Commentary on Theories of Mathematics Education

520 H. Jungwirth
of activity theory. So it was clear almost right from the beginning that theories had
to be connected. The combined approach was induced by that double perspective
on classroom processes being required by the overall research question. But before
I address that networking I want to sketch the theories used for it.
Theories
Micro-sociological Frameworks
A micro-sociological perspective on mathematics teaching and learning has already
proven fruitful in a variety of studies. To be more precise, the attribute refers to
different theories that share a basic understanding of reality. Accordingly, social reality
is always a reality in the making, and theories try to reconstruct the members’
of society ways of settling their affairs and experiencing them as meaningful. Those
theories figuring in the project are symbolic interactionism (Blumer 1969) and ethnomethodology
(Garfinkel 1967). Despite of their differences they are, because of
that shared assumption and, as a consequence, because of their related roles in my
research, regarded here as a theoretical framework of one kind.
According to symbolic interactionism, interaction is the key concept to grasp social
reality. Within interaction objects (anything that can be pointed, or referred to)
get their meanings, and meanings are crucial for people’s acting towards objects
and, in that, for establishing reality. Interaction is thought of as an emergent process
evolving between participants in the course of their interpretation-based, mutually
related enactment. Thus, social roles, content issues, or participants’ motives as well
are not seen as decisive factors; rather, they are also objects that undergo a development
of their meaning. Consequently, neither the course of an interaction nor its
outcome is predetermined. Furthermore, the term “interaction” is not restricted to
events having specific qualities in respect to number of participants, topics, kinds
of exchanges a.s.o. For my concern, symbolic interactionism is conducive to taking
everyday classroom processes seriously however inconspicuous they are. From this
point of view teaching is always a local affair. That theory enables me to focus on
the meanings objects get in classroom interaction, and on the development of those
negotiations by all persons involved; students are considered to be equally important
as the teacher.
Ethnomethodology, too assumes that social reality is made into reality in the
course of action but addresses a different issue. It is interested in the methods the
members of society use to settle their affairs. Those methods are thought of as reflexive
procedures. They are not just ways to get things done but, moreover, accounting
practices that make procedures commonplace procedures. For instance, Sacks
(1974) works out the way in which a joke is established and by that made a joke
by the joke-teller and the audience. Thus, ethnomethodology elucidates the fact that
despite of its formation social reality is taken as a given reality. Within the research
project this theory helps in taking into account the methods by which teachers and