Commentary on Theories of Mathematics Education

522 H. Jungwirth
that makes them interested in different yet related aspects of that reality: meaning
and its negotiation in interaction, and methods to establish a “given” reality, however
interactively that may happen. The relationship of these theories has made me put
them together in one micro-sociological approach. This approach, on the one side,
and linguistic activity theory, on the other side, play rather complementary roles.
Each of them provides perspectives that are not covered by the other one but are
needed to form a better whole: on situational adjustment and formation, on the one
hand, and on certain aspects of structure and overall sense, on the other hand.
Combining both views makes me develop a notion of computer-based (mathematics)
teaching that meets the demands of the research project for a focus on microprocesses,
and on distinguishable, comparable entities. Computer-based classrooms
can be characterized by predominating activities and objectives that are put into
effect. These features give evidence of certain activity complexes that are the outcome
of multitudes of similar negotiations among participants. Different types of
computer-based (mathematics) teaching can be assumed to be established, ranging
from a highly verbal teaching emphasizing subject matter aspects to a teaching that
is totally devoted to carrying out manipulations at a computer. This notion can be
seen as a nucleus of a theory of computer-based (mathematics) teaching.
As for the strategies of networking, that combination of theories can be called,
in the terms of Bikner-Ahsbahs and Prediger, a sort of synthesizing. The microsociological
framework and linguistic activity theory have been connected for the
sake of a new conceptualization of a certain, small section of reality. A theoretical
approach has been developed that goes beyond the understanding provided by the
initial theories. Through the micro-sociological theories the formation of an activity
complex becomes visible, and through linguistic activity theory a multitude of interactions
can be spoken of and treated as an entity. Synthesizing as a process is put
into effect by such a “double movement”.
In order to serve its purpose within the research project that nucleus of a theory
of computer-based (mathematics) teaching has to be applied to the data. The project
wants to give insight into the similarities and differences of computer-based mathematics
and physics teaching in regard to the research question. Such a concern to
understand empirical phenomena is typical for a strategy of networking called “coordination”.
Thus, the basic theories are also co-ordinated. Their connection serves
the purpose to reconstruct concrete computer-based (mathematics) teaching. Empirical
phenomena are interpreted in its light.
Synthesizing and Co-ordinating: Two Sides of One Coin
in Grounded Theory Development
However, those two strategies are not just used one after another; they are two
sides of one coin. Synthesizing has involved co-ordination because the very development
of the connected theory has taken place with the use of data. This reflects
an important facet of the basic understanding of the relationship of theory