Abstract
This article considers the difficulties which researchers in mathematics education undergo while collaborating with colleagues from different traditions of inquiry. In particular we seek to explain how collaboration is possible given that researchers work within incommensurable discourses. Incommensurability, as Kuhn viewed it, means that the proponents of competing paradigms practice their trades in different worlds, as they use similar key words in different ways. Given this scenario, how can researchers participating in different discourses communicate and collaborate? We take the case of a commognitive researcher who tries to collaborate with a cognitive researcher in mathematics education to investigate this question. We argue that although these discourses are indeed incommensurable, at least partial collaboration is possible. This solution is rooted in Kuhn's later conception of incommensurability which means that theories are incommensurable in regard to certain concepts, since during revolutions not all concepts change their meanings. Given this locality, we argue that collaboration is possible, given that there is some partial overlap in the word-use of the two researchers. We illustrate this claim by showing how the notion of 'learning', which is conceptualized differently in the two incommensurable discourses (the ‘cognitive’ and ‘commognitive’), still has some common components, i.e. the ideas of 'change' and ‘conflict’.
