Reconstrucción de la divisibilidad en la Enseñanza Secundaria

Abstract

Within the framework of the anthropological approach to the didactics of mathematics (Chevallard, Bosch y Gascón, 1997), we show the high interdependence between a mathematical organization and a didactic organization. The later would be required to successfully implement the former in the Spanish Mandatory Secondary Education (E.S.O.). We observed that algebraic modelization of the mathematical organization built around the divisibility of natural numbers leads to its extension to integers. It can be considered as a didactic technique (teaching aid), that is, it is an essential instrument to carry out a rather self-sufficient and comprehensive process of study on divisibility. This didactic technique faces many problems as its implementation would deeply modify the prevalent institutional didactic contract in E.S.O.