Early in high school (late 1980's mind you), I decided to take up percussion to play in our award-winning marching band. I started out on cymbals, but that was too simple. Then, I worked on the rudiments of percussion/snare drum. I had to work hard on the "math" of the musical notation, but I soon realized that I had a feel, an "ear" for complex percussion rhythms. And it jived with my already attuned ability in singing. There was something natural that "just clicked."
I see this same pattern in African spiritual music performed by people with no formal education. There's a natural mathematically knowledge they possess without any formal math education.
To me, music is just a higher abstraction of math. One that people with no math education can appreciate without even knowing why.
It's only when educated in math, that the "resonation of the soul" takes place. And I'll superficially agree with the reasons of the other commenters about why the education is lacking.
My point is that we don't have to teach them to feel anything about math. Some people will grok it at a deeper level than others and come to that realization on their own. But I think the overall analogy to music is pretty good. Mozart grokked music theory better than anyone alive today, but that doesn't mean I can't appreciate his genius (given no formal training). And I couldn't integrate an equation today (15 years out of college), but that doesn't mean I can't appreciate math in my life.