One thing that I find such a blessing in is the relationships you build with your children through homeschooling. In the time spent with them, you discuss many things as you teach them, and as they grow, they just naturally discuss things with you.
Our oldest son, for example, can wear me out with discussions. He is very intelligent and very academic and analytical and so he likes to discuss EVERYTHING! Though, he can be tiring, and even frustrating at times, I feel so blessed that he chooses to discuss things with his father and I. He doesn't take things out to just his peers or buddies he's hanging around with. I know he still discusses many of the same things with his friends, but I am just so glad that he still wants to discuss things with us. There are times when he frustrates me because he asks a LOT of questions and I give the best answers I can off of the top of my head, but sometimes I need to take some time to think about what he's asking. You know, chew on it or mull it over for a while before I can put something into words. So sometimes I have to stop the conversation and pick it up again at a later time and he doesn't always like to wait.
This child, well, very nearly man, asks hard questions! He talks to us about ALL KINDS of things -- general, political, spiritual, Biblical, the list goes on and on. He stretches us!
But I am grateful and blessed that he chooses to discuss with us and values our opinions, even though he rarely agrees with them these days. It is so good to be able to know his thoughts and opinions as it not only helps us in still offering some guidance, but it shows me how to pray, not just for him, but for our other younger sons.
So, treasure the time you spend with your children while you homeschool them, and be sure you talk with them from little on up. You won't be sorry you did. Open communication has long time value.