EJMT Abstract

This article presents the Buried Treasure Problem as a carefully designed exploratory task in dynamic geometry, aimed at supporting students’ transition from exploration to formal proof. Grounded in Marton’s Theory of Variation, the study examines how grade 9 learners engaged with the task in a Dynamic Geometry Environment (DGE), GeoGebra. Variation theory is used as an epistemic lens to highlight how the four patterns of variation—contrast, separation, generalisation, and fusion- help interpret dragging activities and guide learners to notice invariants amidst variation. By systematically varying elements of the problem, such as landmark positions, turn directions, and step lengths, students were able to discern critical mathematical features, including midpoint constancy, congruency, and properties of quadrilaterals that remained unchanged despite alterations in the configuration. The task design thus employed key patterns of variation to focus attention on underlying structures essential for deductive reasoning. Findings illustrate how variation-informed design in DGE can support students in recognizing invariants, formulating conjectures, and constructing proofs, thereby bridging intuitive exploration with formal geometric argumentation. The study also extends the notion of variation-invariance duality as a theoretical basis for designing proof-oriented DGE tasks.