The role of representation systems in the learning of numerical structures

The learning of number concepts within the school system and the role of the representation notion has to analyze and interpret the understanding of number concepts in schoolchildren are important topics in numerical thinking research. Our research team is interested in the difficulties young people find on managing numerical structures when they face advanced mathematical questions. The work presented here will show the general aims and some results of a piece of research done by our team in this field.We have chosen the representation concept to point out some curricular lacks and to observe students' work on learning numerical concepts, and consequently to interpret their numerical thinking construction. Such an idea has been continuously considered as it is interesting and useful for the mathematics education researchers (Janvier, 1978, 1987; Kaput, 1987, 1992; Goldin, 1993; Duval 1993, 1995). Though most of the considerations we make here are suitable for other mathematical subjects, our actual contribution is limited to numerical concepts and structures.Since there is no an univocal meaning for this term, it is important to specify the sense in which we are going to use the representation concept. We will carry out such task discussing three different approaches to this concept. Once we have done this, we will present the results of our research