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*To*: "'eXtended Mind, Culture, Activity'" <xmca-l@mailman.ucsd.edu>*Subject*: [Xmca-l] Re: units of mathematics education*From*: Peg Griffin <Peg.Griffin@att.net>*Date*: Sun, 2 Nov 2014 10:42:05 -0500*In-reply-to*: <86D8D1D6-E3A2-4FA2-9F6D-0A55359E31D8@umich.edu>*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>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces@mailman.ucsd.edu>*Thread-index*: AQH+Xv9Oz+qV8FilwXZNhVM4bIuqNAKpoRxhAjo7ulIBmSNOUAJURbIoAzDIDZYCF8y0/AIsrhpIAmrQvawB4I9cJQIpqyo1Am0yQ1QCG5J9cgH5aKn3AjAEQQ0Buf2wXAK6DxDAAbPlNdgBgWpXwQE5rHzbAiXXsGQCI3HnYwGIlI/lAcVQkqkB3tRT4gJa6W6FAk37JheaPSQmQA==

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:*Peg Griffin <Peg.Griffin@att.net>

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

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