Modelling mathematical argumentation: The importance of qualification

Abstract. In recent years several mathematics education researchers have attempted to anal-yse students ’ arguments using a restricted form of Toulmin’s (1958) argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgrad-uate mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role in mathematical argumentation, and that one of the goals of instruction should be to develop students ’ abilities to appropriately match up warrant-types with modal qualifiers