Tall, Dark, and Mysterious

5/31/2005

On teaching college students what they should already know

File under: Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 6:41 pm.

Rudbeckia Hirta succinctly explains that if you can’t do algebra, then you can’t take calculus:

Due to reasons beyond my understanding, high school math and college math are completely unaligned. The K-12 system sends us students whose knowledge is a mile wide and an inch deep: we get students who are shaky at algebra, frightened of fractions, and unsure of how to find the areas of basic plane figures (and completely unable to accept the idea that it is a reasonable request to ask them to solve non-standard problems where the method of solution is not immediately obvious), but they have been exposed to matrix arithmetic, computations from polynomial calculus and other supposedly “advanced” procedures. You would think that the “college prep” track would prepare students for college, but it doesn’t. Recently I read somewhere (maybe in Focus?) that there is more calculus taught in high schools than there is at colleges.

See also: mathematics by pattern matching, word problems, et al. So much of this problem can be traced to the fact that students do not understand that an equation is a relationship among quantities. Each equation they see is a concept unto itself, to be memorized and applied to the word problem on the test that looks like the word problem that I did on the blackboard and that used a similar equation. If the word problem on the test doesn’t look like any of the problems I did in class, then that question is “totally unfair”. Most students will leave the question blank, or solve a completely different problem (one with a ready-made equation) in the space provided.

This New York Times op-ed is about teaching freshman English to illiterate college students, but I’m sure that anyone teaching freshman math to innumerate college students can find plenty to relate to. I’m not sure I’m willing to buy into, wholesale, the author’s belief that content should be ignored in favour of form, but I can’t argue with success:

On the first day of my freshman writing class I give the students this assignment: You will be divided into groups and by the end of the semester each group will be expected to have created its own language, complete with a syntax, a lexicon, a text, rules for translating the text and strategies for teaching your language to fellow students.

…14 weeks later - and this happens every time - each group has produced a language of incredible sophistication and precision.

How is this near miracle accomplished? The short answer is that over the semester the students come to understand a single proposition: A sentence is a structure of logical relationships. In its bare form, this proposition is hardly edifying, which is why I immediately supplement it with a simple exercise. “Here,” I say, “are five words randomly chosen; turn them into a sentence.” (The first time I did this the words were coffee, should, book, garbage and quickly.) In no time at all I am presented with 20 sentences, all perfectly coherent and all quite different. Then comes the hard part. “What is it,” I ask, “that you did? What did it take to turn a random list of words into a sentence?” A lot of fumbling and stumbling and false starts follow, but finally someone says, “I put the words into a relationship with one another.”

An equation is a relationship among quantities. How many times have I tried, and failed, to get this idea across? Imagine getting students to realize it for themselves! Unfortunately, many students lack the intuitive ideas about math needed to know, even subconsciously and with the help of leading questions, that equations are anything other than a jumble of letters, numbers, and symbols. (Even though I spent twenty minutes showing how we could use the definition of a circle and the Pythagorean Theorem to derive the equation of a circle in the Cartesian plane, nearly all of my students were angry that I wouldn’t provide the formula on the test. I mentioned, incorrectly, that they could derive the formula themselves, on the test, if they needed to; of course, I was wrong.) But I would gladly sacrifice 80% of the poorly-learned content in a first-year college math course if I could instead effect a solid understanding of what equations really meant - and how to get one from a sentence or two of information. I wonder if Fish’s lesson could be adapted to the first-year math classroom.

At Critical Mass, where I found the NYT piece, Erin O’Connor isn’t optimistic even about applying it to the English classroom:

[M]ost university composition courses are taught by graduate students who are a) not necessarily good writers themselves, and b) often more interested in using the composition classroom to practice teaching the content they hope to teach as non-composition teaching English professors, and you’ve got a situation in which the Fish vision, regardless of its merits, is pure pipedream.

Ditto. No one teaches precalculus if they can avoid it; at Island U, it got passed from temps to new faculty to the department head, who teaches the courses that no one else will teach. Everyone says that the precalculus course needs to be completely revamped, but given the option, they’d rather take a less thankless teaching assignment than put forth the effort to revamp it. And around and around we go.

Gather ye round and swoon over my (ex) department head.

File under: Righteous Indignation, Those Who Can't. Posted by Moebius Stripper at 8:18 am.

The second semester of the year has ended, this time for real: this brat wrote her final exam last week. Finally. Department Head handled the whole affair, from arranging the exam date to grading the paper, and MLIHASIM got the C that she needed. So, good on her, I guess. Not content, however, to leave the course with her honour even vaguely intact, she penned a valedictory email to Department Head, thanking him for supervising and grading her exam, which she’s sure was a huge burden for him, but what could she do? - if it were up to her, she pointed out, she wouldn’t have had to write that exam at all. She informed him that for the most part she “enjoyed having [me] as a teacher”, and that I was “good at explaining the basics”, but that my “tests and exam were significantly harder than the homework” and in fact contained some “questions that we never did in class.”* Since she hadn’t done math in years and years, she had a tutor “show [her] how to do all of the homework problems” and yet she still found the exam “very hard”. Oh, and she talked to some other students and they agreed with her, and would Department Head “please keep this sort of thing in mind” the next time he hires faculty? If this sounds familiar, it is: she aired precisely this grievance (minus the hiring advice) every single goddamned time we met outside of class, not to mention several times over email.

Department Head forwarded me this note. He also, God bless him, forwarded me his reply, which was basically all,

Dear MLIHASIM,

I’m glad you enjoyed Moebius Stripper as an instructor. As for your other remarks, I’m afraid that your expectations of a college-level math course are incompatible with reality. MS’ exam was no harder than the ones I give when I teach this class with the same text (and hence with similar homework). Math is not about memorization; in fact, mastering it requires that you be able to apply the concepts you learned to new problems. That you did not learn to do this in spite of the effort you put into this course indicates that a C was an appropriate, if not generous, mark for you to achieve. MS taught this course exactly as it should be taught, and exactly as I would teach it - though I don’t think I am as patient as she is! Speaking of which, your hiring advice is rather moot, as I’m the one who will be teaching this course - as well as the follow-up - next semester. Say - I guess that means I’ll have you in my class! See you next term and have a good summer, and I look forward to seeing you in the fall.

Dealing with students who think that they should be allowed to dictate the terms under which they learn (or fail to learn) the subject is frustrating. I can’t imagine how much more frustrating it would be if those students had the support of my boss.

* However, some of the exam questions were actually identical to questions on the review sheet - which MLIHASIM had actually told me she wasn’t going to do, because it too was too hard.

5/30/2005

Behold, the fruits of multiculturalism

File under: 1000 Words, What I Did On My Summer Vacation. Posted by Moebius Stripper at 9:02 am.

Yes, those are sweet basil potato chips. Ridged! And believe you me, you can taste the sweet basil.

And here’s where you, dear reader, (may) come in: note the opportunity (I think?) to win one million (I think) Thai Bhats. According to the currency converter, that’s equivalent to CA 31,062.06 or US 24,736.39, certainly nothing to sneeze at. The inside of the bag is silver foil, and contains no text at all, and hence, no text indicating whether or not I am one million Thai Bhats richer than I was before I purchased a bag of sweet basic potato chips. Is there a number or something to which I’m supposed to send the UPS code or whatnot? Are such instructions here on the back of the bag?

This bag of chips, by the way, is one of the many novelty items featured at Dok Bua, a Thai Restaurant in Brookline, MA, that proudly displays a restaurant review headlined “Where Thai Cuisine Meets Kitsch.” And it’s true! From the Christmas tree at the centre of the room to the “This way to New York” sign above the restroom door - it’s as though Dok Bua was decorated with the aim of distracting us from the food. Which is actually quite good. The food, that is. For what it’s worth, I lingered by the snack counter before choosing a flavour of chip: the options, besides sweet basil, included baked lobster, nori seaweed, Mexican barbecue, and sour cream and onion.

More on the subject of tension between decor and cuisine in Thai restaurants: I’m reminded of my introduction to Thai food, back in 2001, in Waterville, ME, of all places. Unless you’re either in some way affiliated with the summer camp where I’ve worked for the past five years or live in Waterville, ME, you’ve probably never been to Waterville, ME, because there’s no reason to visit Waterville, ME unless you grew up there. Many of the streets in Waterville, ME (pop: 10,000) are unlabelled, because there’s no reason to be navigating them unless your family’s lived there for the past six generations. Among the attractions in Waterville, ME: a post office; a grocery store or two; a few gas stations; a college; a Walmart; a K-Mart; a McDonald’s; a Pizza Hut; and restaurant called Pad Thai. In 2001, Pad Thai was located in a tiny shack by the highway that looked as though it would collapse under the force of a moderate wind. On its roof was a sign bearing a Pepsi ad and - in the types of letters used to spell out the names of movies outside a theatre - the restaurant’s name. My party and I entered with no small measure of trepidation; this place looked as though it would be Pad Thai that week, and Joe’s Burger Shack the next. At the very least, I expected French fries on the menu. But somehow, a talented Thai family had settled in the most immigrant-free town I’d ever set foot in, set up a restaurant, and it was good. Very good.

Three years later, my camp returned to Waterville, ME, and found that Pad Thai had added a second location. Waterville, ME, might have had room for only one McDonald’s, one Pizza Hut, and one K-Mart, but there was a market for two Pad Thais. The second, located on the lower level of a hotel, was decidedly more upscale: it had booths, and jukeboxes, and half of a pink - Ford? I think; I don’t know these things - protruding from the back wall. So, if you drop by Waterville, ME, and have a crving for Thai food, you have your choice of settings: shack, or 50’s diner. Though there’s always takeout, which might be necessary, as both of these unlikely spaces were routinely filled to capacity.

According to some of our campers, who were born and raised in Southeast Asia, Pad Thai’s food was as tasty and authentic as any they’d ever eaten. Only the decor was uniquely American. And if this type of adaptation is what it takes to fill an ethnic restaurant in Waterville, ME, then I’ll take it.

5/25/2005

Dispatches from Unemployia

File under: Home And Native Land. Posted by Moebius Stripper at 11:46 am.

In honour of my departure from Island U, Canada is giving me free money. Hooray! Except that nothing in life is free, and the hidden cost of Employment Insurance is the barrage of questions and forms and reports, oh my. Makes sense, of course, as giving away totally free money is probably unsound policy; but it seems a waste of everyone’s time to require me, for instance, to have another employer document a six-week job in the US when the associated income has no bearing whatsoever on the amount, type, or duration of benefits I receive. NONE. They should have a place on the form where you enter the income from your main job, and if it triggers the “like hell we’re giving you more than 55% of this while you’re not even working” flag, you get to skip to the end. I have plenty of other helpful ideas for streamlining the process, but the EI office will have to hire me before I give them away. And if that right there isn’t “willing and able to accept any suitable offer of employment”, hell if I know what is.

Aspect of the process I’m looking forward to the most: providing the government with “regular reports” to assure them that I’ve been actively looking for work or somesuch. I’m such an overachiever that I’ve got one all written up already! I look forward to explaining to government bureaucrats that in academia, the employer may or may not interview the shortlisted applicants before the job is scheduled to begin. Best case scenario: the poor sod assigned to my file is so convinced that I’m full of shit that he or she calls any of the EIGHT PLACES THAT I APPLIED TO AND HAVEN’T HEARD BACK FROM, and gets told things like, “No, that’s correct. We had a couple of applications for the position of statistics instructor, and some of them looked really promising, and in fact, we might have seriously considered hiring Moebius Stripper if the position advertised had actually existed, which it didn’t. What was your question?” Hee! Yeah, I could do this for a living.

5/23/2005

US-centricism starts early.

File under: Home And Native Land, What I Did On My Summer Vacation. Posted by Moebius Stripper at 8:46 am.

I have this partially-written screed about how my country’s top politicians wouldn’t recognize strategy if it waited for a break in the conversation and said, “Hi, I’m strategy, pleased to make your acquaintance. I’d like to talk with you, you know, when you have a chance.” (This, after all, is Canada, where even concepts would possess neither the temerity to hit people on the head nor the lack of coordination to get tripped over, were one to anthropomorphise them.) These past few days, however, I’ve been sharing a residence - south of the 49th - with two children under the age of two, and my facility with polysyllabic words has suffered noticeably in the interim. Maybe if I had kids of my own I could transition seamlessly between congent political commentary and squeaky-voiced declarations of “Bay-bee! Baaaaaaayyyyy-bee! WHERE’S THE BABY??? Ye-e-e-esss!”, but I don’t. Besides, there are more pressing concerns than the former, anyway: while I was writing the first half of this paragraph, I was enlisted by Baby the Elder for help with “nana in a bowl, peez”, “up peez”, and “Doctor-Sooss! ABC book. Peeez?” And, what could I do? She did ask nicely.

Nevertheless, TD&M headquarters is temporarily begging off all alphabet-related duties after yesterday’s incident. We got through the first twenty-five letters without any problems, with BtE easily identifying the various letters and pictures (”a-poh”, “i-cream”, “fower”); but the story culminated on a sour note. “NO!” she screamed at the last page, and turned to face me. “It’s ZEE,” she informed me. I tried to explain that some things could have more than one name (”like these, see? You can call them steps. Or, you can call them stairs“), but she would hear none of it. “ZEE,” she insisted.

I totally lost that one.

5/17/2005

Quit while you’re ahead

File under: Righteous Indignation, Those Who Can't, Know Thyself, What I Did On My Summer Vacation. Posted by Moebius Stripper at 7:43 am.

….even if that means quitting before you’ve even started. That’s what teacher-in-training Lauren is considering doing - finding another line of work before ever taking a regular teaching position. I can’t relate to everything in her post, especially the USA-specific parts, but boy do I feel this: Politicians, concerned with public sway, bloviate on education and educational policies that have no empirical bearing on scholastic research…In no way do I feel obligated to justify my pedagogy to a parade of political assholes who aren’t even familiar with the term.

Last week, I visited my old high school, an institution that I’d be content to relegate to the domain of the unpleasant memory were it not for the fact that the best damned high school math teacher in the western hemisphere still works there. I’ve known Mrs. C. for nearly half my life, and I’ve kept in touch over email and snail mail with Mrs. C. for the past decade. I owe much of my success as a mathematician to Mrs. C. I owe almost all of my successes as a teacher to her.

Mrs. C. has worked as a high school math teacher for over thirty years - half of that at my school. During my time at the high school, she was consistently the most popular teacher around - no mean feat for someone who taught math, of all subjects. She was loved by her strong students and her weak students alike; she was available for several hours of remedial and extra help every day - not just for her own students, but for other teachers’ students as well. She had stacks of enrichment material for anyone who asked for any. She was frequently solicited for letters of recommendation for graduating students; she mailed mine to me the month after I graduated. It was two pages long, and went into profound detail about my academic ability, my interests, my goals, and my character. And Mrs. C. imposed high standards, too: she prided herself on her classes’ low drop rate, and was known to retain near-failing students who could have easily gotten C’s or even B’s if they’d taken the easier night school classes.

She’s delighted that I’ve decided to teach math - albeit at the college level, rather than at the high school level - and when I dropped in during her lunch hour last week, she listened attentively to my adventures teaching math at Island U. She’d already heard of some of them; back in February, when I was at my most frustrated, I inflicted a tirade upon her inbox, begging for feedback. Last week, I elaborated, on my trials: students who couldn’t do elementary school-level math, building design that facilitated disruptions to classes, students who thought that the final exam was optional, a system that teaches students that “bad marks” translate naturally into “scaled grades”, a general expectation that good teaching is equivalent to spoonfeeding - I could go on. And have, in this space. And did, last week, to Mrs. C.

A few weeks ago, another blog I frequent was visited by a troll, supposedly a high school history teacher, who snootily informed us regulars that she could educate and inspire everyone - regardless of background or attitude; that she never had any of the problems we wrote about; and that every time a student of ours failed, it was our fault and our fault alone. This anonymous commenter was soundly eviscerated, as well she should have been; but I was hoping that Mrs. C.’s feedback to me would be similar. I’d been hoping that she’d sympathize with me and say, “Yes, I dealt with those things back in my first few years of teaching; but as I became more experienced, I learned how to create an environment in which I could teach effectively to receptive students.”

Instead, Mrs. C. nodded sadly and said, “You know, I never used to have those sorts of problems back in your year, or before. Now, I have them all the time. And I don’t know what I could do about them.”

Back when I was a student, she told me, she had a handful of students who didn’t do their homework. But they were a small minority. Students who didn’t do their homework and demanded high marks anyway were virtually nonexistent. Now, the latter group comprises the bulk of Mrs. C.’s class. Getting them to understand that they need to do their homework, she reported, is like pulling teeth. Every week she fields angry phone calls from parents who hold her singly responsible for their children’s poor performance. “And it never used to be like that,” she said. “Never. I don’t know what you can do,” she told me apologetically. “Me, I’m retiring next year.”

And Mrs. C., hardly a conspiracy theorist or superficial thinker, was quick to diagnose the problem: “I blame Mike Harris,” she said simply.

Mike Harris was the premier of Ontario from 1995 to 2002. Harris had once been a teacher; he’d been fired from his job after very little time in the classroom. Many people speculated, only half-jokingly, that his stint as premier was little more than revenge. There was certainly plenty of evidence in that direction. Most egregiously, in 1996, Harris appointed a high school dropout, John Snobelen, as Minister of Education. Snobelen’s public statements on the importance of educational reform were fraught with more grammatical errors per capita than I’d ever seen before; nevertheless, a month into his job, he was awarded - I am not making this up - an honourary high school diploma from an Ontario school. (Aside: my own high school diploma was signed by Snobelen, something I found more than a little insulting.)

Harris ran on a platform of “teacher accountability”. Some of the reforms he proposed were long overdue: for instance, Ontario parents had long been complaining that their children’s report cards were unclear and unnecessarily laden with jargon. An illiterate fifth-grader, for instance, could bring home an evaluation that reported on his creativity, friendliness and enthusiasm but made no mention of his inability to read. That had to change. In addition, the previous government, in a misguided move to make the transition to high school kinder, gentler, and more colour-blind, had replaced the different levels of classes (advanced, general, and basic) with the lowest common denominator, teaching basic prerequisite material to all incoming students.

But, said Mrs. C., the language of “teacher accountability” fostered an adversarial relationship between teachers and parents. Previously, she reported, there was a sincerely held belief that teachers, parents, and students would work to master the subject. But with the calls for parents to “demand better”, teachers were pitted against parents and students. Previously, reported Mrs. C., some parents had expressed difficulty at motivating their children to do their homework; but they appreciated her talking to them about their children’s difficulties. Now, she said, she continues to talk to the parents of students who don’t do the required work - but more often than not, she is told that it’s her responsibility to get them to do their work. Last week, she said, a month before final exams, parents are asking her what she’s going to do about their failing children. “I’ve been talking to you all term about them not doing their work,” she said, “and keeping up with the homework throughout the year is important for this class. There’s not much that I can do at this point, especially if they haven’t started to catch up.” One parent had met with her during parent-teacher interviews to tell her that his daughter, always a C student in math, “needed an 80%” in calculus, “and it’s your responsibility to make sure that happens.” Meanwhile, the student in question never showed up for extra help, despite Mrs. C.’s own invitations. Parents are demanding better.

I’m loathe to chalk up social trends to single causes, but once a attitude has been sanctioned, it spreads quickly. And, at the college level, I’m seeing the effects. This past year, I’ve been astounded by the number of my students who openly express a belief that there is no correlation between their grades and their understanding of the material. If the class average is low, it’s my fault, and I should scale the grades. If I were any good at teaching, they wouldn’t have to spend so much time on homework; the least I could do is give them the grades they need to get to the next course - at which point we repeat the process with the next teacher for the next course.

A mere few weeks into my most recent teaching position, I commented to someone that I liked my job, but it was often exhausting and stressful and that I didn’t think I’d be able to teach math university students who couldn’t add fractions for more than another few years before burning out. Hopefully I can snag a position where my students will be at least vaguely proficient in the prerequisite material (I’m reminded of a former precalculus student who, when reminded by a subsequent teacher how to compute the equation of a straight line, objected: “but we did that LAST term, not this term”), but I’m not terribly optimistic. Maybe it’s time to start looking at other options now.

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