It seems like part of the problem is that people don't really know or agree what mathematical education is for. If we knew for what reasons or purposes we were teaching everyone math, that might help us figure out what math they should learn.
It seems to me like various purposes for math education include:
More generally, people don't even agree what education is for. It could be:
Generally, all these goals are considered good, but sometimes they are in conflict, if you try to optimize for one of them too much. For example the first rule, in extreme, would require learning only details related to one's future job, nothing more; but students could learn more details, and have more practice ...
Post by fellow LW reader Razib Khan, who many here probably know from the gnxp site or perhaps from his debate with Eliezer.