What if we taught young children abstract algebra first?

I think there are two separate points.

Could this work?

Seems like it might. I'm not sure kids are primed to learn strict definitions of things but maybe we could find a way... it would be difficult though because their parents generally won't know abstract algebra. Counting is easier to teach because it comes up at home and at school, but the kids would be learning different things at different places. This isn't necessarily a bad thing, lots of kids learn English at school and a different language at home.

Edit: The kids difficulty with strict definitions could be a good thing. Having a feel for whats going on without being restricted to the definitions could lead to new discoveries.

Should we do this?

I'm not sure this is a good thing though. I love abstract algebra and think its great fun and is, as far as I know, very useful in parts of science (I believe material science uses group theory). However, delaying the time when kids learn to add and count and do concrete math means they learn things they need for life later.

Edit: I'm reminded of this: http://news.ycombinator.com/item?id=618972

There are a lot of approaches to abstract algebra for adults.

http://www.amazon.com/s/ref=pd_rhf_s_1?ie=UTF8&search-al...

Which approach, if any, best fits young children?

This is a good question. I think children are best primed for understanding abstract concepts when they're young. Look at the success of Harry Potter, for example: magic and wizardry. Santa Claus, even. Teaching them to think about counting concrete objects before counting those elusive abstract and imaginary number-objects might not be the most efficient approach.

Possibly this: A new teacher walks into a class and asks, "What is 3 + 5?". A child responds, "5 + 3 as addition is commutative".

I'm not so worried about the order children get taught mathematical subjects but whether they have a good teacher that encourages them to enjoy mathematics and learn how to problem solve.

It's almost always better to teach the concrete and practical before the abstract.

That's like teaching the rules of grammar before teaching them to read and write.