Argument mapping is visualising informal reasoning and argumentation. Typically an argument map is a "box and arrow" diagram in which the boxes contain propositions and the arrows indicate evidential relationships. In this presentation I will:
(a) sketch some of the theoretical background of argument mapping, specifically the notion of a logical model of complex argumentation, and argument maps as a particular way of presenting logical models;(b) briefly review some of the data on the sorts of gains in undergraduates' critical thinking skills which *can* be achieved using training based on argument mapping;
(c) (the main game) describe a particular problem which seems to arise in argument mapping, that certain kinds of arguments appear to resist being captured in standard argument mapping formats. The challenge is then to give an adequate philosophical analysis of these sorts of arguments, and also to develop diagramming conventions appropriate to arguments of that sort. My hope is that the audience will be able to quickly and convincingly explain either that there is no real problem here, or what the solution is.