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observer, who develops the split between observing and observed subject
into a dialogical relation. The first concerns radical realizations of action-
research projects, which consider innovation as an ideological value and
reject the development of progressive knowledge of classroom processes; as
they are ideologically atheoretical, I have not considered them in this paper.
The second is realized, for instance, by theoretical research programs such
as the core of RDM; they share some methodological aspects with classical
natural sciences and with experimental psychology in laboratory settings.
The third is realized by RI, which aims at turning into reality some
examples of anticipated classroom processes. The responsibility for choices
is shared by a larger group that comprises at least researchers and teachers
(it could also include administrators, parent representatives etc.). It is
important to distinguish between action-research projects, in which action is
a value and an end in itself (Model 1), from innovative projects (Model 3),
in which action is both a means and a result of progressive knowledge of
classroom processes. The core of RDM and the core of RI address different
problems, answer different questions, and refer to different models of
enquiring activity.
The human need to turn theoretical elaborations into reality is represented
in the French community by so-called didactical engineering (Artigue, this
volume). It shares some features with RI: for instance, the attention paid to
long-term processes. Yet they cannot be confused. The teacher's role in the
development of research acts as a litmus paper. In didactical engineering,
the split between the time of designing/analyzing (which occurs outside the
classroom, maybe with the participation of teachers, too) and the time of
acting (when teachers are observed by detached observers) seems radical; in
innovative research, teachers, as full members of the research team, are
allowed to take part in the observation of their own classroom as participant
observers (Eisenhart, 1988) and to make decisions even in the course of
action (Davis, 1992; Steffe, 1991). In other words, didactical engineering
derives from RDM, and shares the same model of enquiring activity. It is
MARIA G. BARTOLINI BUSSI
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possible and even desirable to try to coordinate results with RI, but it is
necessary to first take into account the basic difference of perspectives.
3. INSIDE FRAMEWORKS: CONSTRUCTIVISM VERSUS
ACTIVITY THEORY OR PIAGET VERSUS VYGOTSKY
3.1 Foundation Aspects
In every research project, some basic assumptions about learning are sup-
posed to be shared by the research team, even when they are not stated ex-
plicitly. In the following, I shall sketch some contrasting issues from two
major perspectives on the role of social interaction in the process of learn-
ing: constructivism, in its more or less radical forms, and activity theory.
The former refers to Piaget and the latter to Vygotsky, so that a distinction
could be made between Piagetian and Vygotskyan frameworks. The above
distinction, like every radical "either-or" classification, does not give full
justice to the complex reality of research. For instance, the so-called Geneva
school (e.g., Perret-Clermont, 1980) tries to coordinate Piaget and
Vygotsky; the ethnomethodological perspective is introduced into radical
constructivism to study the culture of mathematics classrooms (e.g.,
Bauersfeld, 1988). Besides, connectionist models of the human mind have
entered the scene, even if their appearance is too recent to judge their rele-
vance for and influence on didactical research (a meaningful exception is
reported in Bauersfeld, this volume). Because of this complexity, I shall
adopt the previous distinction, in spite of its limits, to keep the discussion at
the level of the large community of mathematics educators.
The most important difference between Piagetian and Vygotskyan ap-
proaches concerns just foundation aspects and is still the same difference
that divided Piaget and Vygotsky in the 1930s. Constructivism considers
learning as the result of two inseparable complementary processes of inter-
action between the individual and the environment: assimilation, that is, the
process of integration of either new objects or situations into the existing
individual schemes; and accomodation, that is, the individual effort to adjust
schemes to the environment (Piaget, 1936). Activity theory is centred upon