Those sorts of breakdowns are exactly what the kids who were good at math were always doing, and teaching methods eventually caught up and realized they should just teach the tricks.

Well... kinda. "Getting to 10" was what New Math was trying to teach. So you'd take the 1 from 7 and give to 9, because 6 + 10 is easier than trying to finagle your way to 8x2.

Then a bunch of parents who were bad at math asked “new math? How can math change?”

You don't have to be bad at math, strictly speaking. But there was a lot of brute memorization in traditional math. Times Tables, for instance, were something you just memorized straight up without thinking too deeply. Getting 16 out of 7+9 was something you just had to do on your fingers until you had it lodged in your head.

Old Math tended to be slower and more tedious. New Math is more logical, but also somewhat counterintuitive until you get into the swing of it.

The fact that they even asked that question showed how their math education was lacking, but they seem to have won.

I've got friends with kids down in Houston. "New Math" appears to be alive and well, in no small part because it helps kids score higher on standardized tests.