> Like, "New Math" https://www.understood.org/en/articles/9-new-math-problems-a... . None of these methods show WHY, only a rote procedure.

I'm confused by your comment here. Literally the entire point of teaching those various methods is to show WHY the math works. If anything you should be arguing for rote methods. Some are better than others, but ultimately they're all trying give tools to depict the way any math literate adult thinks about arithmetic.