On Tue, 01 Jul 2014 23:07:34 -0600, Joe Niederberger <email@example.com> wrote:
> R Hansen asks: >> Then why do we? > > Because we are trained to, and that's always a bit Pavlovian. >
I was certainly so trained. I was taught to identify mathematics with the sort of arithmetic that RH boasts of being able to teach: Learn the algorithms and perform them without any reasoning. (Could this be why so many students can't do word problems? Do they expect there to be a reasoning-free algorithm for each problem?)
Geometry partially opened my eyes, but I had a teacher who did her very best to keep that from happening by insisting that the only way to approach the subject was to memorize the proofs of the theorems in the textbook; we were not allowed to give our own proofs of those theorems.
It wasn't until I got to calculus that I began to understand that I'd been sold a bill of goods, and that only about five percent of what my teachers had called "mathematics" was really that.
- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver