>>1
In summary, a lot of fart with no solid description of just what the hell happens in his dreamland classroom over the course of an hour or a year or from year-to-year.
Section-by-section commentary:
Instead of a simple statement of ideas concerning math education, the reader is confronted with a story about a musician waking from a nightmare. The story is meant to engage the reader by describing the state of math education in this peculiar manner, by analogy with music education (which actually does not operate as described).
The author is implying that the notation and standard terminology of math is analogous to the notation and terminology of music. The reader is meant to begin thinking that the doing of math is akin to the doing of music, and that just as music is less enjoyable if the learning involves no actual sound of music, math is less enjoyable if the learning involves no actual math which exists independent of notation and terminology supposedly as much as does the music in our ears. Therefore, the author is claiming that learning notation and standard terminology in general is not enjoyable, and for math is akin to studying music without hearing any actual sound. The author is claiming that because notation and terminology of math is not math, teaching notation and terminoloy does not foster desire to learn math. The implication is that somehow the ideas of math are better learned without reference to the standard language by which we communicate ideas of math, because doing math is like playing music. I disagree.
The author continues to imply that adherence to the standard notation of math is overly strict and unenjoyable, and is empty of actual "music" (math). I disagree with the analogy, as I can argue that being able to read and write musical notation can be very useful. Of course, as actual music can be played anytime too, so can doing math, but the author has yet to state what he believes "doing math" actually means.