Bottom-up vs Top-down learning?

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From my experience in grade school and an electrical engineering degree, education is largely "bottom-up". The idea is to teach the basics, and then build on those basics. A simple example would be to teach arithmetic, then algebra, then calculus etc. Electrical engineering followed a similar structure, eg. teach passive components, circuit analysis, then semiconductor physics, then transistor physics, then transistor circuits.

My experience with this is that most of the basics are fairly useless for practical applications and you have to get up to speed with the state-of-the-art regardless. Eg. after spending years doing careful analysis of different circuits, my job mostly obsoleted this by having advanced simulation software which could get better results and handle far more complex circuits than I did.

What if we taught things the other way around, i.e. "top-down"? Start at practical applications, and only explain basics as they become useful to the top-level goals.

This would seem to fit better with the modern technological environment. At this point, fields are so complex that no one can become a full expert. Trying to learn computers bottom-up would be both an utter waste of time and leave you incapable of doing anything practical while you struggle over the extreme complexity of their construction for example. Same with a variety of fields, you're better off just learning what the state of the art is and then dealing with details as they turn up and become useful.

TL;DR:
Bottom-up education:
>start from basics
>build up to (ideally) reach some useful level of knowledge
>technically-oriented
Top-down education:
>start from practical applications
>learn things only as they become useful
>goal-oriented