Mr. Bastian said that he had spent his first several years getting rid of teachers who were weak, disengaged or, in one case, unhinged. In 2009, the teachers’ union chapter leader, who had been reassigned after a physical altercation with a student, barricaded himself in a classroom and claimed that he had planted a bomb in the library. (He had not.)

“I started in a very tumultuous way,” Mr. Bastian said, adding that, as a new principal, he had not had many allies in the department or the school. But over time, he said, he was able to remove the ineffectual teachers and, in the process, gain the trust of the more talented and energetic ones.

District 9, where the schools are, is considered hard to staff because of its concentrated poverty, distance from Manhattan and dearth of public transportation. But Mr. Bastian has seen relatively low turnover in recent years.

He is using money from the Renewal program to pay four of his most experienced teachers extra to serve as mentors to colleagues. He has formed a cabinet, including three of those experienced teachers, the assistant principal and a staff member from the Center for Supportive Schools, a nonprofit that is working with all three schools in the building as part of the Renewal program. The group gathers weekly in his office, laptops ready, to whip through a digital agenda using meeting practices learned in training from the Harvard Graduate School of Education.

Laura Weiss, a member of the cabinet and an English teacher in her ninth year at the school, said that the opportunity to move into a leadership position was one of the reasons she had stayed at the school instead of leaving to teach in the suburbs, where the work might be easier but where she thought she would learn less.