Un Acercamiento Cognitivo y Epistemológico a la Didáctica del Concepto de Variable Aleatoria.

The random variable concept is one of the based concepts of the probability theory and the inferential statistic. From a mathematical point of view, random variable and distribution functions introduce probability and random events in real numbers context. From a model point of view, random variable delimits the context and allows relating random real phenomena to the mathematical context of probability distributions. In his study about fundamental stochastical ideas, Heitele (1975) included the random variable as a fundamental one in school education because it must develop in the curriculum spiral from pre-figurations in early stages of children to developed stages in university students. However few researchers have explicitly focused on the didactics of this concept. This research seeks to find elements to support the didactics of the random variable study in university, helping of the didactic engineering. The focus is on preliminary analysis of this research methodology, particularly, on cognitive and epistemological analysis, and It is based on theory of didactical situations. From the cognitive aspect, a clinical interview was carried out with two university students. From the epistemological aspect, a disciplinal and historical analysis was done. The research allows observing the epistemological complexity of the random variable concept. Students linked the idea of a random variable to complex probabilistic concepts, related it to a mathematical modeling process and connected it to other stochastic and non stochastic mathematical tools. It was reflected in the difficulties and success that the students faced when solving the problem. But also in the historical context and problems that gave rise to the mathematical concept. The cognitive analysis provided elements and aspect which can be studied in depth in the epistemological analysis