The emergence of rational behaviour in the proving process: towards Inside-Out 2

Abstract This paper focuses on proving as a rational process, contributing to the field of teaching and learning of proof, with reference to its relationship with argumentation. Within a larger study that investigates how cognitive role-playing in digital storytelling can foster students’ proving processes, in this paper, we use the components of Habermas’ construct of rationality to characterise the roles students play while proving, considering both knowledge and meta-knowledge perspectives. We do moreover exploit this characterisation as a lens to analyse the synchronous discursive digital interactions of students engaged in a proving activity, with a view to illuminate the emergence of rational behaviour activated by cognitive role-playing. The findings suggest a deeper model which highlights some key meta-level elements required for students to be successful in the conjecturing and proving process, in the perspective of their gradual interiorisation. These elements make evident the cognitive roles’ interconnections, giving rise to a preliminary systemic model to observe them. The latter can help students to recognise their own shifts from one role to another, and develop awareness that these roles cannot be fixed as they represent different yet cooperating facets of a single whole.