In reflecting on the earlier discussion of Jurow's article on generalizing
in interaction I come
away with a feeling of incompleteness. Maybe its ingendered by the fact that
appreciated the careful description of classroom practices and Jurow's
approach to understanding
generalizing as a consequence of changes of modes of participation and
communication, in particular
the patterns labelled "linking" and "conjecturing." Others seemed to be
looking for an analysis of generalization
as "rising to the concrete" a la Davydov and apparently did not take much
away from the Jurow approach.
Looking back at the article, the critical disjuncture (if I am correct) is
signaled on p. 281 where Jurow contrasts
her approach to development as formation of "decontextualized knowledge"
(her quotation marks) and generalization
as "the product of accurated mental representations.... and "an individual
cognitive activity performed to recognize
and acquire objective categories." (My quotes)
She substitutes instead a "situated or practice perspective, (from which)
abstracting is conceptualized not as "moving
away from" situations, but as a product of local practices." (her quotes and
I gather that Michael Roth and others which to substitute "rising to the
concrete" for "product of local practices."
I wonder if his is equivalent to a shift from the use of Vygotsky to
Davyodov. For example, Vygotsky (Collected works,
Vol 3, p. 138) writes
The law: the form of generalization corresponds to the form of
communication. "Communication and genralization
are internally connected. ....
Generalization. What is generalization? Generalization is the exclusion from
visual structures and the incusion in thought structures,
semantic structures. ....
Now if there were someone on XMCA interested in discourse theories of
mathematical thinking, who knows, we might get some
help with disentangling these issues. Are the approaches contradictory?
Complentary? Incoherent? Out of date? On the cusp
of the future?
I am unsure. By convention, I believe we are on the cusp of summer where I
live. I am going for a walk, summer style, to prepare
for those examinations and grant deadlines!
Unless there is more to be written, lets examine language and activity.
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