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Re: [xmca] Further thoughts on Sfard's and Davydov's approaches to learning

Larry, I guess that both counting and measuring can be starting points for good teaching of mathematics (but I'd really like to hear from a maths teacher about that!) and I don't see any barrier to an eclectic approach either. I suppose I am interested in the relation between Activity and Discourse which is implicit in this problem. The problem posed by Doyle, that gaps in teaching may be being solved by things happening outside the classroom is intriguing as well. If kids are measuring and/or counting in everyday life, does this make the choice of how they are introduced to mathematical formalism in the classroom moot? Or is it the whole point? Does this issue have anything to do with the idea that practical intelligence is developmentally prior to word-use? Is there a basis for seeing Discourse as a special case of Activity here? Is it possible to found a philosophical viewpoint on Discourse without an implicit and unstated foundation in Activity? And how would this show up in problems of learning maths? Does basing maths teaching in Activity simply postpone the real work until you get up to mathematical discourse? Is there are class difference? (Discourse for the class of symbolic analysts, Activity for the class of manual workers?) Do the same issues arise in teaching Literature?

Anyone home?


Larry Purss wrote:
Andy, some further thoughts on the topic you opened up on contrasting Anna's
and Davydov's approaches to learning.
I was not able to download Anna's article because of the way its formatted.
However I went to Anna's website and have downloaded two of her articles and
also the introductory chapter of her book written in 2008. [The first half
of this book is elaborating her theoretical position that thinking IS
communication, as particular forms of discourse]
She says her approach is similar to Harre's approach to "discursive
psychology" and both Anna and Harre definitely view thinking in a dialogical
way as a particular form of conversation with one's self.  Anna sees this
communicative perspective on thinking as learning particular "forms of
discourse" which have developed historically and now children must learn
these particular discourse procedures through entering mathematical
conversations as forms of social interaction in order to learn to think

Andy, my understanding of Davydov and Gal'perin is that once  "systems of
discourse" have developed historically as "systems of meaning" it is far
more efficient to start from the very beginning to introduce the entire
system and not build up to the system perspective FROM the more concrete
procedures such as counting objects.  Therefore measurement [as
fundamentally relational] is prior to counting.

If I've got these basic premises of Anna's and Davydov's procedures
accurate, do you see these procedural approaches as complimentary or are
they challenging each others basic assumptions.   If they are pointing to
different procedures and assumptions of the best way to approach learning,
then definitely this is a topic to tease out assumptions about  fundamental
concepts of learning?

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*Andy Blunden*
Joint Editor MCA: http://www.informaworld.com/smpp/title~db=all~content=g932564744
Home Page: http://home.mira.net/~andy/
Book: http://www.brill.nl/default.aspx?partid=227&pid=34857
MIA: http://www.marxists.org

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