Heuristic teaching system construction method based on large language model and knowledge graph

Abstract

The invention discloses a heuristic teaching system construction method based on a large language model and a knowledge graph, and the method comprises the steps: constructing a course knowledge graph covering course core knowledge points and a student knowledge state model under a cognitive heuristic closed-loop framework, carrying out the heuristic instruction fine tuning of a large language model, and carrying out the recognition of the knowledge graph. And a progressive problem chain generation mechanism composed of starting, exploration, verification, migration and reflection stages is designed. According to the method, a complete teaching closed loop covering'knowledge representation-problem generation-learning feedback-difficulty regulation and control-learning condition monitoring 'is formed, the illusion risk of large language model generation content can be reduced, the interactivity and individuation level of the system can be improved, deep understanding of students on abstract concepts and complex algorithms can be effectively promoted, and the teaching experience of the students can be improved. The method can be popularized and applied to multiple computer courses and other science and engineering teaching scenes, and provides technical support for large-scale personalized intelligent education.

Description

Technical Field

[0001] This invention relates to the field of intelligent teaching technology, specifically to a method for constructing a heuristic teaching system based on large language models and knowledge graphs, which can be applied to intelligent and personalized teaching of computer science courses such as data structures. Background Technology

[0002] In recent years, with the development of artificial intelligence technology, the combination of large language models and knowledge graphs has provided a new technological path for intelligent education. Large language models possess strong natural language understanding and generation capabilities, enabling them to provide students with instant answers and explanations in a dialogue format. Knowledge graphs, on the other hand, organize course domain knowledge in the form of nodes and edges, describing the pre-dependencies, compositional relationships, and application scenarios between knowledge points, and possessing characteristics such as structure, queryability, and reasoning ability. In computer science courses (such as data structures and algorithm design), integrating large language models and knowledge graphs holds promise for providing intelligent and personalized support for learning complex concepts.

[0003] However, existing teaching applications based on large language models and knowledge graphs still have several limitations: First, large language models are prone to producing "illusionary" content that deviates from the syllabus or concept definitions when lacking reliable structured knowledge constraints, making it difficult to guarantee the accuracy and consistency of teaching results; Second, knowledge graphs are mostly used as independent knowledge retrieval modules, with loose coupling between them and large language models. The two are often simply superimposed and have not yet formed a collaborative mechanism around the learning process; Third, existing systems generally remain in a passive question-and-answer mode of "students ask questions - system answers," lacking detailed modeling of students' cognitive states and learning paths, making it difficult to adjust the depth of explanation and the difficulty of exercises in a timely manner based on students' real-time performance.

[0004] Core computer science courses, such as Data Structures, are characterized by high levels of conceptual abstraction, complex interrelationships between knowledge points, and high demands on algorithmic and logical thinking. Traditional teaching relies mainly on a uniform pace of classroom lectures and assignments, which often leads students to only superficially memorize definitions and examples, making it difficult to develop a deep understanding of underlying ideas and design trade-offs. Furthermore, in large classes with significant differences in student backgrounds, teachers struggle to accurately assess individual students' cognitive levels and provide targeted, personalized guidance.

[0005] Heuristic teaching emphasizes a problem-centered, student-centered approach. By posing tiered and challenging guiding questions, it encourages students to actively construct and reorganize their knowledge structures through a continuous process of "thinking-verification-correction," making it particularly suitable for abstract computer science courses. However, under traditional teaching conditions, heuristic teaching heavily relies on teacher classroom management and after-class tutoring, making it difficult to implement stably in large-scale teaching scenarios over the long term. It also struggles to generate personalized question sequences and feedback tailored to the different cognitive paths and weaknesses of individual students.

[0006] Therefore, existing technologies urgently need a solution for the deep integration of large language models and knowledge graphs for heuristic teaching scenarios: on the one hand, knowledge graphs can be used to provide structured constraints for large language models, reducing the risk of "illusion" in generated content and ensuring that questions and explanations are closely related to the course knowledge system; on the other hand, dynamic modeling of students' knowledge status and answering process can be performed to automatically generate heuristic question chains with progressive relationships and personalized feedback, thereby enabling proactive guidance of students' thinking processes and adaptive adjustment of question difficulty, thus making up for the shortcomings of existing teaching models and intelligent teaching systems in terms of interactivity, personalization and deep understanding. Summary of the Invention

[0007] To address the technical challenge of deeply integrating large language models and knowledge graphs in heuristic teaching scenarios, this invention provides a method for constructing a heuristic teaching system based on large language models and knowledge graphs. This system is applied to intelligent and personalized teaching of computer science courses such as data structures. By combining the course knowledge graph with student knowledge state modeling, the system constrains and guides the questioning process of the large language model. Within the Cognitive Heuristic Closed Loop (CHL) framework, the system constructs a heuristic question chain with stages of initiation, exploration, verification, transfer, and reflection. The content and difficulty of questions are dynamically adjusted based on student performance and learning trajectory, achieving adaptive matching to learning status and cognitive progress. Simultaneously, the system utilizes knowledge graphs and learning data for visual monitoring and statistical analysis of learning progress, providing teachers with suggestions for optimizing the question chain and improving the teaching effectiveness and personalized support capabilities of courses such as data structures.

[0008] The method for constructing a heuristic teaching system based on large language models and knowledge graphs includes the following steps: Step 1: Modeling the course knowledge graph and student knowledge state; Step 2: Design of a heuristic problem chain; Step 3: Adaptively control the question difficulty and the large model questioning strategy based on knowledge graphs and learning trajectories; Step 4: Learning progress monitoring and optimization of the heuristic question chain.

[0009] Furthermore, step 1, modeling the course knowledge graph and student knowledge state, includes: 1.1 Structured Representation and Query of Course Knowledge Graph: Course Knowledge Graph The core concepts and their relationships in the course are represented in a structured manner, where the node set... Representing knowledge points, edge sets It represents the semantic relationships between knowledge points, including prerequisite dependencies, parallel comparisons, compositional relationships, and application scenarios; 1.2 Representation of students' knowledge status: Based on the construction of the course knowledge graph, the system models students' learning mastery as a time-evolving knowledge state vector, providing foundational support for subsequent heuristic question chain generation and adaptive adjustment. In subsequent steps, the system represents students' knowledge state at time t as a vector. Furthermore, by combining cognitive stage markers, response records, and feedback information, the knowledge state is updated and trajectory modeled.

[0010] Furthermore, in section 1.1, "Structured Representation and Query of Course Knowledge Graphs," a local knowledge graph of linked lists is constructed for linked list operations: , The system uses a graph query function Retrieve nodes associated with the currently learned concept to determine the direction and depth of question generation; let the currently focused knowledge point be a node. ,but: , in, Indicates and For scenarios requiring simultaneous consideration of multiple mastered knowledge points, the relevant set of adjacent or multi-hop related nodes can be used for multi-node joint queries: , On the question generation side, the system generates candidate questions for the knowledge graph based on the node set and edge relationships returned by the query. When extending from the "linked list insertion" related nodes to the "boundary condition handling" nodes, an advanced question, "How to perform an insertion operation when the linked list is empty?", can be generated. The question generation function will... As mentioned above, generated by a large language model The elements are integrated to obtain the final product presented to the students. .

[0011] Furthermore, step 2, the design of the heuristic question chain, includes: 2.1 Heuristic Question Chain Template and Cognitive Heuristic Closed-Loop Modeling Based on the cognitive-inspired closed-loop teaching model, a heuristic question chain template is constructed, which divides the students' learning process into five stages: initiation, exploration, verification, transfer and reflection, and forms a standardized question chain framework consisting of five types of questions. For any knowledge point node in the course knowledge graph The system pre-constructs a set of heuristic problem chain templates for it. Formal representation: , in, , , , , These represent question slots for the initiation phase, exploration phase, validation phase, transfer phase, and reflection phase, respectively. Each slot is a parameterized "question template" containing the question objective, cognitive level, related knowledge points, and structured information about the large language model generation strategy that can be invoked, rather than a fixed text question. During system runtime, targeting the current knowledge point and student knowledge state vector The system is based on its stage marker in the CHL model. Instantiate the above template to generate specific questions. During the startup phase, the system is in the slot. By binding constraints such as "contextualization, realism, and activation of prior experience," contextual questions are generated through a large language model to elicit target knowledge points. : , in, Generate functions for the startup phase issues. This includes contextual information such as learning tasks and learning history. Exploration phase slots The heuristic requirement of "guiding students to propose hypotheses and compare different solutions" is used to generate questions that encourage students to engage in active reasoning and structured thinking; the verification stage slots... Constraints that "expose boundary conditions and counterexamples" are used to generate problems to check the correctness and robustness of the solution; migration phase slots Binding constraints of "new context application and analogy extension" is used to generate questions that support knowledge transfer; reflection phase slots The constraint of "metacognitive summary and strategic reflection" is used to generate reflective questions that help students review their thinking process and refine problem-solving strategies. In terms of interaction strategy, the question chain template encodes a "single-question-driven" presentation rule: at any given time, the system instantiates and presents only one question slot in the template, waits for the student to answer and complete the status update, and then presents the updated knowledge status. and stage markers The decision is whether to continue generating subsequent questions at the current stage or switch to the next stage in the CHL closed loop, thereby ensuring that the pace of heuristic questioning is controllable and the cognitive load is moderate at the algorithm level. 2.2 Problem Chain Instantiation and Dynamic Generation Based on the above template-based modeling, by introducing the student's knowledge state and CHL stage state into the problem generation function, the dynamic instantiation and progressive generation of the problem chain are realized. The system will record students' time. The knowledge state is represented as a vector. The cognitive stage is represented as , will the The specific problem is represented as The student's answer to the question is expressed as Based on target knowledge points Corresponding template The system generates the first question in the problem chain in the following form. : , in, This represents the initial state of knowledge. This usually corresponds to the startup phase. , Generate control parameters for the initial problem. A unified question generation function; this function comprehensively considers students' knowledge mastery, learning history, current stage, and template constraints to generate thought-provoking starting questions; For the first in the problem chain The system will answer the previous question after the student completes the question. After the answer is given, the knowledge state is first updated, and then the next question is dynamically generated based on the updated knowledge state and the stage state. This can be formally represented as: , in, To generate the first Adjustment parameters for each problem This represents the current state of knowledge. The process of updating students' knowledge status is represented as follows: , in, The state update function comprehensively utilizes the correctness of students' answers, reasoning process, coverage of concepts used, and error type information to update the knowledge state vector. The state update is not only based on the binary results of "correct" and "incorrect", but also weights the integrity of the reasoning chain and the logical rigor, thus characterizing the students' cognitive development level from multiple dimensions. During the generation of the problem chain, the system continuously updates the latest knowledge state. Information related to the CHL phase As input, it is used to select the question slots to be instantiated on the one hand, and to control the depth and breadth of questions on the other hand, to ensure semantic coherence and gradual increase in difficulty between questions, and to avoid knowledge gaps or excessive repetition.

[0012] Furthermore, step 3, adaptive control of question difficulty and large-scale model questioning strategy based on knowledge graphs and learning trajectories, includes: 3.1 Evolution of Students' Knowledge Status and Adaptive Adjustment of Problem Difficulty Based on the dynamic generation mechanism of the problem chain, a problem difficulty assessment function and learning trajectory modeling are introduced to characterize the evolution of students' knowledge status and adaptively adjust the problem difficulty, ensuring that students are in the optimal learning range of "moderate challenge" in the long term. To achieve dynamic matching between problem difficulty and student ability, the system updates the knowledge status. Then, regarding the current problem Assess the difficulty and provide a difficulty value. : , in, This is a function for evaluating the difficulty of the problem. This indicates the system's analysis and feedback on the student's answer, including the correctness of the answer, the time taken to answer, the number of times hints were used, and the type of error. For the current CHL stage, by incorporating stage information into the evaluation function, the difficulty weight is adjusted differently according to the teaching objectives of different stages. In the exploration stage, more emphasis is placed on openness and multiple paths, while in the verification stage, more emphasis is placed on boundary conditions and rigor. Based on students' answer accuracy within a certain time window The system employs piecewise functions to implement a basic difficulty adjustment strategy: , in, This indicates the target difficulty level for the next round of questions. When the accuracy rate is low, the system reduces the cognitive load on students by lowering the difficulty of subsequent questions, introducing intermediate transitional questions, or reverting to an earlier stage. When the accuracy rate is high, the system appropriately increases the difficulty of the questions and introduces questions that require the integration of multiple knowledge points or cross-contextual transfer to maintain a moderate challenge. The system is also expanded to include multi-level difficulty levels and multi-threshold strategies to adapt to different courses and teaching scenarios. To depict the evolution of students' knowledge status throughout the learning process, the system represents students' knowledge status at different points in time as follows: , in, These are the knowledge state vectors of students at various key moments. This learning trajectory is not only used for subsequent learning visualization and teacher-side monitoring and analysis, but also serves as input features in the effectiveness evaluation and automated optimization process of the question chain. By comparing the knowledge increment under different question chain configurations... To evaluate the heuristic effect of different problem sequences; 3.2 Fine-tuning of the large language model Based on the question chain framework, the large language model is fine-tuned, and the system encodes the information related to question generation in each step of the interaction into an input vector. This includes the previous round of questions and answers, the current knowledge state, stage markers, and the structured context obtained from the knowledge graph: , in, For the problems that have already emerged in the previous round, For the students' answers, This is the current knowledge state vector. Mark the current CHL stage. For contextual information such as teaching situations and learning history, This refers to structured background information obtained through knowledge graph retrieval and reasoning. The finely tuned large language model Given the input, output the candidate heuristics for this round. : , in, This involves fine-tuning parameters for a large language model. A combination of supervised learning and reinforcement learning is used to... The model is trained to not only possess knowledge-based question-and-answer capabilities in the course domain, but also to learn heuristic questioning strategies, including various questioning patterns from simple to complex, from concrete to abstract, and from single points to connections. During the fine-tuning process, the system will use the knowledge graph retrieval results. and characteristics of students' knowledge status This contextual input ensures that the problems generated by the model are more aligned with the course's knowledge structure in terms of content and more closely match the students' actual level in terms of difficulty. This avoids generating overly generalized problems that deviate from the syllabus or are inconsistent with the knowledge graph, ultimately presenting students with specific problems. The aforementioned unified problem generation function pairs It is obtained by fusing with the results generated from the knowledge graph side; 3.3 Personalized Feedback and Incremental Updates of Knowledge Status After students complete their answers, the system generates personalized feedback based on their current knowledge level and their responses to the questions. Let the first... The question is The student's answer was ,time The knowledge state is Personalized feedback Defined as: , in, A comprehensive analysis is conducted on the accuracy, completeness, reasoning chain, coverage of concepts used, and error types, including conceptual errors, procedural errors, and careless errors, in conjunction with the current CHL stage. Differentiated feedback strategies are generated for different situations. Feedback forms include prompting questions, partial guidance and explanation, and comparative examples, avoiding giving the final answer directly, so as to encourage students to discover and correct their mistakes independently. After feedback is generated, the system incrementally updates the student's knowledge status based on the feedback to obtain the knowledge status at the next moment. : , in, This is a knowledge state increment update function. Based on the feedback content and student performance, it differentiates the weights of different dimensions corresponding to different knowledge points or ability indicators in the knowledge state vector, thereby accurately reflecting the cognitive changes of students after this round of interaction. The system simultaneously records each student's completion status on the question chain, forming a completion rate indicator. : , in, This represents the number of completed issues. The total number of questions, For the first The score for each question and This is the weighting coefficient; this indicator reflects both the students' level of participation and the quality of their answers, providing a quantitative basis for the adaptive adjustment of difficulty and the analysis of student learning in the following sections. 3.4 Knowledge Graph-Driven Semantic Enhancement Reasoning By combining knowledge graphs, the system performs structured semantic analysis and reasoning on student responses; through semantic parsing, the core concepts involved in student responses are mapped as nodes. Then the graph reasoning function is expressed as: , in, To obtain the next relevant concept node based on knowledge dependencies, the reasoning process employs graph traversal and relational reasoning algorithms. It not only considers direct adjacency relationships but also supports multi-hop reasoning to identify implicit prior knowledge, cross-concept associations, and common erroneous paths. On the one hand, the system can determine the next teaching focus. When students frequently ignore the case of an empty linked list when answering the "linked list insertion" problem, the system can deduce that the "boundary condition handling" node should be emphasized. On the other hand, the system encodes the relevant nodes and their local subgraphs obtained through reasoning into a structured context. The input is injected into the aforementioned large language model to provide verifiable knowledge constraints for the model, ensuring that the generated content is highly consistent with the course outline and knowledge structure.

[0013] Step 4, Learning Monitoring and Optimization of the Heuristic Question Chain, includes: 4.1 Monitoring Teachers' Learning Progress Based on the student-side adaptive learning closed loop, it provides teachers with functions for monitoring student learning and evaluating teaching quality, enabling data-driven teaching decisions and problem chain optimization. At the individual level, the system is based on learning trajectories: , Visualize the evolution of students' knowledge status over time, combined with completion indicators. By analyzing answer accuracy and average response time, teachers can identify students' learning bottlenecks and progress stages using knowledge graphs. The system generates a knowledge mastery heatmap, which uses color to represent the mastery level of different knowledge nodes. Nodes that have not been mastered are displayed in cool colors, while nodes that have been mastered are displayed in warm colors, forming a personalized knowledge mastery map. At the group level, the system calculates the overall learning progress of the class. With individual progress Deviation: , The data is displayed in the form of a distribution map to help teachers quickly identify groups of students who are significantly ahead or behind in their learning progress; for each knowledge point, the system calculates its mastery rate in the class. , in, To determine the number of students who have mastered this knowledge point, The total number of students in the class; when the mastery rate of a certain knowledge point is lower than the preset threshold, the system marks it as a common weak point and prompts the teacher to provide targeted explanations or add related question chains; 4.2 Evaluation and Optimization of Problem Chain Teaching Effectiveness Regarding the evaluation and optimization of the problem chain effect, the system quantitatively evaluates the teaching effectiveness of the problem chain itself, and calculates the average accuracy rate for each problem. Standard deviation and average answering time To establish reasonableness assessment indicators for difficulty: , like Too high and Smaller size indicates the problem is relatively easy; if Too low and If the value is large, it indicates that the problem is difficult or unclear, and the system will mark it as a problem that needs to be reviewed. In terms of overall inspirational effect, the system calculates the increment of students' knowledge state before and after the question chain guidance: , The system comprehensively evaluates the effectiveness of heuristic teaching by combining qualitative indicators such as reasoning depth, conceptual relevance, and frequency of proactive exploration behaviors. Based on the above data, the system uses a rule engine and machine learning model to generate optimization suggestions for the question chain, including adjusting the question difficulty configuration parameters. By reconstructing the problem sequence or optimizing the conceptual relationships in the knowledge graph, teachers can conduct manual review and A / B testing, forming a closed-loop mechanism for continuous optimization.

[0014] This invention constructs an intelligent, personalized, and adaptive heuristic teaching system by deeply integrating a large language model with a knowledge graph. Its core innovation lies in: within the Cognitive Heuristic Loop (CHL) framework, it achieves progressive and dynamic generation of heuristic question chains through mathematical modeling, enabling the system to adjust the content, difficulty, and depth of questions in real time based on students' knowledge status and learning trajectory; it utilizes the structured representation of the course knowledge graph for semantic reasoning, ensuring logical coherence and accuracy in content between question generation and the course knowledge system; it transforms the large language model from "passive answering" to "active guidance" through instruction fine-tuning, generating inspiring exploratory questions and personalized feedback; and it establishes a real-time monitoring and learning analysis mechanism to adjust question difficulty and questioning strategies in a closed loop. Through the above technical solutions, this invention constructs a complete teaching closed loop covering "knowledge representation – question generation – learning feedback – difficulty adjustment – ​​learning monitoring and optimization," improving students' depth of understanding of abstract knowledge and their learning initiative while providing teachers with quantifiable learning data and continuously optimized heuristic teaching tools. Detailed Implementation

[0015] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, further illustrates the construction method of the heuristic teaching system based on large language models and knowledge graphs of the present invention: Example:

[0016] 1. Course knowledge graph and student knowledge state modeling 1.1 Structured Representation and Query of Course Knowledge Graph Course Knowledge Graph The core concepts and their relationships in the course are represented in a structured manner, where the node set... Representing knowledge points, edge sets It represents the semantic relationships between knowledge points, including prerequisite dependencies, parallel comparisons, compositional relationships, application scenarios, etc.

[0017] Taking linked list operations as an example, a local knowledge graph of linked lists can be constructed: , The system uses a graph query function Retrieve nodes associated with the currently learned concept to determine the direction and depth of question generation. Let the currently focused knowledge point be a node. ,but: , in, Indicates and The set of related adjacent or multi-hop nodes. For scenarios that require considering multiple mastered knowledge points simultaneously, multi-node joint queries can be performed: , On the question generation side, the system can generate candidate questions for the knowledge graph based on the node set and edge relationships returned by the query. For example, when extending from the "linked list insertion" related nodes to the "boundary condition handling" nodes, advanced questions such as "How to perform an insertion operation when the linked list is empty?" can be generated. Subsequently, the question generation function will... Compared to the aforementioned generation from large language models By integrating these elements, the final product presented to the students can be obtained. .

[0018] 1.2 Representation of Students' Knowledge Status Building upon the constructed course knowledge graph, the system models students' learning progress as a time-evolving knowledge state vector, providing foundational support for subsequent heuristic question chain generation and adaptive adjustment. Specifically, in subsequent steps, the system represents the student's knowledge state at time t as a vector. Furthermore, by combining cognitive stage markers, response records, and feedback information, the knowledge state is updated and trajectory modeled. The relevant formal definitions and update mechanisms will be given in detail in Sections 2 and 3.

[0019] 2. Design of Heuristic Problem Chains 2.1 Heuristic Question Chain Template and Cognitive Heuristic Closed-Loop Modeling To ensure that the heuristic question chain maintains a consistent structure and reusability across different knowledge points and students, this invention first constructs a heuristic question chain template based on the Cognitive Heuristic Loop Model (CHL). The CHL model divides the student's learning process into five stages: Anchoring, Exploring, Verifying, Applying, and Reflecting, corresponding to a standardized question chain framework consisting of five types of questions.

[0020] For any knowledge point node in the course knowledge graph The system pre-constructs a set of heuristic problem chain templates for it. Formal representation: , in, , , , , These represent question slots for the initiation, exploration, validation, transfer, and reflection phases, respectively. Each slot is a parameterized "question template" containing structured information such as the question objective, cognitive level, related knowledge points, and a callable large language model generation strategy, rather than a fixed text question.

[0021] During system runtime, targeting the current knowledge point and student knowledge state vector The system is based on its stage marker in the CHL model. Instantiate the above template to generate specific questions. For example, during the startup phase, the system in the slot... By binding constraints such as "contextualization, realism, and activation of prior experience," contextual questions are generated through a large language model to elicit target knowledge points. : , in, Generate functions for the startup phase issues. This includes contextual information such as learning tasks and learning history.

[0022] Similarly, exploration phase slots The heuristic requirement of "guiding students to propose hypotheses and compare different solutions" is used to generate questions that encourage students to engage in active reasoning and structured thinking; the verification stage slots... Constraints that "expose boundary conditions and counterexamples" are used to generate problems to check the correctness and robustness of the solution; migration phase slots Binding constraints of "new context application and analogy extension" is used to generate questions that support knowledge transfer; reflection phase slots By binding the constraint of "metacognitive summary and strategy reflection", it is used to generate reflective questions that help students review their thinking process and refine problem-solving strategies.

[0023] In terms of interaction strategy, the question chain template also encodes a "single-question-driven" presentation rule: at any given time, the system instantiates and presents only one question slot in the template, waits for the student to answer and complete the status update, and then presents the updated knowledge status. and stage markers The decision is made as to whether to continue generating subsequent questions at the current stage or switch to the next stage in the CHL closed loop, thereby ensuring that the pace of heuristic questioning is controllable and the cognitive load is moderate at the algorithm level. Through the above template design, this invention provides a unified structural foundation for the dynamic question chain generation and adaptive difficulty adjustment described later.

[0024] 2.2 Problem Chain Instantiation and Dynamic Generation Based on the above template-based modeling, this invention introduces the student's knowledge state and CHL stage state into the problem generation function to achieve dynamic instantiation and progressive generation of the problem chain.

[0025] The system will record students' time. The knowledge state is represented as a vector. The cognitive stage is represented as , will the The specific problem is represented as The student's answer to the question is expressed as Based on target knowledge points Corresponding template The system generates the first question in the problem chain in the following form. : , in, This represents the initial state of knowledge. This usually corresponds to the startup phase. , Generate control parameters for the initial problem. This is a unified question generation function. It comprehensively considers students' knowledge level, learning history, current stage, and template constraints to generate thought-provoking starting questions.

[0026] For the first in the problem chain The system will answer the previous question after the student completes the question. After the answer is given, the knowledge state is first updated, and then the next question is dynamically generated based on the updated knowledge state and the stage state. This can be formally represented as: , in, To generate the first Adjustment parameters for each problem This represents the current state of knowledge.

[0027] The process of updating students' knowledge status can be represented as follows: , in, This function updates the knowledge state vector by comprehensively utilizing information such as the correctness of the student's answer, the reasoning process, the coverage of the concepts used, and the type of error. The state update is not only based on binary "correct" or "incorrect" results, but also weights the completeness and logical rigor of the reasoning chain, thus characterizing the student's cognitive development level from multiple dimensions.

[0028] During the generation of the problem chain, the system continuously updates the latest knowledge state. Information related to the CHL phase As input, it is used to select the problem slots to be instantiated (such as continuing to stay in the exploration stage or switching to the verification stage), and to control the depth and breadth of the problems, ensuring semantic coherence and gradual increase in difficulty between problems, and avoiding knowledge gaps or excessive repetition.

[0029] 3. Adaptive control of question difficulty and large-scale model questioning strategy based on knowledge graph and learning trajectory. 3.1 Evolution of Students' Knowledge Status and Adaptive Adjustment of Problem Difficulty Based on the aforementioned dynamic generation mechanism of problem chains, this invention introduces a problem difficulty assessment function and learning trajectory modeling to characterize the evolution of students' knowledge status and adaptively adjust the difficulty of problems, ensuring that students are in the optimal learning range of "moderate challenge" in the long term.

[0030] To achieve dynamic matching between problem difficulty and student ability, the system updates the knowledge status. Then, regarding the current problem Assess the difficulty and provide a difficulty value. : , in, This is a function for evaluating the difficulty of the problem. This indicates the system's analysis and feedback on the student's answer (including the correctness of the answer, the time taken to answer, the number of times the prompt was used, the type of error, etc.). This represents the current CHL stage. By incorporating stage information into the evaluation function, the difficulty weights can be adjusted differently based on the teaching objectives of different stages. For example, the exploration stage emphasizes openness and multiple paths, while the verification stage emphasizes boundary conditions and rigor.

[0031] Based on students' answer accuracy within a certain time window The system can use piecewise functions to implement basic difficulty adjustment strategies, for example: , in, This indicates the target difficulty level for the next round of questions. When the accuracy rate is low, the system reduces the cognitive load on students by lowering the difficulty of subsequent questions, introducing intermediate transitional questions, or reverting to an earlier stage (such as reverting from the verification stage to the exploration stage). When the accuracy rate is high, the system appropriately increases the difficulty of the questions, introducing questions that require the integration of multiple knowledge points or cross-contextual transfer, to maintain a moderate level of challenge. In practical applications, the system can also be expanded to include multi-level difficulty levels and multi-threshold strategies to adapt to different courses and teaching scenarios.

[0032] To depict the evolution of students' knowledge status throughout the learning process, the system represents students' knowledge status at different points in time as follows: , in, These represent the student's knowledge state vectors at various key moments. This learning trajectory is not only used for subsequent learning visualization and teacher-side monitoring and analysis, but can also serve as input features in the effectiveness evaluation and automated optimization process of the question chain. For example, it can be used to compare the knowledge increment under different question chain configurations. To evaluate the heuristic effect of different problem sequences.

[0033] Through the aforementioned student knowledge state evolution modeling and difficulty adaptive adjustment mechanism, this invention constructs a closed loop at the algorithm level of "knowledge state - problem generation - feedback analysis - difficulty adjustment", providing basic support for the overall personalized and adaptive teaching capabilities of the system.

[0034] 3.2 Fine-tuning of the large language model To enable the large language model to generate heuristic questions that align with students' learning progress and CHL stage characteristics, this invention fine-tunes the large language model's instructions based on the aforementioned question chain framework. The system encodes information related to question generation in each interaction step into an input vector. This includes the previous round of questions and answers, the current knowledge state, stage markers, and the structured context obtained from the knowledge graph. , in, For the problems that have already emerged in the previous round, For the students' answers, This is the current knowledge state vector. Mark the current CHL stage. For contextual information such as teaching situations and learning history, This refers to structured background information obtained through knowledge graph retrieval and reasoning.

[0035] The finely tuned large language model Given the input, output the candidate heuristics for this round. : , in, This involves fine-tuning parameters for a large language model. A combination of supervised learning and reinforcement learning is used to... The model is trained to not only possess knowledge-based question-and-answer capabilities in the course domain, but also to learn heuristic questioning strategies, including various questioning patterns such as from simple to complex, from concrete to abstract, and from single points to connections.

[0036] During the fine-tuning process, the system will use the knowledge graph retrieval results. and characteristics of students' knowledge status These questions are also used as contextual input, ensuring that the problems generated by the model are more aligned with the course's knowledge structure in terms of content and more closely match the students' actual level in terms of difficulty. This avoids generating overly generalized questions that deviate from the syllabus or are inconsistent with the knowledge graph. The final specific questions presented to students are... The aforementioned unified problem generation function pairs It is obtained by fusing with the results generated from the knowledge graph.

[0037] 3.3 Personalized Feedback and Incremental Updates of Knowledge Status After students complete their answers, the system generates personalized feedback based on their current knowledge level and their responses. Let the... The question is The student's answer was ,time The knowledge state is Personalized feedback Defined as: , in, A comprehensive analysis should be conducted on the accuracy, completeness, reasoning chain, coverage of concepts used, and error types (such as conceptual errors, procedural errors, careless errors, etc.) of the answer, in conjunction with the current CHL stage. Differentiated feedback strategies are generated for different situations. Feedback primarily takes the form of prompting questions, partial guidance, and comparative examples, avoiding directly providing the final answer, in order to encourage students to independently discover and correct their mistakes.

[0038] After feedback is generated, the system incrementally updates the student's knowledge status based on the feedback to obtain the knowledge status at the next moment. : , in, This is a knowledge state increment update function that adjusts the weights of different dimensions (corresponding to different knowledge points or ability indicators) in the knowledge state vector differently based on the feedback content and student performance, thereby accurately reflecting the cognitive changes of students after this round of interaction.

[0039] The system simultaneously records each student's completion status on the question chain, forming a completion rate indicator. : , in, This represents the number of completed issues. The total number of questions, For the first The score for each question and This is the weighting coefficient. This indicator reflects both the degree of student participation and the quality of their answers, providing a quantitative basis for the adaptive difficulty adjustment and student learning analysis described later.

[0040] 3.4 Knowledge Graph-Driven Semantic Enhancement Reasoning By combining knowledge graphs, the system can perform structured semantic analysis and reasoning on student responses. Assume that through semantic parsing, the core concepts involved in student responses are mapped as nodes. Then the graph reasoning function can be expressed as: , in, This is the next relevant concept node obtained through reasoning based on knowledge dependencies. The reasoning process employs graph traversal and relational reasoning algorithms, considering not only direct adjacency relationships but also supporting multi-hop reasoning to identify implicit prior knowledge, cross-concept associations, and common erroneous paths.

[0041] Based on this, the system can determine the next teaching focus. For example, if students frequently ignore the case of an empty linked list when answering the "linked list insertion" question, the system can infer that the "boundary condition handling" node should be emphasized. On the other hand, the system can encode the relevant nodes and their local subgraphs obtained through reasoning into a structured context. By injecting the aforementioned large language model into the input, verifiable knowledge constraints are provided to the model, thereby effectively reducing the "illusion" phenomenon of the large language model and ensuring that the generated content is highly consistent with the course outline and knowledge structure.

[0042] 4. Learning progress monitoring and optimization of heuristic question chains 4.1 Monitoring Teachers' Learning Progress Based on the adaptive learning closed loop on the student side, this invention further provides teachers with functions for monitoring learning progress and evaluating teaching quality, enabling data-driven teaching decisions and optimization of the problem chain.

[0043] At the individual level, the system is based on learning trajectories: , Visual representations such as line graphs and radar charts are used to show the evolution of students' knowledge status over time. This is combined with completion indicators. By analyzing metrics such as answer accuracy and average response time, teachers can identify students' learning bottlenecks and stages of progress. This can be achieved using knowledge graphs. The system generates a "knowledge mastery heatmap", which uses color to represent the degree of mastery of different knowledge nodes. Nodes that have not been mastered are displayed in cool colors, while nodes that have been mastered are displayed in warm colors, forming a personalized knowledge mastery map.

[0044] At the group level, the system calculates the overall learning progress of the class. With individual progress Deviation: , The data is displayed in the form of a distribution chart to help teachers quickly identify students who are significantly ahead or behind in their learning progress. For each knowledge point, the system calculates its mastery rate within the class. , in, To determine the number of students who have mastered this knowledge point, This represents the total number of students in the class. When the mastery rate of a certain knowledge point falls below a preset threshold, the system marks it as a common weak point, prompting teachers to provide targeted explanations or add related question chains.

[0045] 4.2 Evaluation and Optimization of Problem Chain Teaching Effectiveness Regarding the evaluation and optimization of the problem chain effect, the system quantitatively evaluates the teaching effectiveness of the problem chain itself. For each problem, the average accuracy rate is calculated. Standard deviation and average answering time To establish reasonableness assessment indicators for difficulty: , like Too high and Smaller size indicates the problem is relatively easy; if Too low and If the value is large, it may indicate that the problem is too difficult or the expression is unclear, and the system will mark it as a problem that needs to be reviewed.

[0046] In terms of overall inspirational effect, the system calculates the increment of students' knowledge state before and after the question chain guidance: , The system comprehensively evaluates the effectiveness of heuristic teaching by combining qualitative indicators such as reasoning depth, conceptual relevance, and frequency of proactive exploration behaviors. Based on the above data, the system uses a rule engine and machine learning model to generate optimization suggestions for the question chain, such as adjusting the question difficulty configuration parameters. This involves reconstructing the problem sequence or optimizing the conceptual relationships within the knowledge graph. Teachers can then conduct manual reviews and A / B tests, creating a closed-loop mechanism for continuous optimization.

[0047] The embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Various changes that can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for constructing a heuristic teaching system based on large language models and knowledge graphs, characterized in that: Includes the following steps: Step 1: Modeling the course knowledge graph and student knowledge state; Step 2: Design of a heuristic problem chain; Step 3: Adaptively control the question difficulty and the large model questioning strategy based on knowledge graphs and learning trajectories; Step 4: Learning progress monitoring and optimization of the heuristic question chain.

2. The method for constructing a heuristic teaching system based on a large language model and knowledge graph as described in claim 1, characterized in that, Step 1, Course Knowledge Graph and Student Knowledge State Modeling, includes: 1.1 Structured Representation and Query of Course Knowledge Graph: Course Knowledge Graph The core concepts and their relationships in the course are represented in a structured manner, where the node set... Representing knowledge points, edge sets It represents the semantic relationships between knowledge points, including prerequisite dependencies, parallel comparisons, compositional relationships, and application scenarios; 1.2 Representation of students' knowledge status: Based on the construction of the course knowledge graph, the system models students' learning mastery as a time-evolving knowledge state vector, providing foundational support for subsequent heuristic question chain generation and adaptive adjustment. In subsequent steps, the system represents students' knowledge state at time t as a vector. Furthermore, by combining cognitive stage markers, response records, and feedback information, the knowledge state is updated and trajectory modeled.

3. The method for constructing a heuristic teaching system based on a large language model and knowledge graph according to claim 2, characterized in that, 1.1 In the structured representation and querying of the course knowledge graph, a local knowledge graph of linked lists is constructed for linked list operations: ， The system uses a graph query function Retrieve nodes associated with the currently learned concept to determine the direction and depth of question generation; let the currently focused knowledge point be a node. ,but: ， in, Indicates and For scenarios requiring simultaneous consideration of multiple mastered knowledge points, the relevant set of adjacent or multi-hop related nodes can be used for multi-node joint queries: ， On the question generation side, the system generates candidate questions for the knowledge graph based on the node set and edge relationships returned by the query. When extending from the "linked list insertion" related nodes to the "boundary condition handling" nodes, an advanced question, "How to perform an insertion operation when the linked list is empty?", is generated. The question generation function will... Compared with the aforementioned large language model By integrating these elements, the final product presented to the students can be obtained. .

4. The method for constructing a heuristic teaching system based on a large language model and knowledge graph according to claim 2 or 3, characterized in that, Step 2, the design of the heuristic question chain includes: 2.1 Heuristic Question Chain Template and Cognitive Heuristic Closed-Loop Modeling Based on the cognitive-inspired closed-loop teaching model, a heuristic question chain template is constructed, which divides the students' learning process into five stages: initiation, exploration, verification, transfer and reflection, and forms a standardized question chain framework consisting of five types of questions. For any knowledge point node in the course knowledge graph The system pre-constructs a set of heuristic problem chain templates for it. Formal representation: ， in, , , , , These represent question slots for the initiation phase, exploration phase, verification phase, migration phase, and reflection phase, respectively. Each slot is a parameterized "question template" containing the question objective, cognitive level, related knowledge points, and structured information about the large language model generation strategy that can be invoked, rather than a fixed text question. During system runtime, targeting the current knowledge point and student knowledge state vector The system is based on its stage marker in the CHL model. Instantiate the above template to generate specific questions. During the startup phase, the system is in the slot. By binding constraints such as "contextualization, realism, and activation of prior experience," contextual questions are generated through a large language model to elicit target knowledge points. : ， in, Generate functions for the startup phase issues. This includes contextual information such as learning tasks and learning history. Exploration phase slots The heuristic requirement of "guiding students to propose hypotheses and compare different solutions" is used to generate questions that encourage students to engage in active reasoning and structured thinking; the verification stage slots... Constraints that "expose boundary conditions and counterexamples" are used to generate problems to check the correctness and robustness of the solution; migration phase slots Binding the constraint of "new context application and analogy extension" is used to generate questions that support knowledge transfer; reflection phase slots The constraint of "metacognitive summary and strategic reflection" is used to generate reflective questions that help students review their thinking process and refine problem-solving strategies. In terms of interaction strategy, the question chain template encodes a "single-question-driven" presentation rule: at any given time, the system instantiates and presents only one question slot in the template, waits for the student to answer and complete the status update, and then presents the updated knowledge status. and stage markers The decision is whether to continue generating subsequent questions at the current stage or switch to the next stage in the CHL closed loop, thereby ensuring that the pace of heuristic questioning is controllable and the cognitive load is moderate at the algorithm level. 2.2 Problem Chain Instantiation and Dynamic Generation Based on the above template-based modeling, by introducing the student's knowledge state and CHL stage state into the problem generation function, the dynamic instantiation and progressive generation of the problem chain are realized. The system will record students' time. The knowledge state is represented as a vector. The cognitive stage is represented as , will the The specific problem is represented as The student's answer to the question is expressed as Based on target knowledge points Corresponding template The system generates the first question in the problem chain in the following form. : ， in, This represents the initial state of knowledge. This usually corresponds to the startup phase. , Generate control parameters for the initial problem. A unified question generation function; this function comprehensively considers students' knowledge mastery, learning history, current stage, and template constraints to generate thought-provoking starting questions; For the first in the problem chain The system will answer the previous question after the student completes the question. After the answer is given, the knowledge state is first updated, and then the next question is dynamically generated based on the updated knowledge state and the stage state. This can be formally represented as: ， in, To generate the first Adjustment parameters for each problem This represents the current, latest state of knowledge. The process of updating students' knowledge status is represented as follows: ， in, The state update function comprehensively utilizes the correctness of students' answers, reasoning process, coverage of concepts used, and error type information to update the knowledge state vector. The state update is not only based on the binary results of "correct" and "incorrect", but also weights the integrity of the reasoning chain and the logical rigor, thus characterizing the students' cognitive development level from multiple dimensions. During the generation of the problem chain, the system continuously updates the latest knowledge state. Information related to the CHL phase As input, it is used to select the question slots to be instantiated on the one hand, and to control the depth and breadth of questions on the other hand, to ensure semantic coherence and gradual increase in difficulty between questions, and to avoid knowledge gaps or excessive repetition.

5. The method for constructing a heuristic teaching system based on a large language model and knowledge graph according to claim 4, characterized in that, Step 3: Adaptive control of question difficulty and large-scale model questioning strategy based on knowledge graph and learning trajectory includes: 3.1 Evolution of Students' Knowledge Status and Adaptive Adjustment of Problem Difficulty Based on the dynamic generation mechanism of the problem chain, a problem difficulty assessment function and learning trajectory modeling are introduced to characterize the evolution of students' knowledge status and adaptively adjust the problem difficulty, ensuring that students are in the optimal learning range of "moderate challenge" in the long term. To achieve dynamic matching between problem difficulty and student ability, the system updates the knowledge status. Then, regarding the current problem Assess the difficulty and provide a difficulty value. : ， in, This is a function for evaluating the difficulty of the problem. This indicates the system's analysis and feedback on the student's answer, including the correctness of the answer, the time taken to answer, the number of times hints were used, and the type of error. For the current CHL stage, by incorporating stage information into the evaluation function, the difficulty weight is adjusted differently according to the teaching objectives of different stages. In the exploration stage, more emphasis is placed on openness and multiple paths, while in the verification stage, more emphasis is placed on boundary conditions and rigor. Based on students' answer accuracy within a certain time window The system employs piecewise functions to implement a basic difficulty adjustment strategy: ， in, This indicates the target difficulty level for the next round of questions. When the accuracy rate is low, the system reduces the cognitive load on students by lowering the difficulty of subsequent questions, introducing intermediate transitional questions, or reverting to an earlier stage. When the accuracy rate is high, the system appropriately increases the difficulty of the questions and introduces questions that require the integration of multiple knowledge points or cross-contextual transfer to maintain a moderate challenge. The system is also expanded to include multi-level difficulty levels and multi-threshold strategies to adapt to different courses and teaching scenarios. To depict the evolution of students' knowledge status throughout the learning process, the system represents students' knowledge status at different points in time as: where, This indicates the target difficulty level for the next round of questions. When the accuracy rate is low, the system reduces the cognitive load on students by lowering the difficulty of subsequent questions, introducing intermediate transitional questions, or reverting to an earlier stage. When the accuracy rate is high, the system appropriately increases the difficulty of the questions and introduces questions that require the integration of multiple knowledge points or cross-contextual transfer to maintain a moderate challenge. The system is also expanded to include multi-level difficulty levels and multi-threshold strategies to adapt to different courses and teaching scenarios. To depict the evolution of students' knowledge status throughout the learning process, the system represents students' knowledge status at different points in time as follows: ， in, These are the knowledge state vectors of students at various key moments. This learning trajectory is not only used for subsequent learning visualization and teacher-side monitoring and analysis, but also serves as input features in the effectiveness evaluation and automated optimization process of the question chain. By comparing the knowledge increment under different question chain configurations... To evaluate the heuristic effect of different problem sequences; 3.2 Fine-tuning of the large language model Based on the question chain framework, the large language model is fine-tuned, and the system encodes the information related to question generation in each step of the interaction into an input vector. This includes the previous round of questions and answers, the current knowledge state, stage markers, and the structured context obtained from the knowledge graph: ， in, For the problems that have already emerged in the previous round, For the students' answers, This is the current knowledge state vector. Mark the current CHL stage. To provide teaching context and learning historical information, This refers to structured background information obtained through knowledge graph retrieval and reasoning. The fine-tuned large language model Given the input, output the candidate heuristics for this round. : ， in, To fine-tune the parameters of a large language model, a combination of supervised learning and reinforcement learning is used. The model is trained to not only possess knowledge-based question-and-answer capabilities in the course domain, but also to learn heuristic questioning strategies, including various questioning patterns from simple to complex, from concrete to abstract, and from single points to connections. During the fine-tuning process, the system will use the knowledge graph retrieval results. and characteristics of students' knowledge status This contextual input ensures that the problems generated by the model are more aligned with the course's knowledge structure in terms of content and more closely match the students' actual level in terms of difficulty. This avoids generating overly generalized problems that deviate from the syllabus or are inconsistent with the knowledge graph, ultimately presenting students with specific questions. The aforementioned unified problem generation function pairs It is obtained by fusing with the results generated from the knowledge graph side; 3.3 Personalized Feedback and Incremental Updates of Knowledge Status After students complete their answers, the system generates personalized feedback based on their current knowledge level and their responses to the questions. Let the first... The question is The student's answer was ,time The knowledge state is Personalized feedback Defined as: ， in, A comprehensive analysis is conducted on the accuracy, completeness, reasoning chain, coverage of concepts used, and error types, including conceptual errors, procedural errors, and careless errors, in conjunction with the current CHL stage. Differentiated feedback strategies are generated for different situations. Feedback forms include prompting questions, partial guidance and explanation, and comparative examples, avoiding giving the final answer directly, so as to encourage students to discover and correct their mistakes independently. After feedback is generated, the system incrementally updates the student's knowledge status based on the feedback to obtain the knowledge status at the next moment. : ， in, This is a knowledge state increment update function. Based on the feedback content and student performance, it differentiates the weights of different dimensions corresponding to different knowledge points or ability indicators in the knowledge state vector, thereby accurately reflecting the cognitive changes of students after this round of interaction. The system simultaneously records each student's completion status on the question chain, forming a completion rate indicator. : ， in, This represents the number of completed issues. The total number of questions, For the first The score for each question and This is the weighting coefficient; this indicator reflects both the students' level of participation and the quality of their answers, providing a quantitative basis for the adaptive adjustment of difficulty and the analysis of student learning in the following sections. 3.4 Knowledge Graph-Driven Semantic Enhancement Reasoning By combining knowledge graphs, the system performs structured semantic analysis and reasoning on student responses; through semantic parsing, the core concepts involved in student responses are mapped as nodes. Then the graph reasoning function is expressed as: ， in, To obtain the next relevant concept node based on knowledge dependencies, the reasoning process employs graph traversal and relational reasoning algorithms. It not only considers direct adjacency relationships but also supports multi-hop reasoning to identify implicit prior knowledge, cross-concept associations, and common erroneous paths. On the one hand, the system determines the next teaching focus. When students frequently ignore the case of an empty linked list when answering the "linked list insertion" problem, the system infers that the "boundary condition handling" node should be emphasized. On the other hand, the system encodes the relevant nodes and their local subgraphs obtained through reasoning into a structured context. The input is injected into the aforementioned large language model to provide verifiable knowledge constraints for the model, ensuring that the generated content is highly consistent with the course outline and knowledge structure.

6. The method for constructing a heuristic teaching system based on a large language model and knowledge graph according to claim 5, characterized in that, Step 4, Learning Monitoring and Optimization of the Heuristic Question Chain, includes: 4.1 Monitoring Teachers' Learning Progress Based on the student-side adaptive learning closed loop, it provides teachers with functions for monitoring student learning and evaluating teaching quality, enabling data-driven teaching decisions and problem chain optimization. At the individual level, the system is based on learning trajectories: ， Visualize the evolution of students' knowledge status over time, combined with completion indicators. By analyzing answer accuracy and average response time, teachers can identify students' learning bottlenecks and progress stages using knowledge graphs. The system generates a knowledge mastery heatmap, which uses color to represent the mastery level of different knowledge nodes. Nodes that have not been mastered are displayed in cool colors, while nodes that have been mastered are displayed in warm colors, forming a personalized knowledge mastery map. At the group level, the system calculates the overall learning progress of the class. With individual progress Deviation: ， The data is displayed in the form of a distribution map to help teachers quickly identify groups of students who are significantly ahead or behind in their learning progress; for each knowledge point, the system calculates its mastery rate in the class. ， in, To determine the number of students who have mastered this knowledge point, The total number of students in the class; when the mastery rate of a certain knowledge point is lower than the preset threshold, the system marks it as a common weak point and prompts the teacher to provide targeted explanations or add related question chains; 4.2 Evaluation and Optimization of Problem Chain Teaching Effectiveness Regarding the evaluation and optimization of the problem chain effect, the system quantitatively evaluates the teaching effectiveness of the problem chain itself, and calculates the average accuracy rate for each problem. Standard deviation and average answering time To establish reasonableness assessment indicators for difficulty: ， like Too high and Smaller size indicates the problem is relatively easy; if Too low and If the value is large, it indicates that the problem is difficult or unclear, and the system will mark it as a problem that needs to be reviewed. In terms of overall inspirational effect, the system calculates the increment of students' knowledge state before and after the question chain guidance: ， The system comprehensively evaluates the effectiveness of heuristic teaching by combining qualitative indicators such as reasoning depth, conceptual relevance, and frequency of proactive exploration behaviors. Based on the above data, the system uses a rule engine and machine learning model to generate optimization suggestions for the question chain, including adjusting the question difficulty configuration parameters. The system reconstructs problem sequences or optimizes the conceptual relationships in the knowledge graph. Teachers then conduct manual reviews and A / B tests based on this information, forming a closed-loop mechanism for continuous optimization.

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