Re: Explaining the foundations of math

From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 08/31/04 

Date: Tue, 31 Aug 2004 07:55:50 -0400

William Elliot wrote:
> From: Will Twentyman <wtwentyman@read.my.sig>
> >William Elliot wrote:
> >> On Mon, 30 Aug 2004, Will Twentyman wrote:
>
> >>>When I was in an honors section of Calc I in college, our professor
> >>>made us write a paper explaining how the definition of the limit
> >>>corresponds to the intuitive notion of a limit. Realizing that
> >>>this class was about 50% math majors, it took most of us 3-4 tries
> >>>before we generated a version that he considered acceptable. If
> >>>this is a particularly difficult concept to internalize for math
> >>>majors, I suspect it is even more difficult for non-math major,
> >>>non-honor students to absorb.
>
> >>>I suspect some of the authors have realized this, and decided that
> >>>the students efforts are better directed at being able to *do*
> >>>calculus rather than being able to understand a somewhat obscure
> >>>looking definition.
>
> >> Sigh, more watering down of education.
>
> >>>I'm not saying that decision is correct, just that they are
> >>>removing a barrier to being able to do calculus that appears to be
> >>>unimportant for many students.
>
> >> Just wait until they have to hassle with metric spaces, spaces with
> >>> norms, modern analysis or topology. They'll founder and flop.
>
> >> Not an approach at all helpful for math majors, graduate physics
> >> majors.
>
> >Agreed. I find it interesting that in the 50's the US was near the
> >top of the curve in quality of education. Now that we've started
> >worrying about social issues in the schools, we're plummeting fast.
>
> Sigh. Soon we'll see US plummeting scientifically.

Soon? I figured the programming jobs were fleeing to India for this
very reason. I wouldn't be surprised to see the other sciences
similarly affected?

> But less I stray too far off topic, what are they doing in grade
> school, are they still teaching numbers, ie arithmetic? Or are
> youngsters spared such demeaning demoralization by being taught
> to use hand calculators instead?

I know that graphing calculators are required in middle school/high
school in South Carolina for algebra classes. I have yet to hear anyone
explain *why* a graphing calculator should be required. For that
matter, I have yet to understand why they're allowed on the SAT now.

> These days community colleges are promoting and emphasizing use of
> graphic calculators as algebra. Does this forebode of yet more
> mathematical incompetence?

If a student doesn't actually understand what a graphing calculator
does, how can that student be expected to make sense of of the calculus
methods for graphing? 

-- 
Will Twentyman
email: wtwentyman at copper dot net

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