I don't really understand the question, I suppose. What's the difference between "cultural" and "academic"? (The prevous poster's list didn't clarify the issue for me. I can understood other distinctions -- such as "popular" versus "academic" or "cultural" and "literary" -- but I'm still puzzled by the initial question.)
I think a little bit of literary theory can be taught at any level (if the students are able to think abstractly, maybe ages 10-12 and up?), and that the students will need to slowly build their competence. I get the sense that New Criticism and versions of "reader-response" approaches to literature are still the most widely used (although perhaps not explicitly "taught") method of literary theory until students enter AP English classes or college classrooms. Please correct me if I'm wrong!
The "Cultural, or interdisciplinary, criticism" list in the first respondent's post looks good to me, but I disagree with one item: "Literature as an organic thing: Post-structuralist Criticism." Post-structuralism (and its companion term, postmodernism) doesn't look for organic wholeness but rather for the very opposite of the "organic": a lack of closure, autonomy, completeness, unity, naturalness, etc.
It should be taught as an academic subject with the cultural influence addressed during the instruction. Whatever school of literary theory we follow, whatever form we use, it has to be approached from an academic perspective first. Yes the cultural aspect comes into play, as we are all influenced in the way we think via our own paradigms. If we begin with an academic bent, we will be less likely to be subjective with regard to those paradigms.
I think that there are two major schools of literary theory:
Cultural, or interdisciplinary, criticism:
- Literature as central to religion: Classical Criticism
- Literature as central to culture: Neoclassicism Criticism
- Literature need not be study of the beautiful: Romantic Criticism
- Literature as central to history: Historical Criticism
- Literature as central to the author: Biographical Criticism
- Literature as central to society: Sociological Criticism
- Literature as a thing of science: Eco Criticism
- Literature as central to socio-economic forces: Marxist Criticism
- Literature as central to independence of nations: Post-Colonialist Criticism
- Literature as central to sexual psychology: Freudian Criticism
- Literature as central to gender: Gender Criticism
- Literature as central to persuasion and argument: Rhetorical Criticism
- Literature as central to a system of comparison: Metaphorical Criticism
- Literature as central to anthropology and sociology: Structuralist Criticism
- Literature as an organic thing: Post-structuralist Criticism
- Literature as central to a repeated mythology: Myth Criticism
- Literature as central to repeated symbols and codes in society: Jungian Criticism
Academic criticism (only):
- Literature as a thing unto itself without author/historical intent: New Criticism
- Literature as ideology: Literary Theory
- Literature as central to language, syntax, and diction: Stylistic Criticism
As you can see, most criticism is derived from a culturally-assimilated reading. Only a few schools of criticism exist that are purely insulated from culture and mores. I think that both should be taught. Neither one should be forsaken for the other. A critic must show a moderation between analysis and over-analysis, between author and book, and between the textual and the peripheral.