There is always something to teach, there is always something to learn: how and why should we teach mathematics to senior people?

Abstract This paper is related to the development of educative actions with senior people. More specifically, it refers to the Mathematical Education promoted in the space of university extension activities. It is considered that the engagement of senior people in educational environments can contribute to the maintenance and development of cognitive aspects, which are fundamental to their autonomy. In addition, participation in these environments can favor changes in their physical, social, and psychological aspects, enhancing their self-esteem. In this paper, we discuss results of a research which aimed at understanding possible ways to promote such educational actions and to providing elements to a reflection about its contributions to senior people. Data production occurred within the project Conversation about Mathematics with Senior People. Data were collect through interviews, photos, and notes in a research notebook. Data analysis reveals an active engagement of the women and men in the project as well as provides some indication about contributions to the senior people. About their engagement, we considered: a) their interest in discussing the subjects during the meetings; b) their persistence to perform mathematics tasks on their own; c) their argumentation about the ideas showed; and d) their movement of sharing the activities with other people who were not participating in the project. In relation to contribution to senior people, we considered manifestations that expressed: a) improvement of cognitive aspects; b) opportunity for social interaction; and c) the possibility of learning new subjects related to Mathematics.