[ndriscoll]

In the world that I imagine could exist, we'd do away with algebra 2 and pre-calculus in high school, which are a waste of 2 years, and instead do something like algebra -> geometry -> calc1 -> calc2 -> linear algebra -> abstract algebra, with linear algebra being concrete things like adding arrows and solving systems, and abstract algebra introducing basics of monoids, groups, vector spaces, and homomorphisms. It's sort of unfortunate that even the basic ideas of algebraic thinking (i.e. structures and structural transformations) are pretty much not even hinted at to anyone but math majors, and yet we spend years of school on something called "algebra". So even technical people can't see the point of structural modeling.