But often those real world applications are way harder to understand than the initial abstract problem they had. Involving other subjects only works if the stud

But often those real world applications are way harder to understand than the initial abstract problem they had. Involving other subjects only works if the students are already well versed in those subjects. And before you say "just learn those subjects first then?", often it is easier to first learn the abstract math and then learn those concepts than the other way around, since making sense of those equations is hard even when you do know the math and close to impossible when you don't.