Yeah, teaching the basics of an abstract concept without first explaining how it fits into the bigger picture is IMO not the best way to motivate some people. I'm also a person who wants to understand why it's important instead of just trusting someone that it'll be useful "later".

It'd be cool if, once you start your major, there was basically an overview class explaining why each of your courses is important and what concepts (at a high level) you should be grokking with each course and semester; basically some context to frame your learnings.

I took an automata class where the professor talked into the chalkboard and refused to explain why we were required to learn any of the material. It wasn't until later in the compilers course that we had a teacher who actually took the time to explain how all that mysterious theory actually had a place in the real world. So many light bulbs went off in my head during that class.

I had a similar experience from a different perspective -- I took a course on Theory of Computing, which was 50/50 gate-level CPU design and mathematical work on computability, automata and so on. I found this interesting as an intellectual exercise and to get a grasp on what is computable and what isn't, but then the next semester it proved super useful in the compiler design course.

I am also much more happy with an answer along the lines of "it has no practical use currently but is interesting because of...." than no answer at all.

I actually think you're in the norm. The "why" helps create a belief; a belief is something that ignites action. Without it, someone's belief as to why they should learn [X] is too often defined as "to get a good grade."

High school math was awful at this in the US. I went through a year of calculus and never knew what the heck it was for.

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.