I have been homeschooling for just this school year, with my 5th grade daughter. I just read your post about how 75% of kids would do better homeschooling and 95% wouldn't do worse.
My daughter never seems to want to do or learn anything, and I'm constantly worried that she isn't learning enough. I have almost no support here at all, though my husband is teaching my daughter math. I took her out of public school because I worked at the school for 3 years and thought that the principal was a moron, and because she had developed a strong dislike for math and I wanted to get to the bottom of that (turns out she could never get help because the teacher was helping the kids who always needed help).
How do I know if I should throw in the towel and put her back in?
Here is my response:
Our children never went to a government school, so we never worried about the transition from public school to homeschooling. My understanding is most parents find it good to give the children a bit of a break. One book suggested giving a child a week break for each grade, so you might consider giving your daughter a month break. Part of the thought is children in public school come to see education as a chore, something to be avoided or tolerated, but not enjoyed. It sounds like your daughter may have this feeling.
You might consider trying some of the following:
Talk with her about what she does want to learn. If she excited about butterflies, hit the library and let her just read the books. If she likes dance, sign her up for some classes and start building a collection of music. She may not have any suggestions at first. If she doesn't challenge her to find something she wants to learn. And if she dabbles in something for a couple weeks and then decides to move on, let her.
I would make it clear that she can't play. Don't let her waste time in front of a screen. But give her lots of latitude on what she spends her time on, at least for a couple weeks.
If math has become a boggy-man, I'd put it on the back shelf for now. Our older daughters struggled a bit with math and we let them go slow.
Take her to the library and encourage her to try looking in sections she has never visited before, especially the non-fiction sections.
Find some local homeschooling groups. Many parents have been where you are at and can give you advice. And your daughter can start making friends at park days and co-ops.
I think it helps to remember what is your long term goal(s). I want my children to be competent, happy adults. I want them to develop a habit of life time learning. If they learn algebra in 6th, 8th, 10th or 12th grade it doesn't really matter.