Massachusetts Secretary of Education James Peyser echoed a familiar refrain when asked what school districts should do as COVID-19 cases in Massachusetts soared to new highs.

“The governor and the administration as a whole have been pretty clear that we think students ought to be back in school as much as possible, as soon as possible,” he said in an interview with GBH.

That mantra has been frustrating for local leaders grappling with the day-to-day details of schooling who also want students back. Plans vary from town to town, and residents are often comparing what they have to the communities next door. That’s topped with fundamental disagreement among residents about whether schools should stay open or closed, and if part-time learning in person even works.

Somerville may be ground zero for the debate. There are few things these days that Somerville Mayor Joe Curtatone and school activist Elizabeth Pinsky agree on — except a lack of government leadership from the top.

Curtatone says he will keep Somerville's schools closed until $7 million in school ventilation repairs are complete, citing student and teacher safety.

Pinsky, a pediatrician, said it's plain wrong to subject young children to hours of remote learning and allow the city's highest-needs kids to regress by keeping schools closed.

“The failure starts all the way at the top with the federal government,” she said. “I think the state government has abdicated their responsibility.”

“Loose guidelines to municipalities and school districts of what the things you may or could do or should do at a minimum has led to, again, a patchwork approach,” and caused frustration among local and school officials, Curtatone said.

A second big wave of COVID-19 deaths has also brought renewed turmoil as more than 350 school districts statewide try to hash out their own a game plan for education during the pandemic. Should district leaders look to places like New York City, which sent its students back to school earlier this month? Or should they follow the lead of Boston, which has remained closed to all but the highest needs learners?

Cambridge, Falmouth and Fitchburg shut down in-person learning suddenly in recent weeks, giving rise to complaints about the ping-pong effects of opening and closing. Meanwhile, there are public, charter and private schools that continue to teach in-person part- or full-time thanks to surveillance testing and other precautions.

“The districts that have to make these decisions to go remote are really flying the plane without an instruction manual,” said Jeff Granatino, Marshfield's superintendent.

The quiet South Shore district had the most cases of any school in the state following the holiday break. Like other school superintendents, Granatino wants schools open to in-person learning, but that wasn't possible for logistical reasonsafter cases spiked over the holidays.

While many students and teachers had contracted the virus, dozens of additional staffers had to quarantine for 14 days because they had been in contact with someone who had the virus. That gummed up the works.

“We just felt with that number of staff out it was going to be a challenge to run the district effectively,” he said. “Thirty-two cases in a week was something that we hadn't seen in a while, and that was just concerning.”

Compounding the matter was that district leaders, the school committee and local teachers union representatives were trying to figure out how to meet a new state requirement to offer more in-person teaching.

Earlier this month, the Massachusetts board of education made an emergency decision to require teachers to connect with their remote students for live teaching instruction five days a week. At the same time, Peyser has said that he wants to give communities autonomy and that the state's main role is to bring down the overall virus transmission rate to help schools reopen.

It’s a strategy endorsed by some epidemiologists, but local leaders say more specific or regional guidance is needed.

Curtatone in Somerville says the Department of Elementary and Secondary Education has never formalized a plan to help schools reopen safely, even though Curtatone says he has proposed a regionalized one that would help districts collaborate. In Somerville, there is also fear that students without symptoms could bring the virus home from school and unwittingly infect others.

“What we cannot afford to happen is transmission occurring in our schools on the backs of one of our most vulnerable multi-generational homes,” he said. “That's not a scenario anybody wants.”

But the mood in Somerville is tense. Some parents are outraged that schools have not reopened for the neediest kids who rely on language learning and other services like speech or behavioral therapy provided by schools. Some parents of autistic children, for example, have had a front row seat as their children backslide from months or years of specialized therapy.

Other parents said it is simply not good policy — and a nearly impossible task — to force a lively preschooler to sit in front of a computer to learn much the way a college student does.

Outspoken parents complain that they've been characterized as "the angry white moms." The mayor, who has asserted control of the city's school buildings and kept them closed, pushes back against charges that he's an autocrat.

City Council President Matthew McLaughlin, who also serves on the school committee, says the divisions run deep as leaders in state and federal government continue to relinquish tough choices to local leaders.

“I think no matter what decision you make, it's going to be not a very popular decision with some people,” he said. “But that's what we're here for is to make decisions.”