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[Xmca-l] Re: units of mathematics education

Something like this - i.e. lack of formal arithmetic until 7th - (although the details are a little unclear) was done in the US in the 1920s by a Louis Benezet. My impression is that he was building on ideas of Dewey.


On Nov 1, 2014, at  8:48 PM, Peg Griffin wrote:

> 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.