[Xmca-l] Re: units of mathematics education

[Andy Blunden]

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.
>>
>>     
>
>
>