[jfarmer]

Kids deal with abstraction every day. The very idea of "color" and "number" are abstractions of concrete experience.

Teaching kids basic group theory is very possible. You can play games with shapes in the plane to learn about dihedral groups (without ever using those words). Graph theory, as the author says, is another avenue.

The problem is that what students are practicing isn't math, any more than running after the ball when you miss a swing in tennis is practicing tennis. And you improve at what you practice.