2.1. Construction of Knowledge Tracking Model based on LSTM

Before conducting LRR, students’ mastery status on different knowledge points is obtained through knowledge tracking. Learners’ learning behavior is usually time-series data. LSTM is proposed to deal with Recurrent Neural Network (RNN)’s long-term reliance. It can analyze inputs using time series and has been proven to have superior performance in processing time-series ^14,15]. Therefore, the study adopts LSTM to build a knowledge tracking model. LSTM includes three gating mechanisms. Input gates can control whether input information is updated into the cell unit, represented by Eq. (1).

In Eq. (1), i t stands for the input gate state. W i means a weight matrix. tanh stands for an activation function. c ¯ t refers to candidate cell units. W c stands for vector units’ weight matrix. c t refers to the memory cell node’s latest state. The forget gate state is represented by Eq. (2) ^[16].

In Eq. (2), σ stands for the sigmoid activation function. W f stands for the forget gate’s weight matrix. h t − 1 stands for the input from the previous moment. V stands for the weight matrix of h t − 1 . x t refers to the input value at the current time. b stands for bias term. The output gate is represented by Eq. (3).

In Eq. (3), o t refers to the output gate state. W o refers to the weight matrix. h t refers to the output at the current time. In knowledge tracking, a concept matrix M is constructed for all knowledge, with each column representing a knowledge vector M ( i ) . The knowledge point k t and problem q t at time t are transformed into knowledge point embedding e t and problem embedding z t . z t is merged with the problem response r t , represented by Eq. (4).

In Eq. (4), ⊕ represents the connection operation. The inner product of knowledge point embeddings and each column of knowledge vectors in the concept matrix is calculated. The results are input into the softmax function, represented by Eq. (5) ^[17].

In Eq. (5), β t represents the problem and various knowledge points’ correlation. Most existing knowledge tracking models judge learners’ knowledge status based on their performance in the problem, which cannot reflect their actual knowledge level ^[18]. Therefore, the study utilizes the gating mechanism in LSTM and designs two gating mechanisms, learning and forgetting, to update learners’ knowledge states. The learner’s learning benefit is represented by Eq. (6).

In Eq. (6), w 1 T and b 1 refer to the parameters that need to be optimized. a t t refers to the time spent embedding in answering question q t . y t refers to embedding problems with authority. A learning gate is designed to control learners’ absorption of knowledge, represented by Eq. (7).

Learners’ knowledge gain L ˜ t after one learning interaction ( q t , r t ) is represented by Eq. (8).

The forget gate is represented by Eq. (9).

In Eq. (9), i t t refers to the time interval embedding between the learner’s current interaction and the previous interaction on the same problem. Therefore, the knowledge state update of learners after experiencing a learning interaction is represented by Eq. (10).

The difficulty of the problem can have an impact on the learner’s response to the question. Therefore, attention mechanisms are introduced to capture how different knowledge concepts and problem difficulty affect knowledge tracking for learners in their current knowledge state. When processing input data, the attention mechanism assigns different weights to enable the model to focus on key parts of the input data, thereby improving processing accuracy and efficiency ^19,20]. The attention mechanism is represented by Eq. (11).

In Eq. (11), Q means query. K means key. V means value. d k means the dimensions of Q and K . Learner data are collected and preprocessed. Each knowledge concept’s difficulty d ( k t ) and the problem’s difficulty d ( q t ) are calculated, represented by Eq. (12).

In Eq. (12), c o u n t R q i = 1 represents the frequency that question q i has been correctly answered by learners. c o u n t q i means the frequency that the question q i is answered by learners. c o u n t R k i = 1 means the frequency that the knowledge concept k i has been correctly grasped. c o u n t k i means the frequency that knowledge concept k i is answered by learners.

The attention network’s output is represented by Eq. (13).

Subsequently, the study increases the model nonlinearity through a position Feedforward Neural Network (FNN). FNN consists of multiple levels of nodes that transmit information in specific directions without feedback loops. Therefore, FNN is highly effective in handling static input data and classification tasks ^[21]. The FNN output is represented by Eq. (14).

The study utilizes the sigmoid function to activate the fully connected layer and minimizes the loss of the prediction layer and problem response r t through a binary cross entropy loss function, as shown in formula (15).

In summary, the knowledge tracking model constructed in this study mainly includes three modules: knowledge weight calculation, learning and forgetting, and attention. Fig. 1 shows a specific LSTM based knowledge tracking model.

2.2. Construction of the Collaborative Filtering Based-Learning Resource Recommendation Model

To further improve learning outcomes, this study conducts personalized LRR based on the knowledge mastery of different learners. CF mainly includes two types: heuristic based and model-based ^[22]. Compared to traditional user-based CF, model-based CF has higher flexibility. Therefore, the study adopts model-based CF to build LRR systems. Matrix Factorization (MF) is a method utilized to process high-dimensional data, with the main objective of decomposing a high-dimensional matrix into the product of a low dimensional matrix ^[23]. Neural Matrix Factorization (NMF) combines Generalized Matrix Factorization (GMF) and Multi-Layer Perceptron (MLP) to better capture users and items’ complicated relationships ^24,25]. Fig. 2 shows the specific structure of NMF.

NMF’s input layer is a one-hot encoding in users or items. One-hot representation is embedded into dense vectors in the feature space and merged to obtain the final prediction result. However, one-hot representation cannot reflect any semantic information, which can lead to the appearance of correlation between features. Therefore, the study adopts an embedding layer in the recommendation model and utilizes one-hot input as the table retrieval index. To address the attribute feature processing, attention mechanisms are introduced to reduce the MF irrationality. The model’s attention level λ j for each attribute is represented by Eq. (16).

In Eq. (16), w 1 and w 2 represent weight matrices. V j means the connection vector between the user’s vector q i in the feature space and the user’s attribute a j . b 1 and b 2 mean bias terms. v j means the K-dimensional vector mapped from V j . I u means the user attributes set. The user’s final latent feature vector is represented by Eq. (17).

In Eq. (17), ⊙ represents two vectors’ product element by element. To improve the interaction quality between vectors, paired pooling is utilized to encode features’ correlation in the latent feature space. Paired pooling takes into account the interactions within the set of user attribute features, can further improve user vectors’ interaction quality by multiplying them element by element. Paired pooling is represented by Eq. (18).

To make the model highly nonlinear, a fully connected layer was also added. After linear combination through fully connected layers, the final prediction result is represented by Eq. (19).

In Eq. (19), L represents the quantity of fully connected layers. p u ′ means the user’s ultimate characteristics. σ is the ReLu activation function. To obtain learners’ rating predictions for learning resources, the output layer’s loss function is Mean Squared Error (MSE). Finally, to accelerate the convergence speed of the model, Adam, which has high computational efficiency, is utilized as the optimizer to enhance the loss function. Adam’s calculation is represented by Eq. (20).

In Eq. (20), m t represents the first-order momentum of the current gradient. β 1 means first-order matrix exponential decay rate. g t means the current gradient value. v t means the second-order momentum of the current gradient. β 2 means second-order matrix exponential decay rate. Since m t and v t are both zero vectors at the beginning, bias correction is required, represented by Eq. (21).

In Eq. (21), m ^ t means gradient weighted average. v ^ t means that there is a bias in gradient weighting. The optimized parameter θ t is represented by Eq. (22).

In Eq. (22), θ 0 represents the initial parameter. α means learning rate.

3.1. Analysis of the Effect of Knowledge Tracking Model Based on LSTM

To validate the knowledge tracking model based on LSTM, the maximum sequence length is 100, the learning rate is 0.001, the quantity of hidden layers is 128, and the batch size is 64. Assisment2012 and RAIEd2020, with 80% as the training set and 20% as the testing set. Assisment2012 contains 46674 learners, 177654 questions, and 708631 interactions. The RAIEd2020 dataset is a large dataset. 1500000 records were selected for the experiment. After preprocessing to remove redundant information, 393656 learners, 13523 questions, and 1459846 interactions were included. The Area Under the Curve (AUC) was utilized as the evaluating metric. The new means was compared with five advanced models: Deep Knowledge Tracking (DKT), Dynamic Key Value Memory Network (DKVMN), Self-Attention Knowledge Tracing (SAKT), Learning Process-consistent Knowledge Tracing (LPKT), and Convolutional Knowledge Tracking (CKT). Fig. 3 shows six models’ Receiver Operating Characteristic (ROC) curves. From Fig. 3(a), this proposed means had the highest AUC of 82.37% on the Assisment2012 dataset. Next was LPKT, with an AUC of 77.68%. DKVMN performed the worst. From Fig. 3(b), on the RAIEd2020 dataset, the proposed model still had the highest AUC of 81.54%. The knowledge tracking means using LSTM demonstrated nice application in AUC and had superiority.

To investigate how hidden layers affected this model, experiments were conducted with the quantity of hidden layers set to 50, 75, 100, and 125. Fig. 4 shows the comparison results of AUC indicators for these six models mentioned above under different quantities of hidden layers. From Fig. 4(a), on the Assisment2012 dataset, as the hidden layers increased, all six models’ AUC increased. The proposed model’s AUC remained the highest, reaching 76.27% when the quantity of hidden layers was 125. From Fig. 4(b), on the RAIEd2020 dataset, the proposed model’s AUC was significantly higher than other means, showing an AUC of 77.52% when the quantity of hidden layers was 125. The increase of hidden layers could improve the model performance to a certain extent.

To investigate the proposed model’s improvement effect, ablation experiments were conducted. The AUC of models with removed learning gates (A), removed forgetting gates (B), removed attention mechanisms (C), and the complete model (D) were compared. Fig. 5 shows the ablation experiment results. On both datasets, the complete model performed the best in terms of AUC metrics. The models without attention mechanism had the lowest AUC, which were 72.14% and 70.46%, respectively. Therefore, attention mechanisms could validly enhance model. The proposed improvement strategy could validly enhance the model. The improvement effect of attention mechanism was the most significant.

3.2. Performance Analysis of Learning Resource Recommendation Model

To validate the CF-based LRR means, the FrcSub dataset was utilized and divided into training and testing sets in a 7 : 3 ratio. The FrcSub dataset is a small sample set containing 536 scoring data points, with 20 questions and 8 knowledge points examined. For each student in the test set, 40%, 50%, and 60% of the test questions were selected as the recommended test set, with the remaining questions as the training set. The study utilized the PyTorch framework to build a model, with GMF’s embedding layer dimension of 16 and the learning rate of 0.001. This proposed model was compared with traditional NMF, NFM, and Probability Matrix Factorization-Cognitive Diagnosis (PMF-CD) recommendation models that combined probability matrix factorization and cognitive diagnosis. Recommendation precision, recall, and F1 score were utilized as evaluation indicators. Table 1 shows four models’ recommended results on difficult test questions. This new means performed the best in recommending precision, recall, and F1 score. When the proportion of the test set to be recommended was 60%, this new model’s precision, recall, and F1 score were 94.82%, 92.87%, and 93.74%, respectively. The LRR model based on CF showed high recommendation accuracy and performance.

The Math dataset contains final exam questions from multiple high schools, covering 4209 students, 415 exercises, and 118 knowledge points. To further validate the proposed model’s superiority, the Math dataset was utilized for testing and separated into training, testing, and validating sets in 7 : 2 : 1. This study utilized accuracy and RMSE as evaluation indicators to compare with three currently advanced models, DKT, DKVMN, and DKT-CF. Fig. 6 shows four models’ test results on the Math dataset. From Fig. 6(a), this new means had the highest recommendation accuracy of 93.45%. Next was the DKT-CF, with a recommendation accuracy of 84.29%. DKT had the lowest recommendation accuracy. From Fig. 6(b), the proposed model had lowest RMSE, at 19.93%. The LRR model based on CF had high recommendation accuracy and certain superiority.

Fig. 7 shows the comparison results of exercise recommendation diversity indicators for four models. On both datasets, the proposed model’s LRR list had the best diversity. The CF-based LRR model could effectively improve the LRR diversity. The larger the dataset, the better the recommendation diversity.