Schoolteachers

Kiddushin 82a starts with a mishnah that discuss cases of yichud that arise in occupational scenarios. The Tanna Kamma states that neither a bachelor nor a woman may teach children. The gemara establishes that since the Chachamim argue with R' Yehuda (later in this mishnah) and hold that we do not have a need to institute gezeiros against mishkav zachur, the problem with each of these two scenarios must be with the parents of the schoolchildren, that a bachelor schoolteacher will run into issues with mothers bringing their children from to school and a female schoolteacher will run into issues with fathers bringing their children to school. The only permissible schoolteacher, therefore, would be a married man - although if the issue is one of yichud, why would this solve the problem of yichud with the mothers? Adderabba - to use a married woman as a schoolteacher could generate a heter of ba'alahh b'ir, making her impervious to problems of yichud, while a married man does not have the corresponding heter of ishto b'ir (but rather only ishto babayis). Perhaps we could invoke a leniency of ba'aleihen b'ir by the mothers - but this assumes that none of them are widows or divorcees. Lo n'hira li.

Be that as it may, Rabbi Eliezer is more stringent than the chachamim, and holds that not only may a bachelor not teach schoolchildren, but even a married man may not teach schoolchildren, unless his wife is present. My first instinct upon seeing this mishnah was that Rabbi Eliezer agrees with R' Yehuda and holds that we are chosheish for mishkav zachur (yes, I was motivated to look up this source due to the recent scandals...), but now it seems to me that his stringency as applied to the mothers of the schoolchildren would actually be aligned with the accepted opinion regarding the parameters of yichud. The Ein Mishpat implies that we pasken against like the Tanna Kamma, though, so I'll have to look into that.