The best solution is to offer accelerated math classes in public schools, in both elementary and middle. Mostly in middle school because elementary math can usually be handled through differentiated instruction by the teacher, unless the child is exceptionally advanced.

I really like the way my kid's middle school does it: accelerated 6th grade math covers the entirety of the 6th, 7th, and 8th grade standard math curriculum, which sets the kids up for algebra in 7th grade and geometry in 8th. Because the standard middle school math curriculum is essentially just advanced arithmetic, it's pretty straightforward to bundle this way. It also makes it easy to inject 7th graders who missed 6th grade accelerated math into the accelerated track if they pass the algebra qualifying test before 7th grade.

When I was growing up the G&T program started in 4th grade and cohorts from multiple schools were pulled into a school that ran the "gifted" program. Essentially all the kids were tracked from 4th grade through high school graduation and there was no real possibility for non-G&T kids to get into the "gifted" classes in middle school. In HS that just transitioned into APs and college dual-enrollment; by the time I graduated HS in '99, I had 22 credit hours of college classes banked, including dual-enrollment bio and calc 1 + 2, plus a bunch of humanities APs.

Today -- at least in our bay area public high school -- there's no tracking outside of math and the vast majority of classes can contain students in multiple grades. That absolutely was not the case when I was in school, and imho it's an improvement.

I'm thinking specifically about the USA math curriculum. It's pretty sequential until 8th grade or so.

Filling in gaps is fine for people with good study skills, but that excludes the vast majority of elementary school students.

the "smart" kids do seem to have those skills, though. either that, or they're being tutored on the side, or they just require fewer examples to get it

whatever the case is, i think the idea behind skipping grades is that the kid isn't learning much in the classes they're in. they may not learn much in the next level either, but it allows the school to test that they've learned what they were supposed to (from class or elsewhere), while wasting less of the student and teacher's time

that said, testing out seems like it'd be better than forcing the kids to sit through yet another math class, even if it's one level higher. more time to touch grass, or read in the library, etc.

Yeah the smart kids may need fewer examples or fewer practice reps, but very few kids can skip entirely, say, 4th grade math, and not struggle to catch up. It seems unnecessarily painful, when instead they could be taught smoothly at double the pace.