First, I want to say that the safe way is to get a work visa and get a temporary residence permit at the local police station within 30 days after entering China under the help of the school. Now, the school ask you to apply for F visa, maybe it is not qulified to hire foreigners, so it can't apply for paperwork for you. I heared that some aliens have been cheated. After you arrive in China, they will collect your paspsort and tell you that they apply for work visa for you, then they will tell something wrong take place, the passport is in the Immigration Office, etc.