That's a lot easier than the method I was taught. The "old" way always resulted in me trying to carry state in my head, which doesn't work well for ADHD-limited memory.

Lehrer is talking about "new math" from 60 years ago. (it consisted of talking about set theory, union and intersection, also mentioning commutative and distributive princicples, i.e. mentioning some things that are not super necessary for arithmetic but which you will encounter later if you pursue mathematics further. In this way you would hopefully be more effective in contributing to the arms and space races and defeating communism.) https://en.wikipedia.org/wiki/New_Math

not clear that GP is referring to the same thing at all, perhaps this https://www.parents.com/kids/education/math-and-science/new-...