Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Education » math-teach

Topic: Some important demonstrations on negative numbers
Replies: 70   Last Post: Dec 8, 2012 1:28 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
GS Chandy

Posts: 6,946
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: Some important demonstrations on negative numbers
Posted: Nov 28, 2012 5:28 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Robert Hansen (RH) posted Nov 28, 2012 7:26 AM (GSC's remarks interspersed):
>
> On Nov 27, 2012, at 5:51 PM, Joe Niederberger
> <niederberger@comcast.net> wrote:
>

> > Your war against common sense though,...
>
> I have no war against common sense. That would be
> like having a war against taste or smell. My claim is
> simple. Common sense just isn't synonymous with
> mathematics, or more precisely, with reasoned thought
> and analysis. In fact, the two domains share nothing
> in common, no pun intended. Regardless of the fact
> that reasoned thought can explain common sense and
> fathom its examples, it acts entirely in spite of
> common sense. And "commonplace" is certainly not
> synonymous with "common sense". That has a different
> meaning altogether.
>

As so often, RH's claims arise out of a total misunderstanding of just what he is writing about, in this case, about what 'common sense' may be; and just what its derivates, such as 'reasoned thought and analysis' (and 'synthesis'; and, for that matter, 'mathematics') are. Reasoned thought and analysis (and synthesis' and for that matter, mathematics) in fact all *grow out* of 'common sense'. It is true enough that one person's 'common sense' may be another's 'nonsense' - the great human adventure, in which 'language' has played a crucial role, has always been to try and arrive at an adequate mutual understanding of each others' 'common sense'.

A little reasoned thought and analysis will show that the above is inescapably true in all circumstances. It is a fact that reasoned thought and analysis (and synthesis) can often lead us to results that may seem counter-intuitive (i.e. against 'common sense') - but that does not negate their origins.
>
> Common sense is the perception of the concrete world
> that we all share.
>

True enough.
>
> Common sense is devoid of reasoned
> thought and analysis.
>

Ridiculous.
>
> That is my definition and in
> the context of this discussion, neither unfair nor
> unwarranted.
>

It's a 'definition' arising out of a ridiculous misunderstanding.
>
> Mathematics on the other hand is
> analysis. It is a reasoned and imagined theory about
> abstract and imagined entities, most significantly,
> the real numbers. When we attempt to teach this
> imagined theory and its imagined elements to the
> unaware student, we use concrete examples (common
> sense) as an aid in that task but not as a substitute
> for that task and not as a substitute for the goal of
> the task, reasoned analysis and thought.
>

See all of above.

GSC
("Still Shoveling Away!" - with apologies if due to Barry Garelick for any tedium caused; and with the observation that there is a SIMPLE way to avoid such tedium)


Date Subject Author
11/27/12
Read Some important demonstrations on negative numbers
Peter Duveen
11/27/12
Read Re: Some important demonstrations on negative numbers
James Elander
11/27/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/27/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/27/12
Read Re: Some important demonstrations on negative numbers
Clyde Greeno @ MALEI
11/27/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/27/12
Read Re: Some important demonstrations on negative numbers
Peter Duveen
11/28/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/27/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/27/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/27/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/28/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/27/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/28/12
Read Re: Some important demonstrations on negative numbers
GS Chandy
11/28/12
Read Re: Some important demonstrations on negative numbers
GS Chandy
11/28/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/28/12
Read Re: Some important demonstrations on negative numbers
Peter Duveen
11/28/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/28/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/29/12
Read Re: Some important demonstrations on negative numbers
kirby urner
11/28/12
Read Re: Some important demonstrations on negative numbers
Peter Duveen
11/28/12
Read Re: Some important demonstrations on negative numbers
syeds
11/28/12
Read Re: Some important demonstrations on negative numbers
GS Chandy
11/28/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/28/12
Read Re: Some important demonstrations on negative numbers
Paul A. Tanner III
11/28/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/29/12
Read Re: Some important demonstrations on negative numbers
kirby urner
11/28/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/29/12
Read Re: Some important demonstrations on negative numbers
Paul A. Tanner III
11/28/12
Read Re: Some important demonstrations on negative numbers
Jonathan Crabtree
11/28/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/29/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/28/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/29/12
Read Re: Some important demonstrations on negative numbers
Peter Duveen
11/29/12
Read Re: Some important demonstrations on negative numbers
Peter Duveen
11/29/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/29/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/29/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/29/12
Read Re: Some important demonstrations on negative numbers
Peter Duveen
11/29/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/29/12
Read Re: Some important demonstrations on negative numbers
Jonathan Crabtree
11/29/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/29/12
Read Re: Some important demonstrations on negative numbers
Jonathan Crabtree
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/29/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/30/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/30/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/30/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/30/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/30/12
Read Re: Some important demonstrations on negative numbers
Jonathan Crabtree
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/30/12
Read Re: Some important demonstrations on negative numbers
Clyde Greeno @ MALEI
11/30/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
11/30/12
Read Re: Some important demonstrations on negative numbers
Clyde Greeno @ MALEI
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
12/1/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/30/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/30/12
Read Re: Some important demonstrations on negative numbers
Clyde Greeno
12/1/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
11/30/12
Read Re: Some important demonstrations on negative numbers
Jonathan Crabtree
12/1/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
12/1/12
Read Re: Some important demonstrations on negative numbers
Robert Hansen
12/8/12
Read Re: Some important demonstrations on negative numbers > a MACS syllabus
Clyde Greeno @ MALEI
12/1/12
Read Re: Some important demonstrations on negative numbers
Joe Niederberger
12/2/12
Read Re: Some important demonstrations on negative numbers
Jonathan Crabtree
12/2/12
Read Re: Some important demonstrations on negative numbers > Wallis/Pycior
Clyde Greeno @ MALEI
12/3/12
Read Re: Some important demonstrations on negative numbers > Wallis/Pycior
Robert Hansen

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.