"We listened to the teacher."
Translation:Vi lyttede til læreren.
We heard the teacher and We listened to the teacher. Same difference as in English.
You're both right, actually. There's a difference between "høre" and "høre efter". "Høre" just means "to hear", like passively hearing something, while "høre efter" does have the same meaning as "lytte til"; that is, actively listening. It just can't be used in this context, because "Vi hørte efter læreren" isn't correct Danish. It should be "Vi hørte efter hvad læreren sagde" (We listened to what the teacher said/was saying) which doesn't correlate with the English sentence.