To investigate mechanisms of failure in mathematics, we adopt the "communicational approach to cognition," which describes thinking as an activity of communication and learning mathematics as an initiation to a certain type of discourse. In the search for factors that impede students' participation in arithmetic communication, we examine the arithmetical discourses of two 18-year-old girls with long histories of learning difficulties. The resulting "arithmetical discourse profiles" of the two students help us substantiate the following two claims: (1) Almost any person may become a skillful participant of arithmetical discourse, provided, first, that a discursive mode is found that makes the best of this person's special strengths and second, that in the process of teaching, the general sociocultural context of learning is taken into account as having a central role in enabling or barring one's access to literate discourses; (2) if the potential for successful participation remains often unrealized, it is mainly because of certain widely practiced abuses of literate mathematical discourse. (Contains 2 figures, 6 tables and 14 footnotes.)