Exploring The Didactic Transposition of The Metric Space

The didactic transposition is used to adapt scientific knowledge into taught knowledge for students through two steps, namely external and internal transposition. This process is crucial when applied to mathematics content as it enhances the understanding of complex concepts and makes knowledge more accessible to learners. To create effective lessons and scholarly knowledge objects, teachers must establish connections between their learned knowledge and the lesson structure. Metric and probabilistic metric spaces are two complex structures of knowledge that require understanding and teaching. This article explores the didactic transposition approach for teaching the concept of metric space, including probabilistic metric space, through external and internal steps of transposition, it provides two examples of transposing the Metric Distance notion in the Euclidean space, as well as two examples of the probabilistic metric space, aiming to transpose function distribution distance. It also outlines strategies for introducing metric spaces to students, referencing examples while acknowledging the teaching obstacles posed by this concept.