I might be willing to vigorously advocate a switch over to distant reading as the basic form of professional literary critical work (though even then I see distance and closeness on a spectrum, while many just want to trash close and, worse, symptomatic reading altogether for something wholly innocuous), but when it comes down to what to teach it has become clearer and clearer to me that close reading is the way to go. Retracing complicated character interactions in novels or dealing with their plots does indeed require something more distant (you just can't get at these things without paraphrase, and that's not a heresy at all), but there just isn't anything that brings you into the way language is working like close reading does. There are lots of ways to teach this though, and paper writing is a great time to deploy your full arsenal. I've been fiddling around with some sort of basic introduction to close reading in paper writing to hand out, alongside all sorts of other materials and explanations and presentations and examples. Here is what I came up with:
Composing a paper for a literature class is a strange thing: it often requires much more subtle argumentation than work for classes in other disciplines, even though its job is primarily to do the work that, in these disciplines, comes before any actual arguing—interpretation, or the amassing of various textual material and the extraction of meaning from that material. But this is easily explained. Because the points to be argued are ultimately about the text itself under consideration, however much they may also be points about other less textual issues (society, philosophical issues, etc.), you don’t argue anything by any other means than interpretation itself. So because the point is an interpretive one, not only do you have to argue a point, but you also have to do this by arguing only about the interpretation necessary to make that point.
The analytical tool you use in order to produce such an argument about interpretation or interpretive argument is what we call close reading. Close reading is a technique common to many types of interpretation (religious or philological, for example), but its modern form was perfected at Cambridge and various U.S. universities in the 1920s and 1930s as an alternative to the techniques of evaluative and historical criticism (subsequently historical criticism would also integrate close reading, and close reading would also integrate—to some degree—the demands of evaluation). It is based on certain theories of language, but its aims are primarily practical, and so it takes the form of a procedure: in your argument, isolate a passage from the text that concretizes or exemplifies your point, and then proceed to pull out of that passage specific words, phrases, or formal or rhetorical features (meter, rhyme, metaphor, metonymy, pun, parallelism, anaphora, etc.—which you don’t have to name, but should try to notice) and show how these make your point for you.
We still use this procedure today because it is flexible enough to accommodate a broad argument that might range over several texts or even authors (you don’t have to close read all the time, though you can continually use it to show your point is about texts rather than a broader phenomenon), but also objective enough to allow us to establish whether the argument is indeed about the text (or whether it is a misreading of the words and the way they are working). On the latter point, this is why we call such interpretive arguments, once they are established, readings: others can read what you read in the text, because in some sense close reading does not just provide evidence but also helps to reproduce the acts of attention necessary for your point to become visible as the evidence itself.
But calling the finished interpretive argument a reading also means that the argument is present in more than one passage, or has ramifications upon the text as a whole. Now, while several close readings strung together indeed are the ideal form of an interpretive argument, one or two good ones, together with acute acts of paraphrase, descriptions of character interactions or relationships, or indeed small quotations (all of which should be cited) will work as well. Close reading doesn’t have to involve a lot of pomp, where a big block of text is analyzed and pulled apart to no end, but can also just be the continual citation of small but important phrases that—again—make your point for you in linguistic work which you can describe.