Commentary on Theories of Mathematics Education

<strong>Commentary</strong> on Theories of Mathematics Education: Is Plurality a Problem? 115
and/or the knower structure or none of those. If the epistemic relation dominates,
then “What matters is what you know, not who you are”, if the social one is emphasised
as a key to the field, then “What matters is not what you know, but who you
are”.
Theoretically, there are four different legitimation codes. The ‘knowledge code’
(i) emphasises the possession of specialised knowledge skills and techniques, and
not the characteristics of the knower. The ‘knower code’ (ii) foregrounds dispositions
of the knower, be it ‘natural’, cultivated or related to the social background.
The ‘classical intellectual’ in the humanities provides an example. When the ‘relativist
code’ (iii) operates in a field, the identity of the members is ostensibly neither
determined by specialised knowledge nor by dispositions, which amounts to a kind
of ‘anything goes’. In an ‘élite code’ (iv), the legitimate membership is based on
both possessing specialised knowledge and the right kinds of dispositions.
If the field of mathematics education reflects more the operation of a ‘relativist
code’ than of a ‘knowledge code’, the role of disciplinary knowledge for the academic
identity would be subject to continuous re-negotiation. Moore (2006) suggests
that in general the principles for legitimation in a field composed of discourses with
a weak grammar are social in nature:
In epistemological terms, weak grammar is associated with the conflation of knowledge
with knowing and the reduction of knowledge relations to the power relations between
groups. (p. 41)
It is then not the explanatory power of theories, but the approaches that are under
consideration in competing discourses, that is, who knows, rather than what is
known. Moore points to an early work of Bernstein (1977, p. 158), in which he states
that the danger of such ‘approach-paradigms’ is their tendency to amount to ‘witchhunting’
and ‘heresy-spotting’. Admittedly, such an analysis, if applied to the field
of mathematics education, looks like a somewhat extreme redescription. However,
both of the authors (and many others who report similar experiences) have experienced
review reports for submitted papers that judged the same paper as highly
recommendable for publication, worth publishing with some amendments and not
worth publishing at all. Journal editors might have an interesting collection of such
conflicting recommendations, but as Lerman points out, these cannot be subjected
to research for ethical reasons.
The initiation of young researchers into a field with an ‘approach-paradigm’
tends to be organised in a way that provokes the building of schools of thought,
in terms of shared intellectual roots and also geographically.
Unbalanced Theory Reception
Lerman desribes the field of mathematics education as a ‘region’, that is, it draws
from others and has a face towards practice. Regions draw on a range of specialised
delineated intellectual fields and create an interface between the fields of production
of knowledge and a field of practice (Bernstein 2000, pp. 9, 55). Mathematics