@anthracite @frameacloud @zebratron2084
I remember having things like "attribute blocks" which were meant to be grouped into Venn diagrams, which of course counts as set theory. As I understand it (from Feynman) the big idea of New Math was that all math could be expressed in terms of set theory, and so if they start with set theory then kids will be geniuses who know everything. In practice, of course, if you try to teach basic arithmetic by framing every number and operation in terms of "sets" it will be too complicated to understand. Apparently, from the backlash, there is fundamentalist dogma still around to this day that says Set Theory is Not Real and from the Devil.

But on the other hand, consider this song from Tom Lehrer, bless him: https://youtu.be/UIKGV2cTgqA
This is probably more typical of the complaints of the time. What he's describing (that is, before the introduction of octal, a fair criticism), in a glib way meant to sound complicated, is subtraction the way I do it, the way you do it, the way the dude aggressively making coffee to level the same accusation against "common core" does it. Apparently the old way was to say "3 from 2 is 9"? Perhaps this was memorized with a "subtraction table" of some kind?