was still making WET PAINT signs.

Cut to the next scene: Big Bird surrounded by hundreds - maybe even two hundred - WET PAINT signs, happily making another one because the last one was still wet. And no one handed him a damned crayon, and the episode ended right there.

I burst into tears.

My mother, startled (her toddler was bawling at the end of Sesame Street, after all), hurried into the family room and asked me what was wrong, and I blubbered something about the endless production of WET PAINT signs and how Big Bird would be making them forever because each sign told him to make another one. FOREVER. I couldn’t think of anything worse than spending one’s entire life making WET PAINT signs, and I worried that that was to be Big Bird’s fate. It troubled me more than I could put into words. That happy yellow bird, doing this for the rest of his life. And he showed such promise! Would he never get to have a family? go to the park again? And what of Snuffleuppagus?

Mom obviously hadn’t been expecting this, but she quickly assured me that no, Big Bird wasn’t going to spend his whole life making WET PAINT signs. As a matter of fact, he stopped soon after that episode of Sesame Street ended. Because, uh, Grover told him he didn’t have to make the signs anymore. In fact, just you wait, honey, tomorrow on Sesame Street Big Bird will be doing something completely different.

Will he really? I sniffled.

Yes, honey, he will. I promise.

How do you know?

Because, said Mom, I know all of the people on Sesame Street and they told me what they were going to be doing tomorrow.

And you know, I may have known how to read and count to two hundred, and I may have known all sorts of shapes - not just the easy ones like circle and square and triangle, but also trapezoid and pentagon and parallellogram - by the time I was three, but let me tell you, I ate that shit right up. Okay, cool. Big Bird wouldn’t be making WET PAINT signs forever. Mom said so herself. I could sleep at night.

The next day, I saw that Mom had been right, because there on TV was Big Bird singing a song about cooperation and there were no WET PAINT signs anywhere in sight. Good old Grover. Mom knew everything, apparently.

It wasn’t until several years later that I learned that the sort of structure displayed by the self-producing WET PAINT signs - a set of instructions that includes the instruction to follow itself - had a name: recursion. During my first year of university, some boring CS prof whose name I forget explained this all in the most monotonous way imaginable, and told us that if we wrote a recursive function then it would call itself until it had a good reason not to, that is, a base case that ensured it would stop, infinite loops are bad, yadda yadda, blah blah.

And all I could think of was a computer that would be making WET PAINT signs forever and ever because there was no IF CRAYON branch to lead into a ALL SIGNS ARE DRY base case.

It still bothered me, a decade and a half later, and I took pains to ensure that all of my recursive functions would terminate in good time.

That was Sesame Street’s contribution to computer science. Its contribution to real analysis, unfortunately, had not been subjected to peer review: I remember the Count arranging ten blocks in a row, in a pyramid, in a square, informing us that no matter how you placed them, they’d add up to the same number.

Sure, Count. With a series that converges absolutely.

4/11/2005

Ten inches

File under: 1000 Words, I Made It Out Of Clay, No More Pencils, No More Books, Hubris. Posted by Moebius Stripper at 8:44 pm.

My graduate school had a pottery studio on campus. I joined the pottery club during the first year of my Master’s, but this was a full year before I’d completely lost my motivation to do schoolwork, so I spent little time in the studio.

During my second year, the only course I was taking some ill-conceived algebraic geometry class whose audience consisted of eight graduate students taking the course for credit, and eight professors and postdocs. Two months into the class, the professors and postdocs had taken leave. “No point sticking around when I don’t understand anything,” one of them told me in confidence, and I agreed. Unlike the profs and postdocs, however, I needed the credit, so I compromised by attending the class and not stressing over it. The course was cotaught by two experts, one of whom was clearly more of an expert than the other. One day, after class, as Alpha wrapped up the lesson, Beta turned to me and whispered, I am SO lost in this class.

I took this as permission to ignore all homework assigned by Alpha. A few months later, I gave up on Beta’s assignments as well. Me and five of my classmates.

That year, I was productive in other ways.



When I moved to the Island, one of the first things I did was seek out a pottery studio. I also wanted to take lessons; I felt I’d progressed as far as I could on my own. I soon discovered, to my dismay, that although I now lived in a region known for its potters, none in my city were available to offer lessons. There were two types of lessons, it seemed: ones for student artists studying to be professionals; and one for children and adults who just wanted to poke around with clay.

“We don’t usually offer intermediate-level lessons,” said the artist who apparently was the one to talk to about that sort of thing. “Not much demand for it.” He glanced over at my station, which was surrounded by small misshapen bowls, which were all I’d been able to make this first day working on a new wheel with unfamiliar clay. I can only imagine what he must have been thinking; probably something close to what I think when my C students tell me that they typically get A’s in math. “In order to be eligible for my intermediate-level class,” he said, “You have to be able to throw five ten-inch cylinders, one after another. Can you do that?”

“With certain types of clay,” I replied. “Ones with more tooth than this stuff,” I added, hoping he’d be impressed by my use of the jargon.

He looked skeptical. “There’s still room in my beginner class,” he told me.

I took this all rather personally; I’d taught beginner-level classes, after all. In any case, I knew what one did in such classes, and that wasn’t what I needed to learn. So I set out, during the ten hours a month I could get into the studio, to master the ten-inch cylinder.





They aren’t cylinders, I know. but they were originally. And before they were fired, they were ten inches.

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