# Extracting Searching as Learning Tasks Based on IBRT Approach
## 3 Data and Methods
### Modeling Progress
#### 3.3.1 Improved Bayesian Rose Tree Model
As discussed above, in our experiment, students usually searched and learned using Microsoft UWP official documents. Thus, we propose calculating \(g(D_{m}|T_{m})\)  
Figure 2: IBRT subtree merging strategy. according to the hierarchical association between classes in the application programming interface provided by Microsoft's official website for UWP app development. As discussed in Section 3.2.2, students always learned following the Microsoft API reference for UWP. Thus, we built a tree structure for the knowledge network on the basis of the API reference. Specifically, on the API reference, each class belongs to a unique namespace, and a namespace contains multiple classes. Accordingly, we built each namespace as a subtree of the tree structure, while the classes under the namespace constituted the leaves of the subtree. All namespaces belonged to the set of Windows UWP namespaces. Therefore, these subtrees were used to construct a three-layer tree structure for the UWP knowledge network. In the tree structure, all UWP classes were leaves. Figure 3 shows the tree structure of the UWP API reference, where \"Windows.UI.Xaml.Media\" is a namespace that contains classes such as \"AcrylicBrush\", and \"ArcSegment\". To determine the consistency of the representation of the tree structure, we removed the nodes other than leaves in the tree for the knowledge network. Second, we mapped user queries into the knowledge network to build tree structures for each student. Specially, we mapped user queries to corresponding tree nodes in the tree of the UWP knowledge network by semantic similarity. To this end, we crawled websites about UWP programming to supplement our corpus and trained the word2 vec model. We calculated the semantic similarity from two aspects: (i) the semantic distance between queries and classes; (ii) the belonging of newly added classes (one of the learning outcomes) and the others to the knowledge network tree structure. We propose Equation (3) for mapping a user query to the corresponding tree node. \[\mathit{Semsim}\left(q_{i},\mathit{class}_{j}\right)=\alpha cos\left(v(q_{i}), v(\mathit{class}_{j})\right)+\beta belong\left(\mathit{class}_{q_{i}},\mathit{ class}_{j}\right), \tag{3}\]  
where \(v(q_{i})\) is the semantic vector for \(q_{i}\), and \(v\left(\mathit{class}_{j}\right)\) is the semantic vector for \(\mathit{class}_{j}\): \(belong()\) is an indicator function. when \(\mathit{class}_{q_{i}}\) and \(\mathit{class}_{j}\) belong to the same namespace, \(belong(\mathit{class}_{q_{i}},\mathit{class}_{j})=1\); otherwise, \(belong(\mathit{class}_{q_{i}},\mathit{class}_{j})=0\). Lastly, \(g(D_{m}|T_{m})\) is calculated by the tree edit distance between a student's knowledge network tree and \(T_{m}\) according to the method proposed by [PERSON] et al. (2019). (2) Calculating the marginal probability for LIN  
Figure 3: The tree structure of the UWP API reference. For the students who study according to their learning needs, this paper proposes the following method to calculate the marginal probability \(f(D_{m})\):  
\[f(D_{m})=\prod_{k=1}^{n}p\left(\sum_{i\in 1\ldots[Q]}\sum_{j\in 1\ldots[Q]}r_{q_{i},q_{i}}^{k}|\alpha_{k}\beta_{k}\right), \tag{4}\]  
where \(r\) represents the degree of association strength between two nodes in the tree. We calculated r on the basis of the SAL features which we extracted from students' web search data and learning outcomings. Table 1 shows the influencing factors that we selected to calculate the degree of association strength between user-issued queries in the SAL process. We employed the method proposed by [PERSON] et al. [6] to calculate \(\pi_{Tm}\) as follows:  
\[\pi_{Tm}=1-(1-\gamma)^{child(T_{m})-1}, \tag{5}\]  
where \(child(T_{m})\) presents the number of children in the tree \(T_{m}\), and \(\gamma\) is a hyperparameter. IBRT adopted the influencing factors from three main aspects:  
* Queries: (i) Queries with identical or similar terms tend to have the same learning tasks.