What are the exact rules for working part-time on a student visa?

I'm thinking of studying Chinese at a university and maybe working on a part-time job as an English teacher. I'm a non-native speaker though and officially you need to be a native speaker to get a job as an English teacher/to get the according Z. This discrimination related to Z only applies to English teachers on a legal level, as far as I know. Would a student visa actually allow me to work part-time as an English teacher?