APOS theories and constructionism in the analysis of the understanding of the fraction concept

Abstract

The purpose of this work is to analyze the understanding of the concept of fraction in children of the fifth grade of elementary education through two theories: Constructionism and APOS theory. For the construction and understanding of the students' fraction concept, activities have been designed through the constructs of the APOS theory, characterizing their schemas in terms of levels (Intra, Inter and Trans); all this from the constructionist approach. The methodology applied consisted of a case study with a population of 25 children who developed activities using an object-oriented programming language called Etoys in a constructionist environment. The results show that a high percentage of children were able to understand the concept of fraction and reached the level of process and scheme according to theproposed genetic decomposition.