This paper gives insights into an ongoing study that investigates pairs of students working on geometrical tasks in a cooperative way. The goal of the study is to learn more about students' understanding of geometrical reflection. First results of the study show that «symmetry» and «congruence» are useful categories to describe the students' learning processes on reflections. This paper briefly summarises the theoretical background of the study. Subsequently, it discusses two examples of observed phenomena about these categories of the conceptual understanding.