Commentary on Theories of Mathematics Education

206 B. Dahl
mathematics education? I do not know. But in any case, we should put effort into
writing and publishing papers that has “negative” results unless, of course, the lack
of result is due to poor quality research. A way to move forward is also to try and
falsify present theories.
A second idea is mentioned by Mewborn (2005, p. 7) who suggests to revisit
some of the scholars of yesteryear and see what they can offer today.
A third suggestion is to ask outsiders to the research community to provide criticism
“The system of peer review has important virtues, but it means that even a very
esteemed scientist who goes too far in criticizing fundamental assumptions can be
effectively excluded from the research community” (Johnson 1995, pp. 95–96).
Fourthly, we may also need a series of “State of the Art” articles pulling together
present research in an attempt to create/discover a meta theory. As Mewborn (2005,
p. 7) state: “Authors of handbook chapters typically do a sort of meta-analysis of
the findings of studies in a subfield, but this same type of analysis of frameworks
could be quite instructive”. Therefore papers like Pegg and Tall’s (2005) arevery
important since they gather and display the state of knowledge within a particular
subfield of mathematics education research. Their paper also illustrates the development
of a meta-theory and the adding to the body of knowledge when they compare
the theories of Dubinsky, Sfard, etc. and built on their commonalties.
A fifth suggestion could be drawn from Boero and Szendrei who argue that we
need to develop scientific meeting where the different schools can compare results,
including their vocabulary and methodology (1998, p. 207).
A sixth idea, is that “Practitioners are an important source, perhaps the most
important source, of practical wisdom in education” (Garrison 1986, p. 18).
Lastly, “we must not only discuss the theories in relation to each other . . . but
equally important is it to collect more empirical data that might cast light on these
discussions” (Dahl 2004b, p. 12).
Acknowledgement Many thanks to Dr Hanne Andersen, Dr Cecile Cachaper, and Rev Dr Chip
Sills for feedback and help at various stages. The faults remain my own.
References
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Asiala, M., Brown, A., Devries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework
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Biggs, J., & Tang, C. (2007). Teaching for Quality Learning at University. Maidenhead: Open
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Boero, P., & Szendrei, J. R. (1998). Research and results in mathematics education: Some contradictory
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