They do a lot fewer derivations in math these days than they used to. A lot of it is because math courses teach a lot more stuff than they used to, and a lot of that new stuff is just applications in different domains and special cases of more general stuff. I remember doing something a lot like that Gauss story in algebra, though no one mentioned Gauss.
Nowadays they consider derivations too hard or too sophisticated for kids to solve when it is actually a great way to teach. I recently tutored some high school kids in geometry, and the whole point of teaching geometry is to let kids see how a few rules applied to simple figures let you figure out all sorts of interesting things. That was almost dropped from the course. There was no spine of proofs to unify things. Instead, there were applications and more applications, each with a few definitions and formulas to memorize. It was horrible. Those kids were being cheated.
I wonder how many students would do better learning math if it were presented as a human endeavor, with a history, with stories of discoveries, with problems people faced and how they solved them. They’d still be stuck learning multiplication tables and fractions, but they’d see more of the forest rather than getting stuck with just trees.