Considering teaching one's son Torah, to be like teaching it to all future generations: Kiddushin 30a
Equating the teaching of Torah to one's grandchild, to receiving the Torah at Sinai: Berachot 21b; Kiddushin 30a
Male children require more watching than female children do, when they are supposed to be studying: Nedarim 37b
Disciplining one's children, for purposes other than to coax them into learning: Makkot 8a, 8b [2x]
The rabbinical court in Usha enacted that fathers should gently encourage their sons to learn Torah until the age of 12, and then become more fierce if their sons still refuse: Ketuvot 50a
One should teach [his child] out of a well-edited book, because once an error is learned, it is hard to correct it: Pesachim 112a
Abbaye's mother told him that at the age of six a child should begin learning biblical text, and at ten they should learn Mishnah: Ketuvot 50a
The risks and rewards of accepting a child in school before the age of six: Ketuvot 50a
General Issues
Defining a specific age at which training in mitzvot is mandatory: Yoma 12a; Rashi Berachot 15b "Bameh Devarim"
Why girls become obligated in fasting at the age of 12, while boys become obligated at the age of 13: Rashi Ketuvot 50a ובתינוקת
Teaching a child a path which he will use his entire life: Kiddushin 30a
Mitzvah of Education applies for any Mitzvah where an adult would have a Biblical Requirement to keep that Mitzvah: Chagigah 6a
Education of a Minor for a Mitzvah in which he is ineligible for a reason besides Age, but for which he may be eligible in the future: Chagigah 6a
Not striking an adult child, because it could lead him to sin in striking back: Moed Katan 17a
Abbaye's mother told him that only in their twelfth year should girls start observing communal fasts, and only in their thirteenth year should boys start observing communal fasts, one year before their respective fasting requirements: Ketuvot 50a
Giving children bread after making the Blessing for them, to teach them: Rosh HaShanah 29b
We don't recite Kiddush on Yom Kippur and give the wine to a minor, lest he then drink when he matures: Eruvin 40b
Where the Child's status as a Jew is uncertain: Ketuvot 15b
Lending children money for prohibited interest to educate them about its dangers; one should not do it, lest the child be attracted to the prohibition: Shabbat 149b; Bava Metzia 75a