Apply two of the schools/approaches of literary criticism (New criticism, psychoanalytic, mythological, feminist, postcolonial) to a literary text...

If we use The Great Gatsby as our text of choice, we could examine it through both a New Critical and a feminist lens.

A New Critical reading aims at finding unities in a text and employs the tools of close reading we typically learn in high school, with a focus on plot, theme, setting, characterization, symbols, metaphors and repeated patterns. In Gatsby, we see the color yellow associated with money, and more particularly with Gatsby, who, for example, drives a yellow car. Green is another symbol in the novel, representing desire: the green light at the end of the pier represents Gatsby's yearning for Daisy. What about clocks: do they symbolize Gatsby's desire to stop time? We might also look at name symbolism: does Nick Carraway get 'carried away' by Gatsby? Is Mr. McKee a 'key' to the novel? 

A feminist reading would examine how women are portrayed in the novel. How have gender roles limited Daisy? Would she be a different person if she had had opportunities other than marriage? Why does she hope her daughter will be a beautiful "fool?" What about Jordan? Is she forced into deceptions to live her atypical, androgynous life? What can we say of Myrtle? Is she trapped in a mindset that sees sex with a wealthy man as her only "career" path? Whether conscious or not on Fitzgerald's part, it's difficult not to read the novel as a critique of the constraints still put on women in the newly liberated 1920s.