Ana.
Thanks for your clarification of my point.
(I don't think I could have done it as well.)
Perhaps it will help the conversation if I describe
a bit about "where I'm coming from" in my original
response to Mike's math learning example.
I've been working of late on establishing a more
pragmatic relationship between theories of learning
and recommendations for pedagogy. My central motivation
comes from my perception that there are distinct
metaphors of learning guiding diverse research projects;
however, the imperative to provide comprehensive explanation
of learning (characteristic of research in preparadigmatic
disciplines, Kuhn, 1970) leads theorists of all stripes to
adopt aspects of each others theories, thereby blurring
the initially distinctive character of each endeavor. The
world of practice is thereby misdirected to conceive of learning
as a unitary construct, with the result that efforts to
reform teaching are written in terms of a unitary reform vision
(cf., the Learning Principle of the NCTM's, 2000, new Standards).
My goal is to recover the diverse visions of learning that
ground our research endeavors and inform our culture's common
sense about learning. The purpose is to be able to articulate
pedagogical guidance toward diverse notions of learning in a way
that is hard-edged and specific in contrast with the diffuse
and convoluted guidance that has come about from trying to address
all forms of learning in a single teaching approach. This leaves the
problem of integrating diverse learning objectives to the teacher.
This may seem unfair; but I don't think we help by pretending to
be able to deliver more than what we've actually established in
our theorizing. (These ideas are elaborated in an article coming
out in the next few days in the January/February issue of Journal
for Research in Mathematics Education.)
So, back to the issue at hand.
I take Conceptual Construction (the learning that comes from
reflective abstraction on one's actions in the world) as a
basic metaphor for learning. The constructivist pedagogy I
outlined in my last post is derived in part from broad
epistemological principles as articulated by Piaget, and especially
by constructivist theorists in mathematics education following
Piaget, and in part from the methodology of the "constructivist
teaching experiment" used by constructivist researchers to
develop theories of students' conceptual structures in mathematics.
(Yes, Mike is right that such methods apply most directly to
working with one or two students, rather than with a whole class,
but that's a conversation for another time.)
A second basic metaphor for learning in my framework is enculturation.
In keeping with Ana's comments, below, I too see sociocultural theory
as broadly concerned with enculturation in a way that Piaget never was.
But Vygotsky's interests obviously extended beyond just this single
metaphor as is evident in his discussions of scientific concepts.
Still some sociocultural notions such as Leontev's "appropriation"
do seem to be clearly related to elaborating processes of enculturation.
So my reference to Vygotsky was not directly referencing Vygotsky's
own writing (obviously a mistake in the current context--sorry),
so much as the current sociocultural literature.
My understanding of the zoped, limited as it is, is that learning
involves social relations, language, cultural tools, not just
instrumentally (as for Piaget), but as an essential aspect of
what is learned. It is this aspect of learning that I sought
in the fragment Mike sent about learning/teaching of arithmetic.
My comment was not meant to imply that Vygotskyan theory doesn't
include constructs that could be used to explain this learning/teaching
interaction. Rather I was saying that the distinctively sociocultural
emphasis on sociality and cultural mediation didn't seem to be
necessary for the analysis--i.e., Piaget would suffice.
Thanks for many interesting responses.
David
______________________
To: xmca@weber.ucsd.edu
cc:
bcc: David H Kirshner/dkirsh/LSU
Subject: Two different paradigms (formerly: complexi discussion)
Ana Marjanovic Shane <anashane@speakeasy.net>
02/10/2002 05:45 PM EST
Please respond to xmca <font size=-1></font>
Mike you said:
Both LSV and Piaget are, I believe, constructivists. The issues revolve
>around the organization of the constructive process and the role of others
>(teachers) in it. Coming to Piaget from the cross-cultural literature as
>I did, I was always impressed at his distrust of schooling as a source
>of development because accomodation so dominated assimilation, blocking
>equilibration, but David is suggesting a quite different form of
>educative activity (not to be found in many classrooms at 1:30 ratios
>I am afraid) where getting a delicate balance of accommodation and
>assimilation is the goal of the teacher (my case was taken from
>afterschool, one-on-one activity).
Of course, both PGT and LSV were constructivists. But in looking at the
processes of learning and development they constructed different
figure/background images. Piaget compared different successive actions of
the individual alone as a figure against the background of social
interaction. It's not that social interaction and culture are not
influencing the activities of cognitive construction - they are, but Piaget
wanted to abstract the laws of cognitive construction and elevate them
above the "social interaction noise". On the other hand, Vygotsky's notion
of social mediation creates a theory with different
figure/background picture. The work of the individual here is not just a
Piagetian "cognitive construction", but an interaction between "congnitive
construction" and making sense of the concepts as presented in culturally
supplied symbols and tools; i.e. interpretative activity is part of the
cognitive construction. That is why Piaget's notions of
accomodation/assimilation cannot be fully compared to the cognitive
activity described by LSV.
I think that there is no smooth transition between PGT and LSV positions,
that it is not just a matter of degree of the importance of social/cultural
elements. I think the two positions are paradigmatically different. The
notion of social/cultural mediation cannot be just patched onto the notions
of assimilation/accomodation.
Ana
_____________________
David Kirshner
Department of Curriculum & Instruction
Louisiana State University
Baton Rouge LA 70803-4728
(225) 578-2332 (225) 578-9135 (fax)
dkirsh@lsu.edu
http://www.ednet.lsu.edu/tango3/coedirectory.taf?
_function=detail&Faculty_uid1=135&Users_uid2=135&_UserReference=59F4B47FBE3415E138CD68B2
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