Commentary on Theories of Mathematics Education

16 B. Sriraman and L. English
proven their utility in their respective fields. There are ample reasoned arguments and supporting
evidence for them. (p. 196)
The need to draw upon the most applicable and worthwhile features of multiple
paradigms has been emphasized by numerous researchers in recent years. We
are now witnessing considerable diversity in the theories that draw upon several
domains including cognitive science, sociology, anthropology, philosophy, and neuroscience.
Such diversity is not surprising given the increasing complexity in the
teaching and learning processes and contexts in mathematics.
Are theories in mathematics education being reiterated or are they being reconceptualized
(Alexander and Winne 2006), that is, are we just “borrowing” theories
from other disciplines and from the past, or are we adapting these theories to suit
the particular features and needs of mathematics education? A further question—are
we making inroads in creating our own, unique theories of mathematics education.
Indeed, should we be focusing on the development of a “grand theory” for our discipline,
one that defines mathematics education as a field—one that would give us
autonomy and identity (Assude et al. 2008)?
Over a decade ago, King and McLeod (1999) emphasized that as our discipline
matures, it will need to travel along an independent path not a path determined
by others. Cobb (2007) discusses “incommensurability” in theoretical perspectives
and refers to Guerra (1998) who used the implicit metaphor of theoretical developments
as a “relentless march of progress.” The other metaphor is that of “potential
redemption.” Cobb thus gives an alternate metaphor, that of “co-existence and conflict”,
namely “The tension between the march of progress and potential redemption
narratives indicates the relevance of this metaphor.” (Cobb 2007, p.31)
Home-Grown Theories versus Interdisciplinary Views
We now discuss the issue of “borrowing” theories from other disciplines rather
than developing our own “home-grown” theories in mathematics education (Steiner
1985; Kilpatrick 1981; Sanders 1981). We agree with Steiner (1985) that Kilpatrick’s
and Sanders’ claims that we need more “home-grown” theories would
place us in “danger of inadequate restrictions if one insisted in mathematics education
on the use of home-grown theories” (p. 13). We would argue for theory
building for mathematics education that draws upon pertinent components of other
disciplines. In Steiner’s (1985) words:
The nature of the subject [mathematics education] and its problems ask for interdisciplinary
approaches and it would be wrong not to make meaningful use of the knowledge that other
disciplines have already produced about specific aspects of those problems or would be able
to contribute in an interdisciplinary cooperation. (p. 13)
Actually interdisciplinary does not primarily mean borrowing ready-made theories from the
outside and adapting them to the condition of the mathematical school subject. There exist
much deeper interrelations between disciplines. (p. 13)
Mathematics education has not sufficiently reflected and practiced these indicated relations
between disciplines. Rather than restricting its search for theoretical foundations to home-