This isn't a theological post... but I think it has some very practical ramifications. My son, who is now 17 years old, is not my son by blood. I adopted him when I married his mother almost 13 years ago.
There are lots of things I could discuss about adoption or having adopted children, or about being a step-father and how God is our step-father through Jesus Christ. But instead I want to reflect upon something else. Though I am not his father by blood, and though I do not have the same kind of bond with him that he has with his mother, he is my son in many, many, many ways that go way beyond a legal piece of paper or the amount of years I've been in his life. One of those ways is his sense of humor. Regardless of all the things I have attempted (either successfully or unsuccessfully) to instill into him over the years through instruction and discipline and conscious modelling, he has adopted my sense of humor just as I adopted my dad's. He not only has a good sense of humor -he appreciates the same kind of humor... and sometimes our connection, our shared wavelength in this realm, is uncanny. This has been demonstrated time and time again while playing the game Apples to Apples, since we always wind up being able to read the other's mind. His sense of humor came not by blood but by bond, by relationship.
On the broader scale, this highlights a powerful truth: we may actually instill more into our children through the things we are not conscious of or intentional with than the things we are. They will learn from us or learn to be like us -not intentionally, not consciously, and often not willingly on their part- but it will happen. I never tried to make my son funny. There was no effort or intent involved whatsoever. It never even crossed my mind, and now here he is, almost grown, and it is there in him. I never lifted a finger to try to teach him humor. It happened all on its own.
In some ways this is good, in other ways this can be scary, but it is nevertheless intriguing. Negatively, you will pass onto your children things that you wish you didn't, and they will take on those things and carry them unless they can break the cycle (or unless you can break that cycle, too). It is unavoidable. But on the positive side you will also pass onto them things that will bless and enrich their lives. A good sense of humor is good for the soul.
It is not so much that your children are watching you and taking notes. They are watching you passively. They don't even know they are watching you. They are sponges, and the seeds are sown deep and early. It doesn't mean things can't change, and sometimes the flower of the seeds planted can take years to bloom. It means that you will invariably affect your children's personality and attitudes far more than you can plan or control. Parent them. Learn how to connect with them. Discipline them graciously but honestly. But be on your knees for them and for yourself for the countless things you do not see both about you and about them.