Understanding of Geometrical Concepts in Elementary School Using the Example of Quadrangle, Rectangle and Square

Abstract

Among the first geometric concepts that children learn in early childhood education and primary school are quadrangle, rectangle and square. Studies show that learners have already built up individual definitions, so-called personal figural concepts, for these concepts at an early age. The development of this understanding of geometrical concepts is presented in theories that describe different levels. These models are, however, relatively generic and do not describe the personal figural concepts of learners concerning quadrangle, rectangle and square. From an empirical point of view, there are several studies that shed light on aspects of the personal figural concepts of learners of different age groups. In order to describe the development of geometrical understanding from an empirical point integrating the personal figural concepts, however, studies in primary school that consider all four class levels and provide insights into theoretical indicators of conceptual understanding are particularly lacking. In a first step, the present study therefore pursues the following question: Which understanding of the geometrical concepts `quadrangle', `rectangle' and `square' show primary school students in the classes 1, 2, 3 and 4? A quasi-longitudinal study with N=456 students (approx. 100 in each class level) was conducted. The results give detailed insights into the personal figural concepts of the learners and show that learners increasingly consider the characteristics of these concepts, but that personal figural concepts are also prototypical over a long period of time. Implications for future research and practice are discussed.