## 4 Baselines comparison  
For the sake of better verifying the validity of the new model, DKT-STDRL was compared with DKT based on LSTM and CKT on the same dataset. As the starting model of deep knowledge tracing, the DKT model based on LSTM had an important reference value. In addition, because DKT-STDRL is an improvement based on the CKT model, the comparison with the CKT model was essential. We refer to and reproduce the code of DKT and CKT as baselines, and obtain the evaluation results approach to the reported results. Table 5 compares the prediction effects of DKT-STDRL with DKT and CKT. It was found in the experiments on the five datasets that our DKT-STDRL outperforms the DKT and the CKT in terms of RMSE, AUC, ACC, and \(r^{2}\). Specifically, for ASSISTments2009, DKT-STDRL achieved an RMSE of 0.2826. It decreased by 11.8% and 10.86% compared, respectively, with DKT and CKT. DKT-STDRL achieved an AUC of 0.9591. It increased by 15.42% and 13.54% compared, respectively, with DKT and CKT. DKT-STDRL achieved an ACC of 0.8904. It increased by 12.41% and 11.56% compared, respectively, with DKT and CKT. DKT-STDRL achieved \(r^{2}\) of 0.644. It increased by 36.05% and 32.59% comparedm respectively, with DKT and CKT. For ASSISTments2015, Synthetic-5, ASSISTchal, and Statics2011, DKT-STDRL had similar performance. Experiments verify the prediction effect of the model from two aspects: classification and regression. AUC and ACC of DKT-STDRL were gained. Therefore, the DKT-STDRL model can better classify the prediction results of whether students can answer correctly or not. Moreover, from the perspective of regression, the reduction of RMSE with DKT-STDRL reflects that the new model is more accurate in predicting the probability of students answering correctly or incorrectly. In addition, the \(r^{2}\) of DKT-STDRL has been significantly improved, which shows that the prediction results of the new model are highly correlated with the actual exercise performance of students. The new model learns the essential law of the change of students' knowledge state from the sample data. Therefore, the DKT-STDRL model promotes present KT models predicting more accurately. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters** & **Value** \\ \hline Learning rate & 0.001 \\ Rate of decay for the learning rate & 0.3 \\ Steps before the decay & 8 \\ Batch size & 50 \\ Epochs & 10 \\ Shape of filters of the conv1d & \((16,50,50)\) \\ Layers of the hierarchical convolution & 3 \\ Keep probability for dropout of the & 0.2 \\ convolution & 30 \\ Number of units of each LSTM cell & 0.3 \\ Output keep probability of LSTM cell & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hyperparameters of the DKT-STDRL. **Comparison of the variants of the DKT-STDRL. ** The experiments for comparing DKT-STDRL with its variants, by removing different parts, are helpful to understand the importance of various components in the DKT-STDRL model for advancing the prediction effect of the whole model. Therefore, in addition to the CKT and DKT, four variants were designed by us to observe the different impacts on the prediction effect from the aspects of spatial features, temporal features, prior features, and joint features. The four variants are described as follows:  
* _DKT-TDRL._ To study the influence of spatial features on the prediction effect of the DKT-STDRL model, we removed the part of extracting spatial features with CNN from the DKT-STDRL model and obtaine dthe variant model DKT-TDRL. Specifically, the DKT-TDRL model first takes the input data represented by the embedding matrix and the students' personalized prior knowledge state as the prior feature. Then, through the intermediate data processing process, it is input into BiLSTM for bidirectional time feature extraction. Finally, the prediction result is output;
* _DKT-SDRL1._ For the purpose of studying the impact of time features of DKT-STDRL on the prediction effect, the part of extracting time features was removed from the DKT-STDRL model.