High School Geometry: Instrument of the DevilThere is nothing quite so vexing to the author of a scathing indictment as having the primary
target of his venom offered up in his support. And never was a wolf in sheep’s clothing as
insidious, nor a false friend as treacherous, as High School Geometry. It is precisely because it
is school’s attempt to introduce students to the art of argument that makes it so very dangerous.
Posing as the arena in which students will finally get to engage in true mathematical
reasoning, this virus attacks mathematics at its heart, destroying the very essence of creative
rational argument, poisoning the students’ enjoyment of this fascinating and beautiful subject,
and permanently disabling them from thinking about math in a natural and intuitive way.
The mechanism behind this is subtle and devious. The student-victim is first stunned and
paralyzed by an onslaught of pointless definitions, propositions, and notations, and is then slowly
and painstakingly weaned away from any natural curiosity or intuition about shapes and their
patterns by a systematic indoctrination into the stilted language and artificial format of so-called
“formal geometric proof.”
All metaphor aside, geometry class is by far the most mentally and emotionally destructive
component of the entire K-12 mathematics curriculum. Other math courses may hide the
beautiful bird, or put it in a cage, but in geometry class it is openly and cruelly tortured.
(Apparently I am incapable of putting all metaphor aside.)
What is happening is the systematic undermining of the student’s intuition. A proof, that is,
a mathematical argument, is a work of fiction, a poem. Its goal is to
satisfy. A beautiful proof
should explain, and it should explain clearly, deeply, and elegantly. A well-written, well-crafted
argument should feel like a splash of cool water, and be a beacon of light— it should refresh the
spirit and illuminate the mind. And it should be
charming.
There is nothing charming about what passes for proof in geometry class. Students are
presented a rigid and dogmatic format in which their so-called “proofs” are to be conducted— a
format as unnecessary and inappropriate as insisting that children who wish to plant a garden
refer to their flowers by genus and species. [...]
http://www.maa.org/devlin/LockhartsLament.pdf