Educating Our Children

The Talmud at the end of Masechet Yevamot, addresses the question as to how we are to educate our children.
It began with a discussion regarding a case where the keys to the Beit Midrash were lost on Shabbat. Without the keys, they were locked out. They went to Rav Pedat who suggested that children be asked to play in the area where the keys were lost.
The assumption was that if they found the keys, they could bring them back, even if it involved carrying from a public to a private domain.
The Gemara questioned this ruling and asked that if carrying the keys was allowed, it would also be allowed to feed the children non-kosher meat, because they were below Bar Mitzva age.
The Mishna Berura went into a lengthy discussion of the subject. It was determined that if a father was allowing his young children to transgress Torah laws, the Beit Din would intervene and demand that the father be more careful in educating his children.
The subject did not only include laws related to Shabbat and Kashrut, but also laws involving lying, cursing, and stealing. If firm action wasn’t taken while they were young, they might continue to transgress as adults.
The determining factor is the age of the child and his level of understanding.
There was no need to restrict with an infant or toddler, because they are too young to understand the meaning of the Mitzvot. But from the age where they begin to understand, we must be diligent in their observance of the Torah.