Towards the construction of a mathematical identity through a reflective role-play in problem solving

In this paper we present the design of a role-play in problem-solving, aimed at promoting the construction of students’ mathematical identity. On one hand, there is a role-play on the cognitive functions identified as pivotal of the mathematical identity.On the other hand, there is a role-play concerning the group engagement: actors, who solve the problem; onlookers, who observe and take notes on how the cognitive roles are played by the actors. The double-level structure of actors and onlookers, implemented in a digital environment, allows the onlookers both to view in real-time the storytelling created by the actors do and to discuss it focusing on one cognitive role. All the students are required to fill-in a logbook, concerning their remarks on the cognitive role observed. We discuss the findings of a pilot, which involved 14-year-old students, and the mathematical identity emerged from the students’ logbooks, by analysing the cognitive roles as experienced and perceived by the students.