In this paper we present a model in order to analyse the reasoning processes produced in solving problems situations (situations with an adidactical dimension). Argumentations can be identified by elements of different nature: language, calculations, formulas, graphs… These elements are usually interpreted as signs in a representative setting or as elements of a proof or a demonstration. We choose not to emphasize these components, but to explain that three axes are useful in order to analyse reasoning: the first one is linked to the level of milieu in the situation, which establishes more or less the form and logical status of the mathematical statements; the second one is stated with respect to the functions of the reasoning processes; the third dimension is a semiotic one that considers the forms of the statements. We perform this study using the Theory of Didactical Situations (TDS) and Peirce's semiotic theory. We exemplify this model with an experimental analysis of reasoning processes in a situation about calculus, with 17-years old scientific students. Resumen-En este trabajo presentamos un modelo para analizar el razonamiento producido en situaciones didácticas que implican una dimensión de investigación (situaciones con una dimensión adidáctica). Los razonamientos se traducen por elementos del lenguaje, cálculos, escritura, gráficos que habitualmente se interpretan como signos de un registro de representación, o como elementos de una fase de prueba o demostración. En lugar de centrarnos sobre estos aspectos, mostramos tres ejes necesarios para