R Hansen says: >I am not saying that this doesn?t occur in mathematics. It occurred all my life. But there are conditions that must be met for the effect to occur. i.e., you can?t show a mathy 3rd grader calculus and expect the appreciation you get when you play Beethoven for a musical 3rd grader.
I'm not exactly sure what you are getting at here, unless its just to point out that appreciating math is harder than appreciating music. Sure, of course. A mother sings a lullaby to her child, unless she is a Tiger Mom. (There's plenty of music that a typical 3rd grader is not going to appreciate though.)
The fact is that math appreciation is much harder, if we take appreciation to mean that deeper kind based on understanding. I think it has to come from the general environment; that its too hard to get just from school lessons. The student has to see how math fits in with life. Silly exercises that supposedly fill this gap just always fall short, as you yourself have pointed out many times.
I think it may help if kids actually do things other than play video games, although I suppose video games can require some forms of math appreciation. Doing a bit of real carpentry or such, really sharpens the appreciation for simple things like accurate measurement. And of course all sorts of calculations are needed, albeit simple, have to be made all the time. That encourages mental calculation. And the real cost of miscalculation encourages accuracy. I don't think you'll find many carpenters who say: "I really love carpentry but I hate all the math I have to do".
I know, you'll say that's not Calculus. I don't think we are going to get a large portion of the population to really appreciate calculus, except perhaps at the level of some nicely made videos, graphic novels, etc. that make calculus concepts come alive without requiring any performance from the viewer. But hey, why not?