Gerçel Sayıların Tamlık Özelliğinin Apos Teorisine Dayalı Zihinsel Yapılandırılması
Özet
In this study, the research was conducted in the context of student conceptions of the
completeness property of real numbers, which is the most basic structure of analysis, a field
of modern mathematics. In this context, the historical development of the concept was
examined based on the APOS theory, the learning difficulties in the literature related to the
concept were revealed, students' conceptions of the completeness property were
determined, and a genetic decomposition of the completeness property was created by
utilizing the experiences of the researchers, and a study was conducted to verify and refine
this genetic decomposition. For this purpose, a conceptual understanding test based on the
hypothetical genetic decomposition was created and applied to students studying in the
mathematics education program as a pilot intervention. Mathematical tasks were created in
line with the refined genetic decomposition, a problem situation was posed based on these
mathematical tasks, and an instructional application was carried out based on the ACE
instructional cycle. As a result of the implementation of the instruction, students' mental
constructions related to the property of completeness were examined and the results were
revealed. Accordingly, it was concluded that the role of group discussions as external stimuli
was important in the development of students' mental structures, the dense structure of
rational numbers played a fundamental role in the schemas related to the completeness
property of real numbers, and mental structures and mechanisms were important for the
consolidation of mathematical justifications.
