Which Visa should we apply for to teach one semester in China next Sept-Jan 2016?

Hello Louise! It's suggested you start the process one month before your travel to China. The validiry starts from the date of its issuance. You both need to apply for Z type. Have you finalize your job and employer? If yes, first get the work permits with the assitance of your employer. Then apply for the Z type. You can go to the embassy or consulate having jurisdicton over your residence and submit the following materials: the valid passports, a photocopy of the passports' info page, a filled application form glued with your recent bareheaded photos, the work permit, and the invitation letter or confirm invitation letter from the duly authorized unit.