During a little summer beach vacation, I had the chance to read Carol Dweck’s Mindset. (Yes, this is my beach reading. Don’t judge.) If you’re not familiar with Dweck’s work, she’s the psychologist who pioneered the concepts of the fixed-mindset and the growth-mindset.
In a classic study, students at a middle school were interviewed and asked whether they believed that intelligence was an inherent characteristic (fixed-mindset) or that intelligence was something you can cultivate and improve through hard work (growth-mindset). It will come as no surprise that the growth-mindset group improved their grades over the course of the year by significantly more than the fixed-mindset group did. These effects became more pronounced through high school and college.
Dweck’s book is full of interesting tidbits about the history of testing. For example, Alfred Binet, one of the pioneers of IQ testing, didn’t believe that his tests measured intelligence. Rather, he saw them as a way to identify which students hadn’t properly benefited from their public school education, so that a different, more effective approach might be employed.
Put another way, the test not only wasn’t supposed to measure intelligence, it was designed on the premise that there was no such thing as fixed intelligence, – that anyone could improve and thrive if they had access to the proper tools and strategies.
I’ve written a bit about Dweck in the past, but I’m beginning to see that the implications of her research are even broader than I’d initially suspected. It should go without saying that here at Veritas Prep, we’re advocates of growth-mindset – in fact, the whole notion of test prep is rooted in a growth-mindset mentality! Moreover, I’ve noticed that this fixed vs. growth notion isn’t just applicable to performance on GMAT in general, but has implications for how test-takers attack individual questions.
Here’s a question I tackled with a tutoring student the other day:
How many positive three-digit integers are divisible by both 3 and 4?
My student began by recognizing that if a number is divisible by both 3 and 4, it’s divisible by 12 as well, so the question was really asking how many three-digit numbers were multiples of 12. Then he looked up and told me that he didn’t know what to do.
Now, there is, of course, a way to solve this problem formally. You can find the number of elements in an evenly spaced set by using the following formula: [(High – Low)/Interval] + 1. The smallest three-digit multiple of 12 is 108 (clearly, 120 is a multiple of 12, so you can quickly see that the previous multiple of 12 is 120-12 = 108). The largest three-digit multiple of 12 is 996. (It’s divisible by 3 because 9 + 9 + 6 = 24, which is a multiple of 3. And it’s divisible by 4 because the number formed by the last two digits, 96, is divisible by 4.) So, one way to tackle this problem is to plug these numbers into the aforementioned formula to get [(996-108)/12] + 1 = (888/12) + 1 = 74 + 1 = 75.
But if you don’t know the formula, and you see this question on test day, this approach can’t help you. So rather than offer this equation, I pushed my student to think about the problem with a growth-mindset mentality. I reminded him that you don’t have to solve things formally on this test, and that he could definitely figure out a way to arrive at the correct answer based on logic and intuition. Once he stopped dwelling on the fact that he didn’t know how to do the problem formally, he used the following logic:
Between 1 and 1,000 there are 100 multiples of 10 (1,000/10 = 100). Clearly, between 100 and 999 there are fewer than 100 multiples of 12, as 12 is bigger than 10. If the correct answer is less than 100, it has to be 75, as this is the only answer choice under 100. He was able to solve a question he thought he couldn’t do in about 5 seconds. Thus, the power of the growth-mindset mentality.
Takeaway: Read Carol Dweck’s book. Work on internalizing the main ideas. Switching from a fixed-mindset mentality to a growth-mindset mentality can have a profound impact, not only on how well you perform on the GMAT, but on how ably you tackle problems in every domain of life.