Conocimientos geométricos como respuesta a un problema espacial en el desarrollo de un recorrido de estudio e investigación

Abstract

In this work we intend to tackle the didactic phenomenon of the loss of the raisons d’être of geometric knowledge proposed for Compulsory Secondary Education. Thus, we conjecture that spatial problems may become a possible reason d’être of such knowledge. In search of evidences for our conjecture, we have implemented, in a group of 14 secondary students, a kind of study process known as study and research path, which starts with a question about the spatial problem of designing and constructing a one-litre container. Then, by using the degree of completeness indicators of a local mathematical organisation, we analyse the mathematical activity carried out by the students. Our analysis suggests that: a) with this study process it is possible to address in a functional way part of the geometric knowledge proposed in the Secondary curriculum, and b) the rigidity of the school mathematical activity, usual in Secondary classes, on the one hand, limits the possibility of using different techniques to solve the same task and to construct new techniques; and, on the other hand, does not help to question the validity domain of the techniques used in class.