wilful
Stubbornly doing something on purpose, even when told not to.
Wilful (also spelled willful) means doing something on purpose, especially when you know you shouldn't. When a student gives a wilful answer that's completely wrong, they're not confused or mistaken: they chose to answer that way deliberately. When someone commits wilful disobedience, they heard the instruction clearly and decided to ignore it anyway.
The word carries a sense of stubbornness or defiance. If you accidentally break a rule because you didn't understand it, that's not wilful. But if you break it knowing exactly what you're doing, that's wilful behavior. A judge might ask whether damage to property was wilful or accidental, because intention matters when determining consequences.
Sometimes wilful describes someone who's determined to do things their own way no matter what anyone says. A wilful child might refuse to wear their coat even though it's freezing outside, not because they don't understand it's cold, but because they've decided they won't be told what to do. This kind of wilfulness can show independence and strong character, but it can also lead to unnecessary problems when someone digs in their heels just to prove a point.