Commentary on Theories of Mathematics Education

On Networking Strategies and Theories’ Compatibility 523
and empirical work in that research project. Analysis itself is considered to be a
way to obtain a theory; a view, that, for instance, has been taken by the authors of
grounded theory already several years ago (Glaser 1978; Glaser and Strauss 1967;
Strauss 1987).
I want to underpin that position by an argument that is about the nature of findings.
Are findings depictions of (selected) parts of the reality (of concrete, observed
computer-based classrooms in my case), or are they theoretical reconstructions that
have left those parts of reality behind? Bikner-Ahsbahs (2002) has already pondered
over that question and elaborated a solution by drawing upon Max Weber (1985) and
his concept of ideal types and, in particular, to Alfred Schütz (1981) and his reflections
about sense-making in the life-world (cf. Schütz and Luckmann 1973, too). As
a consequence of those considerations, research findings are idealizations that do not
describe real phenomena. A reference to the modes of sense-making worked out by
Schütz can make that position plausible. The first mode can be thought of as understanding
a situation “live” within its experience together with fellows whose actual
subjective motives, interests, a.s.o., are paid attention to. The argument, however, is
based on the second one. This mode is about integrating interpretations of former
experiences. It takes place as a synthesis of recognition in which, for lack of an
actual focus on concrete, ongoing processes showing the whole richness, and variability,
of real life phenomena, certain former, experienced states of them are taken
as their absolute qualities. That is, “ideal” types of persons, actions, situations, . . .
are created. Accordingly, an ideal type is never identical with concrete samples; it
never describes them. Apart from being necessary for orientation in patterned contexts
which need “typical” actions, behaviours, or readings, members of society can
always switch into that mode of sense-making, as Schütz demonstrates by his card
player example. Card players can raise attention as specific persons playing cards,
having their subjective motives for their doing and their specific versions of acting
in the situation, or as card players “as such”; that is, as ideal types of some sort of
persons without any subjective meanings of the matter, just realizing the objective,
socially shared meaning of a card game.
For my concern here it is important to note that even in everyday life such a
development of ideal types takes place. There is sense-making as a mere reconstruction
of thought which is fundamentally different from understanding a situation
within its co-experience with fellows. Persons doing research are never in the
latter mode. They are always in the state of a member of society in everyday life that
realizes card players as ideal figures (even if researchers are interested in subjective
meanings they do not address them under the aspect of idiosyncratic expressions).
Accordingly, research findings as well are ideal versions of real phenomena. What
makes a difference to those in our everyday social world is the systematic, and
controlled way of their development. However, ideal types are not yet theories, as
Bikner-Ahsbahs has already argued. But they are reconstructions that exist on the
same level and can be used for theory development. Unfortunately, yet not mysteriously,
language does not indicate their theoretical nature; the same words are used
to denote the different stages of concreteness in which objects can appear.
As an overall consequence, co-ordination of theories in an analysis of data is a
synthesis of theories as well because all interpretations of the data are ideal in their