Investigating middle school students’ eye movements on the mathematical representations: An eye-tracking study

Abstract In 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.