Therein lies the rub. Treating abstract and the concrete in isolation was always tough sledding for me.

Bouncing between the two is where the action is.

And units: if I had it all to do over, I would pore over the units sooner rather than later.

I really disagree with the straightforward reduction of engineering to 'math but practical', but I'm finding it hard to express exactly why I feel this way.

The history of mathmatical advancement is full of very grounded and practical motivations, and I don't believe that math can be separated from these motivations. That is because math itself is "just" a language for precise description, and it is made and used exactly to fit our descriptive needs.

Yes, there is the study of math for its own sake, seemingly detached from some practical concern. But even then, the relationships that comprise this study are still those that came about because we needed to describe something practical.

So I suppose my feeling is that, teaching math without a use case is like teaching english by only teaching sentence construction rules. It's not that there's nothing to glean from that, but it is very divorced from its real use.

As someone who is studying maths at the moment I don’t recognise this picture at all. Every resource I learn from stresses the practical motivation for things. My book of odes is full of problems involving liquids mixing, pollution dispersing through lakes, etc, my analysis book has a whole big thing about heat diffusion to justify Fourier analysis, the course I’m following online uses differential equations in population dynamics to justify eigenvalues etc.

Agreed, and it's such a shame! A kid goes to math class and learns, say, derivatives as this weird set of transformations that have to be memorized, and it's only later in in physics class that they start to see why the transformations are useful.

I mean, imagine a programming course where students spend the whole first year studying OpenGL, and then in the second year they learn that those APIs they've been memorizing can be used to draw pictures :D

Well, logarithms were made from physical entities (celestial bodies) but not on engineering per se.

I think this is already enough context to root the mental effort deeper.