According to the Encyclopedia of Children and Childhood in History and Society's article on Judaism:
Owing to the primacy of ritual in traditional Judaism, instruction of children focused on the attainment of ritual literacy as its central goal. In the Talmudic era, boys attended elementary school or studied with a tutor from the age of five, six, or seven until the age of twelve or thirteen. A network of schools operated in the Land of Israel by the second century. School children learned to read the Torah and to write; at age twelve they studied Mishnah. No formal instruction in secular courses such as mathematics, Greek, or GYMNASTICS, was included in the Jewish school curriculum in this period. Initially, the houses of study excluded children from the lower strata of society, but by the third century education was made available to children of all classes. Girls were, by and large, excluded from the elementary schools, however, though some Talmudic sources suggest that fathers taught their daughters informally.
It's this final portion (emphasis supplied) that I'm most interested in learning about. What do the Talmudic sources say and under what conditions did girls learn the Torah? Would we expect certain types of learning to be more heavily emphasized than others?