Commentary on Theories of Mathematics Education

<strong>Commentary</strong> on Modalities of a Local
Integration of Theories in Mathematics
Education
Tine Wedege
Connecting theories is an activity in the practice of many mathematics education researchers.
Broadly speaking the theories—or theoretical perspectives—being connected
come from within the field of mathematics education (“home-brewed” theories)
or from outside (psychological, sociological, anthropological; philosophical,
linguistic etc. theories), and they come from the same discipline or from different
disciplines. As a consequence the researcher needs methods and strategies for
connecting theories. Prediger et al. (2008) have taken the “first steps towards a
conceptual framework” with a terminology—or a meta-language—for dealing with
this issue. The terminology, which is based on the work in the Theory Working
Group of CERME, presents strategies for connecting theories as pairs of strategies
(understanding others/making understandable; contrasting/comparing; coordinating/combining;
synthesizing/integrating locally) within a scale of degree of integration
from “ignoring other theories” to “unifying globally”.
In his chapter, “Modalities of a Local Integration of Theories in Mathematics
Education”, Uwe Gellert integrates a semiotic home-brewed theory (Ernest) with a
structuralist sociological theory (Bernstein) in the analysis of a piece of data from a
5 th grade mathematics classroom. He presents the integration as an example of local
theory development as a self-evident constituent of empirical research. The analytical
challenge in this case is the conflict between explicitness and implicitness in
a teacher’s instructional practice, which is confronted by bringing the two theories
together. But first, he examines the notion of “bricolage” as a strategy for coordinating
theories in mathematics education research. This is done with a reference back
to its origin in anthropology where Lévi-Strauss (1962) introduced the “bricoleur”
(handyman) as opposed to the professional. From there, Gellert argues that bricolage
as a way of theorising (Cobb 2007) prevents the researcher from her/his scientific
responsibility and the research from principled evaluation. On the one hand, his presentation
of the engineer, who pictures the professional in Lévi-Strauss’s work, as a
technician with appropriate and targeted tools, leads me to Schön’s (1983) critique
of the dominant technical rationality model of professional knowledge and to his
concept of reflective practitioner. On the other hand, Gellert’s reflections—in and
T. Wedege ()
School of Teacher Education, Malmö University, Malmö, Sweden
e-mail: tine.wedege@mah.se
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_52, © Springer-Verlag Berlin Heidelberg 2010
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