Sets. Venn Diagrams. We always called it "New Math" but maybe it had some other term at that point.
Well, set theory and stuff like Venn diagrams were part of some New Math curricula beginning in the 1960s, but mostly at the primary (or maybe middle-school) level. They were intended to teach things like Boolean algebra, which would be relevant to new trends (at that time) in computer programming. Again, the emphasis was on getting students up-to-speed to participate in the Space Race, etc.
And I also should note that Venn diagrams were in fact meant to be visual aids to support the new abstract concepts (like Boolean algebra and set theoretical relationships), kind of like the visualizations you're arguing for in Common Core.
Anyhow, they certainly weren't supposed to displace algebra and geometry in high-school curricula. If your school did that, they were doing the "New Math" wrong.