What does it mean to “grasp the rectangle”? Organization of linguistic formulation and activation of argumentative processes in geometrical problems

The purpose of this paper is to explore whether and how the verbal formulation of a task influences the activation of argumentative processes in a geometrical word problem involving figural concepts. The study adopts a multilevel explanatory mixed methods research design. Both the quantitative and qualitative experiments were based on a paradigmatic situation of figural concept proposed by Fischbein. Our main quantitative result is that different formulations of a task impact on students' performance and on the selection of an argumentative or operational option. Moreover, we qualitatively investigated the students' approaches, and this allowed to observe a variety of approaches ranging from a completely operational one to an argumentative one. The analysis highlighted interesting facts about the integration of sentential information and diagrams and the students' strategies.