We present a model for roleplaying (RP) for university students that is aimed at fostering the interactions of each learner with the teacher and coursemates, self- and peer-assessment, as well as an awareness and meaningful learning of mathematics. Specific features of our model are its focus on metacognition and individualized learning, based on a careful distribution of the tasks according to the individual student's profile. Within our model, the students play, alternately, the role of the teacher and their own role: firstly they assign problems to their peers, then they solve problems formulated by their peers, and, finally, they assess their peers' problem-solving processes. We discuss an implementation of the RP within a teaching/learning path regarding mathematical induction, aimed at promoting robust learning and use. We analyse the outcomes of a pilot study carried out with engineering students and identify their common praxeologies in solving the tasks. Moreover, the effects on students' attitudes and learning are highlighted at the linguistic, cognitive, metacognitive and affective levels.