Personally, I think the biggest issue with kids and Algebra is that we spend all those years beforehand teaching various methods of computation without really explaining why we bother in the first place. We give them occasional hints with word problems, but 8 cookies plus 2 cookies really isn't sophisticated enough for them to get the central idea, that math is essentially another language that we use primarily to express relationships, and that the numbers in and of themselves are essentially meaningless, unless given meaning through context. Because up to the point where they enter a Pre-algebra class, math is ALL ABOUT THE NUMBERS... so how can you suddenly say they're meaningless?

In the face of a giant paradigm shift, some embrace the new and go on to success. And some are so stuck in the old mindset that they can't get out. Education is filled with such examples, where advancement to higher levels involves a teacher saying, "Everything you think you know about this subject is wrong." Algebra is just one example, but it also happens to be one nearly everyone experiences.

I recently asked why my daughter was already seeing simple computation represented as Algebra problems in the first grade, and I think I just answered my own question.