Any competent music teacher (I write as the husband of a piano teacher) can perform music with musical expression, and thus show students examples of the beauty of music. But the very best music teachers are also intimately familiar with all the isolated subskills that build into understanding a piece of music, and controlling the performer's muscle movements, and responding to the audience in a live setting to build a coherent, musically expressive performance. My wife teaches skills such as "music mapping,"
generally commenting on the submitted article) is that elementary school mathematics teachers can do NONE of the comparable things with mathematics that a good music teacher can do with music. They cannot isolate and focus on useful techniques, they cannot put on an example performance of solving an interesting, challenging problem, and they cannot make connections between their (poor) understanding of the problems found in elementary mathematics and their students' (often better, but different) understanding of the same problems. In the United States, people mostly seek music instruction for young learners from the private enterprise system. My wife gains most of her new clients, who are crammed into her busy teaching schedule as previous clients graduate from secondary school and go off to university, from friends of current clients who are happy with her work. By contrast, an elementary school teacher in a typical government-run school in the United States teaches on a take-it-or-leave-it basis, with attendance being compulsory in default of a government-approved alternative, and funding guaranteed to the school, and thus employment guaranteed to the teacher, whether the learners learn mathematics or not. Systemic change is necessary to get mathematics taught as music is taught to elementary-age pupils in the United States.
For an eye-opening look at how elementary mathematics teachers could be prepared, and how that would help learners, see Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma.
That book is a very enjoyable--but rather shocking--read, full of information about how to teach mathematics for "Profound Understanding of Fundamental Mathematics."
Any competent music teacher (I write as the husband of a piano teacher) can perform music with musical expression, and thus show students examples of the beauty of music. But the very best music teachers are also intimately familiar with all the isolated subskills that build into understanding a piece of music, and controlling the performer's muscle movements, and responding to the audience in a live setting to build a coherent, musically expressive performance. My wife teaches skills such as "music mapping,"
http://www.amazon.com/Mapping-Music-Learning-Teachers-Studen...
proper hand position,
http://www.amazon.com/Playing-Less-Hurt-Prevention-Musicians...
and how to tie those and many other skills together
http://www.amazon.com/Art-Piano-Playing-Heinrich-Neuhaus/dp/...
as part of a comprehensive process of teaching making music.
The basic problem with mathematics education at the elementary school level in the United States (see my previous reply to this thread
http://news.ycombinator.com/item?id=4034248
generally commenting on the submitted article) is that elementary school mathematics teachers can do NONE of the comparable things with mathematics that a good music teacher can do with music. They cannot isolate and focus on useful techniques, they cannot put on an example performance of solving an interesting, challenging problem, and they cannot make connections between their (poor) understanding of the problems found in elementary mathematics and their students' (often better, but different) understanding of the same problems. In the United States, people mostly seek music instruction for young learners from the private enterprise system. My wife gains most of her new clients, who are crammed into her busy teaching schedule as previous clients graduate from secondary school and go off to university, from friends of current clients who are happy with her work. By contrast, an elementary school teacher in a typical government-run school in the United States teaches on a take-it-or-leave-it basis, with attendance being compulsory in default of a government-approved alternative, and funding guaranteed to the school, and thus employment guaranteed to the teacher, whether the learners learn mathematics or not. Systemic change is necessary to get mathematics taught as music is taught to elementary-age pupils in the United States.
For an eye-opening look at how elementary mathematics teachers could be prepared, and how that would help learners, see Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma.
http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...
That book is a very enjoyable--but rather shocking--read, full of information about how to teach mathematics for "Profound Understanding of Fundamental Mathematics."