Dynamic course planning method based on knowledge graph

Abstract

The invention relates to the technical field of intelligent education planning, and discloses a dynamic course planning method based on a knowledge graph. The method comprises the following steps: acquiring real-time learning data including knowledge point mastering degree, learning behavior and progress; and performing association analysis on the data by using the subject knowledge graph to generate a learning state representation vector reflecting knowledge point association strength and path dependency degree. And inputting the vector into a course planning model for calculation to obtain an adjustment scheme containing the knowledge points to be strengthened, the path rearrangement sequence and the resource index. According to the scheme, the node weight of the corresponding learner in the knowledge graph is updated, and a dynamically evolved personalized knowledge graph is formed. And generating a next-stage learning task instruction based on the graph, wherein a logic mapping relationship between the to-be-learned knowledge point sequence and a preset learning target is clearly revealed. According to the method, structured traceability and diagnosis of learning weak links are realized, and an interpretable personalized learning path with a clear logic basis can be provided.

Description

Technical Field

[0001] This invention relates to the field of intelligent education planning technology, specifically a dynamic curriculum planning method based on knowledge graphs. Background Technology

[0002] Currently, adaptive learning systems generally use isolated data points such as learner test scores, answer accuracy, or learning duration for evaluation and recommendation. These methods treat knowledge points as discrete units, predicting the next content to be learned through rule engines or machine learning models. Their recommendation logic often relies on statistical correlations of historical behavior or pre-set difficulty levels, lacking in-depth mining of the inherent logical connections and dependencies between knowledge points. Knowledge graphs in this field are mostly used for static knowledge structure display or fixed-path resource navigation, and have not yet been deeply coupled with the learner's real-time state to drive dynamic programming.

[0003] Existing technical solutions have shortcomings. Learning status diagnosis remains at the level of superficial data analysis, failing to reveal the root cause of difficulties in learning subsequent related knowledge points due to a weak grasp of prior knowledge—that is, lacking the ability to structurally trace the source of knowledge weaknesses. Course adjustment plans are usually just lists of learning content or sequences of resources, lacking interpretability, and learners cannot understand the logical connection between the current learning task and the overall learning objectives. Static knowledge graphs cannot reflect the dynamic changes in an individual learner's cognitive structure, resulting in an information loop between the planning model and the knowledge ontology, limiting the accuracy and interpretability of adaptive adjustments.

[0004] The problem to be solved is to develop a dynamic curriculum planning method that can integrate the inherent logic of knowledge with the learner's real-time state, perform deep correlation diagnosis, and generate interpretable planning instructions. The key lies in using the topological relationships of the knowledge graph to perform correlation analysis on learning data, in order to generate a state representation that reflects the knowledge structure and learning process, and based on this, dynamically adjust the individualized view of the knowledge graph, thereby driving the generation of personalized learning paths with clear logical mapping relationships. Summary of the Invention

[0005] The purpose of this invention is to provide a dynamic curriculum planning method based on knowledge graphs to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, this invention provides a dynamic curriculum planning method based on knowledge graphs, the method comprising: Acquire a real-time learning data set of the target learner, the real-time learning data set including the current knowledge point mastery sequence, the learning behavior pattern sequence and the learning progress time series data; The pre-constructed subject knowledge graph is invoked to perform correlation analysis on the real-time learning data set to generate a learning state representation vector, which includes the knowledge point correlation strength, learning path dependence degree, and identification of weak links in ability. The learning state representation vector is input into a preset course planning model for dynamic path calculation to generate a set of course adjustment schemes for the current moment. The set of course adjustment schemes includes a list of knowledge points to be strengthened, a learning path rearrangement sequence, and a supplementary teaching resource index. Update the node weights corresponding to the target learner in the subject knowledge graph according to the set of course adjustment schemes, and generate an updated personalized knowledge graph for the learner. Based on the updated learner-personalized knowledge graph, a learning task instruction for the next learning stage is generated. The learning task instruction includes a mapping of the relationship between the sequence of knowledge points to be learned and the preset learning objectives.

[0007] Preferably, the step of calling a pre-constructed subject knowledge graph to perform correlation analysis on the real-time learning dataset to generate a learning state representation vector includes: Extract the knowledge nodes and the edges connecting the nodes that correspond to the mastery sequence of the current knowledge point from the subject knowledge graph. For each knowledge node, calculate the mastery deviation value of the target learner for the knowledge node. The mastery deviation value is the difference between the preset mastery threshold of the knowledge node and the corresponding value in the mastery sequence of the current knowledge point. Based on the learning behavior pattern sequence, the learning behavior characteristics of the target learner at each knowledge node are analyzed. The learning behavior characteristics include the distribution of single learning duration, the number of repeated learning sessions, and the type of interactive operation. The knowledge point association strength is calculated by combining the weights of the associated edges between the nodes and the mastery deviation value. The knowledge point association strength is the weighted sum of the mastery deviation values ​​of the upstream and downstream nodes of the associated edge. Based on the time-series data of the learning progress and the dependency relationship between knowledge nodes, the learning path dependency is calculated. The learning path dependency is the cumulative value of the influence coefficients of learned nodes on unlearned nodes.

[0008] Preferably, calculating the association strength of the knowledge points includes: Obtain the predecessor-successor relationships between knowledge nodes in the subject knowledge graph and determine the directionality of each associated edge; For each associated edge, the mastery deviation value of its upstream node and the mastery deviation value of its downstream node are multiplied to obtain the original associated value of the associated edge. Multiply the original association value by the preset teaching weight of the association edge to obtain the weighted association value of the association edge; The weighted association values ​​of all associated edges are normalized to generate a set of normalized weighted association values. Calculate the statistical mean of the normalized weighted association value set, and use the statistical mean as the final value of the association strength of the knowledge point.

[0009] Preferably, the step of inputting the learning state representation vector into a preset course planning model for dynamic path calculation processing to generate a set of course adjustment schemes for the current moment includes: The association strength of the knowledge points is compared with a preset association strength threshold, and target association edges with association strength lower than the threshold are selected. The knowledge point pairs corresponding to the target association edges constitute the list of knowledge points to be strengthened. The unlearned knowledge nodes are sorted according to the learning path dependency to generate an initial learning path sequence; Based on the identification of the weak links, the initial learning path sequence is processed by node insertion, and a preparatory knowledge point node is inserted before the knowledge node corresponding to the weak link to form the learning path rearrangement sequence. Based on the attributes of the knowledge nodes in the learning path rearrangement sequence, the corresponding teaching resource identifiers are matched from the teaching resource library to generate the supplementary teaching resource index; The list of knowledge points to be strengthened, the reordered sequence of learning paths, and the index of supplementary teaching resources are packaged together to form the course adjustment scheme set.

[0010] Preferably, the step of performing node insertion processing on the initial learning path sequence based on the weak link identifier, inserting a preliminary knowledge point node before the knowledge node corresponding to the weak link to form the learning path rearrangement sequence, includes: The weak link identifiers are analyzed to determine the node identifiers of the weak knowledge nodes and their levels in the subject knowledge graph; In the subject knowledge graph, find all direct predecessor nodes of the weak knowledge node to form a predecessor node set; Calculate the teaching contribution of each node in the predecessor node set to the weak knowledge node. The teaching contribution is determined based on the increase in the mastery of the weak knowledge node after the predecessor node is mastered in the historical learner learning data. Select the predecessor node with the highest teaching contribution as the preparatory knowledge point node to be inserted; In the initial learning path sequence, the preliminary knowledge point node is inserted before the weak knowledge node, and the order of subsequent nodes is adjusted to generate an intermediate path sequence; The intermediate path sequence is subjected to loop detection and elimination processing to ensure that there are no cyclic dependencies in the sequence, and finally the learned path rearrangement sequence is formed.

[0011] Preferably, the step of updating the node weights corresponding to the target learner in the subject knowledge graph according to the set of course adjustment schemes, and generating an updated personalized knowledge graph for the learner, includes: Extract the list of knowledge points to be strengthened from the set of course adjustment plans, and obtain the target strengthening weight for each knowledge point in the list; The target enhancement weight is weighted and fused with the historical weight of the corresponding knowledge node in the subject knowledge graph to generate the updated weight of the knowledge node; Based on the learning path rearrangement sequence, the teaching order weights of the associated edges between knowledge nodes are adjusted. The teaching order weights are calculated based on the order of the knowledge nodes connected by the associated edges in the learning path rearrangement sequence. Based on the supplementary teaching resource index, new teaching resource tags are bound to the associated knowledge nodes, and the resource richness score of the nodes is updated. By integrating the knowledge nodes with updated weights, the related edges with adjusted teaching order weights, and the node data bound with new labels, the updated learner-personalized knowledge graph that reflects the latest learning status of the target learner is constructed.

[0012] Preferably, the step of weightedly fusing the target enhancement weight with the historical weight of the corresponding knowledge node in the subject knowledge graph to generate the updated weight of the knowledge node includes: Obtain the target learner's historical access frequency and historical practice accuracy for the knowledge nodes; A frequency weighting factor is calculated based on the historical access frequency, and the frequency weighting factor is positively correlated with the historical access frequency. A correctness weighting factor is calculated based on the historical practice accuracy rate, and the correctness weighting factor increases when the accuracy rate is lower than a preset standard. The target enhancement weight, the frequency weight factor, and the accuracy weight factor are input into the weight fusion function, and the weight fusion function outputs the comprehensive weight adjustment amount of the knowledge node. The overall weight adjustment is added to the historical weight of the knowledge node to obtain the updated weight of the knowledge node, and it is ensured that the updated weight does not exceed the maximum weight limit preset by the system.

[0013] Preferably, the step of generating learning task instructions for the next learning stage based on the updated learner-personalized knowledge graph includes: From the updated learner personalized knowledge graph, knowledge nodes with weights exceeding the activation threshold are extracted to form a set of nodes to be activated. Based on the weights of the associated edges between nodes in the updated learner personalized knowledge graph, the learning sequence is planned for the nodes in the set of nodes to be activated, and a preliminary learning flow is generated. The preliminary learning flow is compared with the preset teaching syllabus requirements to ensure that the preliminary learning flow covers the set of core knowledge points specified in the teaching syllabus; A suitable learning duration suggestion is assigned to each knowledge node in the initial learning stream. The learning duration suggestion is calculated based on the updated weight of the knowledge node, the content complexity, and the historical average learning speed of the target learner. The data structure containing the set of nodes to be activated, the learning order, the coverage status of the core knowledge point set, and the suggested learning duration is encapsulated into the learning task instruction.

[0014] Preferably, the suggestion to allocate an appropriate learning duration for each knowledge node in the initial learning stream includes: Obtain a content complexity score for a knowledge node, the content complexity score being determined based on the number of sub-concepts contained in the knowledge node, its level of abstraction, and the number of associated external resources; The average time per unit spent by the target learner when learning knowledge nodes of similar complexity in the past is used as the benchmark learning time. The duration adjustment coefficient is calculated based on the updated weight of the knowledge node, and the duration adjustment coefficient is directly proportional to the updated weight. Multiply the baseline learning duration by the duration adjustment coefficient to obtain the initial suggested duration; Based on the system's set total time limit for a single learning phase, the initial suggested time for all knowledge nodes in the preliminary learning flow is scaled proportionally so that the sum of the suggested times for all nodes meets the total time limit. Finally, the suggested learning time for each node is determined.

[0015] Preferably, calculating the teaching contribution of each node in the predecessor node set to the weak knowledge node includes: Obtain a set of historical learner learning data, which records the time sequence information of the mastery of each knowledge node by multiple historical learners during the learning process; From the historical learner learning data set, select all historical learning records that contain the weak knowledge nodes and each of their predecessor nodes; For each predecessor node in the set of predecessor nodes, perform the following steps: In the subset of historical learning records, the historical moment when the predecessor node changed from the "not mastered" state to the "mastered" state is identified; The number of learners whose mastery of the weak knowledge nodes improved beyond a preset improvement threshold within a preset observation time window after the historical time point is counted as the number of learners who effectively improved their knowledge. The total number of historical learners whose predecessor nodes have been transformed into the "mastered" state in the subset of historical learning records is counted. Calculate the ratio of the number of people who have effectively improved to the total number of historical learners, and determine the ratio as the teaching contribution of the predecessor node to the weak knowledge node.

[0016] Compared with the prior art, the beneficial effects of the present invention are: By invoking a pre-constructed subject knowledge graph to perform correlation analysis on real-time learning data, a learning state representation vector is generated, containing the strength of knowledge point associations and the dependence of learning paths. This method goes beyond conventional approaches to state assessment based on isolated scores. It quantifies the influence of currently mastered knowledge points on subsequent or related knowledge points from the perspective of the knowledge network's topological structure, and accurately identifies the node position and dependencies of the learning process within a pre-defined knowledge path. This enables a diagnosis of learning states from surface statistics to deep structural causes, accurately pinpointing cascading skill gaps caused by weaknesses in specific prior knowledge, and providing a structural basis for subsequent interventions.

[0017] The system updates the node weights corresponding to the target learner in the subject knowledge graph based on the results of dynamic path calculation, generating a continuously evolving personalized knowledge graph for the learner. Based on this graph, learning task instructions are generated, containing a mapping between the sequence of knowledge points to be learned and the pre-set learning objectives. This transforms the general subject knowledge graph into a personalized model that dynamically reflects the individual's cognitive state. Feedback from course adjustments directly impacts the knowledge representation layer, making the knowledge graph itself a dynamic cognitive map that records and reflects the learning process. The generated learning instructions not only specify the learning content but also clearly present the role of each knowledge point in achieving the final learning objective and its position in the knowledge structure through relational mapping. This makes the adaptive recommendation decision logic transparent and interpretable, enhancing the rationality of learning path planning and learners' willingness to follow. Attached Figure Description

[0018] Figure 1 This is a schematic diagram illustrating the working principle of the knowledge graph-based dynamic curriculum planning method described in this invention. Figure 2 A flowchart for generating learning state representation vectors; Figure 3 A flowchart for generating a set of course adjustment plans; Figure 4 A bar chart comparing the richness of knowledge point resources; Figure 5 A graph analyzing the teaching contribution of precursor knowledge nodes. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Please see Figure 1 This invention provides a dynamic curriculum planning method based on knowledge graphs. The method includes: acquiring a real-time learning data set of a target learner, which includes a current knowledge point mastery sequence, a learning behavior pattern sequence, and learning progress time-series data; calling a pre-constructed subject knowledge graph to perform association analysis processing on the real-time learning data set, generating a learning state representation vector containing knowledge point association strength, learning path dependence, and weak link identifiers; inputting the learning state representation vector into a preset curriculum planning model for dynamic path calculation processing, generating a curriculum adjustment scheme set for the current moment, which includes a list of knowledge points to be strengthened, a learning path rearrangement sequence, and a supplementary teaching resource index; updating the node weights corresponding to the target learner in the subject knowledge graph according to the curriculum adjustment scheme set, generating an updated learner-personalized knowledge graph; and generating a learning task instruction for the next learning stage based on the updated learner-personalized knowledge graph, which includes a relationship mapping between the sequence of knowledge points to be learned and preset learning objectives.

[0021] Example 1: See Figure 2The system utilizes a pre-constructed subject knowledge graph to perform correlation analysis on the real-time learning dataset, generating a learning state representation vector. This process involves extracting knowledge nodes and inter-node connections from the subject knowledge graph that correspond to the current knowledge point's mastery sequence. For each knowledge node, the system calculates the learner's mastery deviation value, which is the difference between the node's preset mastery threshold and the corresponding value in the current knowledge point's mastery sequence. Based on the learning behavior pattern sequence, the system analyzes the learner's learning behavior characteristics at each knowledge node, including the distribution of single learning duration, the number of repeated learning sessions, and the type of interactive operation. Combining the weights of the inter-node connections with the mastery deviation value, the system calculates the knowledge point association strength, which is the weighted sum of the mastery deviation values ​​of upstream and downstream nodes along the association edge. Based on the dependencies between learning progress time-series data and knowledge nodes, the system calculates the learning path dependency, which is the cumulative influence coefficient of learned nodes on unlearned nodes. The specific steps for calculating the knowledge point association strength involve obtaining the predecessor-successor relationships between knowledge nodes in the subject knowledge graph and determining the directionality of each association edge. For each associated edge, the mastery deviation values ​​of its upstream and downstream nodes are multiplied to obtain the original associated value. This original associated value is then multiplied by the edge's preset teaching weight to obtain the weighted associated value. All weighted associated values ​​are normalized to generate a normalized set of weighted associated values. The statistical mean of this normalized set of weighted associated values ​​is calculated and used as the final value for the knowledge point association strength.

[0022] In practical implementation, the dynamic curriculum planning method based on knowledge graphs requires processing specific example data during the generation of learning state representation vectors. In an implementation scenario involving junior high school mathematics, the pre-constructed subject knowledge graph includes "algebraic expressions," "linear equations in one variable," "inequalities," and "linear functions." There is a connection edge between the knowledge node "algebraic expression" and the knowledge node "linear equation in one variable," with a preset teaching weight defined by the teaching logic. Another connection edge exists between the knowledge node "linear equation in one variable" and the knowledge node "linear function." The real-time learning data set of the target learner is obtained, with the current knowledge point mastery sequence recorded as {"algebraic expression": 85, "linear equation in one variable": 70}, and the preset mastery threshold sequence as {"algebraic expression": 90, "linear equation in one variable": 85, "linear function": 80}. The learning behavior pattern sequence includes a single learning duration distribution of [20, 30, 25] minutes, 3 repeated learning sessions, and interactive operation types of "video viewing" and "multiple-choice question practice" for the knowledge node "algebraic expression"; and a single learning duration distribution of [15, 20] minutes, 2 repeated learning sessions, and interactive operation type of "text and image reading" for the knowledge node "linear equation in one variable". The learning progress time sequence data shows that the learning completion time of the knowledge node "algebraic expression" is earlier than that of the knowledge node "linear equation in one variable".

[0023] A pre-constructed subject knowledge graph is used to perform correlation analysis on the real-time learning dataset. First, the knowledge nodes "algebraic expression" and "linear equation in one variable" corresponding to the current knowledge point mastery sequence, along with their associated edges, are extracted from the subject knowledge graph. Simultaneously, the knowledge node "linear function" which is not in the mastery sequence but has an association is extracted. For the knowledge node "algebraic expression," the mastery deviation value of the target learner is calculated as a preset mastery threshold of 90 minus the current mastery of 85, resulting in a value of 5. For the knowledge node "linear equation in one variable," the mastery deviation value is calculated as a preset mastery threshold of 85 minus the current mastery of 70, resulting in a value of 15. Since there is no current mastery data for the knowledge node "linear function," its mastery deviation value can be considered as the preset threshold or handled by default. Based on the learning behavior pattern sequence, the learning behavior characteristics of the target learner at each knowledge node are analyzed. For the knowledge node "algebraic expression," the learning behavior characteristics are quantified as high learning duration and repetition frequency; for the knowledge node "linear equation in one variable," the learning behavior characteristics are quantified as medium learning duration and repetition frequency.

[0024] In some embodiments, the association strength of knowledge points is calculated by combining the weights of the edges connecting nodes and the mastery deviation value. The predecessor-successor relationships between knowledge nodes in the subject knowledge graph are obtained to determine the directionality of the edges. The knowledge node "algebraic expression" is a predecessor of the knowledge node "linear equation in one variable," and the knowledge node "linear equation in one variable" is a predecessor of the knowledge node "linear function." For the edge connecting the knowledge nodes "algebraic expression" and "linear equation in one variable," the mastery deviation value 5 of the upstream node "algebraic expression" is multiplied by the mastery deviation value 15 of the downstream node "linear equation in one variable" to obtain the original association value 75. This original association value 75 is then multiplied by the preset teaching weight 0.8 of the edge to obtain the weighted association value 60. For the edge connecting the knowledge nodes "linear equation in one variable" and "linear function," assuming the mastery deviation value of the upstream node "linear equation in one variable" is 15, and the mastery deviation value of the downstream node "linear function" uses its preset threshold of 80 as the default value, the original association value is calculated to be 1200. This is then multiplied by the preset teaching weight of 0.6 for this association edge, resulting in a weighted association value of 720. The weighted association values ​​of all association edges are normalized so that the values ​​fall between 0 and 1, generating a normalized set of weighted association values. The statistical mean of the normalized set of weighted association values ​​is calculated, and this statistical mean is used as the final value for the knowledge point association strength.

[0025] It is understandable that the learning path dependency is calculated based on the time-series data of the learning progress and the dependencies between knowledge nodes. The learning path dependency is the cumulative value of the influence coefficients of learned nodes on unlearned nodes. Learned nodes include "algebraic expressions" and "linear equations in one variable," while unlearned nodes include "linear functions." The influence coefficient of the knowledge node "algebraic expression" on the knowledge node "linear function" is calculated through the transitive weight of the intermediate node "linear equation in one variable." The knowledge node "linear equation in one variable" has a direct influence coefficient on the knowledge node "linear function." The indirect influence coefficient of the knowledge node "algebraic expression" is added to the direct influence coefficient of the knowledge node "linear equation in one variable" to obtain the specific numerical value of the learning path dependency.

[0026] In practice, the specific steps for calculating the association strength of knowledge points involve explicit mathematical operations. Optionally, the weighted association value of the associated edges can be calculated using the following formula: in: Indicates from knowledge nodes Pointing to knowledge nodes The weighted association value of the associated edges, This indicates the preset teaching weight of the associated edge. Represents upstream knowledge nodes The deviation value of mastery, Representing downstream knowledge nodes The mastery deviation value is calculated. Based on this formula, the specific weighted correlation value of each related edge in the subject knowledge graph can be calculated sequentially. Then, all weighted correlation values ​​are normalized, for example, using a minimum-maximum normalization method to map all values ​​to the [0,1] interval. Finally, the arithmetic mean of the normalized value set is calculated, and this mean is determined as a quantitative indicator representing the overall knowledge structure's interconnectivity, i.e., the strength of knowledge point associations. In some embodiments, teaching weights are preset. The assigned values ​​are based on the experience of subject teaching experts and reflect the knowledge nodes. Knowledge nodes The strength of support in cognitive logic.

[0027] Example 2: See Figure 3 The learning state representation vector is input into a preset curriculum planning model for dynamic path calculation, generating a set of curriculum adjustment schemes for the current moment. This process involves comparing the association strength of knowledge points with a preset association strength threshold, filtering out target association edges with association strength below the threshold, and forming a list of knowledge points to be strengthened based on the knowledge point pairs corresponding to these target association edges. Unlearned knowledge nodes are sorted according to learning path dependency to generate an initial learning path sequence. Based on the identification of weak links, node insertion processing is performed on this initial learning path sequence, inserting preparatory knowledge point nodes before the knowledge nodes corresponding to the weak links, forming a learning path rearrangement sequence. Based on the attributes of the knowledge nodes in the learning path rearrangement sequence, corresponding teaching resource identifiers are matched from the teaching resource library to generate a supplementary teaching resource index. The list of knowledge points to be strengthened, the learning path rearrangement sequence, and the supplementary teaching resource index are packaged to form a set of curriculum adjustment schemes. The process of inserting nodes into the initial learning path sequence based on the identification of weak links, inserting preparatory knowledge point nodes before the knowledge nodes corresponding to the weak links, forms a learning path rearrangement sequence. This process involves parsing the identification of weak links, determining the node identifier of the weak knowledge nodes, and their level in the subject knowledge graph. In the subject knowledge graph, all direct predecessor nodes of the weak knowledge node are identified, forming a predecessor node set. The teaching contribution of each node in this predecessor node set to the weak knowledge node is calculated, based on the percentage increase in mastery of the weak knowledge node after the predecessor node was mastered in historical learner data. The predecessor node with the highest teaching contribution is selected as the preparatory knowledge point node to be inserted. In the initial learning path sequence, this preparatory knowledge point node is inserted before the weak knowledge node, and the order of subsequent nodes is adjusted to generate an intermediate path sequence. Loop detection and elimination processing is performed on this intermediate path sequence to ensure that there are no circular dependencies, ultimately forming a rearranged learning path sequence.

[0028] In practice, the learning state representation vector is input into a pre-defined curriculum planning model for dynamic path calculation, generating a set of curriculum adjustment schemes for the current moment. This process involves decision-making logic based on quantitative indicators. The pre-defined curriculum planning model receives a learning state representation vector containing the knowledge point association strength, learning path dependence, and identification of weak links. The knowledge point association strength is a numerical value, assumed to be 0.35, with a pre-defined association strength threshold of 0.5. The curriculum planning model compares the knowledge point association strength value of 0.35 with the pre-defined association strength threshold of 0.5, determining that the knowledge point association strength is below the threshold. Based on the mapping relationship between association edges and knowledge points, the curriculum planning model filters out all target association edges with association strength below the threshold. The pairs of knowledge points corresponding to these target association edges are extracted to form a list of knowledge points to be strengthened. For example, the list may contain knowledge point pairs such as "solving linear equations in one variable" and "solving inequalities," or "properties of inequalities" and "application of systems of inequalities."

[0029] In some embodiments, unlearned knowledge nodes are sorted according to their learning path dependency to generate an initial learning path sequence. The learning path dependency is a vector representing the degree of influence of learned nodes on subsequent unlearned nodes. Assume that the currently unlearned knowledge nodes include "Inequality Properties," "Inequality Solving," "Application of Inequality Systems," and "Inequality Application Problems." The curriculum planning model sorts the unlearned knowledge nodes in descending order based on their learning path dependency values. Nodes with higher learning path dependency are considered to have a greater impact on the subsequent learning process and should be learned first. For example, the initial learning path sequence generated after sorting might be ["Inequality Properties," "Inequality Solving," "Application of Inequality Systems," "Inequality Application Problems"].

[0030] Based on the identification of weak areas, the initial learning path sequence undergoes node insertion processing. Preparatory knowledge point nodes are inserted before the knowledge nodes corresponding to the weak areas, forming a rearranged learning path sequence. The identification of weak areas is analyzed to determine the node identifiers of weak knowledge nodes; for example, the identified weak knowledge node is "Inequality Solving". The level of the weak knowledge node "Inequality Solving" in the subject knowledge graph is determined to be "Basic Skills Layer". All direct predecessor nodes of the weak knowledge node "Inequality Solving" are found in the subject knowledge graph, forming a predecessor node set. The predecessor node set includes "Basic Properties of Equations" and "Transposition Rules". The teaching contribution of each node in the predecessor node set to the weak knowledge node "Inequality Solving" is calculated. The teaching contribution is determined based on the proportion of improvement in the mastery of the weak knowledge node after the predecessor node is mastered in historical learner learning data. Assuming the calculated teaching contribution of "Basic Properties of Equations" to "Inequality Solving" is 0.8, and the teaching contribution of "Transposition Rules" to "Inequality Solving" is 0.6. The predecessor node with the highest teaching contribution, "Basic Properties of Equality," is selected as the preparatory knowledge point node to be inserted. In the initial learning path sequence ["Properties of Inequality," "Solving Inequalities," "Application of Systems of Inequalities," "Application Problems of Inequalities"], the preparatory knowledge point node "Basic Properties of Equality" is inserted before the weak knowledge point node "Solving Inequalities," generating an intermediate path sequence ["Properties of Inequality," "Basic Properties of Equality," "Solving Inequalities," "Application of Systems of Inequalities," "Application Problems of Inequalities"]. The intermediate path sequence undergoes loop detection and elimination processing, checking for cyclic dependencies. For example, it checks whether "Solving Inequalities" absurdly becomes a predecessor of "Basic Properties of Equality." If no such loop exists, the intermediate path sequence is confirmed as the final learning path rearrangement sequence.

[0031] Understandably, based on the attributes of knowledge nodes in the reordered learning path sequence, corresponding teaching resource identifiers are matched from the teaching resource repository to generate a supplementary teaching resource index. The attributes of a knowledge node include node type, difficulty tag, and associated skill points. For each knowledge node in the reordered learning path sequence, such as "Basic Properties of Equations," its attributes are used as query conditions to retrieve information from the teaching resource repository. The teaching resource repository stores various resources, such as video course numbers, interactive exercise set numbers, and explanatory document identifiers. The matching process returns several teaching resource identifiers most relevant to the "Basic Properties of Equations" node, such as "Video Course V-203" and "Exercise Set P-871." This matching operation is performed on all nodes in the entire reordered learning path sequence, and the resulting set of resource identifiers constitutes the supplementary teaching resource index.

[0032] In practice, the process of inserting nodes into the initial learning path sequence based on the identification of weak links includes a quantitative assessment of teaching contribution. An optional calculation method is based on teaching contribution. This can be obtained by analyzing historical learner data. Represents the predecessor node Weak knowledge points The evaluation process requires querying a historical learning record database, which contains a large number of anonymized historical learner learning trajectory records. For a specific predecessor node in the predecessor node set... For example, regarding "basic properties of equations," the system filters out all learning records in the database that simultaneously contain the node. and weak knowledge nodes The historical learner sample. Systematic statistics show that in the historical learner sample, the predecessor nodes... Number of time points from "not grasped" to "grasped" state Next, the system performs statistical analysis within a preset observation time window following these state transition points. Internally, weak knowledge points The improvement in mastery exceeded the preset improvement threshold. Number of learners Contribution to teaching The calculation formula is: in: Indicates contribution to teaching. This represents an effective increase in the number of participants. Precursor nodes representing the total number of history learners The count of state transitions. The formula calculates a value between 0 and 1; the higher the value, the more likely the predecessor node is known in historical data. Mastering weak knowledge points The more widespread and significant the positive impact, the better. In some embodiments, the observation time window... and raising the threshold These are system-preset parameters used to precisely define the spatiotemporal and degree standards of "effective improvement." By performing the above calculations on all candidate precursor nodes, the quantified teaching contribution value of each node in the precursor node set can be obtained, providing data support for selecting the optimal preparatory knowledge point node.

[0033] Example 3: The process involves updating the node weights corresponding to the target learner in the subject knowledge graph based on the course adjustment scheme set, generating an updated personalized knowledge graph for the learner. This includes extracting a list of knowledge points to be strengthened from the course adjustment scheme set and obtaining the target strengthening weight for each knowledge point in the list. This target strengthening weight is then weighted and fused with the historical weights of the corresponding knowledge nodes in the subject knowledge graph to generate the updated weight for that knowledge node. Based on the learning path rearrangement sequence, the teaching order weights of the edges connecting knowledge nodes are adjusted. These teaching order weights are calculated based on the order in which the knowledge nodes connected by the edges appear in the learning path rearrangement sequence. Based on the supplementary teaching resource index, new teaching resource tags are bound to the associated knowledge nodes, and the resource richness score of the nodes is updated. The updated weighted knowledge nodes, the edges with adjusted teaching order weights, and the node data with the new tags are integrated to construct an updated personalized knowledge graph reflecting the latest learning status of the target learner. Finally, the target strengthening weights are weighted and fused with the historical weights of the corresponding knowledge nodes in the subject knowledge graph to generate the updated weights for the knowledge nodes. This process involves obtaining the target learner's historical access frequency and historical practice accuracy for that knowledge node. A frequency weighting factor is calculated based on historical access frequency, and this factor is positively correlated with historical access frequency. An accuracy weighting factor is calculated based on historical practice accuracy, and this factor increases when the accuracy falls below a preset standard. The target reinforcement weight, the frequency weighting factor, and the accuracy weighting factor are input into a weight fusion function, which outputs a comprehensive weight adjustment for the knowledge node. This comprehensive weight adjustment is added to the historical weights of the knowledge node to obtain the updated weight, ensuring that the updated weight does not exceed the system's preset maximum weight limit.

[0034] In practice, the node weights corresponding to the target learner in the subject knowledge graph are updated according to the set of curriculum adjustment schemes, generating an updated personalized knowledge graph for the learner. This process begins with the analysis of the structured adjustment schemes. A list of knowledge points to be strengthened is extracted from the curriculum adjustment scheme set. This list is a sequence containing several knowledge point identifiers, for example, a list of knowledge points to be strengthened such as [“quadratic equation root-finding formula”, “properties of quadratic function graphs”]. The target strengthening weight for each knowledge point in the list is obtained. This target strengthening weight is calculated and assigned by the curriculum planning model based on the degree of missing knowledge point association strength. The specific implementation of the curriculum planning model involves using the knowledge point association strength value in the learning state representation vector for decision-making. This model quantifies the degree of missing association strength by comparing the knowledge point association strength with a preset association strength threshold, thereby calculating the target strengthening weight. The model first extracts the knowledge point association strength value from the learning state representation vector. This value reflects the tightness of the connection between knowledge nodes, derived from the weighted sum of the mastery deviation values ​​of upstream and downstream nodes on the associated edge. For each knowledge point pair to be evaluated, the model compares the association strength between the knowledge points and a preset association strength threshold, filtering out target association edges with association strength below the threshold. The corresponding knowledge point pairs are then identified as objects to be strengthened. The degree of missing association strength is quantified by the difference between the threshold and the actual association strength value; the larger the difference, the more severe the association loss. For example, the target strengthening weight for the knowledge node "Formula for solving quadratic equations" is 0.3, and the target strengthening weight for the knowledge node "Properties of quadratic function graphs" is 0.25. For the knowledge node "Formula for solving quadratic equations", the target strengthening weight of 0.3 is weighted and fused with the historical weight of 0.5 for the corresponding knowledge node "Formula for solving quadratic equations" in the subject knowledge graph to generate the updated weight for the knowledge node "Formula for solving quadratic equations".

[0035] In some embodiments, the target reinforcement weight is weighted and fused with the historical weight of the corresponding knowledge node in the subject knowledge graph to generate the updated weight of the knowledge node. The specific process includes calling and calculating multi-source data. The historical access frequency and historical practice accuracy of the target learner for the knowledge node "quadratic equation root-finding formula" are obtained. For example, if the historical access frequency is 10 times and the historical practice accuracy is 65%, retrieved from the learning log database, then a frequency weight factor is calculated based on the historical access frequency. The frequency weight factor is positively correlated with the historical access frequency. One optional calculation method is that the frequency weight factor equals the historical access frequency divided by a baseline frequency constant. For example, if the baseline frequency constant is 20, the calculated frequency weight factor is 0.5. The accuracy weight factor is calculated based on the historical practice accuracy. The accuracy weight factor increases when the accuracy is below a preset standard of 70%. Since the historical practice accuracy is 65%, which is below the preset standard, the system uses an inverse proportional function to calculate the accuracy weight factor, resulting in a value of 1.2. The target enhancement weight of 0.3, the frequency weight factor of 0.5, and the accuracy weight factor of 1.2 are input into the weight fusion function. The weight fusion function outputs the comprehensive weight adjustment for the knowledge node "quadratic equation root-solving formula". The weight fusion function can be designed as a linear combination or a more complex nonlinear function, and its output is the comprehensive weight adjustment. The comprehensive weight adjustment is added to the historical weight of 0.5 for the knowledge node "quadratic equation root-solving formula" to obtain the updated weight of the knowledge node "quadratic equation root-solving formula", ensuring that the updated weight does not exceed the system's preset maximum weight limit, for example, the maximum weight limit is 1.0.

[0036] Based on the rearranged learning path sequence, the teaching order weights of the edges connecting knowledge nodes are adjusted. These teaching order weights are calculated according to the order in which the knowledge nodes connected by the edges appear in the rearranged learning path sequence. If the rearranged learning path sequence is ["Basic Properties of Equations", "Solving Inequalities", "Application of Systems of Inequalities"], then the teaching order weight of the edge connecting knowledge node "Basic Properties of Equations" to knowledge node "Solving Inequalities" will be strengthened, and the teaching order weight of the edge connecting knowledge node "Solving Inequalities" to knowledge node "Application of Systems of Inequalities" will also be adjusted accordingly. The specific values ​​of the teaching order weights can be achieved by calculating the positional difference of the nodes in the sequence or by directly assigning a higher calibration value.

[0037] Understandably, based on the supplementary teaching resource index, new teaching resource tags are bound to associated knowledge nodes, and the resource richness score of the nodes is updated. The supplementary teaching resource index contains a series of resource identifiers, such as {"Video Course V-203":["Basic Properties of Equations"], "Interactive Simulation S-45":["Solving Inequalities"]}. According to the index relationship, the system binds the resource identifier "Video Course V-203" as a new teaching resource tag to the attribute of the knowledge node "Basic Properties of Equations". Simultaneously, the original resource richness score of the knowledge node "Basic Properties of Equations" is updated from 3.5. The update logic is to increase the score brought by binding the new resource, for example, by 0.5, making the resource richness score 4.0.

[0038] In practice, the weight fusion function can be a mathematical function with a clearly defined expression. Optionally, the overall weight adjustment amount... The following formula can be used for calculation: in: This represents the overall weight adjustment amount for knowledge nodes, which is the value that needs to be added to the historical weights. The weighting of the target reinforcement is directly derived from the set of course adjustment plans. This represents the frequency weighting factor, which is calculated from historical access frequencies. This represents the accuracy weighting factor, calculated from the accuracy of historical practice sessions. , , It is a preset harmonic coefficient used to balance the proportion of different factors affecting the overall weight adjustment. For example, it can be set to... , , Example values , , Substituting into the formula, we can calculate... Subsequently, the overall weighting adjustment amount will be... Adding this to the historical weight of 0.5 for the knowledge node "Formula for Solving Quadratic Equations" yields 1.02. Since the system's preset maximum weight limit is 1.0, the updated weight of the knowledge node "Formula for Solving Quadratic Equations" is truncated to 1.0. In some embodiments, the harmonic coefficient... , , The values ​​can be optimized by training on historical data using machine learning methods, so that weight updates better reflect the learner's long-term progress.

[0039] See Figure 4This is a bar chart comparing the resource richness scores of knowledge points. The resource richness scores for all knowledge points were higher after binding than before binding, indicating that the resource support capability of knowledge points was improved after binding new teaching resources. The score for "Basic Properties of Equations" showed a more significant increase; the initial score for "Application of Systems of Inequalities" was lower (around 3.0 before binding), but it still showed a steady improvement after binding. This type of chart is typically used in course resource management scenarios to help teaching administrators intuitively understand the empowering effect of "supplemented teaching resources" on knowledge points, providing data reference for subsequent resource allocation.

[0040] Example 4: Generating learning task instructions for the next learning stage based on the updated learner-personalized knowledge graph. The process involves extracting knowledge nodes with weights exceeding the activation threshold from the updated learner-personalized knowledge graph, forming a set of nodes to be activated. Based on the weights of the edges connecting nodes in the updated learner-personalized knowledge graph, a learning sequence is planned for the nodes in this set of nodes to be activated, generating a preliminary learning flow. This preliminary learning flow is compared with the preset syllabus requirements to ensure it covers the core knowledge points specified in the syllabus. A suitable learning duration suggestion is assigned to each knowledge node in the preliminary learning flow. This suggestion is calculated based on the updated weight of the knowledge node, its content complexity, and the target learner's historical average learning speed. A data structure containing the set of nodes to be activated, the learning sequence, the coverage status of the core knowledge point set, and the learning duration suggestion is encapsulated as a learning task instruction. Assigning a suitable learning duration suggestion to each knowledge node in the preliminary learning flow involves obtaining the content complexity score of the knowledge node. This score is determined based on the number of sub-concepts, the level of abstraction, and the number of associated external resources. The average time spent per unit of learning knowledge nodes of similar complexity by the target learner in the past is used as the baseline learning time. A time adjustment coefficient is calculated based on the updated weight of the knowledge node; this coefficient is directly proportional to the updated weight. The baseline learning time is multiplied by this adjustment coefficient to obtain the initial suggested time. Based on the system's set total time limit for a single learning phase, the initial suggested time for all knowledge nodes in this initial learning flow is scaled proportionally so that the sum of the suggested times for all nodes conforms to the total time limit. Finally, a suggested learning time is determined for each node.

[0041] In practice, the process of generating learning task instructions for the next learning stage based on the updated learner-personalized knowledge graph begins with threshold filtering of node weights in the graph. Knowledge nodes with weights exceeding the activation threshold are extracted from the updated learner-personalized knowledge graph, forming a set of nodes to be activated. The activation threshold is a system-preset value, such as 0.6, used to filter out knowledge nodes that require focused attention and learning in the current learning stage. For example, in the updated learner-personalized knowledge graph, the updated weight of the knowledge node "parallelogram property" is 0.85, the updated weight of the knowledge node "trapezoidal median theorem" is 0.72, the updated weight of the knowledge node "rhombus determination" is 0.65, and the updated weight of the knowledge node "rectangle property" is 0.58. Among them, the knowledge nodes "parallelogram properties", "trapezoidal midline theorem" and "rhombus determination" with a weight exceeding the activation threshold of 0.6 are extracted and form the set of nodes to be activated {"parallelogram properties", "trapezoidal midline theorem", "rhombus determination"}, while the knowledge node "rectangle properties" is not included in the current set of nodes to be activated because its weight of 0.58 is lower than the threshold.

[0042] In some embodiments, based on the weights of the edges connecting nodes in the updated learner-personalized knowledge graph, the learning order of nodes in the set of nodes to be activated is planned, generating a preliminary learning flow. In the updated learner-personalized knowledge graph, there is an edge connecting the knowledge node "Parallelogram Properties" and the knowledge node "Rhombus Criterion," with a weight of 0.8 and a direction pointing from "Parallelogram Properties" to "Rhombus Criterion"; there is another edge connecting the knowledge node "Parallelogram Properties" and the knowledge node "Trapezoid Median Theorem," with a weight of 0.5. The system sorts nodes according to the weight and direction of the edges, with nodes having higher edge weights and pointing in the correct direction being the next learning nodes. Based on this rule, the generated preliminary learning flow sequence is ["Parallelogram Properties," "Rhombus Criterion," "Trapezoid Median Theorem"], with the knowledge node "Parallelogram Properties" placed first because it is a strong prerequisite for other nodes. The preliminary learning flow is compared with the preset syllabus requirements to ensure that the preliminary learning flow covers the core knowledge point set specified in the syllabus. The core knowledge points specified in the syllabus include "parallelogram properties," "rhombus criterion," and "rectangle properties." The system checks the initial learning flow ["parallelogram properties," "rhombus criterion," "trapezoidal midline theorem"] and finds that it covers the core knowledge points "parallelogram properties" and "rhombus criterion," but does not include "rectangle properties," and includes the knowledge point "trapezoidal midline theorem," which is not mandatory in the syllabus but recommended by the learning map. The system records this coverage status; the coverage status information indicates that the core knowledge point "rectangle properties" is not included, while the learning flow includes the additional knowledge point "trapezoidal midline theorem."

[0043] A suitable learning time suggestion is assigned to each knowledge node in the initial learning stream. The learning time suggestion is calculated based on the updated weight of the knowledge node, its content complexity, and the target learner's historical average learning speed. For the knowledge node "Parallelogram Property" in the initial learning stream, its content complexity score needs to be obtained. The content complexity score is determined based on the number of sub-concepts, the level of abstraction, and the number of associated external resources contained in the knowledge node "Parallelogram Property." Assuming the system calculates a content complexity score of 7.5, the average time taken by the target learner to learn knowledge nodes of similar complexity in the past is queried and used as the baseline learning time. Assuming the system matches knowledge nodes with complexity scores between 7.0 and 8.0 from the learning history, and the target learner's average learning time is 25 minutes, this 25 minutes is set as the baseline learning time for the knowledge node "Parallelogram Property." A time adjustment coefficient is calculated based on the updated weight of the knowledge node "Parallelogram Property" (0.85), and the time adjustment coefficient is proportional to the updated weight. Multiply the baseline learning time of 25 minutes by the time adjustment factor to obtain the initial suggested time. Based on the system's set total time limit for a single learning phase, the initial suggested time for all knowledge nodes in the initial learning flow is scaled proportionally so that the sum of the suggested times for all nodes conforms to the total time limit. Finally, a suggested learning time is determined for each node. See Table 1.

[0044] Table 1: Suggested Calculation Table for Study Duration In practice, allocating appropriate learning time to each knowledge node in the initial learning flow involves a quantitative calculation process. It's understandable that calculating the time adjustment coefficient requires a clear mathematical relationship. One possible calculation method is the time adjustment coefficient... The following formula can be used for calculation: in: The duration adjustment factor is a multiplier used to amplify or reduce the baseline learning duration. This indicates that the weight affects sensitivity, and is a preset constant greater than 0, for example... . The updated weight of the knowledge node is obtained directly from the updated learner-personalized knowledge graph. The weighted impact threshold is a baseline value used to determine whether adjustment is needed. It is typically set as an activation threshold or an empirical value, for example... Taking the knowledge node "parallelogram properties" as an example, the updated weights... Substitute into the formula The calculation here This refers to the values ​​used in the example calculations in Table 1. Multiplying the baseline learning time of 25 minutes by the time adjustment factor of 1.10 yields an initial suggested time of 27.5 minutes. The system sets a total time limit of 84 minutes for a single learning phase. Repeat the above calculation for all knowledge nodes in the initial learning flow to obtain the sum of the initial suggested times for all nodes. If the sum of the initial suggested times exceeds the total time limit of 84 minutes, it is compressed proportionally according to the proportion of each node's initial suggested time to the total, so that the final suggested learning time for each node equals 84 minutes; if it does not exceed the limit, no compression is required. In some embodiments, the scaling process ensures that the assigned learning task is feasible in terms of total time and conforms to the learning phase plan. The data structure containing the set of nodes to be activated {"parallelogram properties", "trapezoidal midline theorem", "rhombus criterion"}, the learning order ["parallelogram properties", "rhombus criterion", "trapezoidal midline theorem"], the coverage status of the core knowledge points set, and the suggested learning duration is encapsulated into a data object that conforms to the predetermined interface specification. This data object is the learning task instruction for the next learning stage.

[0045] Example 5: Calculating the teaching contribution of each node in the predecessor node set to the weak knowledge node involves obtaining a historical learner learning data set, which records the time sequence information of multiple historical learners' mastery of each knowledge node during the learning process. From this historical learner learning data set, a subset of historical learning records containing the weak knowledge node and each of its predecessor nodes is selected. For each predecessor node in the predecessor node set, the following steps are performed: In this subset of historical learning records, the historical moment when the predecessor node changed from the "not mastered" state to the "mastered" state is identified. The number of historical learners whose mastery of the weak knowledge node improved by more than a preset improvement threshold within a preset observation time window after this historical moment is counted, and recorded as the number of effective improvement participants. The total number of historical learners in this subset of historical learning records who changed the predecessor node to the "mastered" state is counted. The ratio of the number of effective improvement participants to the total number of historical learners is calculated, and this ratio is determined as the teaching contribution of the predecessor node to the weak knowledge node.

[0046] In practice, calculating the teaching contribution of each node in the predecessor node set to the weak knowledge node relies on the statistical analysis of the group's historical learning data. Obtaining the historical learner learning data set is a prerequisite for performing the calculation. The historical learner learning data set is a structured database that records the time-series information of multiple historical learners' mastery of each knowledge node during the learning process. For example, the mastery time-series information is stored in time series form, including learner identifier, knowledge node identifier, timestamp, and the mastery value obtained at that timestamp. From the historical learner learning data set, a subset of historical learning records containing the weak knowledge node and each of its predecessor nodes is selected. Assuming the weak knowledge node is "Application of Newton's Second Law", its predecessor node set contains "Newton's First Law" and "Composition and Decomposition of Forces". The system queries the historical learner learning data set for all historical learner identifiers whose learning records simultaneously contain the nodes "Application of Newton's Second Law" and "Newton's First Law" or "Composition and Decomposition of Forces", and extracts the complete learning trajectory data of these learners to form the subset of historical learning records.

[0047] In some embodiments, for each predecessor node in the predecessor node set, such as the predecessor node "Force Composition and Decomposition", the following steps are performed: In the subset of historical learning records, the historical moment when the predecessor node "Force Composition and Decomposition" changed from the "not mastered" state to the "mastered" state is identified. The system defines the "not mastered" state as the mastery value is consistently below 60, and the "mastered" state as the mastery value first reaches or exceeds 60. By scanning the time series data belonging to each learner in the subset of historical learning records, the specific timestamp when the mastery value of the predecessor node "Force Composition and Decomposition" first jumped from below 60 to 60 or above is found. Each such timestamp corresponds to a state transition event of a historical learner. The system counts the number of learners whose mastery of the weak knowledge node "Application of Newton's Second Law" improved beyond a preset threshold within a pre-defined observation window after a historical time point. This number is recorded as the effective improvement count. The observation window is pre-defined as 14 days from the state transition point, and the preset improvement threshold is set to 15. For each learner whose predecessor node state transition occurred, the system checks the increase in their mastery value of the weak knowledge node "Application of Newton's Second Law" within 14 days after the state transition point compared to the mastery value at the transition point. If the increase exceeds 15, the learner is counted as an effective improvement count. The system also counts the total number of learners whose predecessor node "Composition and Decomposition of Forces" transitioned to the "Mastered" state within a subset of historical learning records. This number represents the count of independent learners who experienced the aforementioned state transition event, regardless of whether their subsequent mastery of the weak knowledge node improved. The ratio of the effective improvement count to the total number of historical learners is calculated, and this ratio is determined as the teaching contribution of the predecessor node "Composition and Decomposition of Forces" to the weak knowledge node "Application of Newton's Second Law".

[0048] It is understandable that the same steps are performed on the other precursor node, "Newton's First Law," to calculate the teaching contribution of the precursor node "Newton's First Law" to the weak knowledge node "Application of Newton's Second Law," ultimately obtaining a quantified value of the teaching contribution of all nodes in the precursor node set. For example, assuming that in the subset of history learning records, for the precursor node "Composition and Decomposition of Forces," the total number of history learners is 200, of which 150 have effectively improved, then the teaching contribution is 150 / 200 = 0.75; for the precursor node "Newton's First Law," the total number of history learners is 180, of which 108 have effectively improved, then the teaching contribution is 108 / 180 = 0.60.

[0049] In practice, the formula for calculating teaching contribution is as follows: in: The contribution to teaching is represented by a real number between 0 and 1. This indicates the number of learners who have effectively improved their knowledge of weak knowledge nodes, specifically the number of learners whose mastery of these weak knowledge nodes has increased beyond a preset threshold within the observation window following the change in the state of the predecessor node. This represents the total number of historical learners, specifically the total number of historical learners whose predecessor nodes have been transformed into the "mastered" state within the subset of historical learning records. An optional data processing method is to calculate the total number of historical learners... In this case, the system needs to deduplicate to ensure that the same learner is counted only once. Even if the learner undergoes multiple "not mastered" to "mastered" state transitions for the same precursor node within different time periods, typically only the first transition event is selected for calculation to avoid duplicate counting interfering with contribution evaluation. In some embodiments, the preset improvement threshold and observation time window parameters are adjusted according to different knowledge domains. For example, for conceptual knowledge points, the observation time window is set shorter, while for skill-based knowledge points, the window is set longer to allow sufficient practice and internalization time. The calculated teaching contribution is then calculated. The decision will be directly used in subsequent node insertion processing. The predecessor node with the highest value is selected as the preparatory knowledge point node to be inserted. This selection method is based on the historical learning patterns of groups and aims to provide the target learner with the knowledge preparation that is most helpful in overcoming their weaknesses.

[0050] See Figure 5 This is a chart analyzing the teaching contribution of precursor knowledge nodes, using a dual-axis display of two core indicators. The "Acceleration Concept" shows the highest number of learners effectively improved and its teaching contribution is the highest, indicating its strongest support for weak knowledge nodes. This chart is used in course path planning scenarios (such as optimizing node associations in knowledge graphs) to help identify precursor nodes with high teaching contributions to weak knowledge points and assist in adjusting the learning path. The ratio of the number of learners effectively improved to the total number of learners reflects the supporting effect of the precursor node on weak knowledge. It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0051] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic course planning method based on a knowledge graph, characterized in that, The method comprises: acquiring a real-time learning data set of a target learner, the real-time learning data set comprising a current knowledge point mastery degree sequence, a learning behavior pattern sequence, and learning progress time series data; calling a pre-constructed subject knowledge graph to perform correlation analysis processing on the real-time learning data set, to generate a learning state representation vector, the learning state representation vector comprising a knowledge point correlation strength, a learning path dependence degree, and a weak link identification of ability; inputting the learning state representation vector into a preset course planning model to perform dynamic path calculation processing, to generate a current-time course adjustment scheme set, the course adjustment scheme set comprising a list of knowledge points to be strengthened, a learning path reordering list, and a supplementary teaching resource index; updating node weights corresponding to the target learner in the subject knowledge graph according to the course adjustment scheme set, to generate an updated learner individualized knowledge graph; generating a learning task instruction for a next learning stage based on the updated learner individualized knowledge graph, the learning task instruction containing a relationship mapping between a sequence of knowledge points to be learned and a preset learning goal. 2.The knowledge graph-based dynamic course planning method of claim 1, wherein, The calling of the pre-constructed subject knowledge graph to perform correlation analysis processing on the real-time learning data set, to generate a learning state representation vector, comprises: extracting knowledge nodes corresponding to the current knowledge point mastery degree sequence and inter-node correlation edges from the subject knowledge graph; for each knowledge node, calculating a mastery degree bias value of the target learner for the knowledge node, the mastery degree bias value being a difference between a preset mastery degree threshold of the knowledge node and a corresponding value in the current knowledge point mastery degree sequence; analyzing learning behavior characteristics of the target learner on each knowledge node according to the learning behavior pattern sequence, the learning behavior characteristics comprising a single learning time length distribution, a repeated learning number, and an interactive operation type; combining the weights of the inter-node correlation edges and the mastery degree bias values, to calculate the knowledge point correlation strength, the knowledge point correlation strength being a weighted sum of the mastery degree bias values of upstream nodes and downstream nodes of the correlation edges; calculating the learning path dependence degree according to the learning progress time series data and a dependence relationship of the knowledge nodes, the learning path dependence degree being an accumulated value of influence coefficients of learned nodes on unlearned nodes. 3.The knowledge graph based dynamic course planning method of claim 2, wherein, The calculation of the knowledge point correlation strength comprises: acquiring a predecessor-successor relationship between knowledge nodes in the subject knowledge graph, to determine a directionality of each correlation edge; for each correlation edge, performing a product operation on the mastery degree bias value of the upstream node and the mastery degree bias value of the downstream node, to obtain an original correlation value of the correlation edge; multiplying the original correlation value by a preset teaching weight of the correlation edge, to obtain a weighted correlation value of the correlation edge; performing normalization processing on the weighted correlation values of all correlation edges, to generate a normalized weighted correlation value set; calculating a statistical mean value of the normalized weighted correlation value set, and taking the statistical mean value as a final value of the knowledge point correlation strength. 4.The knowledge graph based dynamic course planning method of claim 1, wherein, The inputting of the learning state representation vector into the preset course planning model to perform dynamic path calculation processing, to generate a current-time course adjustment scheme set, comprises: The knowledge point association strength is compared with a preset association strength threshold, and a target association edge with an association strength lower than the threshold is screened out, the target association edge corresponding to a knowledge point pair constituting the to-be-strengthened knowledge point list; According to the learning path dependence degree, the unlearned knowledge nodes are sorted to generate an initial learning path sequence; Based on the weak link identifier, node insertion processing is performed on the initial learning path sequence, a preparatory knowledge point node is inserted before the knowledge node corresponding to the weak link to form a learning path reordering sequence; According to the attributes of the knowledge nodes in the learning path reordering sequence, corresponding teaching resource identifiers are matched from a teaching resource library to generate a supplementary teaching resource index; The to-be-strengthened knowledge point list, the learning path reordering sequence and the supplementary teaching resource index are packaged to constitute the course adjustment scheme set. 5.The knowledge graph based dynamic course planning method of claim 4, wherein, The node insertion processing on the initial learning path sequence based on the weak link identifier includes: Analyzing the weak link identifier to determine the node identifier of the weak knowledge node and its level in the subject knowledge graph; All direct predecessor nodes of the weak knowledge node in the subject knowledge graph are found to constitute a predecessor node set; The teaching contribution degree of each node in the predecessor node set to the weak knowledge node is calculated, and the teaching contribution degree is determined based on the improvement proportion of the weak knowledge node mastery degree after the predecessor nodes are mastered in the historical learner learning data; The predecessor node with the highest teaching contribution degree is selected as the to-be-inserted preparatory knowledge point node; In the initial learning path sequence, the preparatory knowledge point node is inserted before the weak knowledge node, and the order of the subsequent nodes is adjusted to generate an intermediate path sequence; Loop detection and elimination processing is performed on the intermediate path sequence to ensure that there is no circular dependency in the sequence, and finally the learning path reordering sequence is formed. 6.The knowledge graph based dynamic course planning method of claim 1, wherein, The node weight corresponding to the target learner in the subject knowledge graph is updated according to the course adjustment scheme set to generate an updated learner personalized knowledge graph, including: Extracting the to-be-strengthened knowledge point list in the course adjustment scheme set to obtain the target strengthening weight of each knowledge point in the list; The target strengthening weight and the historical weight of the corresponding knowledge node in the subject knowledge graph are weighted and fused to generate the updated weight of the knowledge node; According to the learning path reordering sequence, the teaching order weight of the association edge between the knowledge nodes is adjusted, and the teaching order weight is calculated according to the order of the knowledge nodes connected by the association edge in the learning path reordering sequence; Based on the supplementary teaching resource index, new teaching resource tags are bound for the associated knowledge nodes, and the resource richness score of the nodes is updated; The knowledge nodes with updated weights, the association edges with adjusted teaching order weights, and the node data with bound new tags are integrated to build the updated learner personalized knowledge graph reflecting the latest learning state of the target learner. 7.The knowledge graph-based dynamic course planning method of claim 6, wherein, The target reinforcement weight is weighted and fused with a historical weight of a corresponding knowledge node in the discipline knowledge graph to generate an updated weight of the knowledge node, including: obtaining a historical access frequency and a historical practice accuracy of the target learner to the knowledge node; calculating a frequency weight factor according to the historical access frequency, the frequency weight factor being in a positive correlation with the historical access frequency; calculating an accuracy weight factor according to the historical practice accuracy, the accuracy weight factor being increased when the accuracy is lower than a preset standard; inputting the target reinforcement weight, the frequency weight factor and the accuracy weight factor into a weight fusion function, the weight fusion function outputting a comprehensive weight adjustment amount of the knowledge node; adding the comprehensive weight adjustment amount to the historical weight of the knowledge node to obtain the updated weight of the knowledge node, and ensuring that the updated weight does not exceed a maximum weight upper limit preset by the system. 8.The knowledge graph based dynamic course planning method of claim 1, wherein, The learning task instruction of the next learning stage is generated based on the updated learner personalized knowledge graph, including: extracting knowledge nodes with weights exceeding an activation threshold from the updated learner personalized knowledge graph to form a set of to-be-activated nodes; planning a learning sequence for the nodes in the set of to-be-activated nodes according to the associated edge weights between the nodes in the updated learner personalized knowledge graph to generate a preliminary learning flow; comparing the preliminary learning flow with a preset teaching syllabus requirement to ensure that the preliminary learning flow covers a set of core knowledge points specified by the teaching syllabus; suggesting an appropriate learning duration for each knowledge node in the preliminary learning flow, the learning duration being calculated based on the updated weight of the knowledge node, a content complexity and a historical average learning speed of the target learner; encapsulating a data structure containing the set of to-be-activated nodes, the learning sequence, a core knowledge point set coverage status and the learning duration suggestion into the learning task instruction. 9.The knowledge graph based dynamic course planning method of claim 8, wherein, The appropriate learning duration suggestion for each knowledge node in the preliminary learning flow includes: obtaining a content complexity score of the knowledge node, the content complexity score being determined based on a number of sub-concepts, an abstraction degree and a number of associated external resources included in the knowledge node; querying an average unit time consumption of the target learner when learning a similar complexity knowledge node in the history as a baseline learning duration; calculating a time duration adjustment coefficient according to the updated weight of the knowledge node, the time duration adjustment coefficient being in a positive correlation with the updated weight; multiplying the baseline learning duration by the time duration adjustment coefficient to obtain an initial suggested duration; scaling the initial suggested duration of all knowledge nodes in the preliminary learning flow based on a total duration limit of a single learning stage set by the system, so that the sum of the suggested durations of all nodes meets the total duration limit, and finally determining the learning duration suggestion for each node. 10.The knowledge graph based dynamic course planning method of claim 5, wherein, The teaching contribution degree of each node in the set of predecessor nodes to the weak knowledge node is calculated, including: Acquire a historical learner learning data set, wherein a plurality of historical learners' mastery degree time sequence information of each knowledge node in a learning process is recorded in the historical learner learning data set; From the historical learner learning data set, a historical learning record subset containing the weak knowledge node and each predecessor node thereof is screened out; For each of the predecessor node set, the following steps are performed: In the historical learning record subset, a historical time point at which the predecessor node changes from a "not mastered" state to a "mastered" state is identified; The number of historical learners whose mastery degree of the weak knowledge node exceeds a preset improvement threshold in a preset observation time window after the historical time point is counted, and is recorded as an effective improvement number; The total number of historical learners in the historical learning record subset whose all the predecessor nodes change to a "mastered" state is counted; The ratio of the effective improvement number to the total number of historical learners is calculated, and the ratio is determined as the teaching contribution degree of the predecessor node to the weak knowledge node.

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