Can Everyone Do Algebra?
This weekend on Quartz, Miles Kimball and Noah Smith argued that there's "one key difference between kids who excel at math and those who don't." That key difference isn't intelligence, but rather a conviction that hard work is more important than intelligence.
They write:
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 just much less important than hard work, preparation, and self-confidence.
They go on to present evidence that kids who think hard work matters are more likely to improve their math skills. Fair enough. We all support hard work and wish kids would do more of it.
But is it true that general intellectual ability -- a trait that, as measured by IQ tests, has been shown to be largely genetic and by all accounts is difficult to change -- hardly matters for high-school math? Are they correct that, when some students get A's and other students get B's on their first test in a basic math class, the only significant difference between them is whether their parents taught them math beforehand? I was skeptical, and following a quick Twitter discussion with the blogger Education Realist I decided to take a closer look.
I dug into the National Longitudinal Survey of Youth's 1997 cohort, matching the students' rankings on the ASVAB (an aptitude test battery whose results correlate well with those of standard IQ tests) to their high-school grades in Algebra I and Algebra II/pre-calc.* Here are the results for Algebra I:
As you can see, C's and C+'s are the norm for the bottom 40 percent of the distribution, while A's and A-'s are the norm for the top 20 percent. Those in between tend to get B's and B-'s.
Here are kids' grades in the courses the NLSY classified as Algebra II/pre-calc:
It's fairly similar, but what I find striking is the huge jump -- a full letter grade -- between the fourth and fifth deciles.
These results aren't just an artifact of race and poverty, either. Here's an Algebra II graph restricted to non-black, non-Hispanic kids whose parents earned at least the median income for that demographic:
Looks familiar, no?
Certainly, even with these controls, all that this demonstrates beyond a doubt is a simple correlation -- kids who scored higher on the ASVAB tended to get better grades in algebra too. We can debate what this means; maybe less intelligent kids get demoralized before they get to algebra and as a result don't try as hard as they could, or maybe parental preparation hikes ASVAB scores in addition to algebra grades. (Though it correlates well with standard IQ tests, the ASVAB aspires to measure knowledge as well as ability, and it actually includes some algebra questions.)
But the huge differences between intelligence groupings -- with median algebra grades ranging from C's to A's -- should at least raise the possibility that high intelligence makes it a lot easier to understand algebra, and that significant numbers of kids might lack the ability to understand algebra at an A or B level.
Robert VerBruggen is editor of RealClearPolicy. Twitter: @RAVerBruggen
*I used the cross-sectional sample only. Also, I restricted the sample to students who had grades in these classes (i.e. I excluded students who didn't take the courses, were graded pass/fail, didn't finish, etc.). Tweet me if you'd like my pared-down spreadsheets, or make your own here.
