MILTON — No one was standing in front of an eighth-grade math class at St. Mary of the Hills School, but fractions were slowly appearing in colored chalk, as if written by the invisible hand of a ghost. The voice of an unseen narrator emanated from speakers on both sides of the smartboard, explaining the equation step by step.

While students sat quietly in their seats, listening to this virtual instructor solve the math problem, their real-life math teacher, Marianne Ruggiero, walked around the classroom with her arms folded, peering down at them as they scribbled notes with pencils into spiral-bound notebooks and tapped the keyboards of laptop computers.