Part of my difficulty in teaching intro economics classes was that in order to dumb the material down enough for the freshmen business majors to understand, I had to "teach" things that I didn't really believe. I used to think it must be nice to be a math professor, because then everything you taught would be rigorously correct. (You just wouldn't get into, say, Cantor's diagonal argument in a pre-calc class.)
Well now I wonder if that's even true. (I should've asked math professors at the time, but I don't think I ever did.) In any event, my 2-year-old was playing today and showing me different blocks. He held up a cylinder and said confidently, "Circle." So I said "That's right it's a circle." Then he held up a block that was a triangle with depth, and I told him it was a triangle. I.e. I didn't put in a caveat, "Actually Clark, it's just the two-dimensional face of it that's a triangle. And in a few years we'll talk about calculating its volume."