Hi, R.. Well, I didn't go the homeschooling route myself, although I explored it very thoroughly to see if it was a good option for my son and me.
It's actually a whole way of life, depending on what curriculum (course of study) you choose for the child, and what your teaching style is. I am sort of a natural teacher, so I was always showing my kid something cool about science or art or books anyway. However, I was not a very well disciplined person while my son was growing up, and I realized I was not going to be able to enforce the kind of structure my son would need to have home as his classroom (along with museums, the planetarium, and other field trips). I also really, really suck at math, and I would not have been able to instruct him much beyond the elementary level.
The curriculum I was most familiar with was the Beka system. It was the most well-known and most widely-used of the homeschool systems at that time. It was actually the curriculum used by his first couple of private Christian schools -- my son hated it. It is INCREDIBLY boring and repetitive. My son was a fast learner, and the Beka system that I saw back then didn't allow for an above average or gifted child, not that I could tell. I would've ended up throwing away about half the materials, which would have been a waste. I still would have had to design lessons for him since he wanted to learn at an accelerated rate, but I was not trained to do that at that time, so the Beka elementary stuff would not have worked for my son and me.
The higher levels of the Beka system are mostly independent study. The teacher/parent in those grades is just a facilitator, someone to ask questions of, and not someone who gives much or any instruction. That didn't sit well with me, either. The schools my son was in that used Beka for the upper grades had students who were bascially on their own. Because that school library was so small and limited, these kids basically spent all their time in the public library trying to learn something without much help.
I don't remember the other homeschool curricula I looked at briefly at that time -- it was 20 years ago. Other parents I have spoken to and read articles from have stated that a good teacher/parent is disciplined enough to set up a small schooling environment and teach through scheduled times every "school day," just as a professional teacher does. The parent/teacher has the advantage of being able to tailor lessons to his/her child, to go more quickly through what the child gets easily and to spend more time helping the child through the more difficult parts. The homeschooler can also take the child on more frequent field trips such as to museums and such, walks in the park which can become a biology lesson, and use educational programs and DVDs as well, so it can work out quite well for some folks.
Now, understand that it can take a lot more patience to teach your own kids than it does to teach other people's kids. A parent has more emotionally invested in how well or quickly the child learns, and it's harder to be objective. Discipline problems can be worse if the child is not very compliant and enjoying the process of having Mom or Dad as teacher. My son, for one, refused to do the homework he got from school, never cleaned his room without a fight, and wouldn't follow up even on fun projects that I gave him to do, so my household was not a good situation for homeschooling. It's way more involved than sitting and reading a book to your kids.
So think about it before you invest money and all in homeschooling. It can be a wonderful experience for everyone, but it can also be a disaster. I suggest that you try sitting with your child for a day and play teacher, and see how the two of you feel. You might also talk to people who are already homeschooling kids of that age group and see what they are doing, and think about whether or not that would work for you.
Good luck in this! I hope everything works out for the best.
Peace,
Syl