Brian P. Gill is a senior fellow at Mathematica, a nonpartisan public-policy research and analysis firm. Jennifer S. Lerner is a professor of public policy, management and decision science at the Harvard Kennedy School, and former chief decision scientist for the U.S. Navy.

The prospect of reopening schools this fall is both urgent and terrifying. Fortunately, there are ways to reopen schools while reducing the odds of major covid-19 outbreaks — if we are willing to be creative about how to reopen them and abandon some long-held assumptions about how schools operate.

The challenge lies in making decisions under extreme uncertainty — uncertainty about the transmission of the virus in children, about how far apart students’ desks (and school bus seats) need to be, and about whether kids can successfully wear face masks for six hours a day. Schools in some countries have reopened without experiencing infection spikes, but it is hard to explain away the Israeli school that saw more than 100 infections within a few weeks after reopening.

In a pandemic, the challenge of decision-making is made even harder by the mathematics of contagion. Infections compound, magnifying the risk of any large-scale, synchronized activity. This means that bringing all the students back, in all the schools, on the same day, risks throwing fuel on the fire.

When facing extreme uncertainty coupled with a dire worst-case scenario, it makes a lot of sense to explore options and hedge bets. Doing so not only reduces the chance of catastrophe, but also allows decision-makers to learn as they go and refine strategies accordingly.

What might this mean for reopening schools?

First, don’t open all schools at once. Policymakers should encourage schools across a state (or a metropolitan area) to stagger their start dates, reducing the risk of simultaneous outbreaks that could quickly create a statewide crisis. Some schools could open earlier than usual, getting an early start on compensating for spring’s lost learning.

Second, reduce the number of students in schools and classrooms. We believe this can dramatically slow the spread of covid-19 — even if children are not especially good at wearing masks or maintaining physical distance. Mathematica researchers conducted an analysis for Pennsylvania’s state education department, running more than 25,000 simulations across six different approaches to reopening schools. The analysis found that dividing students into smaller groups, each of which attends school some days and learns from home on others, may allow schools to avoid an outbreak for five to 10 times as long as if they tried to operate normally. Rather than shutting down after a week or a month, many schools might be able to remain open for an entire semester.

In addition, the analysis suggests that shrinking group sizes with part-time attendance could allow schools to open without substantially increasing the risk of large-scale outbreaks. This is not to say that everyone can attend safely: Some students and staff who are at high risk of covid-19 complications may need to teach and learn from home, and some communities with high infection rates may need to postpone reopening. And there is no way for a school to eliminate risk entirely. But for many communities, opening with small classes attending part time is nearly as safe as if the school were entirely closed.

The analysis also found that mitigation practices such as wearing masks on the school bus and eating lunch in classrooms could slow the spread of covid-19 somewhat. But if all the students come to school every day (as states such as Florida and Massachusetts have proposed), with classes and school buses running at full capacity, outbreaks remain far more likely than if students were in smaller groups, coming to school part time. Pandemic math is unforgiving.

Of course, having students in school only two days a week creates a logistical headache for families. But it might allow schools to avoid an outbreak for months — while bringing all the students back every day may lead to frequent, unpredictable closures. By reducing outbreaks and closures, a part-time approach might ultimately produce more total hours of in-school instruction.

As parents ourselves, we would much prefer that our child’s school be open for a predictable two days a week than a highly unpredictable cycle of opening and closing. But more important than our own preferences are these facts: Unpredictably difficult experiences create more stress and more downstream health problems than predictably difficult experiences, even if the experience itself is equivalent in all other respects. And for children, more predictability yields better emotional health, a key predictor of life outcomes.

If we are willing to let go of our long-held societal expectation that all of our kids must be back in school together, on the same Monday-through-Friday schedule starting in late August or early September, we can reopen schools with enhanced predictability and reduced risk. A phased and staggered approach acknowledges the limits of present scientific knowledge, protects against worst-case scenarios and facilitates the development of better solutions.

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