Research & analysing essays...How?

[womblingfree]

I'm researching a private language school for my MA dissertation.

To do this I've asked 5 students and 5 teachers to write short essays of their experiences. They have been given a simple essay title so as not to constrain their answers.

I'm looking to understand and depict participant’s experiences and conduct comprehensive examination through cross comparison of examples.

My question is what kind of research category does this fall under? Discourse analysis? Case study?

Also I'd like to see some examples of presentation if possible.

Any help would be greatly appreciated!