I think the aspect I enjoy the most as a homeschooling parent is teaching the Bible, along with Christian doctrine and church history. Sure, I've always attempted to present each and every subject from a Biblical perspective, but when it comes to teaching the basic creeds, confessions, and essentials of the faith or going through particular books of the Bible, I find that my own understanding and commitment to orthodoxy grows.
I've especially been challenged when my children have asked questions that I could not answer. Not wanting to fudge an answer that I am unsure about, I do some research to provide a good response. When Dr. Rushdoony was alive, these circumstances proved to be good excuses to phone him and chat. In fact, when his health was failing and he acknowledged that it wouldn't be long until he was in heaven, I lamented that he wouldn't be around to answer my difficult questions. He laughed, "Yes, even your long distance plan won't reach that far!" These days, I call upon the men of Chalcedon and pose my questions to them.
I've noted the wisdom in the statement, "You know how well a student is learning by the questions he asks rather than the answers he gives." In fact, I would go so far to say that as someone is learning any subject (the Bible in particular) there should be a host of questions that arise. Correctly applying the Scripture to life is a fundamental aspect of taking dominion in Jesus' name, and there can be no effective apologetic without it. When receiving and digesting any portion of Scripture, the obvious questions that should arise are, "How exactly does this apply to me?" and, "What are the implications of this doctrine?"
Just this week my daughter posed a question that I could not easily answer. The very nature of it demonstrated to me that she is thinking through the implications of the incarnation of Christ and His being fully God and fully man. I went to my "answer men" and they admitted that they had never considered that particular issue before. Her question got us all thinking, and the fruit of the research has given us all food for thought. How blessed I am that in the process of teaching my daughter, I am learning so very much myself!