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" <email@example.com> To: "eXtended Mind, Culture, Activity" <firstname.lastname@example.org> 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 <email@example.com> 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: firstname.lastname@example.org > > [mailto:email@example.com] 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: firstname.lastname@example.org > >> [mailto:email@example.com] 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: firstname.lastname@example.org > >>> [mailto:email@example.com] 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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Schmittau Cultural Historical Theory & MathEdforXMCA.pdf
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