A possibility of a (meta)mathematical education working with the Gödel’s incompleteness theorem

Abstract

The purpose of this paper is to expose understandings and possibilities of working with teachers in being in action of formation during their undergraduate course in Mathematics, by enmeshing them in discussions that focus on important issues in Mathematics, School, Education, the complexity of Education, and Mathematics Education. We assume that addressing philosophical issues pertinent to mathematics and to the conduct of mathematics teachers is vital to the action of being in formation of undergraduate mathematics students. We claim that it is necessary for students to realize what they are talking about when they talk about mathematics and mathematical products, as well as to understand what it means to transpose mathematical knowledge, with its values of certainty and exactitude, implicit in the production of this knowledge, to other non-mathematical realities, such as economic, political, and social ones. To make our arguments explicit we take Gödel's incompleteness theorem as material to be understood and questioned, focusing it as an example of realizing the possibility of metamathematics education, in mathematics teacher education courses, focusing on the questions mentioned above.