Commentary on Theories of Mathematics Education

Preface to Part XV
Tommy Dreyfus
As this book makes amply clear, theory is are a crucial ingredient in any research
study in mathematics education. One role of theory is to give the research study a
framework within which data can be interpreted and arguments leading from the interpreted
data to conclusions can be set forth. Without a theoretical framework, the
interpretation of data is becomes arbitrary and arguments may become difficult to
both, make and follow. While we may occasionally see research reports without an
explicit theoretical framework, this is not an indication that no such framework was
used, though it may be an indication that the authors were not aware that they were
using a framework implicitly, a framework that thus remained hidden not only from
the readers but even form the researchers themselves. The necessity of theoretical
frameworks has long been recognized by the research community. Therefore most
research journals require any submission to have a clear and explicitly specified
theoretical framework. Educational Studies in Mathematics, for example, explicitly
requires this in its advice for prospective authors (ESM 2009): The journal seeks
to publish articles that are clearly educational studies in mathematics, make original
and substantial contributions to the field, are accessible and interesting to an
international and diverse readership, provide a well founded and cogently argued
analysis on the basis of an explicit theoretical and methodological framework, and
take appropriate account of the previous scholarly work on the addressed issues.
In accord with requirements such as this and similar ones by other journals, many
researchers and research groups have developed theories that suit their purposes; this
has not only led to a diversity of theories, but also to a diversity of what is being considered
‘theory’, and a diversity of ways of constructing theories. As a consequence,
a large number of theories with a wide array of characteristics exist and are being
used, more global ones like the Theory of Didactic Situations (TDS; Brousseau
1997) and more local ones like Abstraction in Context (Schwarz et al. 2009); some
developed with the explicit purpose of serving as theories for the domain of learning
and teaching mathematics, like TDS, and others rather constituting a philosophy of
mathematics education, like Realistic Mathematics Education (Gravemeijer 1994).
Indeed, it appears that many researchers tend to prefer developing their own framework
rather than read, learn, understand, adopt, adapt and apply existing ones that
were developed by others. This has led to a plurality of theories (Lerman 2006),
T. Dreyfus ()
Department of Mathematics, Science and Technology Education, Tel Aviv University, Tel Aviv,
Israel
e-mail: tommyd@post.tau.ac.il
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_45, © Springer-Verlag Berlin Heidelberg 2010
479