## 5 Materials and Methods
### Methodology
In order to answer the first research question, we carry out a scan-path analysis evaluating alternative interpretations based on the AOIs examined, taking the following steps:  
* We examined whether there were any differences between the scores and the type of question (if required a systematic approach to solve the question or not, i.e., 1 or 0). With this aim, we calculated the Pearson coefficient to analyze the relationship between the scores, the type of question, the time to solve the question, the scan-path length, and AOIs to be checked from the total number of AOIs defined. [PERSON]'s correlation coefficient is a widely used measure of the strength and direction of the linear relationship between two variables. One important assumption for its proper application is that the data should ideally come from a bivariate normal distribution. However, [PERSON]'s correlation is robust to deviations from normality, especially when sample sizes are sufficiently large. This robustness makes [PERSON]'s correlation applicable and reliable in many practical situations where the normality assumption may not be perfectly met. Therefore, we opted to use [PERSON]'s correlation to examine the relationships between variables in this study,as it provides a straightforward and interpretable measure of linear association that is resilient to moderate departures from normality;
* Additionally, we analyzed the influence of each AOI with a double purpose. First, we wanted to detect the most relevant areas to assess each question correctly. To do so, we performed a feature correlation analysis based on the mutual information between each of the visited AOIs and the result of the interaction. First, we carried out a minimal study of the data variance to discard invariant data that would become impractical for the analytical procedure. Then, we performed a feature correlation analysis between each of the remaining AOIs and the task result. Considering the categorical nature of both features and target, we used the estimate mutual information for discrete variables as the correlation metric;
* Finally, besides the pure analytical analysis of the results, we decided to perform a categorical classification of the participants' behavior with a double purpose. We wanted to examine whether specific patters of AOIs visited to solve the task supposed higher success rates in an inconsistent way with expectations for each item. First, this kind of analysis allows us to identify the flexibility of a task, providing a direct insight into whether the task is somehow guided, with most of the participants following a single route of resolution, or whether it is a highly free task, with not obvious pattern to resolve it. Secondly, it is possible to link those possible patterns with the obtained results to verify if any of them is more effective than others in solving the problem. So, we used a clustering classification to identify the different behavioral patterns during the experiment, using the visits of each participant to each AOI as classification features. We employed the OPTICS algorithm [94] to determine appropriate clustering regarding the participants' behavior. This algorithm offers two significant advantages over other traditional algorithms such as k means. First, it is compatible with Boolean friendly distances, such as Hamming distance. Considering that all the features used during classification are of a Boolean nature, this is a key factor to select this approach. Second, unlike k means, this algorithm detects the optimum cluster amount based on the data distribution itself. Using this approach allows us to avoid predefining the number of clusters to discover during the process.