New Math was a response to the Soviet lead in the space race. It was thought that introducing more abstract concepts, like different bases and set theory, would help kids grok math more.
It was a fool's game. Just like every other "innovation" in mathematics education since, up to and including Common Core (one of which you probably encountered). At the elementary school level, the only way to increase math proficiency is drilling. Drill the basic math facts and standard algorithms until the kid knows them by heart and can do problems as easily as breathing. Only then will they be ready for the higher level, conceptual stuff.
The Soviets were ahead in math and science because they drilled their kids harder. Any kid who didn't want to drill was a traitor to the working class. (Were I a right-wing conspiracy theorist, I'd say New Math and its successors were Soviet psyops designed to sabotage math education in order to weaken the west. Instead I think it's more likely a psyop by the bourgeoisie to make us more compliant and exploitable slaves through mass innumeracy.)
No surprise, then, that today, when Americans really want their kids to learn math, they use the curriculum from a country where they cane you for minor infractions. They use Singapore Math. Math is hard, and hard things can only be mastered through discipline.