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Notes -
Home and homeschool.
This is heavily colored by my own experiences but barring getting your kids into a really good K-12 system I don't think you can beat homeschooling for purely educational outcomes. With the caveat that at least one of the parents is going to need to be heavily involved in running the show, at least during the early years up until middle school. Once you get to that point if your kids are motivated you can basically go autopilot, and once they hit 11th grade early college programs are a popular option.
One more caveat, extracurriculars that get your kids involved with peers and mentors outside the home are going to be critical for obvious reasons.
I was homeschooled, and... it depends. In general, I liked it. My mom is disposed to be a decent teacher, and went on to teach lower elementary in the public schools. I ended up very well educated in literature, because a Kierkegaard and Dostoyevsky book club is my parents' idea of a good time. Math didn't go so well. This is fine, since I don't necessarily want to be a Woman in STEM, but also very common among homeschoolers I know, even with engineer fathers. I think math just inherently requires more structure and pushing for a lot of teens than reading and writing do.
Homeschooled and can attest to the math part. I did read a ton so I have a deeper understanding especially of history compared to most. Went on to become a relatively successful lawyer who only has to do basic algebra so I guess the math didn’t set me back.
May I ask how the hell you have to do basic algebra as a lawyer? My first year contracts professor, when explaining a damage calculation, said you could ask law students to add or subtract but not multiply or divide. Now I only have to do basic arithmetic when calculating damage estimates, but even when I was in oil and gas and was doing more math it never got more complicated than the dreaded adding of fractions.
Tax—in the international space there are some rules (and occasional modeling) where we do really basic algebraic thinking.
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I can't begin to speculate on the overall picture, but for what it's worth I did great at math and I was homeschooled. At the very least it is possible to do well in math as a homeschooled kid.
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This tracks with my personal experience. Both my older sister and I had to retake a lot of math in college. I didn't realize it was so common given that @pairingheap is saying the same thing. Average parents are just generally going to be rusty with their own math by the time their kids are hitting the more advanced stuff I suppose. Not a universal issue as I can recall off the top of my head a least a few other fellow homeschoolers who have gone on to do quite well in STEM. Purely anecdotal of course...
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From the homeschoolers I've spoken with this seems quite common. Great outcomes in many different domains, but a real lack of mathematical maturity.
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