Commentary on Theories of Mathematics Education

104 S. Lerman
social linguistics, critical discourse analysis and psychoanalytical approaches (as in
(4) above), and, further, an emerging new performance model, quite different from
the traditional, based on Vygotskian theories (as in (1) above). If indeed there is a
new performance model, we must be conscious of the dangers of the accountability
regime in many Western countries. Focusing on performance can be misinterpreted
and draw us back into old performance models. This framework formed the basis
of our discourse analytic tool (see Tsatsaroni et al. 2003), and these latter four
constitute the four sub-sections of what I have called socio-cultural theories in the
analysis. Of course further fragmentation of theories into sub-sections would, in
some sense, give us a finer-grained analysis but would also lose both the theoretical
rationale provided here and also the possibility of being able to identify trends over
time.
First, I must identify some caveats. For obvious ethical reasons we were unable
to examine those publications that were rejected. Clearly the gate-keeping procedures
of reviewers and editors of journals, as well as grant committees, doctoral
examiners and others, have profound effects on the development of research directions,
methodologies and other features of the research productions of a community,
but it is just these trends and not what has not been enabled to happen, that had to
be the focus of our study. We wished to be able to say something about the current
state of our research community; we would have liked to supplement this with
a study of how what we described had come about, which would have called for
an examination of what does not get accepted as research, but partly by reason of
time but most importantly for ethical and practical reasons of not being able to gain
access to that information, we limited the study to published research texts. Regarding
PME specifically, the group changed its constitution in 2005 to value equally
with psychology other theoretical fields as the background orientation to research
reports. Indeed prior to and including 2005 reviewers were told by the International
Committee to ensure that the ‘P’ of psychology was present in any research report
to be reviewed. This orientation is reflected in the analysis for PME of course, and
it remains an interesting question for research what will happen to the theoretical
orientations of PME reports from 2006 onwards.
I will discuss here a few of our conclusions, as they relate to the proliferation
of theories in mathematics education research. I have included just one of our data
tables here (see Table 1 below) though I will mention some of the findings that
are not represented in the table. Further analysis of our findings can be found in
Tsatsaroni et al. (2003).
Our analysis showed that 70.1% of all articles in ESM have an orientation towards
the empirical, with a further 8.5% moving from the theoretical to the empirical,
and 21.5% presenting theoretical papers. Most of the papers used theory
(92.7%), and more than four-fifths (86.4%) were explicit about the theories they
were using in the research reported in the article. Similarly, 86.2% of all articles
in the journal JRME had an orientation towards the empirical, with a further 2.2%
moving from the theoretical to the empirical, and 11.6% presenting theoretical papers.
Most of the papers used theory (83.3%), with a relatively higher percentage of
papers that did not use any theory, compared to the other two journals considered