La comprensión de un espacio de trabajo matemático (ETM) en base seis por parte de futuros profesores de primaria y su influencia en el ETM en base diez

Abstract

In the mathematical domain of numbers, base ten plays an important role in primary and secondary schooling, although it is not absolute from the mathematical point of view. However, most people interpret this role as absolute, obtaining what is interpreted as a common or degenerate paradigm where the number is confused with its representation in base ten. This article reports the findings of an experience with future primary school teachers, in the third year of their bachelor’s degree in France. A sequence is proposed to build an ETM to develop the knowledge of numbers using base six as a representation system, in parallel to the ETM in base ten. The analysis of the circulation of the mathematical work by students is presented, approaching different aspects of numbers through the three genesis. The study reveals the establishment of a new representation system, the base six, as a transforming agent of the common paradigm becoming aware of the non-absolute role of base ten.