NEW YORK – They were known as dropout factories: Big high schools in poor neighborhoods where only a quarter to a third of students graduated.

New York City under Mayor Michael Bloomberg has systematically shut down large, failing high schools and replaced them with small schools, many pegged to themes like the fashion industry or the business of sports.

A new study funded by the Bill and Melinda Gates Foundation — which has invested more than $150 million in New York City schools — suggests that the small schools have succeeded in boosting graduation rates for the city’s most academically challenged students.

Proponents say small schools can provide one-on-one support to struggling students, and the specialized programs are supposed to improve students’ motivation by enticing them to apply to schools that match their interests.

“This shows the strategy is working,” said New York City Schools Chancellor Joel Klein, who since 2002 has shuttered more than 20 large high schools with as many as 4,000 students each and replaced them with 216 small schools with names like the Academy of Health Careers or the Law, Government and Community Service Magnet High School.

The study released today by the education think tank MDRC examined students at 105 of the new high schools with 550 students or fewer.

It found that by the end of their first year of high school, 58.5 percent of students at the so-called “small schools of choice” were on track to graduate in four years, compared with 48.5 percent at other schools.

the fourth year, the small schools had an overall graduation rate of 68.7 percent compared with 61.9 percent for the control group. Both numbers were much higher than the rates at the closed schools.

Because New York City’s system for assigning students to high schools is partly a lottery, the study’s authors were able to compare students who got into the small schools with demographically similar students who got into other schools. The small schools are not academically selective; they are open to all eighth-grade graduates.

Both groups were overwhelmingly black and Hispanic and living in neighborhoods with high poverty rates — students who are most at risk for dropping out.

New York’s new high schools typically operate in clusters inside the shells of the schools they replaced.

The eight-story John F. Kennedy High School in the Bronx has been broken up into six schools, including the Bronx Theatre High School, the Marble Hill High School for International Studies and the Bronx School of Law and Finance. The schools all teach required subjects like math and English.

At the theater school, students recently designed costumes and read scenes to each other. Photos in the hallway showed past productions of “Twelfth Night” and “A Raisin in the Sun.”

Principal Deborah Effinger greeted students by name, telling one boy politely to stash his football in his backpack. Color-coded charts on her office wall showed that most students were on track to graduate.

The Gates Foundation shifted its strategy in 2008 from starting new schools to targeting teacher effectiveness and national standards. Foundation spokesman Chris Williams said once they are up and running, the schools are expected to be “fully sustainable without philanthropic investments.”