Defining geometric figures: a teacher education experiment with prospective elementary and infant teachers

Abstract

This article reports a research concerning a prospective elementary and infant teachers education experiment, in a geometry course in the 2nd year of studies of a degree in education. The subject of this study is the construction of definitions, a process developed through working on exploratory tasks. Specifically, we seek to know which features of definitions of geometric figures do prospective teachers attend to when selecting and constructing definitions and how the spatial and geometric structuring of the figures relates to the process of defining. Data was gathered from the participants’ reports, audio and video records of classroom discussions on definitions of quadrilaterals and of parallelepipeds. The results show that initially the participants had misconceptions about definitions, just focusing on the necessary properties of the figures. The work developed led them to consider the sufficiency and inclusiveness of the condition. The participants constructed mostly correct but not economic definitions, mobilizing a deeper knowledge of the figures. The spatial and geometric structuring of the figures influenced the process of defining, but also evolved with this activity. Finally, the construction of definitions in the final stage of the study of figures promoted the articulation between the definitions and their classification.