Commentary on Theories of Mathematics Education

552 U. Gellert
It is interesting though challenging to search for metaphors that promote our understanding
of the mechanisms and effects involved in the networking of theories.
The term “networking” itself has metaphorical character, of course, and Helga Jungwirth
offers another metaphor in her contribution. She argues for different layers on
which situations and practices could be investigated. Layers could be classified according
to their location in time and space and their degree of institutionalization.
There seems to be a linear order of layers that allows one to speak of “neighboring
layers” and layers close enough to each other—although there might be some
dispute over what counts as the top and the bottom layer. Such a scale provides the
basis for claiming that the networking of theories requires closeness of layers. The
notion of different dimensions can be considered another attempt to cover the complexity
of situations and practices. In contrast to the layer-metaphor, it does not give
access to a similar criterion for a fruitful networking of theories, because “closeness
of dimensions” would be at odds with the metaphorical grounds of the very concept
of dimension. However, the metaphor of dimension is more open to complementary,
or even conflicting, accounts for situations and practices than the layer-metaphor. Is
the need for networking theoretical approaches starting on the grounds of harmony
or of conflict?
Helga Jungwirth’s contribution argues in favor of a harmonic co-existence of
different theories in theory networking. She calls the concordance of the socially
established basic understanding of (a section of) reality a fundamental criterion for
compatibility of theories, because otherwise the set of basic concepts of research
runs the risk of becoming contradictory and, thus, would be useless for data analysis
and theory development. This is evident, for instance, where research connects
concepts of partly incompatible theories without sufficient adaptation (like naïvely
juxtaposing Piaget’s developmental stages and Vygotsky’s zone of proximal development).
In fact, the problem is located in the missing adaptation of perspectives
rather than in their incompatibility. Helga Jungwirth draws on Ulich’s (1976) distinction
of “stability-oriented” paradigms and “transformation-oriented” paradigms
as examples for incompatible positions, though this polarization of social understanding
is (meanwhile) not always helpful to describe researchers’ approaches and
interests. Even classical structuralist (thus “stability-oriented”) studies do not take
social actors as passive role players shaped exclusively by structural forces beyond
their control. Anyon’s (1981) well-known analysis of social class and school knowledge
is an example in case, here: Although the mechanisms of reproduction of unequal
class structures can be traced through many layers of school reality (school
location, school building, school facilities, education and formation of staff, school
norms, curricular approach to knowledge, teaching methods, assessment modalities,
...)therearealwaysseeds for resistance and social transformation. Bourne’s (2003)
Bernsteinean distinction between horizontal and vertical knowledge and its relation
to class codes goes beyond a stability-oriented description of class codes and educational
disadvantage. It investigates the potential of the conceptual distinction for
a change of teaching practices in disadvantaged school settings, aiming at a transformation
of students’ social positions. In simple terms: Social transformation is
unlikely to be enacted when the stable social structures are neglected.