Investigation of eye movements of secondary school students on representations used in addition with integers: An eye tracking study

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. Low-achieving 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.