## 3 Multiscale Visualization Design and Development
### Aggregated Data View  
Aggregating complex data according to specific criteria can effectively simplify datasets. This approach not only reduces data complexity but also helps in identifying and highlighting important patterns within data [35]. Choosing appropriate clustering criteria is crucial for uncovering patterns, and these criteria can be based on expert domain knowledge or statistical features identified during data analysis [36; 37]. For spatiotemporal data, segmenting time and dividing space into meaningful units aids in better understanding and analysis. Commonly, time is segmented into temporal cycles like hours, days, or seasons, while space is divided into areas such as cities, regions, or countries [38]. In the context of spatiotemporal learning data analysis, common spatial critiques include interaction pages or AOIs, while temporal critiques might involve learning sessions or problem segments. Thus, MultiScaleAnalyzer adopts AOIs and problem segments as aggregating criteria. This choice allows for a structured exploration of learning data, enabling users to focus on specific areas and time periods that are most relevant to learning analysis. MultiScaleAnalyzer offers two aggregated data views. By default, the system divides the problem interface into predefined AOIs, such as the question area and equation area. Meanwhile, the AOI setting page in the first view allows educators to customize AOIs by drawing rectangular regions, assigning names, and selecting colors. The system calculates fixations and mouse clicks within these AOIs and displays the data on a timeline, as shown in Figure 1b. In this view, the x-axis represents the time, while the y-axis shows the vertical coordinates of the fixations and clicks. Each dot represents a fixation within an AOI, and each mouse icon represents a click, with their positions on the timeline indicating the timing of these events. The size of the dots denotes the duration of each fixation. This view enables educators to analyze students' attention distribution and click activities across different AOIs, offering valuable insights into their engagement patterns and interaction behaviors. The second aggregated view (Figure 1c), offers higher data resolution by reconstructing the students' interactive interface, providing a comprehensive presentation of the learning content. In the view, every piece of question text and equation box on the interface is automatically set as an AOI by the system. Eye movement fixations are shown on horizontal lines below each AOI, arranged vertically in the order of occurrence. The vertical axis represents the number of fixations, and the length of these lines indicates the duration of each fixation. This helps educators to easily recognize the key elements that the student has focused on, along with the duration and sequence of fixations. The color of lines denotes the correctness of the student's final performance (red for incorrect, green for correct). Curved lines in the visualization represent mouse movement trajectories. The starting and ending points of these curves are located below the elements where the mouse movement begins and ends, corresponding to specific AOIs. The curved lines are generated using a cubic Bezier curve formula [39]:  
\[B(t)=(1-t)^{3}P_{0}+3(1-t)^{2}tP_{1}+3(1-t)t^{2}P_{2}+t^{3}P_{3},\,t\in[0,1] \tag{1}\]  
where \(P_{0}\) represents the starting point, \(P_{3}\) is the ending point, and \(P_{1}\) and \(P_{2}\) are control points. The positions of \(P_{1}\) and \(P_{2}\) are adjusted based on the inverse average velocity of the mouse movement to simulate the degree of curvature. Slower movements result in greater deviations from the straight-line path between \(P_{0}\) and \(P_{3}\), while faster movements produce smoother and straighter paths.