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*To*: "'eXtended Mind, Culture, Activity'" <xmca-l@mailman.ucsd.edu>*Subject*: [Xmca-l] Re: units of mathematics education*From*: Andy Blunden <ablunden@mira.net>*Date*: Tue, 28 Oct 2014 10:53:59 +1100*In-reply-to*: <006a01cff209$a388c230$ea9a4690$@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> <54490772.2020805@mira.net> <49BC6E1396C8F94B92715533ED4D20DC1DAE749B@MBXP03.ds.man.ac.uk> <544911FA.3010808@mira.net>, <003a01cfeed5$9e928180$dbb78480$@att.net> <C5E992C0-FEFD-4E41-8730-965752C16996@manchester.ac.uk> <54496BA0.6080104@mira.net> <803A57FD-ED25-490E-847E-71B4E2490A63@umich.edu> <5449BC4B.1020504@mira.net> <15A0050C-24E2-4D3D-A4BD-7C8FBE47F907@umich.edu> <5449F0B6.5040902@mira.net>, <6073CDA7-B612-4CC2-AB79-312CE63F78BB@umich.edu> <1414280432557.55592@ucdenver.edu>, <700B31E6-4D18-43A1-8357-47B8EAF5D08F@umich.edu> <1414337487568.10699@ucdenver.edu> <66AA7EEB-1F34-485D-9227-5F8EB31A56F8@umich.edu> <ced5ad95d0ae4d14ae2db1df8a8cd26e@SN2PR0601MB798.namprd06.prod.outlook.com> <4E081611-A3BD-46F3-AE79-BB41E08CCF87@umich.edu> <544DAD02.9070005@mira.net> <95546616-8723-4803-A0D9-72ECAF4F5143@umich.edu> <544DCA93.1050502@mira.net> <006a01cff209$a388c230$ea9a4690$@att.net>*Reply-to*: <ablunden@mira.net>, "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces@mailman.ucsd.edu>*User-agent*: Thunderbird 2.0.0.23 (Windows/20090812)

Andy ------------------------------------------------------------------------ *Andy Blunden* http://home.pacific.net.au/~andy/ Peg Griffin wrote:

Interesting about money not being in Marx’s unit of analysis, Andy.As I understand what educators following Davidov’s math curriculumwere doing, numbers were not involved in the mathematics educationgerm cells.Here’s a glimpse of the scenario as I understand it (which could bewrong):Children start with strings or lumps of clay or what not (not easily countable). Alyosha’s object is greater than Borja’s. Anyone can perceive the difference. The mathematical recording of that is A>B. In the very same situation, one is less than the other, mathematically, B<A. It isn’t nice or fair that one child’s object should be greater than and another less than, mathematically recorded as A ≠B and as B≠A. How to get to B=A and A=B? How to have a nice, fair situation? The teacher and children work it about and discover the important operations that mathematics has for working on >, <, ≠ and = and the mathematically recordings with + and -. The whole situation of transformations takes this nice set mathematically recorded as: A≠B B≠A A>B A-X= B+X A’=B’ B’=A’ Then of course there’s more fun when Katya’s in on it and transitivity pops in so that even without direct perceptual comparisons mathematics comes to the rescue so you can figure out stuff you wouldn’t know otherwise (do I smell motivation here?): A>B B>K A?K A>K And they work out proudly that you keep the ? (don’t know) answer in the following situation A>B A>K B?K It remains forever a ? for mathematics, maybe direct percept will help but current mathematics for the current situation takes a pass on it. We might use mathematics to come up with some nice questions and suppositions and come to more or less likely answers but… And then you can get to precision with measurement tools that work for the kinds of objects and …It's apparent that mathematics can serve social justice sometimes. AsI understand it, the Davidov mathematics educators take it for grantedthat in “non-mathematics” everyday life learning, children learncounting (including the cardinality principle alluded to earlier inthe discussion and others that I associate a lot with the workdeveloped by Gelman, Gallistel, and her colleagues).And, as I understand it, the great day of the coming together ofmathematics and counting doesn’t happen for the Davidov folks untillater – maybe even fourth grade. Mathematics of the type discussedabove can start in the Davidov style Kindergartens.In the US where we start off with numbers right away, in fourth grade,there have been many children who are confident that 9>7 and 9-2=7 butcan get nowhere with working out all those wonderful equivalences ifthere are no numbers – i.e., they count but don’t do mathematics.Of course, that’s what I understand but I could be wrong. Peg -----Original Message-----From: xmca-l-bounces@mailman.ucsd.edu[mailto:xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Andy BlundenSent: Monday, October 27, 2014 12:31 AM To: eXtended Mind, Culture, Activity Subject: [Xmca-l] Re: units of mathematics educationWell, I think that if you make a decision that mathematics is *not*essentially a social convention, but something which is essentiallygrasping something objective, then that affects what you choose asyour unit of analysis. Student-text-teacher is all about acquiring asocial convention.Remember that when Marx chose an exchange of commodities as a unit ofanalysis of bourgeois society, he knew full-well that commodities arerarely exchanged - they are bought and sold. But Marx did not "include"money in the unit of analysis. Andy ------------------------------------------------------------------------ *Andy Blunden* http://home.pacific.net.au/~andy/ <http://home.pacific.net.au/%7Eandy/> Ed Wall wrote: > Andy > > Asking that question was one of the dumber things I've done on > this list. Apologies to all >> Thanks for reminding me about pre-concepts. I've been thinking aboutsomething similar and wondering if this is part of what makes doingmathematics 'mathematical.' Historically, by the way, mathematics grewout of manipulating such material objects; however, there areindications that, at some point (and it may have happened more thanonce), there was sort of a leap.>> Mathematics is considered a science; for instance, of patterns or, asHegel puts it, quantity. I agree for a mathematician symbols ofvarious sorts are effectively 'things'.>> In the 80s some mathematicians (School Mathematics Study Group) inthe US put together a formal curriculum - my aunt used it - which wasa disaster (and a real pain for the kids involved). Indications arechildren learned little.> > > So to add a little to a discussion that possibly has continued > far longer than it should. Mathematics may have a few characteristics > that may distinguish it from other disciplines such as >> 1. A student has the ability, in principle, to be able toindependently of teachers or peers verify a grade appropriatemathematics statement (not a definition although definitions admit, ina sense, a sort of empirical verification).> > 2. Solutions to problems are, in general, not subject to > social conventions (which probably is included in the above). > Amusingly, I believe in the US a state legislature once tried to set > the value of pi to 3.1417 >> However, I'm not sure how such would fit together into a useful unitof analysis.> > Ed > > >

**References**:**[Xmca-l] In defense of Vygotsky [[The fallacy of word-meaning]***From:*Annalisa Aguilar <annalisa@unm.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Julian Williams <julian.williams@manchester.ac.uk>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Peg Griffin <Peg.Griffin@att.net>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Julian Williams <julian.williams@manchester.ac.uk>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*"White, Phillip" <Phillip.White@ucdenver.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*"White, Phillip" <Phillip.White@ucdenver.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*David H Kirshner <dkirsh@lsu.edu>

**[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] units of mathematics education***From:*Andy Blunden <ablunden@mira.net>

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

**[Xmca-l] Re: units of mathematics education***From:*Andy Blunden <ablunden@mira.net>

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

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