Some schools are trying a new plan to keep students safely in the classroom: Rather than quarantining children who have an in-school contact with a positive case, they are testing them. A lot.

The method keeps children in school after exposure to a classmate or teacher who tested positive for Covid-19 if they test negative at least every other day. Known as test-to-stay, the approach is a higher transmission risk than keeping exposed students at home, but some public-health experts and educators say the trade-off is worth it to avoid missed days in class.

“It’s been really wonderful to keep our kids and staff in school,” said Sara Dail, assistant superintendent at Sterling Public Schools in Illinois, which implemented the approach at the beginning of the school year in August.

Sterling logged 2,000 quarantines last school year among its 2,450 in-person students and 450 staff. Last week, parents of 30 exposed students, including an entire kindergarten class, chose the testing routine, Dr. Dail said. Four chose the 14-day quarantine.

Two students in Louisville, Ky., were tested for Covid-19 at their school in mid-August.

Photo: Jon Cherry/Getty Images

Participants provide a saliva sample put into a tube at school every other day. Their tubes are couriered to a laboratory, which often provides same-day results. The district is also offered testing for all twice a week; the University of Illinois handles most of the logistics.

As the pandemic extends into a third academic year, administrators, lawmakers and health officials are again balancing health risks with best practices for learning. Safety protocols vary across states and school districts. Public-health experts are concerned that a rollback of precautions and the heightened infectiousness of the Delta variant could lead to greater transmission risks in schools.

Hundreds of students and staff across the U.S. have already tested positive, pushing thousands into quarantine and prompting schools to temporarily close or revert to virtual learning.

Centers for Disease Control and Prevention Director Rochelle Walensky has said that bigger Covid-19 outbreaks and quarantines are occurring primarily in schools that haven’t followed the agency’s recommendations, including promoting vaccines for those who are eligible, universal masking, distancing, improved ventilation and screening testing.

A student wearing a mask last month at a high school in Los Angeles.

Photo: Bing Guan/Bloomberg News

Without such mitigation measures, more students and staff will have to sit out of school because they are sick or quarantined, said Jason Newland, a pediatrician and infectious-disease expert at Washington University School of Medicine in St. Louis. “You’ve now really hurt the kids in the end.”

Last school year, the spread of Covid-19 in schools was low where precautions were followed, research suggests. Another finding: The majority of students who quarantined after an in-school exposure never turned up positive themselves.

“There’s been more and more recognition that when masks are on, excluding you from school is very harsh,” said Adam Hersh, a pediatric infectious-disease specialist at the University of Utah Health. Dr. Hersh was senior author on a report the CDC published in May that estimated testing students rather than switching to remote instruction after Covid-19 outbreaks at 13 schools saved more than 100,000 class days overall.

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Some schools in the U.K. deployed test-to-stay this spring and summer. One pilot study, not yet peer-reviewed, found that daily rapid testing of school-related close contacts didn’t lead to a substantial increase in Covid-19 transmission compared with quarantine among students at some 160 schools and colleges. Less than 2% of close contacts who were exposed eventually tested positive.

Health and education officials in states including Massachusetts and Illinois are leveraging existing testing infrastructure to offer frequent testing as an alternative to quarantine. In Illinois, close contacts are tested on the first, third, fifth and seventh days after exposure. The state’s health department said at least 169 districts plan to use the system. In Massachusetts, school districts can choose to have close contacts undergo daily rapid testing, which provides results in about 15 minutes, for at least five days after an exposure.

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“We didn’t want to lose that connection with students because of all the quarantining that could happen,” said Russell Johnston, senior associate commissioner at the Massachusetts Department of Elementary and Secondary Education. “If those results are negative, the student can stay in school. And in the event that it’s positive, we know that we can take immediate action.”

Covid-19 testing can be costly and complicated, but more schools are pursuing it this year after getting more funding and assistance.

Some diagnostics experts say even a short gap between tests or before results are released raises the risk of students or staff becoming infectious and spreading the virus before they are identified and sent home.

“For close contacts, it’s a little scary,” said Alex Greninger, an assistant professor in the department of laboratory medicine and pathology at the University of Washington Medical Center. “You don’t know when you’re going to pop positive.”

Public-health and education officials say test-to-stay depends on schools using layered infection-prevention strategies to limit risks of transmission in schools. In Illinois and Massachusetts, test-to-stay is allowed only in specific circumstances, such as when masks are worn, the contact happens at school or the students don’t have any symptoms.

Joanna Ford, assistant superintendent for student services at Deerfield Public Schools District 109 in Illinois, said that some parents were frustrated with the strictures of the program, but that most were still thrilled the system would keep children in school more often.

“There were huge concerns about the social and emotional impact when kids had to quarantine,” Ms. Ford said.

Write to Brianna Abbott at brianna.abbott@wsj.com