Lockhart's Lament
Yesterday, a friend and former student of mine, Patrick Campbell, introduced me to the short piece written by Paul Lockhart, which was given exposure in the columns of Keith Devlin (links here and here).
I was very encouraged to find something that agreed in very important ways with my perspective. The spirit of the piece, immediately apparent in the choice of parables he starts with, is precisely right and urgently important.
The main principles promoted here are that (1) the primary use or application of mathematics is to give joy, to enrich, to beautify our lives -- mathematics is first and foremost an art, a deeply creative endeavor, (2) mathematics is living, alive, something that one must learn by moving into, being immersed in, playing with, waiting quietly until you hear the music that sings to you, and 3) the large majority of what is taught detracts from (1) and (2).
This critique is valid when aimed more broadly at many academic approaches to "truth". Schooling often leads to a very narrow technical know-how, but an inability to feel, to really innovate - to feel and explore the living world we see from a distance. The life has been removed. As proposed in this video (I love the rant), technical abilities are no indication of insight or a life worth living. Because truly vibrant, living connections to our studies are mostly missing, we become technical masters, not masters of our own destinies. We chose slavery, not freedom.
But at least on our own scale, we (educators) can choose to reverse this by aiming at vibrant classes, living interactions, and dynamic, creative environments. Do books and practice and formality have places in this environment? Heck yes, but in consciously subservient roles to a living path of creative exploration and a habit of constant innovation.
I do think that Lockhart's apparent lack of experience with applications and physics/engineering leads to a few minor mistakes in his viewpoint, but I doubt he would not grant those to me if we were communicating on the matter, judged from what seems to be reasonable responses in the second column.
I highly recommend that you take the time to read Lockhart's Lament.