Commentary on Theories of Mathematics Education

164 D.N. Boote
This suggests another major benefits of design science that Lesh and Sriraman
do not discuss—its tremendous potential as a form of professional development. Involvement
in design science can provide opportunities: to understand the strengths
and weaknesses of educational ideas and specific educational practices; to refine
research, collaboration, and educational skills; and to improve the quality of mathematics
education. This is just as true for the leader of the project and research assistants
as it is for collaborating teachers. Indeed, the professional development for
all participants may be more important and sustaining than the educational practices
developed or the artifacts and knowledge gained.
In summary, Lesh and Sriraman’s advocacy for reconceptualizing mathematics
education as a design science directly challenges the neo-liberal logic of employment
in many countries. Our flight to thinking of mathematics educational as a behavioral
science is one manifestation of a logical of employment that values standardized
work, de-skilled employees, and centralized control. By failing to acknowledge
this larger social and intellectual context affecting mathematics education it is
unlikely that reconceptualing mathematics education research as a design science
will address the problems they raise.
Educating Design Scientists
Many of the advocates of design science are among the most sophisticated researchers
in mathematics and science education. Yet how many mathematics education
researchers are capable doing the kind of sophisticated inquiry that design
science requires? Most educational research methodologists, including Lesh and
Sriraman, ignore the simple precept that ‘ought’ implies ‘can’ (see Boote 2008, for
a detailed analysis). Even if we accept my more modest claims about what design
science is able to do, we still need to acknowledge the challenges involved in doing
design science well. There is no point to recommending research practices that
most researchers cannot follow or to prescribing goals that cannot be attained. The
prescriptions of the advocates of design science seem to be formulated for ‘ideal’
researchers, not typical mathematics educators with limited resources—cognitive,
material, and social. If we wish to make serious prescriptions to improve mathematics
education research, not offering idle advice, mathematics education researchers
must be capable of following their prescriptions.
While the relationship between how we ‘ought’ to do research and how research
‘is’ done is far from obvious, Fuller (1988, 1998) suggest some very useful standards
whenever anyone makes claims about how research ‘ought’ to be done. Any
time an educational research methodologist prescribes or proscribes a standard or
a practice for educational research, the onus is upon them to details the social and
psychological conditions must prevail before the normative criteria are applicable.
Such descriptions should amend the limitations of a research methodology by taking
seriously the mental and social lives of researchers, acknowledging their limitations
and that of their institutions, and providing advice and recommendations tailored to
specific problems rather than sweeping generalizations.