Students' reasoning on linear transformations in a DGS: A semiotic perspective

The aim of this paper is to analyze students' reasoning on linear transformations while using a Dynamic Geometry System (DGS) from a semiotic mediation perspective. Considering design heuristics of Realistic Mathematics Education and the semiotic potential of certain tools and functions of DGS, I have developed a hypothetical learning trajectory and have designed a task for inventing fundamental properties of linear transformations. The task was field-tested in a case study with pair of undergraduate linear algebra students. An analysis of the task-based interviews, with a semiotic mediation lens, shows that the students managed to (re-)invent the fundamental properties of linear transformations.