Commentary on Theories of Mathematics Education

Preface to Part I 5
I concluded, “A lack of attention to theory is characteristic of US research on mathematical
learning and thinking” (p. 369). Although I am confident that a similar
survey today would yield many more articles in which there was serious attention
to a theoretical framework, the States are undoubtedly still behind Europe in serious
theorizing in mathematics education. After all, Europeans engage in the study
of the didactics of mathematics, which they consider both one of the mathematical
sciences and a discipline in its own right, whereas Americans (at least this one) tend
to hesitate to grant either quality to mathematics education.
Whatever one’s stance on theory—whether it is theory of mathematics education,
theory in mathematics education, or theorizing about teaching and learning
mathematics—the main message of the Sriraman and English chapter cannot be ignored:
Mathematics educators need to bring research and practice together through
an organized system of knowledge that will enable them to see beyond the specifics
of each and explain how they can work together. Alan Bishop’s (1977) powerful
metaphor for thinking about our work offers a pragmatic test for theory:
Theories and constructs are a bit like spectacles—some help you to see more clearly the
object you are concerned with, while others merely give you a foggy, blurred image. Change
the object of your concern, however, and the second pair of spectacles might be more useful.
(p. 4)
Bishop’s observation suggests that beyond scope and the other qualities Schoenfeld
(2000) identified, theory needs focus. Sriraman and English’s introduction to
issues surrounding theories and philosophies can help mathematics educators find
that focus, whether the object of their concern is research, practice, or both.
References
Bishop, A. (1977). On loosening the contents. In L. Murray (Ed.), Meaningful Mathematics (pp.
1–4). Melbourne: Mathematics Association of Victoria.
Bishop, A. J. (1988). Mathematical Enculturation: A Cultural Perspective on Mathematical Education.
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Howson, G., Keitel, K., & Kilpatrick, J. (2008). Curriculum Development in Mathematics (paperback
re-issue). Cambridge: Cambridge University Press. (Original work published 1981).
Kilpatrick, J. (1981). Research on mathematical learning and thinking in the United States.
Recherche en Didactique des Mathématiques, 2, 363–379.
Kilpatrick, J. (2008). The development of mathematics education as an academic field. In
M. Menghini, F. Furinghetti, L. Giacardi, & F. Arzarello (Eds.), The First Century of the International
Commission on Mathematical Instruction (1908–2008): Reflecting and Shaping the
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the AMS, 47(6), 641–649.
Silver, E. A., & Herbst, P. G. (2007). Theory in mathematics education scholarship. In F. K. Lester
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