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[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 Blunden*

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*

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.