Yet, while most of the charter schools perform relatively well on tests, a majority of Harlem’s students attend schools that do not. Among elementary schools in Harlem and East Harlem, only a few of the some 25 traditional neighborhood schools with students taking statewide tests had at least 50 percent of children reading at or above grade level.

Parents in some of those schools said they felt their children had missed out on the experiment, as their schools continued to perform poorly and sometimes were considered for closing. Some also described a disconnect between the concept of choice, which most of them wholeheartedly embrace, and the execution of it. Information on schools provided by the city in printed directories is often outdated (the city’s Web site is more current). And the constant churning of schools, and a school grading system that can result in large swings in a few years, has left them wondering which schools are truly successful.

“Parents end up trying to predict what the Department of Education is thinking about implementing,” said Sonja Jones, the president of the Community Education Council, an advisory board elected by parents in District 5, which includes Central Harlem. Sometimes the process is true choice, she said, “and sometimes that’s choice being taken away from you.”

Officials at the Education Department say they are certain that students in Harlem are better off now than they were before the mayor took office. While many Harlem schools still have test scores that remain relatively low for the city, as a group the area’s new schools are performing better than their Harlem “peer schools,” or schools with similar demographics, that have been around longer, the department said.

And as the number of charter schools grows — the Bloomberg administration spent years lobbying state lawmakers to allow more of them to open — the number of students waiting for seats has slowly dropped. In Districts 4 and 5, which encompass most of Harlem and East Harlem, out of an estimated 9,850 charter school applicants, 7,700 did not receive a seat this year, down about 3,000 from 2011, according to the New York City Charter School Center.

“Our work is by no means complete,” said Marc Sternberg, a deputy chancellor in the Education Department, adding, “But many of these schools are producing really remarkable results.”