If you use the word discourse, you are describing a formal and intense discussion or debate.
The noun discourse comes from the Latin discursus to mean "an argument." But luckily, that kind of argument does not mean people fighting or coming to blows. The argument in discourse refers to an exchange of ideas — sometimes heated — that often follows a kind of order and give-and-take between the participants. It's the kind of argument and discussion that teachers love, so discourse away!