> I was shocked when I first set foot in an American classroom in 6th grade - they were learning "longhand" division, something I did in grade 2.

I attended an American public school in the suburbs of New York 20-some years ago, and I very clearly remember learning long division in second grade. I remember it because I missed that day, and the teacher told me to learn it from a friend, which didn't work out so well.

The real trouble with public education in the US is that funding is almost entirely a function of where the school is located. Schools in wealthier neighborhoods will generally be good, and schools is poor neighborhoods will be awful. It's an absurd system.

Wow, you all must be genuises or something.

I went to a decent primary school in Australia and spend a year ( out of phase, so put forward into the second half of Year 3 and then Year 4) in the US at age 8. The thing that threw me at this age, that was part of the natural progression in that stage, was 'subtract with carry' (I'm pretty sure that was it).

I was 'put forward' past this interesting tidbit in my US school, assessed on a test that was almost entirely centeres around it, found wanting, and placed in the lowest class in school with about 7 streams. Each test I moved up a class. All up they regarded it as a triumph of American education :-)

Neither of these schools was terrible, either, and both had 'subtract with carry' around year 3. That's a far cry from longhand division.

No-one at my kids current school is doing long division in Year 2, either, although I have creeping doubts about its rigor.

I am hoping this pace continued for all y'all, so that you were doing calculus in Year 7, and proving exotic conjectures by Erdős in your first or second year of university, etc. :-)

I don't know about exotic conjectures by Erdos (nice one, btw), but in elementary school I distinctly remember in second grade my dad ripped my He-Man comic books because I failed a test in my math class. After that, two things happened: 1) I studied really hard for my final end-of-year exam and remember that we were dealing with simple algebra with variables (e.g. x - 5 = 3, find x), and 2) I never read comic books since (sad, I know).

I was really lucky to have a good math teacher in middle school who introduced us to logic and induction in seventh grade (in hindsight, he prepared me for linear algebra in college, and I haven't even heard the words "modus ponens" since middle school until I got to college, second or third year).

Unfortunately, in high school I decided to coast a little bit on my previous knowledge, so I didn't get good grades, but I didn't read comic books anymore anyway, and my dad couldn't just rip the computer apart because he is a techie too :)

Edit: the seventh grade teacher is in the US, he taught "magnet" (gifted) classes. So, not all hope is lost in the US. Good teachers and good classes exist even in public schools, we just need to bring up the standard.

I genuinely don't have a horse in this race, but I am far from convinced that learning concepts sooner is a recipe for long-term win. In many cases, I think you just get to the same place sooner at much higher levels of effort.