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[Xmca-l] Re: units of mathematics education



No move from numbers to x.  No numbers to begin with in mathematics
education.  Kids count in everyday life but no numbers in the beginning
mathematics classes.  It really is strings!  Not even rulers or tape
measures of strings.
  

-----Original Message-----
From: xmca-l-bounces@mailman.ucsd.edu
[mailto:xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Andy Blunden
Sent: Saturday, November 01, 2014 7:12 PM
To: 'eXtended Mind, Culture, Activity'
Subject: [Xmca-l] Re: units of mathematics education

Phew! So I was not the only one mystified by that expression. However,
wouldn't the kids have been confused by it as well? Or would they react by
saying: "Hey, Teacher! That's stupid!"?
But certainly making the move to using letters only when the children are
reaching out for some more convenient symbol seems the right way to go. I
used to teach the first lesson in algebra by playing "Think of a number,
double it,  ..., what's the number he first thought of?" with a classroom of
kids and then introducing x for the number you first thought of. Vygotsky
tells us to provide the symbol as a means of solving an existing problem.
How did Davydov make the move from numbers to x?

Andy
------------------------------------------------------------------------
*Andy Blunden*
http://home.pacific.net.au/~andy/


Peg Griffin wrote:
> The * was an intrusion!  The expression is just paradoxical.  There 
> cannot be a concrete world such that "Alyosha's string is greater than 
> Boya's string equals Alyosha's string is less that Borya's string."
>
> (By the way, in case you want a smile on this November day,  my 
> favorite paradox is the pragmatic one: " Inform all the troops that 
> communication has broken down."  Can't remember who is the originator 
> of it, though!)
>
> -----Original Message-----
> From: xmca-l-bounces+peg.griffin=att.net@mailman.ucsd.edu
> [mailto:xmca-l-bounces+peg.griffin=att.net@mailman.ucsd.edu] On Behalf 
> Of Andy Blunden
> Sent: Friday, October 31, 2014 7:58 PM
> To: eXtended Mind, Culture, Activity
> Subject: [Xmca-l] Re: units of mathematics education
>
> Could you elaborate on what is meant by this passage, Peg? I am not 
> familiar with this use of * in mathematics, and I am not sure how the 
> > and < relations are being evaluated here. Andy
> ----------------------------------------------------------------------
> --
> *Andy Blunden*
> http://home.pacific.net.au/~andy/
>
>
> Peg Griffin wrote:
>   
>> ...  That mathematical model (*A>B=A<B) DOES NOT have a concrete 
>> world to rise to! Instead, the children see/feel/perceive the strings 
>> and symbols having a relation among relations: A>B = B<A.
>>
>>     
>
>
>