There are very little "rules" as far as home schooling. You don't need any degrees in teaching or any education at all for that matter. You are free to teach your children anything you want. As far as qualifying your results there are three ways. 1)Have a certified teacher review the students work to make sure he/she is advancing at a rate up to his level. This is the one we use.
2)You can have the school board test him/her and look at his work.
3)He/she can take the standardized tests that all children take - FCATS.
The educational board has the right to look at your child's records to make sure you are complying but I don't believe they do this often. You do have to keep certain daily records to comply. But basically your on your own. I like this aspect. I can skip all of the politically correct crap and concentrate on whatever I feel is important. If I want to teach my child about religion I can, if I want to concentrate on math, writing and reading and skip geography I can. There is no requirement for the curriculum at all. All you have to show is that your doing it and the child is advancing. The parents have complete control. Of course different states have different requirements so your state may be different.
You can even register your child with a private school and totally eliminate the public school from the picture. We are registered with the public school so are bound by their rules.