Do you consider yourself a “math person?”
Actually—hold on a second. Whether you answer yes or no, you’re expressing a potentially harmful thought. Such thoughts reflect a fixed mindset about oneself—a belief that you’re born good at some things and bad at others. Carry that line of thinking a little further:
“Math people” grew up solving quadratic equations in their heads as toddlers. They always just “got it.” Everyone else had to work hard to get there. “Non-math people” could more easily run 10 miles backwards than calculate a tip at a restaurant. If you’re a “math person,” congrats on the easy grades and high GRE scores for the rest of your life. If you’re not, then too bad. It’s hopeless.
I believe that such thoughts are not just untrue, but downright harmful. There’s a growing body of research on this issue. Many readers of this blog entry will no doubt have heard of Carol Dweck, her book Mindset, and her TED talk, which currently has over 7 million views. Dweck argues that the way you view yourself has a huge impact on your success. It’s not just those who think they’re “naturally bad at something” who are at risk, by the way. One of the most negatively-impacted groups seems to be very high-performing students who think it’s all about being “naturally good at something.” I would encourage you to leave behind those fixed ideas of being a “math person” and instead adopt a mindset of growth.
In this entry, I’ll share with you a few ideas from research in educational psychology about growth mindsets and what you can do to develop one. In particular, I’ve been reading a book called Mathematical Mindsets by Jo Boaler. I’ll share with you some ideas from this book.
You Can Rewire Your Brain (to Become a “Math Person”)
First of all, know that your brain can be changed. In one intriguing study, researchers looked at the brains of cab drivers in London who had to memorize over 25,000 streets and 20,000 landmarks in order to qualify for their jobs. During the intensive training process, cab drivers showed dramatic growth in the hippocampus—the area of the brain that is used to acquire spatial information. Their brains were so affected by their practice that they showed measurable growth in the very brain matter inside their heads.
This concept that the brain can change and adapt in dramatic ways is called neuroplasticity. There are abundant examples of it. Stroke victims can sometimes regain their speech by rewiring a new region of their brain. People paralyzed in accidents can sometimes regain their movement; in one extreme case, an individual even lost the entire left hemisphere of her brain and was then able to regrow its functions in the remaining right hemisphere.
Aside from these extreme examples, we all experience neuroplasticity when we learn. Your brain is more like a muscle that can grow with exercise than like a computer that’s stuck with the processor it was built with.
Take a few minutes and watch this video of a Swiss watchmaker who has been making watches by hand for 50 years. He tells us, “It’s not easy because you learn all your life. Even at my age, I learn every day and very often by making mistakes.” An expert in nearly any field will tell you the same thing: they’ve made their most significant learning through mistakes rather than successes.
The research backs them up. Not only do experts learn from making an incredible number of mistakes, they seem to learn more when making mistakes than when doing something correctly. Jo Boaler summarizes some research on the issue:
“Students’ brains reacted with greater […] electrical activity when they made mistakes than when their answers were correct. Second […] brain activity was greater following mistakes for individuals with a growth mindset than for individuals with a fixed mindset. The study also found that individuals with a growth mindset had a greater awareness of errors than individuals with a fixed mindset, so they were more likely to go back and correct errors.” Mathematical Mindsets (p.12)
It may not always feel this way, but mistakes are not something that should make you cringe. They’re probably the most worthwhile tidbits from any study session. And they’re even better for you if you open yourself up to growth, log them, and go back to correct them.
Think of it this way: your brain grows a synapse every time you make a mistake. A good practice session shouldn’t be easy. Get out there and start making some mistakes!
Process > Product
A good teacher will make it clear: the route to a right answer is much more important than the right answer itself. Of course, on an exam like the GRE, you want to get as many points as possible. But you get those points by carefully thinking about the problem in front of you and the solution paths it beckons you to use.
In the same way that you don’t improve your free throws by focusing on the “whoosh” a basketball makes when it goes through the net, you shouldn’t try to improve your problem-solving process by going straight to an answer key. Instead, focus on the steps to get there.
When you practice on your own, try thinking of your answer keys and explanations less like the finish line and more like consultants to whom you can turn for feedback along the way. Rather than just checking the right answer, peek at the explanation to see if the work you’ve done is on the right track. If so, continue onward. If not, go back and revise. Try to lead yourself to the correct answer rather than just reading what it is.
Believing You Can Grow is Part of the Recipe for Growth
On the first day of my GRE class, I often ask my students a similar question to the one I asked at the beginning of this blog entry—I ask them to raise their hand if they’ve come into my classroom with an idea floating around in their subconscious that they are “bad at math.” Every time I ask this question, a few reluctant hands pop into the air, followed by an avalanche of others, until a huge majority of hands silently confess this belief.
It’s easy for me to believe that there is no such thing as being “bad at math”—for years, I’ve seen my students bring up their GRE Math scores, sometimes to levels they never thought possible. That said, I’m well aware many folks have been traumatized by math in their prior education. Even many well-meaning teachers may have conveyed the notion that math is a gift, and either you have it or you don’t. Take heart and do what you can to throw out these “fixed” notions that may be rummaging around in your brain. Just like your math ability can be changed, so can your mindset.
Believing that you can get smarter is part of the process in doing so.
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Tom Anderson is a Manhattan Prep instructor based in New York, NY. He has a B.A. in English and a master’s degree in education. Tom has long possessed an understanding of the power of standardized tests in propelling one’s education and career, and he hopes he can help his students see through the intimidating veneer of the GRE. Check out Tom’s upcoming GRE courses here.