This study explores the performance of two mathematically gifted Korean 7th-grade students in tasks involving local organization in geometry. The students understood the necessity of definitions and starting points in defining terms and organizing geometrical properties. They improved the clarity of their definitions and arranged the properties systematically with the belief that the properties of the geometric figures would be discussed only after the defining work was completed. Through these activities, they understood an axiomatic method and its importance in geometry. The results suggest that mathematically gifted lower secondary students can be encouraged to advance into axiomatic geometry through local organization activities. (Contains 2 figures, 1 table and 1 endnote.)