In many cases, women seem to have internalized society’s belief that they are incapable of mastering these fields as well as men. Carol Dweck, a professor at Stanford, and other psychologists have found that female students who are made to believe that math ability is innate have lower scores and are less likely to study math than girls who believe that math skills can be acquired through hard work. Another study showed that female college students got more questions right on math tests when they were told beforehand that “college students are good at math” than when they were told “women are bad at math,” which suggests stereotypes undermine women’s performance.

Insufficient Resources

These gaps could be reduced if every child had access to free public preschools. Earlier this year, President Obama proposed making high-quality preschools available to 4-year-old children of families with incomes of up to 200 percent of the federal poverty line, at a 10-year cost of $75 billion. Studies have shown that every $1 invested in preschools saves society $7 in the future through lower spending on remedial education, higher productivity and less crime.

The country should also make sure that the schools that primarily serve minorities have the resources and support they need to hire qualified teachers so their students are not at a disadvantage relative to children in more affluent areas. States will need to take the lead to make this happen, but the federal government can also assist through grants and other support.

Conventional Teaching Methods

The Knowledge Is Power Program, which operates 141 public charter schools around the country, has effectively used smaller class sizes, longer school days and summer school to help lagging minority students improve test scores in math, reading and science. Teachers at KIPP schools maintain high expectations of all students, working intensively one-on-one with children until they comprehend every important concept. Though the program has been criticized for its dropout rates and admissions policies, one recent independent study of KIPP’s approach showed that middle school students who spent three years in its schools had math scores that on average put them 11 months ahead of where they would have been had they not joined the school; they were 14 months ahead in science achievement.

Teachers also need to make science and math education much more practical and hands-on. Girls have shown much more engagement in subjects when they learn the connection between what they are studying and real-world problems. That may partly explain why so many talented girls prefer to go into life sciences, where that link has generally been more apparent.

Not Enough Role Models

Groups like the National Action Council for Minorities in Engineering have been showing minorities and girls that they can imagine themselves as scientists or engineers, providing role models to speak to middle school students and helping high schools set up engineering academies. A five-year program funded by the National Science Foundation at Bowie State University, a historically black university in Maryland, provides training and mentorship to high school science and math teachers and a summer science academy to 10th graders.