Commentary on Theories of Mathematics Education

DNR-Based Instruction in Mathematics
as a Conceptual Framework
Guershon Harel
Lester (2005) addresses a crucial weakness of the current scientific culture in mathematics
education research (MER)—the lack of attention to theory and philosophy.
He indicates several major problems that contribute to this weakness, one of which
is the widespread misunderstanding among researchers of what it means to adopt
a theoretical or conceptual stance toward one’s work. He offers a model to think
about educational research in MER. The model is an adaptation of Stokes’ (1997)
“dynamic” model for thinking about scientific and technological research, which
blends two motives: “the quest for fundamental understanding and considerations
of use” (p. 465). According to this model, the essential goals of MER are to understand
fundamental problems that concern the learning and teaching of mathematics
and to utilize this understanding to investigate existing products and develop new
ones that would potentially advance the quality of mathematics education.
Another weakness, not addressed by Lester, is that attention to mathematical
content is peripheral in many current frameworks and studies in mathematics education.
Perhaps the most significant contribution of mathematics education research
in the last three decades is the progress our field has made in understanding the special
nature of the learning—and therefore the teaching—of mathematical concepts
and ideas (Thompson 1998). The body of literature on whole number concepts and
operations, rational numbers and proportional reasoning, algebra, problem solving,
proof, geometric and spatial thinking produced since the 70s and into the 90s has
given mathematics education research the identity as a research domain, a domain
that is distinct from other related domains, such as psychology, sociology, ethnography,
etc. In contrast, many current studies, rigorous and important in their own
right as they might be, are adscititious to mathematics and the special nature of
the learning and teaching of mathematics. Often, upon reading a report on such a
study, one is left with the impression that the report would remain intact if each
mention of “mathematics” in it is replaced by a corresponding mention of a different
academic subject such as history, biology, or physics. There is a risk that, if this
trend continues, MER will likely lose its identity. As Schoenfeld (2000) points out,
the ultimate purpose of MER is to understand the nature of mathematical thinking,
I wish to thank Evan Fuller and Ievgeniia Khyzhniak for their help with this paper.
G. Harel ()
Department of Mathematics, University of California, San Diego, USA
e-mail: harel@math.ucsd.edu
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_34, © Springer-Verlag Berlin Heidelberg 2010
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