Extra-mathematical Connections Made by Prospective Elementary School Teachers when Designing Geometric Homework Assignments

infinity We describe the extra -mathematical connections that emerge when a group of 250 prospective elementary school teachers are confronted with two professional tasks that deal with different geometric notions. The analysis considers the theory of extra -mathematical connections and the tool of the Ontosemiotic Approach (epistemic configurations) to evidence the emergence of generic metaphorical and interdisciplinary connections; the former referred to the constitution of a metaphor as a tool to access from an extra -mathematical idea to an intra-mathematical object; while the latter refers to the use of elements belonging to a particular discipline and therefore extra -mathematical, to understand an intra-mathematical object. The results and conclusions revolve around the evidence presented on the emergence of such connections. It contributes to the reflection on the theory of extra -mathematical connections, and it shows the potential of the design of school tasks in the training processes of Primary Education teachers.