Safely reopening our nation’s public schools for full-time in-person learning is a top national priority. Many parents — and public health scholars — believe that it’s long overdue, because closing schools has now been shown to be marginally effective, at best, in controlling the pandemic. Children are generally mildly affected by the novel coronavirus and are unlikely to spread it in classrooms. And keeping children out of full-time school has been associated with a widespread decline in health, well-being and educational achievement among youths.

Now that reopenings are finally underway, it’s crucial that they be done well. Some of the basic mitigation steps are obvious, including masking, social distancing and ventilation. To keep viral spread at schools to a minimum, the Biden administration has also proposed to fund regular and frequent testing of students, staff and teachers who don’t show symptoms of covid-19. The Centers for Disease Control and Prevention also embraces this approach. It looks like a good idea at first glance — and could reassure teachers, parents and students that schools are safe.

But there are downsides to systematic testing that have been insufficiently considered, including costs, lost learning time, logistics and stress for those subjected to such a regime. False-positive results — which say you are infected when you aren’t — pose particular problems. Overall, this kind of widespread testing fails cost-benefit analysis: It will drain already insufficient public school resources while doing little to improve safety. And with nearly 80 percent of teachers and school staffers vaccinated with their first dose, the argument for testing grows even weaker.

First, classrooms have thankfully been found — in studies examining schools in multiple states — to be places of limited disease transmission, compared with communities at large. The rate of transmission within schools from individuals who test positive has been estimated to be on the order of 0.5 percent to 0.7 percent (and this includes people exhibiting symptoms).

A rate that low implies that a testing regimen would need to identify roughly 200 infected people to prevent one person from transmitting the disease in school. It would take an awful lot of tests to achieve those numbers. In New York City, where more than 234,000 asymptomatic students and staff members across approximately 1,600 schools were tested last fall, the overall rate of positive tests was only 0.4 percent. That suggests that — even during a time of high community spread — about 40,000 tests among asymptomatic individuals would need to be performed to prevent one in-school transmission.

And how accurate are these tests? Rapid antigen and saliva PCR tests, which are frequently used in schools, can have a false positive rate of 1 or 2 percent. That may sound low, but statisticians know that, when testing in a setting of low prevalence of disease, even a single-digit false-positive rate can be extremely problematic.

The current prevalence rate for the coronavirus in the United States is roughly 15 cases per 10,000 people per week. (Prevalence in schools tends to be similar to, or lower than, that in the surrounding community.) If you give 10,000 people a test that produces false positives 2 percent of the time, that means you might get 215 positives: 15 true positives and 200 false positives. In other words, more than 90 percent of the positive test results will be incorrect.

And each positive test requires more testing to verify the result — typically with a more accurate PCR nasal swab test. This would lead to anxiety for the student and his or her classmates; missed days of school (often for an entire class, which will probably be required to quarantine); missed days of work for parents (if the children need care when out of school); and investigation by the local public health department. Since most positives would be false, much of that time and effort would be wasted.

One private school in San Francisco with which we worked, and which gave us permission to share its experience — anonymously — has been open since October and has been testing all students and staff members monthly with saliva-based PCR tests; the school had performed more than 1,600 surveillance tests as of March 31. Only 10 came back positive, and eight were determined by clinical review and further testing to be false positives. Of the two true positive tests, one person had mild symptoms and another had a known exposure. In other words, the testing program did not identify any cases among teachers or students that would not have been picked up through ordinary symptom-based and contact-based screening.

Mass asymptomatic testing programs would also come with an enormous price tag: Even with antigen tests described as costing $5, the need for additional supplies drives the per-test cost up to roughly $20; and PCR-based testing can cost as much as $100 per test per student. Even if less expensive “pooled” testing were used — in which samples from multiple students are combined, and students tested individually only if there is a positive result — the costs can mount quickly. In one school district in suburban Massachusetts that took this approach, $320,000 was spent for a semester to monitor 10 schools, researchers found. What’s more, the testing required at least 80 hours per week of staff or volunteer time.

A Rockefeller Foundation report estimated the cost for weekly testing in all public school districts nationwide at $42.5 billion for one year. We think it’s unlikely that many districts can afford to implement such a program, even with the $10 billion allocated for school testing on a national level. But we also don’t think the policy makes sense even where it is affordable.

Educating parents and students about the need to stay home when sick or exposed will be much more effective and cost-efficient than mass screening, particularly as disease prevalence decreases. (Many schools already remind students to check for a fever or other symptoms every day; if they have a cough, they must stay home.) Money allocated for asymptomatic testing could be better spent on other forms of mitigation — medical-grade masks for unvaccinated teachers, improved ventilation and free testing for students with covid-19 symptoms. And of course, resources saved by not implementing mass asymptomatic testing could be put toward furthering students’ academic achievement, mental health and overall well-being in school.

Testing continues to be an essential tool within schools. But it should be reserved for people who show symptoms and those who have had contact with people known to have been infected with the coronavirus. Surveillance testing of asymptomatic teachers and students is not only a waste of resources; it also threatens to radically disrupt the day-to-day functioning of schools. After a lost year of education, that’s the last thing we need.