My research investigates what kinds of mathematics a student is able to create in the context of measuring symmetries. I will be sharing data from a recent teaching experiment where an individual student worked on reinventing formal definitions of both symmetry and symmetry equivalence starting from her own intuitive notion of symmetric figures. Through the lens of the instructional design heuristic didactic phenomenology I will look at the potential this context provided for the student to reinvent specifically an isometry (rigid motion) conception of symmetry, necessary for group theory.