I have written about the differences between discussion, dialogue and debate, but I thought it might be interesting for people to know about the word origins of each. Here are the definitions from the online etymology dictionary.
early 13c., "literary work consisting of a conversation between two or more persons," from O.Fr. dialoge, from L. dialogus, from Gk. dialogos "conversation, dialogue," related to dialogesthai "converse," from dia- "across" (see dia-) + legein "speak" (see lecture). Sense broadened to "a conversation" c.1400. Mistaken belief that it can only mean "conversation between two persons" is from confusion of dia- and di- (1). A word for "conversation between two persons" is the hybrid duologue (1864).
Notice that the word is based in the idea of "speaking across," or bridging.
late 14c., "to quarrel, dispute," from O.Fr. debatre (13c., Mod.Fr. débattre), originally "to fight," from de- "down, completely" (see de-) + batre "to beat" (see battery). As a noun, from early 14c. Related: Debated; debating.
Notice that the root of the word has to do with fighting.
mid-14c., "examination, investigation, judicial trial," from O.Fr. discussion "discussion, examination, investigation, legal trial," from L.L. discussionem (nom. discussio) "examination, discussion," in classical Latin, "a shaking," from discussus, pp. of discutere "strike asunder, break up," from dis- "apart" (see dis-) + quatere "to shake." Meaning "talk over, debate" in English first recorded mid-15c. Sense evolution in Latin appears to have been from "smash apart" to "scatter, disperse," then in post-classical times (via the mental process involved) to "investigate, examine," then to "debate."
Notice that the word has the root of smashing or dispersing.
From a word origin perspective then, it is clear that we generally would want dialogue in the classroom. Of course, debate has its place, especially for developing speaking skills. And discussions are commonplace for their quick and easy nature. But it is dialogue that is the highest form of discourse.