I was surprised and delighted this week to discover two essays bemoaning the state of mathematics education and, in particular, high-school geometry. I had always imagined that my pet obsession with the interactions between mathematics and culture was just that, but apparently the movement contains at least three people. Who knew?
If you start from the origin (that being PoMoCon), traverse two sides of an isoceles triangle, rotate yourself a couple of radians around the point (42, 42) and then slide your way down one of the diagonals of the inscribed parallelogram; you might just find your way to Mark Shiffman’s condemnation of coordinate geometry at FPR. I’ve many a gripe against Descartes, but did not consider his mathematical work to be particularly pernicious until my heart lept at the following paragraph:
It is number, then, and the question of the natural unity and integrity of natural beings, that guides our understanding of nature for the ancients. Extended magnitude is a secondary characteristic of beings, incident to their material aspect. Form is the more fundamental aspect of its being, because it is the form that dictates what material (and how much of it and in what proportions) will be present in the living being or artifact.
Those familiar with my writing about Rene Thom at dearly-departed Culture11 should be struck by just how, well, “Thomistic” Shiffman is being here. Of course, Thom would argue that quantitative geometry is actually going to save the day (and the forms!) through the theory of structurally-stable singularities; but don’t let that scare you away from Shiffman’s eminently readable post.
Changing gears entirely, allow me to point you towards an essay so brilliant, so accurate, so dripping with honesty that it will become required reading for any who wish to carry my standard into the Math Wars. I’m speaking, of course, of Lockhart’s Lament . Descriptions won’t do justice to this baby, read the thing yourself. If you need motivation, just ask Scott Aaronson :
Lockhart says pretty much everything Ive wanted to say about this subject since the age of twelve, and does so with the thunderous rage of an Old Testament prophet. If you like math, and more so if you think you dont like math, I implore you to read his essay with every atom of my being.
. . .
In the end, Lockharts lament is subversive, angry, and radical . . . but if you know anything about math and anything about K-12 education (at least in the United States), I defy you to read it and find a single sentence that isnt permeated, suffused, soaked, and encrusted with truth.
The rest is left as an exercise for the reader .