by Bethany Johnsen
My recent experience studying for the Graduate Record Examination (GRE) brought home to me how little my math education prepared me for what the Educational Testing Service calls "quantitative reasoning." This in itself doesn't necessarily bother me—a Venn diagram of "valuable knowledge and skills" and "skills measured by standardized tests" would have far from perfect overlap, in my opinion. And yet, as I read test prep books about the best strategies for approaching the GRE math section, it struck me that what I was being asked to do both sounded valuable and went against my deepest impulses. When I see a math problem, I automatically put my pencil to paper and work it out. If I can't remember how I was taught to work it out a long time ago, I try different computational strategies more or less at random. On an untimed test, this would have gone fairly well, but the GRE is designed to reward students who can reason their way to the correct answer. There is simply not enough time to work out every problem. And as much as I studied in preparation, there wasn't enough time to reprogram my instinctive approach to math in the months leading up to the test. I can memorize the steps to solving a problem, but I couldn't trust even my simplest reasoning.
This relationship with math is far from uncommon, I think, and I was reminded of it by the very interesting EdWeek article "You May Show Your Work." I related to the student described who, instead of reasoning that two halves add up to one, began working out the problem 1/2 x 2. The author's conclusion that "There's a difference between doing math and knowing math" really struck me. I could—OK, not very well, but still—do some math, but the GRE showed me that I didn't know the first thing about math. The vast majority of my math instructors had indeed enforced the "show your work" rule that the article makes a compelling case against. For that reason, I think it's a great read for any math teacher.