When I asked in high school what math was for to some professors, they said it was more to 'improve your thinking' than to use it in 'real life'. Now, a math course designed to be progressively easy to grasp, personalized when needed, entertaining and showing lots of examples from real life (e.g. relating algebra with 3d and video games) requires a very talented educator; teaching well is really hard and usually there's not enough time or resources to do it. That's why I think one of the most important skills to develop is to learn how to learn.

Yup. I don't recall actually learning anything in math class from 7th grade through my senior year.

I learned trig and geometry from my shop and programming courses... Trying to do graphics in QBasic and determine lengths and angles in carpentry gives concrete examples. It's not as though most math sprang spontaneously from pure thought-stuff - at some point, architects, inventors, astronomers and others in concrete endeavors discovered these rules.

I think it very much depends on the teacher.

It's not difficult to explain the first few topics on calculus in terms of distance, speed and acceleration. Other examples I remember were washing lines (a catenary), the path traced by a stream train's wheels and rocketry.

My teacher in England always had a real world example, but students with the other teacher didn't.