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I recently did an exercise in one of my classes in which I asked each student to teach one or two problems to their classmates. I think some of my students suspected that I just wanted to make them better appreciate how hard teaching can be (like how my parents want me to have grandchildren so I can know how much they’ve suffered). But in truth, my hope was that this activity would help my students to study more effectively at home, and I was happy to discover that this turned out to be the case.
A lot of us, at times myself included, think of studying as a skill distinct from teaching. As I’ve seen with many students, though, the practices that make for a good teacher also make for the most effective student. The things that I think about as I prepare for a class are the same things that you should be thinking about at home when you sit down to work through a new math topic or GRE problem set. With this in mind, here are a few good teaching moves that you can apply to your studying.
Show, don’t tell.
I’m also a writer, so this is a favorite of mine! As a teacher, I know that students learn most effectively when I help them to work through a difficult problem or concept on their own. You want to do the same thing for yourself. When working on a problem, don’t immediately look at the explanation. Instead, be patient; give yourself several chances to figure out the problem first and only use the explanation as a last resort.
For every problem I teach, I prepare lists of questions to ask if students are confused. The goal is to find a way to guide each student toward understanding the solution without giving away how to do it. You can do the same thing for yourself if you get stuck. Here are some questions you might want to ask:
- What information is this problem giving me? Write it down. Focus on what you DO know, rather than getting overwhelmed by what you don’t.
- What else do I know about this topic? Connect the given information to other facts you’ve studied.
- What am I looking for? What do I need to get there? Try to break the problem down into smaller pieces. For example, if you’re looking for the area of a triangle, you’d need the base and the height. See if you can at least figure out a few facts about the triangle, even if you don’t see what the base and height are at first glance.
In addition to thinking of questions, I also make lists of all the reasons why someone might get a problem wrong. After you’ve figured out how to do a problem, make a list of all possible errors, including careless mistakes and errors in understanding. This way, you’ll be a lot less likely to make these errors when you see a similar problem on the test. You’re also confirming that you’ve thoroughly understood the problem and related concepts.
When I teach a problem, I never just want to teach that problem, because my students aren’t going to see this particular problem on the test. I want them to learn some larger lesson that they can apply to a number of other questions. You should be doing the same thing when you study. Look for a lesson about how to approach problems, how to avoid careless errors, your own strengths and weaknesses, etc. Even better, keep a list of these takeaways and refer back to it from time to time as you study.
Teach someone else.
This is a great exercise, because it helps you to reinforce all of the good habits I’ve outlined. Since each of us approaches problem solving differently, this also forces you to look for multiple ways to solve and explain a problem, which can make you a more efficient test taker. Find a study partner or group, or just an indulgent friend, and practice teaching a couple tricky problems to them.
One of my colleagues said something to me over the summer that I’ve kept in mind ever since: as a teacher, if you’re not actively improving, you’re getting worse. The same is true of studying for the GRE. If you’re not regularly looking to expand and improve your range of study tools, your studying will probably become less effective (and less enjoyable) over time. That said, trying to do TOO many new things at once can be overwhelming. Each week, try to incorporate one or two new study moves into your repertoire, starting with some of the ones from this list. Good luck! 📝
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Cat Powell is a Manhattan Prep instructor based in New York, NY. She spent her undergraduate years at Harvard studying music and English and is now pursuing an MFA in fiction writing at Columbia University. Her affinity for standardized tests led her to a 169Q/170V score on the GRE. Check out Cat’s upcoming GRE courses here.