Ortaokul öğrencilerinin tam sayılarla toplama işleminde kullanılan temsiller üzerindeki göz hareketlerinin incelenmesi: Bir göz izleme çalışması
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Dosyalar
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Necmettin Erbakan Üniversitesi, Eğitim Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Temsiller, matematik eğitiminde, fikirlerin veya ilişkilerin yerini alarak somutlaştırma, dönüştürme ve temsil etme işlevi görürler. Öğrenciler, matematiksel temsillerle etkileşime girdiklerinde, gözlenmesi zor olan birçok bilişsel faaliyeti gerçekleştirebilmektedir. Bu bilişsel faaliyetlerin ortaya çıkarılması, matematik eğitimi açısından oldukça önemlidir. Gelişen teknoloji ile göz izleme yöntemi gibi yaklaşımlar bilişsel faaliyetlerin incelenmesinde önemli bir rol oynamaktadır. Bu bağlamda çalışmanın amacı, ortaokul öğrencilerinin tam sayılarla toplama işleminde sıklıkla kullanılan sayma pulu, sayı doğrusu, sembolik ve sözel temsil üzerindeki göz hareketlerinin incelenmesidir. Çalışmaya ortaokul 7. sınıfta öğrenim gören 85 (40 kız ve 45 erkek) öğrenci katıldı. Göz hareketi verileri uygun olmayan 21 öğrencinin verilerinin çıkarılması ile 64 öğrencinin verileri analizlere dahil edildi. Veri toplama sürecinde göz izleme uygulamalarında her bir temsil türünden üçer tane olmak üzere 12 tam sayılarla işlemler sunumu kullanıldı. Göz izleme verileri GazePoint GP3 (60 Hz) göz izleyici ile toplandı ve Gazepoint Analysis Professional Edition programı ile analiz edildi. Göz izleme yöntemi ile sayısal ve görsel veriler elde edildi. Bu sebeple, çalışma nicel ve nitel unsurlar içermektedir. Çalışmanın nicel boyutunda, öğrencilerin göz hareketlerinden elde edilen sayısal veriler kullanılmıştır. Bağımsız değişkenler, dört farklı temsil türü olan sözel temsil, sembolik temsil, sayı doğrusu temsili ve sayma pulu temsilidir. Bağımlı değişkenler, dört temsil türü üzerindeki bakış süreleri, sabitlenme sayıları ve sabitlenme süreleridir. Öğrencilerin temsiller üzerindeki göz hareketlerine ait görsel dokümanlar (ısı haritaları ve bakış yolları) çalışmanın nitel verilerini oluşturmaktadır. Bu dokümanlar ile öğrencilerin temsiller üzerinde nasıl göz hareketleri sergiledikleri, hangi noktalara daha fazla odaklandıkları ve öğrencilerin temsiller üzerindeki göz hareketlerinde benzerliklerin veya farklılıkların bulunup bulunmadığı incelendi. Öğrencilerin temsiller üzerinde göz hareketleri hem temsil bazında hem de temsiller arasındaki ilişkiler bağlamında incelenmesi sebebiyle çalışmanın nitel boyutu, bütüncül çoklu durum çalışması niteliğindedir. Sayma pulu temsilinde, en fazla sabitlenme ve en uzun süre bakış SPc (toplanacak sayıları temsil eden pulların bir araya geldiği) üzerinde gerçekleşti. Sayı doğrusu temsilinde öğrenciler, SDa (birinci okun ucu ile ikinci okun başlangıç noktası) ilgi alanı üzerinde daha uzun süre odaklandı. Ancak SDb’de sabitlenmelerin süresi daha fazla gerçekleşti. Sembolik temsil ilgi alanları üzerindeki bakış süresi, sabitlenme sayısı ve sabitlenme süresi arasında fark gözlenmedi. Temsil türleri birbiri ile karşılaştırıldığında, öğrenciler sözel temsil üzerinde daha fazla sabitlenerek ve daha uzun süre bakarak nasıl odaklandıkları incelendi. Ancak sözel temsil üzerindeki sabitlenme süreleri diğer temsillere kıyasla oldukça düşüktü. Katılımcıların temsiller üzerindeki bakışlarına ait modellerin içerik analizi sonucu, ilişkilendirme (geriye dönük, döngüsel, taramalı ve çapalı bakış), desen (bütünlük ve tekrar durumu) ve gezinme (kısa, orta ve uzun gezinme) olmak üzere üç tema elde edildi. Sayma pulu, sayı doğrusu ve sembolik temsilde çapalı bakışlar daha az gözlendi. Sayma pulu ve sembolik temsilde tekli bütüncül desen daha sık gözlenirken sayı doğrusunda çoklu bütüncül desen daha sık gözlendi. Sözel temsillerde eylem belirten sözcüklere durum belirtilen sözcüklerden daha fazla odaklanma gözlendi. Başarı düzeyleri arttıkça geriye dönük, döngüsel, çapalı bakış sergileme durumunun azaldığı, döngüsel bakış sergileme durumunun arttığı belirlendi. Düşük başarılı katılımcılar yüksek başarılı katılımcılara kıyasla daha fazla tekrarlı desen ve daha uzun gezinmeler sergilediği belirlendi. Elde edilen bulgular, tam sayılarla toplama işlemi, matematiksel temsil ve göz izleme literatürleri bağlamında tartışıldı ve öğretmenler ve araştırmacılar için öneriler sunuldu.
In mathematics education, representations function to concretize, transform and represent ideas or relationships. When students interact with mathematical representations, they can perform many cognitive activities that are difficult to observe. Revealing these cognitive activities is very important for mathematics education. With the developing technology, approaches such as the eye-tracking method play an important role in examining cognitive activities. In this context, this study aims to examine the eye movements of middle school students on the counter, number line, symbolic and verbal representation frequently used in addition to integers. Eighty-five (40 females and 45 males) 7th-grade middle school students participated in the study. The data of 64 students were included in the analyses after the data of 21 students whose eye movement data were not appropriate were removed. During the data collection process, 12 integer addition presentations, three from each representation type, were used in eye-tracking applications. Eye-tracking data were collected with Gazepoint GP3 (60 Hz) eye tracker and analyzed with the Gazepoint Analysis Professional Edition program. Numerical and visual data were obtained with the eye-tracking method. Therefore, the study includes quantitative and qualitative elements. In the quantitative dimension of the study, numerical data obtained from students' eye movements were used. The independent variables were four different representation types: verbal representation, symbolic representation, number line representation, and counter representation. The dependent variables were gaze durations, number of fixations, and fixation durations on the four representation types. Visual documents (heat maps and gaze paths) of students' eye movements on the representations constitute the qualitative data of the study. With these documents, it was analyzed how students' eye movements on the representations, which point they focused on more, and whether there were similarities or differences in students' eye movements on the representations. The qualitative dimension of the study is a holistic multiple case study as the students' eye movements on the representations were examined both based on representation and in the context of the relationships between the representations. In the counter representation, the most fixation and the longest duration of gaze occurred on SPc (where the counters represent the numbers to be added together). In the number line representation, students gazed longer at the SDa (the tip of the first arrow and the starting point of the second arrow). However, the duration of fixations was longer in SDb. No difference was observed between the duration of gaze, number of fixations, and duration of fixations on the symbolic representation area of interest. When the representation types were compared, students fixated more and gazed longer at the verbal representation. However, their fixation durations on the verbal representation were considerably lower compared to the other representations. Content analysis of the models of participants' gaze patterns on the representations revealed three themes: association (retrospective, cyclical, scanning, and anchored gaze), pattern (holistic and repetition), and wandering (short, medium, and long wandering). It was observed that the theme of anchored gaze association in counter, number lines, and symbolic representations was observed less than the other sub-themes. While a single holistic pattern was observed more frequently in counter and symbolic representation, multiple holistic patterns were observed more frequently in number lines. In verbal representations, more focus was observed on action words than state words. As the level of achievement increased, it was determined that backward, circular, and anchored gaze decreased, and circular gaze increased. Lowachieving participants exhibited more repetitive patterns and longer wandering compared to high-achieving participants. The findings were discussed in the context of the literature on integer addition, mathematical representation, and eye tracking, and suggestions for teachers and researchers were presented.
In mathematics education, representations function to concretize, transform and represent ideas or relationships. When students interact with mathematical representations, they can perform many cognitive activities that are difficult to observe. Revealing these cognitive activities is very important for mathematics education. With the developing technology, approaches such as the eye-tracking method play an important role in examining cognitive activities. In this context, this study aims to examine the eye movements of middle school students on the counter, number line, symbolic and verbal representation frequently used in addition to integers. Eighty-five (40 females and 45 males) 7th-grade middle school students participated in the study. The data of 64 students were included in the analyses after the data of 21 students whose eye movement data were not appropriate were removed. During the data collection process, 12 integer addition presentations, three from each representation type, were used in eye-tracking applications. Eye-tracking data were collected with Gazepoint GP3 (60 Hz) eye tracker and analyzed with the Gazepoint Analysis Professional Edition program. Numerical and visual data were obtained with the eye-tracking method. Therefore, the study includes quantitative and qualitative elements. In the quantitative dimension of the study, numerical data obtained from students' eye movements were used. The independent variables were four different representation types: verbal representation, symbolic representation, number line representation, and counter representation. The dependent variables were gaze durations, number of fixations, and fixation durations on the four representation types. Visual documents (heat maps and gaze paths) of students' eye movements on the representations constitute the qualitative data of the study. With these documents, it was analyzed how students' eye movements on the representations, which point they focused on more, and whether there were similarities or differences in students' eye movements on the representations. The qualitative dimension of the study is a holistic multiple case study as the students' eye movements on the representations were examined both based on representation and in the context of the relationships between the representations. In the counter representation, the most fixation and the longest duration of gaze occurred on SPc (where the counters represent the numbers to be added together). In the number line representation, students gazed longer at the SDa (the tip of the first arrow and the starting point of the second arrow). However, the duration of fixations was longer in SDb. No difference was observed between the duration of gaze, number of fixations, and duration of fixations on the symbolic representation area of interest. When the representation types were compared, students fixated more and gazed longer at the verbal representation. However, their fixation durations on the verbal representation were considerably lower compared to the other representations. Content analysis of the models of participants' gaze patterns on the representations revealed three themes: association (retrospective, cyclical, scanning, and anchored gaze), pattern (holistic and repetition), and wandering (short, medium, and long wandering). It was observed that the theme of anchored gaze association in counter, number lines, and symbolic representations was observed less than the other sub-themes. While a single holistic pattern was observed more frequently in counter and symbolic representation, multiple holistic patterns were observed more frequently in number lines. In verbal representations, more focus was observed on action words than state words. As the level of achievement increased, it was determined that backward, circular, and anchored gaze decreased, and circular gaze increased. Lowachieving participants exhibited more repetitive patterns and longer wandering compared to high-achieving participants. The findings were discussed in the context of the literature on integer addition, mathematical representation, and eye tracking, and suggestions for teachers and researchers were presented.
Açıklama
Doktora Tezi
Anahtar Kelimeler
Temsil, Matematiksel Temsil, Göz İzleme, Tam Sayılar, Toplama İşlemi, Representation, Mathematical Representation, Eye Tracking, Integers, Addition
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Karaca, H. (2023). Ortaokul öğrencilerinin tam sayılarla toplama işleminde kullanılan temsiller üzerindeki göz hareketlerinin incelenmesi: Bir göz izleme çalışması. (Yayımlanmamış doktora tezi). Necmettin Erbakan Üniversitesi, Eğitim Bilimleri Enstitüsü Matematik ve Fen Bilimleri Eğitimi Anabilim Dalı, Konya.
