By now, you’ve likely seen talked about, and forgotten the events of Wednesday, June 2 in Detroit’s Comerica Park. It was the ultimate in contradictions: pitcher Armando Galarraga one out away from pure perfection — a perfect game, only the 21st in Major League Baseball history — losing his shot at perfection not because he was imperfect, but because umpire Jim Joyce made an obvious mistake. The pitcher was perfect, but the umpire was not, and the perfect game became an imperfect footnote in the annals of baseball history.
In today’s internet and text-message age, outrage spread quickly as fans watched the video replay and saw clear evidence that Joyce had blown the call. As is historically the case, the loudest cries are always “kill the umpire!” — until Joyce did something monumental, something completely surprising, something that arguably made him a more sympathetic character than even Galarraga himself: Joyce admitted he had made a mistake.
As you prepare for the GMAT — a test with high stakes not unlike those of achieving baseball immortality — you can learn from Joyce’s actions as you strive for Galarragan perfection. Admit your flaws and mistakes, which can be a difficult-but-extremely-valuable thing to do.
Math is a unique subject in the way that it is taught and learned in schools. Many students perceive it as “hard.” It is finite enough to always have one, indisuputable “right” answer, meaning that student contributions that are “wrong” tend to have a negative connotation. Think of your own middle school and high school experience, and if you’re like most people you can probably pinpoint a time at which you stopped actively participating in math classes, or learned to rely on “partial credit” in order to pass tests without fully acing them. Maybe you memorized enough formulas to plug-and-chug, or showed enough scratchwork to get the A-for-effort, but there’s a good chance that you reached a point when you stopped fully understanding math and just started passing the tests. Even as early as elementary school, students identify themselves as “good at math” or “math’s not my thing,” and the consequences can, frankly, be saddening.
Like umpire Jim Joyce, your best strategy as you study the GMAT will be to admit that you need work on truly understanding some of the fundamentals of math. If you find yourself thinking that “I just need to remember the formula,” you’re probably taking the wrong approach — the vast majority of formulas required on the GMAT can be understood or derived and do not need to simply be memorized, and if you do understand why a formula holds, you’re much more likely to be able to apply it in some of the unique ways that the GMAT will ask you to.
Take, for example, an isosceles right triangle. Many GMAT students have memorized that the ratio of the sides in a 45-45-90 degree triangle is: x, x, x*(sqrt 2). However, this ratio can easily be derived by using the base right triangle theory, Pythagorean Theorem. If a^2 + b^2 = c^2, and a = b (two sides in an isosceles triangle are equal), then you can substitute a for b and get:
a^2 + a^2 = c^2
Solving for c, you’d combine the a^2 terms on the left:
2a^2 = c^2
Then take the square root of both sides:
a * sqrt 2 = c
So, the third side — the hypotenuse — is going to equal the length of the either shorter side, multiplied by the square root of 2.
This is just one example of how attempting to understand math more thoroughly can give you multiple ways to solve each problem — essentially, math is just “the logic of numbers,” so it’s likely that 80% of what you need to know for the GMAT can be derived from really understanding that baseline 20%. Unfortunately, many people have already resigned themselves to the feeling that they’re just not good at math, and will attempt to simply memorize as much as they can for a quick turnaround; on the GMAT, which tests “how you think” more than it tests “what you know,” that strategy can severely limit your score.
To become a better GMAT test taker, take a cue from Jim Joyce and learn to admit when you’re wrong and need to improve. By embracing your imperfections, you can then give yourself a chance to achieve GMAT perfection.