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Learning from GRE Math Practice

I’m going to ask you a question whose answer seems painfully obvious.

What is the purpose of doing practice GRE math questions?

Take a minute to really consider that question in its entirety and explore the implications of your answer.

If your answer was any of these, or something similar to these, then it’s too simple:

  • “To get better at them.”
  • “To get a higher score.”
  • “To see what’s on the test.”
  • “To practice my math skills.”

They’re all simplistic because they ignore a vital part of the equation: how, exactly, practice leads to higher scores in the first place. That only happens by learning new skills. Okay, then how do practice questions lead to new skills? That leads us to the more insightful answer, one that affects every step of your studies:

  • “To learn from my errors.”

Unless you understand the importance of learning from mistakes, you will make limited improvement, if any. Time spent doing practice questions, without careful analysis of your methods, and the result is time wasted.

Curiouser and Curiouser…

There are, of course, those who blaze through hundreds of questions with nary a glance at the explanations, but they’re relatively rare (do not be that person!) — this post isn’t meant to address those extreme cases. Instead, there’s a much more sinister, much more common mistake people make when studying. They understand that when they get a question wrong, they should look at the solution and see the correct path. But what they don’t do makes all the difference: they don’t compare their own process to that in the explanation.

Watching a cooking show does not make you a master chef. Even if your practice problems all have video explanations (like does) and careful elaboration, simply seeing the answer and saying, “Oh, I get it” does very little on its own. The next step down the rabbit hole is learning exactly why and how each stage of the solution was the appropriate next step. That part is far more important.

To do that means looking at the solution in stages. First, consider what you needed to see in the initial question in order to start down the right solution path. Why did the answer begin the way it did? Then, from there, look at each individual logical stage in the process, constantly asking that same question—“why?”

Your Goal

…is to never make the same mistake twice. If you could actually live up to that ideal, you’d become an absolute master of the GRE in no time at all. I’ll admit that you’re not actually going to achieve this (nobody does), but the sentiment remains just as important to your studies. You want to learn the mechanics behind each practice problem so well that you will recognize similarities in other questions. A quick check of the solution won’t lead you to that point. Instead, in order to get there, you’ll have to dive deep.

Keep in mind that in the end, how much you improve is a function of how much you learn, not of how many questions you answered. No matter how many questions you answer, there will be others who did more. Don’t be tricked into thinking that you need to follow that lead. It’s cliché, of course, but quality trumps quantity.

Learning from Correct Answers

A correct answer, simply put, doesn’t necessarily mean a correct process. If you pay careful attention to how the author or presenter of the explanation gets the answer to an easy–or medium–difficulty question on the GRE, you might find that there are some real differences between that and how you went about answering the same question. And it’s not enough to simply get a correct answer. Really, you want to get a the right answer for the right reason, and as efficiently as possible.

If you are just starting your studies, then it’s wise to take the same approach to many of your correct answers as you would to the wrong answers. Compare your approach to the solution, step by step, and carefully note differences and how you could have approached the question even better than you did.

The Short and Sweet

Pay very close attention to the solutions to questions, and don’t hesitate to ask questions. Even if you get a question wrong because of a simple slip-up, address it — “how can I avoid that next time?” The more time you spend tracing and retracing your steps and picking apart the underlying logic of the question, the better shape you’ll be in for the next question of the same type.


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