Colleen McEnearney uses two computers to teach algebra to her students in mid-April. (Toni L. Sandys/The Washington Post)

More than a month after schools across the nation shut their doors, educators face a choice: Do they teach virtually in real time, or let students learn on their own?

Proponents of “synchronous” learning argue that live video instruction allows teachers to do regular check-ins, ensuring that students stay on track. But some warn that live sessions are vulnerable to privacy and security breaches, a worry that has proved well-founded. “Asynchronous” learning avoids those issues, advocates say, while granting flexibility to families and teachers whose lives are in chaos or who lack consistent access to online resources.