Changes in students’ mental constructions of function transformations through the APOS framework
Melike Yiğit Koyunkaya 1 * , Burcak Boz-Yaman 2
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1 Department of Secondary Science and Mathematics Education, Buca Faculty of Education, Dokuz Eylul University, Izmir, TÜRKİYE2 Faculty of Education, Mugla Sitki Kocman University, Mugla, TÜRKİYE* Corresponding Author


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.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 18, Issue 4, November 2023, Article No: em0747

Publication date: 01 Oct 2023

Online publication date: 31 Jul 2023

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