Rabindrath Tagore (1861 - 1941), an Indian poet and musician, became the first non-European to win a Nobel Prize in literature. But, he also revealed a lot to us about teaching and learning...even mathematics.
First, the teaching side of things. When Tagore was young, a tutor was hired to teach him music. Tagore writes: "He determined to teach me music, and consequently no learning took place."
That is, Tagore became impatient with the tedious practice tasks he was assigned, desperately wanting to experience the "authentic" side of creating music. But, Tagore notes: "Nevertheless, I did pick up from him a certain amount of stolen knowledge"...by watching and listening when his teacher played on his own or for others. That was real music, not the cheap imitations Tagore felt forced to do.
Second, as an extension of this experience and others, Tangore began to hate formal education. He argued that "proper teaching does not explain things; proper teaching stokes curiosity."
And, it "knocks at the doors of the mind. If any boy is asked to give an account of what is awakened in him by such knocking, he will probably say something silly. For what happens within is much bigger than what comes out in words. Those who pin their faith on university examinations as the test of education take no account of this."
From these two perspectives, Tagore informs us as mathematics teachers. First, we need to assign less tedious exercises and actually do mathematics in front of (and with) our students, so they can "steal" some of the spirit from us. And second, we need to stoke student's curiousity about mathematics.
So...a good place for each of us to start is
to steal some mathematical knowledge ourselves on a regular basis...and let our own curiosity be stoked!