The math-as-music idea is further described, implying that boring math skills are taught too early. The reference to humming and silly songs is the author’s way of saying that "real" (non-standard notational and non-computational skill) math is something that children would naturally do and desire to do. I disagree that skills are necessarliy boring. Also, using the music analogy, learning to play an instrument involves much practice to build skill. Perhaps the author isn’t rejecting all skills, but such specifics are not described.
The author further extends the music-math analogy, describing the pressure of standardized tests and courses that are important for college that don’t actually exist in the learning of music. Perhaps the author means to say that we should discard standard math requirements for college. However, if a student was to actually try to get a music degree, there typically is some kind of assessed audition prior to acceptance into a degree program. What analogous math audition would there be?
The author writes that actual "music" (math) learning occurs late and for few students, happening only for those that specialize in math in college. The idea of students being "bad" at music (math) is mocked as a misinterpretation of what it means to be merely bad at the standard notation and skills, which themselves have earlier been implied to not be real math. The author wants to reader to agree that the standard notation and skills are boring and not very relevant, that facility with them is not the same thing as being good at math, and that deficiency in them is not the same thing as being bad at math. The analogy does not make good sense when considering any aspect of music making that requires skills that require practice. Would we all better learn math by "playing it by ear" or perhaps improvising everything that we play?