Understanding variables is a hallmark of the "formal operational" stage of development.[1] It's the same reason why we hear some people "just don't get" programming. Same reason why languages like LOGO avoid this construct.
If grasping Algebra is actually about attaining this developmental stage, we need to be approaching the problem on a more fundamental level. Kids will move through these stages at a different pace and if you're on the tail end of developmental pace you're going to fall through the cracks.
Searching a little I found this interesting document addressing some of the problems which I have put on my reading list: "The Science of Thinking, and Science for Thinking: A Description of Cognitive Acceleration through Science Education (CASE)" (Philip Adey, 1999).
Assuming the idea of a "formal operational" stage of development applies, the situation looks abysmal (at least in the US and Germany, can't say much about other countries):
From the little I gathered so far (on the internet, so it has to be taken with a grain of salt) it seems that (1) a vast majority (over 60%) of people never reach formal operational maturity. (2) Ideas of how teaching can actually help with it are in it's infancy. (3) Application of said ideas is not very far along. (4) Educational systems keep leaving many (or most) students behind early, especially in math and science, while other students get bored and waste their time in class, being taught a mind-choking curriculum.
Ok, I guess I'm ranting now :-) Saddens me greatly, though.
If grasping Algebra is actually about attaining this developmental stage, we need to be approaching the problem on a more fundamental level. Kids will move through these stages at a different pace and if you're on the tail end of developmental pace you're going to fall through the cracks.
[1] http://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive_...