Commentary on Theories of Mathematics Education

Preface to Part I
Jeremy Kilpatrick
In the chapter, Sriraman and English offer a wide-ranging survey of theories and
philosophies of mathematics education. They begin by pointing out that each of
those theories needs to clarify its ontology, methodologies, and epistemology and
that these might form the foundations of a philosophy for the field. The work and
influence of Lakatos get special consideration in that regard. The authors’ attention
then shifts from philosophy to questions of theory and theory development,
noting the proliferation of complexity in our field—in both phenomena and issues.
They maintain that theory is more prominent today in mathematics education than
in the past and ask what that theory might be, how it has changed, what the effects
of those changes have been, what Europeans think about theory development, and
what the future might hold. Theory, they claim, needs to be better harmonized with
research and practice if the field is to move forward. Discussing the frequent paradigm
shifts in the field, they ask whether those shifts are genuine and whether, when
mathematics educators reject alternative views, valuable ideas are being needlessly
excluded. They imply that calls for more “home grown” theories in mathematics
education are inevitably exclusionary; apparently, no home grown theoretical position
in their view can be either interdisciplinary or inclusive. In their discussion
of European schools of thought, they note the influence of the well-known Royaumont
Seminar, 1 particularly on the modern mathematics movement and subsequent
research efforts in France. The chapter concludes by emphasizing that recent attention
to the social, cultural, and political dimensions of mathematics education permits
the field to move forward in ways not possible in the past. Sriraman and English
endorse calls for a “broadening of horizons” and a “wider exposure to theories and
methodologies,” and they emphasize the value of seeing mathematics as a sociocultural
artifact, getting theoretical frameworks to interact systemically, eliminating
dichotomies in discourse on thinking, and taking critical mathematics education seriously.
1 It is not exactly a “gap in the literature,” as Sriraman and English assert, that the seminar is not
mentioned in several histories of research in mathematics education inasmuch as the seminar did
not deal with such research. The seminar and its influence are, in fact, often noted in analyses of
the school mathematics curriculum during the new math era (e.g., Bishop 1988; Howsonetal.
1981/2008; Moon 1986).
J. Kilpatrick ()
Department of Mathematics and Science Education, University of Georgia, Athens, USA
e-mail: jkilpat@uga.edu
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_1, © Springer-Verlag Berlin Heidelberg 2010
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