For two decades, New York City has been something of an anomaly: Unlike the school boards that reign over thousands of towns and cities, the nation’s largest public school system is ruled by the mayor.

But this year, the city’s method of running its schools is facing a unique and significant challenge that threatens to weaken the mayor’s power.

In June, Mayor Eric Adams’s control of city schools is up for renewal — and debate — by state lawmakers. And while the same cycle happens every few years, the Legislature now seems open to revisiting a school governing model that has become entrenched in New York and embraced by a handful of other big city districts.

Mayoral control brought major changes to New York City’s schools. Mayor Michael R. Bloomberg and his schools chancellors, for instance, made unilateral decisions on issues that faced difficult political headwinds, including shutting down dozens of schools and opening hundreds of new ones, and cultivating the growth of charter schools, which now educate 15 percent of students.

Whether those changes improved the system overall has been vigorously debated. Graduation rates have jumped, for example, but they have also risen across the nation, pushed up by state-level changes. And many New York City students have struggled with college readiness.

In New York last year, hundreds of parents and teachers were galvanized by education cuts and lingering anger over past school closures. They have railed against the system this winter, calling for more checks on the mayor, or for an entirely new model. Democratic lawmakers seem open to listening to them, and the city’s influential teachers’ union has also become vocal in lobbying for changes.