## 3 Method and Model
### Assessment of Emotional Expression in English Spoken Language  
To assess the emotional expression in students' spoken language audio, an emotion evaluation network was designed in this paper to analyze and evaluate emotional features from three types of audios in the previously constructed dataset, ultimately yielding emotional scores for students' spoken language audio. The network structure is shown as Step 3 in Figure 1. Firstly, the audio from the IEMOCAP dataset, students' spoken language audio, and synthesized audio were individually subjected to short-time Fourier transforms (STFT) to convert them from the time-domain space to the frequency-domain space. Subsequently, these frequency-domain representations were fed into the emotion feature encoding network to extract emotional features from the three types of audios. These emotional features were then processed through a MLP to obtain the final emotion evaluation scores, and the network was trained using mean squared error (MSE) loss. During the training process, a two-stage approach consisting of coarse-tuning and fine-tuning was employed. Firstly, the coarse-tuning stage was conducted, followed by the fine-tuning stage. The specific procedures for each stage are outlined below. **Coarse-tuning Stage**: Firstly, we calculated the cosine similarity between the emotional features of the audio from the IEMOCAP dataset and the emotional features of the other two types of audios. Then, using the cosine similarity between the audio from the IEMOCAP dataset and the synthesized audio as a reference, this reference was compared to the cosine similarity between the audio from the IEMOCAP dataset and the students' spoken language audio. By calculating the ratio of the difference between the two to the reference similarity and applying Equation (3), a preliminary emotional evaluation score for students' spoken language was obtained. The specific formula for calculating the evaluation score is as follows:  
\[s_{i}=\left\{ \begin{matrix}10&10-C\leq 1000\times\frac{(d_{2}-d_{1})}{d_{1}} \\ C\times(1+1000\times\frac{(d_{2}-d_{1})}{d_{1}})&-C<1000\times\frac{(d_{2}-d_{ 1})}{d_{1}}<10-C\\ 0&1000\times\frac{(d_{2}-d_{1})}{d_{1}}\leq-C\end{matrix} \right\}, \tag{3}\]  
where \(d_{1}\) is the cosine similarity of emotional features between audio from the IEMOCAP dataset and synthesized audio, \(d_{2}\) is the cosine similarity of emotional features between students' spoken language audio and audio from the IEMOCAP dataset, and \(C\) is the median of teachers' ratings for students' spoken language. During the coarse-tuning process, only the emotion evaluation network was trained without altering the model parameters of the emotion feature encoding network;
2. **Fine-tuning Stage**: In this stage, based on the teachers' ratings for students' emotional expression in spoken language, the emotion evaluation network was fine-tuned with the objective of minimizing the mean squared error between the predicted results and teachers' ratings. During the fine-tuning process, the parameters of the entire network, including both the emotion feature encoding network and the emotion evaluation network, were trained comprehensively. The loss function for the network in the paper is divided into coarse-tuning loss function, \(L_{coarse}\), and fine-tuning loss function \(L_{fine}\), both of which use mean squared error (MSE) loss. Specifically, the loss function formula is as follows:  
\[L_{emotion}=\lambda_{1}L_{coarse}+\lambda_{2}L_{fine}, \tag{4}\]  
where, during coarse training, \(\lambda_{1}\) equals 1 and \(\lambda_{2}\) equals 0, and during fine training, \(\lambda_{1}\) equals 0.1 and \(\lambda_{2}\) equals 1. When the model underwent fine-tuning, lambda values were set to 0.1 and 1 in order to bias the model more towards teacher ratings while also considering the objective factors from the coarse-tuning stage.