So, my stepkids (now: boy 12, girl 11) were falling behind in public school and were being passed on to the next grades despite the fact that they were almost a full grade behind in math and reading.
My now-wife decided to pull them out of public school and home school them to try to get them caught up. In our county, we have an AWESOME "public school at home" program where the kids are home schooled, but still go into a school one day a week for socialization and tutoring by licensed teachers. It was a fuck ton of work for her, but in ONE YEAR in the program, not only did the kids catch up, but they're actually almost a full year ahead now.
But... that was with the full support of a county school system and a full-time investment in her kids. This wasn't a "throw a computer at them and let them figure it out" and it certainly wasn't a "summer is different from winter because Jesus said so" program. It was a guided program designed, administered, and overseen by actually licensed teachers. There were performance goals to hit, regular checkins, and available tutoring for things my wife wasn't capable of teaching correctly.
This year, since both kids were so far ahead, we gave them a choice and let them decide whether they wanted to continue the program now that they're caught up. My stepdaughter wanted to go back to regular school. My stepson wanted to stay in the program. He's in middle school as of this year, and middle school begins to be more self-guided. My wife starts nursing school in the spring so she can't dedicate the 8-ish hours necessary to take both kids through the program beginning next semester. So we let them each do what they wanted. My stepson finishes his mostly-self-guided school day in three hours or so then has the rest of the day to do with as he wishes and is still ahead of where he should be. My stepdaughter is miserable because each day is an 8 hour slog and the curriculum moves too slowly for her now, plus the other kids are dicks to her (as kids tend to be). She's considering going back into the program next year when it will be mostly self-guided for her as well.
But this success story is more about my awesome wife and this particular program. It's been a crazy amount of work and a full-time job for my wife to take both kids through this program, and that's WITH the support of a full teaching staff in a county-run program. It's no surprise to me that other programs are more-or-less a joke. If you're not willing to put in the work and/or your idea of education is "It's that way because the LORD said so now stop asking questions and write Jesus on every line," then you're dooming your children to failure and ridicule.