## 1 Introduction
GKT [15] built a graph neural network (GNN) by using the correlation between knowledge points to predict learning performance. The KT models based on deep learning had significant advantages in automatically extracting features, which was suitable for mining potential rules from massive data without manual operation. Compared with traditional KTs, KTs on the basis of DL catered to the development of big data in education. However, the existing KT models had the problem that they expressed features inadequately. It can be found that most of the existing KTs on the basis of DL used relatively single network structures. For example, DKT just used RNN or LSTM to extract the temporal features of students' learning sequences, CKT just used CNN to extract the spatial features of students' learning sequences, and GKT just used GNN to learn the correlations between knowledge points. The feature extraction abilities of different DL network structures have different advantages and disadvantages. So, KTs based on single networks had limitations in sufficiently extracting features, resulting in insufficiently mining and utilizing information based on original data and a difficulty in obtaining a more accurate prediction. To solve the problem that the KT model does not adequately express deep features, we propose Deep Knowledge Tracing Based on Spatial and Temporal Deep Representation Learning for Learning Performance Prediction (DKT-STDRL), which can fully explore and comprehensively utilize the spatial and temporal characteristics of students' exercise sequences, so as to obtain more accurate prediction results. Inspired by DKT [12] and CKT [14], this model combines the students' exercise history and the spatial features as the joint learning features to further extract the temporal features of students' learning process. Specifically, for a given sequence of students' answer performance, we first extract the spatial features of students' exercise sequences by using multilayer convolution neural networks. The spatial features can represent the learners' personalized learning efficiency, which can be reflected from the performance of continuous problem solving [14]. Then, we extract the temporal characteristics of learners' learning performance sequences through bidirectional long short-term memory (BiLSTM) [16] based on the combination of spatial learning features and the original response performance. The temporal features can represent the changing process of students' knowledge state. Because of the sufficient utilization of bidirectional sequence signals by BiLSTM [17], the DKT-STDRL considers both the past and future learning performance of students so that a better judgment of the current time can be obtained. We sum up our main contributions as follows:  
1. A new KT model is proposed by us, which is called Deep Knowledge Tracing Based on Spatial and Temporal Deep Representation Learning for Learning Performance Prediction (DKT-STDRL). This model tries to combine the advantages of CKT [14] and DKT [12] in extracting the spatial features and temporal features of students' learning process, so as to mine students' learning characteristics in two ways;
2. The DKT-STDRL model combines the spatial features of students learning sequence over the past period of time extracted by the multilayer convolutional neural network with the data of students' historical answers to obtain the joint learning features. Then, we employ BiLSTM to further learn the time-series information of the joint learning features. The overlapped neural networks make the model take into account the spatial learning features when extracting the temporal features of students learning, so it is conducive to mining and obtaining deeper learning information of students;
3. We use BiLSTM to perform a two-way time series analysis of the joint learning features, which enables the model to analyze the learning features of students at each time step from both a past and future perspective, so as to obtain more accurate predictions;
4.