The Igros Moshe YD 3:86 says that the Chachamim commanded that women should not be taught Mishna since it is oral Torah and it is like teaching them tiflos(promiscuity) and it should be avoided. However, they can be taught Pirkei Avos since it has Mussar and has hanhagos tovas.
In The Sefer VaYoel Moshe(Satmer Rebbe) Maimer Lashon Hakodesh 33(page 436) says teaching Rashi to girls falls into the category of teaching tiflos and is an issur chamer Meod.