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[Xmca-l] Re: units of mathematics education

Andy and Peg

      It might be of interest to look at Keith Devlin's column in the MAA, He muses about counting versus comparison (in Davydov's sense). Perhaps of more interest would be the the Measure Up curriculum developed by Barbara Dougherty at the University of Hawaii:  


which is supposed to be a variation of Davydov's. 

        Algebra is a strange course. It is often a mishmash of things and purposes.


On Nov 1, 2014, at  6:11 PM, Andy Blunden wrote:

> 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.