Cultures often overlap other cultures when it comes to language. Think of the way we address our teachers here in Brazil. The Portuguese word for teacher is a title: Professor Marcos, Professora Maria. In many cases we may address our teachers either as Marcos or Professor. Take the same word and translate it. Teacher! Every Brazilian learner knows that; what not every learner knows is that teacher is not a title, therefore it shouldn't be used to address a teacher. That is, English speakers won't say "Hi, teacher!" The same way we would not say "Bom dia, empregada" or ""Bom dia, porteiro" when we get home.
On the other hand we might greet the bus driver with "Bom dia Seu motorista." An American would probably find it very confusing and might end up greeting his dog's vet with "Boa tarde, Seu veterinário!" As a rule, it takes a while for a foreigner to figure out which job titles he can use to address someone and understand that "Oi, Doutor" is the correct form while "Oi, Médico" isn't.
To correctly address your teachers simply call them by their first names or use the following titles with a last name:
Mr Johnson (for a man)
Mrs Gonzales (for a married woman)
Miss Silva (for a single woman)
Ms Costa (if you don't know a woman's marital status)
Instructors that teach at colleges and universities usually have a Doctor's Degree and will be addressed as Professor + last name. (e.g. Professor Gimenez) or simply Professor. You might address them as Doctor +last name. In many cases, they are called by their first names. It will depend pretty much on the person.
Someone who graduated from medical school is also a doctor, but technically he or she is a medical doctor (M.D.) as in Roger Smith, M.D. You can tell Roger is a physician because there's the M (medical) in his title.
Someone with a Ph.D abbreviated from the Latin Philosophiae Doctor (Doctor of Philosophy) has completed his or her Doctorate degree, the highest academic degree after completing about 3 years of studies in a graduate course in a university or college.
As for 'Sir' and 'Madam' (or 'Ma'am'), they're used as a form of polite address for a man or a woman of a higher social rank. The chambermaid in your hotel will probably address you as 'Ma'am' to show that she's at your service. A young boy will say "Yes, Sir" to his teacher, who is in a position of authority.
To sum up, when you find yourself in an English speaking environment, just call your teacher by their first name or use one of those titles followed by their last name!