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parts of a pie or the parts of a surface in a diagram, but they constitute a lit-
THEORY-PRACTICE DIALOGUE
96

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tie "system of relations" that refers conceptually to the structure of a ref-
erential situation (cf. Steinbring, 1992). Mathematical symbols do not de-
note names, but display a system structure that relates variably to the
referent structure.
The epistemological dilemma in every mathematical communication of
the need to take symbolic carriers for the knowledge to be transported, and,
at the same time, to go beyond these concrete carriers, requires a dualistic
conception of mediating processes: In the classroom, mathematics teachers
have to present the learning situations for their students in specific contexts,
which can be shared in communication, and then, by means of generaliza-
tion, they must initiate a process of decontextualization that helps students
to subjectively reconstruct the meaning of the mathematical knowledge hid-
den in the context. Processes of decontextualization support the revelation
of underlying structural relations in the object that make it possible to de-
velop the conceptual relation between object and symbol in the epistemo-
logical triangle.
Fruitful dialogues between researchers and mathematics teachers also
need contextualized situations representing examples of the teacher's object
of professional activity to enable teachers and researchers to share a situa-
tion from which different decontextualizations can be created according to
the objectives of different professional domains. An example will be dis-
cussed in the following.
HEINZ STEINBRING
97
3. ASPECTS OF THE COMPLEX NATURE OF THEORETICAL
KNOWLEDGE IN SOCIAL PROCESSES
3.1 The Need for a Common Context
The implicit premise of much didactical research is to abstract all informa-
tion for practice from seemingly superfluous context-dependent aspects. In
return, this forces teachers to embed this abstract knowledge into their own
context of experience. This implies a fundamental separation between the
researcher's and the teacher's understanding of professional knowledge and
its meaning: Both refer this scientific information to different reference
contexts. Of course, there are necessary and even positive differences be-
tween the referential knowledge domains of the teacher and the researcher,
but the crucial point for a fruitful dialogue is not to take divergent contexts
of reference, but to look jointly at the same context of references, and de-
velop a basis for shared views without supposing there could be identical in-
terpretations in all aspects. Looking at the same context situation is a con-
necting element for different, contrasting, and complementary interpreta-
tions and applications of abstract, general professional knowledge.
The dialogue between theory and practice has to develop both levels. The
decontextualized knowledge and examples of contextualized referential sit-
uations for the abstract information cannot be conveyed directly. However,

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in this way, they open a framework for reconstructing the meaning of this
professional knowledge in relation to a common object of reference and in
agreement with the different experiences from the teacher's or the re-
searcher's professional activity.
Joint reading, interpretation, and analysis of lesson transcripts is an ex-
ample of discussing a common object of interest and developing a dialogue
between theory and practice (von Harten & Steinbring, 1991; Voigt, 1991).
[Lesson transcripts] are well suited because they take classroom reality seriously,
that is have teaching in its concrete form as their object, a fact which induces the