Last week, Miles Kimball and Noah Smith, two economists (one at Michigan, one at Long Island) had a column on the Atlantic‘s website (ht: Joaquin Morales, via Facebook) in which they took to task those who claim that math ability is genetic.
Kimball and Smith argue that that’s largely a cop-out, and that there is no such thing as “I’m bad at math.” Rather, being good at math is the product of good, old-fashioned hard work:
Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence.
How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:
- Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.
- On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.
- The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.
- The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.
Kimball and Smith’s column resonated deeply with me, because I discovered quite late (but just in time!) that hard work trumps natural ability any day of the week when it comes to high-school math–if not PhD-level math for economists.
What follows is a story which, although I have mentioned it to a few colleagues in the past, I’ve never told publicly until today.
Until my early 20s, I never knew that one could become good at math. In high school, I ended up failing 10th-grade math. That year, I’d had mono, so that provided a convenient excuse that I could use when I would explain to people that I had to take 10th-grade math again in the summer. And that summer, I worked really hard at math, and I did exceedingly well, scoring something like a 96% score. But I ascribed my success to the people I was competing with rather than to hard work, since the class was largely made of failures.
When I began studying economics in college, I enrolled in a math for economists course the first semester. I quickly dropped out of it, thinking it was too difficult. The following semester, I took it again, with a different instructor, one who seemed a bit more laid-back and who taught it at a level that was better suited for someone like me. As it turns out, that instructor was a Marxian, and one of the things he taught was the use of Leontief matrices, or input-output models. Like the idiot that I was back then, I decided that that stuff was not important, and so skipped studying it for the final.
Much to my surprise, 60% of the final was on Leontief matrices, and so I failed the course and had to take it again the next semester. Even that second time around, I didn’t do that great, scraping by with a C+ (which was the average score in core courses in the econ major at the Université de Montréal back then, if I recall correctly).
After finally passing Math for Economists I, I realized I had to take Math for Economists II, which was reputed to be very difficult. But for some reason, I remembered my 10th-grade math summer course, and how my hard work had seemed to yield results back then. So I decided to really apply myself in that second Math for Economists course, and I got an A. When I saw my transcript that semester, I finally saw the light: I had been terrible at math all my life because I hadn’t worked hard; in fact, I hadn’t worked at all up until that point, and here I was, getting an A in one of the hardest classes in the major.
I graduated with a 3.2 GPA, which wasn’t that great considering that my alma mater has a 4.3 scale. But it was enough to get admitted into the Masters program in Economics at the Université de Montréal, and so I applied and got in. But then, I remembered that my hard work had paid off handsomely during my senior year, and I decided to apply myself in every single class. Lo and behold, I did well. So well, in fact, that I finished my Masters degree with a 4.1 GPA, which allowed me not only to get admitted for a Ph.D. at Cornell, but to get a full financial ride, including a fellowship for my first year of grad school.
Perhaps more importantly, my cumulative experience with the hard work–excellent results nexus boosted my confidence, and it taught me that I could do well in a graduate program in applied economics. Indeed, Cornell was then known for the difficulty of its qualifier in microeconomic theory (which was administered back then by the economics department and was on all of Mas-Colell et al. and more); in any given year, half of the students would fail.
To be sure, I had to work very, very hard during my first year, but I managed to pass my qualifying exam the first time around (thankfully, us applied economics students didn’t have to take the macro qualifier; we only needed to get a B- in one of the core macro courses). In fact, many of my classmates who seemed to rely on their “natural” ability to do math (including folks who had been math majors in college) ended up failing the micro qualifier.
That series of successes followed by hard work was eventually what gave me the confidence to dabble a little bit in micro theory: in the first essay in my dissertation, I developed a dynamic principal-agent model to account for the phenomenon I was studying empirically. And ultimately, I wrote an article that relied entirely on microeconomic theory (and thus on quite a bit of math), an article for which my coauthor and I won an award.
Ironically enough, in that article, we cited Miles Kimball’s 1990 Econometrica paper on prudence…