NEW YORK — Hundreds of thousands of elementary school students are heading back to classrooms Tuesday as New York City enters a high-stakes stage of resuming in-person learning during the coronavirus pandemic, which is keeping students at home in many other big U.S. school systems. 

Twice delayed, the elementary school reopening comes over objections from school principals  who said the city's complicated, changing plans put them in a staffing bind. 

Meanwhile, officials are worried about recent spurts in virus cases in some city neighborhoods  after a summer of success at keeping transmission fairly stable in the city as a whole. 

"It's a big moment for the city," Mayor Bill de Blasio said on cable news station NY1 Monday night. With in-person learning for middle and high school students scheduled to begin Thursday, he noted, "as many as half a million kids could be in school in the course of this week." 

With over 1 million public school students, New York City initially had a more ambitious timeline than many other big U.S. school systems for bringing children back to schoolhouses this fall. Families have the option of choosing all-remote learning, and a growing number are doing so — 48% as of Friday, up from 30% six weeks earlier, according to city Education Department statistics.

Other students are already back in the city's virus-altered version of in-person school, learning sometimes in classrooms and sometimes at home.

Pre-kindergarteners and some special education students began showing up Sept. 21  as online instruction began for the rest of the student body. 

Students were originally due back Sept. 10. But the start date was pushed back, repeatedly, after the city teachers' union said it wasn't safe to open schools because of outdated ventilation systems, an insufficient number of school nurses and other issues. At one point, the United Federation of Teachers threatened to strike. 

The union was still pressing for changes as recently as Friday, when the city agreed to let more teachers work from home when instructing students remotely, rather than having to come in to school to conduct online classes.

The principals' union said the late-breaking change was too much. Principals had already complained that the city was creating a staffing crunch by planning to have three different groups of teachers — one for all-remote students, another for in-classroom pupils and a third for blended-program students when they're at home.

Saying that de Blasio and Schools Chancellor Richard Carranza "have entered into grossly irresponsible staffing agreements," the Council of School Supervisors and Administrators called Sunday for the state to take control of the school system for the duration of the pandemic.

Gov. Andrew Cuomo said Monday that he understood the concern of the principals' union and that the state would monitor virus testing data to determine whether any steps need to be taken concerning New York City schools.

Both Cuomo and de Blasio are Democrats.

Many other big school systems around the country began the fall term online, though some are reopening physical schools. In Florida, for instance, students opting for in-person learning returned to schools Sept. 21 in Palm Beach County, where the nation's 10th largest school system has over 197,000 students.