Tonight, while cracking the math section of the GRE book for the first time after an extended period of avoidance, I discovered that, in order to find the percentage change between two numbers, it is necessary to divide their difference by the final number. This may not shock anyone, but it did shock me, since I've been simply dividing the final number by the initial number since probably the end of high school. And consistently getting the wrong answer. And not noticing.
How could this happen? I have had some time to reflect on my failure to understand math since the last time I took any math, which was about the middle of my freshman year of college. That was when I was repeating basically the same low-level calculus course I had flunked in high school. Ah, good times. In fact, I received several C's in high school math courses, in addition to failing every single physics exam I ever took.
Tracking for math began in the third grade at my school and continued through the end of high school. From the beginning, I was tracked into the higher end of math courses, and fell continually further behind until I hit calculus, which I had to drop after a semester, because, according to my calculations, you can't get any more behind than simply flunking out. But that's a long time still, and during the intervening years, I spent a lot of it desperately memorizing formulas and trying to find tricks which would make actual quantitative thought unnecessary. I never had any idea why it was possible to divide fractions by reversing the numerator and denominator and multiplying, but I memorized that this is what you do, and I did it. I was equally unclear as to why the probability of an event happening and not happening had to equal 1, but that's what they told me, so I memorized it and proceeded from there. Because schools obviously have an interest in making students proficient in basic arithmetic operations even if they can't fully understand what they mean, my math teachers encouraged such shortcuts. Still, it was abundantly clear to me by the beginning of eighth grade algebra that math meant doom.
For a brief period in high school, I was obsessed with gender bias in education, and I read a lot of books arguing that the reason women performed worse in math and physics than men was that schools either failed to take into account women's specific learning styles, or men were louder and hogged all the teacher's attention. I tried to prove this by undertaking an extensive and thoroughly unscientific study for the school paper, but my results were inconclusive in that they did not reveal a greater proportion of women who were turned off by math, but rather, that the vast majority of all high school students hated math, and school in general. Shocking, the results of social science. So I decided that, even though I had a couple of lackluster teachers, the fault for my math deficiency lay primarily with me. Besides, I knew plenty of girls who were better than me at math, as well as, come to think of it, several inanimate objects that could probably outperform me in the subject.
All the while, I could have--and probably should have--demanded to be re-tracked into a lower level class. At one point, I actually tried to drop down into regular physics (due to that thing with failing every exam in the honors course...), but I was warned that if I did that, I wouldn't be able to take an AP science the next year, and that would kill my chances of elite college admission, which in turn would lead to doom, misery, death. And the whole idea of tracking means that, at every point along the way, doom, misery, and death hang over the misguided soul who even considers stepping off track. You drop down in fifth grade, then you're put in an equally low track the next year, then by seventh grade, you're barred from pre-algebra, and that forecloses the high school honors track, which means no calculus, and then you'll never get into college, and then doom, misery, and death await. Besides, math is not required in college, so if you just manage to scrape by for a few more years, you will escape to that dreamed-of place where the lawns are always green, every English course is serious, and everyone around you is a brilliant and interesting human being (unlike the veritable
apes with whom you're currently forced to share the hallways),
and you will never have to take math again. A glorious future awaits! Surely it is right to sacrifice understanding math for this noble cause!
And I would like to tell you that now that time has passed and I have gained some perspective on my education, I realize the folly of this kind of reasoning. But, actually, I pretty much stand by it. My high school academic record was not so stellar that I would necessarily have gotten into the schools I did without honors-level math. My chances were already a toss-up. My B's and C's in honors and AP courses at least made it appear as though I'd "challenged myself." The end result--getting into the U of C--
was worth it, possibly even at the expense of knowing math.
There is, furthermore, no evidence that I would've understood more math if I'd taken lower-level math courses, which were infamous for their low expectations and apathetic teachers. It's possible that instead of learning more math, I would've simply grown bored by the slower pace at which I was memorizing shortcuts. It did help immensely to repeat calculus in college; the second time around, I at least figured out what calculus was. But if repeating material was the answer, where would I have properly begun? The last concept in math I really understood was proportions, which were taught in about the fifth grade. Possibly tutoring would have helped, though it's unlikely that my parents' could've afforded it, or would've even been bothered by my math ineptitude enough to try to remedy it. I earned mostly B's in math, and that hardly set off alarm bells. Tutoring was usually reserved for the utter failures; I at least had my shortcuts to help me squeak by.
It's not as thoughg my failure in this area really has serious implications for my life and future. I will never have to understand what a matrix is, or what normal force is, and if I did, I wouldn't know what I was missing, because I have no idea what those things are. Still, when I had to take a math placement exam at Chicago, and one of the questions asked us to prove that 1=1, and the only answer I could think of was, "Duh! What else would it equal?!" I did briefly consider that I was missing out on some important aspects of the world. But I guess that's just how it goes sometimes.