Lessons from Pre-Calculus
When my pre-calculus teacher, over podium and outstretched hand, spoke to me that November afternoon, I’d strung from his sentences more than he’d most likely meant. “It’s not like it’s beautiful,” he had said, “but it works out even though you don’t understand what’s going on,” which had factually been an explanation of mathematical patterns but which, in its simplicity, in his confidence in its delivery, had seemed somehow both ordinary and yet inexplicably important: an explanation as or more applicable to everyday near-misses and horseshoes, quad-clovers and serendipities, to the little reliefs and menial mercies of life itself, as it was to fractals or quadratics or whatever other analytical element had been its aim.
I’ve taken as many lessons from pre-calculus class this year as I have from the nightmare of the election season. My altered perspective derived of pre-calculus, as my teacher would explain it, is an extrapolation, the expansion of given points to find some outside or excluded point; the challenges I found in the winter, in response to the election season are, inversely, an interpolation, or a movement from the large to the small, the oversized to the microscopic. I’ve written much about the election and its effects, how I’d cried that first morning of the results in a pair of peony-pink ski socks, unable to get dressed, how our news-junkie family had acquired, like a new, impossible-to-understand but supposedly significant modern painting, a rectangle of black space where we had once watched arguments unfold on CNN. I’ve written less this winter about pre-calculus, despite with what force it has touched me, and it seems strange, given our family’s generations-long proximity to the realm of analytics and science, that I had not come, despite my personal difficulties, to depiction of the subject already.
I want to say that when we watched ‘A Beautiful Mind’ in Honors English last week I admired the equations and not just their shapes in white marker on the facets of the stained glass.
I want to say that I appreciated the microscope I was gifted, age ten, and that I completed the Sudoku books I’d been told to carry on the plane, and that I think of conics when un-peeling the skin of my cutie tangerines. I want to lie that I’m enraptured with the family mythology of my brilliant and ailing grandfather, who went into debt but with his brain, because he’d been told it was his one asset, the one foothold to cling to, and how he’d emerged, an apartment and twenty years later, with an office at Siemens and a PhD on the topic of the molecular structure of paint, with a presidency at the New York Chemistry society and an occupation he’ll follow until he dies, but if I’ve been passed any familial trait it is by adherence to fact, and the truth is that however admirable I found such a story, however clearly I declared this fall that I wanted to understand the subject, that it was only after having maintained my GPA that I found myself so much as approaching an understanding of beauty present in mathematics.
My childhood was a popcorn strand of consecutive mathematical errors and shortcomings. Where today I can logically reason with my sister’s mathematical prowess, from age six to ten I was convinced that my mind was a weak photo copy of her own, run along with faded gray lines and lacking in comparison. I did not get asked out for an alternative math track, so much as get asked to sit the qualifying test.
By eighth grade I had developed such an aversion to the subject that rather than delight in the bowls and hills of parabolas, rather than exult in the unpackaging of factorable equations which my classmates were content to partake in, I used seventh period as my daily restroom timeslot, defiantly devouring Modern Library’s ‘Selected Lord Byron’ and scraps of the New York Times, often pressing the poet’s classically-arranged face against the empty spots in the blue and pink and lemonade yellow problem-solving worksheets we were given as though in substitution of effort. I learned how to answer questions on the spot with a minimal margin of embarrassment, a skill which has left me with a deftness, a lopsided boldness of speech. I mastered the art of footsie. I acquired mastery over three expert-level braids: fishtail, French, and four strand, all of which required a certain concentration and a caution of the hands.
When my eighth-grade math teacher, who I’d been confused to have found reason—unlike the other students, in friending in freshman year on Facebook—tried to place me in Algebra, it was out of sheer defiance that I had my counselor sign me up to take geometry instead. Months later, when middle school classmates analyzed images of our ex-teacher’s wedding cake online—the coconut-shaving frosting, they concluded, had been a tacky choice—I had successfully fleshed out my first high school semester with a foundation built from the understanding of angles, the equations belonging to various shapes. I planned short stories as I listened half-heartedly to the lectures, recorded as many snippets of my teacher and classmates’ speech as I did triangular rules and angular theorems, snippets of clever bits of my teacher and classmate’s speech as I did triangular rules, angular qualities, and yet I emerged as one of the most well-It was memorization. It was easy. In other words, I wrongly believed I had conquered mathematics, molded it to my will; little did I realize it was only a head of a hydra.
Despite what I believed were my best efforts—Girl Scout cookie-induced cram sessions, copious amounts of highlighting, neatly drawn graphs—next level math delivered my first B, and I went into a terror. Somewhere between page seventy and four hundred fifty of Barron’s Complete SAT math, however, the sophomore year-driven aversion was drilled out, or channeled into something productive, and I found myself in the same classroom the next fall with a new, if still menial appreciation for the use of numbers.
Pre-calculus has been different. It has not been semester-long test, an experiment in endurance. I’ve derived from it lessons not of marginal-significance, like hair braiding and the better enjambment to be found in Byron, but those which the American school system, knowing a thing or two, must deliberately, and advisedly intended: how to apply the quadratic formula, how to draw a graph’s inverse, how to pack and unpack combinations in little layers we called fog and gof. Pre-calculus, in the long hours and pre-finals forest of papers, taught me discipline and the strength of effort.
It taught me to respect others, to respect those pieces of the world, different from my own, which they admired; I began minor research into fractals, a phenomenon he spoke enthusiastically of and whose respective Google search returned to me electric blue and mustard colored psychedelic results. It taught me to simplify chaos into order, to scale oversized anxieties—the change of getting into a first-choice college, the likelihood of finding the headband I’d hidden at J-Crew to be in the same location—to probabilities which leant themselves to the realm of m and m’s. It provided the respite of a constant in the face of change with its sinusoids which move predictably onward, its ellipsis which pronounced themselves only in loops so that where I used to understand indifference in its binary nature, I now welcome its simplicity as that comforting sort belonging to my childhood, to plastic sleds and snow-boots, arguments solved with Vermont cookies split down their so-clearly divided sides.
Pre-calculus has simultaneously reintroduced me to mathematics and to myself; it has made me see numbers in patterns and find value in my own attention to detail, a trait to which it yields fast. Its shapes hold literary contortions, its rules the applicability which make its textbooks warehouses of words laid like grain, its lectures provisions of oat to supplement my speech, my scope of the English language, should I select to reap them. I understand that with these grains and oats and golden haystacks of lines I could write a decent to more than decent essay or short story or play: something simple and sober with to it all the order contained a parabolic or linear equation.
I could talk about that early night driving home in Utah in an essay, that night in which I’d had to crane my neck to see the digits but had felt the smooth ink of a Bic pen dip and glide in sinusoids which mimicked the hills we drove into and across; I could talk about the common ground the TI-nspire finds between two inequalities, which turns out a muddy magenta color like the softness formed in a bruise. Maybe I’d speak about limitations in the form posed by asymptotes, or borrow my teacher’s words to end an essay in a statement which seemed to run far beyond the realm of graphing and solving, factoring and computing: “It’s kinda very black and white, so, you gotta get from here to there and make it happen.”
Even for English majors, I would write, there’s a beauty in mathematics. Especially for English majors, I’d state, who are equipped with the sympathies to access these warehouses and exploit them: there is a beauty in mathematics. This winter has been hell, I’d say, borrowing his words to do it. “The little puzzle,” I would explain, “where it’s broken up into a picture, and it’s four by four with one tile missing, and you move the tiles or whatever, I don’t know what those are called, but I remember one time we did a proof that showed that if you take the picture and flip just two tiles, they proved that it is impossible to solve it, you could break it up and fix it and switch them, and it’s impossible to get it back.”
“It’s impossible to get it back”, I’d end the essay, meaning something political but not saying it straight. It’s impossible, I’d concede, and for the first time in a long time I’d be referring to a problem posed by a force existing outside the realm of mathematics.
Alexandra A. Reinecke is a writer and journalist who uses writing as a tool to encourage empathy and affect positive change.
