Cödel's Theorem in the Continuing Education of Mathematics Teachers

The notion of depaysement epistemologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Godel's incompleteness theorem, with the aim of provoking in the participants the experience of depaysement epistemologique. Results show that several of the teachers participating in the activity felt depaysement epistemologique, and this feeling triggered empathy towards their own students. The article ends with a discussion of the real possibilities of integrating the history of mathematics in secondary mathematics courses and in the training of teachers.