Levels of understanding for the arithmetic mean concept by adolescents through the piagetian clinical-critical method

Abstract

This paper presents the results of a research carried out with the objective of knowing the understanding of the arithmetic mean concept by young people in socioeconomic and environmental vulnerability. The piagetian clinical-critical method was used to perform the data collection and analysis. The instruments used in the data collection were constructed by the authors. The sample consisted of twelve teenagers between the ages of fifteen and seventeen, students of Centro de Convívio dos Meninos do Mar - CCMar, in the Brazilian South Coast. The analysis pointed to the existence of three levels of understanding for the concept discussed above, as follows: First approximations or incipient ideas; notions of arithmetic mean based on concrete thought; arithmetic mean as a representative measure of a data set. From this investigation it is possible to indicate that the arithmetic mean concept requires the realization of reflective abstraction, there for, the symbolic elements of thought need to leave the material referents, because this is not a material concept, but a formal one.