[strbean]

I'm not sure we do kids a service by skipping over fundamental aspects of mathematics in order to stick to the 'more concrete' stuff. The staggeringly vast majority of kids will never learn a lick of group theory or category theory, and I think that is unfortunate because the fundamentals aren't difficult or big. Most high school grads will hardly have touched even basic logic, and it is frighteningly common to run into people who don't understand that "A -> B; B; Therefore A" isn't valid.

[AnimalMuppet]

We would do a worse disservice by skipping over more concrete stuff to teach group theory or, worse, category theory.

First, even if you can teach group theory or category theory to an 8-year-old, if you wind up with an 8-year-old who knows category theory but can't add, is that a win? No, it isn't. They need to be able to add in a way that they don't need group theory.

But, second, you can't in any meaningful way teach category theory, or even group theory, to an 8-year-old. But you can teach them to add.

So again, I say, concrete first, then abstractions. First because they can function better knowing one concrete form and no abstract than they can knowing the abstract and zero concrete forms. And second, they are able to learn the most-useful concrete form younger and with less background than they are able to learn the abstraction.