Commentary on Theories of Mathematics Education

Theories of Mathematics Education: Is Plurality a Problem? 103
Fig. 1 Pedagogic modes
Theories in Use in Mathematics Education
In this section I will make some remarks drawn from a recent research project on the
use of theories in mathematics education. Briefly we (Tsatsaroni et al. 2003) examined
a systematic sample of the research publications of the mathematics education
research community between 1990 and 2001, using a tool that categorised research
in many ways. I will refer here to those parts of our research that concern how researchers
use theories in their work, as published in three sets of publications: the
Proceedings of the annual meetings of the International Group for the Psychology of
Mathematics Education (PME) and the two journals Educational Studies in Mathematics
and the Journal for Research in Mathematics Education. The expansion of
theories in use within the mathematics education research community as a whole is
almost entirely due to the social turn (Lerman 2000). The categories are made up as
follows:
1. cultural psychology, including work based on Vygotsky, activity theory, situated
cognition, communities of practice, social interactions, semiotic mediation
2. ethnomathematics
3. sociology, sociology of education, poststructuralism, hermeneutics, critical theory
4. discourse, to include psychoanalytic perspectives, social linguistics, semiotics.
These categories mirror those we presented in Lerman and Tsatsaroni (1998) (see
Fig. 1).
Drawing on Bernstein’s description of the turn from traditional performance pedagogy
to a liberal-progressive competence pedagogy in the late 1950s, we proposed
that this latter could be subdivided into: an individual cognitive focus, that is, Piagetian/reform/constructivism;
a social or cultural focus, for example ethnomathematics
(as in (2) above); and a critical focus, such as a Freirian approach (as in
(3) above). We also suggested that there is evidence of a linguistic turn, to include