In recent years, learning environments have been radically affected by the scientific developments regarding cognitive processes. In our study, we examined high school students' process of abstraction of the knowledge of signum functions in a learning environment created by considering such developments. In the instruction phase, which employed a case study and group studies with two high school students, three specially-designed sequential problems were used. It was observed that the students used the knowledge they had abstracted for the first problem in order to solve the others, and they abstracted the knowledge of piecewise and signum functions accurately to a certain extent. The study also showed that using environmental events and problems to teach about functions strongly contributes to learning.