Generalizing a 16th century arithmetic problem with prospective Secondary education teachers

International audienceThe use of history of mathematics and, in particular, of historical problems is a very useful tool for teacher training. In this work we present some partial results obtained after the design and implementation of an activity based upon an arithmetic problem from the “Conpusicion de la arte de la arismetica y juntamente de geometria” by the Spanish 16th century Dominican friar Juan de Ortega. This activity was conducted with 48 prospective Secondary education teachers enrolled on an on-line Masters’ degree. We focus on the part of the activity related to generalization and, more particularly, on the relation between generalization and use of algebraic language. Our results show that there exists a positive significant relation between generalization and the use of algebraic language. However, we also found out that many students were able to provide correct and satisfactory generalizations using just natural language