Justifying Geometrical Generalizations in Elementary School Preservice Teacher Education

Abstract This article is part of a teacher education experience implemented in Portugal with future teachers and educators of the 2nd year of a basic education degree, in which they have produced evidence of justifications of generalizations in a context of exploratory teaching. The study aims to understand how they justify generalizations about families of geometric figures. Data were collected by audio and video records and from the participants’ written productions, focusing on arguments used to justify generalizations about families of figures. In the analysis, special attention was given to the kind of arguments, its generality degree, the difficulties expressed and the aspects that have promoted the learning of this process. The results show that the participants had some difficulties in building justifications, in part by the lack of understanding about the justification nature. Initially, they expressed difficulties with the study object (a family of figures instead of a unique figure) and difficulties in fully providing arguments and their discourse was mainly based on specific cases. The association of justification to investigate the generalization, as well as the nature and the careful task design and classroom interaction may promote the improvement of justifications.