Changes in students’ mental constructions of function transformations through the APOS framework

This study aims to examine the changes in students’ mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in mathematics teacher education program. The data consisted of video records of the designed teaching sessions, students’ worksheets and the researcher’s field notes. The results indicated that ACE teaching cycle was effective in developing students’ mental constructions of function transformation through sequential activities. Even though all the students initially did not reveal evidence for sufficient theoretical or practical knowledge on function transformation, which was evidence of their action level, through the process, it became evident that all the students provided evidence regarding at least their process level of function transformations. Some of the students also showed evidence related to their object levels of function transformations.