In accord with a previous post, the most important approach is that of following a criterion. Specifically, with Anne Bradstreet who is mentioned in your tag, you may wish to put your primary focus upon her connection with Puritanism. For example, her poem, "Upon the Bruning of Our House," clearly evidences the Calvinistic creed of predestination and the idea that "everything happens for a reason." In addition, the Puritan belief that God is connected to even their most mundane acts is prevalent in the writing of Bradstreet. Her strong faith in God cannot be missed in her blessing of God as her house burns.
For the Puritans, the sole purpose of literature was pragmatic: to teach moral instruction. Bradstreet's poetry reflects the Puritans' knowledge of the stories and language of the Bible and their awareness of the relationship between earthly and heavenly life. Yet, she was among the first American writers to speak of and thus try to find a place for individual feelings within the context of Puritanism. Her attempt to express these individual feelings in the Puritan plain, simple language is confining for Bradstreet at times and she does employ more vivid, color words in the afore-mentioned poem such as pelf, dunghill mists, mold'ring dust, and succorless. So, while Bradstreet adheres to the movement of Puritanism in her poetry, she does individualize as well.
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I can see many answers to this question. I would suggest that there are multiple levels in which a work can be assessed and evaluated. If one is seeking to find or deduce its importance in a particular genre or canon, then perhaps comparing it to other works in the time period would be appropriate. This might take the form of assessing popular or critical reaction to the work. Continuing a method of evaluation would be how the particular work has been received over time. Has the work gained in stature or diminished after its publication? Such evaluation can be done on thematic and artistry levels. The method of evaluation must have some criteria that can be applied to the work in question as well as other works of comparative stature.
There are many many ways of looking at a literary text. That is what you call different schools of literary criticism.
1. The content/ The themes--the subject matter of a work.
2. The form or the structure in which the work is composed e.g. the five-part structure of The Waste Land, the sonnet form and so on.
3. The style and the language of the work, its diction and use of words, how much denotational and inter/intra-textual the text is etc.
4. The genre in which the work is written and how does the generic choice work itself out through the text.
5. If it is a fictional work, a study of its plotline, characters ,their graphs, intensities and consistencies.
6. The rhetorical angle and the metrical patterning in case of verse.
7. Setting the work against a historical context and study the realism and ideology in the text. Neo-Historicism also sees the text as history.
8. A psychological or psychoanalytical reading of the work, taking into account the minds of the characters and applying theories of psychoanalysis to explain their actions.
9. If it is a performance-text (performatory poetry, theatre), a study of the performance-act.
10. Looking at the gender-patterns in the text, finding out any bias, if any, the sexist angle and so on.