Suppose you have been away from math for a while, perhaps since Algebra Two and the SAT in high school. After these necessarily evils, you bid it a hasty farewell and gave it the bum’s rush from your entire life. Now, several years later, you have completed a Baccalaureate degree in something, and wish to go on to advanced degree — all highly commendable — but alas! graduate schools require the GRE, and the GRE involves math. How does one get back into math after years away?
Some folks who have not dealt with math for a wrestle with “math anxiety”, and may even be heard to utter such things as “I’ve never been good at math.” It actually says something quite profound about the American math educational system that such a substantial proportion of intelligent and highly educated people claim to be “bad at math.”
Study after study has shown that “math anxiety” involves self-fulfilling prophecies galore: folks who don’t like math avoid it, don’t practice it, and thus get rusty at it and are more likely to make mistakes because they are rusty — which reinforces the anxiety. In most cultures in which “math anxiety” is not a huge issue, proficiency at math is regarded as the result of simple hard work and practice, not of some kind of genetic windfall that a nerdy few have and most people don’t.
All of this is to say: dive in. You’re an intelligent and well-educated person: you can do this! Do math every day between now and your GRE. Math is not a spectator sport: the only way you learn is by doing it. Yes, you will make mistakes in the beginning. That’s fine. That’s exactly what is supposed to happen in the math-learning process. Just learn from your mistakes and keep working.
Practice, practice, practice
Before you even begin your formal GRE practice, start warming up with mental math. You should be able, in your head, to add and subtract random two digit numbers, and multiply all single digit numbers. Make sure you know your “times table” inside out, and drill it until you know it. Start reviewing arithmetic with fractions and decimals, with percents and ratios. If you are a Magoosh member, you will find our introductory math video lessons helpful. This McGraw-Hill book is also a very gentle refresher.
One of the biggest traps on the GRE Quantitative Section is calculator overdependence. Math-phobes sometimes get lazy and think: I don’t really need to know what 5 times 7 is, because I’ll always have a calculator on the GRE. That is a STUPENDOUSLY BAD APPROACH! One GRE Quant question after another is written specifically to punish all those people who instinctually reach for the calculator all the time. The more you can rely on your own mental math, and not touch the calculator, the more you will avoid these traps, and the more successful you will be. There is no substitute for strong mental math skills. Ideally, you should use the calculator no more than two or three times at most in an entire GRE Quant section.
Get comfortable with estimation. For example, suppose however the question is framed, it involves multiplying 298 times 5.2. A benighted approach would use the calculator to calculate that exact answer. A considerably more sophisticated approach would recognize immediately —- 298 is almost 300, and 5.2 is very close to 5, so (298)*(5.2) must be very close to 300*5, and your mental math has to be good enough that you can do that multiplication in your head: 300*5 = 1,500. Quite often, when ugly numbers are given in the question, answer choices are spaced apart enough that estimation easily will isolate a single answer.
Learn the divisibility tricks. Learn the doubling & halving shortcut. Part of success on GRE math is developing something called “number sense”, which comes only from “playing” with numbers (see Chris’s description of the “99 game” in this post.) The more you can develop a sense of “play” in games such as these, the more it will build your confidence in math.
Math and your brain
I would also recommend getting curious about your own brain and how it interacts with mathematical ideas. This post talks a little about left-brain vs. right-brain approaches to math. Many of the folks who really struggle with math are right-brain, big-picture types, perhaps with aptitude for the arts, and typically not good with details, organization, and precision. These people typically get the big ideas very quickly, but then can’t apply them in the rough and tumble of individual problems.
If this is you, I have some hard left-brain medicine for you. Unrelated to anything specifically mathematical, you need to practice (a) detail management; (b) organization; and (c) precision, in any areas in which it is possible. Organize that messy drawer of your dresser, or your kitchen cabinet, or your medicine cabinet, in the most hyper-rational anal-retentive way possible. Pay attention to subtle precise differences in colors, in fonts, in leaf shapes, in window designs, in bird calls, etc. etc. Volunteer to plan and organize things for people, forcing yourself to manage all the relevant details. In all the environments in which you are the most familiar (your house, your place of work, store where you frequently shop, etc.), practice noticing a new detail, something you have never seen before, each and every time you are there. In all of these, you are trying to exercise your left-brain capacities: just a little strength more on that side of your brain will have huge payoffs in your ability to handle math problems.
You are an intelligent person. Therefore, you are eminently capable of learning enough math to perform well on the GRE Quant section. Don’t let your own habitual fears psyche you out. Practice feeling confidence in math, and practice math questions with a sense of curiosity and adventure. Believe in your ability to develop the necessarily skills and perspectives, and don’t let yourself down!