American students aren't good at math compared with students around the world. But it's still possible to overstate just how bad they are — as Nicholas Kristof did this week in the New York Times.
Kristof argues that American eighth-graders' math skills are humiliatingly bad, citing examples of problems that students in Ghana, Iran, Indonesia, Armenia, Turkey, and Palestine can solve and American eighth-graders can't.
Kristof's basic point is correct: American students really are bad at math, particularly at applying what they've learned in the real world. Math teachers and elected officials from both parties are right to be concerned. But American kids aren't really worse than students in Ghana or Armenia. And Kristof's method — cherry-picking problems from a test on which American students, on average, do pretty well in comparison — actually undermines what he's trying to argue.
What Kristof gets wrong
The problem, as Bob Somerby pointed out: the questions Kristof picked, from the Trends in International Mathematics and Science Survey, a standardized test of eighth-graders, are terrible examples. American students didn't answer those questions well compared with their peers around the world. But they performed much worse on the questions he cites than on the test as a whole.
When you look at the entire test, American eighth-graders aren't bad at all. They did better than average on many questions. And overall, American students scored slightly above average — worse than students in Korea, Singapore, and Japan, but on par with Finland's celebrated test-takers.
This could make you wonder why there's a panic about math education at all. Different international tests measure different things, and some make the US look worse than others.
Why some tests make American students look okay and others make them look terrible
TIMSS, the test Kristof cites, is one on which American students tend to do well. Many developed countries don't participate, including Canada and much of Western Europe aside from Finland, Sweden, and Norway. Its problems often look more like the questions American students encounter in the classroom: the goal is to figure out whether students in the fourth and eighth grades can solve math problems.
Here's a sample problem from TIMSS that's more representative than the problems Kristof chose — American students were slightly better than average at answering it correctly, matching their performance on the test as a whole.
American students fare worse on the Programme for International Student Assessment, given to 15-year-old students in countries in the Organization for Economic Cooperation and Development as well as some others. Those problems are geared at measuring whether students can apply math in real life after they finish their education. Here's a sample problem from the PISA:
At best, American 15-year-olds are ranked 23rd out of 34 countries on PISA — below the international average. And the math woes persist into adulthood. Another test from the OECD, this one focused on measuring adult skills, found that American math abilities were far below the average for 14 developed countries.
PISA is the test most often cited when reformers and journalists say American kids can't do math. That's because the goal of math education shouldn't be for students to be able to do math problems in a vacuum. They should be able to actually use what they've learned as adults. So some reforms, including the Common Core and Singapore's math curriculum, are aimed at helping students understand why math works the way it does, in hopes that this will help them improve.