In one community in northern France, Crépy-en-Valois, two high school teachers became ill with Covid-19 in early February, before schools closed. Scientists from the Institut Pasteur later tested the school’s students and staff for coronavirus antibodies. They found antibodies in 38 percent of the students, 43 percent of the teachers, and 59 percent of other school staff, said Dr. Arnaud Fontanet, an epidemiologist at the institute who led the study and is a member of a committee advising the French government.

“Clearly you know that the virus circulated in the high school,” Dr. Fontanet said.

Later, the team tested students and staff from six elementary schools in the community. The closure of schools in mid-February provided an opportunity to see if younger children had become infected when schools were in session, the point when the virus struck high school students.

Researchers found antibodies in only 9 percent of elementary students, 7 percent of teachers and 4 percent of other staff. They identified three students in three different elementary schools who had attended classes with acute coronavirus symptoms before the schools closed. None appeared to have infected other children, teachers or staff, Dr. Fontanet said. Two of those symptomatic students had siblings in the high school and the third had a sister who worked in the high school, he said.

The research also indicated that when an elementary school student tested positive for coronavirus antibodies, there was a very high probability that the student’s parents had also been infected, Dr. Fontanet said. The probability was not nearly as high for parents of high school students. “When I look at the timing, we think it started in the high school, moved into the families and then to the young students,” he said.

Dr. Fontanet said that the findings suggest that older children may be able to transmit the virus more easily than younger children.

That pattern may also be reflected by the experience in Israel, where one of the largest school outbreaks, involving about 175 students and staff, occurred in Gymnasia Rehavia, a middle and high school in Jerusalem.

There are different theories about why older children would be more likely to transmit the virus than younger children. Some scientists say that younger children are less likely to have Covid-19 symptoms like coughs and less likely to have strong speaking voices, both of which can transmit the virus in droplets. Other researchers are examining whether proteins that enable the virus to enter lung cells and replicate are less abundant in children, limiting the severity of their infection and potentially their ability to transmit the virus.