Mathematical teaching knowledge graph generation method and system based on artificial intelligence

Abstract

The invention relates to the technical field of artificial intelligence and intelligent education, and provides a mathematical teaching knowledge graph generation method and system based on artificial intelligence, which are used for optimizing and improving a teaching knowledge graph generation technology to realize more intelligent and accurate teaching knowledge graph generation, and the method comprises the following steps: obtaining a multi-source teaching data set; extracting a mathematical knowledge point entity set from the textbook text data, and generating an association relationship set among mathematical knowledge point entities in the mathematical knowledge point entity set according to the test question structure data; performing hierarchical classification processing on the mathematical knowledge point entity set based on a preset semantic analysis model to obtain knowledge point hierarchical structure data, and calculating weight distribution data of the mathematical knowledge point entities based on the association relationship set; and generating a dynamic knowledge graph topological structure according to the knowledge point hierarchical structure data and the weight distribution data, wherein nodes in the dynamic knowledge graph topological structure comprise semantic vectors and association strength parameters of mathematical knowledge point entities.

Description

Technical Field

[0001] The present invention belongs to the technical fields of artificial intelligence and intelligent education, and particularly relates to a method and system for generating a mathematics teaching knowledge graph based on artificial intelligence. Background Art

[0002] Currently, traditional educational knowledge graph construction technologies mainly rely on the structured processing of a single data source, such as modeling a static knowledge system based on textbook chapter division, or simply analyzing the association of knowledge points using question tags.

[0003] However, there are obvious deviations between the knowledge network generated by the above traditional technologies and the real teaching scenarios, making it difficult to match personalized teaching needs. At the same time, the nodes of existing knowledge graphs are mostly labeled using a discrete attribute annotation method, and the semantic vector representation and association strength parameters are not coupled and modeled, resulting in problems of feature dimension fragmentation in derivative applications such as knowledge evolution tracking and learning path recommendation.

[0004] Therefore, how to further optimize and improve the teaching knowledge graph generation technology to achieve a more intelligent and accurate teaching knowledge graph generation is a technical problem that needs to be solved currently. Summary of the Invention

[0005] The present invention provides a method and system for generating a mathematics teaching knowledge graph based on artificial intelligence, which is used to optimize and improve the teaching knowledge graph generation technology to achieve a more intelligent and accurate teaching knowledge graph generation.

[0006] In a first aspect, an embodiment of the present invention provides a method for generating a mathematics teaching knowledge graph based on artificial intelligence, which is applied to a knowledge graph generation system. The method includes: obtaining a multi-source teaching data set, where the multi-source teaching data set includes textbook text data, question structure data, and teaching resource data; extracting a set of mathematical knowledge point entities from the textbook text data, and generating a set of association relationships between the mathematical knowledge point entities in the set of mathematical knowledge point entities according to the question structure data; performing hierarchical classification processing on the set of mathematical knowledge point entities based on a preset semantic analysis model to obtain knowledge point hierarchical structure data, and calculating weight distribution data of the mathematical knowledge point entities based on the set of association relationships; generating a dynamic knowledge graph topological structure according to the knowledge point hierarchical structure data and the weight distribution data, and the nodes in the dynamic knowledge graph topological structure include semantic vectors and association strength parameters of the mathematical knowledge point entities.

[0007] In a second aspect, an embodiment of the present invention provides a knowledge graph generation system, which includes a processor and a memory. Among them, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the above method.

[0008] In a third aspect, an embodiment of the present invention provides a computer-readable storage medium, which includes a computer program. When the computer program runs on a knowledge graph generation system, the computer program is used to cause the knowledge graph generation system to execute the steps of the above method.

[0009] In the implementation of the present invention, by combining the semantic parsing of teaching materials text with the logical mining of test question structures, a knowledge point association network that combines subject logic and examination hotspots is constructed through cross-validation of heterogeneous data, overcoming the static defect of traditional knowledge graphs relying on a single data source; coupling the hierarchical classification algorithm with the weight dynamic allocation mechanism to simultaneously capture the subject membership and teaching association strength of knowledge points in the semantic space, making the knowledge topology structure have self-adaptability to teaching scenarios; through the semantic vector space mapping technology, the knowledge point entity features and association parameters are fused in a high-dimensional manner to generate a dynamic knowledge graph topology structure, improving the prediction accuracy in knowledge point evolution tracking and teaching path optimization. Thus, the teaching knowledge graph generation technology can be optimized and improved, thereby realizing the generation of a more intelligent and accurate teaching knowledge graph. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic flow chart of a method for generating a mathematics teaching knowledge graph based on artificial intelligence provided by an embodiment of the present invention.

[0011] Figure 2 It is a schematic structural diagram of a knowledge graph generation system provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0012] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments recorded in this document of the present invention without creative efforts shall fall within the scope of protection of the technical solutions of the present invention.

[0013] See Figure 1 , which is a method for generating a mathematics teaching knowledge graph based on artificial intelligence provided in an embodiment of the present invention. This method can be applied to a knowledge graph generation system, and the specific process is as shown in steps 110-step 140.

[0014] Step 110: Obtain a multi-source teaching data set, where the multi-source teaching data set includes teaching material text data, test question structure data, and teaching resource data.

[0015] In an embodiment of the present invention, the knowledge graph generation system first obtains a set of structured and unstructured raw data from multiple teaching data sources through a data interface module. For example, it can retrieve the electronic text data of the junior high school mathematics textbooks of the People's Education Edition from the authorized textbook database of educational institutions. The electronic text data contains the complete teaching content of several chapters in six textbooks, covering three major knowledge fields: algebra, geometry, and probability statistics.

[0016] Meanwhile, it can obtain the set of middle school entrance examination mathematics test question data from multiple provinces and cities across the country in recent years from the educational resource public service platform, which includes the stems, solution steps, and standard answer analyses of a large number of test questions. Each test question is labeled with a knowledge point examination label and a difficulty coefficient. In addition, it also collects the supporting teaching resource data of mainstream online education platforms through a crawler program, including multiple teaching videos corresponding to textbook chapters, multiple sets of courseware PPT files, and multiple sets of classroom exercise sets, forming a multi-modal data set.

[0017] In the above process, the knowledge graph generation system can use a data cleaning component to perform format standardization processing on the raw data. For example, it can uniformly convert the chapter titles in different versions of textbooks into a three-level coding format of "volume-chapter-section", and perform optical character recognition correction on the mathematical formulas in scanned PDF textbooks to ensure data consistency in subsequent processing links.

[0018] Step 120: Extract a set of mathematical knowledge point entities from the textbook text data, and generate a set of association relationships between the mathematical knowledge point entities in the set of mathematical knowledge point entities according to the test question structure data.

[0019] In an embodiment of the present invention, the knowledge graph generation system uses a natural language processing module to perform in-depth semantic analysis on the textbook text data.

[0020] Taking the knowledge point of the "Pythagorean theorem" in junior high school mathematics as an example, the knowledge graph generation system first extracts core terms such as "right triangle", "square of the hypotenuse", and "Pythagorean theorem" from the continuous text of the third section of Chapter 5 of the textbook through a named entity recognition model, and determines the unique identifier as a mathematical knowledge point entity in combination with the context disambiguation. Then, the dependency syntactic analysis module identifies the semantic structure of "the Pythagorean theorem is applicable to the derivation of the three-side relationship of a right triangle", and establishes a preliminary association between the "Pythagorean theorem" entity and adjacent knowledge points such as "triangle classification" and "square operation".

[0021] Meanwhile, the knowledge graph generation system performs association relationship mining on the test question structure data. For example, it is found from the analysis of a certain middle school entrance examination question that the solution process of "finding the hypotenuse given the length of the right side" requires the simultaneous invocation of two knowledge points, namely the "Pythagorean theorem" and "square root calculation". Based on this, a directional "predecessor dependency" relationship is generated, and the co-occurrence frequency of this relationship in the test question bank is counted.

[0022] For teaching video data, after the knowledge graph generation system converts speech to text through speech recognition, it detects that the teacher mentions "area method" and "string diagram construction" synchronously when explaining the "proof of the Pythagorean theorem", thereby supplementing the "proof method association" relationship type between entities, and finally forming a set containing multiple mathematical knowledge point entities and multiple association relationships.

[0023] Step 130: Perform hierarchical classification processing on the set of mathematical knowledge point entities based on a preset semantic analysis model to obtain knowledge point hierarchical structure data, and calculate the weight distribution data of the mathematical knowledge point entities based on the set of association relationships.

[0024] In the embodiment of the present invention, the knowledge graph generation system starts the hierarchical classification module and uses an improved spectral clustering algorithm to perform multi-granularity partitioning on the set of mathematical knowledge point entities. First, a first-level classification framework is established based on the textbook table of contents structure, and "number and algebra", "geometry and graphics", and "statistics and probability" are used as top-level categories.

[0025] Then, the semantic similarity between knowledge points is calculated through a semantic vector space model. For example, the cosine similarity between the "quadratic formula for finding the roots of a quadratic equation" and the "factorization method" reaches 0.83, so it is classified into the secondary subclass of "algebraic solution method". For knowledge points with multiple membership relationships, such as the "plane rectangular coordinate system" which is involved in both coordinate geometry and function images at the same time, the knowledge graph generation system adopts a soft clustering strategy to assign it dual category membership and allocate corresponding membership degrees.

[0026] In the weight assignment stage, the knowledge graph generation system constructs a knowledge point association graph model and uses an improved PageRank algorithm to calculate the global importance weights of each node. Among them, the "function concept" obtains a higher weight value because it is cited by multiple test questions and is at the intersection of multiple knowledge paths. At the same time, combining local features such as the knowledge point explanation duration and the frequency of exercise appearance in the teaching resource data, the weight coefficient is dynamically adjusted. Finally, a knowledge point hierarchical structure with several levels and multiple subcategories is generated, and a normalized weight value in the range of 0.1 to 0.95 is assigned to each entity.

[0027] In some possible examples, hierarchical classification processing refers to the process of hierarchically organizing mathematical knowledge point entities according to the subject system through multi-granularity semantic analysis and clustering algorithms. Exemplarily, the knowledge graph generation system first establishes a basic classification framework based on the textbook table of contents structure (such as top-level categories like "Number and Algebra", "Geometry and Graphics", etc.), and then calculates the semantic similarity between knowledge points using the semantic vector space model (for example, measuring the association strength between terms through cosine similarity), and combines an improved spectral clustering algorithm to perform multi-level partitioning of knowledge points. For knowledge points with multiple membership relationships (such as "Plane Rectangular Coordinate System" belonging to both coordinate geometry and function graphs), a soft clustering strategy is adopted to assign them multi-category membership degrees. This process realizes the multi-level classification of knowledge points from the macroscopic domain to the microscopic concept by integrating the prior knowledge of the textbook structure and data-driven semantic similarity calculation, and finally forms a classification system with a tree-like inheritance relationship.

[0028] In addition, the knowledge point hierarchical structure data is a structured data set representing the multi-level classification relationship and weights of mathematical knowledge points. The core content of the knowledge point hierarchical structure data includes:

[0029] 1) The hierarchical classification framework, such as a five-layer tree structure represented by "Number and Algebra - Equations and Inequalities - Quadratic Equations with One Variable", where each level expresses the inclusion and derivation logic of knowledge points through the parent-child relationship;

[0030] 2) The attribute data of the knowledge point nodes, including the normalized global weight (reflecting the importance of the knowledge point in the question bank and teaching resources), the local weight (dynamically adjusted based on features such as teaching duration and exercise frequency), and the multi-category membership degree parameter (such as the probability value of a certain knowledge point belonging to two sub-categories at the same time);

[0031] 3) The semantic constraint rules between levels, such as the mapping mechanism between the chapter attribution relationship defined by the textbook table of contents and the data clustering results.

[0032] In the embodiment of the present invention, the knowledge point hierarchical structure data can be stored in the form of an attribute graph model in a graph database or a multi-table association in a relational database.

[0033] Step 140: Generate a dynamic knowledge graph topology structure according to the knowledge point hierarchical structure data and the weight assignment data, where the nodes in the dynamic knowledge graph topology structure include the semantic vectors and association strength parameters of the mathematical knowledge point entities.

[0034] In the embodiments of the present invention, the knowledge graph generation system calls the graph database construction module to fuse the hierarchical classification results with the weight data. In specific implementation, each knowledge point entity is transformed into a graph node object, and the node attributes include multi-dimensional semantic vectors generated by the BERT model, hierarchical classification codes, and comprehensive weight values. The association relationship is transformed into a weighted directed edge, where the weight parameter of the "Pythagorean theorem → square root calculation" edge is calculated as 0.72 based on features such as the co-occurrence times of the two in test questions and the proximity in textbooks.

[0035] For example, the knowledge graph generation system uses a dynamic topology optimization algorithm to continuously update the graph structure. When the "application of the Pythagorean theorem in solid geometry" appears in newly added municipal unified test questions, a new association edge between the "Pythagorean theorem" and the "spatial geometric body" is automatically created, and the weight of this edge is initialized to 0.65 based on the statistical results of several newly added test questions. At the same time, the semantic vector update component periodically recalculates the distributed representation of the nodes to ensure that the newly fused teaching resource data can be timely reflected in the semantic similarity calculation of knowledge points, forming a dynamic knowledge graph with time evolution characteristics, and finally outputting a mathematical teaching knowledge graph instance containing multiple nodes and multiple association edges.

[0036] In some possible examples, the dynamic knowledge graph topology structure is a graph data structure with mathematical knowledge points as nodes and association relationships as edges, and fuses semantics and weight parameters. The main content of the dynamic knowledge graph topology structure can include:

[0037] 1) Node attributes include high-dimensional semantic vectors (such as multi-dimensional distributed representations generated by the BERT model), hierarchical codes (such as "5-3-2" representing the second knowledge point in the third section of the fifth chapter), and comprehensive weights (combining the global importance calculated by the PageRank algorithm and the local feature weights);

[0038] 2) The weight parameters of the directed edges are calculated by compounding co-occurrence frequencies (such as the number of times a knowledge point pair is examined in test questions), textbook proximity (such as chapter spacing), and semantic similarity (such as the results of dependency syntactic analysis) (for example, the weight of the "Pythagorean theorem → square root calculation" edge is 0.72);

[0039] 3) The dynamic evolution mechanism includes real-time topology updates triggered by newly added teaching data (such as automatically creating association edges when new applications of the "Pythagorean theorem" in solid geometry are detected), periodic recalculation of semantic vectors (adapting to semantic changes in teaching resources), and a weight decay model (reducing the contribution of stale data).

[0040] In summary, the embodiments of the present invention construct a mathematical knowledge graph with high completeness and dynamic adaptability through the deep fusion and intelligent processing of multi-source teaching data, significantly improving the accuracy and application efficiency of educational knowledge representation.

[0041] First, multi-modal data cleaning and structured integration technologies are adopted to effectively aggregate heterogeneous resources such as textbooks, test questions, and teaching videos, covering the complete chapter content of textbooks and a vast amount of test question resources, ensuring the global coverage of knowledge elements and multi-dimensional feature extraction.

[0042] Secondly, based on deep semantic parsing and association mining algorithms, accurate extraction of knowledge point entities and their logical relationships is achieved. Through semantic disambiguation, problem-solving path tracking, and multi-modal content analysis, a weighted association network is generated, which can accurately depict the hierarchical dependency relationships and teaching application characteristics among knowledge points.

[0043] Furthermore, an improved semantic clustering algorithm combined with a multi-level weight assignment model innovatively establishes a tree-like classification system and a dynamic weight mechanism, deeply integrating the global importance of knowledge points with teaching scenario characteristics, which can significantly optimize the structural rationality of knowledge organization.

[0044] The finally generated dynamic knowledge graph has the ability of real-time evolution. Through semantic representation update and topological adaptive optimization, it can automatically identify the knowledge association changes in teaching resources, supporting the dynamic expansion of complex knowledge networks and the maintenance of semantic consistency.

[0045] Thus, it can be seen that the embodiment of the present invention breaks through the static limitations of traditional knowledge modeling, effectively improves the accuracy of intelligent recommendation of teaching resources, and provides high-precision knowledge topology support for personalized learning path planning and diagnosis of weak links in knowledge points, promoting the evolution of educational intelligence towards semantic and dynamic directions.

[0046] It can be understood that the topological structure of the dynamic knowledge graph is stored in a graph database, supporting path reasoning based on association strength and multi-dimensional knowledge retrieval.

[0047] In an alternative embodiment, the extracting the set of mathematical knowledge point entities from the textbook text data in step 120 includes:

[0048] Step 121: Perform paragraph segmentation processing on the textbook text data to generate a sequence of text paragraphs.

[0049] In step 121, the knowledge graph generation system performs paragraph segmentation processing on the textbook text data. Taking the electronic version of the People's Education Press junior high school mathematics textbook as an example, the system first identifies the chapter titles, natural paragraph delimiters, and formula chart positions in the PDF document, and cuts the continuous text stream into a sequence of text paragraphs with independent semantics. Specifically, for the fifth chapter of the textbook "Pythagorean Theorem", the system divides the three natural paragraphs containing the theorem definition, proof process, and example analysis into three text paragraph units based on the page break and paragraph indentation features after the secondary title "17.1 Pythagorean Theorem", forming an orderly paragraph sequence. This process processes textbooks of different formats through an adaptive layout parsing algorithm to ensure that the paragraph segmentation results strictly correspond to the original textbook structure.

[0050] Step 122: Perform semantic word segmentation processing on each text paragraph in the text paragraph sequence to obtain a set of word segmentation units for each text paragraph.

[0051] In the embodiment of the present invention, the knowledge graph generation system performs semantic word segmentation on the text paragraph sequence. Taking the segmented Pythagorean theorem definition paragraph as an example, the system calls the mathematical field-specific word segmentation model to decompose "the sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse" into core terminology units such as "right triangle", "right-angled side", "sum of squares", "hypotenuse", and "square".

[0052] At the same time, the system uses the stop word filtering component to remove non-key function words such as "的" and "等", and retains word units with substantial mathematical meanings. For polysemous word scenarios, such as the dual meaning of "方" in algebraic operations and geometric area, the system combines the adjacent terms in the context window to determine its current semantic direction.

[0053] Step 123: semantically encode the word segmentation unit set through a semantic vector generation model to generate a semantic vector for each word segmentation unit.

[0054] In an embodiment of the present invention, the knowledge graph generation system encodes the word segmentation unit through a semantic vector generation model. The system uses a pre-trained multimodal BERT model to map each word segmentation unit to a 768-dimensional semantic vector. For example, the high-dimensional vector generated after encoding the word segmentation unit of "Pythagorean Theorem" can represent its distributed features in multiple semantic spaces such as right triangles, algebraic formulas, and geometric proofs.

[0055] At the same time, the semantic vector of "square root calculation" focuses on reflecting its association characteristics with arithmetic operations, equation solving and other fields. This process captures the long-distance dependencies between terms through the attention mechanism, ensuring that the generated semantic vector has context-aware capabilities.

[0056] Step 124: Perform clustering analysis on the set of word segmentation units based on the semantic vectors to obtain a set of candidate knowledge point entities.

[0057] In the embodiment of the present invention, the knowledge graph generation system performs clustering analysis based on semantic vectors. The system uses a density clustering algorithm to process all the word segmentation units in the Pythagorean theorem chapter, and aggregates the terms with adjacent semantic spaces into candidate knowledge point entities. For example, terms such as "right triangle", "hypotenuse", and "right side" are grouped into the same clustering cluster because the cosine similarity between their vectors is higher than 0.85, forming a candidate entity of "the relationship between the three sides of a right triangle". At the same time, algebraic-related terms such as "sum of squares" and "arithmetic square root" form an independent cluster group, constituting a candidate entity of "square operation". During the clustering process, the system sets a dynamic radius threshold to adapt to the partitioning requirements of different knowledge granularities.

[0058] Step 125: Verify the set of candidate knowledge point entities according to the annotation information in the test question structure data, and generate the set of mathematical knowledge point entities.

[0059] In the embodiment of the present invention, the knowledge graph generation system uses the test question structure data to verify candidate entities. The system retrieves all the test questions in the test question bank that are marked with the knowledge point of "Pythagorean theorem", and extracts the standard terms in their analysis texts. When it is detected that the frequency of occurrence of a certain candidate entity (such as "relationship of the squares of the three sides") in the test question annotation exceeds a preset threshold, the system confirms it as a valid mathematical knowledge point entity. On the contrary, if a certain candidate entity (such as "triangulation") has no corresponding annotation record in the test question bank, an artificial review process is triggered. Through this verification mechanism, the system finally generates a set of mathematical knowledge point entities composed of entities such as "Pythagorean theorem", "square root calculation", and "properties of right triangles".

[0060] In an alternative embodiment, the hierarchical classification processing of the set of mathematical knowledge point entities in step 130 based on a preset semantic analysis model to obtain knowledge point hierarchical structure data includes:

[0061] Step 131: Input the set of mathematical knowledge point entities into the semantic analysis model to generate semantic feature vectors for each mathematical knowledge point entity in the set of mathematical knowledge point entities.

[0062] In step 131, the knowledge graph generation system generates semantic feature vectors of mathematical knowledge point entities. The system inputs the verified mathematical knowledge point entities into the semantic analysis model and extracts context features through a bidirectional long short-term memory network. For example, after being processed by the model, the "Pythagorean theorem" entity generates a feature vector that contains multi-dimensional semantic information such as theorem statements, proof methods, and application scenarios. This feature vector serves as the basis for subsequent hierarchical classification, ensuring that similar knowledge points have a compact distribution characteristic in the vector space.

[0063] Step 132: Generate an initial classification graph structure based on the cosine similarity between the semantic feature vectors.

[0064] In step 132, the knowledge graph generation system constructs an initial classification graph structure. The system calculates the cosine similarity between the feature vectors of all mathematical knowledge point entities, and establishes an undirected edge connection for entity pairs with a similarity exceeding 0.7. For example, the similarity between the "Pythagorean theorem" and the "Pythagoras' theorem" is 0.92, forming a strong connection edge; while the similarity with "probability calculation" is only 0.21, so no connection is established. Based on this similarity matrix, the system generates an initial classification structure containing multiple connected subgraphs, where each subgraph represents a potential class division.

[0065] Step 133: Perform hierarchical division on the initial classification graph structure based on a graph neural network to generate multiple candidate hierarchical node groups.

[0066] In step 133, the knowledge graph generation system uses a graph neural network for hierarchical division. The system inputs the initial classification graph into a graph convolutional network and aggregates node features through a message passing mechanism. For example, during the recognition of the "geometry" category, the network automatically identifies the common features of nodes such as the "Pythagorean theorem", "triangle area", and "similar figures", and groups them into the same hierarchical node group. The system adopts a hierarchical pooling technique to gradually merge fine-grained node groups into coarser-grained categories, forming a multi-level classification path of "geometry → plane geometry → right triangle → Pythagorean theorem".

[0067] Step 134: Correct the candidate hierarchical node groups according to the chapter division information in the teaching resource data to obtain the knowledge point hierarchical structure data.

[0068] In step 134, the knowledge graph generation system corrects the hierarchical structure according to the teaching resource data. The system compares the chapter division information in the textbook catalog and adjusts the automatically generated hierarchical node groups. For example, when the graph neural network classifies the "plane rectangular coordinate system" into the "function" category, the system detects that this knowledge point actually belongs to the "geometry and coordinates" chapter in the textbook, and thus adjusts it to the "geometry → coordinate system" subclass. At the same time, the system integrates the knowledge point explanation order in the teaching video and optimizes the parent-child relationship arrangement between the levels to ensure that the classification result conforms to the actual teaching logic.

[0069] In an alternative embodiment, calculating the weight assignment data of the mathematical knowledge point entities based on the association relationship set in step 130 includes:

[0070] Step 135: Count the association times and association object types of each mathematical knowledge point entity in the association relationship set.

[0071] In step 135, the knowledge graph generation system statistically analyzes the association features of mathematical knowledge point entities. The system traverses the test question analysis data and teaching video subtitles, and records the association times and object types of each entity. For example, the "Pythagorean theorem" forms a problem-solving dependence relationship with "square root calculation" in 85 test questions, and has a conceptual extension association with "area proof method" in 32 teaching videos. The system establishes an association type classification system to distinguish association modes such as "logical derivation", "problem-solving application", and "concept expansion", providing a multi-dimensional basis for weight calculation.

[0072] Step 136: Generate initial weight parameters according to the association times and the association object types.

[0073] In step 136, the knowledge graph generation system generates initial weight parameters. The system assigns a basic weight value to each mathematical knowledge point entity, which is proportional to the product of its total association times and the association type weight coefficient. For example, the "Pythagorean theorem" obtains a relatively high initial weight because it accumulates a score of 158.4 in 117 test question associations (coefficient 1.2) and 45 teaching video associations (coefficient 0.8). At the same time, the system introduces a time decay factor to reduce the contribution of test question data five years ago, ensuring that the weight parameters reflect the latest teaching focuses.

[0074] Step 137: Dynamically adjust the initial weight parameters based on the hierarchical depth in the knowledge point hierarchical structure data to generate adjusted weight parameters.

[0075] In step 137, the knowledge graph generation system dynamically adjusts the initial weights. The system adjusts the weight values according to the depth position of the knowledge points in the hierarchical structure by an exponential function. For example, the "Pythagorean theorem" in the third-level classification, compared with the top-level "geometry" category, its weight needs to be multiplied by the hierarchical coefficient 0.9. However, if the frequency of a bottom-level knowledge point (such as "side length ratio of special right triangles") in test questions is extremely high, the system will break through the hierarchical limit and increase its adjusted weight through an adaptive algorithm to reflect the importance shift in teaching practice.

[0076] Step 138: Normalize the adjusted weight parameters to generate the weight distribution data.

[0077] In step 138, the knowledge graph generation system normalizes the weight parameters. The system uses the maximum-minimum scaling method to map the adjusted weights of all mathematical knowledge point entities to the interval [0, 1]. For example, the "function concept" with the highest original weight (adjusted value 356) becomes 1.0 after normalization, while the lowest "statistical chart recognition" (adjusted value 28) becomes 0.08. This normalization process makes the weight data with different dimensions comparable, providing standardized input for the edge weight setting of the knowledge graph and the path recommendation algorithm.

[0078] As an optional embodiment, after generating the dynamic knowledge graph topology according to the knowledge point hierarchical structure data and the weight assignment data, the method further includes:

[0079] Step 210: Monitor the updated data in the multi-source teaching data set, and extract newly added mathematics knowledge point entities and updated association relationships.

[0080] In the embodiment of the present invention, the knowledge graph generation system continuously monitors the update status of the multi-source teaching data set. When it detects the release of the revised version of the People's Education Edition mathematics textbook, the system obtains the electronic text of the newly added "Preliminary Solid Geometry" chapter through the data interface module, and synchronously collects ten new test questions related to the application of the Pythagorean theorem in three-dimensional space in the supporting city-level joint examination question bank. The system calls the entity extraction component to parse the newly added textbook paragraphs, and identifies newly added mathematics knowledge point entities such as "space rectangular coordinate system" and "rectangular parallelepiped diagonal formula". At the same time, the association relationship mining module extracts the new association relationship of "three-dimensional Pythagorean theorem → calculation of the modulus length of space vectors" from the problem-solving steps of the newly added test questions, and records the occurrence frequency and problem-solving dependence intensity of this relationship in the ten test questions.

[0081] Step 220: Calculate the semantic similarity between the newly added mathematics knowledge point entity and the existing nodes in the dynamic knowledge graph topology according to the updated association relationship and the semantic vector of the newly added mathematics knowledge point entity.

[0082] In the embodiment of the present invention, the knowledge graph generation system calculates the semantic similarity between the newly added entity and the existing nodes. The system inputs the newly added "space rectangular coordinate system" entity into the pre-trained semantic vector generation model, and outputs its 768-dimensional semantic vector representation. The cosine similarity between this vector and the semantic vector of the "plane rectangular coordinate system" node in the dynamic knowledge graph topology is calculated, and the similarity value is measured to be 0.89. At the same time, the system traverses the association relationship library and detects that there is a cross in the problem-solving paths between the newly added "three-dimensional Pythagorean theorem" entity and the original "Pythagorean theorem" entity in six solid geometry test questions. The association strength weight between the two is calculated to be 0.68 through the graph attention network. The above calculation process integrates semantic similarity and teaching practice association features to form a multi-dimensional similarity evaluation index.

[0083] Step 230: If the semantic similarity exceeds the preset threshold, merge the newly added mathematics knowledge point entity into the corresponding hierarchical node group and update the weight assignment data.

[0084] In an embodiment of the present invention, the knowledge graph generation system performs entity merging and weight update operations. When the semantic similarity between "spatial rectangular coordinate system" and "plane rectangular coordinate system" exceeds the preset threshold of 0.85, the system classifies the newly added entity into the "coordinate system" hierarchical node group. The system increases the global weight of the original "plane rectangular coordinate system" node from 0.75 to 0.82 according to the association frequency (12 times) between the two in the newly added test questions and the ratio of the teaching video explanation duration (3:1), and assigns an initial weight of 0.78 to the newly added entity. At the same time, a node instance of the newly added entity is created under the hierarchical path of "Geometry → Spatial Geometry → Coordinate System", inheriting the classification attributes and weight decay parameters of the parent node.

[0085] Step 240: If the semantic similarity does not exceed the preset threshold, create a new hierarchical node group in the knowledge point hierarchical structure data and reassign the weight distribution data.

[0086] In an embodiment of the present invention, the knowledge graph generation system creates a new hierarchical node group to process low-similarity entities. When the maximum semantic similarity between the newly added "basis of topology" entity and all nodes in the existing knowledge graph is only 0.31, the system creates a three-level new node group of "Interdisciplinary Applications → Intersection of Mathematical Branches → Basis of Topology" in the knowledge point hierarchical structure data. The system initializes the weight distribution data of this node group to 0.45, and based on its appearance frequency (5 times per thousand questions) in the middle school entrance examination innovative questions, establishes weak association edges with existing entities such as "geometric transformation" and "concept of continuity", and the initial edge weight is set to 0.35. This process triggers the version iteration of the hierarchical structure data, generating a classification system of version Vx.x.

[0087] As an optional embodiment, the method further includes:

[0088] Step 310: Generate a knowledge point association path according to the dynamic knowledge graph topology structure, and the knowledge point association path includes a connection sequence of at least two mathematical knowledge point entities.

[0089] In step 310, the knowledge graph generation system generates a knowledge point association path based on the dynamic knowledge graph topology structure. The system starts from the "Pythagorean theorem" node and traverses all its associated edges using the depth-first search algorithm to generate six basic teaching paths including "Pythagorean theorem → square root calculation → real number operation", "Pythagorean theorem → similar triangles → proportional line segments", etc. The node connection sequence of each path needs to meet the association strength threshold condition, for example, only including association relationships with edge weights higher than 0.6. The system also detects cross-level associations and includes the new application nodes of the "Pythagorean theorem" in spatial geometry in the path extension range to form an advanced path of "Pythagorean theorem → spatial vector modulus length → solid geometry proof".

[0090] Step 320: Based on the weight assignment data, prioritize the knowledge point association paths to generate a set of recommended teaching paths.

[0091] In step 320, the knowledge graph generation system prioritizes the knowledge point association paths. The system comprehensively calculates the product of the mean weight of all nodes in the path and the edge weight to compute the recommendation index for each path. For example, the path "Pythagorean theorem → Square root calculation → Real number operation" has a relatively high mean of node weights (0.82 + 0.79 + 0.75) and a product of edge weights (0.72 × 0.68), obtaining a priority score of 8.7 and ranking first in the set of recommended teaching paths. The system establishes a multi-dimensional sorting model, taking into account the path length, the balance of weight distribution, and the coverage rate of the teaching syllabus, transforming the originally disordered association paths into a recommended sequence with a clear teaching logic order.

[0092] Step 330: Match the set of recommended teaching paths with the user's historical learning data to filter out the target teaching paths.

[0093] In step 330, the knowledge graph generation system implements personalized path matching. When the user's historical learning data indicates that the student has completed the "Plane geometry → Triangle properties" module with a correct rate lower than 60%, the system filters out the reinforcement path "Pythagorean theorem → Triangle classification → Angle calculation" in the set of recommended teaching paths. The matching process uses a hidden Markov model based on the knowledge state to predict the mastery probability of the student at each path node, and preferentially selects the three paths with the largest predicted improvement space. The system also excludes the knowledge point association paths that have been fully mastered. For example, it filters out the path "Real number operation → Algebraic expression simplification" with a correct rate exceeding 90% in the user's historical record.

[0094] Step 340: Send the mathematical knowledge point entities and association relationships in the target teaching path to the teaching terminal.

[0095] In step 340, the knowledge graph generation system completes the terminal deployment of the teaching path. The system transforms the matched target teaching path into a SCORM standard courseware package, which includes three micro-lessons on the proof methods of the "Pythagorean theorem" node, five progressive exercises for the "Square root calculation" node, and a three-dimensional interactive demonstration module for the "Spatial vector modulus length" node. These teaching resources are pushed to the class teaching terminal through the API interface, presented as a customizable teaching progress roadmap on the teacher's console, and generate a personalized learning task list on the student side. The system synchronously updates the visualization interface of the knowledge graph, displays the topological trend of the recommended teaching path with a highlighted path line, and marks the latest weight parameters and association strength indicators of each node.

[0096] As an optional embodiment, before sending the mathematical knowledge point entities and association relationships in the target teaching path to the teaching terminal described in step 340, the method further includes:

[0097] Step 410: Obtain the learning behavior data fed back by the teaching terminal, where the learning behavior data includes the learning duration of knowledge points and the answering correct rate.

[0098] In step 410, the knowledge graph generation system obtains the learning behavior data fed back by the teaching terminal in real time. Taking the Pythagorean theorem teaching unit as an example, the system receives the learning logs of 32 students uploaded by the class terminal, where it is recorded that the video watching duration of each student for the knowledge point of "proof methods of the Pythagorean theorem" is 45 ± 8 minutes, and the answering correct rate in the exercise module of "application problems of the Pythagorean theorem" is 72.5%. The system filters out outliers through a data cleaning component, for example, eliminates the invalid learning record of 0.5 minutes caused by network interruption of a certain student, and establishes a mapping relationship between the standardized learning behavior data and the "Pythagorean theorem" node and its associated edges in the knowledge graph, forming a time series dataset including timestamps, interaction frequencies, and mastery degree indicators.

[0099] Step 420: Update the association strength parameter in the weight allocation data according to the learning behavior data.

[0100] In step 420, the knowledge graph generation system updates the association strength parameter. Based on the fact that the average answering correct rate of the student group on the association path of "Pythagorean theorem → square root calculation" is lower than the preset threshold of 65%, the system triggers an association strength down - adjustment mechanism and reduces the weight parameter of this edge from 0.72 to 0.68. At the same time, it is monitored that the number of repeated video views on the association path of "Pythagorean theorem → similar triangles" exceeds 3 times the average of the same type. The system increases the weight of this edge from 0.65 to 0.71 according to the positive correlation between the learning duration and the mastery degree. The update process uses a sliding window algorithm, retaining 80% of the weight contribution of the teaching data in the past three months to ensure that the parameter adjustment reflects the latest teaching effect.

[0101] Step 430: Optimize the topological structure of the dynamic knowledge graph based on the updated association strength parameter to generate an optimized knowledge point association path.

[0102] In step 430, the knowledge graph generation system optimizes the dynamic knowledge graph topological structure. For the Pythagorean theorem node, the system detects that the newly added "application in solid geometry" associated edge has received 12 valid clicks due to the update of the teaching video. Through the topological optimization algorithm, the weight of this edge is increased from the initial value of 0.65 to 0.69. At the same time, the "Pythagorean theorem → trigonometric function" associated edge that has not been accessed for two consecutive teaching cycles is removed. The optimized knowledge graph generates three strengthened paths: the core path "Pythagorean theorem → square root calculation → real number operation" maintains the highest weight, the newly added path "Pythagorean theorem → spatial geometric bodies → three-dimensional coordinate system" obtains medium weight, and the historical path "Pythagorean theorem → traditional proof method" is downgraded to a secondary path due to the update of teaching resources.

[0103] Step 440: Merge the optimized knowledge point association path with the target teaching path to generate a new set of recommended teaching paths.

[0104] In step 440, the knowledge graph generation system performs a path merging operation. The system inputs the three optimized knowledge point association paths and the original five target teaching paths into the merging engine. Taking the path "Pythagorean theorem → square root calculation → real number operation" and the path "algebraic foundation → square operation → Pythagorean theorem" as an example, the merging engine identifies the overlapping nodes as "Pythagorean theorem" and "square operation", and calculates the node position offsets as 1 bit and 2 bit differences respectively. According to the principle of the smallest offset, the "Pythagorean theorem" node is selected as the reference merging point, and the subsequent node subsequence is extracted for semantic matching. Finally, the merged path "algebraic foundation → square operation → Pythagorean theorem → square root calculation → real number operation → spatial geometric bodies" is generated.

[0105] In a preferred embodiment, the merging of the optimized knowledge point association path with the target teaching path in step 440 to generate a new set of recommended teaching paths includes:

[0106] Step 441: Obtain the first node sequence of all mathematical knowledge point entities in the optimized knowledge point association path, and extract the second node sequence of the mathematical knowledge point entities included in the target teaching path.

[0107] In the embodiment of the present invention, the knowledge graph generation system extracts node sequence data. For the optimized knowledge point association path "Pythagorean theorem → spatial geometric bodies → three-dimensional coordinate system", the system extracts its first node sequence as [Pythagorean theorem, spatial geometric bodies, three-dimensional coordinate system]. At the same time, the second node sequence [geometric foundation, Pythagorean theorem, similar triangles] is extracted from the historical target teaching path "geometric foundation → Pythagorean theorem → similar triangles". The system verifies the connectivity of the node sequence through the graph traversal algorithm to ensure that there is an effective associated edge between each adjacent node pair in the dynamic knowledge graph topological structure.

[0108] Step 442: Traverse the first node sequence and the second node sequence, identify the overlapping mathematical knowledge point entities that exist in both sequences, and generate an overlapping node set; based on the association strength parameter in the weight assignment data, calculate the difference between the position serial numbers of each mathematical knowledge point entity in the overlapping node set in the first node sequence and the second node sequence to generate a position offset set; according to the numerical distribution of the position offset set, determine the path merging priority of each mathematical knowledge point entity in the overlapping node set; among them, the mathematical knowledge point entity with a smaller position offset has a higher priority.

[0109] In the embodiment of the present invention, the knowledge graph generation system calculates the node position offset. Traverse the first node sequence and the second node sequence, and identify the overlapping node set as {Pythagorean theorem}. The system calculates that the position serial number of this node in the first sequence is 1, and the position serial number in the second sequence is 2, generating an absolute value of the position offset of 1. According to the rule that the smaller the offset, the higher the priority, it is determined that the Pythagorean theorem node has the highest merging priority. At the same time, it is detected that the "square operation" node in other paths is in the 2nd and 4th positions in the two sequences respectively, generating an offset of 2 and listing it in the secondary priority queue.

[0110] Step 443: Use the mathematical knowledge point entity with the highest priority in the overlapping node set as the reference node for path merging, and extract the subsequent node subsequences starting from the reference node from the first node sequence and the second node sequence respectively.

[0111] In the embodiment of the present invention, the knowledge graph generation system determines the path merging reference node. After selecting the Pythagorean theorem node as the reference point, the system extracts the subsequent subsequence from the first node sequence as [spatial geometric body, three-dimensional coordinate system], and extracts the subsequent subsequence from the second node sequence as [similar triangles]. The system checks the weights of the starting association edges of the two subsequences, and confirms that the edge weight of "Pythagorean theorem → spatial geometric body" is 0.69 and the edge weight of "Pythagorean theorem → similar triangles" is 0.71, both of which meet the merging threshold conditions, allowing subsequent semantic matching operations.

[0112] Step 444: Perform semantic vector similarity matching on the mathematical knowledge point entities in the subsequent node subsequences. If there is a continuous node segment with a semantic similarity exceeding the preset threshold in the two subsequent node subsequences, merge the continuous node segment into a shared path segment; insert the shared path segment into the subsequent position of the reference node, and remove the merged continuous node segment from the first node sequence and the second node sequence to generate an intermediate merged path.

[0113] In an embodiment of the present invention, the knowledge graph generation system performs node segment merging. The subsequences of [spatial geometry, three-dimensional coordinate system] and [similar triangles] are input into the semantic matching module, and the semantic vector similarity between "spatial geometry" and "similar triangles" is detected to be 0.48, which is lower than the preset threshold of 0.7, and a shared path segment cannot be formed. The system then retrieves the dynamic knowledge graph topology structure and finds that there is an indirect association path "spatial geometry → projection transformation → similar triangles" between "spatial geometry" and "similar triangles", and the accumulated edge weight value is 0.63. Based on this, a parallel node connection channel is created to generate an intermediate merge path [Pythagorean theorem → (spatial geometry → three-dimensional coordinate system | similar triangles)].

[0114] Step 445: For the remaining nodes that have not been merged, calculate the association closeness between each remaining node and the end node of the intermediate merge path according to the association strength parameter and the weight distribution data, and generate a node connection closeness ranking; in the descending direction of the node connection closeness ranking, attach the remaining nodes to the end of the intermediate merge path in sequence, and if a path branch appears during the attachment, create a parallel node connection channel.

[0115] In an embodiment of the present invention, the knowledge graph generation system processes the remaining node associations. For the unmerged "three-dimensional coordinate system" and "similar triangle" nodes, the system calculates the degree of association between them and the end nodes of the intermediate merge path. It is detected that there is a "coordinate system transformation → similarity judgment" association path between "three-dimensional coordinate system" and "similar triangles" in the topological structure, with an edge weight of 0.58 and a generated connection density score of 7.2. According to the descending order rule, the system preferentially attaches the "three-dimensional coordinate system" node to the end of the intermediate path, forming a coherent path of [Pythagorean theorem → spatial geometry → three-dimensional coordinate system → coordinate system transformation → similar triangles].

[0116] Step 446: traverse all the reference nodes in the overlapping node set to perform the above-mentioned merging operation, generate multiple candidate merged paths, and perform redundant node deduplication processing on the node connection order in each candidate merged path; based on the chapter division information in the teaching resource data, perform integrity verification on the deduplicated candidate merged paths, eliminate path segments that do not meet the chapter level constraints, and generate a verified path set.

[0117] In an embodiment of the present invention, the knowledge graph generation system generates a set of verified paths. The above merged paths are checked for redundant nodes, and it is found that the "coordinate system transformation" node has already appeared in other paths, triggering a deduplication mechanism to replace it with an existing node instance. The system refers to the chapter division information of Chapter 27, "Geometric Transformations", in the People's Education Edition textbook to verify the correctness of the hierarchical attribution of "spatial geometric body → coordinate system transformation", and retains this path segment. Finally, three candidate merged paths are generated: the main path retains the complete spatial geometric extension, the auxiliary path strengthens the traditional geometric association, and the alternative path provides cross-chapter knowledge transfer.

[0118] Step 447: Correct the teaching logic order of the paths in the set of verified paths according to the associated object types in the set of association relationships, so that the prerequisite dependency relationships of each mathematical knowledge point entity are continuously arranged in the paths; sort the paths with corrected teaching logic order according to the path length and the weighted value of the association strength parameter, and select the top N paths with the highest weights to generate the new set of recommended teaching paths.

[0119] In an embodiment of the present invention, the knowledge graph generation system completes teaching logic correction. It is detected that the "similar triangles" node requires "proportional relationship" as prerequisite knowledge in the path. The system inserts the sub-segment [Pythagorean theorem → proportional relationship → similar triangles] into the final path to ensure that the teaching order conforms to the cognitive law. The corrected paths are weighted and sorted according to length and weight. The main path has the highest priority because it contains 6 nodes and an average edge weight of 0.68, generating a new set of recommended teaching paths, including five optimized path schemes suitable for different teaching scenarios.

[0120] As an optional embodiment, the method further includes:

[0121] Step 510: Perform visual rendering processing on the dynamic knowledge graph topology structure to generate an interactive graph interface.

[0122] In step 510, the knowledge graph generation system performs visual rendering processing on the dynamic knowledge graph topology structure. The system calls the graph layout engine and uses an improved force-directed algorithm to map the mathematical knowledge point entity nodes and their associated relationships to a two-dimensional interactive interface. Taking the Pythagorean theorem knowledge system as an example, the core node of "Pythagorean theorem" is automatically positioned at the center of the canvas, and the nodes directly associated with it, such as "Properties of right triangles", "Square root calculation", "Spatial geometry application", etc., are distributed in different concentric circle layers according to the association strength parameter. The node size is dynamically adjusted according to the weight distribution data. For example, the "Pythagorean theorem" node with a global weight of 0.82 is presented as a circle with a diameter of 48 pixels, while the "Chord diagram construction method" node with a weight of 0.65 is displayed as 32 pixels. The associated edges use gradient color coding technology, where the red edges represent the "logical derivation" relationship, and the blue edges represent the "problem-solving application" relationship. The edge width is positively correlated with the association strength parameter, forming an interactive topological network visualization interface.

[0123] Step 520: Mark the frequently-occurring mathematical knowledge point entities and key associated relationships in the interactive graph interface to obtain a marking result.

[0124] In step 520, the knowledge graph generation system implements the high-frequency item marking operation. The system statistically analyzes the user access logs and identifies the nodes that have been accessed more than the threshold of 50 times in the past seven days. For example, the cumulative access volume of the "Pythagorean theorem" node reaches 123 times, triggering the high-frequency marking mechanism. An orange outer glow effect is added to this node, and its associated edge "Pythagorean theorem → Square root calculation" is displayed as a bold blue line because its co-occurrence frequency ranks in the top 5%. At the same time, the system detects that the number of associated edges of the "Spatial geometry application" node has increased by more than 200% in the recent three textbook updates, and adds a dynamic growth identifier to it. The marking process uses a hierarchical rendering technology to ensure that high-frequency items maintain visual prominence during zoom operations, while ordinary nodes are dynamically hidden or displayed according to the zoom level.

[0125] Step 530: In response to the user's touch operation on the marking result, display the associated teaching resource data and test question structure data.

[0126] In step 530, the knowledge graph generation system responds to user interaction operations. When the teacher double-clicks on the "Pythagorean theorem" node in the interactive graph interface, the system triggers the associated resource display protocol. A floating panel pops up on the right side of the interface, and at the top, three thumbnail images of teaching videos corresponding to this node are displayed, including the micro-lesson on theorem proof supporting the People's Education Edition textbook and the video recording of the actual competition of high-quality city-level lessons. In the middle area, five typical middle school entrance examination questions are presented. For the third question, "Calculation of the diagonal of a cuboid", dynamic problem-solving steps are demonstrated. In the bottom area, a knowledge point association statistics panel is shown, listing that the co-occurrence times of the "Pythagorean theorem" and "square root calculation" in the test questions in the past three years are 87 times, and the association strength parameter is 0.72. All resource data are retrieved in real time through the teaching resource data interface to ensure that the displayed content is strictly synchronized with the topological structure of the knowledge graph.

[0127] Step 540: Record the user operation trajectory and update the association strength parameter in the weight assignment data according to the user operation trajectory.

[0128] In step 540, the knowledge graph generation system collects user operation behavior data. The system records the behavior trajectory of a student who clicks on the "Pythagorean theorem" node seven times, hovers over and queries the associated edge of "square root calculation" twice, and spends 18 minutes repeatedly watching the theorem proof video within a 30-minute learning cycle. Based on these operation data, the system updates the association strength parameter in the weight assignment data, increases the interaction frequency weight coefficient of the edge "Pythagorean theorem → square root calculation" by 0.15, and adjusts the local weight parameter of the "Pythagorean theorem" node from 0.82 to 0.85 according to the positive correlation between the video viewing duration and the question answering accuracy rate. The updated parameters are immediately fed back to the dynamic knowledge graph topological structure, triggering the re-coloring of the associated edges and the adjustment of the node sizes.

[0129] As an optional embodiment, the method further includes:

[0130] Step 610: Generate a knowledge point mastery evaluation model according to the dynamic knowledge graph topological structure.

[0131] In an embodiment of the present invention, a knowledge graph generation system constructs a knowledge point mastery evaluation model. The system adopts a graph neural network architecture, with the dynamic knowledge graph topology structure as the underlying framework, and takes the semantic vectors, weight parameters, and association strengths of each mathematical knowledge point entity as input features. For example, for the "Pythagorean theorem" node, the model extracts 24 feature indicators such as its 768-dimensional semantic vector, global weight of 0.85, and 6 associated edges. The model calculates the influence coefficient of the student's mastery status at adjacent nodes on it through an attention mechanism. For example, if the mastery degree of the "square root calculation" node is lower than the threshold, the predicted mastery degree of the "Pythagorean theorem" node will be automatically lowered by 0.2 levels. During the training process, one hundred thousand historical learning behavior data are used to ensure that the model can accurately capture the implicit dependence relationships between knowledge points.

[0132] Step 620: Input the user's answer record into the knowledge point mastery evaluation model to generate predicted data on knowledge point weaknesses.

[0133] In an embodiment of the present invention, the knowledge graph generation system performs weakness prediction analysis. The answer record of a certain student is input into the knowledge point mastery evaluation model. Among the eight questions related to the Pythagorean theorem, four are incorrect, and the error types are concentrated in "application in three-dimensional geometry scenarios". The model detects that the correct rate of the associated questions of this student at the "space rectangular coordinate system" node is only 33%, and predicts that the weakness coefficient of this knowledge point reaches 0.78 (threshold 0.6). At the same time, by analyzing the incorrect problem-solving steps, it is found that this student has a cognitive defect of "ignoring three-dimensional coordinate projection conversion", and accordingly generates predicted data on weaknesses, marking "three-dimensional geometry application → coordinate system transformation" as the key weakness path.

[0134] Step 630: Screen out a reinforcement learning path from the set of recommended teaching paths based on the predicted data on knowledge point weaknesses.

[0135] In an embodiment of the present invention, the knowledge graph generation system screens out a reinforcement learning path. According to the "three-dimensional geometry application" label in the predicted data on weaknesses, the system extracts two relevant paths from the set of recommended teaching paths: the basic path "Pythagorean theorem → cuboid structure → space distance calculation" and the advanced path "three-dimensional coordinate system → vector projection → Pythagorean theorem extension". The system compares the teaching resource coverage of the two paths and selects the advanced path containing five teaching videos and twelve progressive practice questions as the main reinforcement path. At the same time, it is detected that the mastery degree of this student at the "vector basis" node meets the standard, so the preparatory knowledge module in the path is skipped, and the system directly locates to the weak link for targeted reinforcement.

[0136] Step 640: Dynamically bind the mathematical knowledge point entities in the reinforcement learning path to teaching resource data to generate a customized learning plan.

[0137] In the embodiment of the present invention, the knowledge graph generation system generates a customized learning plan. The system deeply binds the selected reinforcement learning path with the teaching resource data, and configures an exclusive learning package for the node of "three-dimensional coordinate system → vector projection", including three stereoscopic geometry modeling demonstration videos and six step-by-step guided practice questions. The time axis of the plan is planned according to a 7-day cycle. On the first day, the basic concepts of the coordinate system are learned. On the second day, the focus is on the principle of vector projection. Starting from the third day, extended application training of the Pythagorean theorem is carried out. A mastery detection link is set for each learning stage. When the correct rate of the student in the "spatial distance calculation" practice questions reaches 80% three times in a row, the system automatically unlocks the content of the next stage. The final plan is pushed through the teaching terminal, and the visualization interface of the knowledge graph is updated synchronously, and the key learning areas are marked with pulse animations.

[0138] As an optional embodiment, after the generation of the customized learning plan described in step 640, the method further includes:

[0139] Step 710: Monitor the learning progress data of the user executing the customized learning plan.

[0140] In the embodiment of the present invention, the knowledge graph generation system continuously monitors the learning progress data of the user executing the customized learning plan. Taking the Pythagorean theorem space application reinforcement plan as an example, the system real-time collects the learning behaviors of students under the path of "three-dimensional coordinate system → vector projection → solid geometry proof", records that it takes 125 minutes to complete the viewing of three teaching videos, completes 12 supporting practice questions with a correct rate of 66.7%. The system maps the learning behavior data to the corresponding nodes in the dynamic knowledge graph topological structure through the progress tracking module, marks the average residence time of the "vector projection" node as 23 minutes, exceeding the average value of similar nodes by 40%, and triggers the progress anomaly detection mechanism.

[0141] Step 720: Adjust the priority order of the knowledge point association path according to the learning progress data.

[0142] In the embodiment of the present invention, the knowledge graph generation system dynamically adjusts the priority of the knowledge point association path. When it is detected that the correct rate of the student in the "solid geometry proof" node drops from 70% to 50% three times, the system reduces the priority order of this node in the recommended path from the second place to the fourth place. At the same time, because the number of video reviews of the student in the "three-dimensional coordinate system" node reaches the threshold, the system increases the priority weight of its associated path "three-dimensional coordinate system → basic spatial modeling", and moves the position of this path two places forward in the recommended sequence. The adjustment process uses a sliding window algorithm, and preferentially responds to the changes in the behavior data within the last three learning cycles.

[0143] Step 730: If it is detected that the predicted data of the knowledge point weak points does not meet the preset optimization conditions, trigger the regeneration process of the dynamic knowledge graph topological structure.

[0144] In an embodiment of the present invention, the knowledge graph generation system evaluates the optimization effect of the weak points of knowledge points. The system detects that in the updated learning plan of the student, the correct rate of the questions related to "spatial geometry application" is still lower than the preset threshold of 60%, and the interaction frequency of the associated edges of the "vector projection" node does not reach the expected growth target. Based on this, the system triggers the process of regenerating the dynamic knowledge graph topology structure, calls the entity relationship mining module to analyze the newly added solid geometry questions in the municipal joint entrance examination, supplements the new association relationship between "spatial vector modulus calculation" and "Pythagorean theorem", and recalculates the node semantic vectors.

[0145] Step 740: Push the regenerated dynamic knowledge graph topology structure to the teaching terminal to update the interactive graph interface.

[0146] In an embodiment of the present invention, the knowledge graph generation system pushes the reconstructed dynamic knowledge graph topology structure to the teaching terminal. The system packages the changed contents including the newly added "spatial vector modulus calculation" node, the updated "Pythagorean theorem → spatial geometry application" associated edge (the weight is increased from 0.69 to 0.73), etc., and pushes the graph update package with version number V3.2 to the class teaching terminal through the encrypted transmission protocol, triggering the asynchronous refresh mechanism of the terminal interface.

[0147] In a preferred embodiment, the pushing the regenerated dynamic knowledge graph topology structure to the teaching terminal to update the interactive graph interface in step 740 includes:

[0148] Step 741: Receive the regenerated dynamic knowledge graph topology structure, extract the node set and edge set in the regenerated dynamic knowledge graph topology structure, the node set includes the semantic vectors and association strength parameters of the mathematical knowledge point entities, and the edge set includes the association relationships between the mathematical knowledge point entities.

[0149] In step 741, the knowledge graph generation system extracts the data of the regenerated dynamic knowledge graph topology structure. The system exports the node set from the V3.2 version graph, including the updated semantic vector (dimension 768) of the "Pythagorean theorem" node, the global weight parameter 0.87, and the initial weight 0.68 of the newly added "spatial vector modulus calculation" node. The edge set data includes the newly added "Pythagorean theorem → spatial vector modulus calculation" associated edge, the initial weight is set to 0.71, and the association type is marked as "extended application".

[0150] Step 742: Compare the regenerated dynamic knowledge graph topology with the historical dynamic knowledge graph topology currently stored in the teaching terminal, identify the newly added mathematical knowledge point entities, deleted mathematical knowledge point entities, and updated association strength parameters in the node set, and identify the newly added association relationships and removed association relationships in the edge set, and generate a difference data set.

[0151] In step 742, the knowledge graph generation system performs version difference analysis. Compare the V3.2 version with the currently running V3.1 version of the teaching terminal, identify the newly added node "Calculation of the modulus length of spatial vectors", the deleted obsolete node "Traditional measurement method", and the weight of the association edge "Pythagorean theorem → Application in spatial geometry" is updated from 0.69 to 0.73. The difference data set also records the removed association edge "Pythagorean theorem → Traditional measurement method" and its historical weight data.

[0152] Step 743: According to the newly added mathematical knowledge point entities and association relationships in the difference data set, match the corresponding textbook text data fragments, question structure data identifiers, and teaching resource data addresses from the multi-source teaching data set, and generate an incremental update data packet.

[0153] In step 743, the knowledge graph generation system constructs an incremental update data packet. For the newly added node "Calculation of the modulus length of spatial vectors", the system retrieves the matching textbook text data fragment (Section 4, Chapter 15, Compulsory Mathematics II, People's Education Edition), the identifiers of five new solid geometry test questions associated (such as 2024_CQ_ZK_GEOM_015), and the corresponding three-dimensional interactive demonstration video resource address (res: / / geo3d / vector_mod.mp4) from the multi-source teaching data set. These data are structurally encapsulated to form the main body of the incremental update data packet.

[0154] Step 744: Perform compression and checksum attachment processing on the incremental update data packet to generate an update data packet to be transmitted, and send the update data packet to the teaching terminal through an encrypted channel.

[0155] In step 744, the knowledge graph generation system completes data security processing. Compress the incremental update data packet using the LZMA algorithm, and attach the SHA-256 checksum to ensure transmission integrity. Transmit the compressed package in slices to the teaching terminal through the TLS1.3 encrypted channel. Each data slice contains a sequence number identifier and redundant check bits to ensure resume from breakpoint and data integrity verification in a network-fluctuating environment.

[0156] Step 745: In response to the teaching terminal receiving the update data packet, perform integrity verification and decompression processing, and extract the differential data set, textbook text data fragments, question structure data identifiers, and teaching resource data addresses in the incremental update data packet.

[0157] In step 745, the knowledge graph generation system causes the teaching terminal to process the update data packet. After the terminal security module verifies the data packet signature, it performs a decompression operation and checks the data integrity. The extracted differential data set shows that three nodes need to be added and the weights of two associated edges need to be updated. The synchronously obtained textbook text data fragments are stored in the local buffer, the question identifiers are mapped to the local question bank index, and the teaching resource addresses are registered with the resource scheduling center.

[0158] Step 746: According to the deleted mathematical knowledge point entities and the removed association relationships in the differential data set, remove the corresponding node graphics and edge connection lines from the current interactive graph interface of the teaching terminal, and release the cached teaching resource data associated therewith.

[0159] In step 746, the knowledge graph generation system causes the teaching terminal to perform old data cleaning. According to the deletion instructions in the differential data set, the terminal removes the "traditional measurement method" node and its associated "Pythagorean theorem → traditional measurement method" edge connection line from the interactive graph interface. At the same time, it clears the outdated teaching resource cache bound to this node, including two sets of offline exercise sets and the local temporary storage files of three old version teaching videos.

[0160] Step 747: Perform node semantic vector matching on the newly added mathematical knowledge point entities and association relationships in the differential data set with the historical dynamic knowledge graph topological structure currently stored in the teaching terminal. If there are existing nodes with semantic similarity exceeding the preset threshold, merge the newly added mathematical knowledge point entities into the attribute set of the existing nodes; otherwise, create independent nodes and insert them into the corresponding hierarchical node group of the historical dynamic knowledge graph topological structure.

[0161] In step 747, the knowledge graph generation system causes the teaching terminal to perform a node merging operation. Perform semantic matching on the newly added "spatial vector modulus calculation" node with the existing nodes, and detect that the semantic vector similarity with the "vector operation" node reaches 0.89 (threshold 0.85). Then, merge this node into the attribute set of the "vector operation" node and inherit its hierarchical position "algebra → vector → vector operation". The extended attributes of the merged node include special labels for spatial geometry applications and are presented in the form of collapsed sub-nodes in the interactive interface.

[0162] Step 748: Adjust the visualization attributes of the edge connection lines between the corresponding nodes in the interactive graph interface according to the updated association strength parameters in the difference data set. The visualization attributes include line thickness, color value, and dynamic effect parameters.

[0163] In step 748, the knowledge graph generation system enables the teaching terminal to update the visualization attributes. The line width of the "Pythagorean theorem → Spatial geometry application" association edge is thickened from 3 pixels to 5 pixels, and the color value is adjusted from #4A90E2 to highlighted blue #0066CC. The newly added "Vector operation → Spatial vector modulus calculation" association edge is initially displayed as a dotted line and changes to a solid line with an additional pulse animation effect after the user's first interaction, to prompt the availability of the newly added teaching resources.

[0164] Step 749: Based on the textbook text data segment and the question structure data identifier, load the associated teaching resource data from the local storage or remote server of the teaching terminal, and bind the teaching resource data address to the corresponding newly added mathematics knowledge point entity node; according to the merged or created node set and the adjusted edge set, re-render the layout structure of the interactive graph interface, and add dynamic highlighting marks to all newly added nodes and edge connection lines, and synchronously record the operation log of this update to the version history database.

[0165] In step 749, the knowledge graph generation system enables the teaching terminal to complete the interface reconstruction. Rearrange the node layout according to the updated hierarchical structure, and the position of the "Vector operation" node migrates 12 pixels towards the central area of the topological structure. The loaded three-dimensional interactive demonstration video resource generates a preview thumbnail and is bound to the right-click menu of the corresponding node. The system adds a fade-in highlighting effect that lasts for 5 seconds to all changed elements, and records the timestamp, data volume, and change summary of this update in the version history database to form a complete operation audit log.

[0166] As an optional but non-limiting embodiment, the hierarchical division of the initial classification graph structure based on the graph neural network in step 133 to generate multiple candidate hierarchical node groups includes:

[0167] Step 1331: Extract the node feature matrix and adjacency matrix from the initial classification graph structure to generate graph structure input data; input the graph structure input data into the multi-layer convolution module of the graph neural network for node feature aggregation to generate a set of node embedding vectors containing global semantic information; calculate the Euclidean distance matrix based on the embedding vectors of each node in the set of node embedding vectors, and construct a hierarchical clustering tree structure based on the Euclidean distance matrix.

[0168] Step 1332: Cut the hierarchical clustering tree structure according to a preset threshold of the number of hierarchical levels to generate a preliminary grouping of hierarchical nodes with different hierarchical depths; perform node density verification on each group in the preliminary grouping of hierarchical nodes. If it is detected that the average Euclidean distance of the nodes within the group exceeds the density threshold, then merge the current group with the group at the adjacent level to generate an optimized candidate group of hierarchical nodes; perform hierarchical label mapping on the candidate group of hierarchical nodes according to the chapter division information in the teaching resource data, and divide the node groups with the same chapter label into the same level to generate a set of candidate groups of hierarchical nodes with hierarchical labels.

[0169] Step 1333: Traverse each hierarchical label in the set of candidate groups of hierarchical nodes, extract the node connection relationships within the corresponding level. If there are cross-level connection edges, then adjust the hierarchical division boundary according to the association strength parameter in the association relationship set to generate a candidate group of hierarchical nodes with corrected boundaries; perform internal node consistency verification on the candidate group of hierarchical nodes with corrected boundaries based on the set of node embedding vectors, and remove abnormal nodes whose semantic differences from the nodes in the same group exceed the preset threshold to generate a final candidate group of hierarchical nodes.

[0170] In step 1331, the knowledge graph generation system extracts the node feature matrix and the adjacency matrix from the initial classification graph structure. Taking the Pythagorean theorem knowledge system as an example, the system arranges the 768-dimensional semantic vectors of 98 mathematical knowledge point entities such as "Pythagorean theorem", "right triangle", and "square root calculation" in sequence to construct a 98×768-dimensional node feature matrix. At the same time, according to the cosine similarity connection relationship between the nodes in the initial classification graph structure, a 98×98-dimensional adjacency matrix is generated, where the adjacency value between the "Pythagorean theorem" node and the "right triangle" node is 0.92. The system inputs the graph structure input data into a three-layer graph convolutional network, and through the neighbor node feature aggregation mechanism, generates a set of node embedding vectors containing global semantic information. For example, after being processed by the convolutional layer, the embedding vector of the "Pythagorean theorem" node integrates the semantic features of related nodes such as "Pythagoras' theorem" and "sum of squares of the hypotenuse". The system calculates the Euclidean distance matrix based on the set of embedding vectors, and uses the hierarchical clustering algorithm to construct a tree structure, where the "Pythagorean theorem" and the "right triangle" are merged in the second-level clustering cluster, and the distance value is 0.15.

[0171] In step 1332, the knowledge graph generation system performs hierarchical cutting and optimization. The threshold for the number of hierarchical levels is set to 5 levels. Horizontally cut the hierarchical clustering tree to generate five preliminary hierarchical node groupings including "algebraic operations", "geometric fundamentals", etc. Detecting that the average Euclidean distance between the nodes of "Pythagorean theorem" and "similar figures" in the "geometric fundamentals" grouping reaches 0.28 (threshold 0.25), the system merges this grouping with the "geometric applications" grouping. Combining the chapter label of "intersection of geometry and algebra" in the teaching resource data, map the merged grouping to the "geometry → Pythagorean theorem system" level to form a candidate node group with hierarchical labels. The system verifies the correspondence between the "square root calculation" node in the "algebraic operations" grouping and the second section of chapter three of the textbook to ensure that the hierarchical labels are strictly aligned with the teaching chapters.

[0172] In step 1333, the knowledge graph generation system corrects the hierarchical boundaries. It is found that there is a cross-level association edge between the "Pythagorean theorem" node and the "spatial geometry" level. The system creates a "spatial application" sub-grouping under the "geometric fundamentals" level according to the association strength parameter of 0.73 between the two in the test questions. Conduct a consistency verification on the reorganized node group. Detecting that the semantic difference between the "trigonometric function" node and the nodes in the same group exceeds the threshold, it is then migrated to the "intersection of algebra and geometry" level. Finally, a set of candidate hierarchical node groupings including "geometry → Pythagorean theorem system → plane applications", "geometry → Pythagorean theorem system → spatial applications", etc. is generated.

[0173] Designed in this way, a multi-level classification system for mathematical knowledge points is constructed through graph neural network and hierarchical clustering techniques. The system first extracts the features and association relationships of knowledge nodes, uses graph convolutional network to aggregate global semantic information to generate node embedding vectors, and forms a tree-like hierarchical structure through hierarchical clustering. Optimize the initial grouping based on node density verification, merge loose groupings and map the hierarchical attribution according to the teaching chapter labels. Adjust the grouping boundaries for cross-level association relationships, and remove abnormal nodes with too large semantic differences. Finally, a candidate hierarchical node group with coherent semantics and compact structure is formed. This process realizes the adaptive division of knowledge points from coarse-grained to fine-grained, retains both the clustering characteristics driven by data and ensures the subject logic of the classification system through teaching semantic constraints, laying a foundation for subsequent hierarchical correction.

[0174] As an optional but not limiting embodiment, the step of correcting the candidate hierarchical node group according to the chapter division information in the teaching resource data in step 134 to obtain the knowledge point hierarchical structure data includes:

[0175] Step 1341: Extract chapter division information from the teaching resource data, and the chapter division information includes a set of chapter titles and chapter level identifiers.

[0176] Step 1342: Semantically match the set of chapter titles with the semantic tags of each node group in the candidate hierarchical node group to generate a set of mapping relationships between chapter titles and node groups; recursively adjust the hierarchical depth of the candidate hierarchical node group according to the chapter hierarchical identifier, so that the hierarchical position of each node group is consistent with the hierarchical identifier of the corresponding chapter title, and generate an adjusted set of hierarchical node groups.

[0177] Step 1343: Traverse the adjusted set of hierarchical node groups, identify the isolated node groups that have not established mapping relationships with chapter titles, and assign temporary hierarchical identifiers to the isolated node groups based on the parent-child relationship of the chapter hierarchical identifier.

[0178] Step 1344: Globally sort the adjusted set of hierarchical node groups according to the chapter order in the chapter division information to generate a preliminary hierarchical structure framework; detect semantic conflicts between node groups at the same level in the preliminary hierarchical structure framework, where the semantic conflicts include semantically duplicate node groups and node groups with inverted logical order.

[0179] Step 1345: Perform a merging operation on the semantically duplicate node groups, and swap the positions of the node groups with inverted logical order based on the chapter order to generate a set of hierarchical node groups after conflict handling; create end knowledge point nodes in the set of hierarchical node groups after conflict handling according to the smallest-grain chapter unit in the chapter division information, and bind the end knowledge point nodes to the corresponding smallest-grain chapter units.

[0180] Step 1346: Perform integrity verification on the set of hierarchical node groups after conflict handling based on the tree structure of the chapter hierarchical identifier to ensure that the node group corresponding to each chapter title exists in the tree structure and the hierarchical depth matches; topologically connect the set of hierarchical node groups that pass the verification according to the chapter order and hierarchical depth to generate the knowledge point hierarchical structure data; where the parent-child relationship of each node group is completely aligned with the hierarchical relationship of the chapter division information.

[0181] Step 1347: Calibrate the weights of the node groups in the knowledge point hierarchical structure data according to the mapping probability values in the set of mapping relationships, so that the path priority of the node groups with high-frequency mapping is improved in the knowledge point hierarchical structure data; mark the node groups that are not aligned with the chapter division information in the knowledge point hierarchical structure data according to the allocation record of the temporary hierarchical identifier, and generate a hierarchical deviation log for subsequent dynamic update triggering.

[0182] In step 1341, the knowledge graph generation system extracts chapter division information. It extracts the set of chapter titles from the electronic version of the People's Education Edition mathematics textbook, including top-level classifications such as "Number and Algebra", "Geometry and Graphics", "Statistics and Probability", and lower-level chapters such as "Chapter 17 Pythagorean Theorem". The system identifies chapter-level identifiers. For example, "17.1 Pythagorean Theorem" corresponds to the three-level hierarchical code "3-17-1", ensuring the complete retention of the multi-granularity characteristics of the chapter structure.

[0183] In step 1342, the knowledge graph generation system establishes semantic mapping relationships. It semantically matches the label "Properties of Right Triangles" of the candidate hierarchical node group with the title of the first section of Chapter 17 of the textbook, measures a similarity of 0.91, and establishes a strong mapping relationship. According to the chapter-level identifier, it adjusts the hierarchical depth of the node group to strictly correspond to the "3-17-1" code. For the "Proof Methods of Pythagorean Theorem" node group, it is detected that it is scattered in Sections 17.2 and 17.3 of the textbook, and the system creates a composite hierarchical identifier "3-17-2 / 3" to achieve multi-chapter mapping.

[0184] In step 1343, the knowledge graph generation system processes isolated node groups. It is found that the "Chord Diagram Construction Method" node group does not match the textbook chapter title. The system assigns a temporary hierarchical identifier "3-17-1-EX1" according to its semantic proximity and marks it as an extended knowledge point of the first section of Chapter 17. This temporary identifier inherits the hierarchical relationship of the parent chapter to ensure logical coherence in the global hierarchical structure.

[0185] In step 1344, the knowledge graph generation system constructs a preliminary hierarchical framework. It arranges the node groups in the order of the textbook chapters to generate a four-layer structure of "Geometry → Pythagorean Theorem → Theorem Proof → Application Examples". It is detected that the content of the "Algebraic Solution" and "Geometric Solution" node groups overlaps at the same level, triggering the semantic conflict warning mechanism. At the same time, it is found that the "Inverse Proposition of the Theorem" node group is located before the "Theorem Proof", resulting in a problem of inverted logical order.

[0186] In step 1345, the knowledge graph generation system resolves structural conflicts. It merges the "Algebraic Proof of Pythagorean Theorem" and "Geometric Proof" node groups into a "Proof Methods" composite node group, retaining the sub-node branches of the two proof paths. It adjusts the "Inverse Proposition of the Theorem" node group to after the "Theorem Proof" to conform to the teaching order of the textbook of "first positive theorem and then inverse proposition". According to the smallest-granularity chapter of the textbook "17.1.3 Practical Application", it creates an end knowledge point node "Solution of Measurement Problems" and binds it to the corresponding exercise micro-lesson resources.

[0187] In step 1346, the knowledge graph generation system completes the hierarchical verification. It verifies that there is a corresponding node group in the hierarchical structure for each teaching material chapter title. For example, it confirms that "17.2 Converse Theorem of Pythagorean Theorem" is mapped to the path "Geometry → Pythagorean Theorem → Exploration of Converse Theorem". It is detected that the hierarchical depth of the temporary node group "Chord Diagram Construction Method" matches that of the parent chapter, and it is allowed to be incorporated into the final structure. The system connects the node groups according to the tree topology of the teaching material chapters to form a standard hierarchical framework of "Geometry → Pythagorean Theorem System → [Basic Concepts | Proof Methods | Practical Applications]".

[0188] In step 1347, the knowledge graph generation system implements weight calibration. It raises the path priority of the frequently mapped "Proof of Pythagorean Theorem" node group and moves its position two places forward in the knowledge path recommendation sequence. It marks the deviation information of the temporary hierarchical node group "Chord Diagram Construction Method" and records its 0.5-level hierarchical difference from the standard chapter structure. The system generates a hierarchical deviation log, which triggers the dynamic adjustment process of this node group when subsequent teaching material versions are updated to ensure the continuous synchronization of the knowledge graph and teaching resources.

[0189] In this way, the candidate hierarchy is systematically corrected based on the chapter information of the teaching resources to construct a knowledge point hierarchical structure that is deeply aligned with the teaching material system. The system establishes the mapping relationship between the node group and the teaching unit through semantic matching of the chapter title, and recursively adjusts the hierarchical depth to strictly correspond to the teaching material identifier. It assigns temporary hierarchical identifiers to the unmapped isolated node groups to ensure structural integrity. Through the global sorting and conflict detection mechanism, it eliminates the semantic repetition and logical inversion problems of the node groups, and creates end knowledge point nodes based on the smallest chapter unit. The integrity verification module verifies the consistency between the hierarchical tree structure and the teaching material topology to solve the chapter coverage deviation problem. The weight calibration mechanism raises the path priority of the frequently mapped node groups, and marks the temporary hierarchical deviation log to trigger dynamic updates. This process realizes the two-way integration of the teaching syllabus logic and the data clustering results, which not only ensures that the knowledge point hierarchy conforms to the standard teaching order, but also maintains the extensibility of the structure through the exception marking mechanism, forming an education knowledge classification system that can evolve dynamically.

[0190] Based on the same inventive concept, an embodiment of the present invention also provides a knowledge graph generation system. Refer to Figure 2 As shown, it is a schematic structural diagram of a possible knowledge graph generation system provided in an embodiment of the present invention. Figure 2 In it, the knowledge graph generation system 200 includes: a processor 210 and a memory 220. Among them, the memory 220 stores a computer program executable by the processor 210, and the processor 210 can execute the steps of the above-mentioned method for generating a mathematics teaching knowledge graph based on artificial intelligence by executing the instructions stored in the memory 220.

[0191] Based on the same inventive concept, an embodiment of the present invention provides a computer-readable storage medium, which includes a computer program. When the computer program runs on a knowledge graph generation system, the computer program is used to cause the knowledge graph generation system to execute the steps of the above-mentioned method for generating a mathematics teaching knowledge graph based on artificial intelligence. In some possible implementation manners, various aspects of the method for generating a mathematics teaching knowledge graph based on artificial intelligence provided by the present invention can also be implemented in the form of a program product, which includes a computer program. When the program product runs on a knowledge graph generation system, the computer program is used to cause the knowledge graph generation system to execute the steps in the above-mentioned method for generating a mathematics teaching knowledge graph based on artificial intelligence. For example, the knowledge graph generation system can execute as Figure 1 the steps shown in.

Claims

1. A method for generating a mathematical teaching knowledge graph based on artificial intelligence, characterized in that, The method includes: Obtaining a multi-source teaching data set, where the multi-source teaching data set includes textbook text data, question structure data, and teaching resource data; Extracting a set of mathematical knowledge point entities from the textbook text data, and generating a set of association relationship data between the mathematical knowledge point entities in the set of mathematical knowledge point entities according to the question structure data; Performing hierarchical classification processing on the set of mathematical knowledge point entities based on a preset semantic analysis model to obtain knowledge point hierarchical structure data, and calculating weight allocation data of the mathematical knowledge point entities based on the set of association relationship data; Generating a dynamic knowledge graph topological structure according to the knowledge point hierarchical structure data and the weight allocation data, where the nodes in the dynamic knowledge graph topological structure include semantic vectors and association strength parameters of the mathematical knowledge point entities.

2. The method according to claim 1, characterized in that, The extracting a set of mathematical knowledge point entities from the textbook text data includes: Performing paragraph segmentation processing on the textbook text data to generate a text paragraph sequence; Performing semantic word segmentation processing on each text paragraph in the text paragraph sequence to obtain a set of word segmentation units for each text paragraph; Performing semantic encoding on the set of word segmentation units through a semantic vector generation model to generate semantic vectors for each word segmentation unit; Performing clustering analysis on the set of word segmentation units based on the semantic vectors to obtain a set of candidate knowledge point entities; Verifying the set of candidate knowledge point entities according to the annotation information in the question structure data to generate the set of mathematical knowledge point entities.

3. The method according to claim 1, characterized in that, The performing hierarchical classification processing on the set of mathematical knowledge point entities based on a preset semantic analysis model to obtain knowledge point hierarchical structure data includes: Inputting the set of mathematical knowledge point entities into the semantic analysis model to generate semantic feature vectors of each mathematical knowledge point entity in the set of mathematical knowledge point entities; Generating an initial classification graph structure according to the cosine similarity between the semantic feature vectors; Performing hierarchical division on the initial classification graph structure based on a graph neural network to generate multiple candidate hierarchical node groups; Correcting the candidate hierarchical node groups according to the chapter division information in the teaching resource data to obtain the knowledge point hierarchical structure data; The calculating weight allocation data of the mathematical knowledge point entities based on the set of association relationship data includes: Counting the association times and association object types of each mathematical knowledge point entity in the set of association relationship data; Generating an initial weight parameter according to the association times and the association object types; Dynamically adjusting the initial weight parameter based on the hierarchical depth in the knowledge point hierarchical structure data to generate an adjusted weight parameter; Performing normalization processing on the adjusted weight parameter to generate the weight allocation data.

4. The method according to claim 1, characterized in that, After generating the dynamic knowledge graph topological structure according to the knowledge point hierarchical structure data and the weight allocation data, the method further includes: Monitoring the updated data in the multi-source teaching data set, and extracting newly added mathematical knowledge point entities and updated association relationships; Calculate the semantic similarity between the newly added mathematical knowledge point entity and the existing nodes in the dynamic knowledge graph topology according to the updated association relationship and the semantic vector of the newly added mathematical knowledge point entity; If the semantic similarity exceeds the preset threshold, merge the newly added mathematical knowledge point entity into the corresponding hierarchical node group and update the weight distribution data; If the semantic similarity does not exceed the preset threshold, create a new hierarchical node group in the knowledge point hierarchical structure data and re-distribute the weight distribution data.

5. The method according to claim 4, characterized in that, The method further includes: Generate a knowledge point association path according to the dynamic knowledge graph topology, and the knowledge point association path includes a connection sequence of at least two mathematical knowledge point entities; Perform a priority ranking on the knowledge point association path based on the weight distribution data to generate a recommended teaching path set; Match the recommended teaching path set with the user's historical learning data to filter out the target teaching path; Send the mathematical knowledge point entities and association relationships in the target teaching path to the teaching terminal.

6. The method according to claim 5, characterized in that, Before sending the mathematical knowledge point entities and association relationships in the target teaching path to the teaching terminal, the method further includes: Obtain the learning behavior data fed back by the teaching terminal, and the learning behavior data includes the knowledge point learning duration and the answering correct rate; Update the association strength parameter in the weight distribution data according to the learning behavior data; Optimize the dynamic knowledge graph topology based on the updated association strength parameter to generate an optimized knowledge point association path; Merge the optimized knowledge point association path with the target teaching path to generate a new recommended teaching path set; The merging of the optimized knowledge point association path with the target teaching path to generate a new recommended teaching path set includes: Obtain the first node sequence of all mathematical knowledge point entities in the optimized knowledge point association path, and extract the second node sequence of the mathematical knowledge point entities included in the target teaching path; Traverse the first node sequence and the second node sequence to identify the overlapping mathematical knowledge point entities that exist in both sequences, and generate an overlapping node set; Based on the association strength parameter in the weight distribution data, calculate the difference in the position sequence numbers of each mathematical knowledge point entity in the overlapping node set in the first node sequence and the second node sequence to generate a position offset set; Determine the path merging priority of each mathematical knowledge point entity in the overlapping node set according to the numerical distribution of the position offset set; among them, the mathematical knowledge point entity with a smaller position offset has a higher priority; Use the mathematical knowledge point entity with the highest priority in the overlapping node set as the reference node for path merging, and extract the subsequent node subsequences starting from the reference node from the first node sequence and the second node sequence respectively; Performing semantic vector similarity matching on the mathematical knowledge point entities in the subsequent node subsequences, if there are continuous node segments whose semantic similarity exceeds a preset threshold in two subsequent node subsequences, merging the continuous node segments into a shared path segment; Inserting the shared path segment to a subsequent position of the reference node, and removing the merged continuous node segments from the first node sequence and the second node sequence to generate an intermediate merged path; For the remaining nodes that have not been merged, the association closeness between each remaining node and the terminal node of the intermediate merge path is calculated according to the association strength parameter and the weight distribution data, and a node connection closeness ranking is generated; In descending order of the node connection density, the remaining nodes are sequentially attached to the end of the intermediate merged path, and if a path branch occurs during the attachment, a parallel node connection channel is created; Traversing all the reference nodes in the overlapping node set to perform the above merging operation, generating multiple candidate merging paths, and performing redundant node deduplication processing on the node connection sequence in each candidate merging path; Based on the chapter division information in the teaching resource data, the candidate merged paths after deduplication are checked for integrity, and path segments that do not meet the chapter level constraints are removed to generate a verified path set; Correct the paths in the verified path set in teaching logic order according to the associated object types in the associated relationship set, so that the pre-dependency relationship of each mathematical knowledge point entity is arranged continuously in the path; The paths after the teaching logic sequence correction are sorted according to the path length and the weighted value of the association strength parameter, and the top N paths with the highest weights are selected to generate the new recommended teaching path set.

7. The method according to claim 1, wherein The method further comprises: Performing visual rendering processing on the dynamic knowledge graph topology structure to generate an interactive graph interface; Marking the frequent mathematical knowledge point entities and key association relationships in the interactive graph interface to obtain marking results; In response to a user's touch operation on the marking result, displaying the associated teaching resource data and the test question structure data; The user operation trajectory is recorded and the association strength parameter in the weight distribution data is updated according to the user operation trajectory.

8. The method according to claim 7, wherein The method further comprises: Generate a knowledge point mastery evaluation model according to the dynamic knowledge graph topology structure; Inputting the user's answer record into the knowledge point mastery evaluation model to generate knowledge point weakness prediction data; Selecting a reinforcement learning path from a set of recommended teaching paths based on the knowledge point weakness prediction data; The mathematical knowledge point entities in the reinforcement learning path are dynamically bound to the teaching resource data to generate a customized learning plan.

9. The method according to claim 8, characterized in that, After generating the customized learning plan, the method further includes: Monitoring the learning progress data of the user in executing the customized learning program; Adjusting the priority order of the knowledge point association paths according to the learning progress data; If it is detected that the knowledge point weakness prediction data does not meet the preset optimization conditions, the regeneration process of the dynamic knowledge graph topology structure is triggered; Pushing the regenerated dynamic knowledge graph topology structure to the teaching terminal to update the interactive graph interface; Pushing the regenerated dynamic knowledge graph topology structure to the teaching terminal to update the interactive graph interface includes: Receiving the regenerated dynamic knowledge graph topology structure, extracting the node set and edge set in the regenerated dynamic knowledge graph topology structure, where the node set contains the semantic vectors and association strength parameters of mathematical knowledge point entities, and the edge set contains the association relationships between mathematical knowledge point entities; Comparing the version of the regenerated dynamic knowledge graph topology structure with the historical dynamic knowledge graph topology structure currently stored in the teaching terminal, identifying the newly added mathematical knowledge point entities, deleted mathematical knowledge point entities, and updated association strength parameters in the node set, and identifying the newly added association relationships and removed association relationships in the edge set, and generating a differential data set; According to the newly added mathematical knowledge point entities and association relationships in the differential data set, matching the corresponding textbook text data segments, question structure data identifiers, and teaching resource data addresses from the multi-source teaching data set, and generating an incremental update data packet; Performing compression and checksum attachment processing on the incremental update data packet, generating an update data packet to be transmitted, and sending the update data packet to the teaching terminal through an encrypted channel; In response to the teaching terminal receiving the update data packet, performing integrity verification and decompression processing, and extracting the differential data set, textbook text data segments, question structure data identifiers, and teaching resource data addresses in the incremental update data packet; According to the deleted mathematical knowledge point entities and removed association relationships in the differential data set, removing the corresponding node graphics and edge connection lines from the current interactive graph interface of the teaching terminal, and releasing the associated teaching resource data cache; Performing node semantic vector matching on the newly added mathematical knowledge point entities and association relationships in the differential data set with the historical dynamic knowledge graph topology structure currently stored in the teaching terminal. If there are existing nodes with semantic similarity exceeding the preset threshold, merging the newly added mathematical knowledge point entities into the attribute set of the existing nodes, otherwise creating independent nodes and inserting them into the corresponding hierarchical node group of the historical dynamic knowledge graph topology structure; According to the updated association strength parameters in the differential data set, adjusting the visualization attributes of the edge connection lines between the corresponding nodes in the interactive graph interface, where the visualization attributes include line thickness, color value, and dynamic effect parameters; Based on the textbook text data segments and question structure data identifiers, loading the associated teaching resource data from the local storage or remote server of the teaching terminal, and binding the teaching resource data address to the corresponding newly added mathematical knowledge point entity node; According to the merged or created node set and the adjusted edge set, re-rendering the layout structure of the interactive graph interface, adding dynamic highlight marks to all newly added nodes and edge connection lines, and synchronously recording the operation log of this update to the version history database.

10. A knowledge graph generation system, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor is caused to execute the steps of any one of claims 1 to 9.

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