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Öğe A structural equation model for factors affecting eighth graders’ geometry achievement(Eğitim Danışmanlığı ve Araştırmaları Merkezi (EDAM), 2017) Ünlü, Melihan; Ertekin, ErhanThe aim of this study is to examine the predictor and explanatory relationships among eighth-grade students' affective factors of attitude toward geometry, geometry anxiety, and geometry self-efficacy, as well as the cognitive factor of spatial visualization skills, with geometry achievement. This relational survey study was conducted on 487 eighth-grade students during the 2012-2013 academic year. The tools used to collect data are the Attitude toward Geometry Scale, Geometry Anxiety Scale, and Geometry Achievement Test developed by the researchers; the Geometry Self-Efficacy Scale developed by Canturk-Gunhan and Baser; and the Spatial Visualization Test (adapted to Turkish by Yildiz). The researchers developed the model in consideration of the relevant literature. This model tests the direct and indirect relationships among the variables of affective factors, spatial visualization skills, and geometry achievement. The model's fit indices were calculated and these fit indices show the model to have good fit (x(2) = 106.226;.x(2) / df = 2.47; RMSEA = 0.05; CFI = 0.97; NFI = 0.95; NNFI = 0.96). Research reveals the relationship between spatial visualization skills and affective factors, between affective factors and geometry achievement, and between spatial visualization skills and geometry achievement to be positive and significant. Affective factors directly explain 26% of the variance in spatial visualization skills and 35% of the variance in geometry achievement, while indirectly explaining 7% of geometry achievement.Öğe Investigating middle school students’ eye movements on the mathematical representations: An eye-tracking study(Springer, 2025) Karaca, Hilmi; Ertekin, Erhan; Çağıltay, KürşatIn mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and decision-making, which are difficult to observe. Therefore, uncovering these cognitive activities is very significant for mathematics education. However, they are not easy to uncover as they cannot be directly observed. Eye tracking is an important approach that can be used to reveal cognitive activities that cannot be directly observed. This study investigated how middle school students examine representations by examining their eye movements. Eighty-five (40 girls and 45 boys) 7th-grade middle school students participated in the study. In the study, gaze durations, fixation count, and fixation duration on four different representation types: verbal representation, symbolic representation, number line representation, and counters representation were compared. The findings showed that students fixated more on the verbal representation and gazed at it for longer. However, fixation durations on the verbal representation were quite short compared to the other representations. In contrast, when examining the counters, there were fewer fixations and shorter gaze durations, but fixation durations were longer. Gazes on the number line and symbolic representation did not differ across all three variables. The findings indicated that gaze on verbal and non-verbal representations differed to some extent, but not entirely. Finally, the findings are discussed in the context of mathematical representation and eye-tracking literature.Öğe Ortaokul Öğrencileri İçin Geometriye Yönelik İnanç Ölçeği Geliştirme Çalışması(Halil İbrahim AKYÜZ, 2018) Ünlü, Meliha; Ertekin, ErhanBu çalışmada, ortaokul öğrencilerinin geometriye yönelik inançlarını belirlemekte kullanılabilecek geçerli ve güvenilir bir ölçek geliştirilmesi amaçlanmıştır. Araştırmanın yürütülmesinde ilgili literatürden yararlanarak inanç maddeleri oluşturulmuş, kapsam geçerliliğinin sağlanması amacıyla uzman görüşüne başvurulmuştur. Toplam 32 maddeden oluşan taslak ölçek araştırmaya katılan 324 ortaokul öğrencisine uygulanmış, eldee dilen verilerle testin yapı geçerliğini sağlamak için öncelikle açımlayıcı,sonrasında doğrulayıcı faktör analizi yapılmıştır. Geçerlik için ayrıca madde toplam korelasyonları ve madde ayırt edicilik indeksleri hesaplanmıştır. Faktör analizi sonucunda beşli likert tipindeki ölçeğin 16 maddeden oluşan 3 faktörlü bir yapıda olduğuna karar verilmiştir. Güvenirlik analizleri sonucu ölçeğe ait Cronbach alfa 0,755 olarak hesaplanmıştır.Öğe Why do pre-service teachers pose multiplication problems instead of division problems in fractions?(ELSEVIER SCIENCE BV, 2012) Ünlü, Melihan; Ertekin, Erhan; Baskan, GA; Ozdamli, F; Kanbul, S; Ozcan, DThe aim of this study was to investigate pre-service elementary mathematics teachers' problem types which were posed for modeling fraction division. Data was collected from pre-service elementary mathematics teachers in the spring semester of 2010-2011 who were enrolled in a teacher education program at a public university. Data collection tool entailed pre-service elementary teachers posing world division problems corresponding to the fractions written in symbolic form. The results of the study revealed that pre-service elementary mathematics teachers posed problems involving fraction multiplication rather than fraction division and they used invert and multiply algorithm. There was evidence that they did not have adequate learning about fraction division.
