As an instructor and also a lover of literature, I think we can dispense with the idea that there's a uniquely right answer to search for as we read. The problem with this approach is that - ironically - it stifles students' interpretive capacity. At the very least it dillutes their inclination to construct meaning. In the artificial pressure to make the text "mean something" students will often overly complicate the simple and overlook the significant. But instead, we should teach our students to regard the literary work as a complex of meaning that's both constructed and dynamic: we make meaning out of the written words that lie in the wake of some authorial intent which we may never fully recover, but which we should strive to.
Let me say here that I reject what is called the Intentional Fallacy as both critically out of date and a fallacy in its own right. The Intentional Fallacy was a concept that appeared in the mid 20th century to describe a flawed theory implicit in literary criticism. Essentially, the argument is that if you use an idea of what the author intended to perform in the work, you would arrive at a simplistic, reductivist - and as some critics thought, a simply wrong - interpretation. The fact that we're beyond notions of right and wrong as it applies to interpreting literature suggests this notion is no longer critically useful. (Consider the huge range of significance we can see in a work like The Lord of the Rings if we know that the Catholic faith was one of Tolkien's most important sources of comfort and personal value.) The Fallacy's fallacy lies in the fact that the early critics who propounded this as a problem "received" their objects for study within a context that imputed to an author a fixed "authority" to make meaning. Follow me here - by reacting against this tradition, critics neglected an important sample of evidence for producing meaning out of a literary work and thus disproportionately emphasized close reading over potentially more informed reading. There are historical implications to this argument that we needn't go into now. But we should never reject a source of information that has direct relevance to our text - especially when, as teachers and students, we place so high a premium on logic and evidence-based argument. (Close reading was one very good spinoff of this period of critical elitism, one that we ought not discard. But the idea that we can determine a "right" understanding of a text seems to me erroneous.)
My view is that we should always use our knowledge of historical and biographical information in our attempts to open up a work for discussion, though we shouldn't limit our range of inquiry to fidelity to such authorial intentions.
So, while there's no single "correct" thing to read for, there're a few worthwhile things to pay attention to as we read.
Below is a checklist for unpacking literary texts, which you may find useful to guide your reading and structure your critical impulses. It's designed to be general enough for use on just about any literary text out there, while also being specific enough (which, admittedly, isn't very) to give you some important things to say about a literary work.
1. What major themes or ideas appear throughout the work?
* are there any ideas that show up several times in the work? If so, you can bet these are important.
* pay special attention to the way works are titled. Titles are privileged spaces, which means they carry much interpretive weight. As we see in James's "Daisy Miller: A Study," this practice can animate an entire class period with interpretive inquiry.
2. What prominent imagery emerges in the text?
* remember that prominent includes not just repeated use, but also extended meditation on. A speaker who lingers over his description of dark, shadowy places may be cluing us in to something important about his tone or thematic project.
3. What role does Gender/Race/Class play in the work?
* often these topics become used to structure a work and introduce important ideas.
4. What is significant about the work's structure? How does it reinforce meaning?
* structure is the way that a text is organized or put together. Subtle writers will often arrange elements in such a way as to enhance ideas that may be implicit. This requires some abstract consideration, since we don't normally think of writing as possessing "shape" or "form". But in literary studies, these are trigger words, and they refer to very specific things in poetry.
* related to structure is a work's style. This refers to the way an author chooses to present specific parts of the work, at the level of words and sentences. Hemingway had a distinctive style which avoided complex sentences; some have argued that this enhanced his work with a sense of "force" or directness.
5. What historical knowledge can we use to explore the work?
* historical knowledge extends to the author's personal life, publication reception, the time of a work's publication, as well as the time in which the work is set. For instance, knowing that Tolkien's major works were all drafted during the World Wars is perhaps useful for analogizing Sauron's aggression against the backdrop of Nazi Germany's aggressive international policies.
* we can also extract meaning from a work based on information that is conspicuously absent; just remember that when we do this, our logic must be very tight and our evidence very compelling - it's difficult to convince critical readers of a point without evidence, or that a lack of evidence is itself evidence of something important.