What should students learn after they are literate and numerate at a functional level? Here's
one argument for why mathematical proofs matter. Matt Rognlie offers
some pros and cons of studying 'classics' (although he is
less charitable towards some than others).
This question is tricky because it's really a matter of
the purpose of education, but in a very specific sense. If we want to satisfy the consumption goal, should students read
To Kill a Mockingbird? I mean, I loved it, but a lot of people don't. What about
The Old Man and the Sea? That one I couldn't stand. From a consumption perspective, shouldn't we be telling everyone to read more Tolkien? Or letting students choose from an array of
comic books? How do we know what readings now will give students more satisfaction in ten and twenty years time?
If, on the other hand, we are after productivity, then all education tends to become vocational, doesn't it? We could argue back and forth a bit about how best to develop "critical thinking skills" and other abstract tools many workers will need, but in general the idea becomes clear: let students try many things, and as they demonstrate interest or aptitude in one, narrow down their training to the specific skills they'll use in that profession. This makes moving between different kinds of jobs more difficult, but these days it usually doesn't pay to be a generalist.
If it's signaling we want to promote, of course, then we have a bit more leeway. The goal is to show a willingness and ability to endure the kinds of pain that you would only do if you really had the traits and talents employers are looking for. Of course, there are lots of ways to endure pain; Hemingway is just one option. Knowledge bowl with canings for the loser would work just as well.
Different cultures have relied on different mixes of these goals throughout history, and some are easier to figure out than others. China has had, since ancient times, a major emphasis on exams determining vocation; it seems to me that this is primarily a signaling education. In aristocratic societies, it seems to largely be a matter of consumption. Western societies have for at least a couple centuries now focused on creating workers with identical skill sets---particularly the "don't question the boss" skill---well suited for factory work, call centers, or middle management.
What should the mix of educational goals look like? What would education that served this mix well look like? What mix(es) would be acceptable from a Christian worldview, and are there any that must be categorically rejected?
(PS - I know some readers may want to say that none of these goals is in line with a Christian worldview, since the goal of education should be "raising children in the nurture and admonition of the Lord," and ultimately God's glory comes above all other goals. Well, OK, sure. I contend that you're still going to promote God's glory by nurturing and admonishing in a way that combines consumption, productivity, and signaling. The question is what types of consumption, productivity, and signaling best promote God's glory, and what combinations implicitly refuse to nurture and admonish. So I'm not looking for a Mardel's answer, nor even the Reformed equivalent. Dig deep here, people.)