When I had my kid tested at 5th grade, she was reading at a grade 16 level but her math was at a grade 4 level.
Why was her math so low ? She couldn't do a lot of the problems w/o a calculator, and had never been exposed to basic equations like the concept of an unknown "x".
I agree that a 7yo has a great deal of trouble with abstractions, yet the very basics of algebra (x + 1 = ?) and sets can be handled successfully if presented correctly for the age group.
Go look at the Singapore math books or Ray's arithmetic if you want to see what average kids are doing overseas or did in the last century.
Yes, the key is to present the lessons correctly and appropriately for that age/grade level.