[Xmca-l] Re: units of mathematics education

[mike cole]

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.
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