On Wed, 02 Jul 2014 13:12:57 -0600, Robert Hansen <email@example.com> wrote:
> > On Jul 2, 2014, at 11:38 AM, Louis Talman <firstname.lastname@example.org> wrote: > >> I was certainly so trained. I was taught to identify mathematics with >> the sort of arithmetic that RH boasts of being able to teach? > > I don?t recall people identifying arithmetic with mathematics back in > those days. I certainly don?t see it in the texts of the era. I am not > questioning your experience, just trying to understand how people could > identify arithmetic with mathematics back then. So far what I have is > that you were taught arithmetic in arithmetic fashion and taught to > identify that with mathematics. I am not sure if how you were taught > arithmetic is how I teach it, but what intrigues me is how you were > taught to identify arithmetic with mathematics. Can you describe this > aspect more? Are you saying that they taught algebra like arithmetic? > > Bob Hansen
Do you mean that when folks talked to your ten-year-old self about your school-work they never said something like "How are you doing at math?" Such identification of arithmetic with mathematics is a deep undercurrent in our society. It has nothing to do with the way the subject is taught.
On the contrary, the fact that arithmetic is taught as a collection of mysterious algorithms that have no intellectual basis but is identified as mathematics has a great deal to do with the "fear and loathing" of mathematics under discussion here. A misconception of what mathematicians do, popular in our society, is that we sit around adding up big columns of numbers.
That this is so is attested by what happened to my Ph.D. advisor when he obtained his first university position. His wife decided to give him an academic hood as a birthday present. The salesperson didn't happen to have a hood with the appropriate blue stripe signifying his field, so he sold her one with the brown stripe for accounting. She concurred with the salesman that that was "close enough". (He never straightened her out; he wore that hood at academic events until he retired fifteen or so years ago!)
- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver