An Inquiry Approach to Construct Instructional Trajectories Based on the Use of Digital Technologies

There are diverse ways to construct instructional activities that teachers can use to foster their students’ development of mathematical thinking. It is argued that the use of computational tools offers teachers the possibility of designing and exploring mathematical tasks from distinct perspectives that might lead their students to the reconstruction of mathematical relations. In particular, a task that involves the construction of a simple dynamic configuration is used to introduce an inquisitive approach to identify mathematical conjectures or relations and ways to explore and support them. In this process, a hypothetical instructional route is sketched where visual, numeric, geometric, and algebraic approaches are utilized to validate those conjectures.