On the other hand if representative samples are examined, then a very small difference favouring females is found (-.05). Studies published in 1974 or later show a smaller average effect size (.14) than studies published before 1974 (.31). In tests of computation, differences favouring females appear up to the age of 15 (about .20) with no differences appearing in older samples. In tests of mathematical concepts there is no systematic male or female advantage at any age. In tests of problem solving there is no difference until the age of 15 after which males have an advantage (about .30). The largest gender differences are found in white samples (.13 to .41 depending on the tests used) with smaller or no gender differences among Blacks, Hispanics, and Asians.

If one shifts the definition of mathematics achievement from scores on standardized tests to grades in mathematics classrooms, then females rather than males appear to have a small advantage. The pattern of girls' higher grades and boys' higher standardized scores has been found for the U.S., Canada (Kimball), and Europe (Burton). This is consistent with the finding that girls tend to get higher grades than boys in all academic areas (March), although girls' advantage in high school mathematics classes is less than in other classes (Bridgeman & Wendler). Furthermore, this female advantage in grades is found in-samples of precocious youth, where the largest male advantage is found on standardized tests (Benbow & Arjmand). At the university level, among students taking the same mathematics courses, females' grades are under predicted by their college-entrance standardized math scores and males' grades are over predicted (Bridgeman & Wendler). Clearly, girls achieve as much or more in their mathematics classrooms than do their male peers, who achieve more on standardized tests.

In contrast to small gender differences in mathematics achievement, differences among ethnic groups, countries or schools-which are often related to privilege-are much larger. Sandra Marshall found small gender differences among Grade 6 students in California on a state-wide test with girls performing better on computation problems and boys on problem solving. These gender differences were consistent across social class and ethnic groups; however, the gender differences were dwarfed by social class and ethnic differences. In general, students from privileged backgrounds perform better than those from marginalized backgrounds. Students from higher social class backgrounds performed better, and Asian students scored higher than whites who scored higher than Hispanics. Gender differences in high achieving samples also vary by ethnicity. In one talent search in the U.S., 27% of the white and 47% of the Asian winners were female (Willis).

Cross-cultural comparisons of mathematics achievement consistently show small or nonexistent gender differences within cultures and large differences across cultures. Harold Stevenson and his colleagues studied elementary school children from the United States, Japan and China. Although within each country girls and boys performed equally well, there were striking differences among the countries with Japanese children receiving the highest scores and children in the U.S. the lowest.