What are "critical methods" and how do they relate to "critical theories"?
All academic disciplines need theories to organize the information they study, and methods dictated by those theories to collect that information and interpret it to determine what it means. Theories are broad generalizations about the ideas and things. To pick an example well-known to most students, economists, since the eighteenth century, have believed in a theory of "market-based economy" which states that, for any given marketplace and product, the product's price, demand, and supply are interrelated such that changing one will change the others in predictable ways. They believe this theory explains the availability of goods, their price, and people's willingness to pay that price, unless government regulation or monopoly of supply or other forces overwhelm the market's ability to regulate itself. Marxist economists may disagree with capitalist economists about whether market-driven economies are good or bad for humanity, but they do not disagree about their existence or the necessity that we study them. For economists, "price" and "demand" and "supply" are "terms of art," essentially untranslatable jargon that members of the discipline agree to use to discuss markets. Economic research methods, obeying their founding theory, can be "quantitative" if they study price, demand, and supply statistically, or "qualitative" if they rely on non-computational methods like interviews and observation. Belonging to the discipline requires all practitioners of "economics" to come to terms with economic theory and methods of study, and to respect others' applications of the theory and methods as long as they are "legal," following the rules of the discipline.
Some disciplines' theories are widely shared, but all have regions of study in which multiple sub-theories contend for approval. In Biology's evolution theory, for instance, in the late twentieth century, some researchers believed the fossil and genetic evidence best could be explained by enormously long periods of steady but small changes in the gene pool. Others believed what they were seeing in the evidence supported long periods of relatively static genetic activity, with few lasting mutations, broken by violent "catastrophic" periods during which many species became extinct and many new species arose because successful mutations allowed them to adapt to the catastrophe (comet/bolide collision with Earth, volcanic or earthquake activity, etc.). "Catastrophism" and "Uniformitarionism" were terms of art used to distinguish these two interpretive theories and each theory regulated the methods used to study evolutionary evidence in different ways. In the early 1970s, Stephen Gould and Niles Eldredge published a theory of "punctuated equilibrium" that sought to synthesize the two competing theories, and the discipline's members tended to coalesce in agreement behind this new theory and the research methods it implied. This "thesis-antithesis-synthesis" pattern commonly occurs as a mechanism to hold disciplines together as they go through normal patterns of growth.
Other disciplines, the study of English literature among them, have an even less homogeneous theoretical consensus among their practitioners, and consequently scholars of English literature tend to practice a wide range of critical methods. This is not the same as having "no theory" or accepting "any method." If that were the case, there would be no discipline of English literary studies and it could not be taught as a post-secondary discipline. For this reason, it is not uncommon to encounter, in the introductions of books or articles on literary analysis, discussions of the interpretive theories used by the authors and the methods of analysis they have adopted, together with an argument for why these theories and methods are appropriate. Especially in the last half of the twentieth century, this multiplicity of competing theories enabled many scholars to become famous for publishing only about theory, discussing actual literary texts only when they supported their theories (and often avoiding mention of texts which would call their theories into question).
Publications of articles or books announcing dramatic new breakthroughs in literary theory have been rare in the early years of the twenty-first century, and some of the previous century's theorists even have declared the formal study of theory to be over (e.g., Terrence Eagleton, After Theory, 2003). Scholars who make such claims rarely look outside English literature as a field and are unaware that periodic theoretical disputes are fundamental to modern scholarship. The waxing and waning of theoretical upheavals has best been explained, with respect to natural science research, by Thomas Kuhn's The Structure of Scientific Revolutions (1970). Kuhn traces the breakdown of Ptolemaic astronomical theory as an accepted way to describe the solar system, describing the process as a predictable failure of the old theory to adequately explain new data. Astronomers patched together the old theory with exceptions and special adjustments until, in a period of great apparent disorder, the Copernican theory of the solar system won general acceptance and its attendant methods were adopted by all practitioners as "legal."
The New Critics (c. 1945-c. 1980) play a somewhat similar role in English 215's view of literary studies. The New Critics established as a given the following methodological principles followed by most scholars today:
If that sounds like what you learned in English 200, that is the reason those methods of close-reading analysis were taught there. New Criticism's other theoretical assumptions have largely been disproved by later theories' challenges, but these basic rules govern most interpretive theories actively practiced in our discipline today.