I am self-conscious about homeschooling. It's not something I would have thought to attempt, if it were just me. I believe teaching, like any skill, improves with practice and study; and I have neither practiced nor studied teaching young children. I think most kids learn more when they spend more time studying; and my six-year-old spends a lot less time “at school” than I did at his age—by a factor of five or more. (On the other hand, when he is at school, he is studying.)
But it has been fun noticing things that I can do as a homeschooling parent that wouldn't work at all in an ordinary school.
My favorite is that I am free to pose problems that are too hard.
The kids have school when I'm at work, but I write out a lot of their schoolwork in advance. One of the problems I recently posed for J. is this: I have a box that does some kind of arithmetic. If I put in 7, out comes 3. Similarly 3↦7, 2↦8, and 1↦9. What if I put in 5? (Of course, anything or nothing might come out, but we can learn that lesson another time.) This turned out to be baffling—but that's OK. It will sit in J.'s binder for days, weeks, or months, until one day he cracks it. I don't think he'll crack it by accident but rather because he tries harder or because he develops a better understanding of how addition and subtraction behave. I think it'll be pretty gratifying, and he'll have earned it.
J. likes puzzles. In that regard, at least, his childhood will be a little like mine. Only without the answers.