https://hdl.handle.net/20.500.12809/244 2026-04-03T22:05:40Z https://hdl.handle.net/20.500.12809/10932 Changes in students' mental constructions of function transformations through the APOS framework Boz Yaman, Burçak; Koyunkaya Yiğit, Melike 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. 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10821 Bilimsel sorgulama destekli BİSDEM Projesi etkinlikleri Ünver Oğuz, Ayşe; Okulu, Hasan Zühtü; Şenler, Burcu; Arabacıoğlu, Sertaç; Muslu, Nilay; Özdem Yılmaz, Yasemin Mevcut etkinlik kitabı sınıf ve fen bilimleri öğretmenlerinin bir mesleki gelişim programı sonucunda, bilimsel sorgulama alanında edindikleri bilgi ve tecrübeler ile tasarladıkları veya uyarladıkları, öğretim programları ile uyumlu fen bilimleri etkinliklerini içermektedir. Sanıyoruz kitabı seçkin kılan en önemli etken de budur. 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10759 A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations Sadek, Lakhlifa; Bataineh, Ahmad Sami; Işık, Osman Raşit; Alaoui, Hamad Talibi; Hashim, Ishak In this paper, we apply the Bernstein collocation method to construct the solution set of the Sylvester matrix differential equation (Sy-MDE) which involves the Lyapunov matrix differential equation. The method depends on the collocation method and Bernstein polynomials. The main advantage of the proposed method is that by using this method Sy-MDE reduces to a linear system of algebraic equations which can be solved by using an appropriate iterative method. We analyze the error and give a theorem that bounds the error. We also give the residual correction procedure to estimate the error. By using the procedure, we obtain a new approximate solution, namely a corrected Bernstein collocation solution. To illustrate how the proposed method is applied, several examples are given. Numerical experiments show the effectiveness and accuracy of the method for solving such types of Sy-MDE. 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10563 Comparing the images formed by uses of lens surfaces Işık, Hakan In this study, university students’ experiences with conventional and novel applications for the surfaces of biconvex and biconcave lenses were examined. This work used practical tools to depict refraction and reflection processes that occur on lens surfaces. In the main activity, the surfaces of each lens were used by the students to examine a single image created by refracted light rays and then two images created by reflected light rays. When the students compared the properties of virtual and real images, they discovered that viewing both real and virtual images at the same time is more beneficial and simulating than viewing each image type separately. 2023-01-01T00:00:00Z