Eye tracking in mathematics and geometry education

Eye tracking is a valuable method for determining where individuals focus their attention, providing insights into the effectiveness of learning materials. This technology allows researchers to analyze eye movements that are difficult to observe directly, such as the sequence and duration of a user's focus on specific areas (Carter & Luke, 2020; Duchowski, 2017). Due to its effectiveness, it is widely used in mathematics education research (Strohmaier et al., 2020), with applications in various areas including numbers and operations (Gomez et al., 2017; Miller Singley & Bunge, 2018; Obersteiner & Tumpek, 2016), mathematical representations (Andrá et al., 2015; Atagi et al., 2016; Bolden et al., 2015; Karaca et al., 2025), learning disabilities (Abreu-Mendoza & Arias-Trejo, 2015; Van Der Weijden et al., 2018), problem solving (Dewolf et al., 2015; Türkoğlu & Yalçınalp, 2024; Van Marlen et al., 2018), and mathematical proof (Panse et al., 2018).

Eye tracking is frequently used in geometry research, where visuals play a significant role (Chvátal et al., 2024; Schindler & Lilienthal, 2019; Solstad et al., 2025; Uygun et al., 2024). This is attributed to the strong link between geometric thinking and visual perception (Chvátal et al., 2024), as geometry integrates both visual and abstract logical thinking (Schindler & Lilienthal, 2019). The eye-tracking approach is therefore highly valuable for geometry studies (Alqassab et al., 2018; Uygun et al., 2024). Research by Shvarts et al. (2019) shows that non-prototypical shapes lead to more eye movements, suggesting individuals first quickly recognize a shape before deciding on further analysis. Eye tracking is also effective in identifying student difficulties and misconceptions regarding geometric concepts (Uygun et al., 2024). Furthermore, eye movements reflect not only visual information focus but also how sensory-motor feedback relates to cultural contexts (Chumachenko et al., 2025), which can inform the design of more effective mathematics and geometry education materials (Strohmaier et al., 2020).

Color and visual perception in the learning process

While color is a perceptual characteristic based on visible wavelengths (Gilbert & Schleuder, 1990). Its effects extend to individuals’ psychological states and cognitive processes. Kwallek et al. (2007) mention that colors are directly linked to emotions, significantly influencing mood and well-being. For instance, warm colors like red are associated with increased arousal and attention, whereas cool colors like blue are often linked to relaxation and satisfaction (Bellizzi et al., 1983; Birren, 1983). Furthermore, studies suggest that color perception can differ based on gender (González & Sueiro, 2017; Shibasaki & Masataka, 2014).

The influence of color on perceptual processes is significant, often dominating other visual elements like shape (Wang et al., 2020). Cognitively, processing colored images requires less effort and time than black-and-white images (Gilbert & Schleuder, 1990), with some findings even suggesting that dark colors can facilitate perception (Çukur & Güller-Delice, 2011). The perception of an object is also influenced by environmental factors, such as background color and the harmony of color combinations (Mauderer et al., 2016; Wang et al., 2020). These findings highlight the fundamental role of color in visual perception.

Written and visual stimuli are used intensively in education, making colors an important part of the learning process (Ozcelik et al., 2009). Colors are powerful visual elements that significantly enrich learning by influencing cognitive processes like perception, memory, and the recall of visual stimuli (Dzulkifli & Mustafar, 2013). They guide emotional responses and affect cognitive activities such as information processing, recall, and association. Therefore, appropriate use of color can attract more attention and improve recall (Skulmowski & Rey, 2018).

Research indicates that colors have a significant effect on learning, as their intensive use in educational materials can positively impact cognitive processes. According to Ozcelik et al. (2009), associating text and visuals with colors enhances learning by facilitating information retention and the transfer of knowledge to long-term memory. Highlighting specific words with color can also improve reading and comprehension by providing visual cues (Song et al., 2021). Similarly, Skulmowski (2022) concluded that color coding and cues in learning content can significantly improve retention and transferability, thereby boosting learning performance. However, while colors can positively direct attention, they can also have a negative impact by distracting learners toward irrelevant elements (Huang & Li, 2023). Also, research indicates that red may have different effects on psychology and perception (Shibasaki & Masataka, 2014), be more distracting than other colors (Ioan et al., 2007), and negatively impact learning performance depending on individual differences (Gnambs et al., 2015). However, colors can also positively influence learning motivation. Boyatzis and Varghese (1994) found that colors can evoke positive emotions like happiness and excitement. Mazlum and Mazlum (2019) suggest that using colors such as blue, pink, and white —which create positive emotions and do not impose spatial constraints— can increase motivation for exploration and imagination, thereby improving learning efficiency. These findings emphasize the importance of careful color planning in educational materials to positively contribute to learning motivation.

Based on Mayer's (2009) Multimedia Learning Theory, the effective use of color is essential for integrating visual and verbal information to optimize learning. Given that color can positively influence learning outcomes and offer new insights into cognitive psychology (She et al., 2024), its deliberate and functional use in educational materials is a vital tool for improving learning quality and advancing the field.

In eye-tracking studies, color is a key feature that attracts attention and directs eye movements (Lima & Ventura, 2023; Wang et al., 2020). Research using this technology shows that colored cues reduce cognitive load by shortening learners' gaze duration, helping them select and organize information, and ultimately improving academic performance (Li et al., 2024; Mauderer et al., 2016; Ozcelik et al., 2009; Wang et al., 2020). Specifically, color coding that links text and visuals in learning materials has been found to reduce distractions and increase information access speed, which positively affects learning performance and fixation time (Ozcelik et al., 2009).

Purpose and importance of research

This study investigated whether student success, number of fixations, and gaze durations differ by color combination when perceptually comparing the areas of rectangle pairs. This analysis was conducted across students at different Van Hiele Geometric Thinking levels (VHGTL) groups and grade levels, as VHGTL is directly related to geometry knowledge, and curriculum outcomes increase in higher grades. This approach is based on the strong link between geometric thinking and visual perception (Chvátal et al., 2024), and the fact that geometry combines visual perception with abstract logical thinking (Schindler & Lilienthal, 2019). Furthermore, colors are salient elements known to influence and direct perceptual processes (Liu et al., 2021). While these connections are established, no previous study has examined their effects on the perception and evaluation of geometric shape areas presented with a colored background. The study's sample size is considered sufficient given its purpose, as similar eye-tracking studies with high-resolution process data and carefully controlled task conditions have employed comparable or smaller samples (e.g. Lai et al., 2013, Mason et al., 2013).

Consequently, this study aims to shed light on students' visual perception processes and provide a novel example for research in geometry education. The research questions of the study are determined as:

In this study, success (accuracy of chosen rectangle) was chosen as a measure, consistent with previous research that identifies it as a key indicator of cognitive processing efficiency in visual comparison tasks (Holmqvist et al., 2011). Eye-tracking metrics were included to reflect attentional mechanisms: fixation count was used to show the distribution of visual attention, while gaze duration indicated processing time and cognitive engagement (Duchowski, 2017; Rayner, 2009). These variables are widely used in research to explore the relationship between visual attention and task performance (Lai et al., 2013).

This study has significant theoretical and practical implications for the design of educational materials. The findings will provide data-driven insights for various stakeholders, including authorities who develop standardized tests. An analysis of student performance on questions with different color combinations can provide empirical guidance for creating more visually accessible and equitable assessments. The research's examination of eye-tracking metrics like fixations and gaze duration can also inform the creators of print and digital instructional content. By identifying how these metrics vary with different color schemes, designers can select combinations that optimize focus and enhance learning. At grade level, these results can empower educators to make research-backed decisions when selecting and designing teaching aids, ensuring that color facilitates rather than hinders student comprehension.

Research design

The variables used in this study included: (1) success in perceptually comparing the areas of rectangle pairs, defined as the accuracy of participants’ verbal responses; (2) the number of fixations recorded by the eye-tracker for each item; and (3) the gaze duration, representing the total time participants visually attended to each stimulus group. The experimental design employed a within-subjects approach, where each participant was exposed to all nine item groups. The Visual Stimuli Form (VSF) was systematically constructed from nine predetermined item groups that varied in background-figure color combinations and rectangle area characteristics.

Participants

This study was conducted in two public middle schools located in a medium-sized province in Central Anatolia, Türkiye. A total of 50 students in the 5th, 6th, and 7th grades of middle school participated voluntarily, 28 females and 22 males, with ages ranging from 10 to 13 (M =11.65; SD = .51). Of these students, 27 were in the high VHGTL group and 23 were in the low VHGTL group.

To select these participants, the VHGTL Test was previously administered to 196 students. Based on their scores, the 30 highest- and 30 lowest-scoring students were invited to participate in the second phase, which involved an eye-tracking procedure. This approach was used to maximize the variability in geometric thinking abilities between the high and low VHGTL groups, which allowed for significant differences in eye-tracking behaviors to be more effectively detected. Following this, students who failed the eye-tracking calibration or chose not to participate were excluded from the sample, resulting in the final group of 50 participants.

Instruments

Visual stimuli form

The Visual Stimuli Form (VSF) developed by researchers was used during the eye-tracking procedure. Each item in the form contained a pair of rectangles, either with equal or different areas, presented against a background from a specific color group. The colors used for the backgrounds and rectangle pairs were classified into three types: warm, cold, and neutral. Red and yellow represented warm colors; blue and green represented cold colors; and white represented neutral. Some example items of the rectangle pairs used in VSF are given in Figure 1.

Figure 1Example items from VSF 

VSF included four items per group: two with equal rectangle areas and two with unequal areas. To prevent easy visual comparison and ensure participants had to process the background and rectangle colors, the difference in area for the unequal pairs was kept between 20% and 25%.

To ensure consistency in color tones, RGB codes were used: 255-255-255 for white, 255-0-0 for red, 255-255-0 for yellow, 0-0-255 for blue, and 0-255-0 for green. The items were coded based on the color types of the background and rectangle pairs. Specifically, "C" was used for cold colors, "W" for warm colors, and "N" for neutral. For example, an item with a cold-colored background and warm-colored rectangles was coded as "CW." In this way, nine distinct item groups were formed.

Procedure

The eye-tracking procedure was conducted individually in a quiet, dimly lit school library to minimize distractions. Before the test, each student was briefed on the procedure, and a five-point calibration was performed. A pilot study with three non-participating students determined an eight-second time limit per item. To prevent carryover effects from previous images, a plus sign on a black background was displayed for one second between each item. Participants advanced to the next item by pressing the "space" key at their own pace.

Figure 2Process Diagram 

For the main study, items were presented to participants in a fixed but random order. Students were instructed to compare the areas of rectangle pairs perceptually, without performing any calculations, and to state their answers aloud. The average session duration was 164 seconds, with a range of 103 to 264 seconds.

The Visual Stimuli Form (VSF) was created with standardized digital properties, ensuring uniform color and size for all visual elements. Stimuli were organized into nine distinct item groups based on varied background-figure color combinations. Each group had four items, with an equal number of identical and subtly different areas to prevent bias. The magnitude of the area differences was controlled to maintain a consistent level of visual difficulty across all stimuli.

Moreover, the eye-tracking task was conducted individually in a quiet, dimly lit school library to minimize distractions and optimize data quality. Before the task, each participant underwent a five-point calibration to ensure tracking accuracy. Stimuli were presented on a 19-inch monitor (1440 × 900 resolution) using a GazePoint GP3 eye tracker with a 60 Hz sampling rate. Items were shown in a fixed, randomized order to control for potential order effects. A pilot study established an eight-second upper time limit per item. Participants responded verbally at their own pace, and their answers were recorded.

Data analysis

At the conclusion of data collection, three independent variables were extracted for each participant: success, number of fixations, and gaze duration per item group. For the success variable, verbal responses were coded as 1 (correct) or 0 (incorrect), with total success scores calculated for each of the nine item groups. Each item group was analyzed separately for these three variables. Since none of the variables were normally distributed, Friedman's test, the non-parametric equivalent of repeated-measures ANOVA, was used to determine significant differences among the nine item groups. When significant differences were found, Dunn's post-hoc test was applied to identify the specific groups where these differences occurred.

Ethical considerations

This study fully complied with ethical guidelines for human participant research. Official approvals were secured from all relevant institutions, and written informed consent was obtained from the parents of all student participants, who were under 18. Students were fully informed about the research's purpose and how their data would be used. To ensure participant anonymity and confidentiality, no personal identifying information was requested or recorded. Participation was entirely voluntary, and students could withdraw at any time without consequence.

Does success in perceptually comparing rectangle areas differ across item groups among students at different VHGTL groups and grade levels?

Students’ success scores on the Visual Stimuli Form (VSF) were analyzed based on the item groups. The mean rank values obtained from the analysis are presented in Table 1.

According to Table 1, the item group with the lowest success score was WC for students in the low VHGTL group, and NW for both students in the high VHGTL group and 5th-grade students. In contrast, 6th-grade students demonstrated the lowest score in the CW item group, whereas 7th-grade students showed the lowest performance in the WW item group. On the other hand, when the item groups with the highest success scores were examined, it was found that students in the low VHGTL group and 6th-grade students performed best in the CN item group, while students in the high VHGTL group achieved the highest scores in the CC item group. Additionally, both 5th- and 7th-grade students exhibited the highest scores in the NN item group.

According to the results of the Friedman test, only the students in the Low VHGTL group showed a statistically significant difference between the item group scores ( ${\chi }_{\left(8\right)}^2$=18.22, p=.02). However, the post-hoc analysis using the Bonferroni correction revealed that none of the pairwise comparisons reached statistical significance (p > .05). Therefore, it was concluded that there was no statistically significant difference between the success scores across item groups for students in the low VHGTL group.

Do the number of fixations during area comparison differ across item groups among students at different VHGTL groups and grade levels?

The number of fixations of the students based on item groups was analyzed, and the mean rank values of the results were provided in Table 2.

According to Table 2, the lowest number of fixations was observed in the CW item group for both the low and high VHGTL groups. Additionally, the low VHGTL group exhibited the highest number of fixations in the CC item group, while the high VHGTL group showed the highest number of fixations in the NN item group. Regarding grade levels, 5th- and 6th-grade students had the highest number of fixations in the CC item group, whereas 7th-grade students exhibited the highest number of fixations in the NN item group. The lowest number of fixations across grade levels was found in different item groups featuring a cold background. However, no statistically significant difference was observed in the number of fixations according to VHGTL and grade levels (p>.05). To clarify, for all student groups, the number of fixations did not demonstrate a significant difference between the item groups.

Do gaze durations during area comparison differ across item groups among students at different VHGTL groups and grade levels?

The gaze durations of different student groups were analyzed based on item groups, and the results were presented in Table 3.

At first glance at Table 3, it is observed that the lowest gaze duration for all student groups was recorded in the NN item group. It was found that students with low VHGTL exhibited the highest values in the CC item group, while students with high VHGTL exhibited the highest values in both the WN and CC item groups, with the WN item group slightly ahead.

When the data were analyzed according to grade levels, a similar pattern was observed: 5th-grade students exhibited the highest values in the CC item group, while 6th-grade students exhibited the highest values in both the WN and CC item groups, with the WN item group again slightly ahead. For 7th-grade students, the highest gaze duration was exhibited in the CN item group, differing from 5th and 6th-grade students, as was the case with the number of fixations. The Friedman test showed that there could be statistically significant differences in the gaze durations of certain groups of items across all groups (p<.001). Dunn's post-hoc test was performed to determine between which item groups these differences occurred, and the results are presented in Table 4. The table shows the test statistics for pairwise comparisons between the reference group NN and other substance groups in each participant group.

According to Table 4, statistically significant differences were observed between the gaze duration of the NN item group and those of all other item groups across all student groups, and it was concluded that all these differences favored the NN item group, which had the lowest gaze duration. However, based on the adjusted significance values obtained through the Bonferroni correction, it was concluded that the only difference between the gaze durations of the NN and CW item groups was not statistically significant only in the 7th-grade student group (adjst. p > .05).