Reasoning and understanding in the resolution of a geometric task: analysis of the didactical pertinence of a learning trajectory in early childhood education

Abstract

This research analyses the didactical relevance of a hypothetical learning trajectory designed to encourage geometric understanding and reasoning in four- and five-year-old children in tasks related to the cylinder concept. To this end, a hypothetical learning trajectory has been designed and implemented in a classroom for Early Childhood Education with a total of nineteen children. Subsequently, a sample of four boys and four girls were selected and the answers given to the teacher were analysed, considering as analytical variables the types of understanding defined by Duval and the characteristics of levels 1 and 2 of Van Hiele. The results show that children develop different learning itineraries, which vary mainly between perceptive and discursive understanding and level 1 and certain characteristics of level 2 of Van Hiele, showing very different evolution flows, but in all cases with a favourable evolution, thus confirming the didactical relevance of the hypothetical learning trajectory designed.

Understanding; Van Hiele levels; Early Childhood education; Hypothetical learning trajectory; Geometry