*It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.*

Well, isn't that quite the off-handed dismissal? Those guys are only better at algebra because they're so bloody persistent!

*Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.*

That's what algebra does! Arithmetic is about grinding out numbers; (numerical) algebra is about patterns numbers exhibit, and how they relate to things they represent.

An algebraic description of some interesting phenomenon might admit many models, not all of which are numeric, but most of which satisfy some of the same laws as numbers. This lets you see what is really of interest, namely the thing for itself, *das Ding an sich*, rather than its arbitrary realization as a number.

Part of the problem, perhaps, is that when we get taught algebra we are always told that these variables we play with stand for numbers. That's convenient because we were already taught how to interpret operators like + and times as operations on numbers. But it also misses the whole point of algebra, which is that what is important is not the carrier but rather the operators and their laws. Sometimes more abstraction actually makes things simpler, because it forces you to separate what *must* be true from what is true only because of your choice of representation.

If we want to get away from overemphasizing useless number-crunching skills, we need more algebra not less. Instead of eliminating algebra because we can't teach it well, shouldn't we just try teaching it better?