There's an aphorism attributed to Laozi, father of Taoism: "A journey of a thousand miles starts under one's feet."
I could certainly apply this wisdom to doing my dishes, cleaning my house, filing my taxes, or writing a blog post. However, while this dusty old saw might strike you as clichéd, it is clichéd by dint of its truth and is applicable to preparation for the GRE.
Now that you're enthusiastic about embarking on this journey, cracking the books, and putting in the effort to succeed at the GRE, your next question might be: "So how exactly am I supposed to begin?"
Assuming that you've taken a practice test and have a pretty good gauge of where you are and where you want to be, many might suggest borrowing a prep book from the library, hiring a tutor, or registering for a course. All these are reasonable strategies depending on your personality and learning style, but especially if you intend to pursue a GRE class or private tutoring, I would like to emphasize one strategy for ensuring you get the most out of this structured instruction.
If you review all GRE quantitative problems, irrespective of the particular concepts tested on any given problem, there is an underlying math fluency that is a prerequisite for success on virtually every math problem. This fluency is a thorough knowledge of:
- arithmetic operations
- properties of numbers
- how to manipulate algebraic expressions
- rules of exponents
- fractions, decimals, and percents
- common geometric formulas
- lines and angles
- order of operations
- coordinate geometry
- basic definitions of math terms
While this list might appear overwhelming, upon closer inspection you might notice that none of these concepts surpasses rudimentary high school mathmatics. In fact, many of you may have covered these concepts in middle school. However, as evident in the popular internet "Do You Know More than a Fifth-Grader?" quizzes, much as these children likely know more about meteorology than I do, many students have forgotten these core concepts or no longer have a strong command of them.
Unfortunately, because of the structure of GRE prep courses and tutoring, there is not sufficient time for most teachers to cover these subjects exhautively. Students have widely varying aptitudes. In a class if a GRE teacher spent much time on order of operations, for instance, many students would find this instruction valuable but others would find it tiresome and redundant; in tutoring, time is necessarily much more limited, and if a tutor covered these concepts in depth with her student, there would be little time left for anything else. Before you even begin a GRE class or tutoring, I strongly recommend you commit to mastering these subjects to the best of your ability.
So, how should you tackle these subjects?
PRACTICE, PRACTICE, PRACTICE:
As you may know, the GRE is a "skills-based" test. In other words, unlike a final exam in college or some standardized tests (e.g. USMLE, ACT, MCAT), the GRE is not meant primarily to test your achievement level in higher mathematics or literature. Instead, it is written to test your problem solving skills and ability to think in an orderly fashion. In other words, just doing a lot of GRE problems will not ipso facto increase your likelihood of success on the GRE.
Nevertheless, there are core concepts that you must know simply by rote memorization and practice. Among these core concepts are those I enumerated in the list above. Unfortunately, in many GRE texts, including the Official Guide put out by ETS, these concepts are sandwiched together in dense paragraphs of impenetrable text.
Frankly, I wonder whether this poor organization in the Official Guide is intentionally byzantine, a method of intimidating students and making them feel overwhelmed right from the outset.
There is no reason to be overwhelmed. Start by breaking this list of concepts into more manageable pieces. Attack each concept by first memorizing the basic information, then do basic problems targeted to test and reinforce these skills.
For instance, for rules of exponents, you might start by learning MADSPM:
Then do problems, ranging from simple to moderately complex, to reinforce these concepts. For example, begin with:
Then work your way up to:
To make progress, you need to pick apart these topics and do them one at a time. Set aside a week or two before your class or tutoring begins to cover these subjects piecemeal. You will find your class or tutoring more rewarding, and you will make much more dramatic progress on your performance on the GRE
This post is meant to discuss how to prepare to prepare. However, a mastery of these math concepts will not only permit you to get more out of the more advanced strategies covered in GRE courses. This mastery is also in fact sufficient to get many quanititative problems right with no additional effort! Many GRE quantitative problems test nothing more than whether you have memorized some basic concepts. You can get halfway to success on Quantitative Reasoning just by relearning math you probably knew by heart when you were a kid!
I hope you've enjoyed this primer on getting your GRE preparation off the ground. If you're interested in pursuing tutoring or a course with one of our expert GRE instructors, I encourage you to explore our entire GRE program.