We Should Teach Things Top-Down

There are two ways to teach subjects where larger concepts depend on smaller concepts, which is common in STEM: bottom-up or top-down. I recall from my university education in Electrical and Computer Engineering almost all courses being taught bottom-up. The thought recently occurred to me that this is contrary to how we tend to care about subjects though, which is usually oriented around how useful the subject is to us. I only need to care how things work under the hood if something is broken, or if I need a deeper understanding of how the thing works for other reasons like performance or environmental impact, or if I'm just curious. But at the end of the day, it's the top-level concept that we use day-to-day and that is useful.

With a top-down approach, I drill deeper as needed, revealing finer and finer details as I need them. If I have no reason to learn how something works, then I simply don't, because I already know how it works as a black box so there's no need to peer inside. This is a satisfying learning approach because first I want or need to know something, then I learn it. With bottom-up, you start with a lack of understanding of what it is we're working towards until finally the big picture is revealed at the end.

Now, obviously in a teaching setting like a university, the point is to learn how everything works, so the usefulness criterion becomes "everything" and you still end up learning how all the parts work, but I still argue that top-down would be a better experience since you start with the end result which is usually closer to real life applicability and work backwards to the fine details. Note that this is how natural sciences work. First we observe real-world phenomena happening, then we study them to see how they work. We don't start with the model and build up to the real-world phenomena.