Re: Explaining the foundations of math

From: Dement (crowdog_at_o2online.de)
Date: 08/31/04 

Date: Tue, 31 Aug 2004 13:19:41 +0000 (UTC)

On 31 Aug 2004, William Elliot wrote:
>From: Will Twentyman <wtwentyman@read.my.sig>
>Newsgroups: sci.math
>Subject: Re: Explaining the foundations of math
>
> >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.
>
>Illiterate kids graduated from grade school, colleges having to teach
>remedial (ie basic high school level) stuff to high school graduates.
>Argg!
>
> >When we're more worried about students' feelings and self-image than
> >whether they are competent, is it any surprise that many are happily
> >ignorant?
>
>Ignorance is bliss, thus also corporate media censorship
>of news and alas, even corporate censorship of science.
>
>Big Brother doesn't want students who can think for themselves.
>
>Big Brother Bush will not publicly thank little Brother Jeb
>for corrupt Florida elections, neither for 2000 nor for 2004.
>It'd give thinking students the false notion that election fraud
> can and has happen to US.
>
>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?

There is actually a math book (forgot the name) which recommends
that kids use calculators right off the bat. The point is is
that many of them already have a nice and intuitive feel for
numbers which they've aquired just by playing around. However,
when they get to elementary school they begin learning "rules"
based on performing some simple (but sometimes counterintuitive)
algorithms which have little to do with the math itself. To
demonstrate the point, the author even aludes to some statistics
showing that many kindergardners (or first graders or whatever) can
subtract (24 - 5 = 9, etc.) faster than 2nd graders, etc. because the
latter are too busy trying to "cross out 2 and make it a one, then,
for some reason, write a "1" next to the "4"...etc.") while younger
students still tend to invent (and improve on) algorithms they
themselves thought up.

Sincerely,
C. Dement
 

 
>These days community colleges are promoting and emphasizing use of
>graphic calculators as algebra. Does this forebode of yet more
>mathematical incompetence?
>
>-- the Dummy Down Dunce Dance
>Forlorn am I to scorn
> the land wherein I'm born
>whence creativity is shorn
> to fit some standard norm
>
>----
>

Relevant Pages

  • Re: Iowqa School to get Laptops
    ... CENTRAL CITY - Soon students in the Central City School ... Snit will now produce evidence that using computers in education ...
    (comp.sys.mac.advocacy)
  • Learning from Poor Minority Students....
    ... Learning from Poor and Minority Students Who Succeed in School ... This is one family's story of success against the odds. ... Relative to the voluminous literature on the causes of school failure, ...
    (soc.culture.hmong)
  • Re: "The National Anthem should be sung in English" - What part of "unconstitutional" do conserv
    ... spent my entire pre-college education in Catholic schools. ... grammar/English are now drilled into the heads of students for countless ... hours in the school day immersed in just those two subjects (with an hour ... party)...also develops one's critical thinking skills. ...
    (rec.music.artists.springsteen)
  • Re: So, heres the (hopefully) next topic of debate
    ... about my schooling to become a goldsmith. ... >> I thought I was getting a great education - especially at Cranbrook...it was ... >> school I was amazed. ... >> throw lots of conceptual ideas at the students using found objects and glue ...
    (rec.crafts.jewelry)
  • Re: DAVE school
    ... extremely proud of the DAVE School and think I need to speak up. ... You should communicate this to the students. ... Or perhapps a teacher is misquoting the policy. ... We think that learning about things AND having our ...
    (comp.graphics.apps.lightwave)