As he explained why the Wissahickon School District — which is reopening for in-person instruction Monday — might have to close its buildings again amid the pandemic, Superintendent James Crisfield started by defining a word.

Attestation, his PowerPoint slide read — a declaration that something is the case. “I wasn’t even sure it was a real word,” Crisfield said, as he began his presentation to community members.

But it has real implications for the Montgomery County district, and others across Pennsylvania. Under new rules, public schools have to revert to virtual instruction once they record certain numbers of coronavirus cases.

With the virus surging, Pennsylvania officials last week told preK-12 schools they could still teach students in person, but only if they pledged — by submitting an “attestation form” — to follow face-covering mandates and protocols for when COVID cases are identified in a school building. Private schools were not required to submit the form.

For Crisfield’s district, the first part was straightforward, since masks were already required in schools. But the second was new — laying out specific numbers of cases that trigger closure of a school building, based on enrollment and levels of community transmission of the virus.

For schools in counties with “substantial” transmission — at this point, a category that includes almost all of Pennsylvania — a building with fewer than 500 students that records five or more COVID cases over 14 days is recommended to close for two weeks. In a school with 500 to 900 students, the threshold for a two-week closure is seven cases; more than 900 students, and the bar is 11 cases.

Fewer cases — two to four in a small school, six to 10 in a large school — warrant shorter, three- to seven-day closures, according to the state.

A Department of Education spokesperson did not respond to questions Wednesday about the rationale for the case counts.

In practical terms, the new rules mean schools may be forced to close on very short notice as case counts hit the state thresholds.

“This is going to be like snow days, except there’s no snow around,” Crisfield said in an interview.

For months, Pennsylvania had recommended that schools in areas with substantial levels of transmission of the virus only provide virtual instruction. Many schools were not following those guidelines — saying they had been operating in-person safely, and had seen few instances of the virus spreading in their buildings.

Instead, Philadelphia-area districts have been taking their cues from county health officials. Apart from Montgomery County — which ordered schools to revert to virtual programs for two weeks amid the surge in coronavirus cases, a shutdown that ends this coming Monday — local counties in recent weeks have permitted or endorsed some level of in-person instruction.

» READ MORE: As COVID-19 cases surge, should schools stay open? Around the Philly region, approaches vary wildly.

For school districts that want to operate in person, “I want to make sure we honor the local control,” Noe Ortega, Pennsylvania’s acting education secretary, said this week.

But some school officials said the state wasn’t giving them much choice. “It feels to me like a backhanded way of closing schools without closing schools,” said Michael Thorwart, school board vice president in the Council Rock School District, which has been offering in-person instruction.

The new rules come as parental backlash over school closures has mounted — and as coronavirus cases and hospitalizations spike and health officials warn of bleak weeks ahead.

Much of the debate over schools and the coronavirus has centered on whether the virus is transmitted in schools — data that Pennsylvania hasn’t been tracking, though local health officials have reported few outbreaks in school settings.

The new state guidelines relate to cases involving students or staff in schools — regardless of where they contracted the virus.

Like a number of school officials, Thorwart was still processing the new metrics this week. “I’m looking at the numbers — I have been provided no science as to where these numbers came from,” Thorwart said.

He also wasn’t sure exactly how the district would apply the new rules. Council Rock South High School, for instance, reported 14 cases over the two weeks ending Nov. 30. Under the new rules, 11 cases trigger a shutdown.

But Thorwart said Council Rock South’s 14 cases could include students learning virtually — numbers that wouldn’t be counted for the purposes of closing a building.

He also didn’t know whether cases recorded over the last two weeks counted toward the numbers that would warrant closing buildings, or whether the count began this past Monday — the day districts were required to submit attestation forms to the state if they wanted to operate in person this week.

» READ MORE: Montgomery County judge denies parents’ effort to stop health board’s order to shut down schools; another lawsuit filed

The state Education Department said Tuesday that more than 99% of public school districts had submitted the forms.

In some cases, schools have already reverted to virtual instruction based on the new requirements. Among them are five in the Downingtown Area School District, which announced temporary closures last week after the school board voted to follow the state’s new rules.

The thresholds were “actually helpful to us,” since they differentiate among school buildings, said district spokesperson Jennifer Shealy. “Rather than having to make a blanket, district-wide decision,” some Downingtown schools continued offering some in-person instruction.

The new rules do come with a caveat. Accompanying the state’s charts is an asterisk specifying that “if case investigations, contact tracing, and cleaning and disinfecting can be accomplished in a faster time frame,” schools don’t have to close for the period prescribed by the state.

For schools like those in the Chichester district, which has been rotating children into classrooms two days a week with virtual school days on Fridays, school time might not be lost if case counts rose to a shutdown level on a Thursday, for instance, and cleaning and contact tracing were performed over the weekend, said Superintendent Dan Nerelli.

He sees the new state rules as another set of conflicting instructions.

“They’re trying to do everything they can possibly do without having the pushback on them for closing schools,” Nerelli said of the state — putting school leaders “in a tough position.”

While he isn’t advocating for a shutdown, Nerelli said: “If it’s that unsafe, tell us to close schools and we’ll do it.”

» Here are Philly’s current COVID-19 guidelines: