“Your daughter has a serious math block”, Mrs Lederer advised my parents at the mandatory conference at the end of my fifth grade year. “She needs a tutor”.
Although I knew, of course, that math wasn’t my strong suit, I wasn’t aware that I actually suffered what sounded like a quasi-medical problem, so Mrs. Lederer’s pronouncement filled me with excitement. A “math block” sounded like a significant, rare, possibly even exotic condition, almost a diagnosis, one that wasn’t too personal to drop casually into conversation for minor dramatic effect, like my friend Ruthie referenced her allergies. I had deep admiration for Ruthie’s deft use of allergies to decline all the food she hated. Aside from giving her an unchallenged pass on kiwis and mushrooms, it placed her in an elite group of classmates with special conditions, of which I had exactly none: no allergies, never a cast, glasses, or braces; not even divorced parents, much more a rarity in the early 70s than now.
Since having a math block was like having math allergy, I expected it would afford me similar protection, as long as I remembered my manners. “No thank you”, I’d say next year when our sixth grade math teacher passed out the pop quizzes we all dreaded. “I have a math block,” I’d explain, “so I can’t do fractions or take math tests”. Here I’d pause, before politely adding, like Ruthie did, “you can ask my parents”.
Despite my parents’ obedient acquisition of a long succession of math tutors, as years progressed it became clear that Archimedes himself could not illuminate the darkness that shrouded the path to my understanding mathematics. The simple truth, reduced to its essence, was if I couldn’t memorize it, like the times tables, I couldn’t do it. Algebra, in particular, would prove to be my undoing. “It’s amazing”, exclaimed Tutor #2, scrutinizing my abysmal practice sheets with growing wonder. “You actually do better when you randomly guess the answer than when you try to work it out”.
This was true. Even with help from the tutors, I failed Algebra twice, took it two more times, and then managed to pass it only after my teacher tutored me one summer, cleverly using the opportunity to feed me every question and every answer that would be on the final test.
Algebra was so traumatic for me that merely seeing a negative number on a piece of paper flooded my body with adrenalin, jump-starting me into high anxiety mode. Already disgruntled by any number system that incorporated the alphabet, I simply could not understand Algebra’s application; lacking that information, I would never conquer it.
“But what is it for?” I would demand of the tutors.
“Math is a language”, they’d intone. But it wasn’t; I was good at languages, and I knew what they were for. You needed language to say “Take your bare ass off my pillow”. Try saying that with integers.
“What is algebra for?” I’d ask the next tutor.
“You’ll find yourself using Algebra over and over again in many different ways throughout the rest of your life.” In the five decades that have since passed, years that have encompassed activities as disparate as practicing law and gardening, grieving and getting high, traveling and voting, hiring people and burying them, shooting pool and raising children, studying Sanskrit and skiing — I cannot recall a single instance that called for the factoring of polynomials.
“What is the purpose of Algebra?”, I paraphrased.
“Algebra”, Tutor #4 declared grandiosely, “is about logic”.
“Logic”, I repeated, stupefied. “Logic?”
Indeed, of all possible answers, “logic” was the least credible. Algebra was anything but logical. It seemed, actually, to defy logic, featuring among other mysteries the categories of “irrational numbers”, which seemed to me not only to be stating the obvious, but also rubbing it in.
While negative and irrational numbers confounded and frustrated me, I was driven to foot-stomping tantrums by the introduction of imaginary numbers. Evidently, these are numbers that don’t even exist — or, if they do, it’s only in your imagination, like playmates and monsters. Their existential nature frustrated me to the point of hysteria, which the tutors could not quell. “How am I supposed to learn something that isn’t real!” I shouted, sweeping my workbook off the dining room table.
What kind of person, I wondered, would devise a system requiring us to make calculations with numbers that didn’t exist?
I’ll tell you what kind. Imagine a bunch of mathematicians in the year 525 – Greek, so they’re in togas, sitting on white marble blocks in a hotel ballroom, fiddling with their protractors or whatever. One quietly tunes his lyre as the group discourses on the wonders of the number systems they’d been inventing:
Thales: You know, guys, we’ve done a hell of a job with the math–we’re rockin it!
Pythagoras: Yep…..right on schedule for A.D. . . . I can’t wait! I really think the number systems we’ve invented could change the world! (Strums a chord)
Polycrates: Listen, Thag, excuse me; guys, something’s been bugging me, ya know, I hate to be a big downer . . . but am I the only one thinking we should somehow . . . back up our work? What if our numbers get lost or . . . stolen . . . you know the Egyptians, they do have that reputation . . . not that I’m ethnic stereotyping . . . but . . . suppose we “misplace” our numbers? It’s happened before, remember? That time we invented last names for everyone, and then lost them all?
Pythagoras: Excellent point, Crate. (And by the way, the last name thing never really caught on, to tell you the truth.) Thales and I share your concern about our number systems being lost or . . . “borrowed”. (Strum) And we studied the problem from every angle, and as we did, we reached a momentous conclusion. (Buzz of excitement from the men.) Tell them, Thales. (Strum)
Thales: Well, what we found was that the world seems to consist of opposites . . . yet . . . it seems a thing can become its own opposite! Therefore, they cannot truly be opposites but rather must both be manifestations of some underlying unity that is neither! (Gasps and murmurs of disbelief.)
Anaximander: Sooo . . . .?
Pythagoras: So, our number systems are an essential part of this theory. . . . Men, Thales and I have reason to believe these number systems are far more important than any of us ever dreamed, and we just can’t risk losing them. They need to be up and rolling by A.D.. So I invented a set of, well – standby numbers . . . as backups, in case we lose the ones we’ve established so far. These backup numbers exist only in our minds, only in memory, you see . . . so I call them . . . (fast thrilling riff of flamenco chords) . . . imaginary numbers!
Pherykides: : Well done, Pythagoras. (Searching toga for pen.) Hey Crate, do you have a
******
Along with Algebra, word problems presented a special challenge. Word problems were an ugly trick math teachers devised to lull their verbal, math-blocked students like me into the false confidence we could solve math problems. Bait and switch!
“Word problems”, I thought triumphantly. Words! Now here finally – sixth grade – was arithmetic at which I could excel, for if anyone could solve a word problem, it was I. I was great with words, I loved words and welcomed them and their problems into my life. Crossword puzzles, Scrabble, newspaper jumble – pitch ’em my way, I thought smugly. Good or well? I or me? Further or farther? Hanged or hung, lit or lighted, lay or lie? Oh yes, I relished a good word problem. If they wanted to throw in a couple of numbers so they’d qualify as “arithmetic”, I was sure I could handle it.
It took just one test to puncture my confidence. These weren’t “word problems” at all. They were just math equations lurking like spies in an unsuspecting community of words: Algebra, undercover.
And, typical of school textbooks in the 1970’s, the action in the word problems was tedious and hopelessly pedantic, consisting of the mind-numbing activities of “Jack”, a boy of undisclosed age, who spent his time sorting fruit into baskets, or riding the train roundtrip between the same two cities. Back and forth and back and forth Jack traveled, his purpose unexplained. With no apparent job or hobby, no requirement he attend school, no parents or authority figures telling him what to do, and evidently, no obligations at all, Jack was a figure of both envy and derision.
Given Jack’s leisurely lifestyle, it was patently unfair to burden us – busy with class, homework, scouts, ballet, and karate – with the task of calculating how fast his train was moving based on what time it arrived at the station, especially when he never even got off. Jack could jolly well figure it out himself. After all, he had nothing but time, and his interest in the answer couldn’t possibly be any any slighter than our own.
Today, I view Jack’s plight with far more insight, and no small amount of pity. If back then we’d only just given him a friendly wave and maybe said, “ Hey, Jack”, that might have given him some relief from his hopeless, helpless fate, with its unavoidable implications of sexual impotence and forlorn human isolation. Marooned on the train, trapped forever in a looping circuit he could not control, Jack’s destiny was to travel continuously but never to arrive. Whatever relief he scrounged from occasionally tossing oranges into this basket and apples into that one would have been minimal indeed compared to the bleak reality of his endless round trip journey to nowhere.
I rarely saw Jack again after I left sixth grade; for all I know, he is still on the train.. Word problems weren’t particularly well-suited for Geometry anyway. And ultimately, it was Geometry that saved me. It was a logical, useful discipline whose application was obvious: you could use it to build houses or draw basketball courts, make newspaper hats and paper airplanes, play air hockey and design bridges. The angles weren’t negative, the theorems weren’t irrational, the proofs weren’t imaginary. Since this made sense to me, my math block improved a bit, and I started getting “9”‘s on math tests instead of “3’s.
Our pal Pythagoras – who frankly had no business fooling with all those numbers that didn’t exist, when there was an infinite amount of perfectly real numbers available and seeking employment – became obsessed with a triangle he met at the 520 B.C. Summer Olympics and ended up writing this theorem about her that became really popular and eventually went platinum. I learned it and still recite it in the car or shower sometimes. It’s the only math theorem I know. Ha, Mrs. Lederer! I knew could do it. Take that!
-by Caro Marks
Copyright 2015
A DIFFERENT DRUMMER 