When we study practice problems, our overall goal is to master the problem we’re working on right now. What does mastery mean? It means that, when we see a future different problem that tests the same thing as this current problem, we will realize that the future problem has certain things in common with this current problem, and we will know what steps to take as a result ” we will, literally, recognize what to do on the future different problem, a problem we’ve never actually seen before.
It’s necessary to get to this level of mastery because the problems we study will never be the actual problems we’re expected to do on the test. But we will see similar problems ” problems that have something in common with problems that we’ve already studied. If we can recognize what to do, then we will be faster (which is always important on this test), and we will be more effective ” we’ll be more likely to get it right because we’ll know that the method we’re using actually worked the last time we saw a similar problem.
This mastery we’re talking about ” the ability to recognize what to do on a new, different-but-similar problem ” comes from the analysis we do after we’ve already finished trying a new problem for the first time. So how do we do that?
First, of course, you have to try the problem itself, and you should generally hold yourself to the time constraints given by the test. Pick an answer to that problem within the expected timeframe, even if you have no idea what the answer is ” every aspect of this test needs to be practiced, including how to guess when you don’t know what to do!
Okay, so you’re done with the problem. Now what? Well, the first thing everybody does is check the answer, right? Interestingly, the analysis doesn’t depend much on whether you got it right or wrong! But we all want to know, so go ahead and check the answer. Just be aware that this doesn’t change your review process much.
Next, answer a series of questions.
1. Did I know WHAT they were trying to test?
- Was I able to CATEGORIZE this question by topic and subtopic? By process / technique? If I had to look something up in my books, would I know exactly where to go? (If I couldn’t do this, I need to take the time to categorize it now, while I’m analyzing the problem.)
- Did I COMPREHEND the symbols, text, vocabulary words, questions, and answer choices? Can I comprehend it all now, when I have lots of time to think about it? If not, I have some work to do with my books (and my teacher or tutor, if applicable). How am I going to remember whatever I’ve just learned for future?
- Did I understand the actual CONTENT (facts, knowledge) being tested? (Go back to your books and teacher to learn / understand anything that gave you trouble.)
2. How well did I HANDLE what they were trying to test?
- Did I choose the best APPROACH? Or is there a better way to do the problem? (There’s almost always a better way!) What is that better way? How am I going to remember this better approach the next time I see a similar problem?
- Did I have the SKILLS to follow through? Or did I fall short on anything? (Again, go back to your books and teacher to learn / understand anything that gave you trouble.)
- Did I make any careless mistakes? If so, WHY did I make each mistake? (It’s critically important to take the time to understand why you made the mistake.) What habits could I make or break to minimize the chances of repeating that careless mistake in future?
- Am I comfortable with OTHER STRATEGIES that would have worked, at least partially? How could I have made an educated guess? (Think about this even for questions you get right ” it’s often easier to develop alternative strategies and learn how to make an educated guess on problems that you got right. Then, you use the lessons learned when you see a harder problem of the same type / category.)
- Do I understand every TRAP & TRICK that the writer built into the question, including wrong answers? (Again, it’s often easier to understand and learn to avoid traps on problems that you got right! Learn how to spot them consciously so that you can still avoid them even on harder problems.)
3. How well did I or could I RECOGNIZE what was going on?
- Did I make a CONNECTION to previous experience? If so, what problem(s) did this remind me of and what, precisely, was similar? Or did I have to do it all from scratch? If so, see the next bullet.
- Can I make any CONNECTIONS now, while I’m analyzing the problem? What have I done in the past that is similar to this one? How are they similar? How could that recognition have helped me to do this problem more efficiently or effectively? (This may involve looking up some past problem and making comparisons between the two!)
- HOW will I recognize similar problems in the future? What can I do now to maximize the chances that I will remember and be able to use lessons learned from this problem the next time I see a new problem that tests something similar?
- If you are not doing the above analysis on every GRE problem you study, then you are not getting the most out of your study. If you have done tons of practice problems but haven’t done the above analysis, then you aren’t done with those questions. Go back and start doing this analysis. It doesn’t matter if you do fewer problems ” obviously, this kind of analysis is going to take lots of time! But this kind of in-depth, high-quality review is exactly how you master this test.
- I would far rather see my students do 20 problems with this kind of analysis than 50 problems without this kind of analysis. Generally, we should be spending about two to five times as long on analysis as we spent doing the problem in the first place. On a 2-minute problem, that means spending 4 to 10 minutes analyzing!
Okay, so what are you waiting for? Start studying! And good luck!