FWIW, this is certainly not what people who do research into how to teach math advocate. In fact, one of the recommendations for teachers is that they should tr

FWIW, this is certainly not what people who do research into how to teach math advocate. In fact, one of the recommendations for teachers is that they should try to get students to come up with the algorithms themselves, or to "guide" them to these algorithms, and then let students use whichever they prefer, because that's the only way to get students to really understand and use them. That said, I've definitely seen some of that "let's just replace method X with method Y" – how harmful that is depends on whether it is just presented as a default or as The New Standard Algorithm, I guess.