Designing non-constructability tasks in a dynamic geometry environment

This chapter highlights specific design features of tasks proposed in a
Dynamic Geometry Environment (DGE) that can foster the production of indirect
argumentations and proof by contradiction. We introduce the notion of open construction
problem and describe the design of two types of problems, analysing their
potential a priori, with the goal of elaborating on the potentials of designing problems in
a DGE with respect to fostering processes of indirect argumentation. Specifically, we
aim at showing how particular open construction problems, that we refer to as nonconstructability
problems, are expected to make indirect argumentations emerge.