A learning path recommendation method based on attention knowledge tracking

Abstract

The application discloses a learning path recommendation method based on attention knowledge tracking, which simultaneously considers the influence of knowledge level and knowledge structure on path quality, and mainly includes three parts of knowledge tracking, search space optimization and learning path recommendation. Firstly, the knowledge tracking model is trained through historical exercise data of learners, and an attention mechanism is integrated to accurately predict the knowledge level change of the learners. Secondly, based on the knowledge structure, the knowledge points associated with the learned knowledge points in the previous step are selected in the knowledge graph as a recommended candidate set, and the search space of the learning path recommendation algorithm is optimized. Finally, the trained knowledge tracking model is used to predict the mastery level of the learners on the knowledge points in the candidate set, which is used as an important evaluation standard of a variety of constraint rules, and the knowledge points recommended in the next step are pushed out from three aspects of interpretability, rationality and effectiveness, and finally a dynamic learning path is formed.

Description

Technical Field

[0001] This invention relates to a learning path recommendation method based on attention knowledge tracking, belonging to the field of online education big data mining technology. Background Technology

[0002] With the deep integration of digital information technology and smart education, remote online teaching has become an indispensable part of modern education. The emergence of online education platforms has provided new ideas and approaches to meet people's growing demand for educational resources and facilitate their access to these resources. However, in the context of big data, as the scale of educational resources continues to expand, learners need to spend more time and energy searching for suitable learning resources, resulting in low resource utilization and learning efficiency. Therefore, learning resource recommendation technology based on online education has emerged. However, existing learning resource recommendation methods often have certain limitations. One limitation is that recommended learning resources are often presented in an unordered set, without dynamic planning for specific learning paths.

[0003] In the learning process, the order in which knowledge is acquired is crucial. An ordered set of learning items that adapts to the learning process can be called a learning path. Knowledge graphs developed by domain experts can provide learners with universal learning paths, but a fixed learning sequence cannot meet the needs of all learners. Learning paths should continuously adapt to the learner's learning status to achieve the ultimate learning goal.

[0004] Existing sequence recommendation algorithms (such as neural network models like RNNs and CNNs) often focus only on the sequential similarity between learning items, neglecting the impact of cognitive structure on adaptive learning. Educational research shows that cognitive structure describes the qualitative development of knowledge, including the learner's knowledge level and the knowledge structure of the learning items, both of which significantly influence the quality of the learning path. Knowledge level reflects the learner's proficiency with the learning items; it is constantly changing and difficult to observe directly, while knowledge structure captures the cognitive relationships between learning items, manifested as inclusion, hierarchical relationships, and prerequisite / successive relationships. However, existing learning path recommendation methods, based solely on knowledge level or knowledge structure, have some limitations. Specifically, knowledge level-based methods cannot address the relational dependencies between learning items, and knowledge structure-based methods cannot reflect the different ability levels of learners, making it difficult to accurately formulate personalized learning paths. Therefore, how to systematically utilize cognitive structures, including knowledge level and knowledge structure, for learning path recommendation remains a challenging problem. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a learning path recommendation method based on attention knowledge tracking. This method can simultaneously consider the impact of knowledge level and knowledge structure on path quality, and ultimately form a dynamic learning path based on attention knowledge tracking.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A learning path recommendation method based on attention-based knowledge tracking includes the following steps:

[0008] Step 1: Train an attention-based knowledge tracking model based on the learner's historical learning data;

[0009] Step 2: Select the questions corresponding to the knowledge points learned at time step t-1 from the given prerequisite graph as the recommendation candidate set to optimize the search space of the learning path recommendation algorithm.

[0010] Step 3: Use the trained attention-based knowledge tracking model to predict the learner's mastery level of the questions in the recommended candidate set, and set recommendation rules for the recommended candidate set from three aspects: comprehensibility, importance and effectiveness, to obtain the questions recommended to the learner at time step t, thereby forming a dynamic learning path.

[0011] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0012] This invention considers both knowledge level and knowledge structure on the quality of the learning path. In the knowledge tracing part, an improved embedding representation method and attention mechanism are added to the deep knowledge tracing, thereby more accurately predicting the probability of learners answering questions correctly. In the search space optimization part, the prerequisite relationships between knowledge points in the knowledge graph are used to generate a candidate set of recommended paths. In the learning path recommendation part, based on the concept transformation model and combined with three constraint rules of interpretability, rationality, and effectiveness, questions are recommended to learners at each time step, ultimately forming a learning path oriented towards the learning objectives. Attached Figure Description

[0013] Figure 1 This is a flowchart of a learning path recommendation method based on attention knowledge tracking according to the present invention;

[0014] Figure 2 This is a schematic diagram of the Attention Knowledge Tracking (AKT) model in this invention;

[0015] Figure 3 This is a schematic diagram of the search space optimization algorithm based on knowledge graphs in this invention;

[0016] Figure 4These are the AUC scores of the six knowledge tracing models on three datasets;

[0017] Figure 5 AUC scores for three different embedding representations on three datasets;

[0018] Figure 6 The AUC scores of the SKT, AKT-NF, and AKT models on the three datasets are given.

[0019] Figure 7 The effectiveness E of each recommendation algorithm under different learning path lengths p ;

[0020] Figure 8 The probability density distribution of the Junyi dataset when the number of questions in the learning phase is between 5 and 50.

[0021] Figure 9 This is a prerequisite relationship diagram centered on the knowledge point congruent_triangles_2, with the specific information of each knowledge point on the right.

[0022] Figure 10 Visualize the learning path recommendations for four different recommendation algorithms. Detailed Implementation

[0023] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0024] like Figure 1 As shown, the learning path recommendation method based on attention knowledge tracking proposed in this invention mainly consists of three parts: knowledge tracking, search space optimization, and learning path recommendation. The specific steps are as follows:

[0025] (1) The knowledge tracking model is trained by learningers’ historical practice data and an attention mechanism is incorporated to accurately predict changes in learningers’ knowledge level.

[0026] Step (1) Each learner's learning record consists of a series of questions and responses for each discrete time step, which can be represented as H l ={x0,x1,…,x t The learner's answers at time step t, along with the relevant knowledge points and the answer results, are combined into triples. in: For the question index, This is an index of the knowledge points corresponding to this question. This represents the answer. Under this symbolic representation rule, This means that learner l answered the question about the knowledge point correctly at time step t. The problem This invention sets knowledge points and questions separately to avoid over-parameterization. In the following steps, since the discussion focuses on the prediction process of learner l's future performance, the superscript l is omitted, and the triple is simplified to (p t ,c t ,a t Given learner l's historical learning records H up to time step t. l ={x0,x1,…x t-1}={(p0,c0,a0),(p1,c1,a1),…,(p t-1 ,c t-1 ,a t-1 )}.

[0027] (101) The composite embedding representation based on the two-parameter logistic model emphasizes that different questions covered by the same knowledge point are closely related, but also have significant individual differences that cannot be ignored. In this invention, the embeddings of questions and question-answer pairs share a set of parameters, rather than using two mapping functions independently. Such an embedding representation not only significantly reduces the number of parameters in the knowledge tracing model, but also further strengthens the connection between the two inputs. Therefore, this embedding representation achieves a relative balance between modeling individual question differences and avoiding over-parameterization. Here, difficulty and discriminability are used as two parameters to construct question p. t Question-answer pairs (p) t ,a t The embedding of ) specifically includes:

[0028] (1011) Constructing knowledge point c at time step t t Related questions p t The embedding expression is:

[0029]

[0030] in, Representing problem p t The corresponding knowledge point c t The embedding vector, where D is the embedding dimension; This is a variance vector, and its row elements represent the knowledge points covered, c. t The variance of all questions in terms of difficulty and discrimination; Let p represent the control problem respectively. t The difficulty and discrimination parameters corresponding to the degree of deviation of the knowledge points.

[0031] (1012) Regarding knowledge point c tQuestion-answer pair (p) t ,a t Similarly, using the corresponding difficulty and discrimination parameters, the embedding is constructed, and the expression is:

[0032]

[0033] in, These are knowledge points - correct answers (c t ,a t The variance vector of difficulty and discrimination. To answer a t The embedding vector, when problem p t The answer was correct (a) t =1) and incorrect (a) t When =0), the embedding vector takes a different form, expressed as:

[0034]

[0035] (102) Add a time decay factor to the attention score at time step t, with the following expression:

[0036]

[0037] Where μ is a learnable decay rate parameter, μ > 0; The query vector representing the question learned by the learner at time step t is obtained by projecting the question's embedding sequence. This represents the key corresponding to the problem learned by the learner at time step τ, obtained by projecting the learner's interaction embedding sequence. In the Transformer model, each encoder has a query and key embedding layer that maps the input to D respectively. q D k Dimensional query, key output, where D q =D k .

[0038] (1021)d(t,τ) is a measure of the time distance between time steps t and τ. It considers the interference of complex learning sequences in a learner's historical learning data on the attention distribution. Specifically, when the learning sequence is long, the learner's practice sequence and corresponding knowledge point sequence often do not follow the path specified by the knowledge graph. Assume a learner's most recent practice sequence is {p}. t' ,p t'+1 ,…p t-1 ,p t The corresponding knowledge point sequence is {c}. t' ,c t'+1 ,…c t-1 ,c t}, where t' << t. If the set of knowledge points recently learned by the learner is {c t'+2 ,…,c t-1} and the knowledge points learned so far t For knowledge points with weak correlation but strong correlation from a distant time step ago, using only the absolute difference to measure the distance between time indices will reduce the attention weight of knowledge points strongly correlated with the current knowledge point and increase the attention weight of recently learned weakly correlated knowledge points. This invention uses a softmax function to adjust the distance between consecutive time indices based on the correlation between past practice problems (knowledge points) and the current problem (knowledge point), employing a context-based time metric method. The expression for d(t,τ) is:

[0039]

[0040] (103) Combining the multi-head attention mechanism, the learner's knowledge state at time step t is calculated. The calculation process is as follows:

[0041]

[0042]

[0043]

[0044] Among them, H i W is the attention output for the i-th representation subspace. i q W i k W i ν For the weight matrix, q t k τ ν τ Mapping to the i-th representation subspace, we get The attention score of the i-th attention head after adding the time decay factor can be calculated using the following formula.

[0045]

[0046] The attention weights are then obtained after normalization using the following formula. (attention value):

[0047]

[0048] The decay rate parameter μ of each attention head's corresponding subspace is different. The outputs of h attention heads are concatenated and connected by a weight matrix W.MHA Weighted summation will output the dimension as (D) ν The state vector of (×h)×1 is then passed to the next layer.

[0049] (104) Combining the question embedding at time t with the knowledge state, the probability of the learner answering the question correctly is predicted. The input of the prediction model is the question embedding x connected to time t. t With knowledge state The vector is output as the probability that the learner answers the question correctly.

[0050] (1041) First, we examine the learner's response to question p. t A preliminary prediction of the students' performance on the test can be made using the following expression:

[0051]

[0052] Where W1 and b1 are the weight matrix and bias vector of this layer, respectively.

[0053] (1402) Subsequently, the results are normalized by a fully connected layer with sigmoid as the activation function, thus obtaining the final prediction probability:

[0054]

[0055] In the above formula, W2 and b2 are the weight matrix and bias vector of the fully connected layer, respectively. M is the number of problems to be predicted. When When the learner's answer to the question is correct, it is predicted to be correct; otherwise, when... At that time, the learner's answer to the question was predicted to be incorrect.

[0056] (1403) Finally, during model training, stochastic gradient descent is used, and the Adam optimizer is employed to iteratively update all parameters used in the knowledge tracing model, minimizing the predicted output probability. With actual label The cross-entropy loss between the two is used for training and learning, and the expression is:

[0057]

[0058] The specific parameter settings are as follows: the maximum number of epochs is 300, and the learning rate is 5×10⁻⁶. -6 The batch size is 64, and the lambda parameter value for L2 loss is 1×10. -5The input embedding dimension of the attention block is 256, the hidden unit dimension is 512, and the dropout rate of the feedforward network is 0.05. In the attention module, the number of attention heads is h = 8, and each head has the same query, key, and value dimensions. The model's output layer consists of two fully connected layers with 512 and 256 hidden units, respectively. All parameters in the knowledge tracing model are initialized using the Xavier method, improving the convergence speed and stability of complex network models. Furthermore, the knowledge tracing model network includes dropout layers and residual connection layers to prevent overfitting and gradient vanishing, respectively. Figure 2 This is a schematic diagram of the Attention Knowledge Tracking (AKT) model.

[0059] (2) Select knowledge points related to the knowledge points learned in the previous step from the prerequisite graph as the recommendation candidate set to optimize the search space of the learning path recommendation algorithm.

[0060] (201) Based on the given prerequisite graph G, read the prerequisite relationships between each knowledge point;

[0061] (202) Map the problem the learner is practicing to G using a knowledge point index, and set that knowledge point as the central focus KP. Set the learning objective for the current learning stage as O = {o1, o2, ..., o}. n};

[0062] (203) Use the depth-first search algorithm to traverse the 1-hop successor knowledge points of the central focus KP, the k-hop predecessor knowledge points of the central focus KP, and the k-1 hop successor knowledge points of the k-hop predecessor, to initially generate a candidate question set S = {s1, s2, ..., s...} m};

[0063] (204) Set distance constraints to further improve the quality of candidate questions, using the shortest path l from the center focus KP to the learning objective O. min Based on the baseline, the sum of the distances |s-KP| from node s in the candidate set to the center focus KP and the distances |so| to the learning target, and the difference l between them, is taken as l. min It needs to be limited to a certain threshold range, and the expression is:

[0064] |s-KP|+|so|-l min ≤l threshold

[0065] Among them, l threshold The distance threshold is set;

[0066] (205) Finally, generate the final candidate set S' corresponding to the central focus KP, where S' represents the set of all questions corresponding to the final candidate knowledge points.

[0067] (3) Use the trained knowledge tracking model to predict the learner’s mastery level of knowledge points in the candidate set, and use it as an important evaluation criterion for various constraint rules. From the three levels of interpretability, rationality and effectiveness, the next recommended knowledge points are derived, and finally a dynamic learning path is formed.

[0068] (301) In terms of comprehensibility, the recommendation rules should be set so that the difficulty of the questions in the recommended learning path is basically in line with the student's knowledge level at the current moment, and the difficulty of question p should be in line with the difference between learner l's knowledge level about question p at time step t. The calculation method is expressed as follows:

[0069]

[0070] in, To predict learner l's knowledge level about question p at time step t using a knowledge tracing model, the difficulty of the question is... p The learning records are analyzed and extracted, and the calculation is performed using three inherent attributes of each record. The expression is as follows:

[0071]

[0072] Where u1, u2, and u3 are weight coefficients, u1 + u2 + u3 = 1, 0 < u < 1. outcome indicates whether the learner's first answer to the question is correct; outcome = 1 indicates a correct answer, outcome = 0 indicates an incorrect answer, and outcome = hint indicates that the learner requested a hint from the learning platform, which is also considered an incorrect answer; num p Z represents the total number of learners who interacted with question p; point represents the score a learner earned practicing the question. From the perspective of question attributes, a higher score indicates a simpler question. fm The score indicates the full marks for the question; proficiency indicates whether the learner has mastered the knowledge point, with proficiency=1 indicating mastery and proficiency=0 indicating no mastery.

[0073] (3011) Based on the understandability rule, it is necessary to provide... Setting threshold limits can prevent recommending information to learners that is significantly out of sync with their current knowledge level. greater than the threshold difference threshold When this happens, the knowledge points corresponding to the problem need to be removed from the candidate set, thereby generating the suboptimal set S1'.

[0074] (302) Recommendation rules are set based on the importance of the questions. Importance features can be comprehensively considered from three aspects: learning frequency, topological level, and centrality. Combining these three features, the importance of each question can be calculated using the following expression:

[0075] importance p =b1*freq p +b2*topo p +b3*center p

[0076] Among them, freq p topo p center p These represent the learning frequency, topological level, and centrality of the problem, respectively. b1, b2, and b3 are weight coefficients, where b1 + b2 + b3 = 1, and 0 < b < 1.

[0077] (3021) Based on the rationality rule, the importance of all questions in the second-best set S1' is sorted in descending order, and the last 20% of questions are deleted to improve the quality of the candidate set and generate the best set S2'.

[0078] (303) Recommendation rules should be set from an effectiveness perspective, ensuring that the recommended learning path maximizes the learner's knowledge level. Using a pre-trained knowledge tracking model, the learner's mastery level of the questions in the candidate set can be predicted. The question with the highest mastery level in the optimal set S2', which is the question recommended to the learner at that moment, is the optimal set S3', expressed as:

[0079]

[0080] The method of the present invention will be further described below with reference to the embodiments.

[0081] The datasets in this embodiment are derived from three real-world datasets: ASSISTments2009, ASSISTments2017, and Junyi.

[0082] ASSISTments2009: This dataset originates from the ASSISTments online tutoring system. "2009" indicates that the dataset describes student learning records generated by the tutoring system during the 2009-2010 academic year. The `problem_id` field represents the problem, and the `skill_id` field represents the corresponding knowledge point. After cleaning and deduplication of the data records, a total of 325,637 learning records from 4,151 learners remain.

[0083] ASSISTments2017: This dataset is the same as ASSISTments2009, both originating from the ASSISTments online tutoring system, recording learning records generated during the 2017-2018 academic year. The problemId field represents the problem, and the skill field represents the corresponding knowledge point. Using the same method as described above, and removing data in the "correct" column that was not 0 or 1, a total of 942,816 learning records from 1709 learners remained.

[0084] Junyi: This dataset was collected from the e-learning platform Junyi Academy, which was built on open-source code released by Khan Academy in 2012. It includes exercises in various subjects such as mathematics, biology, and computer science. The Junyi dataset consists of two parts. One part contains learners' learning records, where the Session_Id field indicates the learning stage, the Problem_Name field indicates the problem, and the KC (Exercise) field indicates the knowledge point corresponding to the problem. To ensure that each learning stage retains at least one learning objective after the problems and knowledge points are divided, data for learning stages with fewer learning records were deleted, leaving 99,552 learners and a total of 1,048,575 learning records. The other part of the data can be used to extract a prerequisite graph, describing the knowledge structure between nodes in the graph, such as (midpoint_formula, distance_formula), indicating that node distance_formula is a prerequisite for node midpoint_formula (a knowledge point may have multiple prerequisites).

[0085] Figure 3 In this algorithm, nodes are the basic units of the prerequisite graph, representing the knowledge points included in the learning content. The connecting lines between nodes describe the prerequisite relationships between knowledge points. The starting node is the predecessor knowledge point of the terminal node, i.e., a prerequisite. When the learner is currently practicing knowledge point 1, the search space optimization algorithm can select a candidate node set {0,2,3,6}. The next step can be to learn either the predecessor knowledge point 3 or the predecessor knowledge point 0 and its successor knowledge point 6, or the successor knowledge point 2, depending on the various constraints proposed. Finally, a learning path from the current node 0 to the target node 8 can be formed.

[0086] In this embodiment, the performance metric used is the area under the receiver operating characteristic (ROC) curve (AUC). AUC is obtained by summing the areas under the ROC curve, and its value ranges from 0.5 to 1. An AUC of 0.5 indicates that the knowledge tracing model's prediction accuracy for learners' answers is the same as that of random guessing. A higher AUC value indicates better model performance, meaning a higher AUC represents better knowledge tracing prediction results.

[0087] The performance metric used to evaluate learning path recommendation algorithms is the degree of improvement in the learner's knowledge level, E. p The expression is:

[0088]

[0089] Among them, E s E represents the learner's initial level of mastery of the learning objectives at their current learning stage (i.e., initial knowledge level). e E represents the learner's level of mastery of the learning objectives after completing all tasks in the current learning stage, with E being the maximum mastery score (usually 1). The task of learning path recommendation is to ensure that learners can effectively improve their E after completing the recommended learning path P. p .

[0090] In the ASSISTments2009 and ASSISTments2017 datasets, 60% of the learning records were used for model training, 20% for the test set, and 20% for the validation set. Since only the Junyi dataset contains knowledge structure information, allowing for further execution of search space optimization and learning path recommendation algorithms, it was used to validate the effectiveness of the learning paths. The experimental dataset cannot directly predict questions not included in the learning records, and there is no real data available to evaluate learners' mastery of the recommended questions. Therefore, real data cannot be directly used to validate the recommendation effect of the learning paths. A new simulated learning scenario needs to be constructed to simulate learners' response behavior after completing the recommended learning path, in order to evaluate the overall effectiveness of the recommended learning path. Learners' historical learning records were divided in a 6:2:2 ratio. The first 60% of the data was used to train the knowledge tracking model and initialize the learners' knowledge level; the middle 20% was masked; and the last 20% was used to select the learning objective for the current stage. The specific steps are as follows:

[0091] (1) All learning records are classified and sorted according to the learning stage identifier and timestamp. The first 60% of the historical learning records for each learning stage are extracted for training the knowledge tracing model. The questions contained in the last 20% of the data constitute the learning objectives O = {o1, o2, ... o...} n The trained knowledge tracking model is used to predict the probability that learners will answer the learning objective correctly. The average score of learners' initial mastery of the learning objective can be calculated, and the expression is:

[0092]

[0093] (2) Use a learning path recommendation algorithm to recommend learning paths, resulting in learning paths P = p1, p2, ..., p m The trained knowledge tracing model is used to predict the probability that learners will answer questions correctly in the learning path. like This indicates that the model's prediction of the learner's performance on that problem is correct; otherwise, the prediction is incorrect. The prediction results of the above learning paths can constitute a new learning record reflecting the learner's performance under the intervention of the recommendation algorithm.

[0094] (3) Integrate the new learning records corresponding to the learning path into the initial training set, use the knowledge tracking model to retrain the new integrated learning history data, and re-predict the accuracy of the learning target. The average score of learners' mastery of the learning objectives after following the recommended learning path can be calculated, expressed as:

[0095]

[0096] (4) Finally, based on E e With E s Calculate the overall effectiveness of the learning path.

[0097] The following existing knowledge tracing models are selected as reference standards and compared with the knowledge tracing model proposed in this invention:

[0098] Multi-Item Response Theory (MIRT): This model is a derivative of IRT. While IRT establishes a model function of learner ability and response accuracy, MIRT uses multidimensional hidden abilities to characterize learner state, reflecting students' ability values ​​in more dimensions.

[0099] Bayesian Knowledge Tracing (BKT): The Bayesian Knowledge Tracing model proposes a latent variable about the student's knowledge state, representing the student's knowledge state as a binary variable of {mastered, not mastered}, and predicts the learner's next knowledge state through the state transition matrix in the Hidden Markov Model (HMM).

[0100] Deep Knowledge Tracing (DKT): This model is the first application of deep neural networks in the field of knowledge tracing, using the hidden units of RNNs to describe the learner's real-time knowledge state.

[0101] An improved model for deep knowledge tracing (DKT+): An extension of DKT, which addresses the problem that DKT models cannot reconstruct observed inputs and predict state fluctuations by improving the loss function.

[0102] Dynamic Key-Value Memory Networks (DKVMN): This model portrays the learner's learning process as two separate processes: reading and writing. Specifically, it uses key-memory units and value-memory units to store concept representations associated with the questions and the learner's mastery level, continuously updating the stored content based on the learner's answering status during the learning process. Table 1 and... Figure 4 The image shows the AUC scores of AKT and its comparative model on three datasets.

[0103] Table 1 shows the AUC scores of AKT and its comparative models on three datasets.

[0104]

[0105] Experimental results show that, compared with traditional knowledge tracing models (MIRT, BKT), DKT's average AUC score is improved by 9.88%, because deep neural networks have powerful feature extraction capabilities and can capture more complex learner state representations. Secondly, the two improved deep learning models each have their advantages and disadvantages. It can be seen that the DKT+ model's performance on several datasets is slightly lower than the original DKT model, indicating that the method is not perfect. However, the DKVMN model's AUC score is improved, demonstrating the effectiveness of the memory matrix in storing learner states. Finally, the knowledge tracing (AKT) model proposed in this invention outperforms other comparative algorithms on all three datasets. Compared with the best-performing DKVMN model, its average AUC score is still improved by 4.07%, demonstrating the effectiveness of the knowledge tracing model in combining improved embedding representation algorithms and attention mechanisms.

[0106] To verify the innovation and superiority of the two-parameter logistic embedding representation in the knowledge tracing model, this embodiment uses an ablation experiment to compare the embedding representation based on the two-parameter logistic model (2PL-IRT) used in AKT with two other different embedding representation methods.

[0107] Random matrix embedding: The inputs to AKT are generated by computed two random matrices, which are the question and the question-answer pair, respectively.

[0108] Single-parameter model (1PL-IRT): The embedding of questions and knowledge points uses difficulty as a single parameter.

[0109] like Figure 5 As shown, the embedding representation method based on a two-parameter logistic model proposed in this invention outperforms the other two embedding methods in terms of accuracy across three datasets. Its AUC score is on average 1.59% higher than the random-embedding method and 0.79% higher than the 1PL-IRT method. The random-embedding method ignores individual differences between questions and fails to uncover hidden knowledge information, resulting in the worst prediction performance. The 2PL-IRT embedding representation method can capture more useful information about the question, and the extended IRT model can construct a representation method that includes a third parameter—a guessed parameter. However, this method actually increases the complexity of the input network and even leads to over-parameterization. Therefore, the embedding representation method of this invention can maximize the accuracy of knowledge tracking.

[0110] To verify the contribution of the attention module in AKT to model performance, this embodiment employs ablation experiments. The first method removes the attention mechanism module, omitting attention weights to ensure learners maintain the same attention across all questions; this model is termed SKT. The second method uses the traditional scaled dot product attention mechanism, considering only the impact of the correlation between knowledge points on attention scores, without considering learners' forgetting behavior; this model is termed AKT-NF. Figure 6 As shown, adding an attention mechanism has a certain effect on improving the accuracy of the knowledge tracking model. AKT-NF improved the AUC score of SKT by 0.61%, 0.56%, and 0.81% on the three datasets, respectively. It can also be observed that the attention mechanism improves the accuracy more significantly on the larger Junyi dataset, increasing it by 0.81%. Furthermore, adding a time decay factor to the attention mechanism further improves the prediction results, suggesting that learners' forgetting behavior provides more valuable information for knowledge tracking.

[0111] To verify the impact of the two-parameter logistic model embedding representation and attention mechanism modules on the overall knowledge tracking model, this embodiment employs ablation experiments, setting up three variants of AKT:

[0112] AKT-1: The embedding representation is generated by a random matrix, and the model does not contain an attention module;

[0113] AKT-2: The embedding representation is generated based on a two-parameter logistic model, but the model does not contain an attention module, i.e., SKT;

[0114] AKT-3: The model uses an improved attention mechanism, but the embedding representation is generated by a random matrix, i.e., random-embedding.

[0115] As shown in Table 2, both improved embedding representations and the addition of attention mechanisms can improve the AUC score of the model, and the combination of the two achieves better performance on all datasets. Taking the Junyi dataset as an example, after using the two-parameter logistic embedding representation, the AUC score of AKT-2 is improved by 0.035 compared to AKT-1; after embedding the attention mechanism module, the AUC score of AKT-3 is improved by 0.0357 compared to AKT-1; and after combining the improved functions of the two modules, the AUC score of AKT is improved by 0.0479. This proves that both the novel model embedding representation method and the attention mechanism module have a significant impact on improving the AUC score, and neither can be omitted.

[0116] Table 2 shows the AUC scores of AKT and its variants on three datasets.

[0117]

[0118] To verify the performance of the learning path recommendation algorithm, the following reference models were selected for comparison with the learning path recommendation algorithm of this invention, including:

[0119] KNN: The K-Nearest Neighbor (KNN) algorithm is based on the idea of ​​collaborative filtering. It calculates the similarity between the learning object and the target learner group by using cosine distance, then sorts them according to similarity and uses them as weights to sum the scores. The question-answering records of the group with the highest score are used as the question recommendation candidate set, thereby generating a learning path.

[0120] GRU4Rec: This model treats learner behavior as a time series for training to predict what learners may learn in the next session. By arranging learning objects at different times in chronological order, a learning path can be formed.

[0121] MCS: Monte Carlo Tree Search (MCTS) is a search method that combines knowledge tracking with the prediction of the degree of improvement in knowledge level for each search path as an index for ranking.

[0122] AKT-NSSO: Uses the knowledge tracing algorithm proposed in this example to predict learners’ mastery level of each question and recommends questions at each time step according to multiple constraint rules, but does not optimize the search space before recommendation.

[0123] SSO-Random: The recommendation problem is randomly selected from the candidate set generated by the search space optimization algorithm in this example, which is considered a simple method based on knowledge structure.

[0124] MKG: The learning path recommendation algorithm based on multidimensional knowledge graph (MKG) aims to mine the semantic relationships between knowledge points, generate multiple possible learning paths based on the knowledge graph, and then score all learning paths according to the scoring system. The learning path with the highest score is the recommended learning path.

[0125] To explore the differences in the effectiveness of different learning path lengths for recommendation performance, the effectiveness of learning paths with lengths of 5, 10, 15, 20, 25, and 30 under different recommendation algorithms was analyzed and compared.

[0126] like Figure 7 As shown, a longitudinal comparison reveals that the method proposed in this invention outperforms other comparative methods in overall learning path recommendation. Generally speaking, the effectiveness of learner-based recommendation algorithms, traditional recommendation algorithms, and learning content-based recommendation algorithms decreases sequentially. Specifically, as shown in Table 3, when the learning path length is 25 (E... p (As shown in Table 5.4), the method of this invention, by using AKT to track the learner's knowledge level, outperforms SSO-Random and MKG, which only consider knowledge structure, by 0.1886 and 0.1791 in Ep, respectively; by using SSO to optimize the search space, the method of this invention outperforms MCS and AKT-NSSO, which only consider the learner's knowledge level, in E. p The scores are 0.0966 and 0.1133 higher, respectively. This demonstrates the superiority of the two improved modules, and the high accuracy of knowledge tracking can greatly increase the effectiveness of knowledge levels in recommendation algorithms.

[0127] Table 3 shows the effectiveness of various recommendation algorithms when the learning path length is 25.

[0128]

[0129] like Figure 8 As shown, a horizontal comparison reveals that, apart from the AKT-SSO and SSO-Random methods that consider knowledge structure, as the path length increases, E... p The number of recommended learning materials also gradually increases, indicating that the richer and more comprehensive the recommended learning content, the greater its ability to improve the learner's knowledge level. For the AKT-SSO and SSO-Random algorithms, when the path length is ≤25, E... p The changes still conform to the above growth pattern; when the path length is greater than 25, E p The improvement begins to decline. Therefore, learners show the highest level of knowledge improvement when the path length is 20 or 25, peaking at a length of 25. Beyond 25, learners may feel the learning path exceeds their learning capacity, leading to a decrease in improvement.

[0130] To enhance the interpretability of the learning path recommendation algorithm proposed in this invention, a visual example of the learning path is provided here. For example... Figure 9 and 10 As shown, one recommendation algorithm of length 10 is selected from various methods for detailed examples of learning paths. Since each knowledge point contains several questions, they are not listed here; only the sequence of knowledge points in the learning path is shown. The learner is currently learning knowledge point 389, with a target knowledge point of 482. Recent learning records show that the learner has failed to answer the questions corresponding to this knowledge point, therefore, a new learning path needs to be planned. KNN continuously recommends the same knowledge point, intending to achieve the learning goal through repeated practice, which is clearly not feasible. AKT-NSSO recommends paths based on the learner's knowledge level, which has some effect, but many knowledge points are not in the prerequisite graph, resulting in poor path logic. SSO-Random randomly selects knowledge points from the candidate set, which, although consistent with the knowledge structure, does not consider the learner's knowledge level, potentially leading to a reverse learning effect. The method of this invention, AKT-SSO, allows the learner to first review preceding knowledge points and master basic knowledge points when encountering difficulties, and then simultaneously return to the learning goal based on changes in knowledge level and knowledge structure. This is clearly a more effective and reasonable learning path recommendation algorithm.

[0131] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A learning path recommendation method based on attention-based knowledge tracking, characterized in that, Includes the following steps: Step 1: Train an attention-based knowledge tracking model using the learner's historical learning data; the specific process is as follows: Step 11, obtain the learner's time step Previous historical learning data ,in, These represent the learner's time step. Learning data, These represent the question the learner answered at time step 0, the knowledge points involved, and the answer result. These represent the questions the learner answered at time step 1, the knowledge points involved, and the answer result. These represent the learner's time step. The questions answered, the knowledge points involved, and the answers provided; Step 12, based on the two-parameter logistic model, at time step Problems are constructed using two parameters: difficulty and discrimination. Question-answer pair Embedding; Step 13, at the time step Add a time decay factor to the attention score; Step 14: Based on the multi-head attention mechanism, calculate the learner's time step. The state of knowledge; Step 15, combined with time step Based on the question embedding and knowledge state, the probability of a learner answering a question correctly is predicted, which serves as the learner's time step. The level of understanding of the issues in the recommended candidate set; Step 2, select the time step from the given prerequisite diagram. The questions corresponding to related knowledge points learned are used as a candidate set for recommendations, thus optimizing the search space of the learning path recommendation algorithm; the specific process is as follows: Step 21, assign learners to time steps The practice questions are mapped to a given prerequisite graph using a knowledge point index. and will learners in time steps The practice questions focus on the relevant knowledge points. Time step The learning objectives are set as follows , Indicate learning objectives; Step 22: Use a depth-first search algorithm to traverse the center and focus points. The knowledge points after the first jump Key points about skipping the front drive and Jump front drive Skip to subsequent knowledge points and generate an initial set of candidate questions. , This represents the questions in the candidate question set; Step 23: Set distance limits for the candidate question set. The questions in the list can be filtered using the following formula: ， in, This represents the questions in the candidate question set S. express The learning objectives for the corresponding knowledge points Indicates the central focus To learning objectives The shortest path, The distance threshold is set; Based on the above selection formula, the corresponding central focus is generated. Recommended candidate set ; Step 3: Utilize the trained attention-based knowledge tracking model to predict the learner's mastery level of the questions in the candidate recommendation set. Set recommendation rules for the candidate set based on three aspects: comprehensibility, importance, and effectiveness, to obtain the time step. The questions recommended to learners form a dynamic learning path.

2. The learning path recommendation method based on attention knowledge tracking according to claim 1, characterized in that, The specific process of step 12 is as follows: 1) At the time step Construction and Knowledge Points Related issues Embedding: ， in, Indicates the learner's time step Learning data, Indicate the problem Corresponding knowledge points Embedded vector, , For the embedded dimension; , These represent control problems. The difficulty parameter and discrimination parameter are related to the degree of deviation of the corresponding knowledge points. Both are variance vectors. The row element represents the knowledge points covered. The variance in difficulty of all problems The row element represents the knowledge points covered. The variance of all problems in terms of discrimination; 2) Knowledge points Question - Answer Correct Constructing embedding representations using difficulty and discriminability parameters: ， in, Representing the embedding of question-answer pairs. These represent knowledge points and correct answers, respectively. The variance vector in terms of difficulty and discrimination. In response The embedding vector, when the problem When given a correct or incorrect answer, They are represented as follows: 。 3. The learning path recommendation method based on attention knowledge tracking according to claim 2, characterized in that, The specific process of step 13 is as follows: 1) Calculate time steps using a context-based time measurement method. and Time distance measurement between : ， in, For time step At any previous time, Indicates the learner's time step The query vector corresponding to the problem learned. Indicates the learner's time step The corresponding key to the problem learned , In the Transformer model, the input historical learning data is mapped to... , Dimensional queries, keys, The superscript T indicates transpose; 2) Calculate the time decay factor The expression is: ， in, For the attenuation rate parameter, .

4. The learning path recommendation method based on attention knowledge tracking according to claim 3, characterized in that, The calculation process for the knowledge state in step 14 is as follows: ， ， , , ， in, Indicates the learner's time step The state of knowledge, Represents the weight matrix, For the first The attention output represents a subspace. , For the number of attention heads, , , Both are weight matrices, , , Mapped to the In each representation subspace, the corresponding subspace is obtained , , , Indicates the first The attention weights for each attention head are calculated using the following formula: ， in, Represents the query vector AND key Attention score Indicator key The attention weights are defined by N, where N represents the number of key-value pairs.

5. The learning path recommendation method based on attention knowledge tracking according to claim 4, characterized in that, The specific process of step 15 is as follows: 1) Utilize the first fully connected layer to address the learner's questions. A preliminary prediction of the students' performance on the test can be made using the following expression: ， in, Indicates the learner's understanding of the problem The probability of a correct answer. and These are the weight matrix and bias vector of the first fully connected layer, respectively. 2) The preliminary prediction results are normalized using the second fully connected layer to obtain the prediction probability: ， in, and These are the weight matrix and bias vector of the second fully connected layer, respectively. Indicates the learner's understanding of the problem The normalized probability of the correct answer. , , For the number of problems to be predicted, when At that time, learners' response to the problem The answer was predicted to be correct; conversely, when At that time, learners' response to the problem The answer was predicted as incorrect; 3) During model training, stochastic gradient descent is used, and the Adam optimizer is employed to iteratively update all parameters in the knowledge tracing model, minimizing the predicted output probability. With actual label The cross-entropy loss between the two is used for training and learning, and the expression is: ， Where L represents the cross-entropy loss.

6. The learning path recommendation method based on attention knowledge tracking according to claim 5, characterized in that, The specific process of step 3 is as follows: Step 31: Set recommendation rules based on comprehensibility. The difficulty of the questions in the recommended learning path should be appropriate for the learner's time commitment. Their level of understanding of the issues in the recommended candidate set is equal; 1) Calculation problem Difficulty The expression is: ， in, , , All are weighting coefficients. , , , ; This indicates the learner's first answer to the question. Is it correct? This indicates that the answer is correct. This indicates an incorrect answer. This indicates that the learner requested a hint from the learning platform, which is also considered an incorrect answer; Representation and Question The total number of learners who generated interaction records; Practice problems for learners The score obtained; Indicate the problem A perfect score; Indicates whether learners have mastered the problem. The knowledge points involved This indicates that the information has been obtained. This indicates that the information is not yet available. 2) Calculation problems The difficulty and the learner's time pace Regarding the question Differences in knowledge levels The expression is: ， in, To use a trained attention-based knowledge tracking model to predict learners at time steps Regarding the issue of the recommended candidate set The level of mastery; 3) Set threshold ,like Greater than Then from the recommended candidate set In the middle, the knowledge points corresponding to problem p are deleted, and a second-best set is generated. ; Step 32: Set recommendation rules based on the importance of the questions, considering three aspects: learning frequency, topological level, and centrality. The expression is: ， in, Indicate the problem The importance of , , These are the learning frequency, topological level, and centrality of the problem, respectively. , , All are weighting coefficients. , , , ; The second-best set All questions are ranked by importance from highest to lowest, and the bottom 20% of questions are removed to generate a preferred set. ; Step 33: Set recommendation rules from the perspective of effectiveness. The recommended learning path should enable learners to reach the highest level of knowledge. From the preferred set Select the questions with the highest level of mastery to generate the best set. Preferred Set i.e., time step The question recommended to the learner is expressed as: ， in, Represents the preferred set The questions that middle school students master at the highest level; the best set Recommended to learners to obtain time steps learning path .

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