The 4 Tenets Of GRE Math Mastery
If you're the TL;DR type, sit back in your easy chair, click "play", and I'll narrate this entire blog to you.
I think we all can picture it. We're taking a math test, but we didn't study very well. The first few problems go okay, but then we try the next problem... and get nowhere. We can't get the one after that, either.
Crap crap crap crap crap.
I've been there. AP Calc did not go well for me. As a high school student, I didn't have a great perspective on what I needed to do to get better, so I just went home every day after class and tried to teach myself from the textbook - with very mixed success. By the end of the class, I was convinced I wasn't that good at math. However, I've come a long way since then.
So if you're intimidated by the thought of learning math for the GRE, or if you've begun the process and it's not going well, I know how you feel. In this article, I'll talk in detail about the process of going from being "bad" at math to being "good" at math, based on what I've learned and observed over the past nine years of working with many GRE students. I divide this process up into four areas: concepts, review, methodology, and experience.
Arithmetic. Algebra. Geometry. Data Analysis.
Fractions, decimals, linear and quadratic equations. The Pythagorean theorem. Word problems. Probability. And many, many more.
To do well at GRE math, you need to be good at the test concepts. (First of all, it's helpful to know what the tested concepts actually ARE - they're covered, among other places, in the ETS Math Review.)
You're fluent in English, right? Well, just like knowing how to read English is a prerequisite for GRE verbal success, being fluent in math concepts is a prerequisite for GRE math success. In fact, it's the foundation for GRE math success. By fluent, I mean the concept is pretty much automatic for you. You don't have to think about it... it's just there when you need it. Fluency is a lot different than familiarity. So we need to keep working on things that we're merely "familiar" with. Show me someone who is fluent with the math concepts that the GRE tests, and I'll bet you he or she can score 160+ without ever opening a GRE prep book.
Therefore, concepts are the most important area students need to address. But you obviously don't have the time to retake algebra and geometry, even if you wanted to (and you don't). So let's think about some practical steps you can take in the next, oh, few months or so.
- Like I said, know what's going to be tested. As you read through the ETS Math Review, highlight anything you don't straight up KNOW.
- Look at all the concepts you've highlighted. This will take a little guesswork, but divide them up into "concepts I once knew" and "concepts I never knew".
Now that you've classified all the concepts, start with the ones you did know at some point. These are going to be easier to make progress on, and you can use that momentum and the inevitable cross-over of certain concepts to tackle the concepts you never knew. Let me illustrate with something most people at one point knew: percents. Here's a series of steps someone might take to become fluent:
- Read what the ETS Math Review says about percents, and do the practice problems at the end of the arithmetic section of the Math Review.
- Use a prep book to refresh percents. I like CliffNotes Math Review for Standardized Tests. The idea is to practice the concept at a basic level.
- Now use a GRE prep book to practice percent questions written in the same style as the GRE. A good choice is the Manhattan Prep 5 lb. book.
- Finally, practice percent questions on actual ETS questions, the kind that are only found in the official ETS books.
If you're working on a concept that you are more shaky on, or if the above isn't going well, there's a preliminary step you can take: learn about the concept using Khan Academy, which has loads of free, helpful videos and exercises that will teach you the concept from the ground up in a friendly, down-to-earth, accessible way. If you think about it, it's unrealistic to expect a GRE prep book - even a good one - to fully cover any given concept. Khan Academy, however, will do just that.
Warning! When you make the jump from conceptual practice to GRE-style practice - like when you go from say, Khan Academy or Cliffs Notes to the Manhattan or ETS books, questions can often seem really difficult. You may have to learn the hard way on many problems - and you won't be able to do some of them at all, if you're like most people. That's ok! Just do the ones you can and move on from the ones you can't.
One of the reasons you're having trouble is that GRE-style questions often incorporate a reasoning component - in other words, you'll not only have to know the math concepts involved, but you'll have to think. Be patient with yourself as you practice - some of the lessons you need to learn will be learned by making mistakes, just like most things in life!
Hopefully, the above process makes sense. The problem is that there are a LOT of concepts to get through. And you don't want to just "get through" them... you want to MASTER them. So practice them until they're second nature, and...
When you're covering lots of concepts, you're going to want to review intelligently. You're only human. You're going to forget certain things unless you periodically reinforce them.
My advice for reviewing is that you review things as you're just starting to forget them. This forces your brain to rebuild the memory, thereby making it even stronger than it was the first time. If you review when you still remember something perfectly well, your brain doesn't have to rebuild the memory and the review won't be as effective. If you wait until the memory has completely faded, you're back to square one. So to be efficient, keep track of what day you've studied each concept. A typical review schedule for a concept might look something like this:
- Day 1: study percents
- Day 2: review percents
- Day 4: review percents
- Day 8: review percents
- Day 16: review percents
Notice that the time between review sessions keeps doubling? Since you're learning the concept more and more each time, it will take longer for the memory to fade. Doubling the amount of time between review sessions is a handy way to anticipate this. Again, you want to get to the point where you think you absolutely KNOW a concept, which is a different feeling than just having memorized it.
Of course, when you review, it's not enough to look over a chapter or the work you did. You will need to be doing new problems, too.
Ok, now let's say you're a month into your GRE math studies, and you're making some progress with concepts. You're getting into the Manhattan 5-lb book to practice as well as the ETS books. Let's talk a little bit about the way you're doing problems.
A fun fact about many GRE math problems is that they can be solved in more than one way. Sometimes, one of the ways is quite a bit faster. Here are a few ideas to improve your problem solving ability:
- Check out my free GRE technique videos. They're designed to give you more ideas about different ways to do certain types of problems.
- Revisit the ETS math questions you've already done. Can you solve the problem in a different way? If you can, do so! It will add tools to your toolbox.
- Make a note of which way of solving the problem was easier for you.
- Write down what you'll try next time you see a problem similar to this one in your GRE journal. (What, you don't have a GRE journal?)
In essence, you want to learn methods, identify problems on which they can be applied, and practice them until the techniques become fluid and you can readily identify the kinds of problems that the techniques work on.
Finally, let's talk about experience. One of the reasons I've become so good at GRE math is that I've not only taken the GRE several times, but I've done every single official GRE math question in the books. On top of that, I've tutored the SAT, ACT, GMAT, ISEE, and other tests for years - tests that cover most of the same math concepts as does the GRE. So I've seen lots and lots of ways test writers try to test these concepts - and learned a lot from my many mistakes.
You need experience, too. At a minimum, you want to use the Manhattan 5-lb book as well as the official ETS books. Definitely attempt all the ETS questions, and do as many Manhattan questions as are feasible for your timeframe. The more questions you've successfully done, the more likely it is that a weird-looking question on the real GRE will actually remind you of something you've done before... and you'll figure it out.
If you're really hardcore, you can get more experience from old SAT tests (pre-2016). Guess who wrote them? ETS. Not all GRE concepts were tested on the old SAT, but most were. Official GMAT math questions are good practice, too, since the overlap of the concepts is almost complete.
A Final Note
I only wish the process of becoming skilled at GRE math was easy. For most of you, it won't be. You have to study consistently and earn your GRE math proficiency. If you wanted to become fluent in a language, how many days a week would you practice it? One? Two? The answer has to be more like 5 or 6. And of course, you'll need to take timed practice tests to test your skills with the clock ticking. But as time goes on and you practice more and more, I think, like many of my students, you'll start to feel more confident, which will help fuel your success.