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In light of the recent interest in mathematical competencies and the ways in which students communicate their ideas, this study aims to explore how undergraduate students communicate their ideas about mathematical tasks through written texts. Forty-three first-year undergraduate students participated in this study. They were given a graph of a function and tangent line and were asked to estimate the value of the derivative at the tangent point justifying their answer. We analyzed the justification of students to the given task by referring to the cooperative principle and to the Anthropological Theory of the Didactic. For the former, we employed the four Grice maxims: Quantity, Quality, Relation and Manner. For the latter, we employed the main components of praxeologies: the type of task, the technique needed to solve the task, the technology as knowledge needed to explain the technique, and a theory as basis to justify the technology. A model of the students' communication about mathematical ideas emerges and is described with reference to data analysis. The model sheds light on the relationship between the discourse of a student solving a mathematical task and how she performs the related problem-solving activity. [ABSTRACT FROM AUTHOR]