I think the reason "new math" gets flack, is because it's a new way of teaching math, and alot of teachers aren't as good at teaching in that way yet. Still, kids should be taught that it can be a way one does calculations. Another thing I think should be incorporated into early childhood education is the use of an abacus, the Japanese do this and it supposedly helps greatly with mental math.
I don't think it's realistic or pragmatic to expect a perfect direct democracy system. Trying to get as close to one as feasibly possible can be a goal though, and once we're at that point, try to continually and slowly improve that direct democracy system until it's even closer and closer and closer, ad infinitum.