Different ways of grasping structure in arithmetical tasks, as steps toward algebra

In this study we propose an analysis of some interesting solving processes of 9-grade students engaged in an arithmetical task. It originates as an item of a national test that has proven to be very critical for Italian students. By changing the way of administering the task, and also by virtue of some interviews, we got the opportunity to observe interesting students’ behaviours, some of which throw, in our opinion, new light on students’ sense-making processes in the borderline between arithmetic and algebra.