[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]

Fri Oct 24 03:49:01 PDT 2014

I have to correct myself here: the phrase "all the basic characteristics 
of ..." is a quote from Vygotsky, Ch. 1 of "Thinking and Speech" - one 
of a number of formulations which Vygotsky uses. I do find though that 
this particular formulation is one which has led to a lot of confusion.
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 the 
> teacher and student is in this case a mathematical text, yes? So for 
> example, completely different problems arise than would arise in the 
> case of reading a story or some other piece of writing. I can see the 
> idea that that teacher-text-pupil relation is an archetype for a whole 
> range of teaching. In itself, it certainly doesn't tell you anything 
> distinctive about teaching mathematics in particular. I think you need 
> to turn to other units specific to different topics being taught.
>
> Different units give different insights. For example, Vygotsky used 
> word meaning while Bakhtin used utterance. Utterance is a much larger 
> unit than word meaning, but it proves useful for providing insights 
> into communication and handling the framing and context, whilst word 
> meaning is useful for understanding concepts and the development of 
> conceptual thought. Davydov's germ cell in which two objects are 
> compared in length is an elementary act of abstraction, and therefore 
> captures the idea of quantity, which should take a student to the 
> point of grasping the general idea of mathematical text and 
> abstracting quantities from real situations. But that doesn't really 
> do for the whole subject or tell you anything about the teacher-pupil 
> relation.
>
> I would not get obsessed on this phrase: "possessing all the basic 
> characteristics of the whole." That phrase can lead you up a blind 
> alley. I think it originates from Engestrom's 1987 book: “a viable 
> root model of human activity ... [must be] the smallest unit that 
> still preserves the essential unity and quality behind any complex 
> activity," which is somewhat more precise than the phrase you have 
> used, but can still lead to misconceptions. The interpretation 
> "possessing all the basic characteristics of the whole," leads to a 
> logical circle: which characteristics are essential, which 
> characteristics are basic?
>
> You need to form a concept of teaching mathematics.
>
> Perhaps you could elaborate a little, Ed, on your ideas for a unit of 
> analysis for mathematics teaching? Why do you need a smaller unit?
>
> Andy
>
>
>
>
> ------------------------------------------------------------------------
> *Andy Blunden*
> http://home.pacific.net.au/~andy/
>
>
> Ed Wall wrote:
>> Andy
>>
>>       The paper ("The Unit of Analysis in Mathematics Education") is 
>> about unifying branches of mathematical education research: nature 
>> and philosophy of mathematics, teaching of mathematics, learning of 
>> mathematics, and sociology of mathematics (this last something he has 
>> promoted for a number of years) under one unit of analysis (i.e. 
>> collaborative projects). Insofar as the section on mathematics 
>> teaching 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 question 
>> isn't directed at Ernest, but at you. I'm interested in the very idea 
>> of a unit of analysis possessing all the basic characteristics of the 
>> whole. The problem I am having with all varieties of the triad is 
>> that they seem yet too 'large'; i.e. in a sense the grain size is too 
>> large to, one might say, pick up the mathematical flavor that 
>> differentiates mathematics teaching from, say, reading teaching. So 
>> it would seem that the choice of the unit of analysis also needs to 
>> be done in a minimal fashion? Without such a unit of analysis, I find 
>> myself unable to talk usefully and coherently with my students about 
>> what I observe that is mathematically problematic (and I don't mean 
>> mistakes) in their planning and teaching of mathematics. There are 
>> times, unfortunately, when it appears I am viewing a well thought-out 
>> reading or grammar lesson.
>>         Anyway I doubt whether mathematics is unique in this regard 
>> and that teachers of all stripes aren't having similar problems with 
>> such 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 or 
>>> mathematics education itself.
>>> But isn't he discussing a number of different proposals for a unit 
>>> of analysis for mathematics teaching, one of which is the one you 
>>> refer to. I take it that he is critically reviewing all such 
>>> proposals before making his own proposal.
>>>
>>> Andy
>>> ------------------------------------------------------------------------ 
>>>
>>> *Andy Blunden*
>>> http://home.pacific.net.au/~andy/
>>>
>>>
>>> Ed Wall wrote:
>>>    
>>>> Andy
>>>>
>>>>       The paper seems to be about unifying mathematics education 
>>>> research. Parts are a bit open to debate (especially arguments 
>>>> concerning the 'nature' of mathematics) and Ernest tends to 
>>>> somewhat gloss over this. However that is not relevant and you are 
>>>> correct Ernest does, among other things, put forth a unit of 
>>>> analysis for mathematics teaching which, as he admits is simplified 
>>>> for 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 about 
>>>> concerning such triads and their elaborations (and this goes back 
>>>> in a sense to things Schwab said elsewhere - the Schwab he quotes 
>>>> in the beginning of his paper) and, as he quotes you heavily, I 
>>>> will ask you: If this triad is indeed a prototype of mathematics 
>>>> teaching (i.e. posses all the basic characteristics of the whole), 
>>>> what makes this a prototype of mathematics teaching and not a 
>>>> prototype of, say, 
> the
>>>>  teaching of reading? This is not a spurious question since, as a 
>>>> mathematics educator (of the type that Ernest wishes to unify - 
>>>> smile), I often find myself needing to help elementary school 
>>>> teachers realize there are actually substantial and observable 
>>>> differences (and substantial similarities) between teaching reading 
>>>> and teaching mathematics and, for sundry reasons, they tend to 
>>>> favor something like the former and cause their students some 
>>>> anguish in the learning of mathematics as time passes. Hmm, I guess 
>>>> I am asking whether the unit of the analysis can, in effect, be the 
>>>> 'world' or should it be, so to speak, among the 'minimum' relevant 
>>>> prototypes. 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 mathematics 
>>>>> teaching:
>>>>> 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' form 
>>>>>> even of simple arithmetic, because it is (as social practices 
>>>>>> are) continually evolving.
>>>>>>
>>>>>> Just one more step then: our conversation with the 7 year old 
>>>>>> child about the truth of 7plus 4 equals 10 is a part of this 
>>>>>> social practice, and contributes to it....? The event involved in 
>>>>>> this Perezhivanie here involves a situation that is created by 
>>>>>> the joint activity of the child with us?
>>>>>>
>>>>>> Peg: Germ cell for the social practice of mathematics... I wonder 
>>>>>> if there is a problem with Davydov's approach, in that it 
>>>>>> requires a specification of the final form of the mathematics to 
>>>>>> be learnt (a closed curriculum). But let me try: One candidate 
>>>>>> might be the 'reasoned justification for a mathematical 
>>>>>> use/application to our project' ... Implies meaningful verbal 
>>>>>> thought/interaction, and collective mathematical activity with 
>>>>>> others. Not sure how this works to define your curriculum content 
>>>>>> etc.
>>>>>>
>>>>>> 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 for 
>>>>>>> mathematics pedagogy
>>>>>>> -- because a germ cell can "grow with" and "grow" the current 
>>>>>>> "social
>>>>>>> practice of mathematics." Whether someone agrees with the choice 
>>>>>>> of germ
>>>>>>> cell made by Davidov (or anyone else), a germ cell needs to be 
>>>>>>> identified,
>>>>>>> justified and relied on to generate curriculum content and 
>>>>>>> practice, right?
>>>>>>> PG                          
>>>>  
>>>>       
>>>     
>>
>>
>>
>>   
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