Commentary on Theories of Mathematics Education

<strong>Commentary</strong> 1 on Re-conceptualizing
Mathematics Education as a Design Science
Miriam Amit
The Handbook of Design Research in Science, Technology, Engineering, Mathematics
Education (Kelly et al. 2008) has been published recently after Lesh and Sriraman
(2005) was written. So, readers who want more details about design research
methodologies should consult this book.
The term design research was borrowed from “design sciences” such as architecture
or engineering—where: (a) many of the most important kinds of systems that
need to be understood were designed or developed by humans, (b) the conceptual
systems that humans develop in order to design or understand the preceding systems
also are used to make new adaptations, and (c) multi-disciplinary perspectives
usually are needed to solve most realistically complex problems.
In the cognitive sciences and learning sciences, the term design research is
widely considered to have been introduced by Ann Brown in her 1992 article
about theoretical and methodological challenges in creating complex interventions
in classroom settings—and by in Alan Collins in his 1992 article describing steps
toward a design science of education. However, as Lesh et al. (2008) point out, the
essential features of design research actually were pioneered much earlier by mathematics
educators who tended to use terms such as “teaching experiments” to refer
to the research methodologies that they used. And, these teaching experiments were
in turn adapted from Krutetsky’s even earlier research where he pioneered teaching
experiment methodologies (Kilpatrick et al. 1969).
In Brown’s case, design research methodologies were introduced explicitly to
help increase the relevance of cognitive science laboratory experiments to teaching,
learning, and problem solving activities in real school classrooms. Whereas,
in Collins’ case, the main goal was to provide stronger theoretical foundations for
projects which design educational software, courseware, or other tools and artifacts
such as assessment systems. But, even though mathematics education certainly
shared the desire to make theory more practical and to make practice more theoretical
by providing solid theoretical foundations, the main purposes that mathematics
educators emphasized was to use research methodologies which would not be based
on assumptions which used machine metaphors to describe the thinking of students,
teachers, or educational decision makers, and would increase the cumulativeness of
research.
M. Amit ()
Department of Science and Technology Education, Ben Gurion University, Negev, Israel
e-mail: amit@bgu.ac.il
B. Sriraman, L. English (eds.), Theories of Mathematics Education,
Advances in Mathematics Education,
DOI 10.1007/978-3-642-00742-2_15, © Springer-Verlag Berlin Heidelberg 2010
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