Most instructors quickly become familiar with a common student query/lament: "Teacher, how come you see all those things and I don't?" The quick answer, of course, is "I've been doing this for longer than you have." But that doesn't actually answer the question, does it? "It takes practice," while more specific (and, in its own way, perfectly accurate), still leaves the student high and dry. Practice what?
Well, practice asking questions. The emphasis on "answers"--what the instructor "sees"--distracts the student from the actual process involved in reaching those answers, which largely consists of asking oneself how the poem/short story/novel/film works. But asking those questions requires a certain degree of technical knowledge: what's a metaphor? A symbol? A chiasmus? How about a rhyme scheme? There are grammatical questions (where's the main verb? Why is the subject of this sentence in line five?); there are "counting" and repetition questions (so, just how many times did "I" appear in the space of one paragraph?); there are definition questions (what does "insouciant" mean?); and so forth. It's important to get students away from the idea that this process ought to move "quickly"--a misconception which discourages rereadings.
I like to get students looking at rhyme schemes. Tomorrow, I'm teaching Tennyson's "The Lotos-Eaters," which builds a kind of joke into the rhyme scheme. The five introductory stanzas share a common scheme of ababbcbcc--a Spenserian stanza, in other words. The first stanza of the choric song, however, goes like this: ababcccdddd. Most of the stanzas that follow offer a debased version of the introductory stanzas, usually echoing either the abab quatrain opening or the closing couplet. (The sailors have a particular affinity for triplets.) As I like to joke, the rhyme scheme gets a bit "stoned" here--it echoes the structure of the opening stanzas but never quite manages to maintain that structure for very long. But how did I get there? It isn't necessary to know that the first stanzas are Spenserian, but it is necessary to a) diagram the rhyme scheme in the first place and b) ask why it changes. (I've found that students often catch on fairly quickly to rhyme's importance.) In turn, that requires the reader to presume that there's some connection between sound and sense. And "sense," of course, pulls the reader back to the poem's surface or literal meaning. Strictly speaking, this can be done "quickly" once you've got in the groove, but there's no reason for a student to expect that everything will come immediately. It's usually easier to get students to see that point when teaching poetry, which many of them perceive as an alien form (even though most of them listen to rhymes all the time via pop music), than it is when teaching prose, which "ought" to be "easy." I imagine that being more "meta" about the process of generating an interpretation, as opposed to simply lecturing on the finished product, ought to help. I can also imagine devoting time to small-group work in which students practice generating not answers, but questions.