[dr_dshiv]

100%.

And why is it so hard to have math education based on good concrete contextualized examples, vs just rules and problem sets? Understanding the “why” behind the math is often lacking… and math doesn’t always need to be applied, that’s ok— but if it can be, it is so much easier to understand

[bsder]

Because math is the tool while physics and engineering are the application.

So, now instead of one concept you have two unfamiliar concepts--one of which is far removed from your pedagogy.

It sucks, but there just aren't that many straightforward applications of abstract math classes.

[dr_dshiv]

The addition of a concrete example almost always makes the pure math easier to understand.

Knowing whether a particular aspect of math has real application is relevant to students. And this remains hard.