>I never said that they were typical 3rd graders. I said that they were musical 3rd graders.
So, not typical, but a small subset probably less than 5%.
>If we are going to make a parallel with math then we must choose topics in math that can take off like this. That precludes calculus and algebra because those require formal thinking skills not yet had in elementary aged students.
You don't think a bright 3rd grader can understand the concept of acceleration? That some accelerations are greater or lesser that others, and that the magnitude of acceleration itself can vary over time? And, that understanding most definitely does not have to be "formal".
But to the musical analogy, I would say that kids learning to read notes on piano, even if the melody comes from Bach (tired of spelling Beethoven) are mostly practicing the eye-hand and muscular coordination needed to do that trick. Ask them to explain the harmonic structure of Moonlight Sonata ;-)