Commentary on Theories of Mathematics Education

166 D.N. Boote
closest to describing improvisational research in this way when she describes the
work of research as bricolage. That is, researchers necessarily use methods and
methodologies as resources as they try to wield then into a functioning whole. However,
while bricolage may be an appropriate description of some sophisticated research,
Janesick underreports how difficult it is engage in this kind of improvisational
research. Increased improvisation in research or teaching methods requires
increased sophistication in explaining to an audience why the reasons generated by
this method warrant the conclusions a researcher wishes to draw from them.
Lesh and Sriraman want us to believe that it is precisely this improvisational ability
to react to complex, dynamic, and adaptable situation that makes design science
an improvement over traditional research design. I agree. It is the improvisational
nature of design research enables it to promise very useful research, but only if
the researcher is able to execute it successfully. Design scientists are choosing to
trade the predictability of traditional research methods for the adaptability of contingent
methods, and most researchers will recognize how much sophistication is
required to make this work. While ultimately this is an empirical question—we will
need to see just how many mathematics researchers are capable of doing design
science—I am sanguine about the prospects. Most active researchers and doctoral
students have enough difficulty doing traditional, less sophisticated forms of inquiry
(Berliner 2002). How can we reasonably believe that the will now be more able to
do an even more difficult form of inquiry?
An important recent shift that may affect our ability to prepare mathematics educators
as design scientists is the increasing prominence of professional doctorates
in education (Scott et al. 2004). These initiatives have sought to reconceptualize
the doctorate in education from being primarily a social and behavioral science
degree to a practice oriented degree. While the US schools involved in this
shift are trailing the UK and Australian schools, one important characteristic of
the US programs is that many are explicitly making design science as a “signature
pedagogy” of their programs (Carnegie Project on the Education Doctorate n.d.;
Shulman et al. 2006) and replacing their traditional dissertations with design research
capstone projects. Such changes may go a long way to better preparing education
researchers for doing design research, but we are just beginning to understand
how we can prepare mathematics educators to do rigorous and useful studies.
Conclusions
Design science has a central role to play in the future of mathematics education
research—we are only beginning to understand its value in bridging the gap between
research and practice. Lesh and Sriraman seem correct when they assert that
design science has the potential to develop more fine-grained, useful knowledge
about mathematics education, that it better responds to the complexities of educational
practice, that it may produce useful educational products, and that it has great
potential to support policy makers, and curriculum and instructional designers. But
it is no panacea and each of these advantages is significantly curtailed. We also need