Commentary on Theories of Mathematics Education

<strong>Commentary</strong> on Networking of Theories—An Approach 509
It also distinguishes between strategies and methods of networking pointing out a
relevant difference:
A strategy is a set of general guidelines to design and support concrete actions in order to
reach a distinct goal. Whereas a strategy is something general and stable, tactics is more specific
and flexible. A battle can never be planned by strategies alone, since it involves many
actions with open results. These actions that must be decided in real time according to the
chosen strategy are then designed by special tactics. Similarly, the more general networking
strategies require specific methods to be developed for their concrete application.
Also this point is illustrated with illuminating examples taken from the special issue
of ZDM.
The final part of the paper discusses how theories can be developed, distinguishing
the different ways and directions this development can be pursued. For example
it points out the “spiral process” through which empirically grounded theories generally
develop and the “more . . . argumentative conections” that make “explicit the
philosophical base”, through which “prescriptive theories” (see Prediger 2004) develop.
More precisely, the authors discuss four directions into which theories can
develop:
– Explicitness
– Empirical scope
– Stability
– Connectivity
They observe that this last issue is deeply connected “with the question of how the
research community as a whole, with its manifold different theories, can develop
further” (ibid., p. 15), a crucial issue that is not answered by the paper, because of
its intrinsic difficulty.
Another relevant issue is pointed out by the authors in different parts of the paper,
namely that “communication of researchers is central for the networking of
theories” (ibid., p. 18). The same point is underlined by Radford:
Although it is not wrong to trace the origins of this problématique back to the need to deal
with the diversity of current theories in our field, it might be more accurate to trace it to the
rapid contemporary growth of forms of communication, increasing international scientific
cooperation and some local attenuations of political and economical barriers around the
world, a clear example being, of course, the European Community. (Radford 2008, p. 317)
The paper clearly pictures the state of the art in the Networking of Theories and summarises
nicely most of the content of the ZDM issue, where of course the interested
reader can find more details. Moreover its reading suggests some issues that could
be interesting research questions to face within the general stream of Networking of
Theories. They must be seen as suggestions for further research and not as critiques
to the paper, which is nice and interesting. I shall sketch them here even if they
are still at a rudimentary stage of elaboration: their deepening could be a relevant
progress towards suitable and robust “metatheories of theories” or “metatheories of
theoretical approaches”.
The first point of this critical exposition concerns complexity as a reason for the
diversity of theories: