Classroom teaching content multi-dimensional dynamic evaluation method based on double knowledge maps

Abstract

The invention relates to a classroom teaching content multi-dimensional dynamic evaluation method based on double knowledge maps, which comprises the following steps of: combining a multi-modal data fusion technology and an elastic path analysis algorithm by utilizing a static knowledge map of a teaching outline and a dynamic knowledge map of classroom teaching; the four dimensions of teaching content coverage, teaching logic and time management, teaching structure compliance and knowledge association tightness are comprehensively evaluated, teachers are helped to discover and solve potential problems, teaching design is optimized, and teaching quality is improved. The method effectively overcomes the problems of one-sidedness, hysteresis quality and subjective judgment of traditional teaching evaluation, realizes transformation and upgrading of teaching evaluation from simple'static rule matching 'to deep'dynamic intelligent diagnosis', effectively improves objectivity, systematicness and real-time performance of evaluation, provides a data-driven decision basis for optimizing teaching design, and improves teaching evaluation efficiency. Teaching evaluation is promoted to be transformed to digitization, standardization and intelligentization.

Description

Technical Field

[0001] The present invention belongs to the field of smart education technology, and specifically relates to a multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs. Background Art

[0002] Classroom teaching evaluation is a key component in ensuring educational quality. Its essence is to measure teachers' teaching effectiveness and promote continuous improvement through systematic analysis of the teaching process and content. Based on connectivism, knowledge is viewed as a network consisting of concepts, their connotations, and their interrelationships. Classroom teaching transfers knowledge by establishing and reconstructing nodes and relationships within this knowledge network. Knowledge connections are the foundation for the reconstruction and visualization of knowledge structures.

[0003] In process evaluation, the level of knowledge delivery is particularly critical. It not only assesses whether teachers have established clear teaching objectives, but also examines whether they can scientifically organize teaching content, effectively highlight key points, and emphasize the internal connections between knowledge points, thereby demonstrating the systematic and holistic nature of knowledge. This process aims to reveal potential deviations or deficiencies in the teaching process, providing empirical evidence and targeted suggestions for optimizing teaching design and improving teaching effectiveness. Therefore, how to objectively and accurately evaluate teachers' classroom teaching content, including the coverage of knowledge points in the syllabus, the explanation of interrelated relationships, and the depth and breadth of teaching, has become a critical issue that needs to be addressed in the education field.

[0004] Currently, classroom teaching content evaluation mainly relies on expert experience or simple quantitative indicators (such as knowledge point coverage), which has the following limitations:

[0005] One-sidedness: Current evaluation focuses only on the number of knowledge points, but ignores the relationship between knowledge, logical sequence and students' cognitive laws, making it difficult to comprehensively evaluate the rationality of the internal structure of teaching.

[0006] Lag: Relying on manual observation or post-class feedback, it is impossible to timely capture deviations between the teaching dynamic path and the syllabus;

[0007] Subjectivity: The scoring criteria are overly dependent on individual subjective experience and lack a unified and objective quantitative standard, which directly leads to greater volatility and uncertainty in the evaluation results.

[0008] With the rapid development of artificial intelligence (AI), the accelerated digital transformation of education, and the deepening application of AI in educational evaluation, the field of teaching evaluation has ushered in a new paradigm. Knowledge graphs, as a typical representative of semantic network technology, structure knowledge through nodes (knowledge points) and edges (association relationships), clearly demonstrating the hierarchical relationships and logical connections between knowledge. Knowledge graphs not only focus on the coverage of knowledge points but also conduct comprehensive assessments from multiple dimensions (such as the compliance of knowledge structures and the closeness of association networks), providing more comprehensive analysis results. These advantages make knowledge graphs more practical and effective in teaching content evaluation, and can better support the modernization of teaching improvement and educational evaluation. However, current knowledge graph applications are mostly limited to a single dimension (such as knowledge point coverage) and fail to deeply explore teaching logic, the rationality of organizational structure, and dynamic associations. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to overcome the defects of the existing technology and provide a multi-dimensional dynamic evaluation method of classroom teaching content based on dual knowledge graphs that combines dynamic and static methods to improve the comprehensiveness, accuracy and objectivity of teaching evaluation.

[0010] The technical solution adopted to solve the above technical problems is: a multi-dimensional dynamic evaluation method of classroom teaching content based on dual knowledge graphs, including the following steps:

[0011] Step 1. Build classroom teaching knowledge graph and course reference knowledge graph

[0012] Step 1.1. Collect multimodal data from classroom teaching, including speech and blackboard writing. Use automatic speech recognition technology to convert the speech data into text. Align it with the blackboard writing using timestamps to form time-stamped fused text data. Based on this fused text data, use a pre-trained large language model to construct a classroom teaching knowledge graph.

[0013] Step 1.2. Based on the syllabus and textbooks, analyze the knowledge point hierarchy and dependencies using rule templates and a pre-trained large language model to construct a course reference knowledge graph.

[0014] Step 2. Based on the classroom teaching knowledge graph and the course reference knowledge graph, evaluate the degree of alignment between the teaching content and the curriculum standards by calculating the knowledge point coverage and checking the knowledge point association coverage;

[0015] Step 3. Use the flexible path matching algorithm to evaluate the logical coherence of the teaching steps. For each knowledge point, set the ideal explanation time and calculate the rationality of time allocation to evaluate the rationality of time planning.

[0016] Step 4. Build a hierarchical rule base to evaluate the compliance of the knowledge point dependencies and the rationality of the hierarchical distribution of the classroom teaching content;

[0017] Step 5. Evaluate the horizontal connections and network connectivity between knowledge points by calculating the matching degree of the edge density between the classroom teaching knowledge graph and the course reference knowledge graph, and analyzing the path generation, path coverage, and path diversity of key knowledge in the classroom teaching knowledge graph.

[0018] Step 6. Use the hierarchical analysis method to comprehensively score the quality of teaching content, and combine it with machine learning to generate dynamic feedback suggestions to provide support for teaching optimization.

[0019] As a preferred technical solution, the method for constructing the classroom teaching knowledge graph in step 1.1 is:

[0020] A pre-trained large language model is used to identify knowledge points and concepts as entities from fused text data, extract the logical relationships between entities, and calculate the teaching duration and frequency of each entity. A Neo4j graph database is used to construct a classroom teaching knowledge graph, where nodes are knowledge points or concepts, edges are logical relationships, and attributes include teaching duration, frequency of occurrence, and timestamps. Nodes are marked as "important" or "ordinary" based on the frequency of occurrence, and the graph content is updated in real time through incremental data access to ensure synchronization with the teaching process.

[0021] As a preferred technical solution, the method for constructing the course reference knowledge graph in step 1.2 is:

[0022] Step A1. Set rule templates based on the syllabus and textbooks, including hierarchical parsing rule templates, dependency rule templates, and important annotation rule templates;

[0023] The hierarchical parsing rule template uses regular expressions or specific grammatical rules based on the chapter structure of the syllabus to analyze and extract the hierarchical attribution of knowledge points;

[0024] The dependency rule template sets logical rules to identify the relationship between knowledge points, defines the logical rules of "prerequisite relationship" and "parent-child relationship", and sets differentiated weights for different dependency types;

[0025] The important marking rule template is to formulate classification standards for node importance and associated edge importance by comprehensively considering the explicit identification in the teaching syllabus and the implicit features in the course materials;

[0026] Step A2. Extract chapter titles and knowledge point lists from the syllabus and course materials, parse the hierarchy and dependencies according to the rule template, use the pre-trained large language model to automatically identify knowledge points, conceptual entities, and their relationships, and count the frequency of entity occurrences as a reference for importance.

[0027] Step A3. Mark the key points, difficult points, or points prone to error clearly marked in the syllabus as "important" nodes. Based on the syllabus and course materials, and taking into account implicit characteristics such as entity frequency and chapter location, additional nodes are marked as "important" or "normal." Edges associated with important nodes are uniformly marked as "important," and other edges are ranked according to their importance based on frequency of occurrence.

[0028] Step A4. Use the Neo4j graph database to build a classroom teaching knowledge graph, where nodes represent knowledge points or concepts and edges represent logical relationships. Each node's attributes include the name of the knowledge point or concept, its importance, and its sequence number. Closed-loop problems in dependency relationships are detected and corrected. Critical paths are given higher weights to clearly distinguish primary and secondary logic.

[0029] As a preferred technical solution, in step 2, the knowledge point coverage calculation method is:

[0030] Extract knowledge point nodes from the classroom teaching knowledge graph and the course reference knowledge graph to form the classroom knowledge point set K teach And the course knowledge point set K ref , and retain the attributes of the knowledge point nodes;

[0031] Use the pre-trained word embedding model to embed the classroom knowledge point set K teach And the course knowledge point set K ref Each knowledge point node in is converted into a vector representation to generate a classroom knowledge point vector set V teach And the course knowledge point vector set V ref ; Calculate the classroom knowledge point vector set V teach And the course knowledge point vector set V ref The cosine similarity of the knowledge points in the θ is calculated, and a threshold θ is set to filter out the matching pairs whose cosine similarity is greater than θ to generate the matching set K match ;

[0032] The knowledge point coverage C is obtained according to the following formula 知识 , which is used to measure teaching integrity;

[0033]

[0034] Where w k is the matching set K match The weight of the kth matching pair in the course knowledge point set K ref If the mark in the middle is "important", then w k =1; if the knowledge point in the kth matching pair is in the course knowledge point set K ref If the mark in the middle is "normal", then w k =2;kteach 、k ref They are the kth matching pairs from the classroom knowledge point set K teach The knowledge points and the knowledge points from the course set K ref Knowledge point, sim(·) is the cosine similarity, w r is the set of course knowledge points K ref The weight of the rth knowledge point in the course knowledge point set K ref If the mark in the middle is "important", then w r =2, if the rth knowledge point is in the course knowledge point set K ref If the mark in the middle is "normal", then w r =1;

[0035] The concept association coverage checking method is:

[0036] Step B1. Perform one-hot encoding on each edge in the classroom teaching knowledge graph and the course reference knowledge graph to generate a type identification vector t(e);

[0037] Step B2. In the course reference knowledge graph, the associated edges marked as “important” are assigned a weight of 2, and the associated edges marked as “ordinary” are assigned a weight of 1. The edges are normalized and mapped to the interval [0, 1] to obtain the associated edge weight vector w(e); the type identification vector t(e) and the associated edge weight vector w(e) are concatenated to form the edge feature vector f e , and construct the edge feature matrix F E ;

[0038] Step B3. Transform the edge feature vector f e Input into the graph attention network, the graph attention network aggregates neighbor node information and dynamically updates the node embedding according to the following formula:

[0039]

[0040] Where h′ i is the updated embedding vector of node i, a ij is the attention coefficient that measures the relative importance of node j to node i, W is the learnable weight matrix used to linearly transform node features, σ is the activation function, N(i) is the set of nodes associated with node i, and h j is the embedding vector of node j, b is the weight basis coefficient that balances the global impact of edge weights on node embedding updates, and w ij (e) is the weight vector of the associated edge between node i and node j;

[0041] Step B4. Combine the edge feature vector and the node embedding vector to construct a multi-dimensional knowledge point association vector to represent the semantic and structural features of the association, and quantitatively evaluate the association integrity between knowledge points according to the following formula: 完整性 ,

[0042]

[0043] Where, E teach is the associated set in the classroom teaching knowledge graph, E ref is the associated set in the course reference knowledge graph, β t(e) is the association type weight, S coon (e) is the semantic similarity score between the knowledge point association vectors.

[0044] As a preferred technical solution, the method for constructing a multi-dimensional knowledge point association vector is: embedding vectors h of nodes i and j i ′、h j ′, and edge eigenvector fe ij Splice in sequence to generate the splicing vector V concat =[h i ′;h j ′;fe ij ], using Hadamard product to enhance the correlation of interactive features and generate enhanced vector V interact =h i ′⊙h j ′;⊙fe ij ,according to Generate knowledge point association vector γ is a learning parameter.

[0045] As a preferred technical solution, the method of using the elastic path matching algorithm to evaluate the logical coherence of the teaching steps in step 3 includes the following steps:

[0046] Step C1. Use the improved depth-first search algorithm combined with timestamps and teaching logic constraints to give priority to accessing strongly connected nodes containing timestamp information, and serialize the classroom teaching knowledge graph into a node sequence P of the actual teaching path. teach =[n1,n2,…,n M ],n M is the Mth node, where M is the total number of nodes in the classroom teaching knowledge graph;

[0047] Step C2. Refer to the order of the textbook and the depth-first search traversal to serialize the course reference knowledge graph into the node sequence P of the ideal teaching path ref =[n′1,n′2,…,n′ Q ],n′ Qis the Qth node in the course reference knowledge graph, where Q is the number of nodes in the course reference knowledge graph;

[0048] Step C3. Initialize the (M+1)×(N+1) distance matrix D, where D[p][q] is the node sequence P teach The first p nodes and the node sequence P ref The minimum matching cost of the first q nodes;

[0049] Step C4. Fill the distance matrix according to the following dynamic programming formula, backtrack from D[M][N], record the matching, insertion, and deletion operations, and generate the optimal alignment path.

[0050]

[0051] Where, w(P teach [p-1]) is the node P teach The weight of [p-1], Cost(P teach [p-1],P ref [q-1]) represents P teach [p-1] and P ref [q-1] semantic matching value, if it matches, Cost = 0, otherwise Cost = ∞;

[0052] Step C5. Calculate the global similarity Sim according to the following formula 全 , quantify the logical consistency between the actual teaching path and the ideal teaching path, and the global similarity Sim 全 The closer it is to 1, the higher the logical consistency between the actual teaching path and the ideal teaching path.

[0053]

[0054] Where, The maximum cost is the cost of deleting all nodes and inserting all nodes. Since teachers are encouraged to supplement and expand content, there is no penalty for the insertion operation;

[0055] Step C6. In the generated optimal alignment path, check whether there are any violations of the knowledge graph logical dependencies. For each logical conflict detected, penalize it by reducing the overall logical consistency score.

[0056] The formula for calculating the rationality of time allocation in step 3 is:

[0057]

[0058] Where, Time reason is the rationality score of time allocation for knowledge points, It is the time when knowledge points are actually explained in class. is the ideal time to explain a knowledge point, and a is the allowable error ratio.

[0059] As a preferred technical solution, in step 4, the method for constructing a hierarchical rule base is: based on the course reference knowledge map or teaching standards, mining knowledge point progression rules, defining knowledge point dependency rules, dividing knowledge points into levels according to Bloom's cognitive taxonomy, and assigning hierarchical labels to each knowledge point through a clustering algorithm; the hierarchical structure is divided into four layers, namely, recognition layer L1, understanding layer L2, application layer L3, and analysis layer L4;

[0060] The method for evaluating the compliance of the knowledge point dependency relationship and the rationality of the hierarchical distribution of classroom teaching content is as follows:

[0061] Parse the classroom teaching knowledge graph based on the hierarchical rule base, extract knowledge point attributes including name, hierarchy, and dependency, and construct a dependency graph;

[0062] Calculate the compliance rate of knowledge point dependencies to quantify whether the classroom dependencies conform to the hierarchical progressive logic. The closer the compliance rate is to 1, the more the dependencies conform to the hierarchical progressive logic.

[0063] The reference course refers to the hierarchical distribution of the knowledge graph, measures the rationality of the overall proportion of knowledge points at different levels, performs hierarchical span detection on the dependency relationship of knowledge points, and identifies and corrects discontinuous jumps in the dependency relationship.

[0064] As a preferred technical solution, in step 5, the calculation of the matching degree of the associated edge density between the classroom teaching knowledge graph and the course reference knowledge graph is performed according to the following formula:

[0065]

[0066] Where DM is the density matching degree of the associated edge, a is the density difference weight coefficient, β is the redundant association penalty coefficient, R is the redundant association ratio, ε is the allowed density difference error ratio, and E teach is the total number of associated edges of all nodes in the classroom teaching knowledge graph, E ref is the total number of associated edges of all nodes in the course reference knowledge graph, and Q is the total number of all nodes in the course reference knowledge graph;

[0067] The path generation method of the key knowledge in the classroom teaching knowledge graph is as follows: traverse any two key knowledge point node pairs (u, v) in the classroom teaching knowledge graph through depth-first search, generate all paths, and count the total number of paths from u to v, which is recorded as Set the maximum path length, filter out the paths with decreasing trend in the teaching stage sequence based on the teaching sequence, retain the paths with non-decreasing trend, and form the actual path set Paths u→v={P1,P2,...,P V}, the actual number of paths is

[0068] The path coverage PC of key knowledge in the classroom teaching knowledge graph is:

[0069]

[0070] Where K key is the set of key knowledge pairs in the knowledge graph taught in class, P ideal is the number of ideal association paths obtained based on the course reference knowledge graph;

[0071] The path diversity analysis method is as follows: paths with a length of 1 to 2 steps are classified as short paths to reflect the association of basic knowledge; paths with a length of ≥ 3 steps are classified as medium-long paths to reflect the depth of knowledge and the complexity of association; the number of paths of different lengths is counted, and the proportion of paths with a length of 1, P, is calculated. l , N l is the number of paths of length l, N total is the total number of paths; the entropy value of the path number is calculated and normalized to obtain the path diversity index value, which is used to measure the uniformity of the path length distribution.

[0072] As a preferred technical solution, in step 6, the method of using the analytic hierarchy process to weight the comprehensive scoring of the teaching content quality is as follows:

[0073] According to the teaching objectives and evaluation focus, the first-level dimensions of teaching content quality evaluation are determined, including: teaching content coverage W1, teaching logic and time allocation W2, teaching structure compliance W3, and knowledge point relevance W4;

[0074] An evaluation panel consisting of educational experts, subject research staff, and frontline teachers was invited to compare the dimensions pairwise based on the importance of the teaching objectives, assigning values ​​using a 1-9 scale.

[0075] According to the pairwise comparison results of the review group, the judgment matrix A is constructed, the maximum eigenvalue and consistency index CI of the judgment matrix A are calculated, and according to the dimension of the judgment matrix A, the corresponding random consistency index RI is found to obtain the consistency ratio CR. If CR < 0.1, the judgment matrix is ​​considered to have satisfactory consistency and pass the test;

[0076] The normalized eigenvector W of the judgment matrix A is used as the weight of each first-level dimension, W = [w1 + w2 + w3 + w4], satisfying ∑W = 1;

[0077] Score each dimension of the judgment matrix A and generate a standardized score S using the minimum-maximum standardization method t ∈[0,1], according to the weight W and score S of each dimension t , get the comprehensive score Score, Score = w1×S1+w2×S2+w3×S3+w4×S4;

[0078] Grading is based on the comprehensive score: Score ≥ 0.8 is excellent, the teaching design is reasonable and no adjustment is required; 0.6 ≤ Score < 0.8 is good and requires local optimization; Score < 0.6 is unsatisfactory and requires reconstruction of the knowledge graph or resetting of teaching objectives.

[0079] The beneficial effects of the present invention are as follows:

[0080] The present invention conducts a comprehensive evaluation from four dimensions: teaching content coverage, teaching logic and time management, teaching structure compliance, and knowledge relevance, thus avoiding the one-sidedness caused by single indicator evaluation.

[0081] By constructing a static knowledge graph of the syllabus and a dynamic knowledge graph of classroom lectures, this method not only assesses whether the teaching content meets the curriculum standards, but also tracks dynamic changes in the teaching process in real time, promptly identifying and correcting deviations in the teaching path. This combined dynamic and static evaluation method can more accurately reflect the actual effectiveness of the teaching process than traditional static evaluation methods.

[0082] This invention uses artificial intelligence technologies such as knowledge graphs, graph attention networks, and elastic path matching algorithms to achieve quantitative evaluation of teaching content, greatly reducing the interference of subjective factors and improving the objectivity and consistency of evaluation results.

[0083] This invention can evaluate the teaching process in real time, identify problems promptly, and provide feedback. Based on this real-time feedback, teachers can quickly adjust their teaching strategies, optimize the organization of teaching content and delivery methods, and thus continuously improve teaching quality. This real-time feedback mechanism can more effectively optimize the teaching process than traditional, lagging evaluation methods.

[0084] This method uses a multi-dimensional dynamic assessment of teaching content to identify weak links in the teaching process and potential cognitive difficulties faced by students. Based on this information, teachers can provide personalized teaching support for students at different levels, meeting the learning needs of different students and improving the relevance and effectiveness of teaching.

[0085] Through the flexible path matching algorithm and logical conflict detection mechanism, the present invention can accurately evaluate the logical coherence of teaching steps, helping teachers to discover possible logical problems in the teaching process, such as unreasonable order of knowledge point explanation, failure to explain prerequisite knowledge points, etc., thereby optimizing the organizational structure of teaching content and improving the logic and coherence of teaching content. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is a flow chart of the multi-dimensional dynamic evaluation method of classroom teaching content based on dual knowledge graphs of the present invention. DETAILED DESCRIPTION

[0087] The present invention will be further described in detail below with reference to the accompanying drawings and examples, but the present invention is not limited to the following embodiments.

[0088] exist Figure 1 In this embodiment, the multi-dimensional dynamic evaluation method of classroom teaching content based on dual knowledge graphs includes the following steps:

[0089] Step 1. Build classroom teaching knowledge graph and course reference knowledge graph

[0090] Step 1.1. Collect multimodal data from classroom teaching, including speech and blackboard writing. Use automatic speech recognition technology to convert the speech data into text and align it with the blackboard writing using timestamps to form time-stamped fused text data. Based on the fused text data, use the pre-trained large language model to build a classroom teaching knowledge graph. Specifically:

[0091] A pre-trained large language model is used to identify knowledge points and concepts as entities from fused text data, extract the logical relationships between entities, and calculate the teaching duration and frequency of each entity. A Neo4j graph database is used to construct a classroom teaching knowledge graph, where nodes are knowledge points or concepts, edges are logical relationships, and attributes include teaching duration, frequency of occurrence, and timestamps. Nodes are marked as "important" or "ordinary" based on the frequency of occurrence, and the graph content is updated in real time through incremental data access to ensure synchronization with the teaching process.

[0092] Step 1.2. Based on the syllabus and textbooks, analyze the knowledge point hierarchy and dependencies using rule templates and pre-trained large language models to build a course reference knowledge graph. Specifically:

[0093] Step A1. Set rule templates based on the syllabus and textbooks, including hierarchical parsing rule templates, dependency rule templates, and important annotation rule templates;

[0094] The hierarchical parsing rule template is: based on the chapter structure of the syllabus, regular expressions or specific grammatical rules are used to analyze and extract the hierarchical attribution of knowledge points;

[0095] The dependency rule template is as follows: setting logical rules to identify the relationship between knowledge points, defining the logical rules of "prerequisite relationship" and "parent-child relationship", and setting differentiated weights for different dependency types;

[0096] The important marking rule template is as follows: taking into account the explicit identification in the syllabus (such as "key points" and "difficult points") and the implicit characteristics in the course materials (such as the frequency of occurrence of knowledge points and chapter weights), a classification standard for node importance and associated edge importance is formulated;

[0097] Step A2. Extract chapter titles and knowledge point lists from the syllabus and course materials, parse the hierarchy and dependencies according to the rule template, use the pre-trained large language model to automatically identify knowledge points, conceptual entities, and their relationships, and count the frequency of entity occurrences as a reference for importance.

[0098] Step A3. Mark the key points, difficult points, or points prone to error clearly marked in the syllabus as "important" nodes. Based on the syllabus and course materials, and taking into account implicit characteristics such as entity frequency and chapter location, additional nodes are marked as "important" or "normal." Edges associated with important nodes are uniformly marked as "important," and other edges are ranked according to their importance based on frequency of occurrence.

[0099] Step A4. Use the Neo4j graph database to construct a classroom teaching knowledge graph, where nodes represent knowledge points or concepts and edges represent logical relationships. Each node's attributes include the name of the knowledge point or concept, its importance, and a sequence number based on its hierarchical position in the course materials. Closed-loop problems in dependency relationships are detected and corrected, and higher weights are assigned to critical paths to clearly distinguish between primary and secondary logic.

[0100] Step 2. Based on the classroom teaching knowledge graph and the course reference knowledge graph, evaluate the degree of alignment between the teaching content and the curriculum standards by calculating the knowledge point coverage and checking the knowledge point association coverage;

[0101] The calculation method of knowledge point coverage is:

[0102] Extract knowledge point nodes from the classroom teaching knowledge graph and the course reference knowledge graph to form the classroom knowledge point set K teach And the course knowledge point set K ref , and retain the attributes of the knowledge point nodes;

[0103] Use the pre-trained word embedding model to embed the classroom knowledge point set K teach And the course knowledge point set K ref Each knowledge point node in is converted into a vector representation to generate a classroom knowledge point vector set V teach And the course knowledge point vector set V ref; Calculate the classroom knowledge point vector set V teach And the course knowledge point vector set V ref The cosine similarity of the knowledge points in the θ is calculated, and a threshold θ is set to filter out the matching pairs whose cosine similarity is greater than θ to generate the matching set K match ;

[0104] The knowledge point coverage C is obtained according to the following formula 知识 , through the knowledge point coverage C 知识 measuring instructional integrity;

[0105]

[0106] Where w k is the matching set K match The weight of the kth matching pair in the course knowledge point set K ref If the mark in the middle is "important", then w k =1; if the knowledge point in the kth matching pair is in the course knowledge point set K ref If the mark in the middle is "normal", then w k =2;k teach 、k ref They are the kth matching pairs from the classroom knowledge point set K teach The knowledge points and the knowledge points from the course set K ref Knowledge point, sim(·) is the cosine similarity, w r is the set of course knowledge points K ref The weight of the rth knowledge point in the course knowledge point set K ref If the mark in the middle is "important", then w r =2, if the rth knowledge point is in the course knowledge point set K ref If the mark in the middle is "normal", then w r =1;

[0107] Among them, the concept association coverage checking method is:

[0108] Step B1. Perform one-hot encoding on each edge in the classroom teaching knowledge graph and the course reference knowledge graph to generate a type identification vector t(e);

[0109] Step B2. In the course reference knowledge graph, the associated edges marked as “important” are assigned a weight of 2, and the associated edges marked as “ordinary” are assigned a weight of 1. The edges are normalized and mapped to the interval [0, 1] to obtain the associated edge weight vector w(e); the type identification vector t(e) and the associated edge weight vector w(e) are concatenated to form the edge feature vector f e , and construct the edge feature matrix F E ;

[0110] Step B3. Transform the edge feature vector f e Input into the graph attention network, the graph attention network aggregates neighbor node information and dynamically updates the node embedding according to the following formula:

[0111]

[0112] Where h′ i is the updated embedding vector of node i, a ij is the attention coefficient that measures the relative importance of node j to node i, W is the learnable weight matrix used to linearly transform node features, σ is the activation function, N(i) is the set of nodes associated with node i, and h j is the embedding vector of node j, b is the weight basis coefficient that balances the global impact of edge weights on node embedding updates, and w ij (e) is the weight vector of the associated edge between node i and node j;

[0113] Step B4. Combine the edge feature vector and the node embedding vector to construct a multi-dimensional knowledge point association vector to represent the semantic and structural features of the association, specifically:

[0114] The embedding vector h of node i and node j i ′、h j ′, and edge eigenvector fe ij Splice in sequence to generate the splicing vector V concat =[h i ′;h j ′;fe ij ], using Hadamard product to enhance the correlation of interactive features and generate enhanced vector V interact =h i ′⊙h j ′;⊙fe ij ,according to Generate knowledge point association vector γ is a learning parameter used to dynamically reconcile splicing and interaction features.

[0115] The association integrity between knowledge points is quantitatively evaluated according to the following formula C 完整性 ,

[0116]

[0117] Where, E teach is the associated set in the classroom teaching knowledge graph, E ref is the associated set in the course reference knowledge graph, β t(e) is the association type weight, S coon (e) is the semantic similarity score between the knowledge point association vectors.

[0118] Step 3. Use the flexible path matching algorithm to evaluate the logical coherence of the teaching steps. For each knowledge point, set the ideal explanation time and calculate the rationality of time allocation to evaluate the rationality of time planning.

[0119] Among them, the method of using the elastic path matching algorithm to evaluate the logical coherence of teaching steps is:

[0120] Step C1. Use the improved depth-first search algorithm combined with timestamps and teaching logic constraints to give priority to accessing strongly connected nodes containing timestamp information, and serialize the classroom teaching knowledge graph into a node sequence P of the actual teaching path. teach =[n1,n2,…,n M ],n M is the Mth node, where M is the total number of nodes in the classroom teaching knowledge graph;

[0121] Step C2. Refer to the order of the textbook and the depth-first search traversal to serialize the course reference knowledge graph into the node sequence P of the ideal teaching path ref =[n′1,n′2,…,n′ Q ],n′ Q is the Qth node in the course reference knowledge graph, where Q is the number of nodes in the course reference knowledge graph;

[0122] Step C3. Initialize the (M+1)×(N+1) distance matrix D, where D[p][q] is the node sequence P teach The first p nodes and the node sequence P ref The minimum matching cost of the first q nodes;

[0123] Step C4. Fill the distance matrix according to the following dynamic programming formula, backtrack from D[M][N], record the matching, insertion, and deletion operations, and generate the optimal alignment path.

[0124]

[0125] Where, w(P teach [p-1]) is the node P teach The weight of [p-1], Cost(P teach [p-1],P ref [q-1]) represents P teach [p-1] and P ref [q-1] semantic matching value, if it matches, Cost = 0, otherwise Cost = ∞;

[0126] Step C5. Calculate the global similarity Sim according to the following formula 全 , quantify the logical consistency between the actual teaching path and the ideal teaching path, and the global similarity Sim 全The closer it is to 1, the higher the logical consistency between the actual teaching path and the ideal teaching path.

[0127]

[0128] Where, The maximum cost is the cost of deleting all nodes and inserting all nodes. Since teachers are encouraged to supplement and expand content, there is no penalty for the insertion operation;

[0129] Step C6. In the generated optimal alignment path, check whether there are any violations of the knowledge graph logical dependencies. For each logical conflict detected, penalize it by reducing the overall logical consistency score.

[0130] Among them, the formula for calculating the rationality of time allocation is:

[0131]

[0132] Where, Time reason is the rationality score of time allocation for knowledge points, It is the time when knowledge points are actually explained in class. is the ideal time to explain a knowledge point, and a is the allowable error ratio.

[0133] Step 4. Build a hierarchical rule base to evaluate the compliance of the knowledge point dependencies and the rationality of the hierarchical distribution of the classroom teaching content, specifically:

[0134] Based on the course reference knowledge map or teaching standards, we explore the progressive rules of knowledge points, define the rules of knowledge point dependencies, divide the knowledge points into levels according to Bloom's cognitive taxonomy, and use clustering algorithms to assign hierarchical labels to each knowledge point to build a hierarchical rule base. The hierarchical rule base consists of four layers: recognition layer L1, understanding layer L2, application layer L3, and analysis layer L4.

[0135] Parse the classroom teaching knowledge graph based on the hierarchical rule base, extract knowledge point attributes including name, hierarchy, and dependency, and construct a dependency graph;

[0136] Calculate the compliance rate of knowledge point dependencies to quantify whether the classroom dependencies conform to the hierarchical progressive logic. The closer the compliance rate is to 1, the more the dependencies conform to the hierarchical progressive logic.

[0137] The reference course refers to the hierarchical distribution of the knowledge graph, measures the rationality of the overall proportion of knowledge points at different levels, performs hierarchical span detection on the dependency relationship of knowledge points, and identifies and corrects discontinuous jumps in the dependency relationship.

[0138] By calculating the matching degree of the edge density of knowledge points in the classroom teaching knowledge graph and the course reference knowledge graph, as well as analyzing the path generation, path coverage and path diversity of key knowledge in the classroom teaching knowledge graph, the horizontal connections and network connectivity between knowledge are evaluated.

[0139] Step 5. Evaluate the horizontal connections and network connectivity between knowledge points by calculating the matching degree of the edge density between the classroom teaching knowledge graph and the course reference knowledge graph, and analyzing the path generation, path coverage, and path diversity of key knowledge in the classroom teaching knowledge graph.

[0140] Among them, the matching degree of the associated edge density between the classroom teaching knowledge graph and the course reference knowledge graph is calculated according to the following formula:

[0141]

[0142] Where DM is the density matching degree of the associated edge, a is the density difference weight coefficient, β is the redundant association penalty coefficient, R is the redundant association ratio, ε is the allowed density difference error ratio, and E teach is the total number of associated edges of all nodes in the classroom teaching knowledge graph, E ref is the total number of associated edges of all nodes in the course reference knowledge graph, and Q is the total number of all nodes in the course reference knowledge graph;

[0143] The path generation method for key knowledge in the classroom teaching knowledge graph is:

[0144] Through depth-first search, we traverse any two key knowledge point node pairs (u, v) in the classroom teaching knowledge graph, generate all paths, and count the total number of paths from u to v, which is recorded as Set the maximum path length, filter out the paths with decreasing trend in the teaching stage sequence based on the teaching sequence, retain the paths with non-decreasing trend, and form the actual path set Paths u→v ={P1,P2,...,P V}, the actual number of paths is

[0145] The path coverage PC of key knowledge in the classroom teaching knowledge graph is:

[0146]

[0147] Where K key is the set of key knowledge pairs in the knowledge graph taught in class, P ideal is the number of ideal association paths obtained based on the course reference knowledge graph;

[0148] The path diversity analysis method is as follows: paths with a length of 1 to 2 steps are classified as short paths to reflect the association of basic knowledge; paths with a length of ≥ 3 steps are classified as medium-long paths to reflect the depth of knowledge and the complexity of association; the number of paths of different lengths is counted, and the proportion of paths with a length of 1, P, is calculated. l , N l is the number of paths of length l, N total is the total number of paths; the entropy value of the path number is calculated and normalized to obtain the path diversity index value, which is used to measure the uniformity of the path length distribution.

[0149] Step 6. Use the Analytic Hierarchy Process (AHP) to comprehensively score the quality of teaching content, and combine it with machine learning to generate dynamic feedback suggestions to support teaching optimization;

[0150] The method of using the hierarchical analysis method to weight the comprehensive scoring of teaching content quality is as follows:

[0151] According to the teaching objectives and evaluation focus, the first-level dimensions of teaching content quality evaluation are determined, including: teaching content coverage W1, teaching logic and time allocation W2, teaching structure compliance W3, and knowledge point relevance W4;

[0152] An evaluation panel consisting of educational experts, subject research staff, and frontline teachers was invited to compare the dimensions pairwise based on the importance of the teaching objectives, assigning values ​​using a 1-9 scale.

[0153] According to the pairwise comparison results of the review group, the judgment matrix A is constructed, the maximum eigenvalue and consistency index CI of the judgment matrix A are calculated, and according to the dimension of the judgment matrix A, the corresponding random consistency index RI is found to obtain the consistency ratio CR. If CR < 0.1, the judgment matrix is ​​considered to have satisfactory consistency and pass the test;

[0154] The normalized eigenvector W of the judgment matrix A is used as the weight of each first-level dimension, W = [w1 + w2 + w3 + w4], satisfying ∑W = 1;

[0155] Score each dimension of the judgment matrix A and generate a standardized score S using the minimum-maximum standardization method t ∈[0,1], according to the weight W and score S of each dimension t , get the comprehensive score Score, Score = w1×S1+w2×S2+w3×S3+w4×S4;

[0156] Grading is based on the comprehensive score: Score ≥ 0.8 is excellent, the teaching design is reasonable and no adjustment is required; 0.6 ≤ Score < 0.8 is good and requires local optimization; Score < 0.6 is unsatisfactory and requires reconstruction of the knowledge graph or resetting of teaching objectives.

Claims

1. A multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs, characterized by: The following steps are involved: Step 1. Build classroom teaching knowledge graph and course reference knowledge graph Step 1.

1. Collect multimodal data from classroom teaching, including speech and blackboard writing. Use automatic speech recognition technology to convert the speech data into text. Align it with the blackboard writing using timestamps to form time-stamped fused text data. Based on this fused text data, use a pre-trained large language model to construct a classroom teaching knowledge graph. Step 1.

2. Based on the syllabus and textbooks, analyze the knowledge point hierarchy and dependencies using rule templates and a pre-trained large language model to construct a course reference knowledge graph. Step 2. Based on the classroom teaching knowledge graph and the course reference knowledge graph, evaluate the degree of alignment between the teaching content and the curriculum standards by calculating the knowledge point coverage and checking the knowledge point association coverage; Step 3. Use the flexible path matching algorithm to evaluate the logical coherence of the teaching steps. For each knowledge point, set the ideal explanation time and calculate the rationality of time allocation to evaluate the rationality of time planning. Step 4. Build a hierarchical rule base to evaluate the compliance of the knowledge point dependencies and the rationality of the hierarchical distribution of the classroom teaching content; Step 5. Evaluate the horizontal connections and network connectivity between knowledge points by calculating the matching degree of the edge density between the classroom teaching knowledge graph and the course reference knowledge graph, and analyzing the path generation, path coverage, and path diversity of key knowledge in the classroom teaching knowledge graph. Step 6. Use the hierarchical analysis method to comprehensively score the quality of teaching content, and combine it with machine learning to generate dynamic feedback suggestions to provide support for teaching optimization.

2. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 1 is characterized in that: The method for constructing the classroom teaching knowledge graph in step 1.1 is: A pre-trained large language model is used to identify knowledge points and concepts as entities from fused text data, extract the logical relationships between entities, and calculate the teaching duration and frequency of each entity. A Neo4j graph database is used to construct a classroom teaching knowledge graph, where nodes are knowledge points or concepts, edges are logical relationships, and attributes include teaching duration, frequency of occurrence, and timestamps. Nodes are marked as "important" or "ordinary" based on the frequency of occurrence, and the graph content is updated in real time through incremental data access to ensure synchronization with the teaching process.

3. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 1 is characterized in that: The method for constructing the course reference knowledge graph in step 1.2 is: Step A1. Set rule templates based on the syllabus and textbooks, including hierarchical parsing rule templates, dependency rule templates, and important annotation rule templates; The hierarchical parsing rule template uses regular expressions or specific grammatical rules based on the chapter structure of the syllabus to analyze and extract the hierarchical attribution of knowledge points; The dependency rule template sets logical rules to identify the relationship between knowledge points, defines the logical rules of "prerequisite relationship" and "parent-child relationship", and sets differentiated weights for different dependency types; The important marking rule template is to formulate classification standards for node importance and associated edge importance by comprehensively considering the explicit identification in the teaching syllabus and the implicit features in the course materials; Step A2. Extract chapter titles and knowledge point lists from the syllabus and course materials, parse the hierarchy and dependencies according to the rule template, use the pre-trained large language model to automatically identify knowledge points, conceptual entities, and their relationships, and count the frequency of entity occurrences as a reference for importance. Step A3. Mark the key points, difficult points, or points prone to error clearly marked in the syllabus as "important" nodes. Based on the syllabus and course materials, and taking into account implicit characteristics such as entity frequency and chapter location, additional nodes are marked as "important" or "normal." Edges associated with important nodes are uniformly marked as "important," and other edges are ranked according to their importance based on frequency of occurrence. Step A4. Use the Neo4j graph database to build a classroom teaching knowledge graph, where nodes represent knowledge points or concepts and edges represent logical relationships. Each node's attributes include the name of the knowledge point or concept, its importance, and its sequence number. Closed-loop problems in dependency relationships are detected and corrected. Critical paths are given higher weights to clearly distinguish primary and secondary logic.

4. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 1 is characterized in that: In step 2, the knowledge point coverage rate is calculated as follows: Extract knowledge point nodes from the classroom teaching knowledge graph and the course reference knowledge graph to form the classroom knowledge point set K teach And the course knowledge point set K ref , and retain the attributes of the knowledge point nodes; Use the pre-trained word embedding model to embed the classroom knowledge point set K teach And the course knowledge point set K ref Each knowledge point node in is converted into a vector representation to generate a classroom knowledge point vector set V teach And the course knowledge point vector set V ref ; Calculate the classroom knowledge point vector set V teach And the course knowledge point vector set V ref The cosine similarity of the knowledge points in the θ is calculated, and a threshold θ is set to filter out the matching pairs whose cosine similarity is greater than θ to generate the matching set K match ; The knowledge point coverage C is obtained according to the following formula 知识 , which is used to measure teaching integrity; Where w k is the matching set K match The weight of the kth matching pair in the course knowledge point set K ref If the mark in the middle is "important", then w k =1; if the knowledge point in the kth matching pair is in the course knowledge point set K ref If the mark in the middle is "normal", then w k =2;k teach 、k ref They are the kth matching pairs from the classroom knowledge point set K teach The knowledge points and the knowledge points from the course set K ref Knowledge point, sim(·) is the cosine similarity, w r is the set of course knowledge points K ref The weight of the rth knowledge point in the course knowledge point set K ref If the mark in the middle is "important", then w r =2, if the rth knowledge point is in the course knowledge point set K ref If the mark in the middle is "normal", then w r =1; The concept association coverage checking method is: Step B1. Perform one-hot encoding on each edge in the classroom teaching knowledge graph and the course reference knowledge graph to generate a type identification vector t(e); Step B2. In the course reference knowledge graph, the associated edges marked as "important" are assigned a weight of 2, and the associated edges marked as "ordinary" are assigned a weight of 1. The edges are normalized and mapped to the interval [0, 1] to obtain the associated edge weight vector w(e); the type identification vector t(e) and the associated edge weight vector w(e) are concatenated to form the edge feature vector f e , and construct the edge feature matrix F E ; Step B3. Transform the edge feature vector f e Input into the graph attention network, the graph attention network aggregates neighbor node information and dynamically updates the node embedding according to the following formula: Where h′ i is the updated embedding vector of node i, a ij is the attention coefficient that measures the relative importance of node j to node i, W is the learnable weight matrix used to linearly transform node features, σ is the activation function, N(i) is the set of nodes associated with node i, and h j is the embedding vector of node j, b is the weight basis coefficient that balances the global impact of edge weights on node embedding updates, and w ij (e) is the weight vector of the associated edge between node i and node j; Step B4. Combine the edge feature vector and the node embedding vector to construct a multi-dimensional knowledge point association vector to represent the semantic and structural features of the association, and quantitatively evaluate the association integrity between knowledge points according to the following formula: 完整性 , Where, E teach is the associated set in the classroom teaching knowledge graph, E ref is the associated set in the course reference knowledge graph, β t(e) is the association type weight, S coon (e) is the semantic similarity score between the knowledge point association vectors.

5. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 4 is characterized in that: The method for constructing a multi-dimensional knowledge point association vector is: embedding vectors h of node i and node j i ′、h j ′, and edge eigenvector fe ij Splice in sequence to generate the splicing vector V concat =[h i ′;h j ′;fe ij ], using Hadamard product to enhance the correlation of interactive features and generate enhanced vector V interact =h i ′⊙h j ′;⊙fe ij ,according to Generate knowledge point association vector γ is a learning parameter.

6. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 1 is characterized in that: The method described in step 3 for evaluating the logical coherence of teaching steps using the elastic path matching algorithm includes the following steps: Step C1. Use the improved depth-first search algorithm combined with timestamps and teaching logic constraints to give priority to accessing strongly connected nodes containing timestamp information, and serialize the classroom teaching knowledge graph into a node sequence P of the actual teaching path. teach =[n1,n2,…,n M ],n M is the Mth node, where M is the total number of nodes in the classroom teaching knowledge graph; Step C2. Refer to the order of the textbook and the depth-first search traversal to serialize the course reference knowledge graph into the node sequence P of the ideal teaching path ref =[n′1,n′2,…,n′ Q ],n′ Q is the Qth node in the course reference knowledge graph, where Q is the number of nodes in the course reference knowledge graph; Step C3. Initialize the (M+1)×(N+1) distance matrix D, where D[p][q] is the node sequence P teach The first p nodes and the node sequence P ref The minimum matching cost of the first q nodes; Step C4. Fill the distance matrix according to the following dynamic programming formula, backtrack from D[M][N], record the matching, insertion, and deletion operations, and generate the optimal alignment path. Where, w(P teach [p-1]) is the node P teach The weight of [p-1], Cost(P teach [p-1],P ref [q-1]) represents P teach [p-1] and P ref [q-1] semantic matching value, if it matches, Cost = 0, otherwise Cost = ∞; Step C5. Calculate the global similarity Sim according to the following formula 全 , quantify the logical consistency between the actual teaching path and the ideal teaching path, and the global similarity Sim 全 The closer it is to 1, the higher the logical consistency between the actual teaching path and the ideal teaching path. Where, The maximum cost is the cost of deleting all nodes and inserting all nodes. Since teachers are encouraged to supplement and expand content, there is no penalty for the insertion operation; Step C6. In the generated optimal alignment path, check whether there are any violations of the knowledge graph logical dependencies. For each logical conflict detected, penalize it by reducing the overall logical consistency score. The formula for calculating the rationality of time allocation in step 3 is: Where, Time reason is the rationality score of time allocation for knowledge points, It is the time when knowledge points are actually explained in class. is the ideal time to explain a knowledge point, and a is the allowable error ratio.

7. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 1 is characterized in that: In step 4, the method for constructing the hierarchical rule base is: based on the course reference knowledge map or teaching standards, mining the knowledge point progression rules, defining the knowledge point dependency rules, dividing the knowledge points into levels according to Bloom's cognitive taxonomy, and assigning a hierarchical label to each knowledge point through a clustering algorithm; The hierarchy consists of four layers, namely, recognition layer L1, understanding layer L2, application layer L3, and analysis layer L4; The method for evaluating the compliance of the knowledge point dependency relationship and the rationality of the hierarchical distribution of classroom teaching content is as follows: Parse the classroom teaching knowledge graph based on the hierarchical rule base, extract knowledge point attributes including name, hierarchy, and dependency, and construct a dependency graph; Calculate the compliance rate of knowledge point dependencies to quantify whether the classroom dependencies conform to the hierarchical progressive logic. The closer the compliance rate is to 1, the more the dependencies conform to the hierarchical progressive logic. The reference course refers to the hierarchical distribution of the knowledge graph, measures the rationality of the overall proportion of knowledge points at different levels, performs hierarchical span detection on the dependency relationship of knowledge points, and identifies and corrects discontinuous jumps in the dependency relationship.

8. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 1 is characterized in that: In step 5, the matching degree of the associated edge density between the classroom teaching knowledge graph and the course reference knowledge graph is calculated according to the following formula: Where DM is the density matching degree of the associated edge, a is the density difference weight coefficient, β is the redundant association penalty coefficient, R is the redundant association ratio, ε is the allowed density difference error ratio, and E teach is the total number of associated edges of all nodes in the classroom teaching knowledge graph, E ref is the total number of associated edges of all nodes in the course reference knowledge graph, and Q is the total number of all nodes in the course reference knowledge graph; The path generation method of the key knowledge in the classroom teaching knowledge graph is as follows: traverse any two key knowledge point node pairs (u, v) in the classroom teaching knowledge graph through depth-first search, generate all paths, and count the total number of paths from u to v, which is recorded as Set the maximum path length, filter out the paths with decreasing trend in the teaching stage sequence based on the teaching sequence, retain the paths with non-decreasing trend, and form the actual path set Paths u→v ={P1,P2,...,P V }, the actual number of paths is The path coverage PC of key knowledge in the classroom teaching knowledge graph is: Where K key is the set of key knowledge pairs in the knowledge graph taught in class, P ideal is the number of ideal association paths obtained based on the course reference knowledge graph; The path diversity analysis method is as follows: paths with a length of 1 to 2 steps are classified as short paths to reflect the association of basic knowledge; paths with a length of ≥ 3 steps are classified as medium-long paths to reflect the depth of knowledge and the complexity of association; the number of paths of different lengths is counted, and the proportion of paths with a length of 1, P, is calculated. l , N l is the number of paths of length l, N total is the total number of paths; the entropy value of the path number is calculated and normalized to obtain the path diversity index value, which is used to measure the uniformity of the path length distribution.

9. The multi-dimensional dynamic evaluation method for classroom teaching content based on dual knowledge graphs according to claim 1 is characterized in that: In step 6, the method of using the analytic hierarchy process to weight the comprehensive scoring of the teaching content quality is as follows: According to the teaching objectives and evaluation focus, the first-level dimensions of teaching content quality evaluation are determined, including: teaching content coverage W1, teaching logic and time allocation W2, teaching structure compliance W3, and knowledge point relevance W4; An evaluation panel consisting of educational experts, subject research staff, and frontline teachers was invited to compare the dimensions pairwise based on the importance of the teaching objectives, assigning values ​​using a 1-9 scale. According to the pairwise comparison results of the review group, the judgment matrix A is constructed, the maximum eigenvalue and consistency index CI of the judgment matrix A are calculated, and according to the dimension of the judgment matrix A, the corresponding random consistency index RI is found to obtain the consistency ratio CR. If CR < 0.1, the judgment matrix is ​​considered to have satisfactory consistency and pass the test; The normalized eigenvector W of the judgment matrix A is used as the weight of each first-level dimension, W = [w1 + w2 + w3 + w4], satisfying ∑W = 1; Score each dimension of the judgment matrix A and generate a standardized score S using the minimum-maximum standardization method t ∈[0,1], according to the weight W and score S of each dimension t , get the comprehensive score Score, Score = w1×S1+w2×S2+w3×S3+w4×S4; Grading is based on the comprehensive score: Score ≥ 0.8 is excellent, the teaching design is reasonable and no adjustment is required; 0.6 ≤ Score < 0.8 is good and requires local optimization; Score < 0.6 is unsatisfactory and requires reconstruction of the knowledge graph or resetting of teaching objectives.

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