Tall, Dark, and Mysterious

7/23/2005

Is there a cognitive psychologist in the house?

File under: Those Who Can't. Posted by Moebius Stripper at 4:36 pm.

The comments to my post on math prerequisites that aren’t being met are the reason that, despite all of the comment spam, I leave these pages world-writable. Some excellent stuff there, and I hope that some curriculum developers in my province are reading what my readers have to say. I have more to say in the prerequisites thread, but first I wanted to address some comments from high school math teachers who assure me that their students aren’t leaving their classrooms without knowing what an equation was, how to add fractions, and so on.

I believe them. To look at the BC high school curriculum, it’s hard to find anything specific that is explicitly wrong with the course. (Aside, that is, from the “This book is brought to you by the letters T and I” thing, which I suppose is a big one.) By the time British Columbian teenagers leave grade twelve, they’ve been exposed to fractions, exponents, quadratic equations, graphs, and logarithms - the prerequisites for college math. They’ve even been exposed to questions that are a lot more open-ended than I expected - questions that demand a modicum of creativity.

The problem is that many students - perhaps most - never properly learned this stuff. Others knew it to some degree at some point, and promptly forgot it.

I’ve been tutoring a student in that second category - he can’t remember how to solve a linear equation (when do you divide both sides by the same number? When do you add stuff to both sides?), he can’t remember how to evaluate powers, he can’t remember…much of anything he learned. And nothing makes me feel like a failure as a teacher than hearing that the mathematics I’ve been trying to teach has come across as something merely to remember.

Can anyone recommend any reading material, accessible to a layperson, on how knowledge is stored? Why, and how, some information gets stored in short-term memory, some finds its way into long-term, and other types of data - a first language, for instance - is not something that people think about as knowing and not as remembering? Because I don’t think it’s something intrinsic about mathematics that it seems to get stored into the most unreliable section of my students’ brains.

As I was thinking about this post, reader Susan made an insightful connection between math (something students memorize) and language (something students learn):

It’s possible for a non-expert to determine whether a child is literate by asking him or her to read something unfamiliar (ideally both outloud and silently) and to explain what they’ve read in their own words.

We need to define and expect something similar as far as being numerate.

To which I add: not expecting anything similar for math gives students no reason to process and learn math instead of just remember it.

I’m only now remembering that I actually did do something similar last term, although I didn’t draw the connection to reading that Susan did. Last term, after one particularly miserably-done test, I gave my students an opportunity to submit (for credit) corrections to the word problems. I gave them a template to follow: they had to describe, in words, what information they were given in the problem, and what they were missing. They had to describe, in words, how those things were related, and then, based on their previous work they had to provide the equations they needed. A few students actually came up to me and said that that exercise really helped them understand what they were doing with word problems. I was shocked - this was the horrible precalculus class - and encouraged. A month later, however, I found that those same students drew a blank when faced with the word problems on the test.

We’ve got a long way to go.

One could argue that I went into it with a negative attitude

File under: Know Thyself, What I Did On My Summer Vacation. Posted by Moebius Stripper at 3:57 pm.

Because I don’t think I want to spend the rest of my life teaching precalculus to students who can’t compute 5*0 without a calculator, and because the local colleges don’t seem intent on letting me do that anyway, and because a temporary lapse of self-awareness made me completely forget the “independent to a fault, don’t need nothin’ from nobody” aspect of my character, I decided to pay a visit to a career counsellor.

Summary: big, fat waste of time. Upon reflection, I think the biggest problem is that I’d assumed, incorrectly, that an employment counsellor was an expert on jobs. It turns out that an employment counsellor’s expertise is actually a step removed from, and hence a step less useful than, that: mine clearly specialized in the “job-seeking process”. Which meant that when I came in with a list of my skills, interests, and possible employers that I’d like to research (this last one is non-trivial, as there are confidentiality issues involved with the employers I’m interested in; I’m not going to go into details), he couldn’t help me with that. He could, however, refer me to a “career exploration program”, where I’d be able to “explore my strengths and weaknesses”, “discover my interests” and other somesuch; this would be explained in greater detail in the pamphlet he gave me. Leafing through it, I noticed that the first day of the three-week program would be devoted to discovering my Myers-Briggs personality type.

INTJ,” I told him. “And I know what my interests and strengths and weaknesses are. I’m a highly analytical, independent worker with no patience for small talk and routine. I have some types of careers in mind; I need more specialized direction than this.”

From the look on his face, I gathered that no one had ever made such a request before.

That wasn’t the only problem. The meeting, actually, started going poorly even before I shook hands with the man: I arrived on time, and spent the next thirty-five minutes in the waiting room while the counsellor was “almost done, really, we’re sorry about this.” At the stroke of n-thirty, he finally emerged from his office and presented himself to the (newly-hired) secretary, and proceeded to admonish her gently for booking half hour appointments instead of full-hour appointments. He needed a full hour, he explained, for new clients. Somehow this didn’t translate into my own consultation lasting for more than twenty-three minutes, or involving the counsellor doing things like actually reading the resume I’d been instructed to print out, but I was ready to leave after twenty-three minutes (see above) anyway, so I wasn’t about to object.

Once in the room, he took a minute, literally, to scan the form I’d filled out in the waiting room. Like all government forms I’ve ever filled out, this one contained an optional section in which one can identify oneself as belonging to one or more of various groups; like all government forms I’d ever filled out, I opted to leave this part blank. Noticing that I am severe-featured and dark-skinned, the employment counsellor quickly proceeded to engage me in a variant of Twenty Questions that I swear to God I play every other month:

“So, where are you from?”
“Ontario.”
“You were…born there?”
“Yes.”
“Where were your parents born?”
“Quebec.”
“I see…”

Just his luck, I’m third-generation, so he reluctantly abandoned that line. But seriously, I understand why there’s an ethnicity field on these sorts of forms, but I understand even more so why filling out such a section is optional, and I resent it when people who really should know better try to coax such information out of me. Am I the first person who has ever chosen not to fill in a few optional fields on a government form? Shee.

(Aside: every now and again someone asks me, point-blank, “What is your ethnicity?” I’ve had bad luck answering honestly, as my experience has been that more people fancy themselves experts on the Israeli-Palestinian conflict than is warranted, and a lot of them are just dying to give their input on the matter. Finding out that the bloodline of their interlocutor intersects with that of some folks who live in that region, by the way, apparently constitutes a capital opportunity to do so. So when the Swedish hosts of a B&B on Denman Island posed the question, I responded in my preferred way: by selecting, at random, a country that lies roughly on the line joining Warsaw to Bombay, and claiming ancestry. “I’m half Turkish,” I lied, and the Swedish wife turned to the husband and said something rushed and excited that had the cadence of I told you, didn’t I tell you? and the husband turned to me and smiled weakly, as though to say, No she didn’t, but what can I do?)

Back to the meeting: the best I could say about it is that unlike almost all of the academic types who have counselled me on employment, Employment Counsellor was not of the mind that I’d never get anywhere without a Ph.D. Alas, he opted for the other extreme, and wrote off my education altogether: “Oh, I see you can use a computer,” he remarked approvingly, as he glanced at my resume, skipping over things like the title of my thesis (understandable), my Dean’s List placement at my alma mater (less so), and a description of the ceramic dinner set I’d been commissioned to make (ok, fine). And, yes, I can use a computer to a degree that puts me in direct competition with only three quarters of the youth in my province, rather than all of them, but, my lord.

Like many members of my demographic - gifted kids of professionals, who were directed to seek scholarship, rather than employment, in their studies, and who were never given much guidance with regards to the latter - I am finding myself suspended between two distinct groups that are, for opposite reasons, ill-suited to help me. On the one hand are the intellectuals who can’t fathom a universe outside the academy, and hence cannot help me find my way in that world; on the other, the folks who never studied a subject as abstract and as technical as mathematics beyond the high school level, and consequently can’t provide the specialized direction I need to apply my own abstract and technical interests and skills outside the academy. Frustrating, because I know that there are math folks employed in statistics and in finance and in the military and elsewhere, and they didn’t hatch ready-made inside their cubicles.