## 4 Use Cases
### Problem Solving Difficulties  
MultiScaleAnalyzer provided valuable insights into the challenges students encountered during problem-solving. For example, the overview analysis in Figure 8 reveals that the error rate for the second step of a problem-solving task (B3.5_2, B7.1_2) was significantly higher than for the first step (B3.5_1, B7.1_1). In the COMPS framework, word problems are designed to be solved through a series of structured steps. The first step involves model formulation, where students abstract textual information into mathematical equations. Figure 5: AOI-based attention pattern of S7. This process begins with identifying and integrating the appropriate name tags into the equation. For instance, in part-part-whole problems like B3.5_1, students were required to recognize which components in the problem represented the \"part\" and which represented the \"whole\". Using name tags including \"gave\", \"left\", and \"total\", students constructed a basic mathematical relationship \"gave + left = total\", which reflected the structural relationship of \"part + part = whole\". The second step involved translating the abstract model into a numerical equation by assigning corresponding values. For known quantities, students directly placed the relevant numbers into the equation, while an unknown value was replaced with the placeholder \"_a_\" to prepare for further operations. For example, in a problem like B3.5_2, the quantity associated with the name tag \"gave\" was unknown, \"left\" was 62, and \"total\" was 87; students had to construct the equation \"_a_ + 62 = 87\", which formed the basis for further problem-solving. Similarly, in Lesson 7, students worked with comparison problems to formulate a conceptual model of \"smaller + difference = bigger\", which followed a similar process of abstraction and numerical representation as seen in the Lesson 3 tasks. Notably, B7.1 and B3.5 were the first problems introducing students to these respective problem types, serving as starting points for distinct conceptual frameworks. Students exhibited a significantly higher error rate in the second step, indicating students' greater difficulties in assigning numerical values to equations. Further analysis using \"Elements Vis\" revealed that a substantial number of students may have struggled with understanding the placeholder \"_a_\". This difficulty was evidenced by various behavioral indicators in the visualization. For instance, some students displayed prolonged fixations on \"_a_\", suggesting that they were attempting to comprehend its meaning and its relation to the equation model (Figure 9a). Additionally, the mouse-dragging trajectories of some students for \"_a_\" showed significant curvature (Figure 9b). Based on Bezier curve analysis, this indicated extremely slow dragging speeds, which reflected a lack of confidence and hesitation when placing \"_a_\" into the equation [15; 25]. Furthermore, some students repeatedly repositioned \"_a_\" within the equation. As show in Figure 9c, one student initially placed \"_a_\" in the position of \"left\" but subsequently moved it to the position of \"gave\". These behaviors collectively indicated that a proportion of students experienced problem-solving difficulties in B3.5_2 due to challenges in comprehending the placeholder \"_a_\" and its connection to the corresponding mathematical model equation. The visual analysis suggests that teachers should provide additional support to help students develop a clearer conceptual understanding of placeholders and their role in mathematical problem-solving. Figure 6: AOI-based attention pattern of S16. Figure 7: “Elements Vis” showing students’ problem-solving strategies. (**a**) S7 comprehensively read the entire problem (model-based problem-solving strategy); (**b**) S16 focused on specific keywords (keyword strategy). Figure 8: Students’ performance of B3.5 and B7.1. Figure 9: “Elements Vis” showing students’ problem-solving difficulty.