My twin daughters just started elementary school I am so full of happiness. 
That's so sweet! What ages are they? For elementary school, obviously they're somewhere between 6 and 12, as US elementary schools have 6 grades, with those ages corresponding to them. But they've been 6 to 10, and 6 to 14, as well, in some areas.
They are 5 they will be turning 6 in November they love it so far which is great because elementary years is the most important in schooling it shows them the importance of education. 
That's pretty cool! Ages for elementary school vary by country, so sometimes it can be much different. But in the Western world, elementary school is always just one part of the compulsory education that's taught and required.
Yes it is required where we live as well kids have to start if they are 5 it's the law and I agree the teaching style etc. is different from state to state heck even county to county. 
In China, it's not wildly different, but slightly. All people must go to school for nine years, at least. So, six years of primary education, at 6 or 7, and then three years of junior secondary education from 12 to 15. Then they have three years of senior middle school. It's funny how it's still slightly similar.
I can see the similarities lol not that much of a difference just seems as if they start at 6 where in US students can start at 5 for Kindergarten long as it is by September. 
I wish I attended a private school.. They're able to determine their own curriculum and staffing policies.. They're usually more successful in terms of student success after graduation. However, only so few get to attend.. 87% of school-age children went to public schools funded by the state, in 2013. Just goes to show you difference in attendance.