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!
n an extended communication (often interactive) dealing with some particular topic
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extended treatment of particulars
a lengthy discussion (spoken or written) on a particular topic
a discussion of a topic (as in a meeting)
discussion; (`talk about' is a less formal alternative for `discussion of')
elaboration, enlargement, expansion
a discussion that provides additional information
a discussion (spoken or written) that enlarges on a topic or theme at length or in detail
a consideration of a topic (as in a meeting) with a view to changing an earlier decision
elaboration of an interpretation by the use of decorative (sometimes fictitious) detail
n an address of a religious nature (usually delivered during a church service)
Sermon on the Mount
the first major discourse delivered by Jesus (Matthew 5-7 and Luke 6:20-49)
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a farewell sermon to a graduating class at their commencement ceremonies
preaching the gospel of Christ in the manner of the early church
zealous preaching and advocacy of the gospel
a sermon on a moral or religious topic
evangelism at a distance by the use of television
v to consider or examine in speech or writing
v carry on a conversation
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argue, contend, debate, fence
have an argument about something
conduct an interview in television, newspaper, and radio reporting
discuss formally with (somebody) for the purpose of an evaluation
go for an interview in the hope of being hired
chaffer, chat, chatter, chew the fat, chit-chat, chitchat, claver, confab, confabulate, gossip, jaw, natter, shoot the breeze, visit
talk socially without exchanging too much information
dispute or argue stubbornly (especially minor points)
bicker, brabble, niggle, pettifog, quibble, squabble
argue over petty things
altercate, argufy, dispute, quarrel, scrap
have a disagreement over something
be against; express opposition to
jawbone, schmoose, schmooze, shmoose, shmooze
talk idly or casually and in a friendly way