Train up a child in the way he should go;
even when he is old he will not depart from it.
Literally, the first line reads "according to the way he will go." Some then have interpreted the meaning to be that if you raise a child according to his inclination, he will set on a crooked path that he will not depart. Certainly that is true, and many parents bemoan that their children did actually depart from the way they should go.
Nevertheless, there is much truth to our traditional understanding of the proverb. Covenant children are likely to grow up in Christian faith and keep it. Even if their faith remains a second-hand faith inherited from their upbringing, they nevertheless keep along the law-keeping path. And even if they consciously reject their parents' faith, they still have ingrained in them Christian instincts hard to shake off.
Indeed, the testimony of many covenant children is that of wandering from the faith and returning to it precisely because of what they learned as children. They remember the Bible stories and verses. They remember the hymns. One covenant child turned to God in the midst of overdosing on drugs because hymns popped into his mind at the time and kept him sane.
Raise up your children in the way they should go. Remember that the way to go is to Jesus for grace and mercy. They should see that that is where you go. They should see that as law-abiding as you might try to be, what really motivates you is the mercy found in Christ, that it is Christ's strength that makes you strong, that it is the forgiveness found in him that gives you hope. It is such hope and love for our Savior that will keep many a child on the right path and not depart from it.