Investigating how lower secondary school students reason about quadrilaterals emerging in dynamic constructions

This contribution focuses on reasoning about quadrilaterals provided by lower secondary school students when working with pre-prepared dynamic constructions. On this topic, we present an exploratory empirical qualitative study carried out within a GeoGebra Classroom environment, and our diagnostic instrument consists of a set of dynamic constructions of quadrilaterals that are based just on a composition of lines and circles. The dynamic constructions consist of the same construction steps as with a straightedge and a compass on paper, without any relational or measurement information provided by the software. The hierarchy in the dynamic constructions is tied to properties of diagonals and takes on various levels and structure (one level, two consecutive levels, two parallel pairs of consecutive levels). For each of the constructions, the participants of the study reasoned which shapes could be found in the construction and why. Various levels of reasoning as well as various levels of students' understanding of quadrilaterals appeared in data. The findings indicate that, at least for the lower secondary school students, the combination of dynamic manipulations and geometric constructions could form a significant space for scaffolding the identification of the features of quadrilaterals and the comprehension of the inclusive relations between them.