Thoughts on children

I have a few thoughts on children, their sin and our own sin. From my own interactions with various people, from all the things I have done and from raising my own children, it seems that our own sin has a direct influence upon the formation of our own children and their subsequent sinfulness.
I would say that the sins we see in our children is a clearer manifestation of our own sin.  Children learn, in part, by imitation. As they see in life, they imitate.  Their imitation may be rawer and less refined, it may be less rationalized and defensible, but therein lies the value.  Are we willing to look at our children's sin and see ourselves, possibly in a way that we were unable to, simply looking at ourselves?