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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*: Sat, 1 Nov 2014 21:45:18 -0500*In-reply-to*: <003301cff63f$27973ff0$76c5bfd0$@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>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces@mailman.ucsd.edu>

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>

**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>

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