The word "Schooldame" is rare and outdated, which is why it's difficult to find direct synonyms for it. However, some possible alternatives include "schoolmistress," "schoolteacher," "educator," "instructor," "tutor," and "pedagogue." Each of these words describes someone who teaches or educates others, and they're more commonly used than "Schooldame." Depending on the context, other synonyms like "principal," "headmistress," or "dean" could also be used. Ultimately, it depends on the tone, context, and era in which the word is being used.