Updated: See below.
Originally posted on 9/19/2011
Could anything possibly be more useless than high school geometry (I avoided saying "pointless" - ha ha)? If ever there were a course better designed to drain the beauty out of math, I can't imagine what it might be. I think geometry is in the curriculum because it gives a fairly visual and intuitive introduction to the axiom / proof approach to math, which is what professional mathematicians do. But for most people math is worth studying because of its usefulness as a collection of tools applicable to the real world. And you can learn its beauty by learning the tools and gradually seeing how they hang together into a coherent architecture of quantitative thinking. But geometry, as taught, gets at virtually none of that. What's taught has virtually no value outside learning the axiom / proof stuff - or at least the applicable parts are a tiny portion of what's taught. And the rigor is of an extremely irritating "memorize these axioms" sort (which is what so much high school education seems to come down to).
It's not that there's no value in learning to distill the underpinnings of intuition into clearly stated basic inputs. Euclid did that (I'm told - I don't read greek) and it's worth understanding the how and why. But to spend an entire year on it is a crime. There's a lot of other useful math that could be taught instead. Basic probability and statistics, for example. Probability is an incredibly interesting subject and doesn't seem to be anywhere in the HS curriculum. But it's absolutely central to decisionmaking. It's intuitive, and sometimes counterintuitive, which is even better. And a lot of it can be taught without much math beyond basic algebra.
It probably won't surprise anyone that Anna has just started taking geometry and is not enjoying it...
Updated on 4/9/2013: I just stumbled on the passage below in a review of the essay "A Mathematician's Lament" by Paul Lockhart. The review is here. The original essay can be found here.
'The author reserves some of his strongest criticism for high school geometry, which he considers an “instrument of the devil.” In fact, his criticism is even more strongly stated: “A geometry class is by far the most mentally and emotionally destructive component of the entire K–12 mathematics curriculum.” Forcing students to follow a rigid and dogmatic format in laying out their proofs, he argues, destroys the very essence of what geometric proofs should be and undermines the students’ intuition.'
