I see ongoing discussion about visas for teachers in China and I'm sure it must be confusing to teachers thinking of coming here.

L Visa is for tour/travel

F Visa is for business,short term project,etc

Z Visa is for work
For a Z visa to be issued the school should be licenced to hire foreign teachers.Many schools are not but still have a foreign teacher,either employed directly by the school or sent to the schoolby a recruiter.I've met several teachers who have worked here in China on F (business) visas.
It helps if you remember that there is a sense in which this is the People's Republic of Guangdong, People's Republic of Henan,People's Republic of Beijing,etc. Officers appear to have a fair amount of discretionary power within the interpretation of the guidelines in their area.It's advisable I think to (a)find out the requirements in the area in which you'll be working,and

(b)talk to the embassy in your country,if you are not yet in China,and ask their interpretation of the rules.Read the information on the website of the Chinese embassy in your country.
Some writers assure us that teachers have been kicked out of the country for not having a Z (work) visa (and for no other reason).Can anyone tell me the name and contact information for one of these people? Perhaps it has happened but I doubt it.It may be necessary to leave mainland China(go to Hong Kong)before getting another visa,but "kicked out...."?
The visa officers I've met in my two years here have mostly been very helpful and understand that the system is new to us.I have no doubt that there are officious people who delight in making life uncomfortable for foreign teachers.But the majority, I'm sure,will respond to civility,patience (and sometimes a little pleading).