I just wanted to pop in and say that my son goes to public school, and had a really hard time with skip counting because they did do the hop along thing with memorization, and he had absolutely no success with that... so finally I sat down with him one day and we went over and over skip counting by various numbers on his fingers, and what eventually made it *click* for him was not memorization but realizing that you're grouping the numbers, that it's a way of counting...
It's hard for me to describe since I don't see it like this ~ that is, when I skip count I just recite the numbers, it's more of an abstract thing for me ~ but when he does it he actually kind of counts the other number in his head, like he's grouping them off. This is probably really confusing.
The point is the groups though ~~ I guess for him being able to visualize that it's not just randomly memorized numbers in a set order but rather, we're counting by groups of things made it make sense. We did groups of lentils, groups of pinto beans, groups of pennies, groups of fingers, groups of toes, groups of crayons, and groups of cars, and finally it made sense to him.