Commentary on Theories of Mathematics Education

508 F. Arzarello
3. Strategies for connecting theories—describing a landscape
4. Developing theories by networking
Already from its introduction the authors’ stream of thought is clear: they stress that
the diversity of theories must be considered as a resource and not as an handicap
and develop the different chapters of the paper with the precise aim of illustrating
this point.
First they point out the different causes of this diversity in Mathematics Education;
specifically they comment the following issues:
– the different epistemological perspectives that define the status of mathematical
knowledge;
– the different research paradigms in mathematics education;
– the cultural and institutional differences that frame empirical research in mathematics
education;
– the high complexity of the topic of the research.
Second, they elaborate the claim of the diversity as a richness showing that such a
diversity of theoretical approaches is a useful challenge for communication and integration
among theories and that it can push them towards a scientific progress. The
claim makes sense not only because there is a diversity of theories but also because
“different approaches and traditions come into interaction”. They conclude that it
is useful to search for connecting strategies among the different theoretical frames.
The authors point out that such a goal can affiliate the development of research in
Mathematics education at least in three ways:
– developing empirical studies which allow connecting theoretical approaches in
order to gain an increasing explanatory, descriptive, or prescriptive power;
– developing theories into parts of connected theory ensembles in order to reduce
the number of theories as much as possible (but not more!) and to clarify the
theories’ strength and weaknesses;
– establishing a discourse on theory development, on theories and their quality
especially for research in mathematics education that is also open to metatheoretical
and methodological considerations.
The core of the paper consists of the description of different strategies that can be
used for connecting different theories. The authors describe a landscape (taken from
Prediger et al. 2008b), which pictures different degrees of theory integration within
a line, which has two opposite extremes: the “ignoring the other theories” level and
the “unifying globally the different theories” level. The paper discusses with great
details the different categories of networking, using the papers of the ZDM special
issue and of this volume for making concrete examples that illustrate the nature of
such categories:
– Understanding others and making own theories understandable
– Comparing and contrasting
– Coordinating and combining
– Synthesizing and integrating