The Old Testament isn't the only place we see God encouraging the continuation of His heritage. In the New Testament book of Ephesians parents and children are given specific instruction.
"Children, obey your parents in the Lord, for this is right. Honor your father and mother - which is the first commandment with a promise - that it may go well with you and that you may enjoy a long life on the earth. Fathers, do not exasperate your children; instead, bring them up in the training and instruction of the Lord." Ephesians 6:1-4
Notice that the tradition hasn't changed. Children are still to obey to ensure a long life.It is stated here that this is the first commandment with a promise attached.
However, this obedience to parents is given with the warning to the parents to bring them up in the Lord. In other words, it is the parents' responsibility to pass on this Godly heritage. And this isn't the use of whatever culture says is the "in" thing or psychology right now.
The only way that I can bring up children in the Lord is to study His training and instructions in His Word. Then I can make sure that my instruction and correction aligns with what God teaches.
How do you specifically bring up your children in the Lord?