Arguably, the kind of person who was helped by learning to do that by hand still learns to do it by hand, but because of curiosity rather than because a teacher told them to.
I remember being thirteen and trying to brute force methods for computing the square root. I didn’t have the tools yet to figure out how to do it in any systematic way, and the internet wasn’t at a point yet where it would have even occurred to me to just search online. Wikipedia wouldn’t exist for another two years.
I probably finally looked it up at some point in high school. I’m not sure exactly when, but I remember spending a lot of time practicing doing a few iterations in my head as a parlor trick (not that I ever had the opportunity to show it off).
If I were thirteen and curious about that now, I’d probably just ask ChatGPT. Then I’d have a whole follow up conversation about how it was derived. It would spit a lot of intimidating LaTeX at me, but unlike with Wikipedia, I’d be able to ask it to explain what those things meant.
This is the thing I don’t get when people talk about LLMs’ impact on education. Everybody focuses on cheating, like learning is inherently a chore that all students hate and must be carefully herded into doing despite themselves.
But that’s a problem with school, not learning. If your actual, self-motivated goal is to learn something, LLM’s are an incredible tool, not a hindrance.