## 4 Proposed Methodology
### Representation of Task Planning in Searching as Learning  
In this section, we focus on the construction of a structured representation for task planning in SAL. While linear structures have been extensively employed for representing task planning, recent research has indicated that learning processes are often intricate search activities requiring learners to navigate among varying learning objectives and tasks [29]. Consequently, a linear structure proves insufficient for capturing the complexity inherent in a learner's task planning strategies. [PERSON] et al. [30] substantiated the advantages of tree-structured representations in modeling search task planning. Moreover, current research has indicated that hierarchical clustering algorithms can effectively capture the subtask structure of learners' search tasks [6]. Accordingly, in the present study, we adopt a tree-structured approach to provide a more nuanced and effective representation of task planning in SAL. \begin{table}
\begin{tabular}{l} \hline \hline \multicolumn{1}{c}{Issuing queries} \\ \hline
1. Why did the learner issue this query? \\
2. Is this query related to the previously submitted queries? \\
3. What is the relationship between the results returned by this query and the results returned by previous queries? \\ \hline \hline \multicolumn{1}{c}{Clicked on URLs} \\ \hline
1. What learning object is the learner interested in? \\
2. Was this click event triggered by the most recent query? \\
3. Is the learner’s learning objective the same as or related to the learning objective of the previously submitted queries? \\ \hline \hline \multicolumn{1}{c}{Programming} \\ \hline
1. Through which queries did the learner acquire his/her learning outcomes? \\
2. To achieve the learning outcomes, did the learner experience struggles or study unrelated content? \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Questions that need to be answered for different types of SAL behavior. Figure 2: Results of SAL Task planning Capability Labeling. To fully leverage the unique context-specific features of SAL and to provide a more accurate representation of a learner's task-based structural divisions, we introduce a novel method for SAL task partitioning based on HCDP. This advanced hierarchical clustering algorithm allows for capturing the intricacies of searching and learning interactions in SAL [31]. To accurately model the structure of a learner's task planning, we consolidate his/her SAL-related interactive activities prior to initiating the modeling process. We complete this based on the observation that learning activities are triggered by issuing search queries. Furthermore, what learners acquire is contingent upon the queries they submit. Hence, in constructing the structural representation of a learner's task planning, we employ queries as the nodes of the structure. While these nodes are represented by queries, it should be noted that they encapsulate not only the search queries themselves but also the subsequent learning that occurs as a result. In traditional HCDP, the algorithmic framework is fundamentally structured around three core procedures: the computation of local densities, the construction of a hierarchical representation of the data, and the extraction of optimal clusters [32; 33; 34]. Given that our research objective specifically aims to establish a hierarchical architecture for task partitioning in SAL, our study focuses only on executing the initial two procedures. HCDP employs k-nearest neighbors for the computation of local densities. The HCDP model computes the local density as follows [34]:  
\[\rho_{i}=\max_{j\in\mathit{k}m(i)}dist(i,j) \tag{1}\]  
where \(\rho_{i}\) is the \(Node_{i}\)'s k-nearest density, \(dist(i,j)\) denotes the distance between \(Node_{i}\) and \(Node_{j}\). For each \(Node_{i}\), SAL establishes a connection to its nearest neighbor with higher density using edge weight \(\varphi\). The computation for \(\varphi\) is as follows.