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[Xmca-l] Re: units of mathematics education
- To: "'eXtended Mind, Culture, Activity'" <email@example.com>
- Subject: [Xmca-l] Re: units of mathematics education
- From: Peg Griffin <Peg.Griffin@att.net>
- Date: Sun, 2 Nov 2014 12:32:07 -0500
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Typo alert: after the + should be a - in the parenthetical following
[mailto:email@example.com] On Behalf Of Peg Griffin
Sent: Sunday, November 02, 2014 10:42 AM
To: 'eXtended Mind, Culture, Activity'
Subject: [Xmca-l] Re: units of mathematics education
Thanks for this and the Hawaii information, Ed. I had looked into the
Hawaii work before but I know nothing at all of Benezet, I'm afraid.
I'm not sure what you (or Benezet) mean by "formal arithmetic," so I don't
know what to make of the implication that the early Davidov mathematics
educators were "something like" an approach that lacked it.
In my understanding, the Davidov mathematics is essentially all about
formal mathematics --symbols and systems of symbols are developed with the
children for relations (=≠ ><) and operations (+ =). Ignoring numbers
until later allows teachers to avoid an epigenetic byway we often see in US
elementary schools where counting relations among number symbols overshadow
other aspects of mathematics. The example I gave earlier is about the
fourth graders in US schools who seem to understand > and < than relations
in a little system of three mathematical statements but they do not
understand that "don't know" is a mathematically correct answer in some of
the little systems -- for them don't know is essentially a personal thing
not a mathematics thing.
[mailto:firstname.lastname@example.org] On Behalf Of Ed Wall
Sent: Saturday, November 01, 2014 10:45 PM
To: eXtended Mind, Culture, Activity
Subject: [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: email@example.com
> [mailto:firstname.lastname@example.org] 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
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: email@example.com
>> [mailto:firstname.lastname@example.org] 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.