Gödel's incompleteness theorem in mathematics teacher formation courses: Previous possibilities

Abstract

In this paper, we present our perspective about the importance of teaching Gödel's incompleteness theorem in formation courses to mathematics teacher. The phenomenon of incompleteness evidenced by the incompleteness theorem is manifested by the existence of true propositions about natural numbers that cannot be proved by any metamathematical argument that can be represented according to arithmetic formalism. Knowing Gödel´s incompleteness theorem and its conclusions is essential in terms of the mathematical culture of a teacher in preparation to teach mathematics in schools, so that he/she can avoid nurturing the notion of complete mathematics and the notion of axiomatic method totalitarianism. This proposal seeks to evidence that Gödel's incompleteness theorem can be explored in formation courses of mathematics teachers1 in exercises in Philosophy of Mathematical Education.