“Why are they so happy to have these devices when just a few years ago they didn’t want them in the classroom?” Dr. Pea asked about school administrators.

The Volusia County School District in Central Florida, bordering Daytona Beach, is one of the places that used to have signs around its schools that admonished students: no cellphones allowed. But the signs have been replaced over the last two years with new ones that read: B.Y.O.T.

Volusia school officials say that they realized they should take advantage of, rather than fight, students’ deep connections with their devices. At the same time, the district found that the cost of providing and maintaining computers for students was becoming prohibitive.

Since the change, Volusia officials say, they have not encountered many tech support problems or complaints from teachers. Rather, students are more engaged, they say, and the only problem that regularly crops up is that students forget to charge the batteries in their devices.

“It’s almost like bringing your homework,” said Jessica Levene, manager of learning technologies for the Volusia district, where 21 of 70 schools are using B.Y.O.T. “Make sure you have your device and that it’s charged.”

She conceded that students could text each other more easily now but said the school was keeping them busy on their devices. And while district administrators worried initially that poorer students would not own devices, they discovered something of “an inverse relationship” between family income and the sophistication of their devices, particularly smartphones, said Don Boulware, the district’s director of technology services.

At Woodward Avenue Elementary School in the Volusia district, fifth-grade teacher Dana Zacharko said her students tended to bring in smartphones or iPod Touches. She said she had found apps that allowed her to teach all kinds of subjects.