GRE considered harmful

Like many Calvin students, I’m working on my applications to graduate school. Unfortunately, this involves taking the GRE.

It’s not just that I have to take yet another standardized test that I’m not naturally good at. I can understand a test as a metric of how well students could conceptualize certain problems, plow through dense text and otherwise screen out people who do not have the skills to succeed in graduate school. However, the way the GRE is set up has a major problem: doing well on it means repressing the very skills that make someone a good candidate for doing research.

Like many other standardized tests, the GRE is aggressively timed. There is barely enough time to complete most of the questions, even working quickly and approaching each problem in the most efficient way possible. Take this as an example this problem from my GRE practice material:

Which numbers are greater than the sum of all the prime factors of 210? Indicate all possible choices.

A.      12

B.      17

C.      19

D.      21

E.      24

The most efficient way that I know of to address this problem is to use the calculator provided on the test to take the square root of 210 (which is between 14 and 15) since it is a theorem that the largest divisor of a number is less than or equal to its square root, then testing the divisibility of 210 by each prime below 15. The prime factors are 2, 3, 5 and 7, which sum to 17, so C, D, and E is the correct answer.

However, my inner mathematician is upset with having to do this computational work. There should be some theorem that relates a number and the maximum sum of its prime factors. I don’t know of it and am too lazy to do the work right now to find it, but this test question raises an interesting question about number theory.

But then I have to squelch that thought. As soon as I start to wonder about it, I lose valuable time. Many of the math questions on the GRE compare two quantities, for which it is often faster to pick numbers and solve for values rather than do the work to actually solve the problem.

Because of this, studying for the GRE has been a process of learning how to shut the inquisitive part of my brain off in order to get through the questions in the correct amount of time. The ability to do this took me some time to develop. The absurdity is that in order to make a good application to graduate school, where I will be doing research, I have to teach myself to ignore the paths that lead to creative solutions.

I found a paper titled “The Harmful Effects of ‘Carrying’ and ‘Borrowing’ in Grades 1-4,” written by Ann Dominick, a researcher in Alabama. She asked students in Grades 2 through 4 to compute 7 + 52 + 186. The ones who had been taught the procedure of “carrying” to do addition gave a wrong answer much more often, and gave much more unreasonable wrong answers. The students in Grade 4 who had been taught “carrying” came to think of each place-value digit independently in a written number instead of numbers as a whole: 186 was not a number greater than 150, but the sequence of digits 1, 8, 6.

Dominick argues that forcing students to use algorithms for adding and subtracting numbers take away the intuitions about how numbers work that children naturally have and develop. They learn to no longer use their own thinking.

The way I need to think in order to do well on the GRE is an analogue. I have to learn to turn off, for a few hours, the way I think about problems, that particular solutions emerge from general rules, and that the process of generalization is usually fun and instructive.

My learning into the intricacies of the GRE did the opposite of what a good education should.