Citywide that year, 29.4 percent of students passed the reading exam and 34.5 percent passed in math, while 68.4 percent of high schoolers graduated in four years.

The New York Times analyzed Renewal test scores by comparing their progress with growth of the city’s scores over all. Most schools failed to narrow the gap between their test scores and the city average.

At some Renewal schools, however, test scores improved more than they did for the city over all, sometimes by a substantial margin. And some principals and community-based organizations say the program has imparted substantial benefits. They say teachers are happy to work in schools where there is support for things like attendance, and where they can focus on academics.

Brian Bradley, principal of the Renaissance School of the Arts in East Harlem, said the additional instruction offered to Renewal School teachers was a significant benefit to his school, especially because he had a lot of new teachers in the fall of 2015. “They moved leaps and bounds,” he said.

Sean Licata, principal of a middle school in the Williamsbridge section of the Bronx, recently renamed Leaders of Tomorrow, said Renewal “really accelerated growth” at his school. When he arrived at the school six years ago, previous administrators had decided that students had to stay in one classroom all day for safety reasons. Teachers circulated between rooms, pushing their materials around on carts.

“It was not a kid-friendly place,” Mr. Licata said.

After the 2015-16 school year, Mr. Licata’s school was merged with another school in the building, and he set out to hire 16 new staff members. He said some of the teacher leadership opportunities available through Renewal, which offered additional pay, allowed him to entice highly rated teachers from other schools. This year, the only teacher who left his school retired.

Ms. Fariña said that as the program has moved along, the city has made adjustments. Parent engagement has been broadened from an initial focus on student attendance to a more comprehensive understanding of family challenges. The community-based organizations paired with certain schools have been changed. Many principals have been removed, and more may be. Nine schools have been closed, and nine Renewal schools have been merged into other institutions, leaving the 78 schools. Ms. Fariña said that gathering more schools under the Renewal banner is “under discussion.”