## 3 Proposed Method
### Model Architecture  
Deep Knowledge Tracing Based on Spatial and Temporal Deep Representation Learning for Learning Performance Prediction (DKT-STDRL) consists of 3 parts: the part of extracting the spatial features of students' learning sequences by CNN, the part of intermediate data processing, and the part of extracting students' temporal features in the learning process by BiLSTM. In the part of spatial feature extraction, a multi-layer convolutional structure [27] is used to obtain students' personalized learning efficiency information as supplementary information. The goal of the intermediate data processing part is to combine the students' practice history and personalized learning efficiency information for the subsequent sequence feature extraction part. Therefore, the intermediate data processing part merges the one-hot coded spatial features and the exercise history features into the joint features of student learning, and then passes them to the next part. The next part, namely, temporal feature extraction, adopts the BiLSTM [16] structure to further extract bidirectional time-sequence features from the student learning joint features, so as to obtain the information about the change of students' knowledge state in the learning process and then predict students' performance in the next time slice. The architecture diagram of DKT-STDRL is shown in Figure 1.  
As shown in Figure 1, it can be noted that the DKT-STDRL improves the model structure of DKT [12] and CKT [14]. DKT directly used LSTM [29] to extract the temporal features (hidden knowledge state of students) of the sequences from the students' practice history, and then output the prediction results of the next time slice [12]. Compared with DKT, DKT-STDRL is improved in two aspects. First, the input information of the sequential learning structure is more abundant. The information data extracted from sequence features is no longer only the original student practice records, but also includes the spatial features extracted from the student practice sequences using CNN [27]. In this way, the spatial features can be regarded as abstract characteristics of students' personalized learning efficiency. Spatial features are added as the input of the temporal feature extraction structure for analyzing and predicting students' practice sequences from the spatial perspective before analyzing students' practice sequences from the temporal perspective. Thus, the learning analysis process of the model is more comprehensive, because the change of knowledge states of students in the learning process and the influencing factors of students' personalized learning efficiency are analyzed at the same time, and then a more accurate prediction can be obtained. Secondly, the learning ability of the structure for temporal features learning is improved. The temporal features learning structure is changed from LSTM [29] to BiLSTM [16], which enables the model to learn not only the forward sequence features, but also the reverse sequence features. The two-way learning mode enhances the ability of the model to adjust internal parameters so that it is easy to obtain more accurate prediction results. The extraction method of bidirectional temporal features is in line with the practical significance, which enables the KT model to consider students' future performance as well as their past performance, which enables more accurate judgments to be obtained when analyzing students' knowledge mastery at each time step. CKT [14] extracted the characteristics of personalized prior knowledge from students' practice records, and then extracted the characteristics of the learning rate based on the characteristics of the personalized prior knowledge using CNN [27], then outputting the prediction. Although the spatial features of student practice sequences are extracted, CKT  
Figure 1: The architecture of the DKT-STDRL model. The red text in the figure shows the shape of the data, where _batch_ equals the batch size. \(k\) represents the max sequence length.