In New York City, mayors often stake their legacies on the records of two huge agencies that touch millions of lives: the Police Department and the public schools.

Zohran Mamdani, the front-runner to be the city’s next leader, has offered voters a plan to overhaul the city’s approach to policing. But with three months until the general election, the state assemblyman’s agenda for New York’s public school system — the biggest in the United States — remains far less clear.

His most significant idea to date would reduce his control over the city’s more than 1,500 public schools. New York’s mayor retains more authority over education policy than nearly any other big city leader in the nation. But Mr. Mamdani supports ending the model of mayoral control and giving more influence to teachers and parents.

He has also backed down from calling for the elimination of a contentious admissions test at a group of eight elite public high schools.

The next mayor will enter City Hall at a precarious moment. New York is confronting threats to school funding from the federal government, dismal literacy rates, an alarming crisis of school absences and stark gaps in outcomes between students from well-off families and those from low-income households.

Yet during the Democratic primary, most candidates devoted scant attention to public schools, rarely speaking about the district’s 900,000 students or its mammoth $40 billion budget, which often represents more than a third of all municipal spending.