| Resumo: | This article reports a research in the context of a K-6 prospective teacher education experiment developed in a geometry course in the 2nd year of their preparation program. This course included the study of the classification of quadrilaterals and prisms. The research is guided by the following question: how does the learning of hierarchical classification of geometric figures evolve from a teacher education experiment that includes the classification of quadrilaterals and prisms and follows an exploratory approach to teaching? Data was collected from audio and video records from the lessons and from the participants’ written reports about the classification of quadrilaterals and prisms. The results show that, in the first stage that focused on quadrilaterals, the participants’ difficulties in classifying derived mainly from their inexperience with the process of classifying geometrical objects and from their strong conceptualization of some quadrilaterals, very attached to prototypical images. In the second stage, the classification of prisms showed a positive and significant evolution, with a lower influence of prototypical images and a higher understanding about the classification process and the identification of hierarchical relationships among “close” and “distant” figures. However, the final evaluation test showed that the prospective teachers still had misunderstandings, most often related to the interpretation of the discourse and logical reasoning than to limited figural concepts.
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