Sistemas de representación de números racionales positivos : Un estudio con maestros en formación

Abstract

This survey is structured into two stages differentiated by the aims and methodology used in its realization. The first stage in mainly based on a didactic assignment, done by applying Research- Action methodology and intended to be performed by a group of students studying to be Teachers of Primary Education in the University of Zaragoza. This assignment aims at increasing future teachers' comprehension of positive rational numbers through implementing the links existing between fractional and decimal notations. In order to achieve this objetive, a pattern with two systems of representation of amounts not whole of magnitude is defined, through which fractional and decimal expressions are conceptualized as results of equalitarian distributions, revealing that fractional and decimal notations admit a similar underlying structure. In the second stage, the methodology of interview is used with three students who took part in the first satage. The aim is to study the relations between these students' previous productions and their performance as teachers who have to correct schoolchildren's tasks. As a result, it can be inferred that the greater the future teachers' comprehension of the pattern is, the more effective they prove to be in detecting and analysing children's errors, and the more sustained reasons they offer in the physical world; on the other hand, the future teachers who have not understood clearly the pattern tend to consider schoolchildren's errors as correct and to give priority to the symbolic language used by the children in their explanations.