During the Victorian years, oppidans, those who were not King's Scholars and therefore lived in town, lodged with either tutors or dames. Puzzlingly enough, the latter could be men or women. The old Etonian, Charles Frederick, helpfully explains the situation in his reminiscences:
For the information of those of my readers who may be non-Etonians, I may as well solve in the outset what is always to them a very puzzling question — wherein lies the difference between a dame's and a tutor's house, and how it is that these so-called dames are often men. It is not difficult to comprehend what a tutor's house is. It is one kept by any of the assistant masters in the regular school work, and where he receives boarders, who arc under his especial care, both as to maintenance and tuition. The dames may be considered to be any who are not tutors. They receive boarders also, but have nothing to say to their tuition; and if, therefore, a parent determine to send his boys to a dame's house, he must also fix upon a tutor for him, as the dames will not take upon themselves to regulate anything of this sort. There are ladies who keep houses at Eton, and these are strictly dames; but there are also men, as, for example, the drawing-master, and these, from not being on the list of regular assistant masters, do not come under the class of tutors. Were even the mathematical masters to have regularly-organized houses, it is doubtful whether they also would not be considered dames. 
Sometime after 1870, when Frederick published his Recollections of Eton, teachers of non-classical subjects, such a mathematics, gained the status of tutors, and the Eton authorities also gradually phased out lodging houses run by women.
An Etonian [Charles Frederick, d. 1892]. Recollections of Eton. London: Chapman and Hall, 1870.
Last modified 26 July 2006