Oh man, I have some vitriolic opinions on the sate of modern teaching -- especially vis-à-vis textbooks and written "pedagogy" that go crazy with this "isolation," "abstraction," and "distillation" of the concept: I hate it, please stop doing this.
I feel even more strongly about this for mathematics and computer science: you cannot strip away the context of a technique/idea/concept, and hope to have people understand why it's useful. For example, I'm currently self-teaching myself mathematics. Calculus and its techniques (integration, differentiation, solving PDEs/ODEs, whatever) are easy -- when you understand the context: physical mechanics. Strip that away and what do you get? Symbols and equations that have zero meaning in the real world. It's effectively indistinguishable from GPT-3 text -- it's utter nonsense that doesn't make any sense unless you've already learned the concepts somewhere else, and can piece together what the hell the author is trying to get across (sometimes, the author doesn't even know, but pretends to know!).
Same with probability and statistics. I cannot understand the sheer myopia needed to completely strip away probability from its gambling context: how does this benefit learners? I wasn't able to teach myself these things from regular stats & prob books, because it's schizophrenic gibberish without any context -- without even a single example of a practical application, much less "why is this useful? Why was this brought into the world? Why are you using Brownian Motion for actions of living things???" And then I picked up some theory of gambling books, and lo and behold everything makes sense. There is no cruft. There are no "gotchas" where you need to slam your head against the desk, and force yourself through the problems for it to "click"; everything just clicks because you understand why a certain technique or concept exists, and where it's applicable.
In short, the original context that lead to the creation of a certain technique/concept is enough of a "stage" to teach it; anything more abstract and you're cutting through bone.
I feel even more strongly about this for mathematics and computer science: you cannot strip away the context of a technique/idea/concept, and hope to have people understand why it's useful. For example, I'm currently self-teaching myself mathematics. Calculus and its techniques (integration, differentiation, solving PDEs/ODEs, whatever) are easy -- when you understand the context: physical mechanics. Strip that away and what do you get? Symbols and equations that have zero meaning in the real world. It's effectively indistinguishable from GPT-3 text -- it's utter nonsense that doesn't make any sense unless you've already learned the concepts somewhere else, and can piece together what the hell the author is trying to get across (sometimes, the author doesn't even know, but pretends to know!).
Same with probability and statistics. I cannot understand the sheer myopia needed to completely strip away probability from its gambling context: how does this benefit learners? I wasn't able to teach myself these things from regular stats & prob books, because it's schizophrenic gibberish without any context -- without even a single example of a practical application, much less "why is this useful? Why was this brought into the world? Why are you using Brownian Motion for actions of living things???" And then I picked up some theory of gambling books, and lo and behold everything makes sense. There is no cruft. There are no "gotchas" where you need to slam your head against the desk, and force yourself through the problems for it to "click"; everything just clicks because you understand why a certain technique or concept exists, and where it's applicable.
In short, the original context that lead to the creation of a certain technique/concept is enough of a "stage" to teach it; anything more abstract and you're cutting through bone.