Abstract

The area concept may appear in a wide range of problem situations. The representations used (geometrical, numerical and algebraic) in such situations entail particular practices that condition the partial area meanings. Thus, this study aims to characterize the partial area meanings mobilized in the resolution of area tasks. Each of the area partial meanings is characterized by a configuration of mathematical objects, which compromised the resolution process through semiotic functions. A top-down / bottom-up approach is implemented to identify these mathematical objects and the relationship between them. First, an analysis of the specialized literature on learning area concept is carried out in order to make an initial characterization of the partial area meanings. Subsequently, an analysis of resolutions of students aged 13-14 years old of a set of area tasks allows the first partial area meanings to be refined. The results showed three partial area meanings, which emerge from a detailed analysis of the mathematical practices involved in the students' resolutions. The relationships between the partial area meanings allow a better understanding of the global area meaning in a task-solving context.