## 4 Proposed Methodology
### SAL Task Planning Ability Predicted Based on the Tree-LSTM Model  
In this paper, we address the challenge by employing the Tree-LSTM model. A Tree-LSTM is a neural network architecture that extends the standard Long Short-Term Memory (LSTM) framework [35]. While standard LSTM models are designed to process sequential data, Tree-LSTM models are adapted to handle tree-structured data. This makes them particularly useful for tasks that involve hierarchical or nested structures, such as natural language sentences, computer programs, or chemical molecules [31]. Therefore, the Tree-LSTM model serves as an instrumental methodology, enabling a more nuanced understanding of hierarchical dependencies and thereby predicting task planning ability from tree hierarchical representation. The key advantage of Tree-LSTMs lies in their ability to capture the hierarchical dependencies within tree-structured data [35; 36]. This is particularly beneficial in educational contexts where learning tasks often involve layered concepts or stepwise procedures. For instance, in the realm of programming education, the Tree-LSTM model can effectively represent and analyze the structure of code, discerning the underlying logic and predicting potential errors or areas of improvement in student submissions [37; 38]. In the context of our research framework, the Tree-LSTM model ingests a tree-structured representation encapsulating the complexities of the learning task as its input. The tree-structured data input represents the hierarchical organization of a learning task, capturing various elements such as the sequence of steps, dependencies among concepts, and the progression of learning objectives. The Tree-LSTM model then processes this input to generate an output in the form of a predictive assessment, quantifying a learner's abilities in task planning. Analogous to the conventional LSTM model, each unit in a Tree-LSTM architecture is equipped with input gates denoted as \(i_{m}\), output gates symbolized by \(o_{m}\), along with a memory cell \(c_{m}\) and a hidden state \(h_{m}\). Unique to the Tree-LSTM model, the updating mechanism for these gate vectors and memory cells is conditioned upon the aggregated states of multiple child units, if present. Moreover, each Tree-LSTM unit is endowed with specialized forget gates \(f_{m,k}\) for each child unit \(k\)[39; 40]. This design intricacy enables the Tree-LSTM to serve as a robust framework for modeling hierarchical relationships, particularly valuable for tree-structure presentation of learning tasks. Let \(S(m)\) denote the subtree of \(m\), and the transition equations of the Tree-LSTM model are as follows [41]:  
\[\widetilde{h}_{m}=\sum_{n\in S(j)}h_{n} \tag{3}\] \begin{table}
\begin{tabular}{l} \hline \hline Search-related features \\ \hline
1. Cosine distance between two sets of query terms. \\
2. Edit distance between two sets of query terms. \\
3. Jaccard distance between two sets of query terms. \\
4. The proportion of identical terms in two search queries. \\
5. Semantics distance between queries. \\ \hline Features of the relationship between searching and learning \\ \hline
1. The average cosine distance between the web page links clicked after queries. \\
2. The average edit distance between the web page links clicked after queries. \\
3. Cosine distance between the sets of UWP terms contained in clicked links after two queries. \\
4. Cosine distance between the sets of UWP terms contained in the search results after \\ two queries. \\ \hline Learning-related features \\ \hline
1. Cosine distance between the sets of UWP classes contained in programming snapshots after \\ two queries. \\
2. Edit distance between the sets of UWP classes contained in programming snapshots after \\ two queries. \\
3. Semantic distance between two programming snapshots. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The SAL features for calculating \(dist(\cdot)\).