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*To*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Subject*: [Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]*From*: Andy Blunden <ablunden@mira.net>*Date*: Fri, 24 Oct 2014 21:49:01 +1100*In-reply-to*: <5449F0B6.5040902@mira.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> <54489B05.6090106@mira.net> <8EF148FA-21A2-4C87-A365-458C24F79107@manchester.ac.uk> <CAGVMwbVGLGWLrjedY4aDZRr0KnhAxHL01_aAkXdjcwt8u7obdQ@mail.gmail.com> <5448B630.8060503@mira.net> <CAGVMwbUHSd2+HtbRuSaMMu1imvLOkx9vxbmph6nr_anNCUovyQ@mail.gmail.com> <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>*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/ Andy Blunden wrote:

I see.The text which is makes up the third point of the triangle with theteacher and student is in this case a mathematical text, yes? So forexample, completely different problems arise than would arise in thecase of reading a story or some other piece of writing. I can see theidea that that teacher-text-pupil relation is an archetype for a wholerange of teaching. In itself, it certainly doesn't tell you anythingdistinctive about teaching mathematics in particular. I think you needto turn to other units specific to different topics being taught.Different units give different insights. For example, Vygotsky usedword meaning while Bakhtin used utterance. Utterance is a much largerunit than word meaning, but it proves useful for providing insightsinto communication and handling the framing and context, whilst wordmeaning is useful for understanding concepts and the development ofconceptual thought. Davydov's germ cell in which two objects arecompared in length is an elementary act of abstraction, and thereforecaptures the idea of quantity, which should take a student to thepoint of grasping the general idea of mathematical text andabstracting quantities from real situations. But that doesn't reallydo for the whole subject or tell you anything about the teacher-pupilrelation.I would not get obsessed on this phrase: "possessing all the basiccharacteristics of the whole." That phrase can lead you up a blindalley. I think it originates from Engestrom's 1987 book: “a viableroot model of human activity ... [must be] the smallest unit thatstill preserves the essential unity and quality behind any complexactivity," which is somewhat more precise than the phrase you haveused, but can still lead to misconceptions. The interpretation"possessing all the basic characteristics of the whole," leads to alogical circle: which characteristics are essential, whichcharacteristics are basic?You need to form a concept of teaching mathematics.Perhaps you could elaborate a little, Ed, on your ideas for a unit ofanalysis for mathematics teaching? Why do you need a smaller unit?Andy ------------------------------------------------------------------------ *Andy Blunden* http://home.pacific.net.au/~andy/ Ed Wall wrote:AndyThe paper ("The Unit of Analysis in Mathematics Education") isabout unifying branches of mathematical education research: natureand philosophy of mathematics, teaching of mathematics, learning ofmathematics, and sociology of mathematics (this last something he haspromoted for a number of years) under one unit of analysis (i.e.collaborative projects). Insofar as the section on mathematicsteaching goes he just says the triad (and he fleshes it out a bit)isn't controversial so I wouldn't say he is always 'critically'reviewing, but that may be a matter of opinion. My questionisn't directed at Ernest, but at you. I'm interested in the very ideaof a unit of analysis possessing all the basic characteristics of thewhole. The problem I am having with all varieties of the triad isthat they seem yet too 'large'; i.e. in a sense the grain size is toolarge to, one might say, pick up the mathematical flavor thatdifferentiates mathematics teaching from, say, reading teaching. Soit would seem that the choice of the unit of analysis also needs tobe done in a minimal fashion? Without such a unit of analysis, I findmyself unable to talk usefully and coherently with my students aboutwhat I observe that is mathematically problematic (and I don't meanmistakes) in their planning and teaching of mathematics. There aretimes, unfortunately, when it appears I am viewing a well thought-outreading or grammar lesson.Anyway I doubt whether mathematics is unique in this regardand that teachers of all stripes aren't having similar problems withsuch units of analysis.Ed On Oct 23, 2014, at 9:41 PM, Andy Blunden wrote:Ed, Paul may quote me, but I actually know little about his work ormathematics education itself.But isn't he discussing a number of different proposals for a unitof analysis for mathematics teaching, one of which is the one yourefer to. I take it that he is critically reviewing all suchproposals before making his own proposal.Andy------------------------------------------------------------------------*Andy Blunden* http://home.pacific.net.au/~andy/ Ed Wall wrote:AndyThe paper seems to be about unifying mathematics educationresearch. Parts are a bit open to debate (especially argumentsconcerning the 'nature' of mathematics) and Ernest tends tosomewhat gloss over this. However that is not relevant and you arecorrect Ernest does, among other things, put forth a unit ofanalysis for mathematics teaching which, as he admits is simplifiedfor the purposes of the paper; i.e. the usual triad of teacher,student, and text (which is hardly unique to Ernest as he notes).At this point I have a question that I've been pondering aboutconcerning such triads and their elaborations (and this goes backin a sense to things Schwab said elsewhere - the Schwab he quotesin the beginning of his paper) and, as he quotes you heavily, Iwill ask you: If this triad is indeed a prototype of mathematicsteaching (i.e. posses all the basic characteristics of the whole),what makes this a prototype of mathematics teaching and not aprototype of, say,theteaching of reading? This is not a spurious question since, as amathematics educator (of the type that Ernest wishes to unify -smile), I often find myself needing to help elementary schoolteachers realize there are actually substantial and observabledifferences (and substantial similarities) between teaching readingand teaching mathematics and, for sundry reasons, they tend tofavor something like the former and cause their students someanguish in the learning of mathematics as time passes. Hmm, I guessI am asking whether the unit of the analysis can, in effect, be the'world' or should it be, so to speak, among the 'minimum' relevantprototypes. It seems that it would be somewhat worthless otherwise(again similarities are important).Ed On Oct 23, 2014, at 3:57 PM, Andy Blunden wrote:Paul Ernest has a position on the unit of analysis for mathematicsteaching:http://www.esri.mmu.ac.uk/mect/papers_11/Ernest.pdf Andy------------------------------------------------------------------------*Andy Blunden* http://home.pacific.net.au/~andy/ Julian Williams wrote:Andy:Now I feel we are nearly together, here. There is no 'final' formeven of simple arithmetic, because it is (as social practicesare) continually evolving.Just one more step then: our conversation with the 7 year oldchild about the truth of 7plus 4 equals 10 is a part of thissocial practice, and contributes to it....? The event involved inthis Perezhivanie here involves a situation that is created bythe joint activity of the child with us?Peg: Germ cell for the social practice of mathematics... I wonderif there is a problem with Davydov's approach, in that itrequires a specification of the final form of the mathematics tobe learnt (a closed curriculum). But let me try: One candidatemight be the 'reasoned justification for a mathematicaluse/application to our project' ... Implies meaningful verbalthought/interaction, and collective mathematical activity withothers. Not sure how this works to define your curriculum contentetc.Julian On 23 Oct 2014, at 16:28, "Peg Griffin" <Peg.Griffin@att.net> wrote:And thus the importance of finding a good germ cell formathematics pedagogy-- because a germ cell can "grow with" and "grow" the current"socialpractice of mathematics." Whether someone agrees with the choiceof germcell made by Davidov (or anyone else), a germ cell needs to beidentified,justified and relied on to generate curriculum content andpractice, right?PG

**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:*Carol Macdonald <carolmacdon@gmail.com>

**[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:*Carol Macdonald <carolmacdon@gmail.com>

**[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>

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