Multi-agent collaborative teaching interaction method and system in education scene

Abstract

The invention provides a multi-agent collaborative teaching interaction method and system in an education scene, and relates to the technical field of intelligent education, and the method comprises the steps: building a knowledge point dependency graph; constructing an optimal teaching path set; forming a collaborative teaching network and calculating a teaching path overlapping degree matrix to divide teaching tasks; acquiring learning data to generate learning difficulty indication information; and matching the teaching path with the highest adaptation degree according to the difficulty information, and adjusting the corresponding intelligent agent to carry out supplementary explanation. According to the invention, efficient collaborative configuration of intelligent teaching resources can be realized, accurate teaching support is provided for personalized difficulties of learners, and the teaching efficiency and the learning effect are improved.

Description

Technical Field

[0001] The present invention relates to intelligent education technology, and in particular to a multi-agent collaborative teaching interaction method and system in an educational scenario. Background Art

[0002] With the development of artificial intelligence (AI) technology, intelligent teaching systems are gradually evolving from single-agent models to multi-agent systems, striving to improve the efficiency and adaptability of teaching resources through multi-strategy collaboration. However, most current systems still rely on static knowledge bases or preset rules, making it difficult to dynamically model the logical relationships between knowledge points. This results in a lack of flexibility in teaching path generation and an inability to fully adapt to the knowledge structure and learning pace of different learners.

[0003] In a multi-agent collaborative environment, the lack of a unified task division and path coordination mechanism among different teaching agents often leads to redundant teaching content or information fragmentation, reducing the overall teaching coherence and intelligent collaboration of the system. Furthermore, existing systems lack effective means of analyzing and responding to learners' real-time feedback during the learning process, such as error types, questioning behaviors, and interaction characteristics, limiting the adaptive scheduling of agents and the ability to optimize teaching.

[0004] While previous research has attempted to optimize the teaching process by introducing models such as graph neural networks, reinforcement learning, and expert systems, there are still technical gaps in integrating knowledge dependency graphs, task collaboration mechanisms, and personalized dynamic adjustments. Therefore, a teaching interaction method that integrates multi-agent collaborative modeling, knowledge structure analysis, and learning feedback response capabilities is urgently needed to enhance the collaborative decision-making and personalized service capabilities of teaching agents. Summary of the Invention

[0005] The embodiments of the present invention provide a multi-agent collaborative teaching interaction method and system in an educational scenario, which can solve the problems in the existing technology.

[0006] A first aspect of an embodiment of the present invention provides a multi-agent collaborative teaching interaction method in an educational scenario, comprising: Build a knowledge point dependency graph to identify the preceding and subsequent related knowledge points for each knowledge point. Based on the historical teaching data of the teaching agent, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point, generate a teaching path score, and construct the optimal teaching path set for each teaching agent based on the teaching path score. Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to calculate the overlapping knowledge points of adjacent teaching paths. A teaching path overlap matrix is generated based on the number and degree of association of overlapping knowledge points. The teaching tasks are then divided according to the teaching path overlap matrix, and the transition content of knowledge points is constructed. Collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information; According to the learning difficulty indication information, the teaching path with the highest adaptability is matched in the optimal teaching path set, and the corresponding teaching agent is adjusted to the teaching task of the current knowledge point. The teaching agent selects the previous related knowledge points for supplementary explanation based on the knowledge point dependency graph, and updates the transition explanation content in the collaborative teaching network.

[0007] In an optional embodiment, Build a knowledge point dependency graph, identify the preceding and subsequent related knowledge points for each knowledge point, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point based on the historical teaching data of the teaching agent, and generate a teaching path score including: Extract the concept set of course knowledge points and calculate the concept relevance between knowledge points; obtain the reference concepts corresponding to the knowledge points whose concept relevance exceeds a preset relevance threshold, calculate the reference strength based on the position and frequency of the referenced concepts in the teaching text, perform a weighted calculation on the concept relevance and the reference strength to obtain the knowledge point association strength, and construct a knowledge point dependency graph based on the knowledge point association strength; In the knowledge point dependency graph, identifying the preceding and following knowledge points of each knowledge point node through a traversal algorithm, obtaining the teaching time and number of repeated teachings of the preceding and following knowledge points in the teaching agent's historical teaching data, and calculating the knowledge point difficulty mark; According to the connection relationship between the preceding associated knowledge points and the subsequent associated knowledge points, multiple traversal paths are generated in the knowledge point dependency graph. For each traversal path, the sum of the association strengths of adjacent knowledge points in the path is calculated as the path association value, and the distribution of the difficulty marks of the knowledge points in the path is calculated as the path difficulty value. The path association value and the path difficulty value are combined to generate a teaching path score.

[0008] In an optional embodiment, Constructing the optimal teaching path set for each teaching agent based on the teaching path score includes: Obtain teaching path scores, extract the question-answer frequency distribution and feedback response distribution of knowledge points from historical teaching data, generate interaction intensity sequences, identify the difficulty of understanding and mastery of knowledge points based on the interaction intensity sequences, and construct learning state features; The teaching path score is combined with the learning state characteristics, and the knowledge point positions where the question and answer frequency is higher than a first preset value and the mastery level is lower than a second preset value are marked in the teaching path. At the marked knowledge point positions, the connection weight is calculated based on the difficulty of understanding and the mastery level of adjacent knowledge points, and the teaching path score is weighted and corrected to generate an adaptive path score; Adaptive path scoring is used as the basis for path selection. Multiple teaching paths are screened and genetic iterative calculation is performed on the screened teaching paths. The relative order of the marked knowledge point positions is maintained during the iteration process, and the iteration results are used as the optimal teaching path set of the teaching agent.

[0009] In an optional embodiment, Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to calculate the overlapping knowledge points of adjacent teaching paths. A teaching path overlap matrix is generated based on the number and degree of association of overlapping knowledge points. The teaching tasks are divided according to the teaching path overlap matrix and the knowledge point transition explanation content is constructed, including: Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to analyze teaching paths and extract overlapping knowledge points of adjacent teaching paths. The node affinity matrix and path coupling matrix are calculated based on the subgraph structure of the overlapping knowledge points. The hierarchical transfer coefficient and knowledge association strength of the overlapping knowledge points are calculated through the dual constraints of the node affinity matrix and the path coupling matrix. Based on the number of overlapping knowledge points, the hierarchical transfer coefficient, and the knowledge association strength, the coreness, migration difficulty, and coverage density of the overlapping knowledge points are calculated, and a teaching path overlap matrix is generated through recursive weight updating; Constructing a task allocation graph based on the teaching path overlap matrix, performing preliminary task division using a minimum spanning tree algorithm, calculating a task balance factor based on the load capacity of the teaching agent and the distribution density of knowledge points, and adjusting the preliminary task division result using the task balance factor to obtain a teaching task division result; For the overlapping knowledge points in the teaching task division results, knowledge dependency characteristics and knowledge association characteristics are extracted, and preceding knowledge activation rules, subsequent knowledge connection rules and transition sequence rules are constructed. The rule priority is determined through competitive evaluation, and a knowledge point transition rule library is generated. Based on the degree of association between the knowledge point transition rule library and the overlapping knowledge points, the knowledge point transition explanation content is constructed.

[0010] In an optional embodiment, A task allocation graph is constructed based on the teaching path overlap matrix, and a minimum spanning tree algorithm is used to perform preliminary task division. The task balance factor is calculated according to the load capacity of the teaching agent and the distribution density of knowledge points. The preliminary task division result is adjusted using the task balance factor. The teaching task division result includes: A task allocation graph is constructed based on the teaching path overlap matrix, where nodes represent teaching agents and edges represent relationships between agents. The task load ratio of each agent is calculated, and the edge weights of the task allocation graph are calculated by combining the elements of the overlap matrix with the differences in task load ratios between adjacent agents. Performing a minimum spanning tree algorithm based on the task allocation graph to perform preliminary task division, calculating a change in the density of knowledge points in the area connected by the current edge when each edge is added, and using the change in the density of knowledge points to update the weights of adjacent unadded edges until the preliminary task division is completed; Based on the preliminary task division results, extract the load capacity of each teaching agent and the knowledge point distribution density in the coverage area, and perform a weighted combination calculation of the load capacity and the knowledge point distribution density to obtain a task balance factor; The direction and number of knowledge point migration are determined based on the difference in task balance factors of adjacent teaching agents, and the task allocation entropy after migration is calculated. When the rate of change of task allocation entropy is less than the preset change rate threshold and the difference in knowledge point distribution density in each area meets the balance requirements, the final teaching task division result is output.

[0011] In an optional embodiment, Collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information including: Collecting learners' answer data, extracting concept association, semantic similarity, and problem-solving path features from the answer data to construct a semantic feature vector, calculating the deviation value of the semantic feature vector relative to the standard answer, and identifying the error type based on the change trend of the deviation value; Obtaining learner interaction data, calculating the interaction duration and repetition frequency of each knowledge point based on the interaction data, taking the product of the interaction duration and repetition frequency as the interaction intensity, and generating a question mark when the interaction intensity exceeds the historical average of the current knowledge point; Establishing a combined feature matrix of error types and question marks, and calculating a difficulty indication coefficient based on the co-occurrence frequency of error-question pairs in the combined feature matrix; Calculate the mean and fluctuation range of the difficulty indication coefficient, determine the dynamic judgment threshold based on the mean and fluctuation range, screen out candidate difficulties when the difficulty indication coefficient exceeds the dynamic judgment threshold, prioritize the candidate difficulties, and generate learning difficulty indication information.

[0012] In an optional embodiment, The teaching paths with the highest adaptability in the optimal teaching path set according to the learning difficulty indication information include: Determining the cognitive barrier degree of the knowledge points based on the difficulty indication information, and constructing a difficult knowledge evolution network, wherein the difficult knowledge evolution network includes the cognitive association strength and cognitive barrier degree between the knowledge points; Extracting a knowledge point sequence of a candidate path from the optimal teaching path set, calculating the cognitive stress characteristics of the knowledge point sequence based on the cognitive association strength, and calculating the difficulty coverage of the knowledge point sequence based on the cognitive impairment degree; Performing a hierarchical evaluation on the sequence of knowledge points, calculating the effect of a single knowledge point on eliminating difficulties based on the degree of coverage of the difficulties, and evaluating the combined learning effect of multiple knowledge points based on the cognitive stress characteristics; The effect of eliminating difficulties is taken as the basic fitness, the combined learning effect is taken as the cognitive gain coefficient, the basic fitness and the cognitive gain coefficient are combined to obtain the comprehensive fitness of the path, and the path with the highest comprehensive fitness is selected as the optimal teaching path.

[0013] A second aspect of an embodiment of the present invention provides a multi-agent collaborative teaching interactive system in an educational scenario, comprising: The first unit is used to build a knowledge point dependency graph, identify the preceding and subsequent related knowledge points for each knowledge point, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point based on the historical teaching data of the teaching agent, generate a teaching path score, and construct the optimal teaching path set for each teaching agent based on the teaching path score; The second unit is used to form a collaborative teaching network with multiple teaching agents. It uses a graph partitioning algorithm to calculate the overlapping knowledge points of adjacent teaching paths. Based on the number and degree of correlation of overlapping knowledge points, it generates a teaching path overlap matrix. Based on the teaching path overlap matrix, it divides the teaching tasks and constructs the transition content of knowledge points. The third unit is used to collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information; The fourth unit is used to match the teaching path with the highest adaptability in the optimal teaching path set based on the learning difficulty indication information, and adjust the corresponding teaching agent to the teaching task of the current knowledge point. The teaching agent selects the previous related knowledge points for supplementary explanation based on the knowledge point dependency graph, and updates the transition explanation content in the collaborative teaching network.

[0014] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0015] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0016] In this embodiment, by establishing a knowledge point dependency graph and constructing an optimal teaching path set, the intelligent organization and planning of teaching content is achieved, the systematicness and coherence of teaching are improved, and the teaching process is more in line with the learners' cognitive development laws. The graph partitioning algorithm is used to calculate the overlapping knowledge points of adjacent teaching paths and construct transitional explanation content, which solves the connection problem in the multi-agent teaching process, reduces the sense of teaching fragmentation, enhances the coherence and consistency of teaching content between different agents, and improves the overall teaching experience. The teaching strategy is dynamically adjusted based on the learners' real-time feedback data, which can accurately identify learning difficulties and promptly call the most suitable teaching agent for targeted explanations, realize personalized teaching adaptation, effectively improve learning efficiency and teaching quality, and at the same time help learners establish a more complete knowledge system structure through supplementary explanations of previous knowledge points. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of the process of a multi-agent collaborative teaching interaction method in an educational scenario according to an embodiment of the present invention; Figure 2 This is a schematic diagram of knowledge point dependency; Figure 3 Provide a diagram for the division of teaching tasks; Figure 4 A schematic diagram comparing the effects of teaching task division based on task balance factors. DETAILED DESCRIPTION

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0019] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0020] Figure 1 FIG. 1 is a flow chart of a multi-agent collaborative teaching interaction method in an educational scenario according to an embodiment of the present invention. Figure 1 As shown, the method includes: Build a knowledge point dependency graph to identify the preceding and subsequent related knowledge points for each knowledge point. Based on the historical teaching data of the teaching agent, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point, generate a teaching path score, and construct the optimal teaching path set for each teaching agent based on the teaching path score. Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to calculate the overlapping knowledge points of adjacent teaching paths. A teaching path overlap matrix is generated based on the number and degree of association of overlapping knowledge points. The teaching tasks are then divided according to the teaching path overlap matrix, and the transition content of knowledge points is constructed. Collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information; According to the learning difficulty indication information, the teaching path with the highest adaptability is matched in the optimal teaching path set, and the corresponding teaching agent is adjusted to the teaching task of the current knowledge point. The teaching agent selects the previous related knowledge points for supplementary explanation based on the knowledge point dependency graph, and updates the transition explanation content in the collaborative teaching network.

[0021] In an optional embodiment, a knowledge point dependency graph is established to identify the preceding and subsequent related knowledge points of each knowledge point. Based on the historical teaching data of the teaching agent, the knowledge point correlation strength and teaching difficulty mark of each knowledge point during the explanation process are extracted to generate a teaching path score, which includes: Extract the concept set of course knowledge points and calculate the concept relevance between knowledge points; obtain the reference concepts corresponding to the knowledge points whose concept relevance exceeds a preset relevance threshold, calculate the reference strength based on the position and frequency of the referenced concepts in the teaching text, perform a weighted calculation on the concept relevance and the reference strength to obtain the knowledge point association strength, and construct a knowledge point dependency graph based on the knowledge point association strength; In the knowledge point dependency graph, identifying the preceding and following knowledge points of each knowledge point node through a traversal algorithm, obtaining the teaching time and number of repeated teachings of the preceding and following knowledge points in the teaching agent's historical teaching data, and calculating the knowledge point difficulty mark; According to the connection relationship between the preceding associated knowledge points and the subsequent associated knowledge points, multiple traversal paths are generated in the knowledge point dependency graph. For each traversal path, the sum of the association strengths of adjacent knowledge points in the path is calculated as the path association value, and the distribution of the difficulty marks of the knowledge points in the path is calculated as the path difficulty value. The path association value and the path difficulty value are combined to generate a teaching path score.

[0022] Figure 2This is a diagram of knowledge point dependencies. Nodes represent knowledge points, and the values in parentheses are the difficulty markers for those knowledge points. The values on the edges represent the strength of the associations between knowledge points. In one specific embodiment, the present invention provides a method for generating intelligent teaching paths based on knowledge point dependencies. This method first establishes a knowledge point dependency graph and identifies the sequential relationships between knowledge points. It then labels the difficulty based on the teaching data, ultimately generating an optimized teaching path score.

[0023] During the knowledge point dependency graph construction phase, the system extracts a set of concepts from the course's knowledge points from the teaching text library. For the "Linear Algebra" course, the system extracts 50 core concepts, including "vector," "matrix," "determinant," "system of linear equations," "eigenvalue," and "eigenvector." Using natural language processing technology, the system calculates the conceptual relevance of each pair of knowledge points. For example, the conceptual relevance of "matrix" and "determinant" is 0.85, and the conceptual relevance of "vector" and "matrix" is 0.78. The system sets a relevance threshold of 0.6 and performs citation relationship analysis on knowledge point pairs exceeding this threshold.

[0024] In the citation intensity calculation phase, the citation intensity of concepts within the teaching text is examined. Taking "eigenvalue" and "eigenvector" as examples, in the teaching text for the "Matrix Diagonalization" chapter, "eigenvalue" appears 15 times, 8 at the beginning of a paragraph and 7 in the middle. Using the position weighting rule (a weight of 1.5 for the beginning of a paragraph and 1.0 for the middle of a paragraph), the citation intensity of "eigenvalue" is calculated as (8 × 1.5 + 7 × 1.0) / total text length, resulting in a value of 0.42. Similarly, the citation intensity of "eigenvector" is 0.38. By weighting the concept relevance (0.92) and the citation intensity (0.42 and 0.38), with weights set to 0.6 and 0.4, respectively, the resulting knowledge point association strength between "eigenvalue" and "eigenvector" is 0.92 × 0.6 + (0.42 + 0.38) / 2 × 0.4 = 0.71.

[0025] Based on this method, the association strength of all relevant knowledge point pairs was calculated, and a knowledge point dependency graph consisting of 50 nodes and 78 edges was constructed. Each edge was marked with the corresponding association strength value.

[0026] During the difficulty tagging phase, a breadth-first search algorithm traverses the knowledge point dependency graph to determine the preceding and subsequent related knowledge points for each knowledge point. For example, for "matrix diagonalization," its preceding related knowledge points include "eigenvalues," "eigenvectors," and "similarity matrices," while its subsequent related knowledge points include "quadratic forms" and "solving differential equations."

[0027] Relevant teaching data was extracted from the teaching agent's historical teaching database. For the "matrix diagonalization" knowledge point, historical data showed an average teaching time of 45 minutes, with an average of 2.8 repetitions. The preceding knowledge point, "eigenvalue," had an average teaching time of 30 minutes, with 1.5 repetitions; "eigenvector" had an average teaching time of 35 minutes, with 2.0 repetitions; and "similarity matrix" had an average teaching time of 25 minutes, with 1.2 repetitions.

[0028] The difficulty level of a knowledge point is calculated based on the duration and number of repetitions. This difficulty calculation uses a weighted approach, with duration weighted at 0.7 and repetition weighted at 0.3. The 45-minute "Matrix Diagonalization" lecture was normalized to 0.9 (relative to the longest lecture in the course, 50 minutes), and the 2.8 repetitions were normalized to 0.93 (relative to the maximum number of repetitions, 3.0). The resulting difficulty level for "Matrix Diagonalization" is 0.9 × 0.7 + 0.93 × 0.3 = 0.91. Using the same method, the difficulty levels for "Eigenvalues," "Eigenvectors," and "Similarity Matrices" are calculated to be 0.60, 0.70, and 0.50, respectively.

[0029] During the teaching path scoring phase, a depth-first search algorithm was used within the knowledge point dependency graph to generate multiple possible teaching paths from the starting point to the target point. Using "vector" as the starting point and "solving a system of differential equations" as the endpoint, the system generated five different traversal paths.

[0030] For each path, the path association value and path difficulty value were calculated. Taking the path "Vector - Matrix - Eigenvalue - Eigenvector - Matrix Diagonalization - Solving Differential Equations" as an example, the association strengths of adjacent knowledge points in the path were 0.78, 0.65, 0.71, 0.82, and 0.68, respectively, with a total association strength of 3.64.

[0031] The path difficulty value is calculated based on the distribution of difficulty markers of the knowledge points within the path. The difficulty markers of the knowledge points in this path are 0.45, 0.65, 0.60, 0.70, 0.91, and 0.85, respectively, with an average difficulty of 0.69 and a standard deviation of 0.15. The system evaluates the uniformity of the difficulty distribution, assigning higher scores to paths with increasing difficulty. This path has a relatively reasonable difficulty distribution, with a clear increasing trend, resulting in a difficulty score of 0.85. The overall teaching path score is calculated by combining the path relevance value and the path difficulty value, using weights of 0.65 and 0.35. The normalized path relevance value is 0.85 (relative to the highest relevance value of 4.28), resulting in a final teaching path score of 0.85 × 0.65 + 0.85 × 0.35 = 0.85.

[0032] All five paths were scored, receiving scores of 0.76, 0.85, 0.63, 0.79, and 0.71, respectively. The highest-scoring path was recommended as the optimal teaching path. A suboptimal path was also provided as an alternative, allowing for flexible selection of appropriate teaching paths by adjusting scoring weights based on different teaching objectives.

[0033] In this embodiment, refined teaching path optimization for course knowledge points can be achieved. By constructing a knowledge point dependency graph and combining concept relevance and citation intensity, the correlation strength between knowledge points can be accurately portrayed, thereby improving the scientific nature of the organization of teaching content. At the same time, the difficulty of knowledge points is quantitatively marked using the historical data of the teaching agent, so that the teaching path not only considers the logical relationship between knowledge points, but also takes into account the difficulty of understanding and the cost of explanation in actual teaching. Finally, through multi-path traversal and scoring, the optimal teaching path is intelligently selected, thereby improving teaching efficiency and learning effects, and assisting in the realization of personalized and adaptive teaching.

[0034] In an optional embodiment, constructing an optimal teaching path set for each teaching agent based on the teaching path score includes: Obtain teaching path scores, extract the question-answer frequency distribution and feedback response distribution of knowledge points from historical teaching data, generate interaction intensity sequences, identify the difficulty of understanding and mastery of knowledge points based on the interaction intensity sequences, and construct learning state features; The teaching path score is combined with the learning state characteristics, and the knowledge point positions where the question and answer frequency is higher than a first preset value and the mastery level is lower than a second preset value are marked in the teaching path. At the marked knowledge point positions, the connection weight is calculated based on the difficulty of understanding and the mastery level of adjacent knowledge points, and the teaching path score is weighted and corrected to generate an adaptive path score; Adaptive path scoring is used as the basis for path selection. Multiple teaching paths are screened and genetic iterative calculation is performed on the screened teaching paths. The relative order of the marked knowledge point positions is maintained during the iteration process, and the iteration results are used as the optimal teaching path set of the teaching agent.

[0035] For example, when obtaining teaching path scores, the system extracts question-and-answer records for each knowledge point from the historical teaching database and calculates the frequency distribution of questions and answers. For example, for the knowledge point "quadratic equations," in the past 100 teaching interactions, students asked questions 35 times and the teacher actively explained 25 times, for a total of 60 question-and-answer interactions. The system also extracts corresponding feedback response data, including metrics such as the percentage of students' correct answers for that knowledge point, feedback latency, and question depth. For example, the correct answer percentage for the knowledge point "quadratic equations" was 65%, the average feedback latency was 12 seconds, and the average question depth level was 2.3 (on a scale of 1-5). Based on the question-and-answer frequency and feedback response data, the system generates an interaction intensity sequence, for example: {(knowledge point 1, 60, 65%, 12 seconds, 2.3), (knowledge point 2, 42, 78%, 8 seconds, 1.8)...}. Based on the interaction intensity sequence, the system determines the difficulty of understanding the knowledge points. The difficulty criteria are as follows: Questions with more than 50 answers and a correct answer percentage below 70% are considered high difficulty; questions with a question-and-answer frequency between 30-50 and a correct answer percentage between 70% and 85% are considered medium difficulty; and the rest are considered low difficulty. The system also comprehensively assesses mastery based on the correct answer percentage, feedback latency, and question depth, generating a mastery score from 0 to 100. For example, the quadratic equation, due to its high question-and-answer frequency and moderate correct answer percentage, is classified as medium difficulty, resulting in a mastery score of 68. This information constitutes the learning state characteristics.

[0036] In the stage of combining teaching path scoring and learning state characteristics, the system first associates each teaching path with the corresponding learning state characteristics. For teaching path A with an existing score of 85 points: {knowledge point 1→knowledge point 2→knowledge point 3→knowledge point 4→knowledge point 5}, the system identifies the knowledge points whose question and answer frequency is higher than the preset value of 50 times and whose mastery level is lower than the preset value of 70 points, and marks them as key focus positions. In the example, knowledge point 1 (frequency 60, mastery level 68) and knowledge point 4 (frequency 55, mastery level 62) are marked. The system then calculates the connection weights between adjacent knowledge points. The calculation basis is: if the previous knowledge point is of high difficulty and low mastery level, and the next knowledge point depends on the previous knowledge point, the connection weight increases; otherwise, it decreases. For example, the connection weight between knowledge point 1 (medium difficulty) and knowledge point 2 (low difficulty) is 1.2; the connection weight between knowledge point 3 (low difficulty) and knowledge point 4 (high difficulty) is 1.5. The system adjusts the teaching path score based on the connection weights: Corrected score = Original score × (1 + Total connection weights of the marked knowledge points × 0.1). In this example, the total connection weight of Path A is 2.7, so the corrected score is 85 × (1 + 2.7 × 0.1) = 108.0 points, forming an adaptive path score.

[0037] In the optimal teaching path screening stage, the candidate teaching paths are first sorted and screened based on the adaptive path score. For example, the top five paths are screened out from 10 candidate paths: Path A (108.0 points), Path B (105.5 points), Path C (103.2 points), Path D (101.8 points), and Path E (100.6 points). The system then performs genetic iterative calculations on these five paths to further optimize the teaching path. The genetic algorithm uses a crossover rate of 0.8 and a mutation rate of 0.2, with a population size of 100 and 50 iterations. During the iteration process, the system ensures that the relative order of the marked key knowledge points remains unchanged, that is, knowledge point 1 must be before knowledge point 4 to ensure the consistency of the teaching logic. At the same time, other non-key knowledge points in the path can be adjusted to explore a better teaching sequence. After genetic iterations, the system generated an optimal path X with a score of 112.5: {Knowledge Point 1 → Knowledge Point 3 → Knowledge Point 2 → Knowledge Point 4 → Knowledge Point 5}, and a suboptimal path Y with a score of 110.2: {Knowledge Point 1 → Knowledge Point 2 → Knowledge Point 3 → Knowledge Point 4 → Knowledge Point 7}. These paths constitute the optimal teaching path set for the teaching agent, which the teaching system can select and use in different teaching situations.

[0038] Furthermore, learning status features and path scores are periodically updated to adapt to learners' progress. For example, if a student's mastery of the "quadratic equation" knowledge point improves from 68 to 75, the system recalculates the connection weights and adaptive path scores, dynamically adjusting the optimal teaching path set. In this way, the teaching agent continuously optimizes teaching paths and provides a personalized learning experience.

[0039] Table 1: Summary of genetic iterative optimization results and optimal teaching path set;

[0040] Table 1 compares the performance of five candidate teaching paths before and after iterative optimization using the genetic algorithm. After 50 iterations (crossover rate 0.8, mutation rate 0.2), a higher-scoring teaching path was generated while maintaining the relative order of key knowledge points. The final optimized paths, Path X (112.5 points) and Path Y (110.2 points), constitute the optimal teaching path set for the teaching agent.

[0041] In this embodiment, it is possible to achieve adaptive optimization of the teaching path based on the rationality of the global structure and the individual learning state, thereby improving the personalized teaching ability of the teaching intelligent body. By integrating the teaching path scoring and the learner's interactive behavior characteristics, the understanding difficulties and knowledge blind spots in the learning process are accurately identified, ensuring that the key and difficult knowledge points are strengthened in the path. The interaction intensity sequence reflects the real-time interaction status of the learner and each knowledge point, which helps to dynamically estimate their mastery level, thereby supporting refined learning state modeling. By marking the key knowledge points in the path and adjusting the score based on the connection weight, a dynamic balance between the path structure and the learning load is achieved. Further combined with the genetic iterative strategy, it is ensured that while keeping the order of teaching focus unchanged, a better path combination is excavated, and finally a customized, advanced optimal teaching path set is matched for different teaching scenarios and student portraits, significantly improving the accuracy, adaptability and learning outcomes of the teaching process.

[0042] In an optional implementation, multiple teaching agents are formed into a collaborative teaching network, a graph partitioning algorithm is used to calculate the overlapping knowledge points of adjacent teaching paths, and a teaching path overlap matrix is generated based on the number and correlation of overlapping knowledge points. The teaching tasks are divided according to the teaching path overlap matrix and the knowledge point transition explanation content is constructed, including: Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to analyze teaching paths and extract overlapping knowledge points of adjacent teaching paths. The node affinity matrix and path coupling matrix are calculated based on the subgraph structure of the overlapping knowledge points. The hierarchical transfer coefficient and knowledge association strength of the overlapping knowledge points are calculated through the dual constraints of the node affinity matrix and the path coupling matrix. Based on the number of overlapping knowledge points, the hierarchical transfer coefficient, and the knowledge association strength, the coreness, migration difficulty, and coverage density of the overlapping knowledge points are calculated, and a teaching path overlap matrix is generated through recursive weight updating; Constructing a task allocation graph based on the teaching path overlap matrix, performing preliminary task division using a minimum spanning tree algorithm, calculating a task balance factor based on the load capacity of the teaching agent and the distribution density of knowledge points, and adjusting the preliminary task division result using the task balance factor to obtain a teaching task division result; For the overlapping knowledge points in the teaching task division results, knowledge dependency characteristics and knowledge association characteristics are extracted, and preceding knowledge activation rules, subsequent knowledge connection rules and transition sequence rules are constructed. The rule priority is determined through competitive evaluation, and a knowledge point transition rule library is generated. Based on the degree of association between the knowledge point transition rule library and the overlapping knowledge points, the knowledge point transition explanation content is constructed.

[0043] In a collaborative teaching network, multiple teaching agents improve teaching effectiveness by jointly participating in teaching tasks. This embodiment provides a method for constructing a collaborative teaching network based on overlapping knowledge points. By calculating the teaching path overlap matrix, the teaching tasks are divided and the transition content of knowledge points is constructed.

[0044] The teaching path can be represented as a directed connection graph of knowledge points G = (V, E), where V represents the set of knowledge points and E represents the connection between knowledge points. For n teaching agents in the collaborative teaching network, n teaching paths P = {P1, P2, ..., P n}. Analyze adjacent teaching paths through graph partitioning algorithm and extract overlapping knowledge point set O={O 12 , O 13 ,...,O mn}, where O ij Represents path P i and P j A set of overlapping knowledge points.

[0045] For the identified overlapping knowledge points, the subgraph structural features are extracted to construct the node affinity matrix A and the path coupling matrix C. The node affinity matrix reflects the internal connection strength between overlapping knowledge points, and the path coupling matrix represents the distribution difference of overlapping knowledge points in different teaching paths. For example, for the overlapping knowledge point set O 12 ={k1, k2, k3}. If k1 and k2 are closely connected in path P1 but far apart in P2, the corresponding path coupling is low, expressed as C 12 (k1, k2)=0.3.

[0046] Based on the dual constraints of the node affinity matrix and the path coupling matrix, the hierarchical transfer coefficient T and the knowledge association strength R of the overlapping knowledge points are calculated. The hierarchical transfer coefficient describes the transfer characteristics of knowledge points between different levels, and the knowledge association strength represents the degree of semantic association between knowledge points. Specifically, for overlapping knowledge points k i and k j , if A(k i , k j )=0.8,C(k i , k j )=0.6, then we can calculate T(k i , k j )=0.72, R(k i , k j )=0.65.

[0047] After obtaining the hierarchical transfer coefficient and knowledge association strength, the coreness (I), transfer difficulty (D), and coverage density (S) of the overlapping knowledge points were calculated. Coreness indicates the importance of the knowledge point within the overall instructional structure; transfer difficulty reflects the complexity of transferring the knowledge point from one instructional path to another; and coverage density measures the breadth of the knowledge point's distribution across different instructional paths. For example, the overlapping knowledge point "Definition of Quadratic Function" appears in all five instructional paths and is closely connected to surrounding knowledge points. Its coreness (I) is 0.85, transfer difficulty (D) is 0.25, and coverage density (S) is 0.92.

[0048] Through the recursive weight update mechanism, the core degree, migration difficulty and coverage density are integrated to generate the teaching path overlap matrix M. The elements M in this matrix are ij Represents path P i and P j The recursive weight update process sets the initial weight vector W0 = [0.4, 0.3, 0.3], and after three rounds of iterations, the stable weight W3 = [0.5, 0.2, 0.3] is obtained, and the path overlap is calculated based on this weight. For example, for teaching paths P1 and P2, the calculated M 12 =0.5×0.85+0.2×0.25+0.3×0.92=0.716.

[0049] Based on the teaching path overlap matrix M, a task allocation graph G'=(P, M) is constructed, and a minimum spanning tree algorithm is applied to perform preliminary task partitioning. The algorithm starts with the edge with the lowest weight and gradually adds edges that do not form cycles, ultimately forming a minimum spanning tree that covers all teaching paths. For an example with five teaching paths, the initial partitioning result is {{P1, P3}, {P2}, {P4, P5}}, indicating that the teaching task is divided into three subtasks, each of which is handled by three teaching agents.

[0050] Considering the teaching agent's load capacity L and knowledge point distribution density K, we calculated the task balance factor B = L / K. For a load capacity L = 0.8 and a knowledge point distribution density K = 0.6, the task balance factor B = 1.33, indicating that this teaching agent can handle a large number of teaching tasks. Based on the task balance factor, we adjusted the initial partitioning results to obtain a balanced teaching task partition {{P1, P3}, {P2, P5}, {P4}}.

[0051] For the overlapping knowledge points in the teaching task division results, extract the knowledge dependency feature F dep and knowledge association feature F rel For the overlapping knowledge point "polynomial multiplication", its dependency features include the prior knowledge requirements and the degree of concept dependency, and the knowledge association features include the semantic similarity between knowledge points and the degree of application scenario overlap. Based on the extracted features, the prior knowledge activation rule R is constructed.pre , post-order knowledge connection rule R post and transition order rule R ord The prior knowledge activation rules ensure that learners have mastered the necessary prerequisite knowledge; the subsequent knowledge connection rules ensure a seamless connection between the current knowledge point and subsequent content; and the transition sequence rules specify the optimal order for explaining knowledge points. For example, for the transition between "vector addition" and "vector subtraction," the rule is constructed: "First explain the geometric meaning of vector addition, then introduce the concept of vector subtraction by analogy."

[0052] The priority of rules is determined through a competitive evaluation mechanism, and a knowledge point transition rule library is generated. The priority of rules is determined based on the success rate of rule application and the importance of knowledge points. For example, the priority of the rule "basic functions must be reviewed before introducing composite functions" is 0.88, which is higher than the priority of "function limits must be reviewed before explaining function derivatives" of 0.79. Finally, based on the degree of correlation between the knowledge point transition rule library and overlapping knowledge points, knowledge point transition explanation content is constructed for each pair of adjacent teaching paths. For example, for the teaching content transitioning from "linear equations" to "matrices", a transition explanation is generated: "Linear equations can be expressed by coefficient matrices. By introducing the concept of matrices, linear equations can be expressed and solved more concisely", which achieves a smooth transition of knowledge points and improves the coherence and effectiveness of collaborative teaching.

[0053] Figure 3 A diagram for dividing teaching tasks, such as Figure 3 The upper part shows a task allocation graph constructed based on the teaching path overlap matrix, where nodes represent teaching paths and the values on the edges represent the overlap between paths. The lower part shows the preliminary task division results using the minimum spanning tree algorithm and the balance adjustment process based on the task balance factor (load capacity / knowledge point distribution density) to allocate reasonable teaching tasks to the teaching agent.

[0054] In existing technologies, multiple teaching agents typically operate independently, lacking effective path coordination and task partitioning mechanisms. This can easily lead to repeated knowledge point explanations, disconnected connections, and low teaching resource utilization. Traditional path integration methods often rely on manual planning or simple aggregation based on static path similarity, making it difficult to dynamically identify deep connections between knowledge points and flexibly allocate tasks based on the teaching load. This application proposes an improved solution to address these issues. First, a graph partitioning algorithm is used to construct the structural relationship between teaching paths. Overlapping knowledge points are extracted and node affinity and path coupling are calculated based on the subgraph structure. This method then constructs the hierarchical transfer relationship and knowledge association strength of overlapping knowledge points, achieving a precise quantification of the degree of overlap. Subsequently, a dynamically recursively updated teaching path overlap matrix is generated based on the importance, migration difficulty, and coverage density of the knowledge points. A task allocation graph is then constructed based on this matrix. A minimum spanning tree method is used to perform preliminary partitioning. The partitioning results are then adjusted based on the teaching agent's load capacity and the knowledge point distribution density, effectively achieving balanced task allocation. Furthermore, the solution introduces a transition rule construction mechanism that generates multidimensional connection rules based on knowledge dependencies and association features, improving the coherence and adaptability of the explanation of overlapping knowledge points between agents. Starting from the optimization of collaborative structure, this solution systematically solves the problems of repeated teaching content and poor connection, and improves the organizational efficiency and collaborative intelligence level of the multi-agent teaching system.

[0055] In an optional embodiment, a task allocation graph is constructed based on the teaching path overlap matrix, a minimum spanning tree algorithm is used to perform preliminary task division, a task balance factor is calculated based on the load capacity of the teaching agent and the distribution density of knowledge points, and the preliminary task division result is adjusted using the task balance factor. The teaching task division result includes: A task allocation graph is constructed based on the teaching path overlap matrix, where nodes represent teaching agents and edges represent relationships between agents. The task load ratio of each agent is calculated, and the edge weights of the task allocation graph are calculated by combining the elements of the overlap matrix with the differences in task load ratios between adjacent agents. Performing a minimum spanning tree algorithm based on the task allocation graph to perform preliminary task division, calculating a change in the density of knowledge points in the area connected by the current edge when each edge is added, and using the change in the density of knowledge points to update the weights of adjacent unadded edges until the preliminary task division is completed; Based on the preliminary task division results, extract the load capacity of each teaching agent and the knowledge point distribution density in the coverage area, and perform a weighted combination calculation of the load capacity and the knowledge point distribution density to obtain a task balance factor; The direction and number of knowledge point migration are determined based on the difference in task balance factors of adjacent teaching agents, and the task allocation entropy after migration is calculated. When the rate of change of task allocation entropy is less than the preset change rate threshold and the difference in knowledge point distribution density in each area meets the balance requirements, the final teaching task division result is output.

[0056] For example, we first obtain a teaching path overlap matrix, which reflects the degree of knowledge point sharing between different teaching paths. For any two teaching paths, the overlap is calculated by calculating the ratio of the number of knowledge points they share to the total number of knowledge points in each path. For example, if path A contains the knowledge point set {1, 2, 3, 4} and path B contains the knowledge point set {3, 4, 5, 6}, then their overlap is the number of shared knowledge points (2) divided by the number of knowledge point unions (6).

[0057] A task allocation graph is constructed based on the overlap matrix. Each teaching agent is treated as a node in the graph. When there is a relationship between agents, an edge is connected between the corresponding nodes. For each teaching agent, the number of teaching tasks it currently undertakes is counted and the ratio of its maximum task load is used to obtain the task load ratio. For example, if an agent currently undertakes 10 teaching tasks and can handle a maximum of 20 tasks, its load ratio is 0.5.

[0058] When calculating edge weights in the task allocation graph, the corresponding element values in the overlap matrix are combined with the differences in the task load ratios of adjacent agents. Specifically, when the difference in the task load ratios between two agents is large, the corresponding edge weight is increased; otherwise, the weight is decreased. This helps prioritize load balancing when assigning tasks. For example, if agents A and B have load ratios of 0.3 and 0.8, respectively, and the path overlap between them is 0.4, the edge weight will be increased accordingly.

[0059] Next, the minimum spanning tree algorithm is used to perform preliminary task division. The algorithm starts with the edge with the smallest weight and gradually adds edges to the spanning tree. When adding each edge, the density of knowledge points in the current connected component is calculated. The knowledge point density represents the number of knowledge points contained in a unit area. For example, if a connected component covers an area of 100 square units and contains 200 knowledge points, the knowledge point density is 2. The weights of unadded edges are dynamically updated based on changes in knowledge point density. When adding an edge causes the knowledge point density of a connected component to increase significantly, the weights of the unadded edges adjacent to the component are increased to avoid excessive concentration of knowledge points. For example, if the knowledge point density increases from 2 to 5 after adding an edge, the original weight of the adjacent unadded edge is increased by 50%.

[0060] After obtaining the preliminary task division results, we extract specific parameters for each teaching agent. The first is load capacity, which includes hardware metrics such as computing resources and storage capacity, as well as a comprehensive evaluation of software metrics such as knowledge coverage and teaching experience. The second is the density of knowledge points in the coverage area, which takes into account the number, type, and degree of relevance of knowledge points.

[0061] The task balance factor is calculated by weighting the load capacity and knowledge point distribution density. Agents with greater load capacity and lower current knowledge point distribution density have larger task balance factors, indicating greater task carrying potential. For example, an agent with a load capacity score of 0.8 and a knowledge point distribution density of 0.3 might have a task balance factor of 0.7.

[0062] The direction and quantity of knowledge point transfer are determined based on the difference in task balance factors between adjacent agents. Agents with lower task balance factors transfer knowledge points to agents with higher task balance factors. The number of transfers is proportional to the factor difference, but the correlation between knowledge points must be considered to avoid distributing strongly correlated knowledge points across different agents. For example, if the task balance factors of agents A and B are 0.3 and 0.8, respectively, then the three weakly correlated knowledge points that A is responsible for may be transferred to B.

[0063] After each knowledge point migration, the information entropy of the overall task allocation is calculated. This entropy value reflects the degree of balance in task allocation, with higher entropy values indicating more balanced allocation. The variance of the knowledge point distribution density in each region is also checked to ensure that density differences between regions are within an acceptable range. When the rate of change in entropy is less than a preset threshold and the density variance meets the requirements, the task allocation is considered optimal.

[0064] For example, a teaching system consists of five agents. Initially, agent A is responsible for calculus-related knowledge points, B is responsible for linear algebra, C is responsible for probability and statistics, and D and E have no assigned tasks. Calculations reveal a high degree of overlap in knowledge points between A, B, and C, with their task load ratios being 0.9, 0.8, and 0.7, respectively. After constructing the task allocation graph, the minimum spanning tree algorithm first connects agents BC, as the edge weight between them is the smallest. While adding additional edges, it was discovered that connecting agents AB would result in an excessively high density of knowledge points in that area, so the algorithm chose to assign some knowledge points to agent D. After multiple rounds of iterative adjustments, agent A ultimately became primarily responsible for knowledge points related to limits and derivatives in advanced mathematics, agent B was responsible for operations on determinants and matrices, agent C was responsible for random variables and distributions, agent D took on some calculus content, and agent E shared knowledge points related to vector spaces. This division maintains a reasonable connection between knowledge points while achieving a basic balance of load.

[0065] Figure 4 This is a schematic diagram comparing the effects of teaching task division based on task balance factors. Figure 4As shown in the figure, the comparison results of the three teaching task division methods on key performance indicators are presented. The dynamic division method based on the task balance factor shows significant advantages in all evaluation dimensions. In terms of task load balance, this method reaches 60.8%, which is much higher than the traditional static division (30.5%) and preset weight division (40.2%); in terms of the rationality of knowledge point distribution, this method achieves a high level of performance of 65.1%, which is 44.8 and 29.5 percentage points higher than the other two methods respectively; in terms of system resource utilization, this method also leads with an excellent score of 70.3%. These data fully prove that the task balance factor that integrates the load capacity of intelligent agents and the distribution density of knowledge points can effectively optimize the allocation of teaching resources, dynamically adjust the direction and number of knowledge point migration, and significantly improve the overall efficiency of the collaborative teaching network.

[0066] The existing technology generally adopts static task division or preset weight mechanism to distribute tasks in multi-agent teaching systems. It lacks dynamic perception and adjustment of the overlap between teaching paths, the actual load capacity of agents and the distribution density of knowledge points, which easily leads to problems such as task imbalance, resource waste and teaching redundancy. In response to the above shortcomings, this application proposes an improved method for constructing a task allocation graph based on the teaching path overlap matrix. By integrating the teaching path overlap relationship and the task load ratio difference between agents into the edge weight calculation, the expression accuracy of the task graph is enhanced. On this basis, the minimum spanning tree algorithm is introduced to complete the preliminary division, and the changes in knowledge point density are perceived in real time during the edge addition process to achieve structural adaptive optimization. Furthermore, this solution calculates the task balance factor by extracting the load capacity of the agent and the knowledge point density of the coverage area, and dynamically adjusts the migration direction and number of knowledge points based on the difference in the factor to optimize the final task configuration. The whole process combines the dual strategies of structural optimization and content allocation, and introduces task allocation entropy as a judgment indicator to achieve quantitative control and dynamic balance of teaching task division. This technology starts from the dynamic coordination of teaching load, significantly improving the rationality of task division and system coordination efficiency, and effectively improving the problems of rough task allocation and difficulty in reconciling differences in teaching resources in traditional methods.

[0067] In an optional embodiment, collecting the learner's answer data and interaction data, extracting error types and question marks, and generating learning difficulty indication information includes: Collecting learners' answer data, extracting concept association, semantic similarity, and problem-solving path features from the answer data to construct a semantic feature vector, calculating the deviation value of the semantic feature vector relative to the standard answer, and identifying the error type based on the change trend of the deviation value; Obtaining learner interaction data, calculating the interaction duration and repetition frequency of each knowledge point based on the interaction data, taking the product of the interaction duration and repetition frequency as the interaction intensity, and generating a question mark when the interaction intensity exceeds the historical average of the current knowledge point; Establishing a combined feature matrix of error types and question marks, and calculating a difficulty indication coefficient based on the co-occurrence frequency of error-question pairs in the combined feature matrix; Calculate the mean and fluctuation range of the difficulty indication coefficient, determine the dynamic judgment threshold based on the mean and fluctuation range, screen out candidate difficulties when the difficulty indication coefficient exceeds the dynamic judgment threshold, prioritize the candidate difficulties, and generate learning difficulty indication information.

[0068] In this embodiment, by collecting learners' answer data and interaction data, extracting error types and question marks, and generating learning difficulty indication information, the system implementation method generally includes four key steps: extracting error types, generating question marks, calculating difficulty indication coefficients, and generating learning difficulty indication information.

[0069] The system first collects data on students' responses throughout the course. This data includes responses from various sources, including in-class quizzes, homework assignments, and online exercises. From this data, the system uses natural language processing to extract three types of features: concept relevance, semantic similarity, and problem-solving path features. Concept relevance is quantified by measuring the degree of match between key concepts in the response and concept nodes in the standard knowledge network. For example, for a physics question, how accurately does a student use the concept of "acceleration"? Semantic similarity uses text vectorization to measure the similarity between a student's answer and the standard answer. For example, for a question about the "process of photosynthesis," how closely does a student's description of "plants use sunlight energy to convert carbon dioxide and water into organic matter" match the standard answer? Problem-solving path features capture the student's thought process and step-by-step sequence when solving a problem, such as whether they follow the standard "hypothesis-deduction-conclusion" process in mathematical proofs.

[0070] After these three types of features form a semantic feature vector, the deviation between this vector and the standard answer feature vector is calculated. By tracking the changing trends of the deviation values at different time points, various error types can be identified, including concept confusion errors, reasoning chain break errors, and application scenario misjudgment errors. For example, if learners are found to frequently confuse the concepts of "current" and "voltage" in electrical problems, and the deviation value increases significantly when these concepts appear, the error will be marked as a concept confusion error.

[0071] At the same time, learners' interaction data is collected, including page dwell time, number of repeat visits, note-taking, and questioning. For each knowledge point in the e-textbook, the interaction duration and repetition frequency are calculated. For example, if a learner dwells on the "cell division" knowledge point page for 5 minutes (interaction duration) and visits it three times within a week (repetition frequency), the interaction intensity is 15 (5 x 3). When the interaction intensity for a knowledge point exceeds the historical average for that knowledge point (e.g., 12), a question mark is generated, indicating that the learner may have difficulty understanding that knowledge point.

[0072] Identified error types are combined with question marks to create a feature matrix. The rows of this matrix represent different error types, and the columns represent question marks for knowledge points. The values in the matrix represent the co-occurrence frequency of error-question pairs. For example, "concept confusion error" and the question mark for the knowledge point "differential equations" co-occur eight times, indicating that learners are significantly confused about the concept of differential equations. Based on this co-occurrence frequency, the system calculates a difficulty indicator coefficient, which reflects the likelihood that a specific knowledge point will cause learning difficulty.

[0073] To accurately identify learning difficulties, the mean and fluctuation of the difficulty indicator coefficient are calculated. For example, in a programming course, the mean of the difficulty indicator coefficient is 0.65 and the fluctuation is 0.15. Based on this, a dynamic judgment threshold of 0.85 (the mean plus 1.5 times the fluctuation) is determined. When a knowledge point's difficulty indicator coefficient exceeds 0.85, it is screened as a candidate difficulty point. For multiple candidate difficulty points, priority scores are calculated and ranked based on factors such as the difficulty indicator coefficient, error frequency, and learner feedback. For example, if the priority score for the difficulty point "recursive functions" is 9.2 and that for "pointer operations" is 8.7, recursive functions are identified as the primary learning difficulty point. Finally, learning difficulty indicator information is generated, including a list of difficult knowledge points, descriptions of associated error types, recommended targeted learning resources, and examples to aid understanding. For example, for the difficulty point "the principle of wave function superposition in quantum mechanics," the system provides a detailed explanation of the principle's differences from classical physics, corrections to common misconceptions, and learning resources with visual simulations.

[0074] In this embodiment, by collecting and analyzing learners' answer data, the solution constructs a multidimensional semantic feature vector that includes concept association, semantic similarity, and problem-solving path characteristics. It then uses the trend of deviation from the standard answer to accurately identify different types of errors, achieving a detailed classification of learning errors. Combined with learners' interaction data, the interaction intensity of knowledge points is calculated, dynamically capturing learners' questioning behavior on each knowledge point, enhancing the ability to perceive potential comprehension barriers. Combining error types with question marks to construct a combined feature matrix, the difficulty indicator coefficient is calculated based on co-occurrence frequency, which can reflect the comprehensive learning difficulty of the knowledge point and its dynamic changes. By setting dynamic judgment thresholds based on mean and fluctuation amplitude, the solution achieves flexible screening and priority sorting of difficulty points, avoiding the misjudgment and omission problems caused by static thresholds. Compared with traditional methods that rely solely on single error identification or simple interaction statistics, the multidimensional fusion analysis and dynamic threshold mechanism proposed in this application effectively improves the accuracy and timeliness of learning difficulty discovery, providing a scientific basis for subsequent personalized teaching strategy adjustment and learning resource allocation, thereby optimizing overall teaching effectiveness.

[0075] In an optional embodiment, matching the teaching path with the highest adaptability in the optimal teaching path set according to the learning difficulty indication information includes: Determining the cognitive barrier degree of the knowledge points based on the difficulty indication information, and constructing a difficult knowledge evolution network, wherein the difficult knowledge evolution network includes the cognitive association strength and cognitive barrier degree between the knowledge points; Extracting a knowledge point sequence of a candidate path from the optimal teaching path set, calculating the cognitive stress characteristics of the knowledge point sequence based on the cognitive association strength, and calculating the difficulty coverage of the knowledge point sequence based on the cognitive impairment degree; Performing a hierarchical evaluation on the sequence of knowledge points, calculating the effect of a single knowledge point on eliminating difficulties based on the degree of coverage of the difficulties, and evaluating the combined learning effect of multiple knowledge points based on the cognitive stress characteristics; The effect of eliminating difficulties is taken as the basic fitness, the combined learning effect is taken as the cognitive gain coefficient, the basic fitness and the cognitive gain coefficient are combined to obtain the comprehensive fitness of the path, and the path with the highest comprehensive fitness is selected as the optimal teaching path.

[0076] For example, the system first obtains information indicating the learner's difficulty. This information can be obtained through the learner's test results, feedback during the learning process, or teacher evaluations. For example, for a high school math learner, the difficulty indication information may show that the learner has cognitive difficulties in knowledge points such as "trigonometric functions," "application of derivatives," and "solid geometry." The system will quantitatively evaluate each difficult knowledge point based on preset scoring criteria, such as dividing the degree of cognitive difficulty into a numerical range of 1-5, where 5 indicates the highest degree of difficulty. In this example, the learner's cognitive difficulty level in "trigonometric functions" is 4, "application of derivatives" is 3, and "solid geometry" is 5.

[0077] Based on the acquired difficulty indicator information, the system constructs a knowledge evolution network for these difficult points. This network includes not only the difficult knowledge points, but also the predecessor and successor knowledge points related to these difficult points. By analyzing the curriculum system and knowledge graph, the strength of the cognitive association between knowledge points is determined. The cognitive association strength indicates the learning dependency between two knowledge points, with a value ranging from 0 to 1, where 1 indicates complete dependency. For example, the cognitive association strength between "trigonometric functions" and "trigonometric identity transformations" is 0.8, indicating that learning "trigonometric identity transformations" is highly dependent on understanding "trigonometric functions."

[0078] After constructing the difficult knowledge evolution network, candidate paths are extracted from a pre-prepared set of optimal teaching paths. These candidate paths are multiple feasible teaching paths designed by teaching experts or generated by advanced teaching path generation algorithms. Each path contains a series of knowledge points arranged in a specific order. For example, a candidate path for solving the difficult point "trigonometric functions" might include the following knowledge point sequence: "Concept of angle" → "Radian system" → "Unit circle" → "Definition of trigonometric functions" → "Graphs of trigonometric functions" → "Properties of trigonometric functions."

[0079] For each candidate path's sequence of knowledge points, its cognitive stress characteristic is calculated based on the strength of cognitive association. This characteristic reflects the amount of information learners need to simultaneously process and memorize during the learning process. When learning highly related knowledge points consecutively, cognitive stress is low; however, when learning unrelated knowledge points, frequent switching of thinking modes is required, resulting in higher cognitive stress. For example, the cognitive association strength between "unit circle" and "definition of trigonometric functions" is 0.9, indicating that these two knowledge points are highly related and thus incur low cognitive stress during learning. However, jumping directly from "trigonometric functions" to "solid geometry" might have a strength of only 0.2, indicating higher cognitive stress.

[0080] The path's difficulty coverage is also calculated based on the cognitive barrier level of each knowledge point. Difficulty coverage indicates how effectively the path addresses a learner's difficulties. For example, a path encompassing "Trigonometric Functions," "Trigonometric Identity Transformations," and "Trigonometric Equations" might provide 85% coverage of the learner's "Trigonometric Functions" difficulty, while coverage of "Solid Geometry" might be only 10%. A hierarchical evaluation of the knowledge point sequence begins by calculating the effectiveness of individual knowledge points in alleviating the difficulty, known as basic fitness. This is determined by analyzing the direct correlation between the knowledge point and the difficulty and the cognitive barrier level of the difficulty. For learners with high-difficulty difficulties, such as "Solid Geometry" (a barrier level of 5), the effectiveness of related knowledge points, such as "Space Vectors," in alleviating the difficulty is given a higher weight.

[0081] The system also evaluates the combined learning effect of multiple knowledge points as a cognitive gain coefficient. This is calculated based on the cognitive stress characteristics of the knowledge point sequence. For example, if a path contains a highly related and well-ordered sequence of knowledge points, such as "Plane Geometry Basics" → "Spatial Concepts" → "Solid Geometry Basic Bodies" → "Solid Geometry Calculation Methods," its combined learning effect score might be 0.9 (out of a maximum score of 1), indicating that this knowledge point combination significantly promotes learning outcomes. Ultimately, the basic fitness and cognitive gain coefficient are combined to determine the overall fitness of each candidate path. This can be calculated by multiplying the basic fitness by the cognitive gain coefficient or by using a weighted summation method. In this example, a path covering knowledge points related to "Solid Geometry" and with reasonable cognitive stress might receive the highest overall fitness score of 9.2 (out of a maximum score of 10). The path with the highest overall fitness is selected as the optimal teaching path recommended to the learner. This path not only covers the learner's primary difficulties but also ensures learning coherence and a reasonable cognitive load across knowledge points, thereby maximizing learning outcomes.

[0082] In this embodiment, by constructing a difficult knowledge evolution network and comprehensively considering the cognitive association strength and degree of cognitive impairment between knowledge points, a systematic characterization and dynamic analysis of learning difficulties is achieved. Based on this network, the knowledge point sequence of candidate paths is extracted from the optimal teaching path set. The cognitive stress characteristics and difficulty coverage of the knowledge points in the path can be accurately calculated, and the adaptability and ability of the path to eliminate learning difficulties can be carefully reflected. Through hierarchical evaluation, not only can the effect of a single knowledge point on eliminating difficulties be quantified, but the learning effect of multiple knowledge point combinations can also be comprehensively evaluated, fully considering the balance between cognitive load and knowledge integration, and improving the scientific nature and pertinence of the teaching path. The basic fitness is combined with the cognitive gain coefficient to form a comprehensive fitness, ensuring that the selected teaching path can effectively cover learning difficulties and maximize cognitive benefits, thereby achieving personalized and efficient teaching strategy optimization. Compared with traditional single difficulty matching or path selection methods, through multi-dimensional cognitive analysis and dynamic comprehensive evaluation, the accuracy of path matching and teaching effectiveness are significantly improved, promoting learners to overcome cognitive barriers more efficiently and improving overall learning quality.

[0083] A second aspect of an embodiment of the present invention provides a multi-agent collaborative teaching interactive system in an educational scenario, the system comprising: The first unit is used to build a knowledge point dependency graph, identify the preceding and subsequent related knowledge points for each knowledge point, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point based on the historical teaching data of the teaching agent, generate a teaching path score, and construct the optimal teaching path set for each teaching agent based on the teaching path score; The second unit is used to form a collaborative teaching network with multiple teaching agents. It uses a graph partitioning algorithm to calculate the overlapping knowledge points of adjacent teaching paths. Based on the number and degree of correlation of overlapping knowledge points, it generates a teaching path overlap matrix. Based on the teaching path overlap matrix, it divides the teaching tasks and constructs the transition content of knowledge points. The third unit is used to collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information; The fourth unit is used to match the teaching path with the highest adaptability in the optimal teaching path set based on the learning difficulty indication information, and adjust the corresponding teaching agent to the teaching task of the current knowledge point. The teaching agent selects the previous related knowledge points for supplementary explanation based on the knowledge point dependency graph, and updates the transition explanation content in the collaborative teaching network.

[0084] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0085] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0086] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-agent collaborative teaching interactive method in an educational scenario, characterized by: include: Build a knowledge point dependency graph to identify the preceding and subsequent related knowledge points for each knowledge point. Based on the historical teaching data of the teaching agent, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point, generate a teaching path score, and construct the optimal teaching path set for each teaching agent based on the teaching path score. Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to calculate the overlapping knowledge points of adjacent teaching paths. A teaching path overlap matrix is generated based on the number and degree of association of overlapping knowledge points. The teaching tasks are then divided according to the teaching path overlap matrix, and the transition content of knowledge points is constructed. Collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information; According to the learning difficulty indication information, the teaching path with the highest adaptability is matched in the optimal teaching path set, and the corresponding teaching agent is adjusted to the teaching task of the current knowledge point. The teaching agent selects the previous related knowledge points for supplementary explanation based on the knowledge point dependency graph, and updates the transition explanation content in the collaborative teaching network.

2. The method according to claim 1, characterized in that Build a knowledge point dependency graph, identify the preceding and subsequent related knowledge points for each knowledge point, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point based on the historical teaching data of the teaching agent, and generate a teaching path score including: Extract the concept set of course knowledge points and calculate the concept relevance between knowledge points; obtain the reference concepts corresponding to the knowledge points whose concept relevance exceeds a preset relevance threshold, calculate the reference strength based on the position and frequency of the referenced concepts in the teaching text, perform a weighted calculation on the concept relevance and the reference strength to obtain the knowledge point association strength, and construct a knowledge point dependency graph based on the knowledge point association strength; In the knowledge point dependency graph, identifying the preceding and following knowledge points of each knowledge point node through a traversal algorithm, obtaining the teaching time and number of repeated teachings of the preceding and following knowledge points in the teaching agent's historical teaching data, and calculating the knowledge point difficulty mark; According to the connection relationship between the preceding associated knowledge points and the subsequent associated knowledge points, multiple traversal paths are generated in the knowledge point dependency graph. For each traversal path, the sum of the association strengths of adjacent knowledge points in the path is calculated as the path association value, and the distribution of the difficulty marks of the knowledge points in the path is calculated as the path difficulty value. The path association value and the path difficulty value are combined to generate a teaching path score.

3. The method according to claim 1, characterized in that Constructing the optimal teaching path set for each teaching agent based on the teaching path score includes: Obtain teaching path scores, extract the question-answer frequency distribution and feedback response distribution of knowledge points from historical teaching data, generate interaction intensity sequences, identify the difficulty of understanding and mastery of knowledge points based on the interaction intensity sequences, and construct learning state features; The teaching path score is combined with the learning state characteristics, and the knowledge point positions where the question and answer frequency is higher than a first preset value and the mastery level is lower than a second preset value are marked in the teaching path. At the marked knowledge point positions, the connection weight is calculated based on the difficulty of understanding and the mastery level of adjacent knowledge points, and the teaching path score is weighted and corrected to generate an adaptive path score; Adaptive path scoring is used as the basis for path selection. Multiple teaching paths are screened and genetic iterative calculation is performed on the screened teaching paths. The relative order of the marked knowledge point positions is maintained during the iteration process, and the iteration results are used as the optimal teaching path set of the teaching agent.

4. The method according to claim 1, wherein Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to calculate the overlapping knowledge points of adjacent teaching paths. A teaching path overlap matrix is generated based on the number and degree of association of overlapping knowledge points. The teaching tasks are divided according to the teaching path overlap matrix and the knowledge point transition explanation content is constructed, including: Multiple teaching agents are organized into a collaborative teaching network. A graph partitioning algorithm is used to analyze teaching paths and extract overlapping knowledge points of adjacent teaching paths. The node affinity matrix and path coupling matrix are calculated based on the subgraph structure of the overlapping knowledge points. The hierarchical transfer coefficient and knowledge association strength of the overlapping knowledge points are calculated through the dual constraints of the node affinity matrix and the path coupling matrix. Based on the number of overlapping knowledge points, the hierarchical transfer coefficient, and the knowledge association strength, the coreness, migration difficulty, and coverage density of the overlapping knowledge points are calculated, and a teaching path overlap matrix is generated through recursive weight updating; Constructing a task allocation graph based on the teaching path overlap matrix, performing preliminary task division using a minimum spanning tree algorithm, calculating a task balance factor based on the load capacity of the teaching agent and the distribution density of knowledge points, and adjusting the preliminary task division result using the task balance factor to obtain a teaching task division result; For the overlapping knowledge points in the teaching task division results, knowledge dependency characteristics and knowledge association characteristics are extracted, and preceding knowledge activation rules, subsequent knowledge connection rules and transition sequence rules are constructed. The rule priority is determined through competitive evaluation, and a knowledge point transition rule library is generated. Based on the degree of association between the knowledge point transition rule library and the overlapping knowledge points, the knowledge point transition explanation content is constructed.

5. The method according to claim 4, characterized in that A task allocation graph is constructed based on the teaching path overlap matrix, and a minimum spanning tree algorithm is used to perform preliminary task division. The task balance factor is calculated according to the load capacity of the teaching agent and the distribution density of knowledge points. The preliminary task division result is adjusted using the task balance factor. The teaching task division result includes: A task allocation graph is constructed based on the teaching path overlap matrix, where nodes represent teaching agents and edges represent relationships between agents. The task load ratio of each agent is calculated, and the edge weights of the task allocation graph are calculated by combining the elements of the overlap matrix with the differences in task load ratios between adjacent agents. Performing a minimum spanning tree algorithm based on the task allocation graph to perform preliminary task division, calculating a change in the density of knowledge points in the area connected by the current edge when each edge is added, and using the change in the density of knowledge points to update the weights of adjacent unadded edges until the preliminary task division is completed; Based on the preliminary task division results, extract the load capacity of each teaching agent and the knowledge point distribution density in the coverage area, and perform a weighted combination calculation of the load capacity and the knowledge point distribution density to obtain a task balance factor; The direction and number of knowledge point migration are determined based on the difference in task balance factors of adjacent teaching agents, and the task allocation entropy after migration is calculated. When the rate of change of task allocation entropy is less than the preset change rate threshold and the difference in knowledge point distribution density in each area meets the balance requirements, the final teaching task division result is output.

6. The method according to claim 1, characterized in that Collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information including: Collecting learners' answer data, extracting concept association, semantic similarity, and problem-solving path features from the answer data to construct a semantic feature vector, calculating the deviation value of the semantic feature vector relative to the standard answer, and identifying the error type based on the change trend of the deviation value; Obtaining learner interaction data, calculating the interaction duration and repetition frequency of each knowledge point based on the interaction data, taking the product of the interaction duration and repetition frequency as the interaction intensity, and generating a question mark when the interaction intensity exceeds the historical average of the current knowledge point; Establishing a combined feature matrix of error types and question marks, and calculating a difficulty indication coefficient based on the co-occurrence frequency of error-question pairs in the combined feature matrix; Calculate the mean and fluctuation range of the difficulty indication coefficient, determine the dynamic judgment threshold based on the mean and fluctuation range, screen out candidate difficulties when the difficulty indication coefficient exceeds the dynamic judgment threshold, prioritize the candidate difficulties, and generate learning difficulty indication information.

7. The method according to claim 1, characterized in that The teaching paths with the highest adaptability in the optimal teaching path set according to the learning difficulty indication information include: Determining the cognitive barrier degree of the knowledge points based on the difficulty indication information, and constructing a difficult knowledge evolution network, wherein the difficult knowledge evolution network includes the cognitive association strength and cognitive barrier degree between the knowledge points; Extracting a knowledge point sequence of a candidate path from the optimal teaching path set, calculating the cognitive stress characteristics of the knowledge point sequence based on the cognitive association strength, and calculating the difficulty coverage of the knowledge point sequence based on the cognitive impairment degree; Performing a hierarchical evaluation on the sequence of knowledge points, calculating the effect of a single knowledge point on eliminating difficulties based on the degree of coverage of the difficulties, and evaluating the combined learning effect of multiple knowledge points based on the cognitive stress characteristics; The effect of eliminating difficulties is taken as the basic fitness, the combined learning effect is taken as the cognitive gain coefficient, the basic fitness and the cognitive gain coefficient are combined to obtain the comprehensive fitness of the path, and the path with the highest comprehensive fitness is selected as the optimal teaching path.

8. A multi-agent collaborative teaching interactive system in an educational scenario, used to implement the method according to any one of claims 1 to 7, characterized in that: include: The first unit is used to build a knowledge point dependency graph, identify the preceding and subsequent related knowledge points for each knowledge point, extract the knowledge point correlation strength and teaching difficulty mark during the explanation of each knowledge point based on the historical teaching data of the teaching agent, generate a teaching path score, and construct the optimal teaching path set for each teaching agent based on the teaching path score; The second unit is used to form a collaborative teaching network with multiple teaching agents. It uses a graph partitioning algorithm to calculate the overlapping knowledge points of adjacent teaching paths. Based on the number and degree of correlation of overlapping knowledge points, it generates a teaching path overlap matrix. Based on the teaching path overlap matrix, it divides the teaching tasks and constructs the transition content of knowledge points. The third unit is used to collect learners' answer data and interaction data, extract error types and question marks, and generate learning difficulty indication information; The fourth unit is used to match the teaching path with the highest adaptability in the optimal teaching path set based on the learning difficulty indication information, and adjust the corresponding teaching agent to the teaching task of the current knowledge point. The teaching agent selects the previous related knowledge points for supplementary explanation based on the knowledge point dependency graph, and updates the transition explanation content in the collaborative teaching network.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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