To me, a teacher's proper role isn't having knowledge and dumping it into someone's brain. It's knowing where to find that knowledge. My three Rs are "reading, research, and reflection": a teacher's job is to (1) provide useful material to consume, via lecture or homework or whatnot, (2) point towards larger resources for further exploration, and (3) guide thought processes to make useful conclusions.
A teacher's job is not to teach. It's to provide a space in which a student can learn. A focus is useful for this, but the focus doesn't need to be an abstract subject. It's a MacGuffin; it can be anything.
> an understanding thereof might be of relevance to someone entering into a loan agreement which they probably, if they really understood it, were not going to be able to repay...
Oh, it's relevant. It's sort of like how being able to load and fire a gun is relevant to the decision whether or not to commit suicide. Sure, it can modify one of the many, many details, but some people just make a noose and hang themselves.
Keep in mind, this is your argument: if more people in the world understood sums and compounding processes, this would have prevented the subprime mortgage crisis and thus the many deaths that were inspired by the resultant fallout. There is no possibility that anything else caused the crisis, and no possibility that anyone is at fault for these deaths other than parents and teachers.
This claim, if true, actually absolves the lenders that you talk about below, because they can be held responsible only for their own understanding of sums and compounding processes.
Amusingly, if you accept your argument, you can also make an interesting inverse version. The fact that lenders understood sums and compounding processes led to their employment at unscrupulous institutions which then mandated their sign-off on high-risk mortgages, which then caused the deaths of all those people.
Your point is lost if it's not applicable to a significant majority. If it's only applicable to a minority, then that minority ought to be identified and specially trained, like we do with peanut allergies.
(1) The subprime mortgage crisis could not have been averted by a larger percentage of the population understanding sums and compounding processes.
(2) The advent of civilization was a contributing factor to everything that's happened in the last several thousand years, including the paper cut I just got.
Please give one example applicable to a reasonable majority of human beings on the planet at this current time where "understanding sums and compounding processes" are a matter of life and death.
This is one of my current problems in curriculum design. I agree fully with Lockhart, and I strongly feel that requiring math is a mistake. But at the same time, you do need significant math skills in order to appreciate science with any meaningful depth, and I feel that science is a requirement.
The proper next step, it seems to me, is to figure out what bits of science we really want to teach and then figure out how to explain math through that.
> How can you teach someone to balance a checkbook?
Outside of America, no one uses checkbooks anymore. There's no reason to use exact change for tipping, either: just estimate a percentage and then round up. Or splitting the bill: the servers virtually always have a calculator at their disposal.
> whereas understanding sums and compounding processes ARE [terribly necessary as a matter of life and death, or even to a certain degree, quality of life or death].
One of the key mistakes of educational strategy is dividing up knowledge into a bunch of subjects like "Language", "Math", and so on. You can find linkages in just about everything; this siloing really only serves to make people think they're particularly good at one thing and not another, when really it's a preference for one perspective over another.
I would look at what you need the address for and actually make the request based solely on that. Generally speaking, you ask for an address in order to send mail of some kind. Inside the US, you basically never need the city/state: they're for error-checking (wait, XXXXX isn't actually in California; it's in Iowa). I had a friend give me an address that the postman told me didn't make sense (no city field), but it still got to him fine: I'd lay good odds that the post office people local to my friend simply had a modified convention.