Middle School Students' Basic Geometric Construction Processes in a Dynamic Geometry Environment

ABSTRACT This study explores three seventh grade students' engagement with geometric constructions (GCs) involving congruent line segments, perpendicularity, parallelism, and angle bisectors within a dynamic geometry environment (DGE). Although GCs have the potential to enhance geometric visualization and reasoning, their integration into teaching remains complex and often ineffective in promoting geometric thinking. Employing a case study design, the construction processes of three students were examined over a 4‐week period through Smart's construction stages and van Hiele's levels of geometric thinking. Rather than following step‐by‐step guidance, the instructional design emphasized problem‐based construction tasks that promoted conceptual understanding. As students used GeoGebra's compass tool, their operational fluency and comprehension of geometric invariants, particularly properties of circles, improved. The dragging property served as a means of conjecture testing and validation, fostering students' ability to reason deductively and articulate justifications. Findings indicate that students engaged in tasks and completed constructions accurately, reflected on underlying geometric properties. Their discourse revealed progression in geometric thinking, characterized by attention to geometric figures' attributes, relationships, and logical coherence. The study values the potential of DGEs, when integrated with tasks based on a constructivist approach, to support students' conceptual development and foster higher‐level geometric thinking.