[Xmca-l] Re: units of mathematics education

[Ed Wall]

Many thanks Natalia and Mike.

Ed

On Nov 2, 2014, at  4:12 PM, Natalia Gajdamaschko wrote:

> Hi Dear All,
> I am a lurker in this discussion thread on math education but find it very interesting! 
> just to add to those two articles that Mike send of Jean Schmittau on Vygotsky/Davydov math curriculum, please, see attached another article Jean wrote with lots of good examples plus Peter's article.
> I use both of them in my class when it comes to discuss math curriculum done differently in my Vygotsky seminar. 
> Cheers,
> Natalia.
> 
> 
> ----- Original Message -----
> From: "mike cole" <mcole@ucsd.edu>
> To: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>
> Sent: Sunday, November 2, 2014 1:45:28 PM
> Subject: [Xmca-l] Re: units of mathematics education
> 
> As a small contribution to this interesting thread, two of Jean Schmittau's
> writings. She has done a lot work with Davydov's ideas in math ed that may
> give those following the discussion some useful info.
> mike
> 
> On Sun, Nov 2, 2014 at 12:03 PM, Ed Wall <ewall@umich.edu> wrote:
> 
>> Peg
>> 
>>      By ''formal arithmetic' I mean the usual US curriculum to which you
>> refer to below; I wasn't talking about 'formal mathematics' when I
>> mentioned Benezet. The point Devlin makes (and I'm not sure I entirely
>> agree) is that the Davydov curriculum is about real number versus counting
>> number. While Devlin and I both have problems with the usual US curriculum
>> it is not entirely evident mathematically why one approach (counting number
>> versus real number) is better than the other.
>> 
>>       I am confused by the statement below concerning an example you gave
>> 'earlier about US fourth graders.' The only example I remember was the one
>> using the Davydov approach with participants Alyosha and Borja.
>> 
>>       I would appreciate it if you would say a bit more about why "I
>> don't know" is a 'mathematically' correct and 'impersonal'  answer in some
>> 'little systems.' I would tend to think otherwise about "We can't know.' in
>> some little (and some large) systems; however, I may misunderstand.
>> 
>> Ed
>> 
>> On Nov 2, 2014, at  9:42 AM, Peg Griffin wrote:
>> 
>>> 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.
>>> PG
>>> 
>>> -----Original Message-----
>>> From: xmca-l-bounces@mailman.ucsd.edu
>>> [mailto:xmca-l-bounces@mailman.ucsd.edu] 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.
>>> 
>>> Ed
>>> 
>>> 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.
>>>>>> 
>>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>> 
>>> 
>> 
>> 
>> 
> 
> 
> -- 
> It is the dilemma of psychology to deal with a natural science with an
> object that creates history. Ernst Boesch.
> <MoxnayforXMCA.pdf><Schmittau Cultural Historical Theory & MathEdforXMCA.pdf>