The Proteus Phenomenon is a name for when people change their behavior when they know that somebody is watching them, like when a kid is being watched by their parents or teacher. It comes from a story in Greek mythology about a man named Proteus who could change his shape when someone tried to catch him.
When people know they are being watched, they tend to act differently than they would if they were alone. For example, a kid might not be as mischievous or disobedient if their parents were in the room. This is the Proteus Phenomenon.