Students’ understanding of geometric figures in the process of constructing a conjecture at the secondary school

Constructing conjectures is a major challenge in learning geometry. However, there are still gaps in our understanding of the knowledge about geometric figures that students use when they construct a conjecture. This article explores the understanding of ninth-grade students, aged 14 to 15, about geometric figures during the process of constructing conjectures. The study's data consists of the students’ responses to two geometry tasks in a questionnaire. The first task does not include an associated drawing, while the second task contains an incomplete drawing. Both tasks aim at the construction of conjectures. The research results highlight the influence of students’ knowledge of geometric figures on the stages of constructing conjectures in geometry. The findings indicate that students’ difficulties arise from inconsistencies in their cognitive structures regarding the figures used in conjecture construction. Students often rely on inappropriate prototypical figures when the task is not accompanied by an associated drawing. Additional findings reveal that informal arguments emerge when drawings are used to support these arguments, which are subsequently validated through experimental verification.