Commentary on Theories of Mathematics Education

Surveying Theories and Philosophies
of Mathematics Education
Bharath Sriraman and Lyn English
Preliminary Remarks
Any theory of thinking or teaching or learning rests on an underlying philosophy of
knowledge. Mathematics education is situated at the nexus of two fields of inquiry,
namely mathematics and education. However, numerous other disciplines interact
with these two fields, which compound the complexity of developing theories that
define mathematics education (Sriraman 2009a). We first address the issue of clarifying
a philosophy of mathematics education before attempting to answer whether
theories of mathematics education are constructible. In doing so we draw on the
foundational writings of Lincoln and Guba (1994), in which they clearly posit that
any discipline within education, in our case mathematics education, needs to clarify
for itself the following questions:
(1) What is reality? Or what is the nature of the world around us?
This question is linked to the general ontological question of distinguishing objects
(real versus imagined, concrete versus abstract, existent versus non-existent,
independent versus dependent and so forth) (Sriraman 2009b).
(2) How do we go about knowing the world around us? [the methodological question,
which presents possibilities to various disciplines to develop methodological
paradigms] and,
(3) How can we be certain in the “truth” of what we know? [the epistemological
question].
Even though the aforementioned criteria have been labelled by educational theorists
as the building blocks of a paradigm (Ernest 1991; Lincoln and Guba 1994;
Sriraman 2009a), others have argued that these could very well constitute the foundations
of a philosophy for mathematics education (Sriraman 2008, 2009a).
B. Sriraman ()
Department of Mathematical Sciences, The University of Montana, Missoula, USA
e-mail: sriramanb@mso.umt.edu
L. English
School of Mathematics, Science, and Technology Education, Queensland University
of Technology, Brisbane, Australia
e-mail: l.english@qut.edu.au
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_2, © Springer-Verlag Berlin Heidelberg 2010
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