I would say it depends on the specific public school, good ones exist but it depends what you consider "good". We moved from an average sort of public school (was the best one within a radius of a couple of fairly low ranking districts so it drew bright kids from some distance) to one that is consistently among the highest ranked in the state (best in the best district in the region). It's been wonderful, but then perhaps I had low expectations that were easy to exceed. Somehow it is officially the same curriculum but what they do all day is very different, and DS7 seems so much more engaged.
The previous school had a fairly substantial gifted program, with multiple pullouts and classes regrouped by ability level for both reading and math, but this just meant "gifted" served a whole 1/3 of the students, making very nearly 1/3 of parents very happy.
Once we moved to the new school I went to the gifted info night and heard their stock talk that said, "at this school gifted identification is not pursued often because we differentiate for all students, so why bother". So I decided with that attitude I was just not even going to inquire. They did indeed differentiate homework to some degree, which was better than nothing. And I noticed there was a good selection of library books.
And then they came to us after maybe 4 months and said DS is clearly out there and they needed to do something (they also referenced IQ testing we'd given them, that they hadn't noticed I guess at the beginning or chose to not worry about initially). So they have a secret gifted program I guess the way I have read on here that some schools do.
They claim they have no other all around gifted kids in DS's grade except DS (though overall they are teaching I think about a grade level higher than the old school because they simply have no students that truly lag their grade level, many of the students seem at least moderately gifted to me). So they define gifted more stringently than elsewhere in the same state. I think due to the overall slight increase in academic level of the classroom and more creative type work DS is just happier overall, even before differentiation etc. When he says something, other children or the teacher gets what he says and say something back, which is sometimes interesting or funny. It makes a big difference.
After testing shows DS capable of math and reading at high school or near levels they are giving him one on one in math twice a week, in which he's learned nearly nothing but has now switched from thinking he is bad at math and not really liking math (because other children are often faster at computation due to his low processing speed) to looking forward to his math time and feeling more confident, so I am all for it.
Individualization in reading hasn't been necessary because there are a couple other kids close to DS for a spelling group. The spelling words are often remedial but overall it is okay.
I wasn't actually looking for a school that would truly individualize instruction for DS because I didn't really expect I would find that at all in a public school. But this one does appear to be planning to do so in math, with the help of the district math curriculum person, youngest child they've designed an individual curriculum for, etc. Time will tell. This is one benefit of being in a public district is there is a large enough student population total that the district does employ someone capable of designing advanced math curricula. That may be an individual to approach ahead of time if you are really hoping for an individualized math plan.
I was more just looking for a school that gave children more personal respect than the previous one and saw children as individuals. Not just lip service to parents but really respectful. And in a generally well educated area so that everyone, teachers and kids, would be likely to be normally bright. I was looking for the "nicest" seeming teachers and principal, people who would be understanding of DS's emotional side. Where when you walk down the hall the teachers don't sound bossy. And this principal had said to me "2nd graders do 20 minutes of homework a night. Of course unless that's too much for the individual child", and that's how I knew the school was a possibility. It is also small, where I thought it was more likely teachers etc would get interested in individual children.
What elementary school has the interest or ability, even if they thought they wanted to, to teach a child math in the way that potential real mathematicians would optimally be taught it? It's not just presenting the next topic in line, it's transmitting a sense of awe and so on that inspires and interests. Would you even want any elementary school attempting it? They might really screw up! Better would be allowing a online math curriculum, or exempting the child from some of the standard requirements (homework for example).
The math professor sounds awesome for teaching math. For my DS (who has a very similar IQ spread with high scores except in processing speed), looking at schools I am more looking to find somewhere that he basically enjoys spending his day. Where teachers are understanding enough to allow him to skip homework in areas he's mastered, etc. Barring moving states for a truly good gifted school.
In looking at schools I asked multiple elementary schools, "Say in 5th grade you have a child who's finished the high school math curriculum. Can they sit in the back and read a text on a personal interest such as chemistry or physics?" The universal answer was no, that no matter the level, the child had to do math in math class... either differentiated or their school's curriculum. I thought that seemed quite closed minded, but that was the answer at a gifted school, at a highly alternative school, etc.
