Commentary on Theories of Mathematics Education

114 E. Jablonka and C. Bergsten
The Social Turn or the Social Branch?
Lerman identifies several strands of research within mathematics education that focus
on language and social practice as the origin of consciousness, behaviour and
learning. These are theories of situated cognition, social practice theory, and research
related to communities of practice, Vygotskian theories and research drawing
on sociology. He observes a ‘social turn’ in mathematics education in the period
from 1996 to 2001. It is not so much the number of papers but the widening of the
range of theories employed that account for the trend. In some periodic publications,
the papers employing ‘Traditional psychological and mathematics theories’
remained constant or even increased in the period from 1990–2001 (in PME and in
JRME).
Given the horizontal knowledge structure of the field of mathematics education,
one wonders whether the addition of new theoretical bases (other than individual
cognitive psychology) can be analysed as a social turn. The sub-fields of mathematics
education might as well grow in parallel and eventually constitute their own
discourses, without one dominating or privileged.
The study by Tsatsaroni et al. (2003), on which Lerman draws, is now some years
old and it is not evident what an updated similar investigation would show. A quick
look at the most recent issues of ESM and JRME, certainly too small in quantity
to justify any conclusions, does not indicate a continuation of the trend pointed out
in 2003, in terms of a social turn in mathematics education research. A systematic
investigation of the PME proceedings shows an oscillating pattern between 1990
and 2005 (see the data provided in Lerman 2006).
A Plurality of Rival Discourses Within an ‘Approach-Paradigm’?
Mathematics education as a pluralised field in its present form, can also be seen
as a series of rival sub-areas with little dialogue. Such a description draws attention
to the relation between knowledge structures and the ways in which a hierarchy
between the ones who posses the knowledge is formed, if there is any. Maton
(2006) describes ‘the humanities’, in his interpretation of the two-culture debate (cf.
Snow 1959), as a field with a horizontal knowledge structure but with a hierarchical
‘knower structure’. The ‘scientific culture’, on the other hand, is characterised by a
hierarchical knowledge structure but with a horizontal knower structure. Maton sees
in the two-culture debate a struggle for control over epistemological modes between
fields characterised by contrasting rules and measures of achievement. He assumes
that the knower structures in a field are created by systematic principles that arrange
actors and discourses, and he includes this dimension into an analysis of knowledge
formation. These principles are conceptualised as ‘legitimation codes’ in terms of
the relation between the actors, who are positioned in a distinct formation of knower
and knowledge structure, and how they relate to these two structures (Maton 2006,
p. 49 sqq.). He distinguishes an epistemic from a social relation. The actors in a field,
as a basis for its distinctiveness and status, may emphasise the knowledge structure