Laura Fuchs has been teaching Advanced Placement U.S. government and politics at H.D. Woodson High School in Washington for six of her 10 years there. She is in her early 30s, wears her hair pulled back in a bun and has a no-nonsense way of dealing with her students. But that apparent sternness belies a genuine love of teaching and a deep well of patience, two qualities that have prepared her for teaching a college-level course at a school like Woodson.

Many students in Washington go to charter schools or to one of seven magnet high schools in the district, which admit students based on specific eligibility criteria. Woodson, serving around 600 students in the second-poorest ward in the city, is one of nine high schools in Washington with open enrollment. In 2016, it had a graduation rate of 76 percent — up from 53 percent in 2012. Last year only 1 percent of its students met math standards on national standardized tests, and 4 percent met reading standards. Woodson is among the lowest-performing schools in the city, and as at many of Washington’s public schools, 100 percent of the students receive free or subsidized lunches. “A lot of students are not at the poverty line; they’re significantly below it,” Fuchs says.

On the day I visited last fall, Fuchs’s class was learning about Social Security. Most of Fuchs’s students were already familiar with the program, but only its disability-insurance component. Many were surprised to learn that it’s also a retirement program. Next, Fuchs brought up the 1950s baby boom and discovered that some of her students didn’t realize that the country’s birthrate is lower today than it was in the past. One student chimed in jokingly: “That’s O.K., these high school students can catch them up!” Fuchs steered them back to the matter at hand. “When it comes to the A.P. exam, you need to know what Social Security is — it’s called an entitlement, which means if you qualify according to the law, you receive it,” she explained.

A.P. U.S. government, like the 38 other A.P. courses developed by the College Board, a nonprofit organization, is a difficult class. Students are expected to read college-level textbooks, grasp complicated vocabulary and concepts and spend 30 minutes to an hour each night on homework. At the end of the year is an arduous final exam designed, distributed and graded by the College Board. If students score a 3 or better on a 5-point scale, they typically receive college credit. (Though the College Board does not consider a 1 or a 2 to be a failing grade, they are commonly understood to be — and students receive no credit for them.) As of last year, D.C. Public Schools required that all its high schools offer at least eight Advanced Placement classes.