Commentary on Theories of Mathematics Education

<strong>Commentary</strong> 3 on Re-conceptualizing
Mathematics Education as a Design Science
David N. Boote
Mathematics education faces many challenges which Lesh and Sriraman clearly
identify—in many countries mathematics teaching and mathematics education research
have growth too far apart; in many countries most mathematics researchers
and scholars do not embed their insights into usable, widely-disseminated curricular
or instructional products; in many countries policy, curricular, and instructional
development too rigid, presuming unrealistic images of school life; and, as a result,
those polices, curricula, and instructional methods are not readily adaptable
by teachers to their local contexts. Moreover, the solution that Lesh and Sriraman
suggest to address these vexing problems—reconceptualizing the field as a design
science—has considerable merit. Yet many of their assertions and arguments supporting
this solution are either too broad or simply inaccurate. As a result, their
justifications are off base and their conclusions too sweeping.
My general strategy in this response is to suggest that the advocates of design research,
Lesh and Sriraman included, need to be more careful with their claims and
their language choices, lest design science and its variants become yet another educational
fad that is quickly dismissed for being oversold (see also Cobb et al. 2003;
Collins et al. 2004; Design-based research collective 2003; Ford and Forman 2006;
Hoadley 2004; Sandoval and Bell 2004; Steffe and Thompson 2000). Design science
is one crucial component needed to foster and improve mathematics education, but
we must have a realistic sense of its role and the challenges involved in using it.
Analysis of Arguments Supporting Design Research
An interesting and important tension emerges in the very title of Lesh and Sriraman’s
chapter on “Mathematics as a design science” (emphasis added). The title
seems to allude to a metaphor that they intend to explore, why it might be interesting
to think of mathematics education like a design science. Metaphors can provide
us with powerful insights, helping to describe new dimensions and aspects of an
object of study that were hitherto unrecognized. Indeed, Black (1954) argued that
all major advances in thinking have been produced by the introduction of powerful,
D.N. Boote ()
College of Education, University of Central Florida, Orlando, USA
e-mail: dboote@mail.ucf.edu
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_17, © Springer-Verlag Berlin Heidelberg 2010
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