Commentary on Theories of Mathematics Education

<strong>Commentary</strong> 3 on Re-conceptualizing Mathematics Education as a Design Science 165
While Lesh and Sriraman make many excellent points about the limitations of
traditional forms of mathematics education research, they ignore what is possibly
its greatest advantage over design science—traditional research is easier. Whereas
traditional research is hard enough to do well, the methods of any particular research
method are at least circumscribed and greatly limit the range of possibilities
presented to the researcher. In design science, on the other hand, everything
is contingent—the goals, the instructional methods, methods of data collection and
analysis, theoretical framework, etc. Moreover, all of these choices are contingent
and open to change at any time.
This novelty means that design scientists cannot simply replicate what prior researchers
did or said; there are no templates to follow. As science studies have shown
(e.g., Rabinow 1996), even attempts at replication studies in a laboratory setting require
some degree of improvisation because authors of prior studies cannot detail
exactly every method they used in their study. More specifically, I argue that all
research is fruitfully seen as an improvisational activity taking into account the contingencies
of local circumstances (see Ryle 1979).
More specifically, design science is at the extreme end of Weick’s (1998) continuum
of improvisation. This progression implies increasing demands on imagination
and sophistication on the part of the researcher, and increasing understanding of the
reasons and purposes underlying various instructional and research methods.
1. Interpretation is required any time a researcher or teacher must ‘fill in’ part of
the necessarily incomplete codification of a research or instructional method.
This need for interpretation explains why some replication studies, ostensibly
performed in exactly the same way, obtain different results. Researchers and
teachers must interpret their methods and those interpretations will affect the
results. It should be noted, however, that they need not be aware that they are
interpreting; they may believe that they are following the prescribed methods.
2. Embellishment is seen whenever we choose to augment or change prescribed
methods to suit local circumstances or to intentionally obtain different results.
It implies that we consciously chooses the change, but intends the results of the
change to be easily compared to the canonical methods.
3. Variation implies a greater degree of change and novelty in research methods,
with whole pieces added, removed or considerably altered. Direct links with
canonical methods become more difficult and require increased sophistication
to explain connections and comparisons with canonical methods.
4. Full-blown improvisation implies that all possibilities are contingent and alterable.
But just because aspects of the research methods are alterable does not
imply that a researcher has complete freedom to do as she chooses, however.
She is still constrained, if she wants to do good research, by the necessity of doing
research that she will be able to present in ways that persuade her intended
audience.
Traditional quantitative research tends toward interpretation and embellishment,
many qualitative research methods require embellishment and variation, and design
science seems to require full-blown improvisation. Janesick (2000) comes