It is well known that, over at least the last two decades, there has been a growing interest in Brazil in the study of social representations in various fields, such as: education, psychology, anthropology, sociology, politics, as well as in the areas of health, the environment, etc. The study of social representations seeks responses to the problems detected and solutions to confront them. We understand that the psycho-social look expressed in social representations will also make it possible to look again at questions referring to difficulties which students attending the teacher training courses for high schools present in relation to the learning of mathematics and to the difficulties which the teachers of Mathematics and of the Methodology of Mathematics feel in relation to the teaching of this discipline. We intend, in this paper, to focus on some representations with respect to mathematics, with a view to contributing to the debate about the manner in which students and teachers perceive this area of knowledge and how it is taught.