Conjecture-Generation through Dragging and Abduction in Dynamic Geometry
1. Introduction and theoretical framework
Mathematics education supervisors and leaders have been encouraging the use of technology, such as Dynamic Geometry Systems (DGSs), in the classroom (for example, [3, 4, 5, 6, 7]). Several studies in the teaching and learning of Geometry have shown that a DGS can foster learners’ constructions and ways of thinking, and they have shown how, thanks to the dragging tool, a DGS can be powerful for explorations in open problem situations [8, 9, 10]. In this chapter we focus on reasoning and conjecture-generation in Geometry when a DGS, and in particular, the dragging tool, is used. A feature offered by a DGS is the dragging tool, that can be exploited in various ways by the solver, and that can support conjecture-generation. Research carried out by Arzarello, Olivero, Paola, and Robutti [9, 11] led to the description of a set of dragging modalities, classified through an a posteriori analysis of solvers’ work, that can be...