The third is to challenge students. With unusual concepts, preferably.

How else to create students capable of solving problems we cannot anticipate today?

Not to mention, that understanding strange problems is a very efficient way to broaden horizons.

You're missing general problem solving. If all people do is encounter problems they've already seen before, well, we have lookup tables for that kind of thing.

Not entirely wrong but it's a little too easy to use that argument for squashing any criticism for education content.