El momento del trabajo de la técnica en la completación de Organizaciones Matemáticas: El caso de la regla de Ruffini

According to the Anthropological Theory of the Didactic (ATD), the “work of the technique” is considered as a dimension of mathematical activity that plays a crucial role in the development and progressive completion of school mathematical practice. Among its functions, we can highlight its capacity to connect the study process and to create new mathematical objects. However, these didactic functions have to be considered in relation to the other dimensions of mathematical activity and, more especially, to the exploration of new types of tasks and the constitution of an appropriate theoretical environment. This paper focuses on the school mathematical practice around “Ruffini’s rule”, a technique for polynomial division and factoring. We will show a specific way of enlarging and progressively completing this rule, considering the “work of the technique” as an essential tool.