Beyond calculus, the report found that high schools with high numbers of black and Latino students were less likely to offer physics, chemistry, and even algebra II. And even in schools where advanced math and science were taught, black and Latino students were concentrated in less rigorous courses. While black and Latino kids made up 36 percent of students in schools where calculus was offered, they only comprised 21 percent of the students in calculus classes. Students who don’t speak English fluently made up 5 percent of students at schools who offered the course, but just 1 percent of those who took it.

The one ray of good news, as Catherine Lhamon, the assistant secretary for civil rights, said, is that girls made up 49 percent of the student body and also 49 percent of students enrolled in calculus. But Lhamon called the fact that half of all schools don’t offer calculus at all “galling.” Black and Latino students were also less likely to be enrolled in gifted-and-talented programs and to take advanced-placement courses that can translate into college credit.

States have some flexibility in what to measure as they consider how they plan to prove to Washington that they are educating all students equally under the country’s new education law. While King stopped short of explicitly encouraging states to track access to advanced coursework, he reiterated that it would be an appropriate thing to measure.

Natasha Ushomirsky, the director of K-12 policy at Education Trust, a nonprofit focused on helping low-income students of color succeed, wants to see more districts and schools consider not only access to, but success in, such courses once kids are enrolled. Some states, such as Florida and Indiana, she pointed out, moved that direction years ago, and the new education law may encourage others to follow suit. But, Ushomirsky cautioned, schools will need to look beyond averages at how different subgroups of students are doing. Will it be enough to reduce educational inequities that have long been entrenched? “I think we’re absolutely hopeful,” she said.

The Education Department points in the report to several Obama-administration efforts to reduce these racial gaps, including a letter outlining how schools and other groups can use federal funds to support STEM education, and a $4 billion proposal by President Obama to expand computer-science education.

Some schools are doing good work at reducing gaps in access to advanced courses already and might serve as a roadmap for others. At Elmont Memorial High School in Elmont, New York, for instance, teachers and administrators disaggregate data by teacher and then have teachers whose students are doing well in particular subjects share “best practices” with other teachers, said Kevin Dougherty, the school’s principal. The school also considers the opinions of parents, students, and counselors in deciding which kids are capable of succeeding in an advanced course instead of relying strictly on a list of prerequisites. “The parents and students have a voice,” Dougherty said. The school axed a two-year-long geometry course that had been a “dumping ground” for low-achieving students before Dougherty became the head of the school, too. Afterward, the portion of students earning an “advanced” distinction on their diplomas went up.

Yet not all schools are taking such deliberate steps to reduce gaps. “These data should serve as a sobering reality check,” King said. While the secretary acknowledged that some groups (Republicans and teachers’ unions, for instance) think the department is trying to be too involved in how states interpret the law, he issued a stern warning. “We will not,” he said, “compromise away the rights of all students to an excellent education.”

This article is part of our Next America: Higher Education project, which is supported by grants from the Bill & Melinda Gates Foundation and Lumina Foundation.

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