Commentary on Theories of Mathematics Education

<strong>Commentary</strong> 3 on Re-conceptualizing Mathematics Education as a Design Science 161
they should produce useful knowledge. Fair enough. These normative claims, on
their face, also seem quite credible.
Lesh and Sriraman now wish to convince us that design science is the one and
only means of addressing all of these problems. Here is where the main problems
with their argument arise. First, they wish to convince us that design research,
as they have articulated it, will address all seven of these problems. Second, by
omission, they would have us believe that these seven problems are the only problems
facing mathematics education research. Third, they would have us believe that
reconceptualizing mathematics education research as a design science would not itself
create more or different problems. Forth, we need to examine whether design
science can benefit us in other ways that its advocates do not mention. Fifth, we
need to ask whether there are any cultural or ideological limitations to their claims
about the state of mathematics education. Their arguments falter on all five counts.
Moreover, even once we develop a clearer sense of the uses of design science, we
face an additional problem that has not yet been identified—design science is very
difficult to do well.
Over-stating the Benefits of Design Science
It is unreasonable to assume that design science could successfully address all seven
of the problems Lesh and Sriraman raise. They do provide plausible arguments
supporting their claim that design science may (2) provide more finely articulated
knowledge of effective mathematics education; (3) produce more tangible products
that may improve mathematics education; (4) support at least some policy makers,
curriculum designers, and instructional designers to support some teachers; (5) produce
products that may be more readily adaptable to complex, dynamic, adapting
nature of educational practice; and (7) produce some more useful knowledge. Of
course, even if their arguments are plausible they are, nevertheless, empirical claims
that can only be justified through empirical study. As such, published design science
studies in mathematics education suggest that they may be justified in suggesting
that it is a good means of addressing these problems.
I do not see, however, that (1) design science, in and of itself, will help mathematics
education researchers to develop research methods better suited to their
problems, or that (6) mathematics education researchers working as design scientists
will be any better (or worse) at systematically accumulating knowledge than
other researchers. All design sciences borrows their methods from existing research
fields. Thus, if any advances in methodology can be claimed it is through the more
thoughtful, sophisticated use of existing research methods both in and out of design
studies, not something inherent to design science. The problems are of knowledge
accumulation are the result of “the messy, complicated nature of problems
in education [that] make . . . generativity in education research more difficult than
in most other fields and disciplines” (Boote and Beile 2005, p. 3, citing Berliner
2002). While Lesh and Sriraman might counter that the processes of embodying
knowledge in tangible products better enables iterative and recursive accumulation