Mathematical representations of 5 and 6-year-old children when solving an open-ended problem

Abstract

Problem solving and representation are two fundamental processes of mathematical activity. The development of these processes provides a key basis for learning mathematics at all school levels, which is why it is so important to promote them from an early age. The aim of this article is to describe the representations and ways of solution posed by a group of children in pre-school education (5-6 years), in a Catalan school, when solving an open-ended arithmetic problem. The study follows a descriptive-interpretative methodology. A school task is designed and implemented from which individual written productions are obtained. In addition, interviews were conducted with each of the students and the corresponding video recordings were made. The data are systematised and a two-phase analysis is carried out: initially the types of representation are characterised and then the calculation methods used by the children. The results indicate that all the participating pupils produce representations to solve the problem. All the children make iconic representations, and a few combine iconic and symbolic representations. As for the ways of solving the problem, continuous counting predominates, although in some cases proposals are made in which more complex reasoning is evident. In these cases, the children propose groupings which are expressed by means of drawings and symbols.