BERLIN — At GutsMuths elementary school in Germany’s capital, the first day of class was much as it is every year: Parents waved goodbye as children ran around, and teachers sought to establish order. Many wore face masks, the only obvious sign of the pandemic.

As novel coronavirus case numbers continue to rise around the world, many students in Germany returned to classrooms this week, in a closely watched effort to reopen schools in the European Union’s most populous country.

Andreas Stehning, a professional driver, expressed mixed feelings as he dropped off his daughter Luisa, 10, at GutsMuths school.

He had cut back work during the pandemic to devote time to home schooling. “It was not easy,” he said. “To become a teacher overnight is not everyone’s cup of tea. But what else should we have done?”

Germany’s new daily confirmed cases topped 1,200 this week — the most since early May. He watched with concern as the country relaxed restrictions in recent months, and he worried the virus could spread at school.

Fears of new spikes in infections have loomed over Europe’s debate over how and when to reopen schools. Countries have pursued different approaches. Sweden never closed most of its schools, and Denmark was quick to reopen, instructing teachers to move many classes outside. In harder-hit countries, like Italy, schools have remained closed since March and are only reopening in the coming weeks.

The state-level authorities that set education policy in Germany pursued a middle path, at first allowing only some students to return, with eligibility varying region to region. Many parents’ and teachers’ associations see the approach as a patchwork of conflicting strategies, but some supporters of Germany’s federal model say it is pragmatic.

Because of its system of government, Germany’s pandemic response has been decentralized, with local health offices setting rules within broad national guidelines. Proponents say this allows for measures tailor-made for circumstances that differ widely. Critics say it leads to confusion.

Schools did not reopen all at once, and there was no uniform approach. Students returned to the classroom in several northern states last week. Berlin and three other states followed suit on Monday and Wednesday. The rest of the country is set to reopen in the coming weeks. In some classrooms, masks will be mandatory. In others, including in Berlin, they won’t be. In many cases, authorities have left key decisions up to the discretion of school principals.

“My best hope is for coordinated chaos,” said Tobias Kurth, the director of Charité’s Institute for Public Health in Berlin, who has been following the back-to-school plans in the 16 federal states. “I’d like to see a clear message for all of Germany.”

Despite the nationwide uncertainty, many students and teachers at GutsMuths were largely relieved to be back. Asked by their teacher whether they were excited to return to school, almost all students in a fourth-grade class raised their hands.

“I woke up at 4:30 a.m. to check if it’s finally time to go,” one told his classmates.

The return to near-normalcy, GutsMuths principal Catrin Herfet-Sternberger said in a speech to students in an outdoor schoolyard, was only possible because “because we adhered to social distancing rules, because we wore masks where it was necessary.”

Many students wore face masks, despite the lack of a requirement, and used hand sanitizer at the school’s entrances as they filed in. Some classes were held outside. Signs reminded students to maintain social distance.

Civil service employee Karina Lukasenoka, 42, said her daughter had adapted to life during the pandemic. “Sometimes she even reminds me: ‘Mom, put on your mask! Mom, disinfect your hands,' ” Lukasenoka said, as her daughter mingled with classmates.

Unlike France, Britain or Italy, Germany did not impose a full lockdown — it instead appealed to citizens’ sense of responsibility and relied on local measures. Compliance with mask-wearing rules and social distancing appeals has declined in recent months as fatigue builds, but the issue has not been politicized to the degree it has in the United States.

Although Germany has seen a per-capita infection level six times lower than that of the United States, German health officials worry that growing complacency could lead to setbacks.

In the United States, where school reopening has been the subject of controversy, nearly 100,000 coronavirus cases among children were confirmed in the last two weeks of July, according to data from the American Academy of Pediatrics and the Children’s Hospital Association. President Trump has maintained that U.S. schools should still reopen for in-person instruction this fall, citing the false claim that children are nearly immune to the coronavirus.

Among researchers around the world, there is still much uncertainty over basic questions about how the virus affects children and the degree to which they spread it. There is some evidence to suggest that infection rates are lower among younger age groups, according to the latest assessment by the Robert Koch Institute, Germany’s public health authority. But results vary study to study.

Among children, “infectiousness has been so far rarely studied and therefore cannot be conclusively assessed,” according to the assessment.

Public health expert Kurth said he supports school reopenings because the alternative, children staying home as parents return to work and struggle to find child care, “is not feasible.”

That does not mean a lack of risk, Kurth said. Last week, two schools in the state of Mecklenburg-Vorpommern closed within days of reopening because of new coronavirus cases.

Kurth said his cautious optimism is contingent on schools offering regular testing, organizing students into cohorts that do not mix, urging the ill to stay home and regular mask use. And while authorities have urged schools to keep students distanced, that has proven unrealistic in many cases. “I can’t separate the schoolyard into lots of small areas for each class — that makes not a lot of sense for children,” Herfet-Sternberger said.

Heinz-Peter Meidinger, the president of the German teachers’ association, said masks should be mandatory inside classrooms. At least one state is following that guidance, but most are not or are still in the process of deciding.

Germany’s state-level education ministries say they are prepared to be flexible in case of a rise in infections.

“We have many plans in the drawer,” said Fabian Schmidt, a spokesman for Baden-Württemberg’s Ministry of Cultural Affairs and Youth. With a mid-September start date, the state, in Germany’s southwest, is the last of the country’s 16 states to open schools.

Those contingency plans include more distance learning, Schmidt said but declined to go into further detail.

The real test, public health officials say, will come with the colder weather, when activities are forced inside, and the regular cold and flu season picks up.