The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out of date. It is also argued that Toulmin's model is related to argument as a product rather than to the argumentation processes that are crucial from the educational perspective. This involves Toulmin's view of language too, which seems inappropriate to deal with the complexity of argumentation processes at any school level.