BRATTLEBORO — School attendance rebounded Tuesday in the Windham Southeast Supervisory Union a day after news of an unexplained potential threat caused nearly half of its 2,500 students to stay home.

Educators — learning from authorities that “a person who had previously made nonspecific threats regarding school-age people might be returning to the area” — decided to robocall families in Brattleboro, Dummerston, Guilford, Putney and Vernon Sunday to report schools in their towns would lock all doors to outsiders Monday.

The recording’s last-minute nature and lack of specifics alarmed many parents still reeling from last month’s school shootings in Newtown, Conn. But after a full day of news reports explaining the situation, nearly 95 percent of students returned to classes Tuesday.

“We’re going to maintain our security precautions,” said Windham Southeast Superintendent Ron Stahley, noting schools would continue to work with police to ensure a general sense of safety.