“teaching it symbolically is absolutely the wrong way to teach it”
Absolutely right. I was not advocating that. You start with concrete, physical examples and, as the brain matures around age 12 or 13, you progress to symbolic math building upon the physical examples.
I remember that being a difficult transition for me, but you reach a certain “aha!” Point one day where it quickly starts to make sense.
So many kids cannot make that transition today and graduate from high school still depending on fingers and toes.
They never taught division by fractions intuitively when I was in school. I “glommed onto” it by myself at about age 10, by thinking of pie slices. The problem with mathematics instruction is that it is too abstract. I am an EE and have absolutely no problem with complex numbers and actually “think” in complex numbers. It’s takes an effort to think about what physical entities they represent. Richard Feynman taught himself how to repair radios when he was ten, so electronics and electromagnetism did not seem completely abstract to him.