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*To*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Subject*: [Xmca-l] Re: units of mathematics education*From*: Ed Wall <ewall@umich.edu>*Date*: Sun, 2 Nov 2014 14:03:00 -0600*In-reply-to*: <002801cff6b3$8e5dbb00$ab193100$@att.net>*List-archive*: <https://mailman.ucsd.edu/mailman/private/xmca-l>*List-help*: <mailto:xmca-l-request@mailman.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca-l.mailman.ucsd.edu>*List-post*: <mailto:xmca-l@mailman.ucsd.edu>*List-subscribe*: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:xmca-l-request@mailman.ucsd.edu?subject=subscribe>*List-unsubscribe*: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:xmca-l-request@mailman.ucsd.edu?subject=unsubscribe>*References*: <1414042156116.36175@unm.edu> <544911FA.3010808@mira.net>, <003a01cfeed5$9e928180$dbb78480$@att.net> <C5E992C0-FEFD-4E41-8730-965752C16996@manchester.ac.uk> <54496BA0.6080104@mira.net> <803A57FD-ED25-490E-847E-71B4E2490A63@umich.edu> <5449BC4B.1020504@mira.net> <15A0050C-24E2-4D3D-A4BD-7C8FBE47F907@umich.edu> <5449F0B6.5040902@mira.net>, <6073CDA7-B612-4CC2-AB79-312CE63F78BB@umich.edu> <1414280432557.55592@ucdenver.edu>, <700B31E6-4D18-43A1-8357-47B8EAF5D08F@umich.edu> <1414337487568.10699@ucdenver.edu> <66AA7EEB-1F34-485D-9227-5F8EB31A56F8@umich.edu> <ced5ad95d0ae4d14ae2db1df8a8cd26e@SN2PR0601MB798.namprd06.prod.outlook.com> <4E081611-A3BD-46F3-AE79-BB41E08CCF87@umich.edu> <544DAD02.9070005@mira.net> <95546616-8723-4803-A0D9-72ECAF4F5143@umich.edu> <544DCA93.1050502@mira.net> <A20F993F-947D-4800-B5A2-896CAB22007A@umich.edu> <5452D88F.3090401@mira.net> <012a01cff51c$c6d1c780$54755680$@att.net> <5454221 A.3070407@mira.net> <008801cff5f4$8d61b590$a82520b0$@att.net> <545568B9.5080502@mira .net> <003301cff63f$27973ff0$76c5bfd0$@att.net> <86D8D1D6-E3A2-4FA2-9F6D-0A55359E31D8@umich.edu> <002801cff6b3$8e5dbb00$ab193100$@att.net>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces@mailman.ucsd.edu>

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. >>>> >>>> >>> >>> >>> >> >

**Follow-Ups**:**[Xmca-l] Re: units of mathematics education***From:*mike cole <mcole@ucsd.edu>

**References**:**[Xmca-l] Re: units of mathematics education***From:*Peg Griffin <Peg.Griffin@att.net>

**[Xmca-l] Re: units of mathematics education***From:*Peg Griffin <Peg.Griffin@att.net>

**[Xmca-l] Re: units of mathematics education***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: units of mathematics education***From:*Peg Griffin <Peg.Griffin@att.net>

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