The discussion at the bottom of the blog post is also very interesting. The socratic approach is very good to "break the ice" and introduce the application, but I wonder how scalable this approach is. Does the teacher need to be very knowledgeable/entertaining to pull this off?
BTW, I'm working on a new project, which is essentially "math lessons by email" that will walk readers through the math material from the NO BULLSHIT guide to MATH & PHYSICS. Anyone interested in learning or reviewing basic math (expression, equations, functions, algebra, geometry) should signup: https://confirmsubscription.com/h/t/4C2D9C45B88734F3 (it's free)
Worse, I think they don't teach generalisable skills.
That's probably the core problem with all school-level math and science teaching. You learn a vocabulary of basic symbols and some rules for manipulating them, but you don't learn math skills - in the sense of understanding the real world well enough to make the leap from symbols and abstractions to useful life skills.
The point of math teaching shouldn't be to know how to solve problems like these, but to learn how/when you can use math to answer your own questions for yourself.
There's also a deeper level where you can teach the process of abstraction as an end in itself. I suspect that may be too far for most people - although I haven't completely convinced myself that's true yet.