The reason new math failed is because it was organized and administered by committees (comprised of people who don't do math). So your example is humorously evi

The reason new math failed is because it was organized and administered by committees (comprised of people who don't do math). So your example is humorously evidence to my claim. What does a committee do when they are tasked with designing a curriculum or standards? They identify what should be tested, and then they pick the order that the topics are taught, likely outlining a time constraint on how long should be spent on each topic. This is the problem. If you're looking for things to test your students on then you will invariably add pointless content. Physicists are no exception (they invented the elaborate and pointless notation for vectors, the bra and ket). I don't propose we test students on mathematical notation, not at all. I propose we actually have them do mathematics (craft proofs, make conjectures), and I assert that any committee trying to craft a curriculum would ruin that. They have already ruined proofs in high school geometry.