Winston Churchill said: “The pessimist see difficulty in every opportunity. The optimist sees opportunity in every difficulty.” While the words of the good prime minister have much wider implications, consider how this phrase might reframe one’s approach to GMAT math.
I realize many folks come to the GMAT having bid mathematics a fond (or not-so-fond) farewell way back in high school. Now, a college degree later, one has to re-acquaint one’s self with such topics as solving for x and angles in a triangle; some topics, such as combinations (nCr) might be entirely new — even more daunting for our would-be GMAT taker. If one is facing the long uphill climb toward mastery on GMAT math, how does one view this onerous task optimistically?
I realize that every practice question you get wrong can be discouraging. Mathematics can be a demanding task-master. For any particular math problem, there may be, say, twenty different mathematical facts, from easy to hard, that you need to know to solve a problem, and if you know nineteen of those twenty, you get the problem incorrect. In school math, there might have been partial credit, but on the GMAT, if you choose an incorrect answer for almost-correct work, you get zilch for that.
In fact, if in your mathematical reasoning, you overlook a frequently overlooked mathematical step, then you can bet your bottom dollar that the GMAT test-writer will have an incorrect answer choice corresponding to this frequently overlooked step — that’s Test Writing 101! Given the low success rate of a beginning GMAT-studier, rusty at math, how can one maintain the vital engagement necessary for progress without becoming jaded or discouraged? Of course, part of the answer is the emotional maturity and security not to take personally the initial lack of success.
There’s a wonderful story about Thomas Edison. He and his team were trying to develop a commercially viable light bulb, and the problem was finding the right material for the filament. They tried a plethora of different possible materials, and each one melted or burnt out as soon as the current passed through.
Finally, the Edison’s foreman, utterly exhausted and frustrated, came to complain to the great inventor: “We should give up! We’ve tried a thousand ways with no success! We’re wasting our time!” Edison immediately responded, “A waste of time? Nonsense! We now know a thousand ways that it doesn’t work!” While that kind of optimism may sound over-the-top to the point of lunacy, it is precisely this level of indefatigable perseverance that brought about the light bulb, the archetypal symbol of a good idea.
You see, every math problem you get wrong is an opportunity to learn and grow. You have to be disciplined about studying solutions and taking explicit notes about the mistakes you made and ideas you overlooked. The mark of an excellent student is: never making the same mistake twice.
While striving for that ideal takes discipline, the promise of holding to that standard is: every problem you get wrong represents a mistake from which you are determined to learn. Thus, say, for 200 questions you get wrong, you would have learned “200 ways it doesn’t work”, and by extension, understand 200 mistake that you will not repeat in the future.
In some cases, it may be a matter of knowing a formula, although generally it’s minimally helpful to memorize formulas, and considerably important to remember arguments and logical interconnections. In some topics, especially in GMAT probability questions, how one frames the problem is very important, more important than any of the individual solution techniques. For each math question one gets wrong, one has to study the solutions at multiple levels of analysis.
This approach takes energy and discipline. It takes an Edison-like optimism in the face of frustration. Very challenging, but if you want climb into the higher reaches of the GMAT score percentiles, then one attains extraordinary results only by making an extraordinary effort. Not everyone can do this, but those who are able to able to turn every challenge, every difficulty, into an opportunity for learning & growth, will have reason to be optimistic about the GMAT as well as about their careers in the modern business world.