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Bog'liq
1994 Book DidacticsOfMathematicsAsAScien

constructiviste. Ecoles russe et occidentale. Even if contributions are lim-
ited to researchers from French-speaking countries (Western school) and
from the Moscow Institute for Psychology and Pedagogy (Russian school),
the book is very stimulating. The same position on social interaction as a
founding element of individual development is shared, by means of direct
derivation from Vygotsky, as regards the Russian researchers, and by means
of the Geneva school, as regards Western researchers. Apart from that, the
two schools have developed in relative isolation from each other.
Differences are relevant: For instance, when problem-solving is concerned,
the starting point is given, on the one side, by a general model proposed by
the teacher to solve a general class of problems (Moscow school) and, on
the other side, by a collection of students' early conceptualizations to be
modeled (Western school). In the former case, group work itself is often
structured on the basis of the analysis of the item of knowledge. In the latter
case, group work is often organized to provoke cognitive conflicts between
learners. The purposes are different: internalization of interpsychological
activity as such versus restructuring of early conceptualizations. I do not
wish to assume personal responsibility for criticizing the development of the
Vygotskyan school in Russia on the basis of the very scarce documents
available to a Western researcher. Yet, according to Engestrom (1991), con-
crete research and experimentation inspired by activity theory has been
strongly dominated by the paradigm of internalization with a scarce em-
phasis on the individual's creation, which was carefully studied by
Vygotsky in The Psychology of Art. According to Davydov (1991), who
was a student and a colleague of Vygotsky, the very difference between
individual and collective activity is still an unsolved problem of activity
theory.
3.3 The Problem of Choice
As I have argued above, there was a parallel destiny for Piagetian- and
Vygotskyan-oriented research. With the relevant exception of the Geneva
school, which is nevertheless engaged in psychological and not in didactical
research (e.g., more attention has been focused on peer interaction than
teacher-learner interaction), both seem to have led to extreme consequences
for the individual and the social foundation. Later, because of the establish-
ment of two competing schools with rigid membership to be defended, the
APPROACHES TO CLASSROOM INTERACTION
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127
reference to some radical slogans seems to have substituted the reference to
the original papers. So, which framework to choose?
The problem does not seem so dramatic, in a sense, in theoretical re-
search. As often happens in the development of science, the selection of
"narrow" pieces of reality to be modeled can solve the problem of both ac-
ceptable modeling and theoretical coherence: "Narrowness" could result, in
turn, in a limitation of either the number of subjects involved, the duration
of observation, or the items of knowledge. A good example is the theory of
didactical situations (Brousseau, 1986), which is successful for microdidac-
tical studies, in which a given item of knowledge and a given problem sit-
uation is considered; the teacher has paid a price, but recent developments
are going to fill the gap (Margolinas, 1992).
The situation is different in innovation projects in which the impact with
complex reality is strong and unavoidable from the very beginning. No co-
herent theoretical framework is supposed to be sufficient to manage such
complexity as a whole.
I can give an example by referring to the Mathematical Discussion in

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