Commentary on Theories of Mathematics Education

<strong>Commentary</strong> on Networking of Theories
—An Approach for Exploiting the Diversity
of Theoretical Approaches
Ferdinando Arzarello
Prelude The comments to the article of A. Bikner-Ahsbahs and S. Prediger are
divided in two parts. The first part underlines the innovative aspects of the idea of
networking theories which is summarised in that paper. The second part points out
some possible continuations of this research within a more general setting.
Networking of theories is a recent topic developed within the community of Mathematics
Education researchers. In fact it is well known that the research community
uses a variety of different and sometimes contrasting theories for framing and
designing their researches and this variety of approaches can create difficulties in
communication of their results, because of the difference of languages and the incommensurability
of the theoretical frames in use. This situation is unpleasant and
may create a sense of disease since it marks a strong difference with respect to the
paradigm of disciplines like mathematics. However the issue of having a shared
language that allows to compare and contrast different theories within Mathematics
Education is not an easy task for researchers because of objective difficulties that
one meets when aiming at unifying theory. The situation is very complex and a great
ingenuity is needed to overcome them in a substantial way.
The paper by A. Bikner-Ahsbahs and S. Prediger faces this issue; it grows up
from the discussions in the last meetings of CERME (Bosch 2006; Pitta-Pantazi and
Philippou 2007; Durand-Guerrier to appear), from the special issue of ZDM (Prediger
et al. 2008a) dedicated to “Comparing, Combining, Coordinating Networking
Strategies for connecting Theoretical Approaches”, and from the discussion of a research
group1 about Networking of Theories which met several times in these last
years.
The paper under examination is divided into four parts:
1. What are theories, and for what are they needed?
2. Diversity as a challenge, a resource, and a starting point for further development
1 The group consists of: Michèle Artigue, Ferdinando Arzarello, Angelika Bikner-Ahsbahs, Marianna
Bosch, Tommy Dreyfus, Stefan Halverscheid, Agnès Lenfant, Ivy Kidron, Susanne Prediger,
Kenneth Ruthven and Cristina Sabena.
F. Arzarello ()
Dipartimento di Matematica, Università di Torino, Torino, Italy
e-mail: ferdinando.arzarello@unito.it
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_47, © Springer-Verlag Berlin Heidelberg 2010
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