It's important to realize that jr. high algebra is largely syntactic transformations. a - 2 = 3 is a syntactic transformation of a - 1 = 4. Most of algebra is

It's important to realize that jr. high algebra is largely syntactic transformations. a - 2 = 3 is a syntactic transformation of a - 1 = 4. Most of algebra is taught as a series of syntactic transformation rules. The skill students acquire is learning to apply the right rules to solve a larger problem. If algebra were taught in a more abstract way, there would be an even more pronounced stratification of aptitude, such that the educational system would not be able to teach to the variety of different levels. At least when it's taught as syntactic transformation, the best students are still largely bounded by working memory rather than intellect.