On learning mathematics, learning to run, and learning the other stuff

From Lockhart's Lament (PDF)

SALVIATI: ...I'm complaining about the complete absence of art and invention, history and philosophy, context and perspective from the mathematics curriculum ...A real appreciation for poetry does not come from memorizing a bunch of poems, it comes from writing your own.

SIMPLICIO: Yes, but before you can write your own poems you need to learn the alphabet. The process has to begin somewhere. You have to walk before you can run.

SALVIATI: No, you have to have something you want to run toward. Children can write poems and stories as they learn to read and write. A piece of writing by a six-year-old is a wonderful thing, and the spelling and punctuation errors don't make it less so. Even very young children can invent songs, and they haven't a clue what key it is in or what type of meter they are using.

SIMPLICIO: But isn't math different? Isn't math a language of its own, with all sorts of symbols that have to be learned before you can use it?

SALVIATI: Not at all. Mathematics is not a language, it's an adventure. Do musicians “speak another language” simply because they choose to abbreviate their ideas with little black dots?