Looking at more than 2,000 U.S. high schools that one might imagine are most likely to succeed based on their student demographics, a new study finds strikingly wide variations in the share of top-achieving students in mathematics. A small subset of those public schools, for example, about 4 percent, have rates of high-flyers at least three times the average for all the schools examined—with a handful as high as ten times the average.
The variation is even more pronounced for girls, with many of the advantaged schools deemed to be “extremely unlikely” to produce top-achieving females in math, even though a small group are virtually off the charts with their high success rates (compared with the average for girls across schools), the study finds.
“Our biggest finding is that schools do seem to matter a lot for high-achieving students,” said Glenn Ellison, an economics professor at the Massachusetts Institute of Technology who co-authored the study, which was published as a working paper by the National Bureau of Economic Research, based in Cambridge, Mass. “Even among schools with fairly similar demographics, we see a lot of difference in the [rates] of high-achieving students.”
The study identifies high performers in math as those who posted strong scores on the American Mathematical Contest 12, developed by the Mathematical Association of America. The contest, consisting of a 25-question, multiple-choice test on precalculus topics, is used as the first step in identifying students for the U.S. Olympiad for math. Students who scored above 100 (on the 0-to-150 scale) were counted as high achievers. For some perspective, only 5 percent of all students who participated in the test in 2007 reached that level. The authors also note that scoring above 100 is roughly equivalent to a perfect score of 800 on the math SAT.
The study did not include magnet or charter schools. It focused on schools that generally had similar student demographics in terms of family income and parents’ educational attainment, as well as race and ethnicity.
“Most of the schools in our study are already relatively affluent, high-income kinds of schools,” Ellison said.
“Demographics are found to be very strong predictors of high math achievement,” explains the study, which was coauthored by MIT’s Ashley Swanson. “But substantial heterogeneity remains after controlling for several variables.”
For example, the study estimates that 38 percent of the 2,165 public high schools in the sample produce high-scoring students at less than one-half the average rate, and that 2 percent produce high-scoring students at more than five times the average.
The study does caution that some of the variation may well be explained by the self-selection of students into certain public schools.
In an email, Ellison identified some of the high schools that had the largest numbers of high-achievers in the math contest, based on 2007 data. The top five were:
• Lynbrook High School in San Jose, Calif.;
• Naperville North High School in Naperville, Ill.;
• Vestavia Hills High School in Vestavia, Ala.;
• H.M. Gunn High School in Palo Alto, Calif., and
• New Trier High School in Winnetka, Ill.
He cautioned that these were all schools with demographic profiles that lend themselves toward favorable performance.
At the same time, Ellison highlighted three examples of schools that stood out as having a lot of high-scoring students relative to their demographic profile.
• Vestavia Hills High School (also listed above);
• Revere High School in Richfield, Ohio; and
• Canton High School in Canton, Mass.
He explained, for instance, that Vestavia Hills High School is “one of the schools that we would label as doing extremely well relative to similar schools nationwide. You would not expect it to do nearly as well as Gunn and New Trier.” For instance, he notes, “only 16 percent of adults have graduate degrees, its student body is only 5 percent Asian-American. ... It should do better than the average school in our sample, but you would not expect it to do anything close to as well as it actually does.”
The study finds the math variation across similar schools to be even more pronounced when considering female students. "[T]he estimates suggest that many schools are extremely unlikely to produce high-achieving girls,” the study says. “There are more schools in the lower and extreme upper tails for girls.”
Ellison told me that in about 35 schools, the rate of female high-achievers was at least ten times the average rate for all 2,165 schools.
“Ten times the average rate is a big difference,” he said.
When including both genders, only about six schools met the threshold of being at least ten times the average rate.
The researchers offer some speculation about what may be happening. They suggest that while almost all the schools in the sample likely see it as their responsibility to provide English and math courses that help students excel on the SAT, there is “much less uniformity in whether schools encourage gifted students to develop more-advanced problem-solving skills and reach the higher level of mastery of high school mathematics needed to do well on the AMC 12.”
But Mr. Ellison told me answering the question about the variation that exists is the job of future research.
“Obviously, I’m hoping people will jump on this and figure out what these schools are doing,” he said.
Echoing a point made by some other researchers and STEM advocates, Mr. Ellison observes that nurturing high achievers, and those with the potential to become high achievers, is vital to the nation’s economic well-being.
“So much of the education debate is about bringing up the struggling students, which I’m all in favor of, but high-achieving students are important when we talk about success in scientific and technical fields,” he said. “These are future medical researchers or leading business people or leaders in various fields. ... Those students matter a lot to the economy.”
Indeed, there is some evidence that the United States is not exactly a world leader in producing top-tier performers in math and science. Only about 10 percent of U.S. students scored in the two highest achievement categories in math on the Program for International Student Assessment, or PISA, well short of the figures for a host of other nations, including South Korea, Japan, France, Germany, and New Zealand. In fact, the U.S. results were below the average for the 34 nations in the Organization for Economic Cooperation and Development that participated in the test of 15-year-olds.
The new study cites some research from last year on this matter, including one that finds that even the best-performing U.S. states (and high-performing demographic groups) have a lower percentage of high achievers than do many countries.
In their conclusion, the authors offer up a hopeful note about the ability of this nation to catch up with other countries if more schools do a better job of nurturing their top math talent.
“Our results suggest that the high-achieving math students we see today in U.S. high schools may be just a small fraction of the number of students who have the potential to reach such levels,” it says.