People need to be studying things that are (1) at the edge of their current capabilities, which is to say doable but slightly challenging, (2) interesting, stimulating, and relevant to them.

Classrooms fail at this. Some kids are good at math, but do not like writing. And vice versa. A little boy might be doing algebra very early, but does not like nonfiction. Give him time! Let him work out his math and progress with it, perhaps he'd get interested in reading a biography of a mathematician or scientist at some point.

Likewise, maybe another boy is reading and writing at an advanced pace, is devouring classic works, but is behind in math "for his age" - that's okay! Give him time. If he needs more time in arithmetic or doing long division by hand, let him spend time there while reading at a high level. He'll get there.

Subdividing based on age is asinine and crazy. It means a majority of people will be studying at a skill level incorrect for them in an important discipline. That's before even considering how boring school is for most kids.

Me? I loved physics, liked chemistry, and hated biology. Because the way it was taught, physics was cool with acceleration, chemistry was interesting in terms of mixing things, but biology was a bunch of boring memorization of genome and species and things like that which didn't seem very important to me. So, I really enjoyed my Freshman "introductory earth sciences" (physics, chemistry, and a little geology if I remember correctly) and had a fun and enjoyable time, but then I was forced to move into rote memorization biology my sophomore year... I tried to skip ahead to physics, but they said no. Long story short, I wound up dropping out of two high schools, and got into a university despite that before dropping out of there too. Was a great decision for me! The school system is broken - it doesn't meet kids where they're at or where they want to be. Instead, it forces a strict curriculum that requires memorization and obedience to pass.

Look at home schooling if you want inspiration. There's a big community devoted to it, and home schooled destroy mainstream teaching methods on almost every metric except for social interaction/emotional maturity. (A big problem for homeschooling, parents need to be diligent in getting their kids representative social experiences if they're home skilled, at least enough for them to relate to other people their age)

But that's really it - on just about every other metric, home schooling wrecks on mainstream teaching methods. I think the biggest problem is that mainstream schooling instruction is bureaucratic centrally planned with age being the overwhelmingly important decision on what the kids learn.

How asinine! Everyone goes through cycles of being interested in different things. If a kid has a knack for language and is doing hardcore immersion, learning the Chinese characters that will let them read/write Mandarin, Cantonese, and Japanese, and they're learning Mandarin and Japanese at a high level and starting to read literature in the native languages... do you really want to break that up because now it's time for geometry?

You introduce the kids to a little bit here and there, when they're ready for it they learn it. Learning is one of the most exciting and coolest things in the world. The fact that schools somewhat make learning dreadful and boring is one of the most laughable things in the world. But again, you've got to meet the student where he is at. Statistics can be taught via sports, or via census data, or via business, or via hard science experiments, or... y'know? You've got to find one that stimulates the pupil. One training going 100 kilometers per hour towards another one going 180 kilometers per hour isn't going to get it done for the vast majority of kids.