This is a common misunderstanding. Labor Standards Act Art. 16 only applies when (1) the employer terminates the contract in accordance with Art. 11 or 13, or (2) the worker terminates the contract in accordance with Art. 15, which would be very unusual for a foreigner.
You may think you have an indeterminate (non-fixed term) contract, but as a foreigner you cannot actually (legally) have such a contract unless you are a permanent resident, according to the Supreme Court, so if the contract claims to be indeterminate but you don’t qualify, the length of the contract is automatically reduced to fit your period of legal residency.
Bottom line, for the vast majority of foreign teachers, there’s nothing to invalidate a three month notice period in a contract.
Yes, well, that would be different. 