Any time a student refers to a teacher as a pedagogue he or she is not suggesting that the teacher has feet which are a foot-and-a-half (sesquipedalian) long.
The Greek ped used in English is a shortened form of the Greek pais (paid-), which means a "child"; usually a "boy", because in old Grecian times, boys were considered "more important" than girls.
Actually, pedagogue means "a child's guide" or "guiding a child". In ancient Athens, the pedagogue was a slave who led his master's children (boys) to school or provided private tutoring. In the U.S., the equivalent of "guiding a child" is now "home schooling". In time, the word became known as a "teacher".
This Greek ped is used primarily in technical terms; such as pedagogics, which refers to the "science of teaching". There is more information about pedoagogue, pedagog on this page.
Another derivative from the Greek ped is a word meaning "education" or the results of "education"; such as, "knowledge" or "learning". The Greek element pedia is found in other Greek words; such as, cyclopedia and encyclopedia, "circles of knowledge".