When the parent is the teacher, at home, what they say goes. First, you teach them to respect you, to honor you that they might live a long life as stated in the Bible. Then, once respect is formed and trust is established, you can teach. Not just when sitting down for "school" but in the marketplace, at a friend's house, in any given situation.
I completely had the mindset that education was limited to "school." I realized this was when I grew up and noticed I had terrible eating habits. I was not a healthy eater by any means. I have no one to blame but myself because I chose to eat what I wanted when I wanted. The thing is, I learned in health class the right things to eat. It's just, APPLYING what I learned in class to real, everyday life was just not connecting. It didn't seem relevant. I knew that I should eat a certain amount of fruits and veggies a day and I knew why, but relating what I learned for hours a day to my everyday life was not connected in any way.
Yes, I was influenced from what I learned in public school and I did gain knowledge in both public school and a private colleges. But what I didn't get was the whole life application thing.
If you think about it, the largest problem in the American Christian Church is hypocrisy. Living one way, but knowing and even living another. I'm a firm believer that we can raise our children not to be hypocrites by leading the way in our homeschool. Discipling and training them up in every area of their lives in a Biblical fashion. We need to form that relationship so that when we say 2 plus 2 is 4 they believe us and when we say evolution is false and God is the Creator, they believe us just the same. They should take our word, and take God's Word as truth in and out of the "classroom" situation. They should heed our voice when we say, "Stop! Don't cross the street!" and should trust us just the same when we say, "Stop! Don't hang out with those friends!"