After the first day of school at Mark T. Sheehan High School in Wallingford, Conn., Mackenzie Bushey, a 15-year-old junior, came home upset that a teacher enforced a no-cellphones policy by confiscating students’ phones before class. She needed her cell, Mackenzie told her family last month, to notify police should a gunman attack her school.

And also, she said, “to say my final goodbye to you.”

Mackenzie’s mother, Brenda Bushey, blames her daughter’s fears on monthly active-shooter drills at Sheehan High. “I understand they’re trying to think about the children’s best interests,’’ Ms. Bushey said in an interview. “But you can’t help but think of how it’s affecting them.”