Commentary on Theories of Mathematics Education

<strong>Commentary</strong> 1 on Re-conceptualizing Mathematics Education as a Design Science 149
Hence, when engineers design such things as software, the underlying design document
tend to be one of the most important parts of the products that they produce;
they don’t simply test for success, they design for success; and success means sharability
with other people, and modifiability in other situations, or in unforeseen future
situations. Successful software is modularized and documented, and designed
so that it will be easy to modify and adapt to continually changing circumstances.
Lesh and Sriraman claim that it is not enough to demonstrate that something
works; it also is important to explain why and how it works. They argue that lack
of accumulation is the foremost shortcoming of both research and development in
mathematics education. Moreover, in mathematics education, funding agencies as
well as professional organizations and sometime even part of the research community
have ignored their responsibilities to build infrastructure—and have chosen
instead to emphasize simplistic “quick fix” interventions that are precisely the kind
practitioners do not need.
What is needed is not one study or one project that “answers teachers’ questions”;
we should expect that realistic solutions to realistically complex problems will need
to integrate concepts and procedures drawn form more than a single “grand theory”
of education.
There is a need to design research methodologies so that they draw on multiple
theoretical and practical perspectives and, integrate continuing research agendas
being conducted by multiple researchers at multiple sites and, build infrastructure
which helps researchers, developers, and practitioners build on one another’s work
over long periods of time.
References
Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating
complex interventions in classroom settings. The Journal of the Learning Sciences, 2(2), 141–
178.
Collins, A. (1992). Toward a design science of education. In E. Scanlon & T. O’Shea (Eds.), New
Directions in Educational Technology (pp. 15–22). New York: Springer-Verlag.
Kelly, A. E., Lesh, R. A., & Baek, J. Y. (2008). Handbook of Innovative Design Research in
Science, Technology, Engineering, Mathematics (STEM) Education. New York: NY: Taylor &
Francis.
Kilpatrick, J., Wirszup, I., Begle, E., & Wilson, J. (1969). Soviet studies in the psychology of
learning and teaching mathematics. School Mathematics Study Group. Stanford, CA.
Lesh, R., & Sriraman, B. (2005). Mathematics education as a design science. ZDM-The International
Journal on Mathematics Education, 37(6), 490–505.
Lesh, R., Kelly, A., & Yoon, C. (2008). Multi-tier design experiments in mathematics, science,
and technology education. In A. Kelly, R. Lesh, & J. Y. Baek (Eds.), Handbook of Innovative
Design Research in Science, Technology, Engineering, Mathematics (STEM) Education. New
York: NY: Taylor & Francis.